The Necklace A Closer Look at Character Essay Example For Students

The Necklace: A Closer Look at Character Essay English 102 P Buss Essay 1 In any literay work, it is absolutely essential to have characters, whether major or minor. It is also necessary to develop these characters through out the story. Character development gives the reader insight to the more important meanings or lessons of the story. These lessons are usually brought out by the events that take place within the story. Looking at Guy De Maupassants piece The Necklace, we see a very clear development of the main character Mathidle. We will write a custom essay on The Necklace: A Closer Look at Character specifically for you for only $16.38 $13.9/page Order now In the story, we see a change in her attitude about life. This change come about when she has to learn one of lifes little lessons the hard way. She and her husband are forced to live a life of hard work and struggle because of her own selfish desires. Mathilde changes from a woman who spends her time dreaming of all the riches and glory she doesnt have, to realizing that she over looked all the riches she did have. The story opens with the description of how miserable Mathilde is. Maupassant describes her as suffering constantly, feeling herself destined for all delicacies and luxeries. (Pg 4) She sits dreaming of silent rooms nicely decorated and her own private room, scented with perfume to have intimate tete- a-tetes with her closest friends. Then she is awakened, only to realize that she is in her own grim apartment. In her eyes, she lives a tortured and unfair life. Mathidle has a husband named Losiel. He is much the opposite of his wife. He is completely content with his lifestyle. He seems to be a very passive person, who doesnt let status or riches effect him. Of course, if he had the chance to be rich he would, but he doesnt dwell on the fact that he is part of the middle class. He seems ot be a hard worker and does his best to provide for his wife. He demonstrates is simplicity the one night at dinner Losiel and Mathilde sit down to eat. Mathidle is dreaming of fancy four course meals, while he is ecstatic because they are eating boiled beef. Losiel is aware that his wife has not yet adjusted to her status. One night, he had come home from work very excited. He had worked extra hard to get he and his wife invited to one of the biggest parties ever. Losiel thought this would be please his wife, when in fact it only made her upset. Here was Losiel trying to please his wife and she just started to cry. This just goes to show how ungreatful she really is. When Losiel had inquired about why she was upset, she had said it was because she had nothing to wear. She was hinting to her husband that she needed a dress. Then Losiel, because he wanted his wife to be happy had willingly given up his vacation money so his wife could have a dress to wear. Still, that wasnt good enough for her. Mathilde wanted more. Luckily, Mathilde had a friend in the upper class. She had gone to her friend and had asked to borrow jewlery for the occasion. This just helped to prove her need to have more. When she arrived at her friends house she had many things to choose from. Mathilde had seen all kinds of things that delighted her but one thing imparticular had caught her eye. In a black satin box, a superb diamond necklace, and her heart throbbed with desire for it. Her hands shook as she picked it up. She fastened it around her neck, watched it gleam at her throat and looked at herself ecstatically. .u3b3a498ef9f05fba0661b7e1d46637c0 , .u3b3a498ef9f05fba0661b7e1d46637c0 .postImageUrl , .u3b3a498ef9f05fba0661b7e1d46637c0 .centered-text-area { min-height: 80px; position: relative; } .u3b3a498ef9f05fba0661b7e1d46637c0 , .u3b3a498ef9f05fba0661b7e1d46637c0:hover , .u3b3a498ef9f05fba0661b7e1d46637c0:visited , .u3b3a498ef9f05fba0661b7e1d46637c0:active { border:0!important; } .u3b3a498ef9f05fba0661b7e1d46637c0 .clearfix:after { content: ""; display: table; clear: both; } .u3b3a498ef9f05fba0661b7e1d46637c0 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u3b3a498ef9f05fba0661b7e1d46637c0:active , .u3b3a498ef9f05fba0661b7e1d46637c0:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u3b3a498ef9f05fba0661b7e1d46637c0 .centered-text-area { width: 100%; position: relative ; } .u3b3a498ef9f05fba0661b7e1d46637c0 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u3b3a498ef9f05fba0661b7e1d46637c0 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u3b3a498ef9f05fba0661b7e1d46637c0 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u3b3a498ef9f05fba0661b7e1d46637c0:hover .ctaButton { background-color: #34495E!important; } .u3b3a498ef9f05fba0661b7e1d46637c0 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u3b3a498ef9f05fba0661b7e1d46637c0 .u3b3a498ef9f05fba0661b7e1d46637c0-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u3b3a498ef9f05fba0661b7e1d46637c0:after { content: ""; display: block; clear: both; } READ: Teenage Pregnancy Vs Parental Consent In Regards T Essay (Pg 6) She had gotten all she wanted. Once again, Mathildes selfish desires had been fulfilled. After going to the ball and basically being the life of the party, she returned home to her drab apartment, only to remember the events of the evening where she was in the sporlight and people looked at her. It was at that moment that she had noticed that the necklace was missing. She and her husband had searched everywhere for it yet, the necklace was no where to be found. For the next ten years Loisel and Mathilde worked their fingers to the bone to repay Mathildes friend for the necklace that Mathilde had carelessly lost. They had to move to a different apartment, this worse than the last. They also had to borrow money from the various people