...Application: Week 2 Numerical Problems Edilsavier Hernandez Walden University 1. Problem 3.5 form page 106, Chapter 3 a. Brandywine’s 2001 income statement: Brandywine Homecare December 31, 2011. Statement of income Revenues: $12,000,000 Expenses: (expenses - $9,000,000)+(depreciation - $1,500,000): total expenses: $10,500,000 Net income: $1,500,000 b. Net income, total profit margin, and cash flow Net income: total revenues – total expenses: $1,500,000 Total profit margin: [net income / revenues] *100 = $12.5 Cash flow: net income + depreciation: $3,000,000 c. How changes affect if depreciating value doubles: Now depreciating value is $3,000,000 Net income: total revenues – total expenses: $0 Total profit margin: [net income / revenues] *100 = $0 Cash flow: net income + depreciation: $3,000,000 d. Impact if depreciating expenses halves Now depreciating value is $750,000 Net income: total revenues – total expenses: $2,250,000 Total profit margin: [net income / revenues] *100 = $18.75 Cash flow: net income + depreciation: $3,000,000 2. Problem 4.5 form page 141, Chapter 4 Balanced sheet: a. The balanced sheet differs from the one presented in Exhibit 4.1 for Sunnyvale due to difference in the cases of total assets, total liabilities, and debt ratio. The values of assets and liabilities for BestCare HMO is showing less values than does of Sunnyvale Clinic. The assets and long term investment of Sunnyvale is showing...
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...362 Chapter 9. Root Finding and Nonlinear Sets of Equations } a=b; fa=fb; if (fabs(d) > tol1) b += d; else b += SIGN(tol1,xm); fb=(*func)(b); Move last best guess to a. Evaluate new trial root. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machinereadable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). } nrerror("Maximum number of iterations exceeded in zbrent"); return 0.0; Never get here. } CITED REFERENCES AND FURTHER READING: Brent, R.P. 1973, Algorithms for Minimization without Derivatives (Englewood Cliffs, NJ: PrenticeHall), Chapters 3, 4. [1] Forsythe, G.E., Malcolm, M.A., and Moler, C.B. 1977, Computer Methods for Mathematical Computations (Englewood Cliffs, NJ: Prentice-Hall), §7.2. 9.4 Newton-Raphson Method Using Derivative Perhaps the most celebrated of all one-dimensional root-finding routines is Newton’s method, also called the Newton-Raphson method. This method is distinguished from the methods of previous sections by the fact that...
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...Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machinereadable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). Numerical Recipes in C The Art of Scientific Computing Cambridge New York Port Chester Melbourne Sydney EXXON Research and Engineering Company Harvard-Smithsonian Center for Astrophysics Department of Physics, Cornell University CAMBRIDGE UNIVERSITY PRESS William T. Vetterling Saul A. Teukolsky Brian P. Flannery Second Edition William H. Press Polaroid Corporation Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 1RP 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC, 3207, Australia Copyright c Cambridge University Press 1988, 1992 except for §13.10 and Appendix B, which are placed into the public domain, and except for all other computer programs and procedures, which are Copyright c Numerical Recipes Software 1987, 1988, 1992...
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...CHAPTER 1 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...
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...SUBJECT: NUMERICAL METHODS CODE: BUM2313 FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY INSTRUCTION: Use MATHEMATICAL SOFTWARE such as EXCEL/ MATLAB/ MAPLE/ C to facilitate the computation. SUBMIT the solution in HARDCOPY & SOFTCOPY. Please save the solution in CD for softcopy. Do the assignment in group as allow by your lecturer. QUESTION 1 The nonlinear resistive circuit shown below is described by the nonlinear equation f ( x) g ( x) ( E x) 0 R TOPIC: CHAPTER 1, 2,3 & 4 DUE/DURATION: MARKS: ASSESSMENT: ASSIGNMENT 2nd May 2014 (before 5 P.M) WEEK 11 100 The function g ( x) gives the current through the nonlinear resistor as a function of the voltage x cross its terminals as shown in the following Figure 1. Figure 1 Assuming that g ( x) 9sin( x 5) 10 and consider the three following cases: Case 1: E 5, R 1, Case 2: E 15, R 3, Case 3: E 4, R 0.5. (a) (b) (c) By using an appropriate method that you have learned in this course, find all the solutions of the nonlinear resistive circuit equation for the all cases. Select suitable starting points for xl and xu by plotting f over the interval [0,4] for the all cases, and visually selecting a good starting point. Find the lowest root over the the interval [0,4] by using (i) Bisection method and (ii) False position method. Use the starting points xl and xu in (b) and terminate the computation if a 104. (For (a) and (b) use two decimal places, for (c) use eight decimal places) (20...
