Developing Teams in Business Assignment Essay

What is a Team? A team is individuals whom are moulded into a group who work together to achieve an objective or task. Benefits of a team Being in a team is very beneficial as every individual has their own opinions and views , a whole team can manage to gather information and materials much easier than an individual , also within a team there is more creativity which is a benefit as there isn’t only one brain but more than one. Furthermore being in a team enables individuals to gain skills such as communication skills, listening skills and being able to be open willingly and share opinions. Team Recruitment Recruiting the right team members is the key to the success of your team. When the leaders of any group recruit new members, there are a number of skills, qualities needed as well as a process that each member has to go through in order for them to be an successful addition to the team. This process is called job analysis from where a person specification is drawn up and following all the qualifications and qualities that a new team member would be expected to have. There are different types of teams which consist of: Formal Informal Different size teams Temporary Permanent What is a formal team? A formal team is a team where individuals are put together for a specific  reason, each individual within the team is given a specific role. Formal teams are mostly permanent teams, for example within the supermarket Tesco they would have different formal teams likes, customer services team, marketing team, human resources these teams also have sub teams such as groceries and the butchery. All these teams work effectively to reach their objective What is an informal team? An informal team is a team which is less structured compared to a formal team, theses times are about the individuals within the team, the team its self has minimal rules and expectations compared to a formal team. This type of team would hold social events , have irregular meeting maybe at break times the team does not have a specific leader all team members are equal and take on the same role therefore there is no co-ordination. What is a different size team? A different size team is basically what the name of the team is, it is a team that has different sizes of team members. The size of team varies on the task that needs to be completed. Temporary teams A temporary team is a team that is set up for a short period of team, the team is not long lasting, the team would come together for their objective and as soon as their objective is completed they would split up. Permanent teams A permanent team is a team that works together continuously, the team is long term and work is reoccurring. What type of teams would Tesco use? As Tesco is a large company they would use all the above types of teams such as: Formal team: E.g.: The customer service team at Tesco represent  customers this team may consist of over 5 member it also may most likely be a mixed gender team. The team members would have all the same skills such as communication skills, attentiveness, positivity, the ability to read customers and a calming presence. Together the team should form a well-rounded team as individual has the skills for the position they are given. Informal team: E.g. A team of trainees at Tesco may hold informal sessions to track their progress within the company and their development within the company these meetings may not be compulsory and may not be happen all the time all the members in the team would be on the same level so in this case they would all be trainees within the company. Within the team they may talk to each other about their progress and what they think they could do better, but it wouldn’t be a case where the team would have a manager sit them down and speak to them. Different size team: E.g. Tesco could have a team of HR that could consist of 3 members but then they could also have a team of customer service employees that team could consist of 6 members. Initially in a team 5 is the magic number even though 5 is an odd number it is a good size for a team as the team is also small enough to involve all members in addition to that if a decision needs to be made having an odd team helps. Temporary teams: E.g. Within Tesco 8 different employees may be put together for a project for example to market a new product coming out within the company , therefore the members would all work together to put I’m ideas to market the product , after the product is published the team will disperse. Permanent teams: E.g. The administration team for Tesco would be a permanent team as that team helps the business function, this team would classify as a permanent team as it is a team that the business needs in order for it to function well. What is a leadership? A leader is a person who leads a group of people, an organisation or a team, being a. Leader doesn’t necessarily mean you do this but also being able to be a leader is a trait of leadership. A leader is being able to think on behalf of your group, being able to fix a crisis if one rises without hesitation, a leader is someone inspirational, confident, and assertive. Being a leader is not taught. Whereas being a mange can be taught. A leader  knows it’s members strengths and weaknesses for example a manager at Tesco could know that one of his/she’s employee is not as confident on tills but is good speaking to customers the leader would know to not put that employee on the sales team but with customer services where the employee feels comfortable. Leadership styles 1.Autocratic leaders : These leaders make decisions without consulting their team members, even if their input would be useful. Although these leaders do not consult their members this type of leadership can also be advantage for example when a decision needs to be made quickly/instantly the leader can make the decision without the input of members. On the other hand this role can also be demoralizing 2.Democratic leaders: These leaders are the ones who make the final decisions, but they would consult their team members and include their opinions in the decision-making process. They encourage creativity, and people are often highly engaged in projects and decisions. As a result, team members tend to have high job satisfaction and high productivity. This is not always an effective style to use, though, when you need to make a quick decision. 3.Participative leadership: This is a way leadership in which it involves subordinates in the goal setting with the problem solving team building. As well as retail the final decision making authority 4.Laissez-faire: These types of leaders give their team members a lot of input in how they do their task and how they set their deadlines. These type of leaders do not get involved but do support their team and offer advice if the team needs it. This type of leadership can damage a team as they do not have a lot of guidance as some members may lack time management, knowledge, skills or self motivation. Leadership skills and attributes What skills and attributes are needed to be a good / effective leader? A good leader must have the skills applicable to lead a team, these characteristics encourage members to follow the team leader. Within Tesco  the leader of sales has to have the right attributes and skills to control their team if they didn’t the team would not functional properly these skills consists of: Communication Effective team leaders communicate clearly. Quality verbal and written communication skills allow leaders to present expectations to team members in a way workers can understand. Effective communication skills also allow team leaders to listen to the input of others. Organization Effective team leaders possess exceptional organizational skills. Organizational skills help team leaders plan objectives and strategies, which allow team members to perform optimally. Organized team leaders put systems in place that maintain order and guide team members toward meeting company goals and objectives. Confidence An effective team leader is confident in his abilities, as well as confident in the abilities of his team members. A confident leader is secure in the decisions he makes that affect his team. A self-confident team leader also reassures team members of his authority within the organization. Respectful A quality team leader is respectful of his team members. A respectful leader empowers employees by encouraging them to offer ideas about decisions that affect them. This lets team members know that the leader respects their input and opinions. Fair A quality team leader treats team members fairly. He is consistent with rewards and recognition, as well as disciplinary action. A fair leader ensures all employees receive the same treatment. Integrity An effective team leader is honest and open with his team members. Leaders who possess integrity gain the trust of team members because he does what he says he will do and treats others the same way he wants to be treated. Influential Influential leaders help inspire the commitment of team members to meet  company goals and objectives. Influential leaders also help manage change in the workplace by gaining the confidence of workers through effective decision making and communication. Delegation Effective team leaders know how to share leadership through delegation. Delegating certain tasks to trustworthy team members allows the leader to focus on improving workplace functions and production. Facilitator Effective team leaders are powerful facilitators. As a facilitator, team leaders help workers understand their goals. They also help organize an action plan to ensure team members meet their goals and objectives more efficiently. Negotiation Team leaders utilize negotiation skills to achieve results and reach an understanding in the event of a workplace conflict. Team leaders who negotiate effectively streamline the decision-making process, as well as solve problems for the best interest of everyone involved. (http://smallbusiness.chron.com/10-effective-qualities-team-leader-23281.html

Child Care Center †An analysis of how incentives work on the human mind Essay

Understanding the concept of incentives, positive and negative, and how they impact the behavior of people is a core aspect of economics. In fact, economists love to tinker with incentives and identify different measures that can motivate and de-motivate a person from doing an action or from abstaining from it. The power of incentive is such that economists believe that with the right incentive, any person can be compelled to do any task. Incentives can cause tremendous action, inaction or opposition, merely based on the quantity and quality of the incentive. Every incentive has three flavors to it: economic, social and moral. The case of the childcare centers of Israel will help one understand the impact of incentives, and how a wrongly conceptualized incentive can severely affect the very purpose of the incentive. A study of childcare centers in Israel provided statistics that the parents who came later to collect their children were on an average eight per center, per week. This was an alarming statistic for the centers and they had to spend extra money on holding back staff and paying them for overtime services. A few economists decided to try a negative incentive by imposing a nominal $3 fine on parents coming late by more than ten minutes, in twenty childcare centers in Israel†¦ The management and the economists believed that this would deter parents from coming late to collect their child. To their utter dismay, within a couple of weeks of the penalty, the number of parents who came late shot up to 20 per week, per center, displaying an astounding increase of 150%. One major factor that one can identify that led to such a drastic increase is the low penalty. The penalty for the whole month totaled to sixty dollars, which was about 16% of the total monthly service fee per child. From the parent’s perspective, for an addition al 16% of monthly fee, he could come at his own convenience and collect the child. Since, such a penalty was being levied by the childcare center; it became an additional responsibility for the center to provide the best amenities for the child until the parent turned up. It further alleviated the moral conflict within the parent, when he turned up late, as now he could come late and be relieved of the moral binding to come on time, with the penalty. A similar parallel can be drawn to students who were asked to pay a nominal fee for low attendance. Colleges perceived that by introducing a low penalty for every day of attendance below the stipulated percentage, students would be more regular. To their utter dismay, with the introduction of the penalty, the percentage of students who fell below the required the minimum attendance increased significantly, as they were aware that by paying a nominal penalty they could get away with a few more holidays in the year to enjoy. On the contrary, in the absence of the penalty the parents had at least a moral obligation to come on time and collect their children. In case a much severe punishment was imposed like a hundred dollars a day, the number of erring parents would significantly reduce. However, that would increase the animosity between the parents and the childcare center management, which could even lead parents to transferring their children to a far less punishing center. If the childcare centers of the entire region imposed a high penalty for late parents, there is a strong possibility that one of the parents might themselves open a childcare center and compete with the existing one. However, the economists and the management of the childcare centers missed an important perspective. What if instead of punishing the late parents, they provided an incentive for parents who consistently came on time? The incentive can be in two kinds, for the parents and for the children. A nominal monetary incentive for the parents might simply fail, as again they might want to sacrifice a few dollars a day to enjoy their game of tennis or strive more at work. Hence, if a cash incentive is to be provided, it has to be substantial and there must be an element of scarcity; i. e. the top ten consistent parents being awarded. This would create a competitive spirit in the minds of the parents. It has also to be kept in mind that such an incentive would affect the finances of the childcare centers, and would also be useless if the children coming to the center are from the elite class of society. The most effective measure to reduce late parents could be achieved by involving the children in the incentive process. By motivating the children to push their parents to come on time and win the best parent award, the childcare center might get its desired benefits, as children are highly competitive and would influence their parents to come on time to pick them up. The childcare center should focus on the children of parents who turn up regularly late to the center, yet create an impression of equality in the minds of the other children too. Hence, it can be understood from the above discussion that an incentive can have several consequences on its desired participants. An incentive scheme is very successful when the people participate willingly in the process, and reaches less than desired outcome when the participants are forced into the process. A fine example of a forced incentive process is one when a company introduces a new scheme, which has to be promoted by its sales executives, though everyone knows the promotion and the product are unsalable. An incentive to be successful has to be organic, achievable, realistic and participative. References Donald Edward Campbell (2006), Incentives: motivation and the economics of information, Cambridge University Press Jean-Jacques Laffont, David Martimort (2002), The theory of incentives: the principal-agent model, Princeton University Press Sullivan Arthur; Steven M. Sheffrin (2003), Economics: Principles in action. Pearson Prentice Hall. pp. 31.