to . The Necklace A Closer Look at Character Essay Example For Students The Necklace: A Closer Look at Character Essay The Necklace: A Closer Look at Character Essay English 102 P Buss Essay 1 In any literay work, it is absolutely essential to have characters, whether major or minor. It is also necessary to develop these characters through out the story. Character development gives the reader insight to the more important meanings or lessons of the story. These lessons are usually brought out by the events that take place within the story. Looking at Guy De Maupassants piece The Necklace, we see a very clear development of the main character Mathidle. We will write a custom essay on The Necklace: A Closer Look at Character specifically for you for only $16.38 $13.9/page Order now In the story, we see a change in her attitude about life. This change come about when she has to learn one of lifes little lessons the hard way. She and her husband are forced to live a life of hard work and struggle because of her own selfish desires. Mathilde changes from a woman who spends her time dreaming of all the riches and glory she doesnt have, to realizing that she over looked all the riches she did have. The story opens with the description of how miserable Mathilde is. Maupassant describes her as suffering constantly, feeling herself destined for all delicacies and luxeries. (Pg 4) She sits dreaming of silent rooms nicely decorated and her own private room, scented with perfume to have intimate tete- a-tetes with her closest friends. Then she is awakened, only to realize that she is in her own grim apartment. In her eyes, she lives a tortured and unfair life. Mathidle has a husband named Losiel. He is much the opposite of his wife. He is completely content with his lifestyle. He seems to be a very passive person, who doesnt let status or riches effect him. Of course, if he had the chance to be rich he would, but he doesnt dwell on the fact that he is part of the middle class. He seems ot be a hard worker and does his best to provide for his wife. He demonstrates is simplicity the one night at dinner Losiel and Mathilde sit down to eat. Mathidle is dreaming of fancy four course meals, while he is ecstatic because they are eating boiled beef. Losiel is aware that his wife has not yet adjusted to her status. One night, he had come home from work very excited. He had worked extra hard to get he and his wife invited to one of the biggest parties ever. Losiel thought this would be please his wife, when in fact it only made her upset. Here was Losiel trying to please his wife and she just started to cry. This just goes to show how ungreatful she really is. When Losiel had inquired about why she was upset, she had said it was because she had nothing to wear. She was hinting to her husband that she needed a dress. Then Losiel, because he wanted his wife to be happy had willingly given up his vacation money so his wife could have a dress to wear. Still, that wasnt good enough for her. Mathilde wanted more. Luckily, Mathilde had a friend in the upper class. She had gone to her friend and had asked to borrow jewlery for the occasion. This just helped to prove her need to have more. When she arrived at her friends house she had many things to choose from. Mathilde had seen all kinds of things that delighted her but one thing imparticular had caught her eye. In a black satin box, a superb diamond necklace, and her heart throbbed with desire for it. Her hands shook as she picked it up. She fastened it around her neck, watched it gleam at her throat and looked at herself ecstatically. .ue5f3f16e73b892a72b6765abe88aad13 , .ue5f3f16e73b892a72b6765abe88aad13 .postImageUrl , .ue5f3f16e73b892a72b6765abe88aad13 .centered-text-area { min-height: 80px; position: relative; } .ue5f3f16e73b892a72b6765abe88aad13 , .ue5f3f16e73b892a72b6765abe88aad13:hover , .ue5f3f16e73b892a72b6765abe88aad13:visited , .ue5f3f16e73b892a72b6765abe88aad13:active { border:0!important; } .ue5f3f16e73b892a72b6765abe88aad13 .clearfix:after { content: ""; display: table; clear: both; } .ue5f3f16e73b892a72b6765abe88aad13 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ue5f3f16e73b892a72b6765abe88aad13:active , .ue5f3f16e73b892a72b6765abe88aad13:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ue5f3f16e73b892a72b6765abe88aad13 .centered-text-area { width: 100%; position: relative ; } .ue5f3f16e73b892a72b6765abe88aad13 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ue5f3f16e73b892a72b6765abe88aad13 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ue5f3f16e73b892a72b6765abe88aad13 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ue5f3f16e73b892a72b6765abe88aad13:hover .ctaButton { background-color: #34495E!important; } .ue5f3f16e73b892a72b6765abe88aad13 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ue5f3f16e73b892a72b6765abe88aad13 .ue5f3f16e73b892a72b6765abe88aad13-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ue5f3f16e73b892a72b6765abe88aad13:after { content: ""; display: block; clear: both; } READ: Environmental protection Essay (Pg 6) She had gotten all she wanted. Once again, Mathildes selfish desires had been fulfilled. After going to the ball and basically being the life of the party, she returned home to her drab apartment, only to remember the events of the evening where she was in the sporlight and people looked at her. It was at that moment that she had noticed that the necklace was missing. She and her husband had searched everywhere for it yet, the necklace was no where to be found. For the next ten years Loisel and Mathilde worked their fingers to the bone to repay Mathildes friend for the necklace that Mathilde had carelessly lost. They had to move to a different apartment, this worse than the last. They also had to borrow .