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...Zhang† Abstract. We propose, analyze, and test an alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization. This algorithm arises from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations. The per-iteration computational complexity of the algorithm is three fast Fourier transforms. We establish strong convergence properties for the algorithm including finite convergence for some variables and relatively fast exponential (or q-linear in optimization terminology) convergence for the others. Furthermore, we propose a continuation scheme to accelerate the practical convergence of the algorithm. Extensive numerical results show that our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed. Key words. half-quadratic, image deblurring, isotropic total variation, fast Fourier transform AMS subject classifications. 68U10, 65J22, 65K10, 65T50, 90C25 DOI. 10.1137/080724265 1. Introduction. In this paper, we propose a fast algorithm for reconstructing images from blurry and noisy observations. For simplicity, we assume that the underlying images have square domains, but all discussions can be equally applied to rectangle domains. Let 2 2 2 u0 ∈ Rn be an original...
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...Introduction to Finite Element Method Mathematic Model Finite Element Method Historical Background Analytical Process of FEM Applications of FEM Computer Programs for FEM 1. Mathematical Model (1) Modeling Physical Problems Mathematica l Model Solution Identify control variables Assumptions (empirical law) (2) Types of solution Sol. Eq. Exact Sol. Approx. Sol. Exact Eq. Approx. Eq. ◎ ◎ ◎ ◎ (3) Methods of Solution (3) Method of Solution A. Classical methods They offer a high degree of insight, but the problems are difficult or impossible to solve for anything but simple geometries and loadings. B. Numerical methods (I) Energy: Minimize an expression for the potential energy of the structure over the whole domain. (II) Boundary element: Approximates functions satisfying the governing differential equations not the boundary conditions. (III) Finite difference: Replaces governing differential equations and boundary conditions with algebraic finite difference equations. (IV) Finite element: Approximates the behavior of an irregular, continuous structure under general loadings and constraints with an assembly of discrete elements. 2. Finite Element Method (1) Definition FEM is a numerical method for solving a system of governing equations over the domain of a continuous physical system, which is discretized into simple geometric shapes called finite element. Continuous system Time-independent PDE Time-dependent...
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...Science Ithaca, NY 2008 - 2012(projected) • – Department of Energy Computational Science Graduate Fellow (Full Scholarship, 4 years) – Emphasis on machine learning/data mining and algorithm design/software development related to bioinformatics and optimization • Oregon State University B.Sc. Mathematics, B.Sc. Computational Physics, B.Sc. Physics Corvallis, OR 2004 - 2008 – Graduated Magna Cum Laude with minors in Actuarial Sciences and Mathematical Sciences – Strong emphasis on scientific computing, numerical analysis and software development Skills • Development: C/C++, Python, CUDA, JavaScript, Ruby (Rails), Java, FORTRAN, MATLAB • Numerical Analysis: Optimization, Linear Algebra, ODEs, PDEs, Monte Carlo, Computational Physics, Complex Systems, Iterative Methods, Tomology • Computer Science: Machine Learning, Data Mining, Parallel Programming, Data Structures, Artificial Intelligence, Operating Systems • Discovering and implementing new ideas. Give me an API and a problem and I will figure it out. • Diverse background in Math, Computer Science, Physics and Biology allows me to communicate to a wide scientific and general audience and begin contributing to any group immediately. • I have worked in many places in a myriad of fields. I can readily learn and adapt to a new discipline, area or environment and start pushing real results quickly. Research and Work Experience Bloomberg LP Financial Software Development Intern New York, NY Summer 2011 • – Developed end-to-end...
