What Impact Has Globalisation Had On Employment Relations Essay

What Impact Has Globalization Had On Employment Relations - Essay Example Globalization is the procedure that includes the worldwide coordination between nations regarding trade of new items, worldwide perspectives and various parts of culture and thoughts. Globalization on the planet economy had started from 1980 and in the long run, had spread all over the globe. As per Ronald Robertson, globalization is â€Å"the pressure of the world and the strengthening of the awareness of the world as a whole† (Cuyvers, Lombaerde and Rayp, 2011). On the off chance that it is accepted as far as single nature, at that point globalization is the procedure that involves various extents of societies, orders and networks. Based on the standard expressed by David Ricardo, globalization permits the nations to advance as far as their center abilities (Ricardo, 1992). Business relations are characterized as the connection that exists between the administration of an association and their workers. It includes the different kinds of complaints, aggregate dealing, associa tions and issue goals that exist in the work advertise. This article would clarify the effect of globalization on the work relations of the world. With regards to the exposition, the analyst would concentrate on the real effect of globalization on the businesses, the representatives and the associations. Toward the end, before finishing up on the examination investigation, the specialist would break down the impingement of globalization on a state or country. ... These businesses found that the expense of work assets in the creating economies were a lot less expensive. This is the explanation behind the directors of the corporate organizations in the created countries to grow business in the less evolved countries like, Russia and India, by enrolling a greater amount of their people (Arnold, 2008). Simultaneously, after the rise of globalization, the business supervisors in the creating countries like, China and Brazil had begun to encounter further extent of rivalry in their local business condition. This was because of the expanding outside organization internationalization in these countries. Subsequent to encountering a further extent of rivalry in the household advertise, the business organizations in these creating economies have ended up being progressively effective. Therefore, the level of degree of work openings extended in their organizations. The rising degree of national earnings in the vast majority of the nations, post-globaliz ation, means the way that the size of tasks for the vast majority of the organizations on the planet have expanded, which infers that the pay limits of the businesses have likewise expanded. The businesses of the organizations like, Ford Motors and Tesla have extended so as to gain admittance to the wide and modest base of work asset (US Census Bureau, 2000). Additionally, comparably, the organizations from the creating nations like, Toyota and Tata have extended their business in the created countries. Against It ought to be viewed as that the level of work versatility in the worldwide market have gotten high after the development of globalization. This is the reason the gracefully of work market to the businesses had

Role of management consultants Essay Example for Free

Job of the executives experts Essay The article talks about the job of the board specialists in the current world. The interest for the board specialists was realized by the adjustments in business patterns and needs as we are moving towards globalization. In any case, the creator proceeded with that in spite of the fact that there are a few changes in the business circumstance achieved by modernization and globalization, the job of the executives specialists continue as before. It is their obligation to make supervise that business tasks stay beneficial and proficient. In addition, the obligation of the board advisors is to investigate business circumstances so as to decide issues or troubles, and through cautious preparing and arranging, make out goals so as to determine hindrances that frustrate the development of organizations. The creator refered to a few significant jobs that administration specialists must be able to complete and furthermore attributes that they should display so as to offer gainful types of assistance to their customers. The ability and experience is exceptionally significant in the board consultancy. The executives advisors should know an assortment of business circumstances from easy to complex, and approach broad assets so as to work with their customers effectively and fittingly. Objective setting and arranging are different jobs of the board experts. Cooperating with their customers, they should have the option to set a bearing for the administration by deciding squeezing needs and prerequisites. The board specialists must have the option to utilize their insight, abilities, and encounters to accomplish the objectives and targets of the administration. Additionally, experts ought to consistently be available to administer, direct, and bolster the administration so as to guarantee that everything is working out in a good way as arranged, and furthermore to decide whether there are a few issues or concerns neglected all the while. Another attractive nature of the board experts is adaptability and versatility. Specialists ought to have the option to define plans and business arrangements that are reasonable to the business or the management’s needs and concerns. Adaptability and versatility implies the capacity to tweak plans and business arrangements, and yet have the option to make changes varying so as to ensure that the most ideal arrangements are done. Furthermore, the board advisors ought to have the option to help the progress from the executives changes in an easy manner without making a lot of unsettling influence the business setting. The article completely talks about the significant of the executives experts to the board and management, and to the business association in general. It is profoundly intriguing that the best impact is gotten most from the administration advisors who are accountable for the administration. With the thoughts communicated in the article, the noteworthiness of the executives experts is acknowledged, particularly in guaranteeing that administration, oversight, and the business setting is well en route to accomplishing its hierarchical crucial, and goals.

How to Cite a Blog Post in MLA, APA, or Chicago

How to Cite a Blog Post in MLA, APA, or Chicago (14) As new forms of online communication become acceptable sources in an academic setting, questions regarding proper citation continue to arise. You might be confused about how to cite certain things, but we promise it’s easier than it seems. Luckily, we’ve got you covered as you look to cite a blog post for your next paper (regardless of which citation style you’d like to use). To cite a blog post, you should make note of the following pieces of informations: The name of the blog the post has been published on The title of the specific post you’re citing The date the post was published The author of the post The publisher of the blog site The URL or direct link to the post Use the following structure to cite a blog post in MLA 8: Author’s Last Name, Author’s First Name. “Title of Post.” Blog Name, Publisher (only include this information if it is different than the name of the blog site), Date blog post was published, Link to post (omit // or //). Here’s how the above example would be cited in MLA 8: Kirschenbaum, Michele. “10 Ways to Spot a Fake News Article.” EasyBib, 4 Jan. 2017, www.easybib.com/guides/10-ways-to-spot-a-fake-news-article/. Use the following structure to cite a blog post in APA 7: Author’s Last Name, First Initial. (Year, Month Day post was published). Title of post. Title of Blog. URL Here’s how the above example would be cited in APA: Kirschenbaum, M. (2017, January 4). 10 ways to spot a fake news article. EasyBib Blog. https://www.easybib.com/guides/10-ways-to-spot-a-fake-news-article/ In Chicago, blog posts are generally only cited in the body of a project and also in the footnotes Example: “In EasyBib’s blog post on January 4th, 2017, the author shares many ways to spot a fake news article….” Footnote: Michele Kirschenbaum, “10 Ways to Spot a Fake News Article,” EasyBib (blog), January 4, 2017, /10-ways-to-spot-a-fake-news-article/. If the blog post was used significantly in your project, or if your instructor prefers a full citation in the bibliography, use the following structure: Author’s Last name, First name. “Title of Blog Post.” Title of Blog (blog), Date, Link to post. Here’s how the above example would be cited in Chicago: Kirschenbaum, Michele. “10 Ways to Spot a Fake News Article.” EasyBib (blog), January 4, 2017, /10-ways-to-spot-a-fake-news-article/. Find more blog examples with these additional guides: APA Chicago MLA 7 Or use EasyBib linked here to create your citation! We have forms for over 50 source types including blog!

Essay on Critical Thinking and Ethical Decision Making

Critical thinking and ethical decision making are crucial for academic success as well as career success. Both critical thinking and ethical choices allow an appreciation of diverse points of view using analytic approaches, create a tolerance for and an appreciation of ambiguity, allow for creative problem-solving, and give the ability to integrate knowledge from diverse viewpoints into unified ideas and strategies. To better understand how critical thinking and ethics impacts our success, we must analyze these skills and how they relate to us academically, and to our future careers. One way a strong analysis of critical thinking and ethics can impact our success is by allowing us to have a full understand of what critical thinking.†¦show more content†¦Once a strong understanding of critical thinking and ethics is developed, one can recognize factors that can negatively affect this thought process and our morals Allowing a recognition of the barriers to critical thinkin g is another way that it can lead to success academically and in our future careers Barriers to critical thinking include emotions, resistance, and stress. Emotions can negatively impact our ability to make ethical decisions. Fear of failure can lead to less risk taking, and even the inability to express our ideas that could lead to success. Anger is another strong emotion that can cloud our ability to make ethical decisions and think critically. Often in a business environment, employees can react to changes in their field with anger rather than using critical thinking skills. Personal biases, which are almost always emotionally related, will also act as a barrier to our success in critical thinking. Resistance is the use of immature defense mechanisms that are impulsive, maladaptive, and non-analytical, and acts as a barrier to critical thinking. When one feels overwhelmed, whether it’s from work or from school work, it is natural to turn to defense mechanisms. Whe n this becomes a habitually way to deal with issues, resistance becomes a barrier to our success and critical thinking abilities. Stress can also play a role in negatively affecting our critical thinking ability. In today’s business world,Show MoreRelatedThe Importance of Critical Thinking and Ethical Decision Making on Social Work1149 Words   |  5 PagesIt is my belief that in order for someone in the social work profession to serve vulnerable populations it was intended to serve, it is imperative to use critical thinking and ethical decision making in tandem to achieve the optimal result. The balance is a delicate and often complex. It requires a close examination or critically thinking, of all the issues not just within yourself, but the community as a whole, the individuals within it, and the client population that the social work serves. TheRead MoreThe Direct Relationship Between Critical Thinking And Ethics1268 Words   |  6 PagesRelationship between Critical ly Thinking and Ethics Manuel Ortuno Jr. Foundations for University Success/GEN 201 21 September 2014 Ms. Alisa Hewitt The Direct Relationship between Critical Thinking and Ethics Critical thinking and ethics are two topics that every person should be educated on starting from childhood in order to be functional members of any society. To better understand the issue, one must first know what critical thinking and ethics are; â€Å"Critical thinking is the path to freedom fromRead MoreEthics in Criminal Justice Administration1433 Words   |  6 PagesNowhere is ethical behavior more important than the administration of criminal justice. Lack of ethical behavior undermines the purpose of the criminal justice system. The cost of unethical behavior will be the downfall of the criminal justice system and only by gaining a true understanding of what ethical behavior is and how to maintain it will the system continue to flourish. While the ethical standard individuals develop through the years are important; utilizing critical thinking skills ensuringRead MoreHow Does Critical Thinking And Ethics Affect Your Decisions Essay1242 Words   |  5 PagesHow Does Critic al Thinking and Ethics Affect Your Decisions Introduction Critical thinking and ethics go hand and hand with the responsibly of one’s professional and social interactions. Critical thinking is a six step process one takes when making a decision and/or is given a new idea or concept. Ethics, while it is different for each individual it is the morals of right and wrong. Unconsciously when an individual makes a decision, their ethics and critical thinking processes are what guide themRead MoreThe Moral Decision Making : An Ethical Decision1517 Words   |  7 PagesEthical decision-making is a vital part of my critical thinking, serving as a constant factor or theme throughout the process. History is full of leaders who, more than likely, were extraordinary critical thinkers capable fully dedicated to making solid decisions. However, a great decision developed through critical thinking does not equate to the â€Å"right† decision or an ethical decision. For example, one could argue Adolf Hitler and his inner circle were except ional critical thinkers capable ofRead MoreComputer Technology : The Concepts Of Safety-Critical Software1748 Words   |  7 PagesI tend to agree with John about the overall topics of the article. The concepts of safety-critical systems goes far beyond our belief. With the increase of technology in the 21st century, the idea of most modern machinery being developed or operated by a computer has become the defined norm. In the process of developing safety-critical software, there is the common assumption that the program will be tested thoroughly for life threating errors. As such, effective communication among developers mustRead MoreCritical Thinking Application Paper985 Words   |  4 PagesCritical Thinking Application Paper According to Foundation for Critical Thinking (2009), â€Å"Critical thinking is that mode of thinking—about any subject, content, or problem—in which the thinker improves the quality of his or her thinking by skillfully taking charge of the structures inherent in thinking and imposing intellectual standards upon them† (Defining Critical Thinking, para. 9). Thinking is part of everyone’s human nature. People who can separate their thoughts, analyze them, and changeRead MorePersonal Motives For Corporate Social Responsibility933 Words   |  4 PagesAnnotations and Critical Analysis Motives for Corporate Social Responsibility (Graafland, J. Mazereeuw-Van der Duijn Schouten, C. 2012) analyze the motivations of directors to take responsibility for the labor, environmental and social aspects in business. It distinguishes the Corporate Social Responsibility (CSR) by conducting a survey consisting of a sample of 473 executives. What is more, the motives are classified as three types: â€Å"financial motives†, which is external, â€Å"ethical and altruistic†Read MorePolicing1068 Words   |  5 Pagessystem make important decisions every day that involves critical thinking, and the choices they make will have an impact in society; therefore, it is important that these professionals be unbiased to everyone they come in contact with. This paper will analyze the relationship between ethics and professional behavior in the administration of criminal justice. It will also explain the role of critical as well as a seminar proposal on ethics that will include five areas of ethical conduct. The readerRead MoreEthics in Criminal Justice Administration Essay1533 Words   |  7 Pagesadministration are faced with ethical issues everyday and must deal with this ethical issues in a professional manner. The administration in criminal justice especially the policing administration struggle with ethics and professional behavior in certain situations and may find it difficult to handle. The criminal justice administration has the obligation of making moral judgments of what is right or wrong and must be done professionally and with the use of critical thinking. This paper will analyze