Comparison Of Trade Rivalries Essays - Trade Policy, Free Essays

Comparison Of Trade Rivalries Essays - Trade Policy, Free Essays Comparison of Trade Rivalries The German-Great Britain trade rivalry like the U.S.-Japan trade rivalry involved a rising power cutting into the trade of an already dominant trading power. There were several causes of the German-Great Britain trade rivalry according to Hoffman. The first was German's industry's zeal in procuring new contracts and expanding markets. They did this by fulfilling contracts even if they were very small and coneztly trying to stay up with market demand. Second, Germans had a knowledge of languages that the English firms lacked. Third, German industry was aided by their government. In contrast Great Britain did not even supply consular assiezce in helping develop markets in British colonies. Fourth, British trade was hurt by the conservatism of British manufacturers who were unwilling to develop new markets or hold onto those it already possessed. These four factors are just some of the factors that helped German industry grow and rival that of Great Britain. These four factors are all very similar to the Japan-U.S. trade rivalry. Japan like Germany was able to catch up to the U.S. because the U.S. was large and arrogant and refused to believe it could face competition from Japan. Like Britain, U.S. industry believed that they could hold onto markets and would not face competition. British and U.S. industry were startled by the fast rate of growth and industrialization that allowed Germany and Japan to transform themselves quickly into trading rivals. This fast rate of growth also caused friction between both sets of countries. Relations between Germany and Great Britain were damaged as they bickered over markets in particular colonies in Africa . This is similar to the friction between the U.S. and Japan unfair trading practices and closed markets. Both the U.S. and Great Britain in response to losing markets toyed with the idea of economic nationalism and tariffs. As Britain lost markets to Germany many in Britain felt that Britain should adopt tariffs on goods while others known as the free traders believed that a free trade would benefit Britain by creating markets. This split between Tariff Reformers and Free Traders is similar to the split in the U.S. between those in favor of free trade and those opposed to it. Germany's grab for new markets in the 1890's through commercial treaties such as the 1891 treaty with Austria-Hungry is similar to both the United States and Japan's free trade zones with neighboring countries using treaties such as ASEAN and NAFTA. The German-Great Britain trade rivalry is different then the U.S.-Japan trade rivalry because a large sector of Japan's market for selling goods is the United States who it is competing against; this was not true of Germany. Both Britain and Germany were competing for markets outside of both their countries. Also the trade rivalry between Japan and the United States did not involve a fight over colonies. Trade rivalries between rising and dominant powers change little over time. The German-British trade rivalry and the Japan U.S. rivalry were very similar in their causes, effects, and the solutions that both sets of governments used to overcome their trading rival.

How to Get Your CDL in Wyoming, Nevada and New Mexico

How to Get Your CDL in Wyoming, Nevada and New Mexico This article is useful for anyone who wants to get your CDL in Wyoming, Nevada or New Mexico. If you want to learn about earning a CDL at other states, we have put together a comprehensive guide on how to get a commercial driver’s license in every state of the country. WyomingIf your vehicle has a gross vehicle weight rating of 26,001 pounds, or more or carries 16+ passengers (including the driver), or you transport hazardous material in an amount which must be placarded,   you are required to have a CDL.To obtain a CDL, you must  complete a series of written knowledge tests, a vision screening, and a driving skills test.Written Knowledge TestsAll written tests are multiple choice, and require a passing score of  80 percent correct. Written tests are valid for two years.You must take a written test  if:You  never been previously licensed in the United States, any U.S. Territory, Canadian Province, or GermanyYour  driving record indicates your last license has been expired, revoked, or denied for two years or longer, or your  privilege to drive has been revoked, canceled or disqualifiedYou are  upgrading your  class of license or adding any endorsementsYou are  removing the air brake restriction â€Å"L;† and you are  removing the Air Over Hydraulics restrictionIf you have  a CDL license with a hazmat endorsement â€Å"H,† you will be required to take the hazardous materials test upon transferring your  out-of-state CDL license. If you already have a  Wyoming CDL, you must  retake the hazmat test if you have not  passed the test within the previous two years.Vision ScreeningYou must receive  a vision reading of 20/40 with both eyes to pass the vision screening. If you cannot  meet this standard with or without glasses, you will have to  obtain a vision statement from an  eye doctor. If you wear contact lenses or glasses during the vision screening, you will be required to wear them at all times while d riving. A vision reading of worse than 20/40 in one eye will restrict you to intrastate driving only.Skills TestA skills test will consist of a vehicle pre-trip inspection, a basic control skills test and an over-the-road skills test. You can only take a skills tests after you have  successfully completed all applicable written tests.You must  test in a  vehicle representative of the class of license for which you are applying. Skills tests will not be conducted in a loaded commercial vehicle; simulated weight is the only thing allowed in trailer. Additionally, placarded vehicles are not allowed to be used for skills testing.The fee for a skills test is $40.Applicants for a Wyoming CDL who hold a valid U.S. Military license must pass all written tests for the class of license they currently hold.DisqualificationsWyoming law  states CDL holders may be disqualified from driving a commercial motor vehicle, have their license canceled, or be prohibited from obtaining a CDL if th ey are convicted of 2 or more serious moving violations in a 3-year period, which may include the following:Speeding 15 mph+Following too closelyNot posessing  a CDL or driving without a CDL on your personImproper or no endorsementsReckless drivingErratic or improper lane changeUse of cell phone OR texting while drivingYou  will have their license cancelled and will be disqualified from driving a CMV or from obtaining a CDL if convicted of:Driving under the influenceDriving with a blood alcohol of .04% or greaterLeaving the scene of an accidentDriving under suspension in a CMVDriving a motor vehicle used in a felonyNegligent operation of a CMV causing a fatalityNevadaCommercial Learner’s Permits (CLPs)Beginning in early 2016, CLPs will be administered  instead of a Commercial Driver’s License Instruction Permit (CDL IP).  