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...industries are dependent. The precision in class of the machine tools themselves, their control frameworks and the association encompassing them to a great extent focus the profitability and intensity of designing commercial enterpries.(Marcuse, 2002) The machine tool industry faces two noteworthy difficulties today. One is that about innovation in machine tools has changed its own technology improvements. Over a century of transformative advancement, predominantly including phenomenal technology upgradations and enhanced control of large scale manufacturing, the primary advancement in machine tool industry over two decades has included computerization and automation of small and medium scale enterprises regarding the current scenario of numerical control and different parts of the microelectronic setup. This adjustment in the overall structure of the machines and innovative change is constraining significant changes both inside(internal) of the business and in its association with clients(external). The other issue is that the focused circumstance on the planet where business is evolving quickly, bringing about serious modification issues for most machine tool makers. Despite the fact that this is an industry in which remote exchange has dependably been critical, the rise of new competitors (especially Japan in numerically controlled machine instruments and recently industrialized nations in ordinary machine tools) with new systems and new sorts of specialization has rolled out...
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...List of available projects - HTTrack Website Copier HTTrack Website Copier - Open Source offline browser Index of locally available projects: No categories · vedic maths Mirror and index made by HTTrack Website Copier [XR&CO'2002] © 2002 Xavier Roche & other contributors - Web Design: Leto Kauler. file:///C|/My%20Web%20Sites/vedic%20maths/index.html12/22/2005 8:49:27 AM Vedamu.org - Vedic Mathematics - Course INDEX I. Why Vedic Mathematics? II. Vedic Mathematical Formulae Sutras 1. Ekadhikena Purvena 2. Nikhilam navatascaramam Dasatah 3. Urdhva - tiryagbhyam 4. Paravartya Yojayet 5. Sunyam Samya Samuccaye 6. Anurupye - Sunyamanyat 7. Sankalana - Vyavakalanabhyam 8. Puranapuranabhyam 9. Calana - Kalanabhyam 10. Ekanyunena Purvena Upa - Sutras 1. Anurupyena 2. Adyamadyenantya - mantyena 3. Yavadunam Tavadunikrtya Varganca Yojayet 4. Antyayor Dasakepi 5. Antyayoreva 6. Lopana Sthapanabhyam 7. Vilokanam 8. Gunita Samuccayah : Samuccaya Gunitah III Vedic Mathematics - A briefing 1. Terms and Operations 2. Addition and Subtraction 3. Multiplication 4. Division 5. Miscellaneous Items IV Conclusion file:///C|/My%20Web%20Sites/vedic%20maths/vedic%20maths/www.vedamu.org/Mathematics/course.html12/22/2005 8:49:34 AM Vedamu.org - Vedic Mathematics - Why Vedic Mathematics Vedic Mathematics | Sutras EKĀDHIKENA PŪRVE•A The Sutra (formula) Ekādhikena Pūrvena means: “By one more than the previous one”. i) Squares of numbers ending in 5 : Now we relate the sutra to the ‘squaring of numbers...
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...SUBJECT: NUMERICAL METHODS CODE: BUM2313 FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY INSTRUCTION: Use MATHEMATICAL SOFTWARE such as EXCEL/ MATLAB/ MAPLE/ C to facilitate the computation. SUBMIT the solution in HARDCOPY & SOFTCOPY. Please save the solution in CD for softcopy. Do the assignment in group and each group consists of five members. QUESTION 1 The nonlinear resistive circuit shown below is described by the nonlinear equation TOPIC: CHAPTER 1, 2,3 & 4 DUE/DURATION: ASSESSMENT: ASSIGNMENT 2nd May 2014 (before 5 P.M) WEEK 11 MARKS: 100 f ( x) g ( x) ( E x) 0 R The function g ( x) gives the current through the nonlinear resistor as a function of the voltage x cross its terminals as shown in the following Figure 1. Figure 1 Assuming that g ( x) 9sin( x 5) 10 and consider the three following cases: Case 1: E 5, R 1, Case 2: E 15, R 3, Case 3: E 4, R 0.5. (a) (b) (c) By using an appropriate method that you have learned in this course, find all the solutions of the nonlinear resistive circuit equation for the all cases. Select suitable starting points for xl and xu by plotting f over the interval [0,4] for the all cases, and visually selecting a good starting point. Find the lowest root over the the interval [0,4] by using (i) Bisection method and (ii) False position method. Use the starting points xl and xu in (b) and terminate the computation if a 104. (For (a) and (b) use two decimal places, for (c) use eight decimal places)...