Catch Me If You Can

Focus: To emphasize the use of making inferences using all aspects of a book as a means of thinking about and comprehending texts. Introduction/Connection: To begin the lesson the teacher will begin with a discussion on review reading strategies the children already know and discuss how these strategies can help them as readers. Then the teacher will explain to students that when reading we have learned to infer what a character might be feeling based on the illustrations in the text. She will ask the children what they think the word infer means. After a few student responses she will explain that infer means to understand what is happening in the text without the author actually telling us. She will explain that inferring is about reading faces, reading body language, reading expressions, and reading tone as well as text. She will ask the children if they can think about the word inference, what it means, and any examples of inferring that they may know. After a few student responses she will explain that Inferring is a reading strategy to be used as a means of ensuring that we understand stories we read. We will then discuss inferring in our everyday lives (the weather, how our mom or teachers might be feeling). It will be emphasized that when we make infer we use our brain to really think about what we already know; in books when we infer using the pictures and text we can get a better understanding of what is happening in the story. Key Questions: * What are reading strategies? * Why do we have reading strategies? * Where can you find the reading strategies if you get stuck? * What reading strategies do you know and use already? * Why do you use them? What do you think the word infer means? * Can you think of examples of when you have made an inference? * Why might good readers make an inference? Whole Group Teaching/Active Engagement: The teacher will focus the children’s attention on the selected book, Bully. She will ask the children to look at the book and think about what they see depicted on the cover. She will t them what they can infer just by looking at the cover an d reading the title. Then ask the children to listen carefully as she reads the first two pages of the book. Once completed the teacher will ask the children to close their eyes and think about what they just heard in the first two pages of the text. After a few moments she will ask them to make an inference about what they think is happening in the story. She will ask the children to â€Å"turn and talk† to share their inference with their shoulder partner on the carpet. The teacher will listen to the partnerships and their responses and get a quick assessment of what the students’ inferences sound like (whether they are on target, missing key information, etc). After the share time, she will call upon several students to share their answers with the class. The teacher will then comment on the children’s abilities to infer the story parts based on their observations of the cover and listening to a few pages. She will then read a few pages of the story to give the children an idea of whether their inferences were on target or not and allow them to give â€Å"yes† or â€Å"no† signals to indicate if they were correct or not. Key Questions: * What do you see on the cover? * What can you infer from listening to the first few pages in the book? From what you saw on the cover and the pages, what can you infer will happen in this book? * Why did you make that inference? * What in the book made you think of that? * Were you correct? How do you know? Differentiation: * Depending on the student who is called on to respond during the whole class instruction, questioning will be scaffold in order to meet the child’s specific learning needs (IEP, ELL support). Children will also have been paired in reading partnerships based on current reading levels. There will be a variety of books available for the different reading levels * Students will be allowed to use pictures or words (preferably both) to show that they understand inference. * Students will be given the opportunity to â€Å"act out† their inferences/predictions. * Students will be given the option to work independently or in pairs during one of the assignments. Small Group Active Engagement/Link: To link the mini lesson to independent, and partner reading, and guided reading time, the teacher will remind tudents to make inferences as they read their books independently. She will ask the children to re-state what their focus is to ensure understanding and clarify any misconceptions. The children will return to their tables and groups to participate in independent, partner, or guided reading time. The teacher will meet with the group select ed for that day and continue to work on the use of inferencing to enhance comprehension of stories. Independent Reading Time: 10 minutes Partner Reading Time: 10 minutes Share: After independent and partner reading, a reading partnership that was observed using the inference strategy will be asked to come up at the end of the reading workshop time to share with the class what inferences they made while reading their book and explain how this helped them to better comprehend or understand the story. They will also be asked what they feel they can improve upon for share time the next day. Key Questions: * Did you make any inferences while you were reading? * How did you use this strategy? * Were your inferences correct? * How did you know? Closing: The teacher will commend the entire class on their reading stamina and employment of their first grade reading strategies! Everyone will give himself or herself a pat on the back! Resources: * Read Aloud – Bully, by Judith Caseley * Post-its * Leveled Books _____________________________________________________________ Observations / Comments: Next Teaching Points/Subsequent Lesson: * The subsequent strategy on the Reading Strategies – Comprehension: Retelling. Will be explored in the next day’s reading workshop lesson. Next Teaching Points Alterations (Based on Observations):

Identify and Explain foreign subsidiary transactions and how Essay

Identify and Explain foreign subsidiary transactions and how determination of functional currency affects group profit for Qantas - Essay Example 2) Maintenance and overhauling cost of each subsidiary is shown in their financial statement as opposed to financial statement of parents. Each subsidiary is likely to incur this cost based on their need for maintenance. This is also based on the underlying principle of matching concept whereby each subsidiary (JETSAR) recognizes the revenue it earns from freight and air passengers it is necessary to match the maintenance cost incurred against the revenue earned. Qantas Ltd cannot undertake the transaction as this would result in bearing expenses for revenue that has not been earned by the parent company. 3) External segment tours and travel revenue of Jetstar would be recorded in the subsidiaries books of account (Qantas, 2010). This is the revenue that does not contain any inter group transaction (that are automatically eliminated in the consolidated statements) but rather pertains to sales made to external customers (Hodge, 2009). This segment is not targeted by Qantas Limited and revenue arises as a result of operations conducted by Jetstar Pacific. The business reason for this transaction not being undertaken by Qantas Ltd is that Jetstar is essentially targeting its flight at different routes in order to maximize cost saving for the entire group such as undertaking the route to New Zealand. The revenue principally arises as a result of operations undertaken by Jetstar and thus are recorded in subsidiaries books. The functional currency is defined as the currency of the primary economic environment in which the entity operates (Hodge, 2009). If the functional currency of the subsidiary of Qantas Limited is Australian dollar (AUD) then the subsidiaries financial statements would involve the statement of Assets and liabilities, revenue and income in the Australian dollar only. If the subsidiary has a functional currency other than the Australian dollar for example the American dollar

Profiling Research Paper Example | Topics and Well Written Essays - 500 words

Profiling - Research Paper Example In this case, these experts are expected to undertaking their profiling in a way that do not violate people’s privacy or have an aspect of discrimination. In fact, these practices are applied professionally in order to help people as tools for security, through they are based on historical grounds and statistics. Profiling is perceived to have an aspect of discrimination, thus developing controversy around the issue, whereby people think that it should not be undertaken based on gender, race, color and people’s appearances. Therefore, there is nothing right with condemning due to the actions done by other people in the past, who they share similar patterns. This has resulted to case such as people being stopped in the airport for investigation since they share similarities with people who did wrong in the past. On the other hand, the subjects of the profiling should be treated with respect through the provision of an explanation for the profiling, and unless they have done nothing wrong, they are expected to have nothing to hide. A psychological profile can be created through an investigation in the absence of physical evidence or description of eyewitness to supplement with a description. Therefore, the experts apply their knowledge and the things they know about unknown suspect concerning his actions and try to generate information. For instance, in a case involving serial murderer killing female employees in a certain company, the experts may presume that murder is a male former employee or a client. Other issue that has brought controversy relates to racial profiling, which is a practice that has involved a significant risk to the basic principles of the constitution. Racial profiling is perceived to be targeting people of certain skin color through investigations, thus alienating communities and preventing them from participating in policing efforts. This has also caused the law enforcement to lose credibility and trust in the

Communication Essay Example | Topics and Well Written Essays - 750 words - 9

Communication - Essay Example the film’s running time of 87 is generous, considering the genre. This was a massive box office hit film generating more than $5 million on the first week of release. City Lights was the first Charles Chaplin’s first production after the technology in talking movies was first introduced. Nonetheless, the film did not the technology in its development, wisely so, since the sound equipment used would have trapped the film in sound sets and stages. Since the movie was built on the comedy genre, the actors staying up close to the equipment and this would not have produced the bouts of laughter an expectation, the audience relished. After watching the film, one must contend that the few sound used underscore the silent comedy without any overbearing the audience. In the opening scene, where the mayor unveils a civic statue only to find Charlie Chaplin on its arms enjoying slumber, the speech is shown by sounds sounding like shrills and screeches. Additionally, when Charlie Chaplin swallows the whistle and accidentally causes a concert to stop, followed by a scene in which he makes a call for cab to a stop and then another in which he surrounds himself with dogs. The first and the sequence of scenes as mentioned above, provide, perhaps the only moments when sounds is used. According to Gehring (12), the character, Little Tramp dwelt in the language understood all over the world then, pantomime. A part from these, music is only used in the film, when the synchronized score is used to aid with the movement of the comedy. The music a composition, partly by the director-Charlie Chaplin helped in alleviating the need for talkies The main character in the story, Tramp falls overhead with a blind flower-girl and pulled along by a drunken millionaire, and ends up doing a shift as a municipal manure sweeper and in the ends up winning the

Abu Dhabi Aviation Co Essay Example | Topics and Well Written Essays - 1000 words

Abu Dhabi Aviation Co - Essay Example The company has seen its expansion of its operations to cover the region and several contracts throughout the Middle East and beyond. It serves countries like Qatar, Kuwait, Saudi Arabia, Republic of Yemen, Spain Eritrea and Australia. Abu Dhabi Aviation Co. has operated 2 Bell 212 helicopters which are in support of long-term contracts involving a major oil company in the Republic of Yemen. Now the company is targeting an approach of 1,000,000 flight hours in helicopters and an average of over 55,000 hours in fixed wing aircraft. The mission of the Abu Dhabi Aviation Co. is to provide innovative solutions in every part of the globe while exceeding stakeholder, customer and employee expectations. Its vision is to be one team, propelling Abu Dhabi Aviation safety and cost-effectively into the future. It outlines its values as Quality, Safety, Customer Focus, Teamwork, integrity, and Ethics. The goals of the company are that they are never compromised in the provision of safety which i s their top priority and fundamental core value. Secondly, they value timely, innovative, efficient, reliable, cost-effective and best quality services and thirdly they are committed to achieving the highest levels of customer satisfaction. Employee profileThe Abu Dhabi Aviation Co. has employed more than 900 personnel, which includes over 150 pilots and over 150 aircraft maintenance engineers (Abu Dhabi Aviation, 2010). It is governed by a board of directors ranging from the Chairman, the Vice Chairman, and board members.