Soothing Quotes About Heartbreak

A famous—and true—adage goes like this: A friend is one who walks in when others walk out. All those who have had their hearts trampled upon will agree that the presence of a friend can ease the pain. So if you have a friend going through a tough heartbreak, just be around. If you find yourself at a loss for words, dont fret. These love and heartbreak quotes can help you to soothe your friend aptly express your feelings without making you sound like a know-it-all. Heartbreak Quotes Anonymous If we deny love that is given to us, if we refuse to give love because we fear pain or loss, then our lives will be empty, our loss greater. Robert Frost â€Å"The only way out is through.†Ã‚   Haruki Murakami, Norwegian Wood â€Å"What happens when people open their hearts?  They get better.†Ã‚   Cormac McCarthy, All the Pretty Horses â€Å"Scars have the strange power to remind us that our past is real.†Ã‚   David GraysonLooking back, I have this to regret, that too often when I loved, I did not say so. Jim Henson â€Å"Only time can heal your broken heart. Just as only time can heal his broken arms and legs.†Ã‚   Javan Love can sometimes be magic. But magic can sometimes ... just be an illusion. Richard Puz, The Carolinian â€Å"Death leaves a heartache no one can heal, love leaves a memory no one can steal. (From an Irish headstone) Robert James Waller, The Bridges of Madison County â€Å"The human heart has a way of making itself large again even after its been broken into a million pieces.†Ã‚   Marcel Proust â€Å"We are healed of a suffering only by experiencing it to the full.†Ã‚   In reality, in  love  there is a permanent suffering which joy neutralizes, renders virtual delays, but which can at any moment become what it would have become long earlier if one had not obtained what one wanted—atrocious. Spanish ProverbWhere there is love, there is pain. Charles M. Schulz Nothing takes the taste out of peanut butter quite like unrequited love. Laura Fitzgerald, Veil of Roses â€Å"Given enough time and distance, the heart will always heal.†Ã‚   Shannon L. Adler â€Å"Time doesnt heal all wounds; only distance can lessen the sting of them.†Ã‚   John Christopher, The Sword of the Spirits â€Å"And though I remember her name I cannot recall her face. All things pass.†Ã‚   Steve Goodier â€Å"It’s true that laughter really is cheap medicine. It’s a prescription anyone can afford. And best of all, you can fill it right now.†Ã‚   Amy Hempel â€Å"Consolation is a beautiful word. Everyone skins his knee—that doesnt make yours hurt any less.†Ã‚   Jean de la Fontaine â€Å"Sadness flies away on the wings of time.†

Freedom of Contract in English Law Free Essays

string(158) " a seller automatically assumes certain obligations to the buyer as a result of terms which are automatically implied in every contract regulated by the Act\." In earlier days, agreement was built on a very classic and simple basis: it is concluded at the moment that the acceptance of an offer takes place and that is all. In consequence, equal parties were non-existent and stronger parties had the possibility to impose unfair and domineering conditions upon those who were weak and vulnerable. It is in this context that both legislations and courts agreed that State action was indispensable to ensure fairness among individual parties, in an era where the exercise of law of freedom were extremely restricted. We will write a custom essay sample on Freedom of Contract in English Law or any similar topic only for you Order Now In today’s English law, freedom of contract is one the foundation of contract law. The existence of freedom of contract requires three main considerations: the freedom to contract or not to contract, the freedom to choose with whom to contract, and the freedom to decide the terms of the contract. Thus parties are totally free to engage or not to engage in agreements. However, freedom of contract can fail to have the desired or expected effect in contracts where power relations are not equal. The stronger party can impose its â€Å"will† to the weaker party. In order to deal with any potential conflict that can arise from this matter, English legal systems has set up rules ensuring the effective and fair exercise of freedom of contract. This essay will discuss and examine those rules in question, established by the English law in order to effectively balance freedom of contract and fairness between the contracting parties as well as fair contractual terms. And also on the other hand limits of freedom of contract will be exposed. Freedom of contract, as its appellation suggests, has a strong relationship with contract. In order to identify this relationship, it is important to understand what is meant by â€Å"contract† and the rules governing it. In English law, a contract is a legally binding agreement reached on a set of promises (or obligations) and specific terms. The validity of any contract requires 4 main features: an offer, acceptance, consideration and intention to create legal relations. Thus, when one party (the offeror) makes an offer which the other (offeree) accepts, then agreement is concluded. However, the mere fact of an agreement is insufficient for a contract to be completely valid. This implies that a party must promise to give or do something for the other. This idea of exchanging promises is known as â€Å"consideration† and is an essential requisite of any valid contract. In Currie v Misa(1875) it (consideration) was held to constitute a benefit to one party or a detriment to the other. For instance, when a bottle of wine is bought from a shop, the benefit received is the bottle of wine, and the detriment is the money paid to the shop. Yet it is important to take into concern the rules governing consideration. First of all, consideration must not be in the past(as mentioned in the a. This rule suggests that if one party willingly performs an act, and the other party then makes a promise the consideration said to be in the past. Therefore past consideration is regarded as no consideration at all. For instance, a pregnant woman named Julie, knowing that her neighbour, Lucy, is concerned about her health, offers to do the housework for her. This takes Lucy tremendous amount of time to do, and Julie is so content with the result that she promises to pay Lucy ? 30 for her effort. If Julie fails to pay, Lucy will not have the possibility to sue for breach of contract as Julie’s promise to pay was after the completion of the work. The fact of this case is supported by the case of Re McArdle(1951,CA) in which it was held that no valid contract existed since the home improvements were past consideration; they had been carried out before any promise to pay had been made. Another rule is that consideration must move from the promisee which is very similar to the concept of law of privity. So for instance if A makes a promises to B, the promise will only be enforceable if B can equally show that he has provided consideration for A’s promise. This rule clearly demonstrates the fairness (among parties) of the doctrine of consideration. Finally, consideration must be sufficient but need not to be adequate. This rule stipulates that a good consideration must be of some value but there is not necessity for a bargain to be of adequate value. For example, if someone is willing to sell his Ferrari for ? 1, the contract will not be in vain due to lack of consideration and therefore will be sufficient. In this case, Courts will not measure the adequacy of the consideration (the fact that a Ferrari is offered to be sold at only ? 1) as it is up to one party to decide whether or not he agrees with the other party promises. The contract in English law enhances principle of freedom of contract. Indeed, the terms of the contract is freely determined and agreed by the parties. However, there are various circumstances in which additional terms may be implied into the agreement. The aim of implied terms is often to provide a supplement to a contractual agreement in the interest of making bargain more effective, to achieve fairness between the parties and to alleviate hardship. Term may be implied by custom. Here it is suggested that a contract must always be examined in the light of its surrounding commercial context. So the parties automatically assume that sometimes their contract will be subject to the customs of a particular locality or trade and therefore do not deal specifically with the matter in their contract. One of the cases illustrating this is Hutton v Warren(1836). A term may equally be implied into a contract y Act of Parliament in the form of statutes. Under the Sale of Goods Act 1979, ss 12-15 for instance, a seller automatically assumes certain obligations to the buyer as a result of terms which are automatically implied in every contract regulated by the Act. You read "Freedom of Contract in English Law" in category "Essay examples" The seller is required by statute to promise that he has lawful authority to transfer ownership of the goods(s12)(the seller would for example break this term if it turns out that the goods were stolen);that the goods being sold will match the description he provided the buyer(s13)(for instance a shirt described as 100 per cent cotton should not contain man-made fibres); that the quality of the goods being sold will satisfy the buyer(s14(2)); that the good will be suitable for any purpose specified by the buyer(s 14(3)); and that the goods being sold will match any sample shown to the buyer prior to the contract being made(s 15). Breach of any of these terms will put the buyer in a strong position and be given the option to be discharged from the contract or alternatively carry on with the contract and claim damages for the breach. This will lead us to the concept of remedies mentioned in the following part. In English contract law, a crucial aspect of the contractual relationship is the enforcement of the contract, as the obligation that pact must be kept firmly by parties is considered as the backbone of any contractual relationship. However, a problem can occur if a contract is not adequately performed and one of the parties renounces to perform its obligations. This is where the concept of non-performance and the remedies available to the injured party become applicable. Breach of contract arises from the non-respect of the pact (or terms) agreed between parties. The aggrieved party is then given the common law right to claim for a remedy resulting from any quantifiable loss or harm suffered. Damage (financial compensation) is the most basic remedy available to the innocent party. In today business environment, it is not rare for the parties to agree in advance the damages that will be payable in the occurrence of a breach of contract. These damages are referred to as liquidated damages. An illustration of liquidated damages is the charges imposed for cancelling a flight or the booking of a hotel room. But sometimes, there is a temptation for a party with stronger trading power to try imposing a penalty clause (punitive payment for the non-performance of a term or condition) as demonstrated in Wilson v. Love (1896) case. Other remedies such as quantum damages and injunction may be granted at the discretion of the court as part of its equitable jurisdiction. So, as mentioned above, remedies is all about compensating the aggrieved party for causing him loss or harm. This can be avoided by the consideration of the prevailing rules of freedom of contract. In other words, Freedom of contract allowing individual parties to freely contract or not to, and no one being forced to do it , whoever therefore who gives a contractual promise must then keep it. Or on the contrary case, as described in earlier parts can be constrained by legal authorities to honour its commitment or compensate the other party. However, performance of a contract becomes sometimes impossible due to the circumstances beyond the control of either of the parties and not due to their fault. The legal term referring to this situation is frustration. An example of this unforeseen event is illustrated in the case of Taylor v Caldwell (1863) in which it was held that contract was impossible to perform due to an external and unforeseen event. Consequences are that the contract is killed and parties discharged from further liability. This limits the exercise of freedom of contract in a sense that the agreement formed by the parties is nullified, regardless individual parties will. Another limitation of freedom of contract is that the choice of other contracting party is not always free. For example, an employer is not totally free to hire the person of his choice. The fact that insurance contracts are sometimes made obligatory by parties equally render the exercise of freedom of contract limited, as concerned parties did not freely choose to contract with an insurance company. So far, this paper has been about the relationship between the exercise of freedom of contract and law of contract. However not only is freedom of contract concerned with contract law but also with another component of the English private law, which is tort law. A tort is a civil wrong. In other words, it refers to the liability of a person who causes harm to another with the obligation to repair the damages suffered by the victim. An example of tort is damage to commercial interests, e. g. inducement of breach of contract. Also known as tortious interference, inducement of breach of contract arise where the wrongdoer convinces a party to breach the contract against the claimant, or where the wrongdoer prevents one party from performing his obligations(agreed with the other party), thus stopping the claimant from receiving the performance promised. Furthermore, after mentioning the existence of a duty of care, which is an element required making negligence claim (concerned with a wrongdoer’s careless conduct which cause damage or loss to the defendant), the claimant (the injured party) can prove that this duty has been broken by the defendant (the other party). Hence the close relationship between duty of care and the requisites of freedom of contract in the sense that if parties freely agree to contract (including the terms of it), then, it is suggested, that they owe a duty of care to each other because the careless conduct (which can affect the contract) of one party can prevent the other one from receiving the performance promised, regardless to the external factor that caused the misconduct of the blamed party. This fact is supported by the case of Garret v. Taylor (1620) in which the court upheld a judgment for the claimant. To conclude, the purpose of this essay has been to describe and make a connection between law of contract as well as law of torts and freedom of contract. Thus, English legal systems have established multiple rules of conduct from different parties to a contract in order to ensure fairness between them. Henceforth, contracting parties are given freedom to contract with whoever they want, including the terms of the contracts. Also, thanks to rules such as of duty of care, or of doctrine of remedies, an injured party is now given the possibility to claim for compensation of loss or harm caused by the blamed party, who will be then obliged by legal authorities to repair the damages caused to the aggrieved party due to non-respect of the rules established. In the end, it must be acknowledge that English Law has stroke an appropriate balance between freedom of contract and fairness. References: Currie v Misa (1875) LR 10 Ex 153; (1875-76) LR 1 App Cas 554:Definition of consideration Garret v. Taylor, 79 Eng. Rep. 485 (K. B. 1620): Tortious interference Hutton v Warren (1836) 1 M;W 460:Implied terms Re McArdle(1951,CA ):Past consideration being unacceptable Sale of Goods Act 1979, ss 12-15 : Statutory implied terms Taylor v Caldwell (1863) 3 B ; S 826; 122 ER 309; [1863] EWHC QB J1: impossibility of performance of contract Wilson v. Love (1896) : Liquidated damages How to cite Freedom of Contract in English Law, Essay examples

