Solving Large Systems of Linear Simultaneous Equations

Solving Large Systems of Linear Simultaneous Equations NICOLE LESIRIMA METHODS OF SOLVING LARGE SYSTEMS OF LINEAR SIMULTANEOUS EQUATIONS PROJECT DESCRIPTION Linear systems simulate real-world problems using applied numerical procedure. The main aim of this project is to consider what factors affect the efficiency of the various methods of solving linear simultaneous equations. So far, one of the main factors is rounding errors that can produce inaccurate solutions. Moreover, MATLAB programs have been produced to time the calculation speed to determine the efficiency of the methods. Generally, these methods are subdivided into two; direct and iterative methods. Direct methods are commonly used to solve small systems of equations. The iterative methods are used to solve real-world problems that produce systems of equations for which the coefficient matrices are sparse. The relevance of studying these methods have its real world applications. The real world applications can be seen in various fields such as science and engineering, accounting and finance, business management and in operational research. The approach provides a logical framework for solving complex decisions in a wide range of industries. The advantage is that, decisions are founded on data analysis. Environmentalists and meteorologists may use large systems of simultaneous linear equations to predict future outcomes. For instance, to predict weather patterns or climate change, a large volume of data is collected over a long span of time on many variables including, solar radiation, carbon emissions and ocean temperatures. Queen Mary University of London (2015). This data is represented in the form of a transition matrix that has to be row reduced into a probability matrix that can then be used in the prediction of climate change. The objective of an enterprise is to maximize returns while maintaining minimum costs. Whereas the use of large systems of simultaneous linear equations may provide a basis for evidence based business decision making in an enterprise, it is important to know which linear systems are most appropriate in order to minimize undesirable outcomes for an enterprise. PROJECT REPORT OUTLINE Chapter 1 Introduction Large systems of linear simultaneous equations are used to simulate real-world problems using applied numerical procedure. The real world applications can be seen in various fields such as science and engineering, accounting and finance, business management. The approach provides a logical framework for solving complex decisions in a wide range of industries. The advantage is that decisions are founded on data analysis. The aim of this project is to explore the efficiency of a large systems of linear simultaneous equations in the optimal decision making of an enterprise. Chapter 2 Direct Methods: Gaussian Elimination and LU Factorisation Direct methods of solving linear simultaneous equations are introduced. This chapter will look at the Gaussian Elimination and LU Factorisation methods. Gaussian Elimination involves representing the simultaneous equations in an augmented form, performing elementary row operations to reduce the upper triangular form and finally back substituting to form the solution vector. LU Factorisation on the other hand is where a matrix A finds a lower triangular matrix L and an upper triangular matrix U such that A = LU. The purpose of this lower triangular matrix and upper triangular matrix is so that the forward and backward substitutions can be directly applied to these matrices to obtain a solution to the linear system. An operation count and computing times using MATLAB is calculated so as to determine the best method to use. Chapter 3 Cholesky Factorisation Introduction to the Cholesky method. This is a procedure whereby the matrix A is factorised into the product of a lower triangular matrix and its transpose; the forward and backward substitutions can be directly applied to these matrices to obtain a solution. A MATLAB program is written to compute timings. A conclusion can be drawn by comparing the three methods and determining which is the most suitable method that will produce the most accurate result as well as take the shortest computing time. Chapter 4 Iterative Methods: Jacobi Method and Gauss-Seidel This chapter will introduce the iterative methods that are used to solve linear systems with coefficient matrices that are large and sparse. Both methods involve splitting the matrix A into lower triangular, diagonal and upper triangular matrices L, D, U respectively. The main difference comes down to the way the x values are calculated. The Jacobi method uses the previous x values (n) to calculate the next iterated x values (n+1). The Gauss-Seidel uses the new x value (n+1) to calculate the x2 value. Chapter 5 Successive Over Relaxation and Conjugate Gradient Other iterative methods are introduced. The Successive Over Relaxation method over relaxes the solution at each iteration. This method is calculated using the weighted sum of the values from the previous iteration and the values form the Gauss-Seidel method at the current iteration. The Conjugate Gradient method involves improving the approximated value of xk to the exact solution which may be reached after a finite number of iterations usually smaller than the size of the matrix. Chapter 6 Conclusion All the project findings and results are summarised in this chapter. Conclusion can be made from both direct methods and iterative methods whereby the most accurate method with the shortest computing time can be found. Drawbacks from each method will be mentioned as well its suitability for solving real world problems. PROGRESS TO DATE The project to date has covered the direct methods of solving simultaneous equations. Gaussian Elimination This involves representing the simultaneous equations in an augmented form, performing elementary row operations to reduce the upper triangular form and finally back substituting to form the solution vector. For example, to solve an mxn matrix: Ax = b The aim of the Gaussian elimination is to manipulate the augmented matrix [A|b] using elementary row operations; by adding a