To obtain a CLP, you must have a base non-commercial or commercial license. You must  have a CLP to get a CDL.A CLP is valid for 180 days, and must be held for 14 days prior to taking a skills test.Commercial Driver License  (CDL)You must have a CDL to drive a commercial motor vehicle, which is  a motor vehicle or combination of motor vehicles used in commerce to transport passengers or property if the motor vehicle meets the following considerations:The vehicles have  a gross combination weight rating of 26,001 pounds+, inclusive of a towed unit(s) with a gross vehicle weight rating of more than 10,000 poundsThere is  a gross vehicle weight rating of 26,001 pounds or moreThe vehicle(s) are  designed to transport 16 or more passengers, including the driverThe vehicle(s) are  of any size and are used in the transportation of hazardous materials that require placardingYou must be at least 21 years old to be issued a CDL to operate a commercial motor vehicle in interstate commerce and to receive endorsements for passengers or hazardous materials. You must be at least 25 to receive an endorsement for vehicle co mbinations over 70 feet in length.  CDLs issued to applicants age 18 to 20 will contain Restriction R (no passengers or hazmat) and Restriction 2 (intrastate commerce only).Requirements  Ã‚  to ApplyYou must list all states where you have held any commercial or non-commercial driver’s license in the past 10 years. Your driving history in each state will be checked.Commercial drivers must meet the Residency Proof of Identity requirements for a Nevada driver’s license.You must self-certify the type of driving you do and, if needed, submit a Medical Examiner’s Certificate.  Your employer may require a physical even if the state does not.If a physical is required, you must obtain it from a physician listed in the National Registry of Certified Medical Examiners.New MexicoAnyone applying for a CDL Permit, a first-time Commercial License or a Commercial License renewal must have the following documentation:A state birth certificate, U.S. passport, or other proo f of lawful presence in the U.S.A Social Security CardDOT Medical Certification2  verifiable proofs of physical residency in New MexicoA valid New Mexico driver’s/CDL licenseIf  you do  not have a current, valid DOT Medical Certificate on record, you  will be required to submit a copy of your medical certificate.Knowledge TestsYou must  to pass all required CDL Knowledge Tests for the Class and/or type of vehicle you  want to operate.If you  fails any one CDL Knowledge Test, you must wait one week (7 days) from day of testing before retesting.Any applicant may take any one CDL Knowledge Test 3x within a one-year period. After failing 3x, you  must wait one year from the first time tested before retesting.No documentation of any kind and no cell phones are permitted in the test area.If you are  found cheating or committing an offense while testing, you will have your  CDL application or license disqualified for one year and must  obtain a Class D license if holding a CDL.Skills TestsThe Skills Tests, which is made up of the Pre-Trip, Basic Control Skills, and Road Testing, are administered by a third party examiner and will normally take two hours.If you  fail, you  must wait one week from the day of testing before retesting.You  may take the test 3x  within a one-year period. After the third fail, you  must wait one year from the first time tested before retesting.Each part of the Knowledge and Skills Test is graded independently. A passing score is 80% or higher

There are questions and i need to answer .I will write it in Essay

There are questions and i need to answer .I will write it in assignment criteria - Essay Example Employees, like the employers, want to feel being part of the organization and the products produced. However, in many organizations, employees are isolated and only reduced to production machines, with no attachment to what they do. This leads to low employee morale and other major challenges in the working environment. According to several theories of motivations, such as the drive theory, employees need to be motivated. When this term is used, many employees tend to think that high salaries are the only means of motivating the employees. While this act may produce positive results, this will however, work in the short term. Other main areas that need to be addressed include creating an effective and convenient environment in which the employees can work. This is especially through ensuring safety of the employees. Constant communication between employees and employers is also vital. It enables the two addresses the current challenges affecting employees, and the company early befo re it can become a challenge. Operations management becomes imperative when dealing with some of these issues. It is the process through which the management seeks to increase quality, reduce the cost of operation, and use as minimal resources as possible. Employers are focusing on increasing productivity, while at the same time ensuring that all the factors are considered. In terms of performance, the employees focus on speed, flexibility, dependability, cost, and quality. These five performance objectives of operations management are imperative in ensuring that the company becomes more productive. Customers focus on efficiency and quality. The speed at which the company supplies foods and services to the customers is vital. The kind of technology that is employed in any given company also becomes imperative. It must be flexible and dependable. This means it must be ready to accommodate the changes and new demands in the market. However, reducing the cost of operation is one of the major issues that the operations management seeks to solve. As the cost of operations reduces, so do the profits increase. For this reason, the operations managers may decide to employ strategies such as outsourcing. It is the process through which employers seek higher employees who can provide quality services but at a low cost. This is mostly done through acquiring employees from abroad. This has assisted many companies to solve the problem of increased cost of operation. Other areas of focus include the means of transportation used to deliver goods and services to the employees. The means but is both cost effective and efficient. Goods must reach their intended destination within the intended time. It is upon the operations manager to organize, control, and coordinate all the operations within the organization. This is vital if the company is to realize its goals and objectives. However, it will be difficult to achieve some of this goals, speed, and quality of goods unless the right technology is employed. Integration of information technology is important. Apart from increasing productivity, it also leads to high quality work at a minimum time. Challenge facing our manufacturing company This manufacturing company has become ineffective due to the problems of high employee turnover and general reduction in productivity. As a result, the profits of the company have decreased, with the increased cost of operation. With this problem likely to escalate, there is need to address it objectively.