Capital Budgeting Techniques and Sensitivity Analysis

Question: Discuss about the Capital Budgeting Techniques and Sensitivity Analysis. Answer: Introduction: Sensitivity analysis can be understood as research of the uncertainty within the production of a mathematical model or system that can be allocated to several uncertainty sources within its inputs (Ai, Croce and Li 2013). Sensitivity analysis serves as techniques employed for determining the ways in which several values of certain variable impact on a a dependent variable within a specific cluster of assumptions. Sensitivity analysis is generated for analyzing the impact that the great range of variables has on the desired outcome. This analysis is relied on the variables effecting valuation that a financial model can indicate through employing the price and EPS variables (Borgonovo and Plischke 2016). For instance, Apple Inc employs sensitivity analysis along with the consideration of long-term cost of capital. Sensitivity analysis that is employed by Apple Inc serves as a technique of evaluating alterations in particular projects NPV or the IRR for the given change within one of the variables. This signifies the extent to which a project is NPV or IRR is sensitive for a considered change in one among the variables (Fujimori et al. 2014). Apple Inc considers that the more the NPV of a project is sensible the more critical can be the variable. The following steps are deemed associated with the implementation of the sensitivity analysis that is mentioned under: Definition of the underlying relationship among the variables Evaluation of the impact of the alteration of the changes in all the variables on the projects NPV Reorganization of all the variables that has an impact on the NPV and IRR of certain projects Sensitivity analysis of the efficiency criteria for the purpose of investment project analysis serves as the calculating technique of researching and deciding the impact of changes in the individual values considered on the investment project analysis (Gospodinov, Kan and Robotti 2014). Apple Inc stated that strong implementation of the sensitivity analysis within the investment decision-making under certain uncertainty situations includes numerous major input parameters like the income, investment value, costs, discount rate in accordance with the impacts and effects of the alterations of these parameters (Kuehn, Simutin and Wang 2016). This is on the values of numerous basic criteria that can be considered as investment decision-making process namely the criteria of internal rate of return, net present value and the payback period. Sensitivity analysis serves as major criteria for the evaluation of investment projects serves as extremely complex process. With the help of the sensitivity analysis, the investors will be capable to obtain a great number of information regarding the impact of the input parameters on the criteria those are examined for conducting effective investment decision-making (Lee and Su 2014). Apple Inc stated that information can also be gathered regarding the impact of input parameters based on the criteria value that can further enhance investment decision making. Capital budgeting serves as a process though which investors determine which projects to select. Sensitivity analysis offers superior insight for the investors to take effective business decisions. Scenario Analysis Scenario analysis serves as the technique of evaluating likely future events through taking into account certain alternative possible outcomes. For this reason, for Apple Inc. scenario analysis can serve as a technique that can be the major form of projection, which does not attempt to indicate one accurate picture of the future (Mnster et al. 2014). Scenario analysis acts as a technique of anticipating the expected portfolio value that is in response to certain unfavorable event and might be employed to analyze theoretical worst-case circumstances. Moreover, scenario analysis serves as a process in order to ascertain and evaluate the likely events that can take place in the upcoming years. This serves as a vital tool that is increasingly used in making projections over the upcoming years (Rangvid, Santa-Clara and Schmeling 2016). Scenario analysis is increasingly associated with capital budgeting techniques. An investments scenario analysis might include the following steps: Revealing the best-case output within most suitable value for all the inputs is an option of scenario analysis. For instance, Apple Inc considers that at the time of calculating net present value, the most suitable value for discount rate is used along with considering likely cash flow growth along with lower tax rate (Tian 2013). With implementation of effective capital budgeting techniques such as NPV and IRR, it can be stated that scenario analysis is a model output that is calculated for over an ample scenarios. Scenario analysis is widely employed in order to estimate proper investment value in several situations. Scenario analysis is greatly used in taking investment decisions through implementation of capital budgeting techniques like NPV and IRR (Zabarankin, Pavlikov and Uryasev 2014). For Apple Inc, scenario analysis was deemed most vital techniques for evaluating risks associated with the investment projects. The scenario analysis served as the techniques those are used by investors along with using the discount rates must be used for projects with several risks. Capital Asset Pricing Model Capital Asset Pricing Model (CAPM) is a model employed for theoretically determining suitable asset based rate on return in order to make decisions regarding adding assets within an efficiently diversified portfolio. Capital asset pricing model explains the prediction of the relationship that can be observed within the risk associated with asset along with its expected return (Ai, Croce and Li 2013). Taking into consideration that the Capital Market Line (CML), the market portfolio is deemed to encompass segmentation of all the risks assets. This is done through employing the market value of the assets in order to determine the weights (Borgonovo and Plischke 2016). The CML line is deemed to be arrived from CAPM that decides the anticipated return at numerous risk levels. In the capital asset pricing model, CML is only applicable only in case of an investors final portfolio and in the world of CAPM; the investors are likely to hold portfolios that rely on the CML. In CAPM, the capital market line is deemed higher than the efficient frontier as it focuses on the consideration of the risk-free asset within a portfolio (Fujimori et al. 2014). The capital asset pricing model signifies that market portfolio is majorly the efficient frontier. The assumptions of CAPM are deemed unrealistic and such reality simplification is vital for preparing useful models. Tolerance of the CAPM models assumptions that facilitates derivation of a well built, idealized through a model of manner within which the financial markets gauges risk and changes it within anticipated return. The capital asset pricing model indicates that the market portfolio serves as efficient frontier (Rangvid, Santa-Clara and Schmeling 2016). Within the CAPM, the securities are priced so that the anticipated risks counterbalance the decided returns. There are two aspects within the CAPM model, which requires generating Capital Market Line. The capital market line indicates the investment returns of an investor for a particular portfolio. The capital market line employs the CAPM formula in order to calculate the anticipated return of a portfolio or security (Rangvid, Santa-Clara and Schmeling 2016). CML serves as the graphical representation of the CAPM formula. It explains the relationship between the systematic risk and expected return related with a portfolio. The CAPM formula that consists of formula on capital market line is helpful in deciding whether a security can be considered for effective investment decision making. The association between the CAPM formula and capital market line are indicated in the formula below: is deemed to denote the point associated with the market portfolio (M). All the portfolios selected by a rational investor are deemed to have a point that relies on the capital market line (Mnster et al. 2014). Considering this formula, it can be said that the CAPM model can be employed in order to measure the systematic risk associated with a single share. Moreover, the transformation line, which remains tangential to the efficient set along with having intercepted within risk-free rate Rf, is the capital market line. This defines that a particular composition of the risky assets those investor wishes to hold. This is deemed as market portfolio (M). Moreover, CML serves as the transformation line, which is observed to be tangential with the efficient frontier (Mnster et al. 2014). Capital Market Line Capital Market Line (CML) serves as a line that connects returns with no-risk investments along with overall market returns (Zabarankin, Pavlikov and Uryasev 2014). The difference between efficient frontier and capital market line is that capital market line involves less risk investments ad all the portfolios within it are efficient frontiers. Capita market line is employed in order to analyze the performance of portfolio. Certain points below any other point within the line will offer decreased returns along with similar risks and for such reasons these are not ideal. Capital market line is deemed a measure used to analyze performance of portfolio. Capital Market Line (CML) is a graph used within the capital asset pricing models in order to signify rates of return within the market portfolio (Borgonovo and Plischke 2016). Capital market line explains rates of return for the effective portfolios those are relied on the degree of risk along with risk free rate of return for a particu lar portfolio. Capital Market Line initiates from considering the assumption that all the companys investors needs to possess market portfolio. Intensity of risk is deemed to be positively correlated to the anticipated return (Zabarankin, Pavlikov and Uryasev 2014). The Capital Market Line serves as the linear combinations of the risk-free asset and portfolio. Portfolios under the capital market line are deemed inferior that indicates new efficient set. Capital Market Line is observed to remain within the capital asset pricing model in order to indicate the rates of return for efficient portfolios likely to face the risk level for a market portfolio along with risk-free return rate (Borgonovo and Plischke 2016). The capital market line is generated through drawing a tangent line from the point of intercept on the efficient frontier to the situation where the expected return on a holding is similar to the risk-free return rate. The capital market line facilitates the investor in taking into account the risks of several additional assets within the remaining portfolio. The capital market line results from the association with the market portfolio along with the risk-free asset (Zabarankin, Pavlikov and Uryasev 2014). All the points in consideration to CML have increased risk-return profiles to certain portfolio within the efficient frontier with the exception of the market portfolio that serves as point within efficient frontier within which capita market line is a tangent. From the CML perception, such portfolio encompasses all the risky assets and has less holding on the risk free assets. As per CAPM, market portfolio signifies efficient frontier and this can be gathered as cluster of portfolios (Lee and Su 2014). The market portfolio in combination to the risk-free asset is able to produce an increased return than the efficient frontier. Therefore, it can be said that the combination of the market portfolio along with the risk-free asset leads to emergence of capital market line. The major techniques employed for project analysis are the NPV and IRR analysis. Sensitivity analysis considers the NPV and IRR of an investment project at the time more than one variable alterations (Lee and Su 2014). The idea that exists based on all the variables except the one evaluated and analyze the way sensitivity of the NPV or the IRR are to changes within that variable. Reference List Ai, H., Croce, M.M. and Li, K., 2013. Toward a quantitative general equilibrium asset pricing model with intangible capital.Review of Financial Studies,26(2), pp.491-530. Borgonovo, E. and Plischke, E., 2016. Sensitivity analysis: a review of recent advances.European Journal of Operational Research,248(3), pp.869-887. Fujimori, S., Kainuma, M., Masui, T., Hasegawa, T. and Dai, H., 2014. The effectiveness of energy service demand reduction: A scenario analysis of global climate change mitigation.Energy policy,75, pp.379-391. Gospodinov, N., Kan, R. and Robotti, C., 2014. Misspecification-robust inference in linear asset-pricing models with irrelevant risk factors.Review of Financial Studies,27(7), pp.2139-2170. Kuehn, L.A., Simutin, M. and Wang, J.J., 2016. A labor capital asset pricing model. Lee, M.C. and Su, L.E., 2014. Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate.Universal Journal of Accounting and Finance,2(4), pp.69-76. Mnster, J.G., Samuelsson, J., Kjeldsen, P., Rella, C.W. and Scheutz, C., 2014. Quantifying methane emission from fugitive sources by combining tracer release and downwind measurementsa sensitivity analysis based on multiple field surveys.Waste Management,34(8), pp.1416-1428. Rangvid, J., Santa-Clara, P. and Schmeling, M., 2016. Capital market integration and consumption risk sharing over the long run.Journal of International Economics,103, pp.27-43. Tian, W., 2013. A review of sensitivity analysis methods in building energy analysis.Renewable and Sustainable Energy Reviews,20, pp.411-419. Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with drawdown measure.European Journal of Operational Research,234(2), pp.508-517.