multiple of the pivot rows to the rows beneath the pivot row i.e. Rià ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¯Ã†â€™Ã‚   Ri +kRj. Once the augmented matrix is in the row echelon form, the solution is found using back substitution. The following general matrix equation has been reduced to row echelon form: This corresponds to the linear system Rearranging the final solution is given by For all other equations i = n 1, . . ., The operation count and timing the Gaussian Elimination was performed. The total number of operations for an nxn matrix using the Gaussian elimination is with O(N3). LU Factorisation This is where a matrix A finds a lower triangular matrix L and an upper triangular matrix U such that A = LU. The purpose of this lower triangular matrix and upper triangular matrix is so that the forward and backward substitutions can be directly applied to these matrices to obtain a solution to the linear system. In general, L and U is an m x n matrix: L =   U =   For higher order matrices, we can derive the calculation of the L and U matrices. Given a set of n elementary matrices E1, E2,†¦, Enapplied to matrix A, row reduce in row echelon form without permuting rows such that A can be written as the product of two matrices L and U that is A = LU, Where U = En†¦E2E1A, L = E1-1 E2-1†¦En-1   For a general nxn matrix, the total number of operations is O(N3). A Matlab program has been produced to time the LU Factorisation. So far, this method has proven more efficient than the Gaussian Elimination. Cholesky Factorisation This is a procedure whereby the matrix A is factorised into the product of a lower triangular matrix and its transpose i.e. A = LLT   or    =      The Cholesky factorisation is only possible if A is a positive definite. Forward and backward substitution is employed in finding the solutions. The method was also timed at it can be concluded that it is the most effective and efficient direct method for solving simultaneous equations. The indirect methods have been introduced with a short outline of what each method entails. Work Still to be Completed       As from the objectives layed out from the terms of reference, the following are the objectives that are yet to be completed. Week 13 16: Evaluating the convergence rate of the iterative methods in detail as well as finding out which method improves the solution efficiency.   Production of MATLAB programs analysing the different methods and other methods. Over the next 3 weeks, the conditions for convergence will be analysed. One of the most important conditions that will be studied is the spectral radius. This is a condition applied on the indirect methods to determine how fast or slow a method takes to achieve the state of convergence. Moreover, the project will also produce Matlab programs for the iterative methods and employ the spectral radius on these programs to determine the speed of convergence for large sparse matrices. Weeks 17 19: Introduction to the Successive Over-Relaxation (SOR) method and the Conjugate Gradient method. Successive Over-Relaxation method improves the rate of convergence of the Gauss-Siedel method by over-relaxing the solution at every iteration. While the Conjugate Gradient improves the approximated value of x to the exact solution. Matlab programs will be produced for the two methods together with the speed of convergence of different sizes of matrices. Week 20 24:Writing the findings and conclusions of the report, finalising on the bibliography and doing a review of the project as a whole.   Preparing oral and poster presentation.

Essay --

A1. Documents ïÆ' ¼ Fourth quarter balanced scorecard attached with excel spreadsheet. ïÆ' ¼ Balance sheet attached with excel spreadsheet. ïÆ' ¼ Income statement attached with excel spreadsheet. B1. Adequacy of Funds According to Ralph Estes’ Dictionary of Accounting (1981), a pro forma financial statement is described as â€Å"a financial statement created on events and transactions that are assumed, but has not yet happened.† On the other hand, a historical financial statement gives organizations financial measurements on how well the company has performed in the past. For that reason, without financial statements it would be difficult for management, investors, executive board members, and customers to analyze and evaluate how well a company does financially. The format in pro forma financial statements are similar to historical financial statements, but primarily focuses on the future theories and not past factual financial information. Also, a budget is a financial disposition to control future aspects in operations of money. Therefore, having a financial budget is extremely important especially when starting a business. During my simulation, I focused more on using a financial budget throughout to predict how much money I would spend during the expansion process of building the company. I kept my financial risk managed, so the company would not have any debt in the process. Unfortunately, this also backfired against me when I needed to invest more for the future of the company. The two points in my balanced scorecard are how well I did against the average companies. (Below is part of the final Balanced Scorecard for Investment in Future and Financial Risk). Average Typhoon Investment in Future 85.62 1.00 Financial Risk 0.91 1.00 Now... ...tion provided a purchase of the market search, but could have used a better overview of what tools or directions a business owner could use to succeed. There are many ways to achieve the ultimate goal of perfection towards the customer’s expectation in my simulation and benchmarking would have been an impactful improvement to achieve quality assurance goals. That being said, in the simulation there should be some evaluation of defects of the units that were sold to the customers. In a few of the quarters, feedback review of the quality of the product would also be another part of the simulation. Therefore, the quality assurance from the customer’s standpoint is vital in order to gain revenue and manufacturing growth for a company. Benchmarking would be an impactful improvement towards new business owners for this simulation to achieve quality assurance goals.