Communication Techniques Personal Statement Example | Topics and Well Written Essays - 500 words

Communication Techniques - Personal Statement Example When we grow older, I have learned to tailor my conversation with her according to her preferences and made her understand my ideas through elaboration. Through this openness to new communication techniques anchored in responding according to my sister's requirements, I was able to build a harmonious relationship. My experience in studying sign language strengthened my determination to choose communication as a major. Sign language classes exposed me to the hardships and needs of people who are disabled. I used to pity them knowing that they do not have avenue where they can truly express themselves. However, it also challenged me to make a difference in communication as I am able and free to communicate my ideas. When I was young, I have developed an interest in communication through mass media especially during the nights when I watch documentaries with my father. It opened my eyes on social issues which typical people ignore. Having the chance to explore this field, I choose to become an intern at a Korean news station (KEMS) within the past six months. My first assignment was to report on the animal festival' in downtown San Jose through capturing two interviews on my camera. I was initially nervous but find it rewarding to see my work aired on the television. Man is a social being and communication is as old as man himself.

Direct and iterative method

Direct and iterative method INTRODUCTION TO DIRECT AND ITERATIVE METHOD Many important practical problems give rise to systems of linear equations written as the matrix equation Ax = c, where A is a given n Ãâ€" nnonsingular matrix and c is an n-dimensional vector; the problem is to find an n-dimensional vector x satisfying equation . Such systems of linear equations arise mainly from discrete approximations of partial differential equations. To solve them, two types of methods are normally used: direct methods and iterative methods. Directapproximate the solution after a finite number of floating point operations. Since computer floating point operations can only be obtained to a given precision, the computed solution is usually different from the exact solution. When a square matrix A is large and sparse, solving Ax = c by direct methods can be impractical, and iterative methods become a viable alternative. Iterative methods, based on splitting A into A = M−N, compute successive approximations x(t) to obtain more accurate solutions to a linear system at each iteration step t. This process can be written in the form of the matrix equation x(t) = Gx(t−1) + g, where an n Ãâ€" n matrix G = M−1N is the iteration matrix. The iteration process is stopped when some predefined criterion is satisfied; the obtained vector x(t) is an approximation to the solution. Iterative methods of this form are called linear stationary iterative methods of the first degree. The method is of the first degree because x(t) depends explicitly only on x(t−1) and not on x(t−2), . . . , x(0). The method is linear because neither G nor g depends on x(t−1), and it is stationary because neither G nor g depends on t. In this book, we also consider linear stationary iterative methods of the second degree, represented by the matrix equation x(t) = Mx(t−1) − Nx(t−2) + h. HISTORY OF DIRECT AND ITERATIVE METHOD Ø Direct methods to solve linear systems Direct methods for solving the linear systems with the Gauss elimination method is given byCarl Friedrich Gauss (1777-1855). Thereafter the Choleski gives method for symmetric positive definite matrices. Ø Iterative methods for non-linear equations The Newton_Raphson method is an iterative method to solve nonlinear equations. The method is defined byIsaac Newton (1643-1727)andJoseph Raphson (1648-1715). Ø Iterative methods for linear equations The standard iterative methods, which are used are the Gauss-Jacobi and the Gauss-Seidel method.Carl Friedrich Gauss (1777-1855)is a very famous mathematician working on abstract and applied mathematics.Carl Gustav Jacob Jacobi (1804-1851)is well known for instance for the Jacobian the determinant of the matrix of partial derivatives. He has also done work on iterative methods leading to the Gauss-Jacobi method. Another iterative method is the Chebyshev method. This method is based on orthogonal polynomials bearing the name ofPafnuty Lvovich Chebyshev (1821-1894). The Gauss-Jacobi and Gauss-Seidel method use a very simple polynomial to approximate the solution. In the Chebyshev method an optimal polynomial is used. DIRECT AND ITERATIVE METHOD Direct methods compute the solution to a problem in a finite number of steps. These methods would give the precise answer if they were performed ininfinite precision arithmetic. Examples includeGaussian elimination, theQRfactorization method for solvingsystems of linear equations, and thesimplex methodoflinear programming. In contrast to direct methods,iterative methodsare not expected to terminate in a number of steps. Starting from an initial guess, iterative methods form successive approximations thatconvergeto the exact solution only in the limit. Aconvergence criterionis specified in order to decide when a sufficiently accurate solution has (hopefully) been found. Even using infinite precision arithmetic these methods would not reach the solution within a finite number of steps (in general). Examples includeNewtons method, thebisection method, andJacobi iteration. In computational matrix algebra, iterative methods are generally needed for large problems. Iterative methods are more common than direct methods in numerical analysis. Some methods are direct in principle but are usually used as though they were