Merger, Acquisition, and International Strategies Assignment

Merger, Acquisition, and International Strategies - Assignment Example Through strategic positioning of the products and services of Skype, Microsoft strategically noticed the level of usage of Skype, through the voice and video calling application in addition to other features. Strategically, the acquisition connected the business of Microsoft Corporation and blended well with other services and products of this corporation. This also facilitated the strategic evaluation of the priorities of its products, as well as the development of business strategies of the corporation (Gaughan, 2010). The fact that Skype was a computer to computer based telephone program, made it even more ideal for Microsoft Corporation. Once it was acquired, the corporation was able to provide voice services to its wide range of clients across the globe, and this placed the corporation strategically for providing a wide range of services. This was not only a strategic decision for marketing the products of the corporation, but also a wise move that has seen the corporation incre ase its market share (Frankel, 2007). The justification for the opinion is that Microsoft is able to generate revenue through Skype, both locally and internationally through the services of the acquisition. This is facilitated by the fact that the services are computer based, and thus cheaper than the rates of other companies (Ulijn, 2010). Identification of a probable candidate corporation that has not been involved in mergers or acquisitions, and explanations why this company would be a profitable target Although mergers and acquisitions are applied by corporations strategically to finance and effectively manage the dealings of the corporation, through effective combination of various companies as well as similar entities that have a common enterprise for effective and rapid growth, there are corporations that have purely ignored this corporate strategy. Most corporations purchase companies and business entities for the purpose of combining their enterprise strategies (Gaughan, 20 10). An evaluation of the business-level strategy and one corporate-level strategy of a corporation that operates internationally, which is recommended for improvement The practice has clearly demonstrated that corporations that operate at the international level are subjected to more barriers and risks, due to the dynamic changes associated with the various regions across the globe. For the purpose of effective management of these risks, there is need for such corporations to evaluate the business-level strategies for the purpose of realizing the true value of conducting business at the international level (Frankel, 2007). A business-level strategy is fundamental for increasing the business value of any corporation. It is a very critical point for the corporation to identify and apply and appropriate business-level strategy. The practice of mergers and acquisitions has been applied by most corporations for the purpose of realizing the business-level strategies that are ideal for th eir cases. It is a very common trend which has seen most international corporations change their image in order for them to meet the demands and values of the consumer base. Apple has ideally identified such features through its technologically marketing strategies. The corporation has adopted modern quality appeals to

ETHICAL CONSUMERS . myth or reality Essay Example | Topics and Well Written Essays - 1750 words

ETHICAL CONSUMERS . myth or reality - Essay Example The result was obvious and very predictable. It led to huge scale destruction and exploitation of resources of the planet earth, pollution, human and animal abuse and a long run destruction of everyone at this planet. That was the time when the experts and media people jumped on to the scene and started creating awareness amongst the public. The masses wanted to follow the ethical path and wanted to stop the companies from their unethical actions for making profits. They all agreed that it is the responsibility of all of them to stop this destruction and unethical actions, somehow or other. That was when; the consumers became conscious about their power, about the difference that they could make. They understood the fact that these companies depend of them and they can use this dependency to make these companies work their way. Consumers developed common platforms and came up with useful strategies. It started to work. By boycotting, the products of those companies involved in unethical means of production pressure grew on the companies to change their course of action. Moreover, the decreased profits made the companies to do it so as well. The process of acquiring products that are produced without violating ethical grounds and code of conduct can be termed as ethical consumerism and these consumers are called as ethical consumers (Wetherly, & Otter, pp.12-18, 2008). People were unaware of the term of ethical consumerism before the past three decades. This is after the early 70’s era that the masses became conscious about the violation of moral and ethical standards for more profits by companies. These actions were certainly crossing the limits of patience of the public, that is why the masses had to stand up by themselves for the sake of this planet, its eco-system and betterment of their coming generations and making sure that they leave a better world for their coming generations. Following are some of most notable

Public administration Essay Example | Topics and Well Written Essays - 250 words - 2

Public administration - Essay Example The process of formulating a new public policy often follows three stages: agenda setting, option-formulation, and then finally implementation. This obviously revolves around the problem to be solved. A perfect example is the problem of health care in the US. The Affordable Care Act/ Obama Care is an example of public health policy that was recently implemented in the US. President Obama signed into law The Patients Protection and Affordable Care Act (ACA) in March 23rd 2010. This policy aims to help more Americans gain access to health insurance at affordable rates. This is because millions of US citizens are uninsured. The ACA works in phases to reduce the number of uninsured by introducing an Individual Mandate. By 2014 every uninsured individual (Adults and Children) will be required to have some form of health insurance by paying up to $285/year to virtual health insurers online. Women will not pay higher premiums and insurers will have issue a cover regardless of enrollees having pre-existing medical conditions. Under ACA, insurers are also requires to spend at least 80% of their premiums in actual health care. The ACA strives to push health insurance prices down and also maintain quality of care in the

Gender Role in Triffles Essay Example for Free

Gender Role in Triffles Essay The roles and rights of women in the Victorian era up to nineteen hundreds differ drastically from where women stand today. In the play â€Å"Trifles† by Susan Glaspell, females are portrayed to be an insignificant part of society compared to the importance of males. Susan Glaspell’s play Trifles is a murder mystery type of play that discovers and analyzes gender roles and corrupt relationships due to the Victorian time period. The typical stereo type for women in the nineteen hundreds was being nothing but a housewife. A good house wife in this time was considered to have children, take care of the children and clean the house, and there not much more to it. In the nineteen hundreds women did not have many career options, they had almost none. Women’s education was not seen as an important thing to promote. Stated by Helen Nickson in the article Life of Women in the Victorian Era, â€Å"The only role of women in the Victorian era was to get married and look after the homely chores The ladies did not do things themselves but told others what to do. They were just supposed to marry and raise children. The women of lower class worked in the factories, garment industries, laundries or various other jobs to support themselves.†. Women were treated more like an object or a servant rather than a person or spouse. One of the main characters in the play Trifles named Hale states a short simple statement that when looked into, states a strong opinion. Hale states to another male in the play, â€Å"Well, women are used to worrying over trifles.†. This statement shows how the men in this day thought women lacked common sense or intelligence. When trying to investigate the murder in this story, the men took no part of the women’s opinions. Women’s rights have come a long way since the Victorian Era. Women had little say in just about everything whether it had to do with marriage decisions or political things. Set up marriages were a common thing women had no say in. In today’s world women can vote, support themselves and choose who they marry. Some people wouldn’t believe the simple rights women have today were fought for way back when even in the nineteen hundreds. Women had little almost no career options in the Victorian Era. The few career choices were only for single women who needed to support themselves, if one was a house wife that was there life. Men had high expectations of their own wife’s classiness and manners in public places in the nineteen hundreds. Many males were very judgmental, much in like the play Trifles, of any opinion from a women back in the day. In an online article by Rachael Hurvitz, she states â€Å"For Victorians, divorce was not only extremely expensive, it was very hard to do. Women and men stayed in unhappy marriages for numerous reasons. Many stayed away from divorce because of the stigma attached to divorced women. It was also considered a societal taboo†. Women feared divorcing the one they were married to strictly due to the opinions of others in society. In Trifles a woman ends up murdering her own husband, rather than divorcing. The investigators don’t suspect her at first strictly because she is a wife and a female. When another female suggests that the husbands wife could be a possibility, the men just laughed to each another. Before women had fought for their rights, they lacked respect from society. Women have come a long way today, now having equal rights to anything men can do, including career choices and political voting. Works Cited Glaspel, SusanTrifles Literature: Eleventh Edition Nickson, Helen. Life of Women in the Victorian Era. Web.: http://ezinearticles.com/?Life-of-Women-in-the-Victorian-Eraid=2359711 Hurvitz, Rachael â€Å"Women and Divorce in the Victorian Era† http://www.clas.ufl.edu/users/agunn/teaching/enl3251/vf/pres/hurvitz.htm