Things Fall Apart Essay -- essays research papers

Things Fall Apart By Chinua Achebe Bantam Doubleday Dell Publishing Group, Inc. New York, New York Copyright 1959 Author Biography Albert Chinualumogu Achebe, or Chinua Achebe, was born November 16, 1930, in Ogidi, Nigeria. His parents were Janet N. Achebe, and Isaiah Okafo, a teacher in a missionary school. Mr. Achebe was educated at the University College of Ibadan, but also attended Government College in 1944. He wrote his first novel, Things Fall Apart, in 1958. During the Biafran War, he was in the Biafran government service. After the war, Mr. Achebe taught at several universities, both in Nigeria and in the United States. In 1967 he cofounded a publishing company with a fellow author, Christopher Okigbo. Mr. Achebe’s later works include No Longer at Ease, Arrow of God, and Anthills of the Savannah. A serious car accident left Mr. Achebe paralyzed from the waist down in 1990. The majority of his novels deal with Africans struggle to free themselves from European colonial and political influences, due to his experiences in the Biafran War and the Nigerian Civil War. Main Characters Okonkwo- Okonkwo is the main character in the novel. He is a distinguished man in the clan, and has been since a young age, when he established himself as a skilled wrestler. He had a very lazy father, and this was a source of much embarrassment to him, so to overcome this, he is an overbearing husband, and father. He feels that he always has to prove that he is different than his father, which is eventually his downfall. Unoka- Unoka is Okonkwo’s father. He was a very lazy man and always an embarrassment to his family, especially his son. He is the reason that Okonkwo is so scared of failing. Nwoye- Nwoye is Okonkwo’s son, and he is lazy and complacent, like his grandfather. Okonkwo’s way of changing this is to be especially hard on him, which drives him further away, eventually to join the missionaries. Ezinma- Ezinma is Okonkwo’s daughter, and he is proud of her, even though he won’t show this because he thinks that it is a weakness. She is smart and pretty. Okonkwo wishes that she were a boy so that he could pass on his knowledge and fortune to her. Mr. Brown- Mr. Brown is the first missionary to arrive in Umuofia. He is nice enough to the clan, so they decide to let him stay, but soon enough he brings others, both from the clan and from outside, into the c... ...alk to you.† This is an important excerpt from the book because it shows how the natives tried to negotiate with the white men peacefully. All they wanted was for the clan to return to the way it was before the white men came, and they even agreed to let the white men stay and practice their religion as long as they didn’t bother anyone. But the Christians had to have everything, so there was a conflict. 5.Obierika is talking. Chapter Twenty Five Obierika, who had been gazing steadily at his friend’s dangling body, turned suddenly to the District Commissioner and said ferociously: â€Å" That man was one of the greatest men in Umuofia. You drove him to kill himself; and now he will be buried like a dog†¦.† He could not say anymore. His voice trembled and choked his words. This quote is significant because it shows the falling apart of the clan as a whole. Okonkwo was a one of the strongest men in Umuofia, both in physical strength and mental determination. His taking his own life is a sign that the natives are losing the battle against the stronger white men. If he is not strong enough to endure the white men, than it is obvious that no one else in Umuofia will last much longer.

Evaluating The War in Iraq :: War, Iraq

Evaluating The War in Iraq Is the war in Iraq right? Is this not a form of terrorism?, to have U.S. troops stationed in Iraq for six year now. How about pushing our system of government onto another country, isn’t that a form of terrorism? Isn’t this wrong of the US and our fellow Americans to still believe that we’re doing the right thing, when we’ve never received a straight answer as to why we’re even in another country fighting? These are all questions we should be asking, and the answer should be, that it’s morally wrong of the U.S. to be doing so. However, many of us Americans are too blind to see this, to ask these questions, and to do something powerful about it. Many seem to look at it as though, the middle east has done wrong to us, so we must do wrong to them. In addition, after the September 11th attacks, the United States government took it upon it’s self to punish those terrorist held responsible for it’s attacks. Among these people are: Saddam Hussein, Osama bin Laden, and anyone that represented the Al-Quaeda organization. Nevertheless after searching out these terrorist, we took them into our country, into our prison systems, and into our courts to hold justifications over their heads. Each one dying for the terror they imprinted into our once great nation. However is this really morally right? To take away life?, I don’t believe so, but our government and many others do. This is not a justification for any action. Consequently, after finding and executing all of our said terrorist, it wasn’t enough. The U.S. took it upon it’s self to begin an unexplained war with the middle east on March 19th, 2003. And what is the reason for this? Honestly there is no true reason for this. The U.S. has been given so many reasons that the government tried to justify and that us, Americans bought into. For instance, at first we went to Iraq to find WMD’s. However there was no proof of this only suspicion. And after said invasion, there was still no evidence of WMD’s. So, moving forward, the U.S. quickly kept troops stationed in Iraq for a second reason. Which accordingly, the number of terrorist were growing. Namely they have grown and still remain at large. Finally, there were more foolish reasons about oil and other nonsense that could not reach any justification.