not, e.g.GMRESand theconjugate gradient method. For these methods the number of steps needed to obtain the exact solution is so large that an approximation is accepted in the same manner as for an iterative method. In the case of asystem of linear equations, the two main classes of iterative methods are thestationary iterative methods, and the more generalKrylov subspacemethods. Ø Stationary iterative methods Stationary iterative methods solve a linear system with anoperatorapproximating the original one; and based on a measurement of the error (the residual), form acorrection equationfor which this process is repeated. While these methods are simple to derive, implement, and analyse, convergence is only guaranteed for a limited class of matrices. Examples of stationary iterative methods are theJacobi method,Gauss–Seidel methodand theSuccessive over-relaxation method. Ø Krylov subspace methods Krylov subspacemethods form anorthogonal basisof the sequence of successive matrix powers times the initial residual (theKrylov sequence). The approximations to the solution are then formed by minimizing the residual over the subspace formed. The prototypical method is theconjugate gradient method(CG). Other methods are the generalized minimal residual method and the biconjugate gradient method EXAMPLE OF DIRECT METHOD GAUSS ELIMINATION METHOD :- Inlinear algebra,Gaussian eliminationmethod is analgorithmfor solvingsystems of linear equations, finding therankof amatrix, and calculating the inverse of aninvertible square matrix. Gaussian elimination is named after German mathematician and scientistCarl Friedrich Gauss. Elementary row operationsare used to reduce a matrix torow echelon form.Gauss–Jordan elimination, an extension of this algorithm, reduces the matrix further toreduced row echelon form. Gaussian elimination alone is sufficient for many applications. EXAMPLE Suppose that our goal is to find and describe the solution(s), if any, of the followingsystem of linear equations: The algorithm is as follows :eliminate x from all equations below L1 and then eliminate y from all equations below L2 .This will form a triangular form.Using the back substitution Each unknown can be solved . In the example, x is eliminated from l2 by adding 3/2L1to L2. X is then eliminatedmfrom L3 by adding L1 to L3 The result is: Nowyis eliminated fromL3by adding− 4L2toL3: The result is: This result is a system of linear equations in triangular form, and so the first part of the algorithm is complete.The second part, back-substitution, consists of solving for the unknowns in reverse order. It can be seen that Then,zcan be substituted intoL2, which can then be solved to obtain Next,zandycan be substituted intoL1, which can be solved to obtain The system is solved. Some systems cannot be reduced to triangular form, yet still have at least one valid solution: for example, ifyhad not occurred inL2andL3after the first step above, the algorithm would be unable to reduce the system to triangular form. However, it would still have reduced the system toechelon form. In this case, the system does not have a unique solution, as it contains at least onefree variable. The solution set can then be expressed parametrically . In practice, one does not usually deal with the systems in terms of equations but instead makes use of theaugmented matrix(which is also suitable for computer manipulations). The Gaussian Elimination algorithm applied to theaugmented matrixof the system above, beginning with:which, at the end of the first part of the algorithm That is, it is inrow echelon form. At the end of the algorithm, if theGauss–Jordan eliminationis applied: That is, it is inreduced row echelon form, or row canonical form. EXAMPLE OF ITERATIVE METHOD OF SOLUTION A. JACOB METHOD :- The Jacobi method is a method of solving amatrix equationon a matrix that has no zeros along its main diagonal (Bronshtein and Semendyayev 1997, p.892). Each diagonal element is solved for, and an approximate value taken in. The process is then iterated until it converges. This algorithm is a stripped-down version of theJacobi transformationmethod ofmatrix diagonalization. The Jacobi method is easily derived by examining each of the equations in thelinear system of equationsAx=b in isolation. If, in theith equation solve for the value ofwhile assuming the other entries ofremain fixed. This gives which is the Jacobi method. In this method, the order in which the equations are examined is irrelevant, since the Jacobi method treats them independently. The definition of the Jacobi method can be expressed withmatricesas B. Stationary Iterative Methods Iterative methods that can be expressed in the simple form Where neighter B nor c depend upon the iterative count k) are called stationary iterative method. The four main stationary iterative method : the Jacobi method, the Gauss Seidel method ,Successive Overrelaxation method and the symmetric Successive Overrelaxation method C. The Gauss-Seidel Method We are considering an iterative solution to the linear system where is ansparse matrix,xandbare vectors of lengthn, and we are solving forx. Iterative solvers are an alternative to direct methods that attempt to calculate an exact solution to the system of equations. Iterative methods attempt to find a solution to the system of linear equations by repeatedly solving the linear system using approximations to the vector. Iterations continue until the solution is within a predetermined acceptable bound on the error. Iterative methods for general matrices include the Gauss-Jacobi and Gauss-Seidel, while conjugate gradient methods exist for positive definite matrices. Use of iterative methods is the convergence of the technique. Gauss-Jacobi uses all values from the previous iteration, while Gauss-Seidel requires that the most recent values be used in calculations. The Gauss-Seidel method has better convergence than the Gauss-Jacobi method, although for dense matrices, the Gauss-Seidel method is sequential. The convergence of the iterative method must be examined for the application along with algorithm performance to ensure that a useful solution to can be found. The Gauss-Seidel method can be written as: where: ¯ is theunknown in during theiteration,and, is the initial guess for theunknown in, is the coefficient ofin therow andcolumn, is thevalue in. or where: ¯ K(k)is theiterative solution to is the initial guess atx Dis the diagonal ofA Lis the of strictly lower triangular portion ofA Uis the of strictly upper triangular portion ofA bis right-hand-side vector. EXAMPLE. 