Iimmigration Essays - Canadians, Illegal Immigration,

Iimmigration Nikki Bumbacco Ms Harrison ENG OAC July 21, 2000 It is a fact that almost all of the people in Canada are immigrants, or come from immigrant descent. If it were not for the millions of people who have fled to Canada in hope of a better life, Canada would never have prospered into what it is today. As a result of this fact, it is hard to believe that immigrants are still faced with many hardships when they enter Canada. Most immigrants have good intentions in mind when coming to a new country. Immigrants coming to Canada believe that they will be able to keep their culture, become successful and prosper. These misleading hopes set the immigrant up for a life of continuous disappointment. Canadian Literature portrays the immigrant experience in a negative light. The Canadian experience for immigrants appears to be programmed for failure. Immigrants try to adopt a new identity in hope that this will enable them to succeed in the future. Venturing to new lands often compels immigrants to isolate themselves from society, by holding onto their own traditions and disregarding the new culture. Immigrants who seek to become successful in Canada are often let down by what they have found, and are left feeling fearful, desolate and helpless. Immigrant characters in Canadian literature often express a fear of losing their identity and culture. For most immigrants, culture is the only thing that truly belongs to them when they come to a new country. In the novel The Black Madonna by Frank Paci, Assunta Barrone is one of the main characters who has immigrated from Italy to a small town in Northern Ontario. Her refusal to adapt or change herself in any way to become more ?Canadian' exemplifies her desire to keep her Italian heritage. ?It had been a long time since she had stepped off that train with her dowry trunk. And in all that time she had never ceased to puzzle him. He didn't know whether she had purposely refused to adapt to the new ways or if she was incapable of doing so. She was certainly stubborn. She had strange old-country customs that she insisted on maintaining even though they were primitive and embarrassing? (Paci 11). Assunta's desire to keep her customs was what helped to preserve her Italian identity. By keeping her identity Assunta felt like her homeland was somehow constantly with her. The poem ?Alien? by Mary Elizabeth Colman also exemplifies the immigrants fear of losing their identity. ?Dear hills of home, why did I leave your arms?/ How can I love this vast, clamorous land?/ Whose noisy people hold me in contempt (Colman 9-11). This immigrant is in fear of the new land which they have come to, and is afraid of the people around them. Because immigrants hold their culture so close to them when they travel to new lands, they defend it with every ounce of their being. Without culture or identity immigrants are defenceless in a new country. The immigrant in Canadian literature is often regretful of leaving their homeland because of the disappointments they discover about Canada. Most immigrants believe that getting a Canadian passport and citizenship is their key to unlocking ?the good life' In Canadian literature the opposite of this occurs because the ideal of what Canada is does not meet it's reality. This is best exemplified through the short story ?Hunky? by Hugh Garner and the poems ?Land of Opportunity? by F.R. Scott and ?I Fight Back? by Lillian Allen. In the story ?Hunky? the main character Hunky is a German immigrant working in the tobacco fields for a very arrogant employer. Hunky wants nothing more than to become a Canadian citizen because he feels that having his citizenship is the key to obtaining ?the good life'. ?He placed great stress on the fact that he hoped to become a Canadian citizen in the fall. His longing for citizenship was not only gratitude and patriotism towards the country that had given him asylum, but a craving for status as a recognized human being? (Garner 135). The poem ?Land of Opportunity? by F.R. Scott exemplifies the disappointment of the Canadian status. ?Canadian Imperial Bank of Commerce/These are privileged names in my country/But I AM ILLEGAL HERE.? (Scott, 2-4). The poem goes on to say ?I come to Canada/And found the Doors/ of Opportunities Well Guarded ? (7-9). This poem expresses the immigrant woman's disappointments found when she came to Canada. In the poem ?I Fight Back? by Lillian Allen,

Ernest Hemingway Bio essays

Ernest Hemingway Bio essays Ernest Miller Hemingway was born on 21 July, 1899, the first son of Clarence and Grace Hall Hemingway and the second of their six children. Clarence Hemingway was a medical doctor with a small practice in Oak Park, Illinois; his wife was a music teacher with an active interest in church affairs and Christian Science. As a boy, Hemingway seemed to enjoy the best of both worlds. He grew up close to metropolitan center in a suburban or semi-rural community that was also sheltered by distance from the violence and vice of Chicago itself. Moreover, Dr. Hemingway owned a cabin in northern Michigan where his oldest son spent summers developing a life-long passion for hunting and fishing apart from middle-class society. Acting as a counterweight, Hemingway's mother tried to instill conventional values in her children in the designated role of family disciplinarian. She insisted that Hemingway attend church, that he take music lessons, and that he generally embrace the prevalent Protestant work ethic values of mainstream, Anglo-Saxon America during the Progressive era. Hemingway appears to have rankled at the strictures that his mother's sense of moral order imposed upon him. She was forceful if not domineering with Ernest. A major rift arose between them when Hemingway returned to the United States from service with the American Red Cross in World War I. Despite the wounds (physical, psychological, and spiritual) that he had received, Grace Hemingway complained bitterly about the slow pace of his re-adjustment to normal, civilian life. She demanded that he leave the seclusion of recuperating at the family's Michigan retreat for gainful employment. Ultimately, the budding author left his childhood's nest in the wilderness and entered into the domain of Paris in the 1920s, thereby upping the ante while breaking the rules of game. More tragically, Hemingway's father suffered from diabetes, financial misfortunes, and chronic depression. All...

Contemporary Trust Law Assignment Example | Topics and Well Written Essays - 2500 words

Contemporary Trust Law - Assignment Example If there are no beneficiaries with equitable interests in the trust assets, there is in theory no one "in whose favour the court can decree specific performance": Morice v Bishop of Durham (1804) 9 Ves.399. The complexity, of course, with this approach is that it frustrates the requirements of a settler or testator, who may want to profit a legitimate public object or useful social experiment which does not fall stringently within the definition of charity. A trust, for example, for the promotion of a particular sport (such as angling or yacht racing) is not charitable unless linked to education: Re Nottage [1895] 2 Ch. 649 and Re Clifford [1912] 1 Ch. 29. Similarly, a trust to be relevant income for the purposes of research into a proposed new alphabet also falls outside the description of charity: Re Shaw [1957] 1 W.L.R. 729. To what extent, however, is it legitimate to use the mechanism of a trust for the haulage out of mere purposes where there are no beneficiaries vested with equitable ownership in the trust property The law that a valid trust "must be for the benefit of individuals" (Bowman v Secular Society Ltd [1917] A.C. 406, 441, per Lord Parker) is not complete. A trust for charitable purposes is valid even with the absence of an equitable beneficial owner to put into effect the trust. Here, of course, it is the Crown (acting through the Attorney-General or the Charity Commissioners) who takes on the role of parens patriae on behalf of the public at large. Apart from this, there are several well-known "inconsistent" exceptions, classified by Lord Evershed M.R. in Re Endacott [1960] Ch. 232, where the trustee may perform the terms of the trust if he so wishes, but the court will not compel him to do so. These so-called "trusts of imperfect obligation" comprise (1) trusts for the creation of monuments and graves; (2) trusts for the saying of masses; and (3) trusts for the maintenance of particular animals. They will be valid (though unenforceable) provided they do not offend the rule against continuous trusts. Presumably, in the dearth of a beneficiary, the trustee is mutually the legal and beneficial owner of the trust property so that, if he fails or refuses to carry out the trust, the property will relapse back to the testator's residuary estate upon a resulting trust as to both the legal and equitable title. In reality, there is no trust here at all, rather a meagre power to apply for the stated purposes, with a contribution over or a resulting trust in evasion of exercise of the power. There are, of course, other cases where there may be a conviction despite the lack of an equitable owner. The understandable example is that of a discretionary trust in favour of a large class which is too large to list but, nevertheless, theoretically certain in definition. In the same way, there is no equitable title to the estate of a deceased person until such time as the administration is completed. The personal representatives are simply the legal owners during the administration