Promotion of Effective Communication †Workbook Essay Example for Free

Promotion of Effective Communication – Workbook Essay Question  1 Look at your company’s policies and procedures on completing records and maintaining effective communication, what is your role? Answer: I browsed and read my organisation’s policy regarding the service user’s rights and those legislations which promotes equality, diversity, and discrimination. a. Each service user has a right to information regarding their care service that does not discriminate on the basis of race or ethnic origin, creed, colour, religion, political affiliation, disability or impairments, marital status, parenthood, sexual gender or sexual orientation. b. Each service user has the right of access to their personal care records and to comment on them accordingly. Service users have the right to appoint an advocate to make their wishes and preferences known if they are unable to do so. c. Each service user has the right to be assured that no personal or confidential information concerning their affairs will be disclosed to a third party without their express permission. d. Each service user has the right to communicate using their preferred methods of communication and language. When completing records and reports look through your staff hand book or induction pack you were given at work and explain any rules and regulations or policies you need to follow when completing records and reports at work some of which might include: †¢ Records should be completed as soon as possible after the event †¢ Details should be accurate †¢ Details should be relevant †¢ Details should be legible †¢ Details should clearly indicate if it is a fact, opinion or hearsay. Opinions are acceptable as long as it is clearly stated as such. †¢ Always record as little as possible but detailed and as much as necessary. 2, 3, 10, 11 Describe ways that you provide support to individuals to communicate their needs. How might your communication alter with different individuals ? What aids might be used to support effective communication ? Answer: To support individuals and key people to communicate their needs you will need to: a. Arrange the individual’s environment to facilitate effective communication and promote understanding. This can be done by ensuring privacy going into a quiet room, if the area is noisy because of the volume of a radio or television it needs to be reduced. Poor lighting in the room needs to be changed and some more that you can think of. b. As a care worker you need to check that the individual have the appropriate support to communicate their views. This could be making sure the individual who uses glasses and an hearing aid is supported by making sure the glasses is at client’s reach or that hearing aids is switched on and working properly. c. Appropriate styles and methods of communication should be used with respect to the individual. Such as: Active listening – showing be gestures that you are listening, sitting or standing half turned away gives the message that you are not listening. Responding appropriately – nodding your head.  Good body language and maintaining eye contact – Leaning forwards can be used effectively when you want to emphasize your interest or support. The methods that can be used to communicate effectively are: a. Support equality and diversity †¢ This can be done by using appropriate language that the service user understands also using the appropriate register of language, for instance not using phrases that could be referred to as jargon. Another method is to use the appropriate way of speaking within a speech community. For instance communicating with young people may mean using their style of language e.g. whats up with you, hello mate. †¢ Provision of communication aids and use of non-verbal communication if service user has hearing or vision impairments or learning and physical disabilities. b. Are effective when dealing with, and challenging discrimination †¢ Working with key people demands that you communicate in a language that they understand and also using simple words. For example the use of clinical words that is not commonly understood would not be necessary if you know they are not familiar with them. †¢ Sometimes we come across people who cannot understand us for one reason or the other instead of ignoring them it would be helpful to source a skilled interpreter but we still need to make effort to communicate with the person by learning some of the ways of communication or a few useful words from their language. The methods to support individuals to communicate are: Ensure environment is suitable (lighting, noise background) Provide interpreter if necessaryAllow sufficient time for individuals to understand the content of communication. Use relevant aids for communication (e.g. cards, symbols, hearing aids, large print) Provide advocate to speak for a service user Ensure written material is in suitable formats or language. Specific aids that may be used to support effective communication : Aided communication is communication supported or replaced by materials or equipment. There are simple materials or equipment used everyday such as a pen and paper to write messages, alphabet charts, pictures or symbols or photographs. Communication aids can be categorized into 3 broad groups: Symbolic Aids This is commonly the use of signs and symbols, it requires individuals to undertake a form of training on the correct forming of signs used and types of symbols: †¢ British Sign Language used as a communication aid for individual with hearing loss. †¢ Makaton used as an aid to support speech and not intended to replace it. †¢ Picture Exchange communication systems (PEC) This aid helps individuals to be independent as they able to exchange a picture for what they want from a compiled album of pictures. †¢ Deaf Blind manual alphabets Slightly modified version of the BSL. Finger- spelling alphabet is used. Technical Aids †¢ Talking microwaves usually for individuals with sight loss †¢ Computers which read out the text on the screen. †¢ Light writer this is a portable device into which the individual types in what they would want to say. Human Aids †¢ Interpreter is a person who supports the communication between two people who do not have the same language. This also includes the sign language. †¢ Translator is a person who changes the written word into an easier format for the individual to read. This could be into Braille or symbols. †¢ Advocate This is someone who speaks on behalf of an individual when they are not able to do so. 4, 5, 19 In relation to the promotion of effective communication, give examples of what you do to maintain the following laws and guidelines: a) Data Protection Act b) Access to Health Records Act c) The General Social Care Council Code of Conduct d) Standard 37 National Minimum Standards for Care Homes e) Caldicott Report Answer: a) To maintain Data Protection Act it is necessary to complete the records as soon as possible after the event and always record as little as possible but detailed and as much as necessary; to make sure that the details are accurate, relevant and legible and that they clearly indicate if it’s a fact, opinion or hearsay. Another important thing is that opinions are acceptable as long as it is clearly stated as such. The information shared by the individuals must be confidential to ensure data protection. In case that the information suggests that the client is under risk, the consent of the individual needs to be obtained before passing the information to an appropriate member of the staff, and even when the consent is not given it becomes important to report. b) To maintain the Access to Health Records Act I have to make sure that the records are accurate, legibly written, shareable so that the information can be used to provide individuals with the support and care required. The  members of a care team are fully informed of new developments and changes in a client’s care plan and the evidence of the actions taken in specific circumstances are available if the need arises. I can access information and records about an individual by: talking to the service user, accessing previous records after permission has been sought from the appropriate person, talking to colleagues who know the individual, to family members or to other professionals c) To maintain The General Social Care Council Code of Conduct, as a social care worker, I must establish and ensure the confidence of service users and carers. This includes: communicating in an appropriate, open, accurate and straightforward way; respecting confidential information and clearly explaining agency policies about confidentiality to service users and carers. I must be accountable for the quality of my work, I have to maintain clear and accurate records required by procedures established for my work. 6,7 Where can you find out about an individuals communication and language needs, information about communication and language skills to improve your practice ? Answer: I can find out about an individuals communication and language needs by asking my manager or the service user, discussing with other care workers who know the individual, talking to family members, to a speech therapist or other professionals for advice, exploring the internet or consulting a library for more information. In order to improve my practice, I can find out about information, communication and language skills by asking my supervisor or manager, or colleagues who have confronted with similar cases. I can also consult the case notes of the individual, or relevant documents provided by the organization that will help me learn how to communicate effectively – for example the induction manuals, search for information via the internet or specialist organizations for the particular condition, attend relevant training courses to communication, supervision and appraisal sessions. 9  What factors may affect communication skills, abilities and behaviour of an individual ? How may they react as a result of these factors? Answer: Factors that can affect communication skills, abilities and behaviour of an individual are: Physical Impairments visual and hearing Language barriers accents, different language Cognitive or sensory impairments learning difficulties, memory loss, Illness – dementia, stroke Environmental problems – poor lighting, noisy environments If this happens, the individual in question becomes withdrawn from others around them, isolated from others. This may affect his self-esteem and self-confidence negatively. That individual may also become confused, angry and frustrated. 12  If you were trying to have a conversation with an individual how would you arrange the environment and position yourself to communicate effectively? Answer: First of all, I have to make sure that there isn’t any background noise that could make the communication difficult. Then, another important step to achieve effective communication with individuals is arranging the environment to aid communication. Here are some factors that can hinder or disturb good communication: Poor lighting, because individuals with poor sight are unable to see you Background noise from the radio, other individuals, TV and so on Obstacles between me, the care worker, and the individual, for example furniture and household items Insufficient distance to keep appropriate space within me and the individual to avoid encroaching or invading on their personal space 13, 14  Describe some conflicts that might occur as a result of communication difficulties. How would you deal with these conflicts? Answer: Some of the conflicts that might occur as a result of communication difficulties are: individuals can become frustrated and isolated when the  communication between themselves and their workers is encountering problems. These problems or dilemmas are sometimes the result of: a difference in the language spoken by the service user and the worker the service user has visual impairments or hearing difficulties the individual might have a physical illness or disability either physical disability or learning disability. There are many ways to solve the conflicts that might occur. It depends on the nature of the problem. For example, for: †¢ Language differences: If there are conflicts due to language differences, then an interpreter will be appropriate for any serious discussions or communications. Efforts should be made to learn a few important words to communicate with the individual or teach the individual some words in the workers language if they are willing to facilitate communication. Non verbal communication will be an effective method in solving this kind of conflict. †¢ Hearing difficulties: Individual with hearing difficulties need to be assisted to ensure their hearing aids are working and fitted properly. It would be necessary that a worker will assist the individual to clean the equipment, change the batteries when appropriate. Workers will also need to give the client the appropriate space and communication pace that would make communication effective. If the need arises words can be written down for clarity. The use of signs and telecommunication services such as type talk service are very useful. †¢ Visual difficulties: Individual with visual difficulties need to be provided with glasses or contact lenses so they can observe non verbal communication. This will prevent misunderstandings during communication with people. †¢ Physical disabilities: Communications with individuals in this category will be according to the type of physical disability or illness. If the illness has affected the individual’s ability to speak and understand, for instance a stroke then the use of short, simple sentences, gestures, writing and drawing or using flash cards, the use of closed questions which only need yes or no should be useful. †¢ Some illness do not affect the clients understanding, so there is no need to speak slowly but will need to be patient to receive a response as the client might have difficulty with their speech e.g. stroke. †¢ Learning disabilities: The method of communication will depend on the level of the disability. I will need to communicate at the pace and space suitable for the client. Physical contacts are of an advantage to be used along with  verbal communication. †¢ Cultural differences: People have different cultural backgrounds, therefore it is necessary to find out from the individuals their communication preferences or alternatively check their care plan records or ask people such as their family, f riends, colleagues or key people who have worked with them. 15, 16  When communicating difficult, sensitive or complex messages, how might your style of communication alter? What type of environment would be most appropriate for this sort of communication ? Answer: Communicating with individuals who are distressed or upset due to bereavement this could be sensitive, complex or difficult. In this situation, I will ask if the person would want to discuss any concerns with me or maybe another person of their choice. I can use non verbal communication while been a good listener such as making good eye contact with the individual as she talks, which will depict that I’m willing to listen. If the client is displaying a behaviour that dictates that they are able to put others or themselves at risk, then I might need to involve the attention of appropriate members of the care team. For this sort of communication, the environment must be comfortable and appropriate. I would come across times when I need to discuss matters with individuals that are referred to as sensitive issues. If an individual needs to discuss his personal needs with me, I have to ensure that he feels comfortable and encouraged to communicate these issues. On the other hand, I might want to discuss with the service user about their changing needs such as diet, incontinence, mobility and so on. Communicating bad news, like a bereavement of a spouse or close person to the individual will also require certain communication skills. The things that should take into account are: †¢ Remember individuals have a right to their privacy, therefore the immediate environment should be arranged to ensure privacy. For example a client’s bedroom or apartament should be free from visitors at the time. †¢ Individual’s preferred method of communication should be made available. †¢ Communication should be made at the pace of the individual, giving enough time for both of us to understand the content of the communication. †¢ Observe and respond appropriately to reactions fromà ‚  individuals. 17  Who do you need to gain permission from to access records and why ? Answer: I need to gain permission of my manager or client to access records. Accessing information will help me to improve my practice and also my responsibility. Within the organization there should be relevant documents to access information or if I work with individuals in their own home the care plan should contain useful information. 18  Define the following words: a) Fact b) Opinion c) Judgement Why is it important that you aware of the difference of these words when reporting and recording information about individuals ? Answer: a) A fact is a true statement that cannot be disputed, knowledge or information based on real occurrences; something demonstrated to exist or known to have existed. b) An opinion is a personal belief or judgment that is not founded on proof or certainty- it is the result of emotion or interpretation of facts, a subjective statement or thought about an issue or topic. An opinion may be supported by an argument, although people may draw opposing opinions from the same set of facts. c) A judgement is a cognitive process of reaching a decision or drawing conclusions. Judgments are also personal and developed from experience; they differ from person to person. For example, if a client is dying and all the symptoms and signs show the evidence, reports and records should show these facts. On the other hand if the client only refused to talk, people might have different opinions and judgments to explain the reason. Records and reports will need to be verified to deduce the correct and most suitable reason. It is important to aware of the difference of these words when reporting and recording information about individuals because I have the responsabiliy to provide seamless services for individuals, and this thing can be done only if the  information is correct, precise.