Zoe’s Tale PART I Chapter Ten

There were two messages on my PDA after dinner that evening. The first was from Gretchen. â€Å"That Magdy character tracked me down and asked me out on a date,† it read. â€Å"I guess he likes girls who mock the crap out of him. I told him okay. Because he is kind of cute. Don't wait up.† This made me smile. The second was from Enzo, who had somehow managed to get my PDA's address; I suspect Gretchen might have had something to do with that. It was titled â€Å"A Poem to the Girl I Just Met, Specifically a Haiku, the Title of Which Is Now Substantially Longer Than the Poem Itself, Oh, the Irony,† and it read: Her name is Zoe Smile like a summer breeze Please don't have me cubed. I laughed out loud at that one. Babar looked up at me and thumped his tail hopefully; I think he was thinking all this happiness would result in more food for him. I gave him a slice of leftover bacon. So I guess he was right about that. Smart dog, Babar. After the Magellan departed from Phoenix Station, the colony leaders found out about the near-rumble in the common area, because I told them about it over dinner. John and Jane sort of looked at each other significantly and then changed the subject to something else. I guessed the problem of integrating ten completely different sets of people with ten completely different cultures had already come up in their discussions, and now they were getting the underage version of it as well. I figured that they would find a way to deal with it, but I really wasn't prepared for their solution. â€Å"Dodgeball,† I said to Dad, over breakfast. â€Å"You're going to have all us kids play dodgeball.† â€Å"Not all of you,† Dad said. â€Å"Just the ones of you who would otherwise be picking stupid and pointless fights out of boredom.† He was nibbling on some coffee cake; Babar was standing by on crumb patrol. Jane and Savitri were out taking care of business; they were the brains of this particular setup. â€Å"You don't like dodgeball?† he asked. â€Å"I like it just fine,† I said. â€Å"I'm just not sure why you think it's an answer to this problem.† Dad set down his coffee cake, brushed off his hands, and started ticking off points with his fingers. â€Å"One, we have the equipment and it fits the space. We can't very well play football or cricket on the Magellan. Two, it's a team sport, so we can get big groups of kids involved. Three, it's not complicated, so we don't have to spend much time laying out the ground rules to everyone. Four, it's athletic and will give you guys a way to burn off some of your energy. Five, it's just violent enough to appeal to those idiot boys you were talking about yesterday, but not so violent that someone's actually going to get hurt.† â€Å"Any more points?† I asked. â€Å"No,† Dad said. â€Å"I've run out of fingers.† He picked up his coffee cake again. â€Å"It's just going to be that the boys are going to make teams with their friends,† I said. â€Å"So you'll still have the problem of kids from one world staying with their own.† â€Å"I would agree with this, if not for the fact that I'm not a complete idiot,† Dad said, â€Å"and neither is Jane. We have a plan for this.† The plan: Everyone who signed up to play was assigned to a team, rather than allowed to pick their own team. And I don't think the teams were entirely randomly assigned; when Gretchen and I looked over the team lists, Gretchen noted that almost none of the teams had more than one player from the same world; even Enzo and Magdy were put on different teams. The only kids who were on the same â€Å"team† were the Kyotoans; as Colonial Mennonites they avoided playing in competitive sports, so they asked to be the referees instead. Gretchen and I didn't sign up for any teams; we appointed ourselves league managers and no one called us on it; apparently word of the intense mockery we laid on a wild pack of teenage boys had gotten around and we were feared and awed equally. â€Å"That makes me feel pretty,† Gretchen said, once such a thing was told to her by one of her friends from Erie. We were watching the first game of the series, with the Leopards playing against the Mighty Red Balls, presumably named after the game equipment. I don't think I approved of the team name, myself. â€Å"Speaking of which, how was your date last night?† I asked. â€Å"It was a little grabby,† Gretchen said. â€Å"You want me to have Hickory and Dickory talk to him?† I asked. â€Å"No, it was manageable,† Gretchen said. â€Å"And besides which, your alien friends creep me out. No offense.† â€Å"None taken,† I said. â€Å"They really are nice.† â€Å"They're your bodyguards,† Gretchen said. â€Å"They're not supposed to be nice. They're supposed to scare the pee out of people. And they do. I'm just glad they don't follow you around all the time. No one would ever come talk to us.† In fact, I hadn't seen either Hickory or Dickory since the day before and our conversation about touring the Obin planets. I wondered if I had managed to hurt their feelings. I was going to have to check in on them to see how they were. â€Å"Hey, your boyfriend just picked off one of the Leopards,† Gretchen said. She pointed at Enzo, who was playing in the game. â€Å"He's not my boyfriend, any more than Magdy is yours,† I said. â€Å"Is he as grabby as Magdy is?† Gretchen asked. â€Å"What a question,† I said. â€Å"How dare you ask. I'm madly offended.† â€Å"That's a yes, then,† Gretchen said. â€Å"No, it's not,† I said. â€Å"He's been perfectly nice. He even sent me a poem.† â€Å"He did not,† Gretchen said. I showed it to her on my PDA. She handed it back. â€Å"You get the poetry writer. I get the grabber. It's really not fair. You want to trade?† â€Å"Not a chance,† I said. â€Å"But he not's my boyfriend.† Gretchen nodded out to Enzo. â€Å"Have you asked him about that?† I looked over to Enzo, who sure enough was sneaking looks my way while moving around the dodgeball field. He saw I was looking his way, smiled over at me and nodded, and as he was doing that he got nailed righteously hard in the ear by the dodgeball and went down with a thump. I burst out laughing. â€Å"Oh, nice,† Gretchen said. â€Å"Laughing at your boyfriend's pain.† â€Å"I know! I'm so bad!