Camera Shots in The Great Gatsby Essay Example | Topics and Well Written Essays - 500 words

Camera Shots in The Great Gatsby - Essay Example This paper illustrates that the clip begins with an extreme long shot that brings Buchanan’s house into view. This shot is helpful in according a general impression of Buchanan’s opulence as the shot turns into a medium one. For instance, the long shot gives the audience a view of the green lawns and exquisite architecture that characterizes Tom’s house. It is notable that just before the scene, Carraway’s scene manifests as less dramatic since it is characterized by quick shots showing his dour residence and lush vegetation. The camera rapidly pans across the lake and it ushers the audience into Tom’s compound. The camera uses an eye-level position as Buchanan greets and hugs Carraway. The eye-level position accords the audience the immense figure of Buchanan. In addition, it introduces the audience to the brute nature and overconfident persona of Buchanan. Thereafter, a high-angle shot shows the audience into the splendor of Buchanan’s hous e and manifests the child-like nature of Daisy Buchanan and Jordan Baker. This shot precedes a close-up shot of Daisy’ hands. It is notable that Daisy is interested in letting Caraway observe the diamond ring on her index finger. Daisy manifests as a vain and superficial character whose beauty is the primary obsession in life. The camera tilts to remove an up-close shot of Daisy’s face. A properly lighted background that demonstrates her beautified face enables this shot. Thereafter, the camera pans into Carraway’s bewildered face and compliments with a medium shot that ushers his response to Daisy’s narcissistic questions. A slightly high angle shot gives the audience the view of Baker’s face and tilts along her tall frame as she stands up. It is notable that she is enacting impressions on Carraways. These camera movements manifest Baker’s attempts at appearing sophisticated more than she could be.