Fluctuating Present Value Of A Cash Flow Finance Essay

Fluctuating Present Value Of A Cash Flow Finance Essay Answer: A cash flow stream is a series of cash receipt and payments over the life of an investment. It is the inflow and outflow of cash, which matters in practice. It is the cash, which a firm can invest, or pay to creditors to discharge its obligations, or distribute to shareholders as dividends. The assets are the items which are owned by the business. The level of interest rates arising in the capital market is associated with the cash flows `and the assets , when the rates increases , the availability of the funds decreases. As a result when the interest rates increase in the capital market, the obligation increases which leads to decrease in the availability of funds to invest in the investments. The present value of cash flow is equal to the sum of the present value of individual cash flows. The equation for present value of cash flow stream is as follows- PV= Where, PV=present value r= rate of interest t= the year n= the last year, where the cash flow occurs Interest rate is the rate at the interest is paid by the lender to the borrower for use of money by the borrowers from the lenders. So, the rise in the interest rates , the availability of cash flows streams due to higher rate of interest , the present value of cash flow streams will decline. 2. List and explain the points of financial impact on a company if it raises the credit standards required of its customers who utilized trade credit offered by the company. Answer: Credit standards are the criteria to decide the types of customers to whom goods could be sold on credit. If the firm has more slow-paying customers, its investments in accounts receivable will increase. Trade credit refers to the credit that a customer gets from providers of goods in the normal flow of business. In practice, the buying firms do not have to pay cash immediately for the purchase made .This deferral of payments is a short term financing called trade firms. The credit standard policy has significant impact on the financial condition of a company-The following are the financial impact on a company due to rise in credit standard . Decrease in credit sales- A rise in credit standards will have a limit on the buyers who will borrow from the company and as a result the sales will decrease as most of the buying firms do not pay cash immediately. This will lower the sales of the company leading to less in revenue generation. Decrease the demand-The rise in credit standards will lower the demand by the buyers which will lead to decrease in demand and decrease in revenue earning. Relatively faster average collection period- A rise in credit standards will make the average collection period relatively faster for the new customers leading to better collection process and increase in volume of cash in inflow. Prompt in collection by existing customers- The rise in standard will pull the collection by the existing customers and make the payments from them prompt and on time. Better return on investment- The rise in credit standards will lead to better return on investments made and credit allowed will be selected as the customers will be prompt in payments and the selection of the customers will be limited. 3. Define Weighted Average Cost of Capital and explain why a company must earn at least its Weighted Average Cost of Capital on new investments. What are the financial implications if it does not? Answer:- Weighted average cost of capital is organisations the calculation of cost of capital where each category of capital is proportionally weighted .A firm obtains capital from various sources due to the risk differences and contractual agreements between the firms and the investors, the cost of capital of each source of capital differs The cost of capital of each source of capital is component source of capital. The component costs are combined according to the weight of each component capital to obtain average cost of capital. The combined cost of all source of capital is called overall cost which also known as weighted average cost of capital. Thus, it is the overall return that firm must earn on its existing business operation in order to maintain or increase the current value of current stock. A company must earn at least weighted average cost of capital in new investments. By taking weighted average, the interest to be paid by the company for a investment is calculated. Wei ghted average cost of capital is the expected rate of return, weighted by proportion each to the overall financial structure. The minimum rate of return on the new investments must be earned so as not to reduce the shareholders. A firm should earn at least its average weighted rate on capital investment in its assets the weighted average cost of capital is used a discount rate to calculate the present value of the of a specific investment. If the firm does not earn the least average weighted cost of capital in its new investments, the firm will incur loss in that new investment, and so it should discontinue or should not invest further. The average weighted cost of capital is the minimum expected rate of return from an investment, so it should be calculated first and then the decision for the investment should be made. 4.As a corporation what are the benefits and ramifications of using convertible debt to finance a publicly traded company? As an investor what are the benefits and ramifications of purchasing convertible debt in a publicly traded company? Are there any conflicts between the goals of the investor and the goals of the corporation? Answer:- Convertible debt are the debts like bonds and debentures with an option to convert it into common stock in future date. The following are the benefits and ramifications of using convertible debt to finance a publicly traded company:- Attractions for the investors:-convertible debts will attract investors by providing safety of debt along with the option to convert it into common stock in future. The investors will lend money to the company with the view that the company will make regular interest payments and the return of capital. If the company achieves growth in future and the stock value increases, the investors has the option to convert it into common stock. Lesser fixed-rate borrowing cost-Convertible debt will allow the issuers to issue the debts at lower cost. Increase in total debt gearing -The convertible debt will increase the total amount of debt level in the company .It will provide additional funding to the company which will be beneficial to the issuers. Financing option- The convertible debts are good financing option for start up companies as equity shares pose a challenge for them. As the convertible debts carry low interest payments by the company, while remaining competitive. Fixed limited income- The convertible debt holders obtains fixed limited income until its conversion and it will benefit the company because more of operating income is available for the common stock holders. Voting solution is deferred- With the convertible debts, the voting rights of existing shareholders happens only on eventual conversion of debts. Ramifications of convertible debts to company- There are some complications for issuers as well .First one , is that financing with convertible debts draws the risk of debasing not only the EPS of its common stock, but also the control of the organisation. If a heavy part of the issue is purchased by one buyer, like investment banking company or insurance company, conversion will change over or take over the voting control from original owners of the company and toward the converters. This issue may not be a significant matter for bigger companies with millions of stock holders, but for the small company, it will be a real and important consideration. Due prominent use of debt will adversely affect a companys capability to finance operations in clips of economic downturn. If the company faces any downfall, it will experience great trouble in raising capital further. The following are the advantages and ramifications to the investors.- Safer investment -The convertible debts are the safer investment compared to buying common stock with returns They are less explosive than stocks and their value can only come down to a price where the yield would be equal to a non-convertible bond of the same terms. Strong protection- The convertible debts provide strong protection to the investors in the times of market fluctuations and at the same time providing periodic returns. Interest payments-The convertible debt holders have a right on the receiving of interest and periodic returns in spite of any downturn in the market. Larger claim on companys assets Convertible bond holders have a larger claim on the assets of the company as compared to the shareholders in case of collapse. More protection from economic downtrend- The convertible debt holder will have a gain during the economic downtrend due the option of conversion into equity shares. As a result, the market stock of share stocks will increase with market prices dissimilar for the debts where the interest rates are fixed. This means that bond holders will gain as during inflation because his money looses value more. Ramification to the investors- Convertible debts could have complication in the view that the debt holder will be obtaining considerably lower yield to maturity in comparison to the non-convertibles. But it is only a worry when the issuers equity does not gain the upward price predictions that would make taking the lower grant speculation worthy. Finally, the ability for predictions are reduced to a great extend when a call provision is bonded to the convertible bond. This will limits the upside and will let the debt holder to declare their debt at a discount to market. The goals of an investors towards the convertible debts is to invest in debts at lower cost and gain fixed returns whereas the goal of a issuing company is to achieve higher operating income with lower borrowing cost. 5) Which two of the six methods used to evaluate projects, and to decide whether or not they should be accepted, do you prefer as a financial manager?   Explain why you decided on these two and not the other four. List the perceived deficiencies of the four not selected. The six methods which are used to evaluate projects, and to decide whether or not they should be accepted are as follows:- Investment decisions for a project evaluation postulate special aide due to the following reasons The projects influence the long term growth of the firm. The decision for a project will affect the risk factor of the firm Evaluation of the project is an important tool as it involves commitment of large amount of finances or stocks They are one of the most difficult conclusions to arrive at. The six methods are as follows:- Accounting rate of return (ARR) Internal rate of return (IRR) Net Present Value (NPV) Payback Period Profitability index Modified Internal rate of return Accounting rate of return ARR is also referred as Return on investment (ROI), as it uses the information of accounting revealed by the financial statements, to measure the gainfulness of an investment. The calculation of ARR involves the ratio of the average tax after profit divided by the average investment done Disadvantages: it can be calculated in a lot of ways profit is not a good alternate option for cash flow adjustment is not considered to calculate the time value of money Impulsive break-off date Contrary decisions can be made. Net Present Value NPV is the method of measuring the investment proposals. It is the discounted cash flow technique that explicitly acknowledges the time value for money. It rightly takes that cash flow coming up from various time periods differ in values and are comparable only when their corresponding present values are taken out. Advantages Says if the finances invested will increase the firms value Takes into account all the cash flows Takes into account the time value of money Takes the risk of future cash flows. Profitability Index The profitability Index is the ratio of present value of cash influxes to the initial of cash outlay of investment at a required rate of return Advantages Says if the finances invested can increase the firms value Takes into account all cash flows of the project Takes the time value of money Takes the risk of future cash flows Provide ranking and selection of projects when capital is rationed out. Internal Rate of Return (IRR) IRR is the way of DCF(Discounted Cash Flow), which takes into consideration the intensity and timing of cash inflows and outflows. The concept of IRR is quite simple to understand in the case of a one-period project. Disadvantages It needs to have a projection of the COC (Cost of Capital) to make a decision The given value-maximizing decision when used to compare mutually exclusive projects may not give the proper decision The given value-maximizing decision when used to choose any projects when there is capital rationing may not give the proper decisions Its not useful in the situations in which sign of cash flows for a project changes more than once during the life of the project. Payback Payback is the number of years needed to retrieve the original cash expenditure invested in a project. If the project yields constant annual cash influxes, the computation of payback period is carried out by dividing cash outlays by the annual cash influxes. Disadvantages 1) the decision criteria is not that concrete to show if an investment increases the firms value 2) Refuses the cash flows beyond the payback period 3) Refuses the time value of money 4) Refuses the risk of future cash flows I will take into consideration the Net present value and the profitability index for the consideration of two of the techniques for the project which will be undertaken due to the advantages which has been described above. I dint find much disadvantages in those methods and so I have given the advantages of those two methods which will be taken under consideration by me, the other methods I dint find of much worth in respect to evaluation for the concerned project as they have less advantages and more disadvantages and so I have written the same above for them. 6.What are the benefits and costs of placing a financially troubled company into a Chapter 11 Bankruptcy proceeding? Is this a legitimate and ethical vehicle for management to use for the benefit of the companys stakeholders? A)   Bankruptcy is a legal process for financial debtors who seek to eliminate their debts. Bankruptcys governs the federal statutory law which is there in the Title 11 of the U.S. Code. It provides for federal procedures of statutes and courts which objects the debtors to put their financial matters under the hold of the bankruptcy court. Chapter 11 Bankruptcy Chapter 11 bankruptcy says to restructure a business under some kind of supervision, rather getting liquidated because the business will still be functioning, but in case of a whole new different circumstances, the benefits of the retirement may or may not be ceased. Protection Benefits Federal law entitles a person to get pensions with some protection. When an employee announces himself to be bankrupt, finances for pensions are not to be utilized for the repayment to creditors. Also, all the retirement benefits you have earned being an employee will not be enforced to him. Federal Insurance The federal government assures standard and effective retirement plans. Any employer who cannot fund Federal government will fund temporarily. This type of insurance is not eligible for 401(k) plans. Chapter 11 Bankruptcy is the most costly anatomy of Bankruptcy in respect to average cost front. It is the most expensive form of bankruptcy and the small businesses should also take this into consideration before filling the bankruptcy. It is expensive as it involves two separate elements which are debt repayment plan and reorganization plan a. The reorganization plan means the person has to convince the court and the debtors that you can put in profit very soon which should be detailed and supported by proper research wherein you have to show a budget through which you need to assess how you are going to pay your creditors in the next several years. Its a process wherein you have to negotiate the same with the creditors and the court. A minimum of $15,000 have to be paid if there is no disputes and expensive attorneys over your reorganization plan but for Chapter 11 bankruptcy it will exceed to $ 100,000 and also this amount can vary depending upon the attorneys and disputes filed by the creditors. I understand that its not an ethical and legitimate step for the stakeholders but when there is no words to express the matter in concern and already the things have gone wrong and worse there can be few things which, if kept in mind can at least fetch some benefits for the stakeholders Filling in Court This is the first way when you can file in the court for a recovery notice wherein you owe the creditors and attorneys that you will come up with the company in a stipulated years of time and also by paying a fees for the time being just to show a courtesy to the creditors and the attorneys. Cost Minimization In this approach, an effort to minimize the cost of Chapter 11 Bankruptcy can be exercised while it may not work in most cases. The matters can be sorted out with the help of an attorney a fee agreement which would imply that most of the paper work preparation planning and filling must be carried out by the concerned person and he would simply pay his attorney to act as a legal coach in case of any need or questions. Most of the attorneys may not accept this type of payment agreement due to the complexity of plan of Chapter 11. Warning The rate of success in Chapter 11 bankruptcies is exceedingly low, which means that a very small percentage of reorganization plans will actually obtain approval from the court. As without the approval the plan will be worthless. There will be higher chance of spending lot of money and putting together a plan along with creditors negotiation and attending to win approval from the court, but this could be a failure too.

