In: Science

Submitted By nemoz3122

Words 2895

Pages 12

Words 2895

Pages 12

INTRODUCTION

Background Of the Study

In mathematics, optimization problem is a problem where it consists of maximizing or minimizing a real function by systematically choose an input values within an allowed set and compute the value of the function. An additional, it also means solve the problem so that we can the goal as quickly as possible without wasting a lot of resources.

Optimization also can be deviating from a target by the smallest possible margin. Generally, a large area of applied mathematics is comprised by the optimization theory and techniques to other formulations. In the simple case, optimization is like finding a good value or a best available value of some problems given a defined domain, including a many of different types of objectives functions and different types of domains.

In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the scalar field, and whose the magnitude is that rate of increase. The variation in space of any quantity can be represented by a slope in simple terms. The gradient is like represents the steepness and the direction of the slope. The gradient or gradient of a scalar function f〖:R〗^n→R^1 is denoted by ∇f or ∇ ⃗f where ∇ denotes the vector of the differential operator.

Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and this matrix is later named after him. Hessian matrix is the matrix of second derivatives of a multivariate function. In mathematics it means the gradient of the gradient of a function. Hessian matrix is relevant in many places such as in economy too.

Let a real-valued function f〖:R〗^n→R^1 be given and if all the second partial derivatives of f exist and are continuous over the domain of the function, then the Hessian matrix of f is

H(f)_ij (x)=D_i D_j f(x)=(δ^2…...

...The Case of the Filing System I had to really give this assignment some thought since most of my problem solving decision have to do with how to make my job more efficient. I had to consider if any of my decision-making or problem-solving solutions had ever affected the culture of the company in any way. Since, I have never held an official position as a manager or had the ability to manage a project within a company I kept running into a road block in deciding what decision or problem I had experienced in my current or pass workplace that I could discuss. In thinking about this I realized that sometimes the decision-making or problem-solving that can have a big impact on the company is a big way can be the smallest contribution an individual employee can make. In my experience in working, I have realized that you are only as effective as you are organized. In saying this, my discussion is based on the filing system at a pass job that was a huge problem for the accounting department. The current filing system in the accounts payable department was time consuming and not efficient. It was next to impossible to find files or file anything without fear of never finding your files. A major problem with the current filing system was that you had too many years in one location. It is very important when working in any area of accounting that you keep accurate records for auditing reasons. These records not only affect the individual employee, but the company......

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...University of Phoenix | Solving a Problem | Wedding Day Disaster | | Rachel Bronson | 12/10/2012 | | Step One: Finding a Problem Challenges are something that doesn’t always have to be found, since occasionally they will happen in the shape of an obvious issue or problem. In other examples, they won't always present in this way, they may offer as a chance to improve a present situation. It's a good habit to be prepared for as well as continuously searching for a problem to fix. Step Two: Stating the Problem Find the best method to express the issue or problem. While doing so, think about using as many solutions as is possible since every solution will open up different doors as well as offer different suggestions. Selecting the right solution is the most difficult part of this process, and it may be better to wait to determine which solution to use until later in the creative process when we have got more facts as well as suggestions available. Step Three: Research the Problem Analyze and get any kind of connected information to deal with the issue or problem at hand. Appropriate investigative ways incorporate thinking about experiences, getting any related information through recently experience, getting interviews of people educated on the subject matter, or old-fashioned study. Getting any information to help come up with a solution will only benefit you in the long run. Step Four: Come up with a Solution Discuss and gather as many......

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...Problem Solving Renae L. Hayworth BEH225 Janurary 20, 2012 Ann Reed Problem Solving “Trial and Error, information retrieval, algorithms, and heuristics an all assist at problem solving. There are two ways most people think. Divergent thinking is usually someone who is open minded and can think outside the box. Convergent thinking can be thought of thinking inside the box or narrow minded thinking” (Morris & Maisto, 2010). When I try to solve a problem, I tend to think outside the box. However, my methods are never the same, depending on the situation. Trial and error are great if it is an easy problem. For example, buying new pants, I know this can be an obstacle. When I was young I could just go and pick out my size and leave. I never had to try on a pair of paints because my body didn’t change much. As I have gotten older and now have a child, my body has changed. I know have to grab pants that I think will fit and try them on. Not all woman jeans are made the same; some sizes are smaller or bigger than other brands. This can be a struggle and therefore, I need to use trial and error. I grab let’s say three pairs of pants and one will fit. This will be the ones I buy. Information retrieval is something I think of as when I studied for my driver’s license. I needed experience but I needed to study the driver’s manual. This helped me learn the rules of the road, because these rules of the road will keep me safe. Also, my grandfather has given me tips......

