...Sciences Building; email: goryunov@liv.ac.uk Lectures: Monday 1pm and 2pm in Lecture Theatre B, Central Teaching Hub (no. 221 on the Campus Map), Tuesday 13.00 in Lecture Theatre (room 101), Electrical Engineering Building (no. 235 on the map). Attendance at lectures is compulsory. (See the Student Charter.) Make sure you scan your card. Tutorials: Normally on Tuesday afternoon. The tutorials will be in groups of about 20. They form an integral part of the course and attendance is compulsory. They start in Week 1. Set work Work will be set by the lecturer weekly on Monday at the 2pm lecture. It will be already available on VITAL from the previous Friday. The set work consist of two very similar parts: • set C – for solving and detailed discussion at the coming Tuesday tutorial, and • set H – written solutions to which you should hand to your MATH103 tutor by 4 pm next Thursday. All the problems are to be studied before the Tuesday tutorial. Your submitted solutions are marked by your tutor and handed back the following Tuesday; the lecturer’s solutions are available online the same day. Web publications All module materials will be available on VITAL as soon as they are needed in the class. Hard copies of some houndouts will also be distributed, but only once. Closer to the end of the semester, past papers will be put on VITAL. Class Tests There will be one class test during the module; the date will be announced at least a week in advance. Examinations The course will be assessed...
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...Environmental scan What is it? The environmental scan provides a systematic overview of the external factors that are important to the organisation (or sector) and indicates whether the organisation can influence them or not. In general the factors are classified in factors influencing the demand/need for services (and products), the supply of inputs to the project/organisation concerned, the competition and collaboration and general policy factors. The factors are also classified with respect to the positive (+) or negative (-) influence on the organisation and whether or not the factor can be influenced or just be appreciated (known and understood). What can you do with it? Making an environmental scan results in identifying the impact of relevant factors in the environment of an organisation or sector. Whereas people often complain as powerless victims about negative factors in their environment, the environmental scan helps you to take action or adapt yourself to your environment. Scanning promotes an active response to positive (opportunities) and compliant factors, and leads to insights how to live with the ‘hard facts’. While the scan is a simple tool, it nevertheless helps to get a comprehensive view of the chief factors, helping to go beyond reacting to scattered observations. Basic (sub-) questions • Which (negative) factors are most opportune to try to influence? • Which factors are most crucial to adapt your behaviour to? • What are opportunities...
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...2.9 Cholesky Decomposition 89 compared to N 2 for Levinson’s method. These methods are too complicated to include here. Papers by Bunch [6] and de Hoog [7] will give entry to the literature. CITED REFERENCES AND FURTHER READING: Golub, G.H., and Van Loan, C.F. 1989, Matrix Computations, 2nd ed. (Baltimore: Johns Hopkins University Press), Chapter 5 [also treats some other special forms]. Forsythe, G.E., and Moler, C.B. 1967, Computer Solution of Linear Algebraic Systems (Englewood Cliffs, NJ: Prentice-Hall), §19. [1] Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). [2] von Mises, R. 1964, Mathematical Theory of Probability and Statistics (New York: Academic Press), pp. 394ff. [3] Levinson, N., Appendix B of N. Wiener, 1949, Extrapolation, Interpolation and Smoothing of Stationary Time Series (New York: Wiley). [4] Robinson, E.A., and Treitel, S. 1980, Geophysical Signal Analysis (Englewood Cliffs, NJ: PrenticeHall), pp. 163ff. [5] Bunch, J.R. 1985, SIAM Journal on Scientific and Statistical Computing, vol. 6, pp. 349–364. [6] de Hoog, F. 1987, Linear Algebra and Its Applications, vol. 88/89, pp. 123–138. [7] Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X) Copyright (C) 1986-1992 by Cambridge University Press. Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal...