† I said, and just about toppled over. â€Å"You don't deserve him,† Gretchen said, sourly. â€Å"You don't deserve his poem. Give them both to me.† â€Å"Not a chance,† I said, and then looked up and saw Enzo there in front of me. I reflexively put my hand over my mouth. â€Å"Too late,† he said. Which of course made me laugh even more. â€Å"She's mocking your pain,† Gretchen said, to Enzo. â€Å"Mocking it, you hear me.† â€Å"Oh, God, I'm so sorry,† I said, between laughs, and before I thought about what I was doing gave Enzo a hug. â€Å"She's trying to distract you from her evil,† Gretchen warned. â€Å"It's working,† Enzo said. â€Å"Oh, fine,† Gretchen said. â€Å"See if I warn you about her evil ways after this.† She very dramatically focused back on the game, only occasionally glancing over and grinning at me. I unhugged from Enzo. â€Å"I'm not actually evil,† I said. â€Å"No, just amused at the pain of others,† Enzo said. â€Å"You walked off the court,† I said. â€Å"It can't have hurt that much.† â€Å"There's pain you can't see,† Enzo said. â€Å"Existential pain.† â€Å"Oh, boy,† I said. â€Å"If you're having existential pain from dodgeball, you're really just doing it wrong.† â€Å"I don't think you appreciate the philosophical subtleties of the sport,† Enzo said. I started giggling again. â€Å"Stop it,† Enzo said mildly. â€Å"I'm being serious here.† â€Å"I so hope you're not,† I said, and giggled some more. â€Å"You want to get lunch?† â€Å"Love to,† Enzo said. â€Å"Just give me a minute to extract this dodgeball from my Eustachian tube.† It was the first time I had ever heard anyone use the phrase â€Å"Eustachian tube† in common conversation. I think I may have fallen a little bit in love with him right there. â€Å"I haven't seen the two of you around much today,† I said to Hickory and Dickory, in their quarters. â€Å"We are aware that we make many of your fellow colonists uncomfortable,† Hickory said. It and Dickory sat on stools that were designed to accommodate their body shape; otherwise their quarters were bare. The Obin may have gained consciousness and even recently tried their hand at storytelling, but the mysteries of interior decoration still clearly eluded them. â€Å"It was decided it would be best for us to stay out of the way.† â€Å"Decided by whom?† I asked. â€Å"By Major Perry,† Hickory said, and then, before I could open my mouth, â€Å"and we agree.† â€Å"You two are going to be living with us,† I said. â€Å"With all of us. People need to get used to you.† â€Å"We agree, and they will have time,† Hickory said. â€Å"But for now we think it's better to give your people time to get used to each other.† I opened my mouth to respond, but then Hickory said, â€Å"Do you not benefit from our absence at the moment?† I remembered Gretchen's comment earlier in the day about how the other teens would never come up to us if Hickory and Dickory were always hanging around, and felt a little bit ashamed. â€Å"I don't want you to think I don't want you around,† I said. â€Å"We do not believe that,† Hickory said. â€Å"Please do not think that. When we are on Roanoke we will resume our roles. People will be more accepting of us because they will have had time to know you.† â€Å"I still don't want you to think you have to stay in here because of me,† I said. â€Å"It would drive me crazy to be cooped up in here for a week.† â€Å"It is not difficult for us,† Hickory said. â€Å"We disconnect our consciousnesses until we need them again. Time flies by that way.† â€Å"That was very close to a joke,† I said. â€Å"If you say so,† Hickory said. I smiled. â€Å"Still, if that's the only reason you stay in here – â€Å" â€Å"I did not say it was the only reason,† Hickory said, interrupting me, which it almost never did. â€Å"We are also spending this time preparing.† â€Å"For life on Roanoke?† I asked. â€Å"Yes,† Hickory said. â€Å"And how we will be of best service to you when we are there.† â€Å"I think by just doing what you do,† I said. â€Å"Possibly,† Hickory said. â€Å"We think you might be underestimating how much different Roanoke will be from your life before, and what our responsibilities will be to you.† â€Å"I know it's going to be different,† I said. â€Å"I know it's going to be harder in a lot of ways.† â€Å"We are glad to hear that,† Hickory said. â€Å"It will be.† â€Å"Enough so that you're spending all this time planning?† I asked. â€Å"Yes,† Hickory said. I waited a second to hear if anything else was coming after that, but there wasn't. â€Å"Is there anything you want me to do?† I asked Hickory. â€Å"To help you?† Hickory took a second to respond. I watched it to see what I could sense from it; after this many years, I was pretty good at reading its moods. Nothing seemed unusual or out of place. It was just Hickory. â€Å"No,† Hickory said, finally. â€Å"We would have you do what you are doing. Meeting new people. Becoming friends with them. Enjoying your time now. When we arrive at Roanoke we do not expect you will have as much time for enjoyment.† â€Å"But you're missing out on all my fun,† I said. â€Å"You're usually there to record it.† â€Å"This one time you can get along without us,† Hickory said. Another near joke. I smiled again and gave them both a hug just as my PDA vibrated to life. It was Gretchen. â€Å"Your boyfriend really sucks at dodgeball,† she said. â€Å"He just took a hit square on his nose. He says to tell you the pain isn't nearly as enjoyable if you're not around to laugh at it. So come on down and ease the poor boy's pain. Or add to it. Either works.†

The Good Friday Agreement