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...contributes to the development of FD methods. One powerful tool – FE analysis − is applied to optimization of plasmon-enhanced AFM tips in apertureless near-field optical microscopy. Another tool is a new FD calculus of “Flexible Local Approximation MEthods” (FLAME). In this calculus, any desirable local approximations (e.g. scalar and vector spherical harmonics, Bessel functions, plane waves, etc.) are seamlessly incorporated into FD schemes. The notorious ‘staircase’ effect for slanted and curved boundaries on a Cartesian grid is in many cases eliminated – not because the boundary is approximated geometrically on a fine grid but because the solution is approximated algebraically by suitable basis functions. Illustrative examples include problems with plasmon nanoparticles and a photonic crystal with a waveguide bend; FLAME achieves orders of magnitude higher accuracy than the standard FD methods, and even than FEM. Keywords: wave propagation, computational methods, flexible approximation, photonic crystals, plasmon particles, apertureless near-field microscopy, AFM tips, field enhancement, optimization....
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...of Ford Motor Company's plants will yield a $2.5 billion savings. By the year 2010, Ford will have converted 80 percent of its plants to flexible manufacturing.” (www.ford-motorcompany.com) Looking at local FMS systems, we have Nissan in Sunderland and Greggs in Longbenton. Both these companies have fantastic FMS systems, with virtually no human input, loading- manufacture-unloading is all completed by FMS, this removes the need for human input, which greatly improves quality and output. There are more benefits to FMS, using humans for repetitive work can be dangerous for the body, fatigue is a large part in human operation and if done for long periods of time (i.e. a 10-20 years of work) the human body begins to shut down, creating problems such as arthritis and repetitive strain injury. Industrial Robots and Engineering systems Task 2 One Japanese manufacturer, by installing a flexible manufacturing system, has reduced the number of machines in one facility from 68 to 18, the number of employees from 215 to 12, space requirements from 103000 square feet to 30000 and processing time from 35 days to a 1.5 days. “Ford has poured $4,400,000 into overhauling its Torrence Avenue plant in Chicago, giving it flexible manufacturing capability. This will allow...
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...to process a high variety of products in low volumes and with short delivery times. In lieu of these, manufacturing process should have the efficiency of a line flow and flexibility of a job shop. One way to cope with these kind of needs are through the automated manufacturing environments. These consist of Computer Numerical Control (CNC) machines. CNC Machines have the capability of processing several manufacturing operations and provide the required flexibility in an efficient manner. It is usually use in the metal – working industry. It is equipped with a limited – capacity tool magazine and can automatically change tools between operations in slight time. However, during the changing of tool in the magazine, it must be loaded carefully to best utilize the machine’s flexibility. Set – up time of loading tool magazine is considered long and accounting for a lot of percentage in production time. Because of this, there is a need to reduce the number of tool – magazine setups in order also to reduce the machine processing times. This need is an important and vital problem in automated manufacturing. The paper addresses the said problem. It described the problem as follows. Consider a set of parts that have immediate production requirements on one group of identical machines. Processing each part requires a set of cutting tools and different parts may have a subset...
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...saved on a file - when MATLAB runs a script file] and function files[can accept input arguments from the command window return outputs to the command window but variables created and manipulated within the function do not impact the command window]) outvar = the name of the output variable; arglist = function’s argument list formatted output, or for output generated by combining variable values with literal text, use the fprintf command A for loop ends after a specified number of repetitions established by the number of columns given to an index variable.--> for index = start:step:finish statements end A while loop ends on the basis of a logical condition while condition statements end True value = approximation + error True numerical error (ET ) = true value-approximation...
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