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...Stage II Maths Studies | Directed Investigation - CODES | | | | Suppose all letters are given a number from 1 to 26. E.g. a=1, b=2, c=3 etc then “put out the cat” becomes 16 21 20 15 21 20 20 8 5 3 1 20. If we use the following randomly chosen matrix A= 1483852321 ------------------------------------------------- as a multiplier for each of these then ‘put’ = B = 16 21 20 becomes 452 273 110 1. Verify this and ascertain the code for “out”, “the”, and “cat”. How can this message be coded by one matrix calculation? PUT = 16 21 20 x 1483852321 = 16 x 14+21 x 8+20 x 316 x 8+21 x 5+20 x 2(16 x 3+21 x 2+20 x 1) = 224+168+60 128+105+40 (48+42+20) ------------------------------------------------- = 452 273 110 OUT = 15 21 20 x 1483852321 = 15 x 14+21 x 8+20 x 315 x 8+21 x 5+20 x 2(15 x 3+21 x 2+20 x 1) = 210+168+60 120+105+40 (45+42+20) ------------------------------------------------- = 438 265 107 THE = 20 8 5 x 1483852321 = 20 x 14+8 x 8+5 x 320 x 8+8 x 5+5 x 2(20x 3+8 x 2+5 x 1) = 280+64+15 160+40+10 (60+16+5) ------------------------------------------------- = 359 210 81 CAT = 3 1 20 x 1483852321 = 3 x 14+1 x 8+20 x 33 x 8+1 x 5+20 x 2(3x 3+1 x 2+20 x 1) = 42+8+60 24+5+40 (9+2+20) = 110 69 31 This message can be coded by one matrix calculation by putting it vertically in a 3 x 4 matrix and then multiplying it by the randomly chosen matrix like so: C A T T H E O U ...
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...Computer Project: QR Method for Calculating Eigenvalues Name _____________________________ Purpose: To see how eigenvalues can be calculated by iterative methods that employ QR factorization, and get some understanding of why such methods work. This type of algorithm is used in all professional software for general eigenvalue calculations today, such as MATLAB's eig function. Prerequisite: Sections 5.2 and 6.4 MATLAB functions used: qr, *, eye, :, tic, toc , for, eig qreigdat, qrbasic, qrshift and randint from Lay's Toolbox Part I. Background. It is not easy to calculate eigenvalues for most matrices. Characteristic polynomials are difficult to compute. Even if you know the characteristic polynomial, algorithms such as Newton's method for finding zeros cannot be depended upon to produce all the zeros with reasonable speed and accuracy. Fortunately, numerical analysts have found an entirely different way to calculate eigenvalues of a matrix A, using the fact that any matrix similar to A has the same eigenvalues. The idea is to create a sequence of matrices similar to A which converges to an upper triangular matrix; if this can be done then the diagonal entries of the limit matrix are the eigenvalues of A. The remarkable discoveries are that the method can be done with great accuracy, and it will converge for almost all matrices. In practice the limit matrix is just block upper triangular, not truly triangular (because only real arithmetic is done), but it is still easy to...
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...Matrix Calculations Using Calculators The calculators most commonly used by Foundation Studies students at UTAR are Casio fx-350MS, fx-570MS, and fx-570ES. Casio fx-350MS has no matrix function and cannot be used to perform matrix calculation. Both Casio fx-570MS and Casio fx-570ES have matrix mode. Casio fx-570ES can display fully a 3×3 matrix with all its 9 elements visible. Casio fx-570MS has only a 2-line display and can only show matrix elements one at a time. Hence the operations for matrix computation are different for these two series of calculators. The general procedures in matrix calculations are as follows: (1) Enter Matrix mode of the calculators. (2) Assign a variable to store the matrix. There are 3 variables available: MatA, MatB, and MatC. (3) Select the dimension or order (1×1 to 3×3) of the matrix. (4) Input the elements of the matrix; the data will be automatically saved in the matrix variable assigned. (5) Exit the matrix input or edit mode by pressing the coloured AC key. (6) Press SHIFT MATRIX or SHIFT MAT (Matrix function is at numeric key 4) to recall the stored matrix and perform matrix calculations as needed. (a) Casio fx-570ES (a) Entering a matrix. 1. 2. 3. 4. Press the MODE key. Select 6:Matrix mode. A display Matrix? will be shown to let us select one of the 3 possible matrix variables allowable. Let us choose 1:MatA by pressing 1. The next display permits us to select the order (m×n) of the matrix MatA. Let us choose 1: 3×3 by pressing 1. An...