The conflict about Northern Ireland The importance of the Good Friday Agreement Introduction: The Irish Island has for centuries been characterized by a conflict between the British and the Irish, and has political, economical and religious roots. After Ireland became independent in the early 19th century, the battles continued in Northern Ireland, who was left under British rules. Irish Catholics in Northern Ireland who had been discriminated for a long time by British Protestants started using weapons and violence exploded.In the years between 1969 and 1998, more known as â€Å"the Troubles†, were over 3600 people killed in the conflict, among them nearly 2000 civilians. Since 1998 a peace agreement is signed between the parties called the Good Friday Agreement, but Northern Ireland is by some means still a segregated county with Catholics and Protestants living apart from each other (Pettersson T, and Simmons, D. 2010). The power struggle on the Irish Island has been a stru ggle between Catholics who wished to see a unified Ireland, and by Protestants who opposed for Northern Ireland to remain under British Rule.The Good Friday agreement was signed in 1998 and can be seen as the turning point in the conflict about Northern Ireland. In 1921 the Anglo-Irish treaty was signed, and after centuries of British rule, 26 of 32 counties of Ireland gained independence. The 6 remaining counties formed Northern Ireland, which continued to be governed within the United Kingdom. A majority of the population in Northern Ireland were Protestants and did not want to be a part of Ireland (leonidassthlm 2009).From the period 1921 to 1972 the developed government in Northern Ireland operated with autonomy from London, and power remained exclusively to the Unionist party which had support from the Protestant majority community that favoured to be a union with Britain. The Catholic minority in the country supported the Nationalist party, and they were not allowed to have a role in government, and were discriminated in many areas such as employment, voting rights and housing (dfa. ie 2 June 2012). In the 1960s, a civil rights movement was formed with both Catholics and Protestants; it discussed the unfair conditions for Catholics inNorthern Ireland. The movement protested against the unfair conditions, and was sometimes met with police brutality. Every summer Protestants celebrated a former king’s battle, in which he had won over his Catholic enemy (leonidassthlm 2009). In 1969 non-violent campaigners for civil rights protested against the celebration they thought represented discrimination of Catholics (leonidassthlm 2009). They were met with an inhibitory and hostile response from the authorities, pushing Northern Ireland in a sustained period of political crisis.The years that followed was a turbulent and violent time in Northern Ireland, and many people lost their lives in the conflict, including many civilians (www. bbc. co. uk 2 June 2012) . The Catholic Army IRA (Irish Republic Army) had been inactive up until the late 1960s, but after â€Å"the Troubles† started in 1969 they became more and more active in what they believed in. IRA fought for Catholic civil rights and a unified Ireland (leonidassthlm 2009). IRA was not the only group that fought for what they believed in.Protestant loyal groups grew stronger with tens of thousands of members that fought for Northern Ireland to still belong to Britain. Violence escalated and it became harder for the British army, who was there to support the Protestant parties, to control the violence. Both sides used violence and weapons against each other to reach their goals. One Sunday in 1972 during a non-violent demonstration for human rights were 13 people killed by British soldiers. This Sunday was later called the â€Å"Bloody Sunday† (Pettersson, T and Simmons, D. 010). The support for IRA grew after the Bloody Sunday, and more British troops were placed in No rthern Ireland to prevent the violence. However, it can be questioned how much the British troops really did to prevent the violence, because it is a matter of fact that they were British soldiers, and that Britain did not want to let go of Northern Ireland to make it a unified Ireland (www. landguiden. se 2 June 2012). Both sides were guilty of violence and massacres and one of the worst attacks after the Bloody Sunday was the Bloody Friday.IRA blasted 20 car bombs in Belfast and 9 people died in the attack. About 500 people died in the year of 1972 caused by terror attacks. Civilians in Northern Ireland were getting tired of the violence that had escalated a long time ago, and wished for a change to come. They had seen family and friends getting killed in demonstrations and wanted an end to the violence that had been going on for centuries (leonidassthlm 2009). From 1974 to 1994 were numerous attempts made to try and solve the conflict in Northern Ireland.All attempts were made fr om London, and even though many people were tired of the violence and the conflict; was it still hard to gain support for a solution that would mean sharing of power between Catholics and Protestants. But there was some progress in the attempt of solving the conflict between Catholics and Protestants. The British Parliament made a deal with the independent Ireland in 1985, the deal meant that Ireland would be asked in questions that had anything to do with Northern Ireland. The deal had positive effects and a close cooperation between Ireland and England arose.Ireland accepted Northern Ireland as being part of Britain as long as a majority of the people wanted it (Pelling, J. 18th May 2008). After many years of violence a peace process were finally starting to take place. In 1994, IRA and its Protestant enemies called for a cease-fire. After numerous failed attempts to start the talks of a peace agreement, IRA broke the cease-fire after 17 months when they blasted a car bomb in Lond on that killed two people and hurt 39. It took 18 months after this attack until a new cease-fire was agreed (Pettersson, T and Simmons, D. 010). At last, after years of hope, crushed expectations and new terror attacks, a peace agreement was finally signed. The Good Friday Agreement was signed on 10 April 1998 and was aimed to form the lasting settlement following the cease-fire in Northern Ireland (bbc. co. uk 2004). The Agreement is seen as a turning point in the conflict about Northern Ireland and when the agreement was presented to the public, a majority of people allowed to vote supported the proposition (Pettersson, T and Simmons, D. 2010).The breakthrough the agreement represented was that, for the very first time in Northern Ireland’s history, it brought all the main political parties represented in Northern Ireland- those groups linked to paramilitary as well as those who were committed to constitutional means into the same negotiation forum and obtained a new set o f arrangements for democratic governance. The purpose of the agreement was to end the violent conflict and