101−x2+ 23= 6, −x1+ 112−x3+ 34= 25, 21−x2+ 103−x4= − 11, 32−x3+ 84= 15. Solving forx1,x2,x3andx4gives: x1=x2/ 10 −x3/ 5 + 3 / 5, x2=x1/ 11 +x3/ 11 − 34/ 11 + 25 / 11, x3= −x1/ 5 +x2/ 10 +x4/ 10 − 11 / 10, x4= − 32/ 8 +x3/ 8 + 15 / 8 Suppose we choose(0,0,0,0)as the initial approximation, then the first approximate solution is given by x1= 3 / 5 = 0.6, x2= (3 / 5) / 11 + 25 / 11 = 3 / 55 + 25 / 11 = 2.3272, x3= − (3 / 5) / 5 + (2.3272) / 10 − 11 / 10 = − 3 / 25 + 0.23272 − 1.1 = − 0.9873, x4= − 3(2.3272) / 8 + ( − 0.9873) / 8 + 15 / 8 = 0.8789. x1 x2 x3 x4 0.6 2.32727 − 0.987273 0.878864 1.03018 2.03694 − 1.01446 0.984341 1.00659 2.00356 − 1.00253 0.998351 1.00086 2.0003 − 1.00031 0.99985 The exact solution of the system is (1,2,-1,1) APPLICATION OF DIRECT AND ITERATIVE METHOD OF SOLUTION FRACTIONAL SPLITING METHOD OF FIRST ORDER FOR LINEAR EQUATION First we describe the simplest operator-splitting, which is calledsequential operator-splitting, for the following linear system of ordinary differential equations:(3.1)where the initial condition is. The operators and are linear and bounded operators in a Banach space The sequential operator-splitting method is introduced as a method that solves two subproblems sequentially, where the different subproblems are connected via the initial conditions. This means that we replace the original problem with the subproblemswhere the splitting time-step is defined as. The approximated solution is. The replacement of the original problem with the subproblems usually results in an error, calledsplitting error. The splitting error of the sequential operator-splitting method can be derived as whereis the commutator ofAandB The splitting error iswhen the operatorsA andB do not commute, otherwise the method is exact. Hence the sequential operator-splitting is called thefirst-order splitting method. THE ITERATIVE SPLITING The following algorithm is based on the iteration with fixed splitting discretization step-size. On the time intervalwe solve the following subproblems consecutively for:(4.1)where is the known split approximation at the time level. We can generalize the iterative splitting method to a multi-iterative splitting method by introducing new splitting operators, for example, spatial operators. Then we obtain multi-indices to control the splitting process; each iterative splitting method can be solved independently, while connecting with further steps to the multi-splitting method

The Ethical Issues behind Cosmetic Surgery

The article I chose is entitled â€Å"Ethnic Differences Emerge in Plastic Surgery† and was written by Sam Dolnick for the New York Times on February 19, 2011. It explains that cosmetic plastic surgery is no longer an opportunity limited to wealthy suburbanites. In New York City, there has been a surge of immigrants having plastic surgeries that are correlated with their ethnic beauty standards.Furthermore, doctors practicing in various ethnic enclaves throughout the city have seen; Italians having their knees reshaped, Egyptians getting face-lifts, Iranians getting nose jobs, Dominican women getting their buttocks’ lifted, Asians having â€Å"double eye-lid surgery† or receiving a crease in their eyelids to make their eyes appear rounder, and Russians getting breast implants.The article goes on to contrast the cultural beauty standards or tastes between one group of wealthy Long Island suburbanites with Washington Heights’ ancestrally Dominican citizens, where, in Long Island suburbs they want fat removed from their behinds, and in Washington Heights they want their rear ends enlarged and rounded. There are three ethical issues present in this article, the first being the usage of surgery to improve patients’ psychological self-esteem issues versus the usage of surgery for traditional health reasons.The second issue is the fact that doctors are willing to offer layaway plans to help patients afford operations, but even more precarious, unlicensed practitioners are performing illegal surgery throughout most ethnic enclaves. The third is the belief that American pop culture and media have a role in affecting people’s personal awareness and ideals of beauty, and this is making them much more willing to have unnecessary cosmetic plastic surgery performed. John Stuart Mill’s Utilitarian doctrine is the first ethical theory I chose to apply to these ethical problems.Mill argued that morality is based on the consequenc es you take, and that consequences must be a means to increase utility or pleasure (Utilitarianism: Of What Sort of Proof the, para 3,9). To the first ethical issue, Mill would most likely say that people who undergo cosmetic plastic surgery are moral because they are acting accordance with increasing happiness. However, they are acting upon a lower pleasure, which is vanity, and although this may bring some joy, it is something that can become an endless pursuit.Towards the second issue, Mill would most likely say that the legality of the operations, and