The Effect of Catalyst an the Rate Of Reaction Essay -- GCSE Chemistry

The Effect of Catalyst an the Rate Of Reaction Chemistry Coursework Does The Number of Drops of Catalyst Effect The Rate Of Reaction Candidate Name: Ben Dodds Candidate Number: 7158 School: Oundle School Completion Date: Introduction We are studying the reaction between zinc and sulphuric acid, the reaction is catalysed by copper sulphate and this experiment is to test whether the amount of drops effect the rate of reaction. Word Equation Zinc(s) + Sulphuric acid(aq) Ã   Hydrogen(g) + Zinc Sulphate(aq) Symbol Equation Zn + H2SO4 Ã   H + ZnSO4 This reaction is catalysed by Copper sulphate (CuSO4) Ionic Equation - Cancel Spectator ion (SO42-) Zn + 2H+ Ã   Zn2+ + H2 For this reaction to work there must be hard collisions between the zinc and the hydrogen ions (acidity ion) from the acid, The faster the harder and the more often the collisions happen so I predict the more catalyst the faster the reaction. Planning Safety * Sulphuric acid at 2M is a corrosive substance but diluted to 1M it is an Irritant, so wear a Lab coat to protect your cloths and wear safety specs to protect your eyes. * Zinc is very flammable so do not put a Bunsen burner near it. * Copper sulphate is very nasty and corrosive when it gets in your eyes so wear safety specs. * Hydrogen is explosive when mixed with oxygen and burnt; so don't use a Bunsen burner near the experiment. Method ====== First a clamp stand was taken and a gas cyringe was fitted so that when it is connected to a conicle flask the conicle flask will touch the bench. 1 gram of zinc was taken along with 2M sulphuric acid and distilled sollutions. The solutions were mixed to form 1 M acid and a certain number of dfrops of catalyst wes added in the conicle flask and the... ...zincand the amount of copper sulphate were not kept constant. Did I do enough readings I think I have done enough readings as the trend of my predictions were there but I could have done a greater range. The only problem with that is I would have to dilute the acid again as the times were very quick for 15 seconds so it would be to awkward to collect if I did 30 drops of copper suphate it would have been to quick to record. Could your results lead to any findings outside the range of results covered? Yes I could as my graph is a straight line graph so I could extend it and look at maybe 40 or 50 drops and look at what the rate is for them What additional relevant work could you do to extend your theory? We chose to vary the amount of drops of catalyst but what you could vary is maybe whether the temperature, pressure, concentration of the acid or amount of zinc.

Preventing Sexual Harassment in the Workplace Essay examples -- Preven

The Los Angeles Times recently ran survey results that found that four out of five teenagers suffer sex harassment at school. One in ten students said that he/she had been forced to commit a sexual act during school hours. The surveyors state that the findings provide evidence that sexual harassment in schools has reached â€Å"epidemic† proportions. Employment training programs now ten years after the sexual harassment prohibition and the well-publicized Thomas hearings begin with myths and facts about sexual harassment or pre-tests on knowledge of the prohibitions against the activity. These tests still come up with â€Å"true† for the answers to myths like, â€Å"Women working in a predominantly male job should expect to live with rough language and dirty jokes† or â€Å"Only certain kinds of men harass women workers.† Sexual harassment, a form of sex discrimination violates the equal protection clause of the 14th Amendment to the U. S. Constitution, Title IX of the Education Amendments of 1972, and in the employment context Title VII of the Civil Rights Act of 1964 as amended in 1991. Unwelcome sexual advances, requests for sexual favors, and other verbal or physical conduct of a sexual nature constitutes sexual harassment when submission to or rejection of this conduct explicitly or implicitly affects an individual's employment or education, unreasonably interferes with an individual's work or educational performance, or creates an intimidating, hostile or offensive work or educational environment. Sexual harassment can occur in a variety of circumstances. The victim as well as the harasser may be a woman or a man. The victim does not have to be of the opposite sex. The victim could be anyone affected by the offensive conduct. ... ...vention and claims defense. A program to eliminate sexual harassment from the workplace is not only required by law, but it is the most practical way to avoid or limit damages if harassment should occur despite all preventative efforts. Unfortunately, â€Å"Boys will† still â€Å"be boys† and †girls too. Bibliography http://www.dfeh.ca.gov/sexualHarTypical.htm http://www.dfeh.ca.gov/employerObligations.htm www.eeoc.gov/laws/vii.html www.dfeh.ca.gov King & Barlow, Sexual Harassment: When a Quick Response May Not Be Prevention Enough, 1999 Brower & Associates, Sexual Harassment Prevention Training, 1999 Parham & Rajcic, Sex and Power in the Schools, 1996 Liebert, Cassidy & Frierson, Finding the Facts: Harassment Investigations School Policy Legal Insider, April 1999 Equal Opportunity Commission: Policy Guidance on Sexual Harassment, 1990

Essay --

Friendship is the best thing among humans, but sometimes it can be used in a wrong way that could betray someone. In the play Julius Caesar by William Shakespeare, friendship is not what it appears to be. It is easy to manipulate friendship with trickery. Cassius, Brutus, and all the other conspirators knew that they could use this to their benefit. The conspirators used friendship to blind Caesar from what was real happening. It was not friendship that was the cause of Caesar demise, but it was dishonesty. Also they used flattery along with other manipulation to get rid of any thoughts of distrust that Caesar may have had about their honesty. These are the ways one to gain someone’s trust. Friendship can be a wonderful part of life, but if it is not true friendship in which people are open and honest with each other, then it can turn into a very bad thing, sometimes even death. This friendship would soon be lost into disloyalty with Caesar’s assassination. Even though Caesar murdered by Brutus and Cassius, friendship still was a strong subject because it hided conspirator’s real pu...

Annie Leibovitz Biography and Image Sample Analysis

Annie Leibovitz is a famous American portrait photographer and is best known for taking extraordinary and yet unique photos of celebrities. She is one of the most demanded photographer for celebrity pictures and became a celebrity herself that way. Most of the photographs she taken have been featured mostly in magazines such as Rolling Stones, Vanity Fair and Vogue. Leibovitz has always been interested in the arts since a young age. Her mother was a dance instructor and influenced her to take dance classes not only from her, but from many other teachers. In high school she focused in music. She specialized in the guitar and wrote numerous songs, eventually becoming the head of her schools’ folk sing club. When she attended university however, she took an interest in visual arts and considered being a painting instructor as a career. It wasn’t until her family was stationed in the Philippines (her father was an Air Force lieutenant colonel) and a trip down Japan, that she was awestruck by the wonderment of photography. When she went back to school, she took night classes for photography. â€Å"A thing that you see in my pictures is that I was not afraid to fall in love with these people.† – Annie Leibovitz. This quote is a little look of how she sees her images, and how much she loves what she takes. Indirectly she also means that we should love what we take pictures of because what's the point of making others like a photograph you don't like. Photograph One â€Å"Where Romance is Celebrated† (2009) This is a photograph featuring Zac Efron as Prince Philip and Vanessa Hudgens as Princess Aurora in the Disney film, Sleeping Beauty, recreating the awakening kiss scene. This is one of the many photographs Leibovitz took for Disney Parks â€Å"What will you Celebrate?† campaign portraying highlight movie moments of different Disney animations. The atmosphere of the photograph is enchanting and the gesture of the two faces together is quite romantic. The costumes and make up enhances the features of the models, making them look too perfect. The dark background and roses make the photo also very surreal; almost fairy tale-like. In this photograph the roses and the bed frames around Efron and Hudgens to make emphasis on them together. Leibovitz also uses Rule of Thirds to make their faces the centre of interest. She uses artificial lighting above them making an angelic effect and intensely shines on the princess's face, making her complexion paler thus contrasting with the dark background. Photograph Two â€Å"John Lennon and Yoko Ono† (1980) In this photograph is the last photograph ever taken of John Lennon embracing Yoko Ono naked on a bed before he was assassinated. It is an intimate moment between the two; holding each other tenderly while he's giving her a kiss displays their deep love for one another. The bareness and position he is in also displays the vulnerability of human passion. The one evident compositional element is making John Lennon the centre of interest, by making the eye focus on him because he's curled up in a ball or fetal position. Also Yoko's black clothing contrasts Lennon's light skin. Leibovitz uses natural lighting, but since this is on of her earlier photographs the lighting is nothing to creative and simple. Conclusion and Legacy In the being the majority of her images were in black and white because of her lack of education, but later self taught herself about colour development and uses that more often. Leibovitz approach to taking her images is unexpected and out of the box; one never really knows what her next piece will turn out. She captures her effects with artificiality, flair and outrageousness that makes her artwork different from other portrait photographers. Generally she doesn't really care about other's opinions on how to take photos and often gets in trouble by the media by doing things that might offend other people. But all in all, we should admire her genius as a photographer and her â€Å"risk taking† attitude on how to interact with her subjects and audience. I first got interested in Leibovitz because of the Miley Cyrus incident and the work we went over in class, she truly is fascinating in how she see celebrities in such unusual poses. Out of the two photographs that I chose in this essay, the one I like the most is â€Å"Where Romance is Celebrated† because the Disney series are my favorite works by her. I just can't help loving and reminiscing my childhood.