to find a political compromise that would accord for â€Å"parity of esteem† to both the nationalist and unionist political views in Northern Ireland (Fahey, T. 007). At the heart of the Good Friday Agreement lies the statement that it was made for the people of Ireland alone: â€Å"By agreement between the two parts respectively, and without external impediment, to exercise their right of self-determination on the basis of consent, freely and concurrently given, North & South, to bring about a united Ireland, if that is their wish, accepting that this right must be achieved & exercised subject to the agreement and consent of a majority of the people of Northern Ireland† (Fraser, T,G. 1999 p. 83).The Good Friday Agreement has provided the divided society in Northern Ireland to settle its differences, and a model of governance based on the â€Å"parity of esteemâ €  has replaced the old system with majority rules. Unionists and nationalists have both agreed on proportional inclusion of each group in the government, and this is the first time such an agreement have been accepted by both parties. The voting system now works to ensure that either unionists or nationalists can vote against each other’s group interests. (www. bbc. co. uk 2 June 2012).The Agreement respects both parties’ goals to join the Irish Republic or to remain being a part of the United Kingdom. The agreement is divided into three strands: strand one is dealing with institutional arrangements in Northern Ireland, strand two deals with the relationship between Ireland and Northern Ireland and strand three deals with the relationships between the United Kingdom, Ireland and Northern Ireland. As mentioned before, the agreement focus mainly on the people of Ireland, and equality and rights lies at the centre of the Good Friday Agreement.The agreement protects hu man rights in Northern Ireland, as well as equality, mutual respect and partnership. The human rights commission and the equality commission are the two institutions in Northern Ireland responsible for ensuring that political, social, civil and cultural rights of every civilian are respected (www. bbc. co. uk 2 June 2012). The Good Friday agreement is such an important part in the history of Northern Ireland, and it is very interesting to see that it took so many years for it to be formed, and also that when it was settled the majority of the population voted yes to the proposition of the agreement.This proves that the majority of the population were at this time exhausted by the violent conflicts, and both Catholics and Protestants actually wanted it to end. Many years of bloody violence have left a deeply segregated society in Northern Ireland. The Good Friday agreement appreciates the importance of talking about the victims of the conflict that suffered and still are suffering fr om it. The agreement is committed to nurture a culture of tolerance to the discriminated community through promotion of mixed housing, integrated education and the support of integrated employment in companies (bbc. o. uk 2 June 2012). Northern Ireland was ruled from London until the peace agreement was signed, and by 1998 the peace process had come so far that it was possible to create a Northern Ireland government with both nationalists and unionist groups that would have equal rights in the community. The first years after the implementation of the Good Friday Agreement were shaky for the new government and the British sometimes went in and took over the governmental work.But the peace process were going the right way and in 2005 it had a breakthrough when IRA choose to give up their weapons and volunteers were instructed to form political and democratic agendas with only peaceful means. (www. dn. se October 14th 2002). In 2007 were the power of government divided between Protest ants and Catholics, but although the power is shared between the two is Northern Ireland still segregated in some parts (Pelling, J. 18th May 2008).Sharing of power have been important for the peace agreement to last, but there are a number of people that disagree with this solution and violence have occurred even after the peace agreement was signed. However, Northern Ireland is a good example where people have become so tired of conflicts that they step by step is building the ground for a lasting peace. Conclusion: It is truly amazing that a conflict that lasted for so long and was so deeply rooted in people’s hearts and minds, came to a solution because of the Good Friday Agreement.As discussed before in the essay, everything was not easy after the implementation of the agreement and some issues were still there. But the facts remain that the Good Friday Agreement provided Northern Ireland with something it had never experienced before: equality rights for everyone indepe ndent on religion, mutual respect and human rights. For me that have grown up in a community with different religions and nationalities it is hard to understand how it must have been for (mainly) Catholics before the agreement.Before the Good Friday Agreement Catholics were discriminated in many areas and today there is no change of being stopped by the police, army or someone else because of someone’s religion. I believe that the main aim of the peace agreement was to divide the power equally between Catholics and Protestants as well as eliminate discrimination. This essay have focused on the importance of the Good Friday Agreement in Northern Ireland in particular, but I believe it is a good example that a conflict that are centuries old, can end on good terms for all the parties involved.I am thinking of younger conflicts around the word that can look at the Good Friday Agreement for inspiration and hope of a better future. References books: Fahey, T. (2007) Conflict and C onsensus: A Study of Values and Attitudes in the Republic of Ireland and Northern Ireland. Boston: Brill Academic Publishers. Fraser, T, G. (1999) Ireland in Conflict 1922-1998. Chapter 9, p. 83. Florence, KY, USA: Routledge. Internet Sources: BBC. (2012) The Good Friday Agreement [online] BBC. Available from: http://www. bbc. co. uk/northernireland/schools/agreement/. [Accessed 2 June 2012]Department of foreign affairs and