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...PROBLEM FINDING AND PROBLEM SOLVING “The most important part of any business or invention is that it must solve a real need and a real problem. Observe the world around you – everything you do, and especially everything you don’t like to do – solve a real problem and the world is yours.” - Aaron Patzer, Founder, Mint.com There is a whole problem process, which involves finding the problem, shaping it and then solving it. Problem finding means discovering something that troubles you and your society at large. It requires intellectual vision and insight into what is missing. Problem shaping, is then breaking it into parts, analyzing the problem and looking at it from different perspectives. Once all that is done, you are left with the simple process of solving the issue to the best of your ability. So, how do we get started? NAILING A PROBLEM “The problem is we don’t understand the problem” ~ Paul MacCready. You need a solid idea for a business and it doesn’t have to be cool, it just needs to provide a solution to a common problem. In my experience, problems in need of solutions have always been preceded with statements like “there needs to be a way to …” and “I wish there was a way to …”, however, that’s only the tip of the iceberg. There are a lot of problems to be solved, the key is to find them before someone else can. 1. Start with Why Almost everyone has seen Simon’s Ted Talk. Most people like it, impart it, and the go back to building products that......

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...Solve a Problem Paper The creative process applies four stages of solving a problem. These stages are; searching for challenges, identifying the problem, investigating the problem, and producing ideas. The first stage of critical thinking is to search for challenges. Some challenges are apparent and do not require much to identify, others are “so small or subtle that few people notice them” (Ruggiero, 2009). The second stage is to identify the problem. In this stage is to receive and absorb problem in a way that will allow the most solutions. The third stage is investigating the problem. This stage is a fact finding stage. It permits the gathering of information either experienced or gaining new information through exploration in order to solve the problem, which brings us to producing ideas; the fourth and final stage. The purpose of producing ideas is to compose as many ideas that lead to solving the problem. I used six techniques to develop curiosity in my search. I was observant to what is occurring around me, looked for and understood when things could be improved, recognized when something was not satisfying, searched for the reason the problem occurred, identified the impact to others, and finally noticed the potential for controversy. My problem lies with spending money, more specifically eating out every day of the week for breakfast, lunch and dinner. I do not enjoy cooking; however, eating out has become very expensive. On average I spend......

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... Creative Techniques for Problem Solving Korbinian Dennerlein H0954189 Strategy, Innovation & Management Control Vienna University of Economics and Business Course: 5876 Personal skills -‐ Problem solving Instructor: Desislava Vacheva (BSc.MSc.) Korbinian Dennerlein H0954189 CREATIVE TECHNIQUES Innovation and creativity foster and generate a crucial resource in today’s constantly changing business environment. It is essential to handle this resource carefully and to act target oriented in order to gain a sustainable competitive advantage. Nevertheless, it is important not to lose focus on the core business and to keep the balance between exploitation and exploration. Therefore, it is important to apply creativity in the right way. This application should preserve the stable and working organization from being too chaotic. A general way to divide the various approaches is to cluster them into divergent and convergent techniques. Divergent techniques aim at generating a high number of ideas in order to have a wide range of possible solutions to choose from. In comparison, convergent techniques deal with a certain problem and search step-by-step for a single right solution.1 In the beginning of this paper I want to explain one divergent concept in detail and briefly......

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...Scientific Method and the Problem-Solving Approach The term "environment" refers to the sum total of our surroundings, including biotic and abiotic factors. Environmentalism is a social movement dedicated to protecting the natural world from undesirable changes brought about by human choices. In contrast, Environmental Science refers to the pursuit of knowledge about the workings of the environment and our interactions with it. It incorporates the study of both "hard" science subjects such as biology, chemistry, and ecology and social sciences, such as economics and policy. In this paper, I will review an environmental situation and attempt to apply methods of study from both the "hard" and social sciences. Consider this. A dairy farmer in Wisconsin loves to fish in a tiny lake adjacent to his property. In recent weeks, he has had terrible luck, catching few or no fish every time he goes out. He also notices that the lake has an unusually high amount of algae in it. Clearly, the reason for a short supply of fish and an increased amount of algae in the lake is contributed to algae blooms. These blooms are caused by “loads” of nitrogen flowing into the canal. Based on this information, I predict large amounts of chemical fertilizers are being applied on nearby farms and subsequent run-off enters the lake (Withgott & Laposata, p. 9). This occurrence then produces massive algae growth which not only obstructs sunlight, but also starves the water of oxygen, resulting......