Computational Efficiency of Polar

Lecture Notes on Monte Carlo Methods Fall Semester, 2005 Courant Institute of Mathematical Sciences, NYU Jonathan Goodman, [email  protected] nyu. edu Chapter 2: Simple Sampling of Gaussians. created August 26, 2005 Generating univariate or multivariate Gaussian random variables is simple and fast. There should be no reason ever to use approximate methods based, for example, on the Central limit theorem. 1 Box Muller It would be nice to get a standard normal from a standard uniform by inverting the distribution function, but there is no closed form formula for this distribution 2 x unction N (x) = P (X < x) = v1 ? e? x /2 dx . The Box Muller method is a 2 brilliant trick to overcome this by producing two independent standard normals from two independent uniforms. It is based on the familiar trick for calculating ? 2 e? x I= /2 dx . This cannot be calculated by â€Å"integration† – the inde? nite integral does not have an algebraic expression in terms of elementary f unctions (exponentials, logs, trig functions). However, ? 2 e? x I2 = ? /2 e? y dx 2 ? /2 ? 2 e? (x dy = +y 2 )/2 dxdy . The last integral can be calculated using polar coordinates x = r cos(? ), y = r sin(? with area element dxdy = rdrd? , so that 2? I2 = r = 0? e? r 2 /2 rdrd? = 2? r = 0? e? r 2 /2 rdr . ? =0 Unlike the original x integral, this r integral is elementary. The substitution s = r2 /2 gives ds = rdr and ? e? s ds = 2? . I 2 = 2? s=0 The Box Muller algorithm is a probabilistic interpretation of this trick. If (X, Y ) is a pair of independent standard normals, then the probability density is a product: 2 2 1 1 ? (x2 +y2 )/2 1 e . f (x, y ) = v e? x /2  · v e? y /2 = 2? 2? 2? 1 Since this density is radially symmetric, it is natural to consider the polar coordinate random variables (R, ? de? ned by 0 ? ? < 2? and X = R cos(? ), and Y = R sin(? ). Clearly ? is uniformly distributed in the interval [0, 2? ] and may be sampled using ? = 2? U1 . Unlike the original dis tribution function N (x), there is a simple expression for the R distribution function: 2? r G(R) = P (R ? r) = r =0 ?=0 r 1 ? r 2 /2 e rdrd? = 2? e? r 2 /2 rdr . r =0 The same change of variable r 2 /2 = s, r dr = ds (so that r = r when s = r2 /2) allows us to calculate r 2 /2 e? s dx = 1 ? e? r G(r) = 2 /2 . s=0 Therefore, we may sample R by solving the distribution function equation1 G(R) = 1 ? e? R 2 /2 = 1 ?U2 , whose solution is R = ? 2 ln(U2 ). Altogether, the Box Muller method takes independent standard uniform random variables U1 and U2 and produces independent standard normals X and Y using the formulas ? = 2? U1 , R = ?2 ln(U2 ) , X = R cos(? ) , Y = R sin(? ) . (1) It may seem odd that X and Y in (13) are independent given that they use the same R and ?. Not only does our algebra shows that this is true, but we can test the independence computationally, and it will be con? rmed. Part of this method was generating a point â€Å"at random† on the unit circle. We sug gested doing this by choosing ? niformly in the interval [0, 2? ] then taking the point on the circle to be (cos(? ), sin(? )). This has the possible drawback that the computer must evaluate the sine and cosine functions. Another way to do this2 is to choose a point uniformly in the 2 ? 2 square ? 1 ? x ? 1, 1 ? y ? 1 then rejecting it if it falls outside the unit circle. The ? rst accepted point will be uniformly distributed in the unit disk x2 + y 2 ? 1, so its angle will be random and uniformly distributed. The ? nal step is to get a point on the unit circle x2 + y 2 = 1 by dividing by the length.The methods have equal accuracy (both are exact in exact arithmetic). What distinguishes them is computer performance (a topic discussed more in a later lecture, hopefully). The rejection method, with an acceptance probability ? ? 4 78%, seems e? cient, but rejection can break the instruction pipeline and slow a computation by a factor of ten. Also, the square root needed to compute 1 Re call that 1 ? U2 is a standard uniform if U2 is. for example, in the dubious book Numerical Recipies. 2 Suggested, 2 the length may not be faster to evaluate than sine and cosine.Moreover, the rejection method uses two uniforms while the ? method uses just one. The method can be reversed to solve another sampling problem, generating a random point on the â€Å"unit spnere† in Rn . If we generate n independent standard normals, then the vector X = (X1 , . . . , Xn ) has all angles equally n likely (because the probability density is f (x) = v1 ? exp(? (x2 + ·  ·  ·+x2 )/2), n 1 2 which is radially symmetric. Therefore X/ X is uniformly distributed on the unit sphere, as desired. 1. 1 Other methods for univariate normals The Box Muller method is elegant and reasonably fast and is ? ne for casual omputations, but it may not be the best method for hard core users. Many software packages have native standard normal random number generators, which (if they are any good) use e xpertly optimized methods. There is very fast and accurate software on the web for directly inverting the normal distribution function N (x). This is particularly important for quasi Monte Carlo, which substitutes equidistributed sequences for random sequences (see a later lecture). 2 Multivariate normals An n component multivariate normal, X , is characterized by its mean  µ = E [X ] and its covariance matrix C = E [(X ?  µ)(X ?  µ)t ].We discuss the problem of generating such an X with mean zero, since we achieve mean  µ by adding  µ to a mean zero multivariate normal. The key to generating such an X is the fact that if Y is an m component mean zero multivariate normal with covariance D and X = AY , then X is a mean zero multivariate normal with covariance t C = E X X t = E AY (AY ) = AE Y Y t At = ADAt . We know how to sample the n component multivariate normal with D = I , just take the components of Y to be independent univariate standard normals. The formula X = AY w ill produce the desired covariance matrix if we ? nd A with AAt = C .A simple way to do this in practice is to use the Choleski decomposition from numerical linear algebra. This is a simple algorithm that produces a lower triangular matrix, L, so that LLt = C . It works for any positive de? nite C . In physical applications it is common that one has not C but its inverse, H . This would happen, for example, if X had the Gibbs-Boltzmann distribution with kT = 1 (it’s easy to change this) and energy 1 X t HX , and probability 2 1 density Z exp(? 1 X t HX ). In large scale physical problems it may be impracti2 cal to calculate and store the covariance matrix C = H ? though the Choleski factorization H = LLt is available. Note that3 H ? 1 = L? t L? 1 , so the choice 3 It is traditional to write L? t for the transpose of L? 1 , which also is the inverse of Lt . 3 A = L? t works. Computing X = L? t Y is the same as solving for X in the equation Y = Lt X , which is the process of ba ck substitution in numerical linear algebra. In some applications one knows the eigenvectors of C (which also are the eigenvectors of H ), and the corresponding eigenvalues. These (either the eigenvectors or the eigenvectors and eigenvalues) sometimes are called principal com2 ponents.Let qj be the eigenvectors, normalized to be orthonormal, and ? j the corresponding eigenvalues of C , so that 2 Cqj = ? j qj , t qj qk = ? jk . t Denote the qj component of X by Zj = qj X . This is a linear function of X and t therefore Gaussian with mean zero. It’s variance (note: Zj = Zj = X t qj ) is 2 t t t 2 E [Zj ] = E [Zj  · Zj ] = qj E [XX t ]qj = qj Cqj = ? j . A similar calculation shows that Zj and Zk are uncorrelated and hence (as components of a multivariate normal) independent. Therefore, we can generate Yj as independent standard normals and sample the Zj using Zj = ? j Yj . (2) After that, we can get an X using Zj qj . X= (3) j =1 We restate this in matrix terms. Let Q be the orthogonal matrix whose columns are the orthonormal eigenvectors of C , and let ? 2 be the diagonal ma2 trix with ? j in the (j, j ) diagonal position. The eigenvalue/eigenvector relations are CQ = Q? 2 , Qt Q = I = QQt . (4) The multivariate normal vector Z = Qt X then has covariance matrix E [ZZ t ] = E [Qt XX t Q] = Qt CQ = ? 2 . This says that the Zj , the components of Z , are 2 independent univariate normals with variances ? j . Therefore, we may sample Z by choosing its components by (14) and then reconstruct X by X = QZ , which s the same as (15). Alternatively, we can calculate, using (17) that t C = Q? 2 Qt = Q Qt = (Q? ) (Q? ) . Therefore A = Q? satis? es AAt = C and X = AY = Q? Y = QZ has covariance C if the components of Y are independent standard univariate normals or 2 the components of Z are independent univariate normals with variance ? j . 