how the surgery is paid for, is superfluous to morality. If there is a tendency for patients to come out feeling and looking better, than the surgeon has done his or her job and there is nothing immoral going on. However, if there is a tendency for people to leave these places, where layaway is acceptable and the surgeons do not have licenses to practice, in pain and vexation, there is something immoral about this particular situat ion.One could further argue, that performing surgery illegally and allowing layaway for surgery is based in greed. To this I believe Mill would still say that it is the patients responses that matter, for they are the ones who choose to have the surgery illegally, and if they have gained more pleasure through the experience, the actions taken by the illegal surgeons or greedy doctors was moral (Utilitarianism: Of What Sort of Proof, para 6).To the last part, is media and pop culture responsible for unnecessary surgery, and people unhealthy personal beauty obsessions, he would say, generally no. Although he might say that certain parts of media are potent at changing the way people view their bodies and other people’s bodies, and may make people obsessively drawn into the lower pleasures of cosmetic bodily improvement. Immanuel Kant’s Deontological ethics is the second theory I chose to administer to the article. Kant argues that for an action to have genuine moral wort h, it must be done out of duty, or from pure intentions.People or semi-rational beings must not allow subjective experiences and past events, or particular circumstances, determine what actions are morally right, but must act to achieve the categorical imperative, thus making every intention and every action together an end in itself (Groundwork: Moving from popular, para 2-4, 6-7). To the first, again being the usage of surgery for traditional reasons, versus the usage of surgery for patients who have psychological self-esteem issues; they believe that having cosmetic surgery will result in looking better and therefore bring happiness.Kant would strongly see this as immoral, as it is first off not being used to preserve one’s life, and it is seeking out happiness through picking means which Kant believes will only lead to pain (Groundwork: Moving from popular moral, para 15-16). Also cosmetic plastic surgery is not universafiable because it means that our self-love is based off of subjective contingent circumstances, and not based off of self-love because we are semi-rational beings.To the second ethical theory being layaway plans and illegal surgery, Kant would probably see the layaway plans as bad in that if everyone had layaway, there would not be any true ownership, and everyone would be in debt to someone else. Illegal surgery is also not universifiable in that, if it were universifiable, there would be no legality, and the state laws for surgical practices would not exist. As to whether Kant would see people receiving cosmetic plastic surgery as victims of our hyper-idealized beauty popular culture and media, he would probably say yes, there is a problem.Pop culture, the media, and social networks certainly do have an insidiously furtive part in how we behave, and what we believe is beautiful. To go out of your way to make yourself more beautiful because someone or something tells you to do so, especially if it is instilled upon you in a covert w ay, is not acting in accordance with freedom. It is dually leading you to use surgery as a mere means to happiness, and using you as a mere means to waste your money on advertised beauty/ diet products, more surgery, and more repetitive mindless television shows.In terms of which ethical theory best resolves the ethical issues spurred by this article, I would have to say Kant’s theory of good intentions is most critical and affirmative. All of these ethical issues I have raised have questionable intentions behind them. If I were to go with Mill, I certainly would be a lot more lenient with these issues. That is not necessarily a bad thing, since these peoples actions are not necessarily questionable. Their actions are somewhat good, because whether you are the patient, the doctor, or the pop culture media (entertainment) you are aiming at or supposedly affecting happiness (in a Mill sense).But their intentions are somewhat convoluted, and in my opinion, impure. I believe most of the doctors have greed as their intention, especially those who are willing to perform surgery illegally. Sure, the illegal surgeons may be acting in a proper way, that is, they may perform the surgery properly. But behind it all is an intention of surreptitiously avoiding the rules of the state to save money, meanwhile being completely liable to malpractice and putting in jeopardy their lives and the lives of their patients.The patients may know that these doctors are quacks, but if they don’t, then in fact they are being lied to and are being placed under the knives of surgeons who are dishonest and hence treating the patients as a mere means. Furthermore, I believe anyone who is getting cosmetic plastic surgery based off of established beauty standards, unless in some horrific accident or bearing some horrific deformity is impure in their reasoning.They are giving into standards that are not their own, but have been environmentally, and artificially created, beefed up and branded. Thus, in a Kantian sense, people are acting not under a categorical imperative, but under empirical knowledge that has been conjured through culturally relative or subjective circumstances. In sum, Kant would say be happy with what you look like, and don’t attempt to change it based off of your cultural preferences or media created beauty bombardments, because you are not acting freely and with duty.