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...Problem-Solving Process: Part I HUM/111 March 30, 2014 Pam Strunk Problem-Solving Process: Part I The situation in my life what I have chosen to use for is assignment is my sons weight. This is something his father and I have weekly discussions about. The problem is my son is overweight for his age and height and we want him to be a healthier weight. The issue is that his father believes he does not eat a healthy diet and I disagree with this. His father only sees and spends time with our son every other weekend and assumes that the diet I feed him is full of fast food and candy. I spend every day with my son and almost the 2 days every other weekend that he is with his father and know that he does eat a healthy diet that I prepare for him. The way that I distinguish what is a problem and what is an issue in this situation is by thinking about the main thing we both agree on and what we disagree on to some extent. In this situation the main thing we both agree on is that my son could be at a healthier weight, this is the problem. Something we disagree on to some extent is weather my son is eating a healthy diet, this is the issue. Another way is to ask myself the following questions to determine whether it was a problem or an issue. If the answers to these questions are yes then the subject is an issue and not a problem. If not, then it is a problem and not an issue. Does the subject arouse...

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...Practice Problem Set 3 for Econ 4808: Optimization A. Unconstrained Optimization (Note: In each optimization problem, check the second-order condition.) 1. Consider the function: y = 2 x2. a. Determine the average rate of change of the function in the closed interval [1,4] of the argument. b. Determine whether the function is concave or convex, using geometric test and a specific value of ( = 0.3. c. Do the concavity/convexity test using the derivative conditions. 2. Consider the function: y = 2x. a. Determine the average rate of change of the function in the closed interval [1,4] of the argument. b. Determine whether the function is concave or convex, using geometric test and a specific value of ( = 0.3. c. Do the concavity/convexity test using the derivative conditions. 3. Use the derivative condition to test whether the function y = 8 + 10x - x2 is concave or convex over the domain [0,7]. 4. In a cross-country study of the relationship between income per-capita (Y) and pollution (S), Grossman and Krueger estimate a cubic relationship as S = 0.083Y3 - 2.2Y2 + 13.5Y + X, where X represents other factors not linked to income. For this exercise, consider X as a fixed quantity for a country. Identify and characterize the extreme values of this function. 5. In the model of perfect competition, all firms are price-takers since they treat price (P) as a market-determined constant. Assume that P = 12. A firm's total revenue (TR) function is......

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...Problem-Solving Process part 1 Buddy Kemp HUM/111 April 27, 2014 Deborah Arnold M.Ed. Problem-Solving Process part 1 A problem is defined as a situation that is unacceptable. An issue is when two people disagree. The difference is that a problem can be solved easily by coming up with a solution that will fix the problem or make it better. An issue would be resolved when the two people who are disagreeing decide to agree on the view that makes more sense. For example, if I had a problem with my sewage not going down properly. I would seek help to tell me what the problem is. If I were told, the problem is because of tree roots getting into the pipes and keeping the water from being able to get through, the solution would be simple. The solution would be to get a plumber to come in and get all of the roots out of the pipes. This problem would then be resolved. An issue on the other hand, could be two people who disagree about Obama care. A solution to this would be much more complicated. In order to resolve this issue, people who are in disagreement, would need to decide which view is more reasonable. A problem that we are experiencing at the moment is with my son. My son, who is 14, stays out all hours of the night, takes off when he feels like it, and he is using drugs. When he is faced with consequences of his actions, he feels that he has done nothing wrong and should be able to do what he wants when he wants. One of the bigger problems......

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...Monee Problem Solving GS 1140 Homework #1 6/22/14 Today we as people face problems some large some small. No matter the size these problems all need solving, but keep in mind the objective is to choose the best solution. We must practice our problem-solving skills often to enhance them. Knowing the perceived problem, identifying the real problem, and applying the Building Blocks of the Heuristics are a few of the known methods in problem-solving. A common mistake made today in problem-solving is not knowing the perceived problem. The perceived problem can have your attention misled to something less important than the actual problem and only focused on treating the symptoms, which can give us quick satisfaction but temporary results. Like “the leak” example referred in chapter 1 the perceived problem seemed to be the leaking on the floor making a mess. Solution was putting a bucket under leak to catch the water, quick satisfaction but temporary results. Identifying the real problem can be a little tricky because it’s a lot more difficult to find and can be often overlooked. The real problem in “the leak” example used in chapter 1 was the cause of the leak. If they find the cause of the leak and fix it the problem is fixed no leaks, no buckets, mess, and best of all long term results. Now the thought of never making a mistake or faulty judgments is unreal but methods and techniques such as “the Building Blocks of the Heuristic”......