3 Brownian motion examples We illustrate these ideas for various kids of Brownian motion. Let X (t) be a Brownian motion path. Choose a ? nal time t and a time step ? t = T /n. The 4 observation times will be tj = j ? t and the observations (or observation values) will be Xj = X (tj ).These observations may be assembled into a vector X = (X1 , . . . , Xn )t . We seek to generate sample observation vectors (or observation paths). How we do this depends on the boundary conditions. The simplest case is standard Brownian motion. Specifying X (0) = 0 is a Dirichlet boundary condition at t = 0. Saying nothing about X (T ) is a free (or Neumann) condition at t = T . The joint probability density for the observation vector, f (x) = f (x1 , . . . , xn ), is found by multiplying the conditional densities. Given Xk = X (tk ), the next observation Xk+1 = X (tk + ? ) is Gaussian with mean Xk and variance ? t, so its conditional density is v 2 1 e? (xk+1 ? Xk ) /2? t . 2? ?t Multiply these together and use X0 = 0 and you ? nd (with the convention x0 = 0) f (x1 , . . . , xn ) = 3. 1 1 2? ?t n/2 exp ?1 2 ? Deltat n? 1 (xk+ 1 ? xk )2 . (5) k=0 The random walk method The simplest and possibly best way to generate a sample observation path, X , comes from the derivation of (1). First generate X1 = X (? t) as a mean zero v univariate normal with mean zero and variance ? t, i. e. X1 = ? tY1 . Given X1 , X2 is a univariate normal with mean X1 and variance ? , so we may v take X2 = X1 + ? tY2 , and so on. This is the random walk method. If you just want to make standard Brownian motion paths, stop here. We push on for pedigogical purposes and to develop strategies that apply to other types of Brownian motion. We describe the random walk method in terms of the matrices above, starting by identifying the matrices C and H . Examining (1) leads to ? 2 ? 1 0  ·Ã‚ ·Ã‚ · ? ? ? 1 2 ? 1 0  ·Ã‚ ·Ã‚ · ? ? .. .. .. . . . 1 ? 0 ? 1 ? H= ?. .. ?t ? . . 2 ? 1 ?. ? .. ? . ? 1 2 0  ·Ã‚ ·Ã‚ · 0 ? 1 ? 0 .? .? .? ? ? ? ? 0? ? ? ?1 ? 1 This is a tridiagonal matrix with pattern ? 1, 2, ? except at the bottom right corner. O ne can calculate the covariances Cjk from the random walk representation v Xk = ? t (Y1 +  ·  ·  · + Yk ) . 5 Since the Yj are independent, we have Ckk = var(Xk ) = ? t  · k  · var(Yj ) = tk , and, supposing j < k , Cjk = E [Xj Xk ] = ? tE [((Y1 +  ·  ·  · + Yj ) + (Yj +1 +  ·  ·  · + Yk ))  · (Y1 +  ·  ·  · + Yj )] = 2 ?tE (Y1 +  ·  ·  · + Yj ) = tj . These combine into the familiar formula Cjk = cov(X (tj ), X (tk )) = min(tj , tk ) . This is the same as saying that the ? 1 ?1 ? ?. ?. C = ? t ? . ? ? ? 1 matrix C is 1  ·Ã‚ ·Ã‚ · 2 2  ·Ã‚ ·Ã‚ · 2 . . . 3  ·Ã‚ ·Ã‚ · . . . 2 3  ·Ã‚ ·Ã‚ · ? 1 2? ? ? 3? .? .? .? .. . (6) The random walk method for generating X may be expresses as ? ? ? Y ? X1 1 1 0  ·Ã‚ ·Ã‚ · 01 ? ? ? ?1 1 0  ·Ã‚ ·Ã‚ · 0 ? ? . ? ?.? ?.? v? ? . ? ?.? 1 0 . . ? . .? ? . ? = ? t ? 1 1 ? ? ? ? ?. . .. ? ? ? ?. . . .. ? ? ? ? 11 1  ·Ã‚ ·Ã‚ · 1 Yn Xn Thus, X = AY with ? ? 1 0  ·Ã‚ ·Ã‚ · 01 ?1 1 0  ·Ã‚ ·Ã‚ · 0 ? ? ? v? .? .? . ?1 1 1 0 .? A = ? t ? ?. . ? .. .. ?. . ? . 11 1  ·Ã‚ ·Ã‚ · 1 (7) The reader should do the matrix multiplication to check that indeed C = AAt for (6) and (7). Notice that H is a sparse matrix indicating short range interactions while C is full indicating long range correlations.This is true of in great number of physical applications, though it is rare to have an explicit formula for C . 6 We also can calculate the Choleski factorization of H . The reader can convince herself or himself that the Choleski factor, L, is bidiagonal, with nonzeros only on or immediately below the diagonal. However, the formulas are simpler if we reverse the order of the coordinates. Therefore we de? ne the coordinate reversed observation vector t X = (Xn , xn? 1 , . . . , Xn ) and whose covariance matrix is ? tn ? tn? 1 ? C=? . ?. . t1 tn? 1 tn? 1  ·  ·  · t1 t1 .. .  ·Ã‚ ·Ã‚ · ? ? ? , ? t1 and energy matrix ? 1 ? 1  ·Ã‚ ·Ã‚ · 0 ? 0 .? .? .? ? ? ?. ? 0? ? ? ?1 ? 2 ? ? ? 1 2 ? 1 0  ·Ã‚ ·Ã‚ · ? ? .. .. .. . . . 1 ? 0 ? 1 ? H= .. ?t ? . . ?. . 2 ? 1 ? ? .. ? . ? 1 2 0  ·Ã‚ ·Ã‚ · 0 ? 1 We seek the Choleski factorization H = LLt ? l1 0 ? m2 l2 1? L= v ? m3 ?t ? 0 ? . .. . . . with bidiagonal ?  ·Ã‚ ·Ã‚ · ? 0 ? ?. .. ? . ? .. . Multiplying out H = LLt leads to equations that successively determine the lk and mk : 2 l1 l 1 m2 2 2 l1 + l 2 l 2 m3 = 1 =? l1 = 1 , = ? 1 =? m2 = ? 1 , = 2 =? l2 = 1 , = 1 =? m3 = ? 1 , etc. , The result is H = LLt with L simply ? 1 0  ·Ã‚ ·Ã‚ · ? ? 1 10 1? .. L= v ? . ?t ? ? 1 ? . .. .. . . . . 7 ? ? ? ?. ? ? The sampling algorithm using this Y = Lt X : ? ? ? 1 Yn ? Yn? 1 ? ? ? ? ?0 ? ? 1? ? ? ? ? . ?= v ? ?.? ?t ? ?.? ?. ? ? ?. . Y1 0 information is to ? nd X from Y by solving ?1 0 1 .. . ?1 .. .  ·Ã‚ ·Ã‚ ·  ·Ã‚ ·Ã‚ · .. . 0 0 Xn . ? ? Xn? 1 . . . 0 . . ?1 X1 1 ? ? ? ? ? ? ? ? ? Solving from the bottom up (back substitution), we have Y1 = Y2 = v 1 v X1 =? X1 = ? tY1 , ?t v 1 v (X2 ? X1 ) =? X2 = X1 + ? tY2 , etc. ? t This whole process turns out to give the same random walk sampling method. Had we not gone to the time reversed (X , etc. variables, we could have calculated the bidiagonal Choleski factor L numerically. This works for any problem with a tridiagonal energy matrix H and has a name in the control theory/estimation literature that escapes me. In particular, it will allow to ? nd sample Brownian motion paths with other boundary conditions. 3. 2 The Brownian bridge construction The Brownian bridge construction is useful in the mathematical theory of Brownian motion. It also is the basis for the success of quasi Monte Carlo methods in ? nance. Suppose n is a power of 2: n = 2L . We will construct the observation path X through a sequence of L re? ements. First, notice that Xn is a univariate normal with mean zero and variance T , so we may take (with Yk,l being independent standard normals) v Xn = T Y1,1 . Given the value of Xn , the midoint observation, Xn/2 , is a univariate normal4 w ith mean 1 Xn and variance T /4, so we may take 2 Xn 2 v 1 T = Xn + Y2,1 . 2 2 At the ? rst level, we chose the endpoint value for X . We could draw a ? rst level path by connenting Xn to zero with a straight line. At the second level, or ? rst re? nement, we created a midpoint value. The second level path could be piecewise linear, connecting 0 to X n to Xn . 4 We assign this and related claims below as exercises for the student. 8 The second re? nement level creates values for the â€Å"quarter points†. Given n X n , X n is a normal with mean 1 X n and variance 1 T . Similarly, X 34 is a 2 42 2 4 2 1 1T normal with mean 2 (X n + Xn ) and variance 4 2 . Therefore, we may take 2 Xn = 4 1 1 Xn + 22 2 T Y3,1 2 and n X 34 = 1 1 (X n + Xn ) + 2 2 2 T Y3,2 . 2 1 The level three path would be piecewise linear with breakpoints at 1 , 2 , and 3 . 4 4 Note that in each case we add a mean zero normal of the appropriate variance to the linear interpolation value.In the general step, we go from the level k ? 1 path to the level k paths by creating values for the midpoints of the level k ? 1 intervals. The level k observations are X j . The values with even j are known from the previous 2k? 1 level, so we need values for odd j . That is, we want to interpolate between the j = 2m value and the j = 2m + 2 value and add a mean zero normal of the appropriate variance: X (2m+1)n = 2k? 1 1 2 mn X 2k? 1 + X (2m+2)n 2 2k? 1 + 1 2(k? 2)/2 T Ym,k . 2 The reader should check that the vector of standard normals Y = (Y1,1 , Y2,1 , Y3,1 , Y3,2 , . . . t indeed has n = 2L components. The value of this method for quasi Monte Carlo comes from the fact that the most important values that determine the large scale structure of X are the ? rst components of Y . As we will see, the components of the Y vectors of quasi Monte Carlo have uneven quality, with the ? rst components being the best. 3. 3 Principle components The principle component eigenvalues and eigenvectors for many types of Brownian motion are known in closed form. In many of these cases, the Fast Fourier Transform (FFT) algorithm leads to a reasonably fast sampling method.These FFT based methods are slower than random walk or Brownian bridge sampling for standard random walk, but they sometimes are the most e? cient for fractional Brownian motion. They may be better than Brownian bridge sampling with quasi Monte Carlo (I’m not sure about this). The eigenvectors of H are known5 to have components (qj,k is the k th component of eigenvector qj . ) qj,k = const  · sin(? j tk ) . 5 See e. g. Numerical Analysis by Eugene Isaacson and Herbert Keller. 9 (8) The n eigenvectors and eigenvalues then are determined by the allowed values of ? j , which, in turn, are determined throught the boundary conditions.We 2 2 can ? nd ? j in terms of ? j using the eigenvalue equation Hqj = ? j qj evaluated at any of the interior components 1 < k < n: 1 2 [? sin(? j (tk ? ?t)) + 2 sin(? j tk ) ? sin(? j (tk + ? t)) ] = ? j sin(? j tk ) . ?t Doing the math shown that the eigenvalue equation is satis? ed and that 2 ?j = 2 1 ? cos(? j ? t) . ?t (9) The eigenvalue equation also is satis? ed at k = 1 because the form (8) automatically satis? es the boundary condition qj,0 = 0. This is why we used the sine and not the cosine. Only special values ? j give qj,k that satisfy the eigenvalue equation at the right boundary point k = n. 10