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...Assignment 1 Yang Liu May 5, 2015 Assignment 1, Part 1 (1) Table 0.1: Estimate a logit using solver Product of probability Log likelihood Intercept Eduation coefficient Age coefficient 2.06641E-11 -24.60262143 -11.15550863 0.531907452 0.113507304 (2) M EE d = M E Ag e = βE d e X β (1 + e X β )2 β Ag e e X β (1 + e X β )2 = 1 N βE d (i ) e X βi Σ N 1 (1 + e X βi )2 = 1 N β Ag e(i ) e X βi Σ N 1 (1 + e X βi )2 1 Result: Table 0.2: Add caption Marginal Edu effect Marginal age effect 0.085732302 0.018294992 (3) Table 0.3: linear probability model Coefficients t Stat -1.541134276 0.097414096 0.020646694 Intercept EDUC AGE Std. Err. 0.429125046 0.025225082 0.005153578 -3.591340779 3.861794961 4.00628341 (4) H = −Σi p i (1 − p i )x i x i = X ΩX The diagonal of matrix Ω equal to p i (1 − p i ) The Hessian matrix 8.058949138 105.838015 300.4357025 H = 105.838015 1434.435526 3840.728111 300.4357025 3840.728111 12190.99391 (0.1) The variance-covariance matrix equals to the inverse of Hessian matrix Table 0.4: variance-covariance matrix Constant Constant Edu Age Edu Age 10.2699517 -0.511915922 -0.091816163 -0.511915922 0.029972725 0.003172894 -0.09182 0.003173 0.001345 2 (5) According to Student’s t distribution, under 49 freedom degree, the probabilities that these coefficients are 0s are less than 0.005. We can say these...
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...Paragraph 1: Introduction (100 words) It is important to look at how and why researchers may link medical information with other non-medical information, for example, where people live, their income and their education. An understanding of how these factors affect an individual’s health can help us to look beyond the healthcare system for ways to improve the health of New Zealanders. These factors are called the social determinants of health. This essay will take a closer look at some of these social determinants and how they can influence people’s health and well-being. It will also discuss research articles that provide examples of influences of social determinants of health relating to adults. Paragraph 2: SDH approach. Your discussion...
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...July 26, 2014 Epidemiology on Mononucleosis Mononucleosis is a viral disease caused by the Epstein-Barr virus (EBV), that affects people between the ages of ten and thirty-five, but anyone at any age can contract the disease. This disease is found mainly in adolescents. It is also known as “the kissing disease”, and it is indistinguishable from other members of the herpes virus group (123helpme, 2014). The most frequent mode of transmission is intimate salivary contact. It can also be transmitted from shared drinking and eating utensils, toothbrushes, etc. Mono is not likely to spread by sneezing or from hard surface contact. It is also known as Glandular Fever, because it affects the lymph nodes in the neck, arm pits and groin. It may last anywhere from one to eight weeks, and some people suffer from mononucleosis for months at a time. It is all dependent of one’s immune system. Recuperation is a slow process, which can demand twice as much sleep and resting periods. This disease can drain strength and energy and as well muscle loss. Balance is also affected. Usually exposure to this virus happens at late adolescence for half the population. The peak incidence for girls is 14-16 and boys 16-18. After initial contact with the virus, there is an incubation period of 4-6 weeks and then the symptoms start appearing. Symptoms include fever, sore throat and lymph adenopathy. Fevers may reach as high as 102 degrees Fahrenheit and may remain high for 3-4 weeks. Other symptoms...
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...As a FNP practicing in Kentucky, which ranks near the bottom of all states in areas such as education, income, and health, I will use, The Social Determinants of Health Model, to guide my future practice. According to, The WHO, “The social determinants of health are the circumstances in which people are born, grow up, live, work and age, and the systems put in place to deal with illness. These circumstances are in turn shaped by a wider set of forces: economics, social policies, and politics” ("Social determinants of," 2013). In other words, in order to promote, maintain, or return a person to health, it is imperative to understand the circumstances of that person’s social and physical environment currently and historically. In addition, it is important to consider barriers to health imposed by community economics, worldview, and social policies in place. With these concepts in mind, I can individualize a care plan in partnership with the patient. By understanding the prevailing attitudes, social policies, and economics specific to the location of my future practice, I can also address conditions that create health disparities. For example, I might observe that I am seeing a large percentage of patients that smoke, or are obese, or have diabetes. To address these unhealthy habits on an individual basis, I will understand that people cannot be treated without understanding their personal and community environment. My goal in practice will be promoting optimum health in the individual...