trade. (2011) March 25. The Good Friday Agreement [online]. Ireland: Department of foreign affairs and trade. Available from: http://www. dfa. ie/home/index. aspx? id=335. [Accessed 2 June 2012] Landguiden (2011) Northern Ireland [online]. Stockholm: Landguiden. Available from: http://www. landguiden. se/Konflikter/Nordirland Pelling, J. (2008) May 18. Nordirland fortfarande delat (Northern Ireland is still divided). [online]. Available from: http://www. svd. se/nyheter/utrikes/nordirland-fortfarande-delat_1263273. svd [Accessed 2 June 2012]Pettersson, T and Simm ons, D. (2010) August 17. Northern Ireland [online]. Uppsala: Sakerhetspolitik. Available from: http://www. sakerhetspolitik. se/Konflikter/Nordirland/Fordjupning/. [Accessed 1 June 2012] TT-Reuters (2002) October 14. Storbritannien tog over styret av Nordirland (Great Britain takes over governmental work in Northern Ireland). [online]. Available from: http://www. dn. se/nyheter/varlden/storbritannien-tog-over-styret-av-nordirland [Accessed 2 June 2012] Reference videos: BBC (2012). Importance of the Good Friday Agreement [Online video]. Available from: < http://www. bbc. co. k/learningzone/clips/importance-of-the-good-friday-agreement-1998/11507. html> [accessed 3 June 2012] Youtube/Leonidassthlm (2009). Varldens Konflikter: Nordirland del 1 [Online video]. Available from: [accessed 2 June 2012] Youtube/Leonidassthlm (2009). Varldens Konflikter: Nordirland del 2 [Online video]. Available from: [accessed 2 June 2012] Youtube/Leonidassthlm (2009). Varldens Konflikter: Nordirland de l 3 [Online video]. Available from: [accessed 2 June 2012]

On Teenagers and Tattoos

The Impact on Society of Teenage Tattooing The Impact on Society of Teenage Tattooing Does the tattoo define the person, or does the person define the tattoo? In modern society tattoos are widely accepted except when applied to the skin of an adolescent. Adolescents with tattoos face judgment from a variety of people such as authoritative figures, parents, and their peers. This article (On Teenagers and Tattoos, by Andres Martin, MD. ) provides examples of how society views adolescents with tattoos. Tattoos are something we see on people on an everyday basis, but on adolescents, it is not very common.Many adults believe that those in the younger generation sometimes get tattoos to enrage affronts to their authority. Parents in general do not approve of their children decorating their bodies with modifications such as tattoos because of their irreversible and permanent nature. Like makeup, fashion or hairstyles tattoos can also be just another way to fit in with their peers. When give n the chance it is important to understand the motivations and significance of a tattoo before making an erroneous judgment.Tattooing is a way of fitting into a peer group or expressing one’s own individuality. Adolescents often turn to tattooing as a way to take back some control of their evolving bodies as well as their lives. When an adolescent feels that there is a lack of stability in his life (such as divorce, abandonment, and repeated family relocations) he may feel that getting a tattoo may return a sense of control and stability into his life. Adolescents are often influenced by peers to get a tattoo but do not put any thought into its permanence or how they may feel about it in the future.Author Andres Martin says â€Å"The frequency of self-made tattoos among hospitalized, incarcerated, or gang-affiliated youth suggests such motivations: a sense of stability may be a particularly dire need under temporary, turbulent or volatile conditions. † In every argumen t there are two sides to be heard, and the other side in this case is the adolescents. Adolescents believe in expressing themselves through art. They also believe tattoos are a way of representing their individuality. I believe that teenagers get tattoos for various reasons that are important to the person.Some get them for personal reasons such as a memorial tattoo for a deceased family member, or a ribbon to show support for someone fighting their battle with cancer. An inspirational quote such as a bible verse, poem, or a song lyric may also be another choice for the adolescents tattoo. Fantasy characters are also a popular choice. On the other hand there are various negative reasons teenagers get tattoos as well; for instance, to defy their parent’s authority, to represent a gang affiliation, to draw attention to themselves, and sometimes as a dare.I have observed that some older people have an aversion to tattoos on teenagers as opposed to some young parents that find it acceptable. Older people may assume that the adolescents tattoo is gang related or that they are a troubled youth. Some people believe that the parents of an adolescent with a tattoo may be neglectful or unaware of what is going on in their child’s life. Some older people are against body modifications of any form and look down on those who have them. After reading through this article I found that it thoroughly explains the pros and cons of adolescents with tattoos.Although I do respect the writers view on the subject, I disagree. I personally believe that as a part of growing up a teenager should be allowed to get a tattoo but only after being fully informed of the consequences that getting a tattoo may bring. Some of the problems that might ensue are possible rejection from a specific field of work for the visibility of a tattoo, a wrong assumption about the character of a person with a tattoo, or even later in life having to cover a tattoo or get it removed because your own personal feeling about it has changed.I personally have been debating on getting a tattoo myself, although my family doesn’t approve It’s my body and I will make the final decision. I am very well aware that in five maybe ten years from now I could quite possibly hate my tattoo and regret not listening to my family. I am also aware of how expensive and painful laser removal is but I’m prepared to suffer the consequences if and when I decide to get a tattoo. Most adolescents don’t think beyond the tattoo itself or its ramifications Martin, Andres. Baker College Composition. Revised Edition ed. Boston Ma: Pearson Learning Solutions, n. d. 320-23. Print