Basics of Topological Solutons

Basics of Topological Solutons Research into topological solitons began in the 1960s, when the fully nonlinear form of the classical field equations, were being thoroughly explored by mathematicians and theoretical physicists. Topological solitons were first examined when the solutions to these equations were interpreted as candidates for particles of the theory [1]. The particles that were observed from the results were different from the usual elementary particles. Topological solitons appeared to behave like normal particles in the sense that they were found to be localised and have finite energy [4]. However, the solitons topological structure distinguished them from the other particles. Topological solitons carry a topological charge (also known as the winding number), which results in these particlelike objects being stable. The topological charge is usually denoted by a single integer, N; it is a conserved quantity, i.e. it is constant unless a collision occurs, and it is equal to the total number of partic les, which means as |N| increases, the energy also increases. The conservation of the topological charge is due to the topological structure of the target space in which the soliton is defined. The most basic example of soliton has topological charge, N = 1, which is a stable solution, due to the fact a single soliton is unable to decay. 3 If the solution to a nonlinear classical field equation has the properties of being particle-like, stable, have finite mass; and the energy density is localised to a finite region of space, with a smooth structure; then this solution is a topological soliton. In addition to solitons existing with topological charge, N, there also exist antisolitons with -N. In the event of a collision between a soliton and an antisoliton, it is possible for them to annihilate each other or be pair-produced [1]. It is also possible for multi-soliton states to exist. Any field composition where N > 1, is known as a multi-soliton state. Likewise, multi-solitons also carry a topological charge which again means they are stable. Multi-state solitons either decay into N well separated charge 1 solitons or they can relax to a classical bound state of N solitons [1]. The energy and length scale [1] (a particular length which is determined to one order of magnitude.) the constant in the Lagrangian and field equations which represents the strength of the interaction between the particle and the field, also known as the coupling constant. The energy of a topological soliton is equal to its rest mass in a Lorentz invariant theory. [5] [6] Lorentz invariant: A quantity that does not change due to a transformation relating the space-time coordinates of one frame of reference to another in special relativity; a quantity that is independent of the inertial frame. In contrast to the topological soliton, the elementary particles mass is proportional to Plancks constant, ~. In the limit ~ à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 0, the elementary particles mass goes to zero where as the topological solitons mass is finite. The quantization of the wave-like fields which satisfy the linearized field equations [1] determines the elementary particle states, where the interactions between the particles are determined by the nonlinear terms A fundamental discovery in supporting the research of topological solitons is that, given the coupling constants take special values, then the field equations can be reduced from second order to first order partial differential equations.[1] In general, the resulting first order equations are known as Bogomolny equations. These equations do not involve any time derivatives, and their solutions are either static soliton or multi-soliton configurations. [1] In these given field theories, if the field satisfies the Bogomolny equation then the energy is bounded below by a numerical multiple of the modulus of the topological charge, N, so the solutions of a Bogomolny equation with a certain 4 charge will all have the same energy value. [1] The solutions of the Bogomolny equations are automatically stable [1] because the fields minimize the energy [1]. As well as this they naturally satisfy the Euler-Lagrange equations of motion, which implies the static solutions are a stationary point of the energy. [1] Kinks are solutions to the first-order Bogomolny equation which we shall see in the following chapter Figure 2.2 shows a model of an infinite pendulum strip, with the angle à Ã¢â‚¬   being the angle to the downward vertical [3]. The energy (with all constraints set to 1) is E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   1 2 à Ã¢â‚¬   02 + 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  Ãƒâ€šÃ‚   dx (2.1) where à Ã¢â‚¬   0 = dà Ã¢â‚¬   dx . For the energy density to be finite this requires à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 2à Ã¢â€š ¬nà ¢Ã‹â€ Ã¢â‚¬â„¢ as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ and à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 2à Ã¢â€š ¬n+ as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã… ¾, where n ± à ¢Ã‹â€ Ã‹â€  Z. To find the number of twists, N, this is simply N = n+ à ¢Ã‹â€ Ã¢â‚¬â„¢ nà ¢Ã‹â€ Ã¢â‚¬â„¢ = à Ã¢â‚¬   (à ¢Ã‹â€ Ã… ¾) à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬   (à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾) 2à Ã¢â€š ¬ = 1 2à Ã¢â€š ¬ Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ à Ã¢â‚¬   0 dx à ¢Ã‹â€ Ã‹â€  Z This is the equation for the topological charge or the winding number. If we set nà ¢Ã‹â€ Ã¢â‚¬â„¢ = 0 and n+ = 1 then N = 1, this gives the lowest possible energy for a topological soliton. This is called a kink, and it is the term we use for the one spatial dimension soliton with a single scalar field. The name kink is due to the shape of the scalar field when plotted as a function of x [1]. Knowing that a kink gives the minimum of the energy, it is possible to apply the calculus of variations to derive a differential equation à Ã¢â‚¬  (x) and then solve it[3] to give the shape of the kink. Given a differentiable function on the real line, f(x), it is possible to find the minimum of f(x) by finding the solutions of f 0 (x) = 0, i.e. by finding the stationary points of f(x) [3]. It is achievable to derive this differential equation, f(x), by making a small change to x, i.e. x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ x + ÃŽÂ ´x, and from this calculate the change in the value of the function to lea ding order in the variaton ÃŽÂ ´x [3]. ÃŽÂ ´f(x) = f(x + ÃŽÂ ´x) à ¢Ã‹â€ Ã¢â‚¬â„¢ f(x) = f(x) + ÃŽÂ ´xf0 (x) + à ¢Ã‹â€ Ã¢â‚¬â„¢ f(x) = f 0 (x)ÃŽÂ ´x + If f 0 (x) 0. If f 0 (x) > 0 then we can make ÃŽÂ ´f(x) The term [à Ã¢â‚¬   0 ÃŽÂ ´Ãƒ Ã¢â‚¬  ] à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ equates to zero on the boundary because it must satisfy ÃŽÂ ´Ãƒ Ã¢â‚¬  ( ±Ãƒ ¢Ã‹â€ Ã… ¾) = 0 as we cannot change the boundary conditions, so ÃŽÂ ´E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ {(à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ Ã¢â‚¬   00 + sin à Ã¢â‚¬  )ÃŽÂ ´Ãƒ Ã¢â‚¬  } dx (2.6) This equation can be minimised minimised further to the second order nonlinear differential equation, à Ã¢â‚¬   00 = sin à Ã¢â‚¬   (2.7) The solution of this differential equation with the boundary conditions, à Ã¢â‚¬  (à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾) = 0 and à Ã¢â‚¬  (à ¢Ã‹â€ Ã… ¾) = 2à Ã¢â€š ¬ is the kink. Therefore the kink solution is, à Ã¢â‚¬  (x) = 4 tanà ¢Ã‹â€ Ã¢â‚¬â„¢1 e xà ¢Ã‹â€ Ã¢â‚¬â„¢a (2.8) where a is an arbitrary constant. When x = a, this is the position of the kink (à Ã¢â‚¬  (a) = à Ã¢â€š ¬). It is clear to see à Ã¢â‚¬   = 0 is also a solution to the differential equation , however, it does not satisfy the boundary conditions. It is possible to find a lower bound on the kink energy without solving a differential equation [3]. First of all we need to rewrite the energy equation (2.1), using the double angle formula the equation becomes, E = 1 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   à Ã¢â‚¬   02 + 4 sin2   à Ã¢â‚¬   2   dx (2.9) By completing the square the equation becomes, E = 1 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   à Ã¢â‚¬   0 à ¢Ã‹â€ Ã¢â‚¬â„¢ 2 sin   à Ã¢â‚¬   2 2 + 4à Ã¢â‚¬   0 sin   à Ã¢â‚¬   2 dx (2.10) Therefore the energy satisfies the inequality, E > 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ à Ã¢â‚¬   0 sin   à Ã¢â‚¬   2   dx = 2 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ sin   à Ã¢â‚¬   2   dà Ã¢â‚¬   dxdx = 2 Z 2à Ã¢â€š ¬ 0 sin   à Ã¢â‚¬   2   dà Ã¢â‚¬   = à ¢Ã‹â€ Ã¢â‚¬â„¢4   cos   à Ã¢â‚¬   2 2à Ã¢â€š ¬ 0 = 8 (2.11) In order to obtain the solution which is exactly 8, the term à Ã¢â‚¬   0 à ¢Ã‹â€ Ã¢â‚¬â„¢ 2 sin à Ã¢â‚¬   2 2 would have to be exactly 0. Therefore the lower bound on the kink energy is calculated by the solution to the equation, à Ã¢â‚¬   0 = 2 sin   à Ã¢â‚¬   2   (2.12) This is a first order Bogomolny equation. Taking this Bogomolny equation and differentiating with respect to à Ã¢â‚¬   0 gives, à Ã¢â‚¬   00 = cos   à Ã¢â‚¬   2   à Ã¢â‚¬   0 = cos   à Ã¢â‚¬   2   2 sin   à Ã¢â‚¬   2   = sin à Ã¢â‚¬   (2.13) This shows that a solution of the Bogomo lny equation (2.12) gives the output of the kink solution (2.7). To calculate the energy density ÃŽÂ µ, equation (2.1), we need to use the fact that the Bogomolny equation shows that ÃŽÂ µ = à Ã¢â‚¬   02 . From equation (2.8) we have, tan à Ã¢â‚¬   4   = e xà ¢Ã‹â€ Ã¢â‚¬â„¢a , therefore 1 4 à Ã¢â‚¬   0 sec2   à Ã¢â‚¬   4 = e xà ¢Ã‹â€ Ã¢â‚¬â„¢a This equation gives, à Ã¢â‚¬   0 = 4 e xà ¢Ã‹â€ Ã¢â‚¬â„¢a 1 + tan2 à Ã¢â‚¬   4   = 4e xà ¢Ã‹â€ Ã¢â‚¬â„¢a 1 + e 2(xà ¢Ã‹â€ Ã¢â‚¬â„¢a) = 2 cosh (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) = 2 (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) (2.15) Therefore it can be seen that the energy density is given by ÃŽÂ µ = 42 (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) From this we get the solution of a lump with a maximal value of 4 when x = a. This maximal value is the position of the kink. The position of the kink is also the position of the pendulum strip when it is exactly upside down, this is due to the fact à Ã¢â‚¬  (a) = à Ã¢â€š ¬ [3]. Using this interpretation for the energy density, it can be verified that the energy is equal to the lower bound E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ ÃŽÂ µdx = 4 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ 2 (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a) dx = 4 [tanh (x à ¢Ã‹â€ Ã¢â‚¬â„¢ a)]à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ = 8 (2.16) For N > 1 i.e. more than one kink, E > 8|N|. In order t o obtain the lower bound of N > 1 kinks, the kinks must be infinitely apart to create N infinitely separated kinks. This means there must be a repulsive force between kinks. We shall now look at applying Derricks theorem [3] to kinks to show that it does not rule out the existence of topological solitons. Derricks Theorem: If the energy E has no stationary points with respect to spatial rescaling then it has no solutions with 0 Derricks theorem can only be applied to an infinite domain. Firstly, the energy terms need to be split according to the powers of the derivative, E = E2 + E0 = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ 1 2 à Ã¢â‚¬   02 dx + Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ (1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  ) dx (2.17) Now consider the spatial rescaling x 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ x ÃŽÂ » = X, so that à Ã¢â‚¬   (x) 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à Ã¢â‚¬   (X), with dx = ÃŽÂ »dX, d dx = 1 ÃŽÂ » d dX . Under this rescaling the energy becomes E (ÃŽÂ »), E(ÃŽÂ ») = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ 1 2 ( 1 ÃŽÂ » dà Ã¢â‚¬   dX ) 2ÃŽÂ »dX + Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ (1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  ) ÃŽÂ »dX = 1 ÃŽÂ » E2 + ÃŽÂ »E0 (2.18) It is now important to see whether E(ÃŽÂ ») has a stationary point with respect to ÃŽÂ », dE (ÃŽÂ ») dÃŽÂ » = à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 ÃŽÂ » 2 E2 + E0 = 0 (2.19) if ÃŽÂ » = qE2 E0 , where ÃŽÂ » equals the size of the soliton. From this we can see a stationary point exists, so by Derricks theorem we cannot rule out the possibility of a topological soliton solution existing. We already know this is the case due to already finding the kink solution earlier. If it is found that à Ã¢â‚¬  (x) is a solution then the stationary point corresponds to no rescaling [3], so ÃŽÂ » = 1, meaning E2 = E0. This is known as a virial relation. In order to extend the kink example to higher spatial dimensions, we will rewrite it using different variables. If we let à Ã¢â‚¬   = (à Ã¢â‚¬  1, à Ã¢â‚¬  2) be a two-component unit vector, where à Ã¢â‚¬    · à Ã¢â‚¬   = |à Ã¢â‚¬  | 2 = 1. By writing à Ã¢â‚¬   = (sin à Ã¢â‚¬  , cos à Ã¢â‚¬  ), the energy from (2.1) can be rewritten as E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ ( 1 2  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   dà Ã¢â‚¬   dx  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   2 à ¢Ã‹â€ Ã¢â‚¬â„¢ H  · à Ã¢â‚¬   + |H| ) dx (2.20) where H = (0, 1). [3] In this new formulation à Ã¢â‚¬   represents the direction of the local magnetization (restricted to the plane) in a ferromagnetic medium [3] and H represents the constant background magnetic field which is also restricted to lie within the same plane as à Ã¢â‚¬  . There is only one point in which the systems ground state is equal to zero in terms of à Ã¢â‚¬  , which is à Ã¢â‚¬   = H |H| = (0, 1 ). Any structure with finite energy has to approach this zero energy ground state at spatial infinity, therefore the boundary conditions are à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ (0, 1) as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢  ±Ãƒ ¢Ã‹â€ Ã… ¾. As à Ã¢â‚¬   takes the same value at x = à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ and x = +à ¢Ã‹â€ Ã… ¾, then these points can be identified so the target space, which is the real line R, topologically becomes a circle, S 1 of infinite radius. Therefore we have the mapping à Ã¢â‚¬   : S 1 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ S 1 between circles, because à Ã¢â‚¬   is a two-component vector so it also lies on a circle of unit radius. [3] The mapping between circles has a topological charge (winding number), N, which counts the number of times à Ã¢â‚¬   winds around the unit circle as x varies over the whole real line. [3] The topological charge is equal to the equation defined earlier in (2.2), but using the new variables it is given by the expression N = 1 2à Ã¢â€š ¬ Z à ¢ 蠁 ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   dà Ã¢â‚¬  1 dx à Ã¢â‚¬  2 à ¢Ã‹â€ Ã¢â‚¬â„¢ dà Ã¢â‚¬  2 dx à Ã¢â‚¬  1   dx (2.21) If we consider a restricted ferromagnetic system in which there is the absence of a background magnetic field (H = 0); it is still possible for a topological soliton to exist if there is an easy axis anisotropy. [3] Magnetic anisotropy is the directional dependence of a materials magnetic property, and the easy axis is a energetically favorable direction if spontaneous magnetization occurs.