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...1. I think I am a problem- solving person because I take my time to understand all the facts accurately, and look for strategies for coming up with solution. “Good problem solvers are optimistic about the possibilities for solving a problem through a careful, persistent analysis. They start by breaking the problem into parts starting at a point where they can make some progress, and working from there. They are active in trying different problem solving methods, such as making diagrams, asking themselves questions, and trying to pin down abstractions as concrete examples.” 2. The characteristic I think I need to improve is that I do not know where to start when doing a project, essay, etc. 3. The way I think I can improve the characteristic of not checking for accuracy is by starting to re-check every step of the problem, going step by step approaching all the details, and re-read the instructions from the beginning, to avoid any guessing. Another way to improve is try to carry-out a self- testing procedure and test my own answers by not following my intuition and check for accuracy in my answers before finish and handle the assignment. 4. Hay que tener en cuenta que una persona que tiene problem-solving skills, que es la que escojimos anoche como “attitude- efectiva”es tambien aquella que re-lee y explora, que mira muy bien los detalles , entonces si escojes la ineffective como la que discutimos anoche la de “do not check” “no chekiar “ es como que......

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...Some Problems in Symmetric and Asymmetric Cryptography A thesis submitted for the partial fulfillment of the degree of Doctor of Philosophy in Mathematics By SANTOSH KUMAR YADAV Under the supervision of Prof. Sunder Lal and Prof. S. C. Arora DEPARTMENT OF MATHEMATICS DR. B. R. AMBEDKAR UNIVERSITY, AGRA (FORMERLY AGRA UNIVERSITY) 2010 *Sanskrit verse dating back to the pre-Christian era Dedicated to my Teachers, Friends, Students and Family Members DECLARATION I do hereby declare that the present research work has been carried out by me under the supervision of Prof. Sunder Lal and Prof. S. C. Arora. This work has not been submitted elsewhere for any other degree, diploma, fellowship or any other similar title. Santosh Kumar Yadav Research Scholar CERTIFICATE This is to certify that the thesis entitled “Some Problems in Symmetric and Asymmetric Cryptography” submitted to Dr. B.R.Ambedkar University, Agra for the degree of Doctor of Philosophy by Mr. Santosh Kumar Yadav, is a bonafide record of research work done by him under our supervision. To the best of our knowledge, this thesis has not previously formed the basis for the award to any candidate of any degree, diploma, fellowship or any other similar title and the work has not been submitted to any university or institution, for the award of any other degree. S. C. ARORA SUNDER LAL (Co-supervisor) (Supervisor) Professor Professor of Mathematics, and Department of Mathematics Pro-Vice......

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...Engineering and Technology Vol:7 2013-06-25 Optimization Using Simulation of the Vehicle Routing Problem International Science Index Vol:7, No:6, 2013 waset.org/Publication/15351 Nayera E. El-Gharably, Khaled S. El-Kilany, and Aziz E. El-Sayed Keywords—Discrete event system simulation, optimization using simulation, vehicle routing problem. points or require a solution to be found quickly. Computational time on the fastest computers for optimization methods has been too long for many practical problems. Cognitive, heuristic, or combination heuristic-optimization solution procedures have been good alternatives [8]. The aim of this work is threefold; to present a new mathematical formulation of the VRP problem that uses fewer decision variables, to show how to model the TSP problem as a discrete event simulation model, and to employ the developed simulation model in finding the optimum/near optimum solution of the problem. This paper is organized as follows: in Section II, the basic concepts of VRP and the solution techniques found in literature will be briefly discussed. In Section III, proposed problem formulations will be presented followed by the simulation model development and optimization using simulation in sections IV and V. Finally, in section VI, the conclusions drawn from this work are presented. I. INTRODUCTION II. LITERATURE REVIEW HE vehicle routing problem (VRP) is one of the most intensively studied problems in operations research, and this is due to......

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... Problem Solving and Judgment Selina Appel, Denise Locke, Christina Stamatien, and Amber Hamilton PSY 640 May 12, 2014 Dr. Brian Newbury Problem Solving and Judgment What is problem solving? Problem solving is a complex mental process that includes identifying, analyzing, discovering and solving problems. “Problem solving is described in terms of searching a problem space, which consists of various states of the problem” (Anderson, 2009, p. 212). Often times, problems can be difficult, and decisions can be challenging. Most problem solving issues require a lot of thought, emotion, and research in order to come up with a conclusion. The main goal in problem solving is to hinder and conquer obstacles and find the best solution to resolving the issues. Individuals use different strategies for problem solving in everyday life, whether at home, at work, or just in general. This paper will illustrate bullying in the workplace, and how to strategize. This paper will also demonstrate problem solving in the workplace, methods to problem solving, judgments in problem solving, and an implemented plan. Methods to Problem Solve Bullying in the workplace is a psychological harassment that impacts the mental health of individuals’ wellbeing. Bullying can lead to employee stress and it targets the physical and mental health of the individual (Namie & Namie, 2013). Bullying in the workplace is not acceptable behavior and there are ways to identify or deal with bullying.......

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