[7] The energy for this system is E = Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ ( 1 2  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   dà Ã¢â‚¬   dx  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   2 + A 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ (à Ã¢â‚¬    · k) 2   ) dx (2.22) where A > 0 is the anisotropy constant and k is the unit vector which specifies the easy axis. [3] For this type of system there are two zero energy ground states, à Ã¢â‚¬   =  ±k. The kink in t his system, also called a domain wall, interpolates between the two zero energy ground states and has boundary conditions à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾ and à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬â„¢k 15 as x à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ +à ¢Ã‹â€ Ã… ¾. Therefore the domain wall does not have a full twist of a kink and only has a half-twist. It is possible to map this system to our original kink example by a change of variables. If we set k = (0, 1) for convenience, and choose A = 1 2 . Setting à Ã¢â‚¬   = sin à Ã¢â‚¬   2   , cos à Ã¢â‚¬   2 , then the energy equation becomes E = 1 4 Z à ¢Ã‹â€ Ã… ¾ à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾Ãƒâ€šÃ‚   1 2 à Ã¢â‚¬   02 + 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ cos à Ã¢â‚¬  Ãƒâ€šÃ‚   dx (2.23) which is equal to the energy equation (2.1) but with a normalization factor of 1 4 . The domain wall boundaries are à Ã¢â‚¬   à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ (0,  ±1) as x à ¢Ã‹â€ Ã¢â‚¬Å" à ¢Ã‹â€ Ã… ¾ are exactly the kink boundary conditions à Ã¢â‚¬   (à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã‹â€ Ã… ¾) = 0 and à Ã¢â‚¬   (à ¢Ã‹â€ Ã… ¾) = 2à Ã¢â€š ¬. [1] This chapter will focus on topological solitons in (2+1) spatial dimensions. It would be incorrect to use the term soliton for these solutions due to their lack of stability, instead they are often referred to as lumps. The solutions for these lumps are given explicitly by rational maps between Riemann spheres. [1] For this chapter we shall be looking at one of the simplest Lorentz invariant sigma models in (2+1) spatial dimensions which renders static topological soliton solutions; the O(3) sigma model in the plane. [1] A sigma model is a nonlinear scalar field theory, where the field takes values in a target space which is a curved Riemannian manifold, usually with large symmetry. [1] For the O(3) sigma model the target space is the unit 2-sphere, S 2 . This model uses three real scalar fields, ÃŽÂ ¦ = (à Ã¢â‚¬  1, à Ã¢â‚¬  2, à Ã¢â‚¬  3), which are functions of the space-time coordinates (t, x, y) in (2+1) spatial dimensions. [2] The O(3) model is defined by the Lagrangia n density L = 1 4 (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦)  · (à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦)  with the constraint ÃŽÂ ¦  · ÃŽÂ ¦ = 1. For this equation the indices represent the space-time coordinates and take the values 0, 1, 2, and à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µ is partial differentiation with respect to X µ . [2] From (3.1), the Euler-Lagrange equation can be derived, which is à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦ + (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦) ÃŽÂ ¦ = 0 (3.2) Due to the dot product in à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦, this shows that the Euclidean metric of R 3 is being used, and this becomes the standard metric on the target space S 2 when the constraint ÃŽÂ ¦  · ÃŽÂ ¦ = 1 is being imposed. [1] For the sigma model we are exploring, the O(3) represents the global symmetry in the target space corresponding to the rotation s: ÃŽÂ ¦ 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ MÃŽÂ ¦ Where M à ¢Ã‹â€ Ã‹â€  O(3) is a constant matrix. [1] The sigma in the models name represents the fields (à Ã¢â‚¬  1, à Ã¢â‚¬  2, à Ã†â€™), where à Ã¢â‚¬  1 and à Ã¢â‚¬  2 are locally unconstrained [1] and à Ã†â€™ = p 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬   2 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬   2 2 is dependent on à Ã¢â‚¬  1 and à Ã¢â‚¬  2. The energy for the O(3) sigma model is E = 1 4 Z à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦d 2x (3.3) where i = 1, 2 runs over the spatial indices. In order for the energy to be finite, ÃŽÂ ¦ has to tend to a constant vector at spatial infinity, so without loss of generality we are able to set the boundary condition ÃŽÂ ¦ à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ (0, 0, 1) as x 2 + y 2 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã… ¾. Topologically we have R 2 à ¢Ã‹â€ Ã‚ ª {à ¢Ã‹â€ Ã… ¾}, which is interpreted as a sphere S 2 via the stereographic projection. (The sphere itself has finite radius.) Therefore we are considering mapping between spheres ÃŽÂ ¦ : S 2 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ S 2 . Just like in our kink example, mapping between spheres means there exists a topological charge, which can be found using N = 1 4à Ã¢â€š ¬ Z ÃŽÂ ¦  · (à ¢Ã‹â€ Ã¢â‚¬Å¡1ÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡2ÃŽÂ ¦) d 2x (3.4) The topological charge represents the number of lumps in the field configuration [1], since generally there are N well-separated, localized areas where the energy density is concentrated and each area has one unit of charge. However, as the lumps approach each other this is no longer the case. In order to apply Derricks theorem to the energy (3.3), we would need to consider the scaling x 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ x ÃŽÂ » = X and y 7à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ y ÃŽÂ » = Y which would give E (ÃŽÂ ») = E. The energy is independent of ÃŽÂ », therefore any value of ÃŽÂ » is a stationary point since the energy does not change from spatial rescaling. If we integrate the inequality  (à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  ± ÃŽÂ µijÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡jÃŽÂ ¦)  · (à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  ± ÃŽÂ µikÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡kÃŽÂ ¦) à ¢Ã¢â‚¬ °Ã‚ ¥ 0 (3.5) over the plane and use the equations (3.3) and (3.4) for the energy density and the topological charge respectively [1], then we get the Bogomolny bound E à ¢Ã¢â‚¬ °Ã‚ ¥ 2à Ã¢â€š ¬ |N| (3.6) This Bogomolny bound is the lower bound of the energy in terms of lumps. [1] If the field is a solution to one of the first-order Bogomolny equations à ¢Ã‹â€ Ã¢â‚¬Å¡iÃŽÂ ¦  ± ÃŽÂ µijÃŽÂ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡jÃŽÂ ¦ = 0 (3.7) then the energy is equal to the Bogomolny bound. In order to analyse the Bogomolny equations it is best to make the following changes of variables. For the first change in variable let X = (X1, X2, X3) denote the Cartesian coordinates in R 3 and take X = ÃŽÂ ¦ to be a point on the unit sphere, (X2 1 , X2 2 , X2 3 ) = 1. Let L be the line going through X = (0, 0, à ¢Ã‹â€ Ã¢â‚¬â„¢1) and ÃŽÂ ¦ and set W = X1 + iX2 to be the complex coordinate of the point where L intersects the plane at X3 = 0. We then get W = (à Ã¢â‚¬  1 + ià Ã¢â‚¬  2) (1 + à Ã¢â‚¬  3) (3.8) where à Ã¢â‚¬  1 =   W + W 1 + |W| 2   , à Ã¢â‚¬  2 = i   W à ¢Ã‹â€ Ã¢â‚¬â„¢ W 1 + |W| 2   , à Ã¢â‚¬  3 = 1 à ¢Ã‹â€ Ã¢â‚¬â„¢ |W| 2 1 + |W| 2 ! (3.9) As ÃŽÂ ¦ tends to the point (0, 0, à ¢Ã‹â€ Ã¢â‚¬â„¢1) then L only intersects X3 = 0 at à ¢Ã‹â€ Ã… ¾, therefore the point (0, 0, à ¢Ã‹â€ Ã¢â‚¬â„¢1) maps to the point W = à ¢Ã‹â€ Ã… ¾. This method of assigning each point on the sphere to a point in C à ¢Ã‹â€ Ã‚ ª {à ¢Ã‹â€ Ã… ¾} is called stereographic projection as seen in Figure 3.1.[3] The next change in variable comes from using a complex coordinate in the (x, y) plane by letting z = x + iy. Using this formation it is possible to rewrite the Lagrangian density, from (3.1) L = 1 4 ( à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  1) 2 + (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  2) 2 + (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  3) 2   . Firstly we need to partially differentiate à Ã¢â‚¬  1, à Ã¢â‚¬  2, à Ã¢â‚¬  3, giving à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  1 = à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW + à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW 1 + |W| 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW) W + W à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW   1 + |W| 2 2 W + W   (3.10) à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒ Ã¢â‚¬  2 = i à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW à ¢Ã‹â€ Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW 1 + |W| 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW) W + W à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µW   1 + |W| 2 2 W à ¢Ã‹â€ Ã¢â‚¬â„¢ W Finally, from simplifying (3.37) we get the equation for the topological charge in the new formulation to be N = 1 4à Ã¢â€š ¬ Z 4 1 + |W| 2 2 à ¢Ã‹â€ Ã¢â‚¬Å¡zW à ¢Ã‹â€ Ã¢â‚¬Å¡zW à ¢Ã‹â€ Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã¢â‚¬Å¡zW à ¢Ã‹â€ Ã¢â‚¬Å¡zW   d 2x = 1 à Ã¢â€š ¬ Z |à ¢Ã‹â€ Ã¢â‚¬Å¡zW| 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ |à ¢Ã‹â€ Ã¢â‚¬Å¡zW| 2   1 + |W| 2 2 d 2x (3.38) In this formulation it is clear to see E à ¢Ã¢â‚¬ °Ã‚ ¥ 2à Ã¢â€š ¬ |N|, with equality if and only if Bogomolny equation is satisfied à ¢Ã‹â€ Ã¢â‚¬Å¡W à ¢Ã‹â€ Ã¢â‚¬Å¡z = 0 (3.39) This equation shows that W is a holomorphic function of z only. [4] Due to the requirement that the total energy is finite, together with the boundary condition [4] W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 0 as |z| à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ à ¢Ã‹â€ Ã… ¾, this means that N is finite. [3] The simplest solution for the Bogomolny equation would be W = ÃŽÂ » z , where ÃŽÂ » is a real and positive constant. Applying this to the equation (3.9) yields the solution for t he N = 1 solution ÃŽÂ ¦ =   2 ÃŽÂ » 2 + x 2 + y 2 , à ¢Ã‹â€ Ã¢â‚¬â„¢2 ÃŽÂ » 2 + x 2 + y 2 , x 2 + y 2 à ¢Ã‹â€ Ã¢â‚¬â„¢ ÃŽÂ » 2 ÃŽÂ » 2 + x 2 + y 2 (3.40) If we change the negative sign in the second component to a positive sign then we get the solution of the anti-Bogomolny equation (3.7) (with the minus sign), which also has E = 2à Ã¢â€š ¬ but has N = à ¢Ã‹â€ Ã¢â‚¬â„¢1. This soliton is located at thee origin because W(0) = à ¢Ã‹â€ Ã… ¾. [3] The N = 1 general solution has 4 real parameters and is given by the Bogomolny solution W = ÃŽÂ »eiÃŽÂ ¸ z à ¢Ã‹â€ Ã¢â‚¬â„¢ a (3.41) where ÃŽÂ » is the size of the soliton, ÃŽÂ ¸ is the constant angle of rotation in the (à Ã¢â‚¬  1, à Ã¢â‚¬  2) plane and a à ¢Ã‹â€ Ã‹â€  C is the position of the soliton in the complex plane, z = x + iy. The O(3) sigma model can be modified to stabilise a lump, and the simplest way in doing this is by introducing extra terms into the Lagrangian which break the conformal invariance of the static energy. [1] These new terms must scale as negative and positive powers of a spatial dilation factor. [1] An example of this is the Baby Skyrme model which is given by the Lagrangian L = 1 4 à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦  · à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦ à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 8 (à ¢Ã‹â€ Ã¢â‚¬Å¡Ãƒâ€šÃ‚ µÃƒÅ½Ã‚ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ½ÃƒÅ½Ã‚ ¦)  · (à ¢Ã‹â€ Ã¢â‚¬Å¡  µÃƒÅ½Ã‚ ¦ ÃÆ'- à ¢Ã‹â€ Ã¢â‚¬Å¡ ÃŽÂ ½ÃƒÅ½Ã‚ ¦) à ¢Ã‹â€ Ã¢â‚¬â„¢ m2 2 (1 à ¢Ã‹â€ Ã¢â‚¬â„¢ à Ã¢â‚¬  3) (3.42) where the constraint ÃŽÂ ¦  · ÃŽÂ ¦ = 1 is implied. As we can see the first term in this Lagrangian is simply that of the O(3) sigma model. The second term in (3.42), is known as the Skyrme term and the final term in this Lagrangian is the mass term. The complete understanding of topological solitons is unknown and there are very limited experimental tests of many of the theories of topological solitons and their mathematical results. However, there is evidence of topological solitons existing in some physical systems, for example in one-dimensional systems they exist in optical fibres and narrow water channels. [1] Topological solitons can be applied to a range of different areas including particle physics, condensed matter physics, nuclear physics and cosmology. They also can be applied within technology, which involves using topological solitons in the design for the next generation of data storage devices. [3] In August 2016, a 7 million pound research programme, being led by Durham University, was announced into looking at how magnetic skyrmions can be used in creating efficient ways to store data. [10] Magnetic skyrmions are a theoretical particle in three spatial dimensions which have been observed experimentally in condensed matter systems. [11] This type of soliton was first predicted by scientists back in 1962, but was first observed experimentally in 2009. [10] In certain types of magnetic material it is possible for these magnetic skyrmions to be created,manipulated and controlled[10], and because of their size and structure it is possible for them to be tightly packed together. The structure inside the skyrmions [10] Due to this and the force which locks the magnetic field into the skyrmion arrangement, any magnetic information which is encoded by skyrmions is very robust. [10] It is thought that it will be possible to move these magnetic skyrmions with a lot less energy than the ferromagnetic domain being used in current data storage devices of smartphones and computers. Therefore, these magnetic skyrmions could revolutionise data storage devices, as the devices could be created on a smaller scale and use a lot less energy, meaning they would be more cost effective and would generate less heat. This project has given an insight into the very basics of topological solutons by analysing the energy and topological charge equations for kinks in one spatial dimension and lumps in (2+1) spatial dimensions. From the energy equation for a kink, we could derive the solution of a kink and find the lower energy bound. From the lump model, we successfully changed the variables for the energy, topological charge and the Lagrange equation for a lump to be able to analyse the Bogomolny equation. From this change of variables of the Lagrange equation we successfully solved the Euler-Lagrange equations of motion for the lump model. This research project has been captivating and has given me an insight into how the complex mathematics we learn is applied to real world situations. I first became interested in this topic after attending the London Mathematical Societys summer 33 school in 2016, where I had the privilege of attending a few lectures given by Dr Paul Sutcliffe, one of the authors of the book on Topological Solitons. It was in these few lectures where I first learnt about topological solitons and some of their applications, and this inspired me for my research project as I wanted to study the topic further. Although this project has been thoroughly enjoyable, it came with challenging aspects, due to its complex mathematics in such a specialised subject. As a result of this topic being so specific, I was very limited in the resources I had for my research, my main resource being the book on topological solitons by Dr Paul Sutcliffe and Dr Nicholas Manton. I have gained a lot of new skills from this research project and it has given me an opportunity to apply my current mathematical knowledge. There is an endless amount of research that can be continued within this subject. I, for example, would have liked to do some further research into the (2+1) spatial dimension model of the Baby Skyrmion and, like the lump example, solve the EulerLagrange equations motion . As well as this, I would have liked to input the equations of motion I solved for the lump model in Maple, so it was possible to simulate two lumps colliding and from this graph the energy density. It would have been really interesting to research further into topological solitons in three spatial dimensions, specifically Skyrmions, to learn further about their technological applications. However, the mathematics used for this model is very challenging and specialised, and goes beyond my understanding and knowledge.

Advice to Youth Satire

Andy Diaz â€Å"Advice to Youth† The Object of Mark Twain’s article is to point out that the youths of our society are being told to become just like everyone else and that discourages their individuality. He uses sarcasm, so that he can assume the role of an elder in society, the kind of people he attacks, which instructs younger people how to act. Mark Twain does an exemplary job in copying exactly the types of teachings for youth that have been passed down through the ages. The idea of respecting one’s elders has been around for a long time. The article gives expresses of both adult and teen satire. But it mostly, pokes fun at the stereotypical advice and coaching given to youth through the use of firearms. However, the last sentence has a much darker and more of a bitter tone, and attacks the teachings he has just mocked, â€Å"Build your character thoughtfully and painstakingly upon these precepts, and by and by, when you have got it built, you will be surprised and gratified to see how nicely and sharply it resembles everybody else’s. Twain uses satire in describing the story of the boy who almost shoots his grandmother with what he thought was an unloaded gun. Instead of the classic â€Å"life lesson† story where the gun turns out to be loaded and ends up killing someone, he twists it so that the gun isn’t loaded after all and no one gets hurt. The rule at the root of this piece is the idea that individuality should be educated and that rational teachings are normalizing our youth. Mark Twain is great at mocking known teachings because he looks at it from a different angle, not suggesting that they are wrong but rather questioning if they are limiting originality and freedom of thought. Although, he runs into the certain obstacle that people who follow rational wisdom and tell their children the kinds of things he mocks won’t be as open to his argument because he doesn’t preach rational wisdom himself. He uses irrational wisdom to prove his point.

Reluctant Fundamentalist Essay

In The Reluctant Fundamentalist, Mohsin Hamid uses a variety of literary devices to create the tone of confusion and agitation. By doing so, Mohsin Hamid also develops a theme of change. All these literary features combine to make an enthralling page-turner. One literary device used by the author to create restlessness in the reader is diction. The author intentionally uses words to create discomfort in the reader. â€Å"The twin towers of New York’s World Trade center collapsed. And then I smiled. Yes, despicable as it may sound (4-6). †The fact that the protagonist smiles at America’s misfortune only puts the reader at unease. Furthermore, the author himself suggests that the smile was a despicable reaction. However by making the reader anxious, Mohsin Hamid does only but one thing; lure in the reader to continue reading. This quote also denotes Changez’s change towards America. This is because, although Changez was â€Å"the product of an American university; (he) was earning a lucrative American salary; (he) was infatuated with an American woman (28-30)† his initial reaction to this incident was a smile. The repetition of the word â€Å"American† only creates the motif that Changez has supposedly become American. However after the attack, Changez’s smile only suggests otherwise; thereby creating the theme of change. Another literary device used by Mohsin Hamid to create a sense of confusion is the use of ambiguity through dramatic monologue. â€Å"It is hateful to hear another person gloat over one’s country’s misfortune. But surely you cannot be completely innocent of such feelings yourself (22-24). † Because the American does not speak, the reader is forced to create the personality of the American in his or her own mind. Thus, when the protagonist accuses the American of being guilty of such feelings, the protagonist is essentially accusing the reader of those feelings. The ambiguity of this quote further agitates the reader, yet at the same time forces the reader to continue reading in hope of finding more truths about the reader’s self. One more technique the author uses to develop the theme of change as well as compel the reader to continue reading is foreshadowing. After reflecting on his reaction to the attack, Changez still doesn’t know why he smiled; â€Å"So why did part of me desire to see America harmed? I did not know, then (30-31). † Although Changez is not sure why he smiled at the present time, this quote indicates that later on, the reader will find out why he smiled; another reason requiring the reader to finish reading the book. Simultaneously however, the author also foreshadows a lot of change is about to take place since we already know Changez is back in Pakistan and telling this story to an American at a Pakistani cafe. Literary devices and techniques are abundant in this passage, though they all merge to create a sense of perplexity and irony. At the same time however, they all merge to create the theme of change. Though all this contrariness simply obliges the reader to continue reading the book. Not only will the reader finally understand Changez’s reaction to the attack but the reader will also discover new truths about him or herself as he/she continues to read the book.

Flannery O Connor - 1912 Words

Curiosity about the possibility and conditions of change in identity has been remarkably intense, in fiction and in psychology, during the last century. In talk about literature, this has led to the development of a crude but useful terminological distinction of two sorts of characterization: static and dynamic. A static character, in this vocabulary, is one that does not undergo important change in the course of the story, remaining essentially the same at the end as he or she was at the beginning. A dynamic character, in contrast, is one that does undergo an important change in the course of the story. More specifically, the changes that we are referring to as being undergone here are not changes in circumstances, but†¦show more content†¦The story reveals his feelings about girls throughout the first half of the story. Then finally in the end he has a complicated conversation with his mother. Another difference between the two stories is the setting. The short story, â€Å"Speaking of Courage† took place after the main character, Norman Bowker, returned to his home after the Vietnam War. While in â€Å"Speaking of Courage†, the story took place a few years following World War I. â€Å"Speaking of Courage† took place in Norman Bowker’s van most of the time as he was making revolutions are the lake. In â€Å"Soldier’s Home† the story was mostly on the front porch of Krebs home and inside his kitchen. The dialogue and structure of the two stories are also different. In â€Å"Soldier’s Home† the first half of the story contained no dialogue and in the second half of the story, it contained a whole conversation to the end of the story. In â€Å"Speaking of Courage†, the whole story was mixed up and contained dialogue throughout the whole story. The two stories contained many differences. Both of the stories had a lot of differences but there were more similarities. The main plot of both stories were different, but the theme of the two short stories were similar. The dialogues contained in both stories were also different and the short story â€Å"Speaking of Courage† contained much more dialogue than â€Å"Soldier’s Home†. The point of view, and the characters in the story’s meaning were similar but the structure and dialogueShow MoreRelatedReview Of Flannery O Connor1228 Words   |  5 Pagesauthor of two novels and multiple classic short stories, Flannery O’Connor is widely regarded as one of the greatest fiction writers in American literature. However, as a Southern and devoutly Christian author in the 1950s, O’Connor was often criticized for the religious content and â€Å"grotesque† characters often incorporated into her works. They were considered too â€Å"brutal†, too â€Å"sarcastic.† (The Habit of Being: Letters of Flannery O Connor). O’Connor begged to differ. Through her essay, â€Å"Some AspectsRead MoreFamily, By Flannery O Connor1803 Words   |  8 Pages In every home, there is a different definition of family and how family should treat each other. Two short stories were read by an author named Flannery O’Connor. â€Å"A Good Man is Hard to Find†. It was about a dysfunctional family who encounters a criminal named â€Å"The Misfit†. The grandmother which is the main character is very judgmental towards others and sometimes her own family at times. This story starts off with a disagreement on where to go for a family trip, but they decide on going to FloridaRead MoreThe, By Flannery O Connor1305 Words   |  6 Pagesdisparity between Blacks and their White counterparts can been seen through not only the South, but also throughout America. Flannery O’Connor, often considered one of the great Southern authors of her time, implemented an artistic writing style which gave her writing a unique Southern gothic appeal that previous novels and stories did not possess. Born in Savannah, Georgia, Flannery Oâ€℠¢Connor grew up in a turbulent time regrading race relations. Living most of her life in predominantly white Georgia, itRead MoreFlannery O Connor s Revelation1307 Words   |  6 PagesFlannery O’Connor believed in the power of religion to give new purpose to life. She saw the fall of the old world, felt the force and presence of God, and her allegorical fictions often portray characters who discover themselves transforming to the Catholic mind. Though her literature does not preach, she uses subtle, thematic undertones and it is apparent that as her characters struggle through violence and pain, divine grace is thrown at them. In her story â€Å"Revelation,† the protagonist, Mrs. TurpinRead MoreA Good Man By Flannery O Connor1235 Words   |  5 PagesA good man is hard to find is a short story written by, Flannery O’Connor, in which the she describes the story of a family going out for a trip to Florida. The grandmother in the family seems to be apparently the main character in the story and the main one who tries to convince the family that is dangerous to go out when there’s a man named the Misfit who is ready to attack and kill anyone in his way. No one in the family seemed to believe her, and yet; they all decided to travel. In their wayRead MoreFlannery O Connor And Religion961 Words   |  4 PagesFlannery O’Connor and Religion in Literature In Flannery O’Connor’s short stories, she often relates them to religion or incorporates a religious form in her stories. O’Connor highlights Christian themes throughout her writing. From her stories familiar to the bible, to death and religious views, its simple to see O’Connor’s religious understanding of God. She ties in her Christian views through her writing, which have a distinct and unique quality. O’Connor often expresses her views of God throughoutRead MoreA Good Man By Flannery O Connor Essay1049 Words   |  5 PagesMicah Gonzales Vernon English 1302.03 31 March 2015 A Good Man is Hard to Find In â€Å"A Good Man is Hard to Find, the author, Flannery O’Connor states many points in this short story. It is to be said that O’Connor is a very religious, catholic, in fact (Vol. 2 pg. 97). O’Connor has stated her religious views in most of her fiction stories. O’Connor was also known for her stories on violence. Readers sometimes find O’Connor’s fictions to be weird with such turning points in her stories. â€Å"A GoodRead MoreA Good Man By Flannery O Connor1239 Words   |  5 Pagesis not mentioned directly in the story. Mystery has it, that she has been explaining her story as if she was the good man or who knows what she could be talking about referring someone or telling someone that good men are hard to find. The author Flannery O’connor wrote this story in 1953, where there must different events occurring causing the relations of racism and different inventions throughout the history that had been shaping America. There fore, a lot of important events that must it beenRead MoreA Good Man By Flannery O Connor946 Words   |  4 PagesIn 1955, Flannery O’ Connor published the short story â€Å"A Good Man Is Hard to Find† which became her best-known short story. Although many appreciated her work it received much criticism for its peculiar character, The Misfit. His callous violent behavior made people uncomfortable with her work describing it as consistently distorted and manipulative. The Misfit’s unsentimental and cruel behavior characterizes true psychological disturbance similar to that of Charles Manson and Jeffrey Dahmer. Read MoreA Good Man By Flannery O Connor1795 Words   |  8 Pagesshort story authors in her era, Flannery O Connor wrote many short stories before her death in 1964. A faithful Catholic, religion was a primary theme in her works; she wrote mostly about southern life with religious themes recurring in her work. One of her most famous stories was the 1 955 short story A Good Man Is Hard to Find. The story depicts the heartless execution of a family by a group of escaped inmates led by their leader known as The Misfit. Though O Connor disagreed, many critics associated