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...employer (Mikkonen & Raphael, 2010). Secondly, losing a job is a stressful event that lowers one’s self esteem, disrupts daily routines, and increase anxiety (Mikkonen & Raphael, 2010). Lastly, unemployment increase the likelihood of turning to unhealthy coping behavior such as tobaccos and problem drinking (Mikkonen & Raphael, 2010). • Insecure employment consists of intense work with non-standard working hours and intense working condition, which can result in a higher rate stress, bodily pains, and higher risk of injury (Mikkonen & Raphael, 2010). It can also lead to psychological and physiological health problems such as heart disease, high blood pressure and even sleep deprivation. • Education is a major key factor of social determinant of health. People with higher education tend to be healthier and make better choices than those with a lower educational attainment. Research shows that there are various pathways by which educations leads to better health such as the level of income, employment security and working conditions (Mikkonen & Raphael, 2010). Having some sort of education like a high school diploma, degree or master can help people move up or down the social hierarchy and can help have better access to other societal and economic resources • But on the other hand, it’s important to remember that lack of education in itself I can the cause poor health, especially if the person is unable to pay extensive tuition for a higher education because of financial reason...
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...Assignment No 6: Submission date 19th November 1, 2012 LOAD FLOW CALCULATIONS y12 = -j2.5 P3, Q3 V1 2 V3 V2 z12 = j0.4 z13 = j0.4 Y13=-j5 P2, Q2 P1, Q1 3 1 Node | Vpu | δo | P | Q | Type | 1 | 1.0 | 0 | - | - | Reference | 2 | 1.0 | - | -1.0 | - | P-V | 3 | - | - | -0.6 | -0.3 | PQ | 6.1 Establish the equations for power injection (Pi,Qi) at all nodes. 6.2 Calculate the unknown variables in the table shown above by analytical solution. 6.3 Develop analytical expressions for Jacobian matrix elements. 6.4 Calculate the Jacobian matrix in power flow balance. Assume per unit values are given referred to Vref = 60 kV, line to line Sref = 100 MVA, 3-phase After analytical solution the voltage at node no. 3 will be V3 = 0.93 pu which is below the acceptable limit i.e. 57 kV, line to line. Two alternatives to bring V3 up to 57 kV are proposed: A: Reduce active power consumption P3 from 60 MW to 50 MW. B: Reduce reactive power consumption Q3 from 30 MVAr to 20 MVAr. In order to test these two alternatives we can use a linear approximation where the Jacobian matrix (in power flow balance) is applied: ∆Q3∆P2∆P3=∂Q3/∂V3∂Q3/∂δ2∂Q3/∂δ3∂P2/∂V3∂P2/∂δ2∂P2/∂δ3∂P3/∂V3∂P3/∂δ2∂P3/∂δ3∆V3∆δ2∆δ3 For alt A : ΔQ3 = 0, ΔP3 ≠ 0 as the proposed change. For alt B : ΔP3 = 0, ΔQ3 ≠ 0 as the proposed change. 6.5 Test both alternatives and choose the best. 6.6 Check the best solution found under 6.5 by exact analytical solution of the equations...
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...Critique Paper on the Discussion of the Determinants and Consequences of Heterogeneous IFRS Compliance Levels Following Mandatory IFRS Adoption: Evidence from a Developing Country The Philippines known as one of the developing countries in Southeast Asia has also become one of the countries supporting the shift and full compliance with the International Financial Reporting Standards (IFRS). The change from following the U.S GAAP or the localized version of the U.S GAAP to the International Financial Reporting Standards has become one of the main priorities in the accounting system of the country. However, there is a need to fully understand whether or not there really is an economical benefit in the full compliance of the IFRS. This is needed in order to ensure that the full compliance is the best decision for the country. The full compliance with the International Financial Reporting Standards have been said to provide many benefits for the members of the European Union focusing more on the developed countries who are globally competing and interacting with one another. However, it is difficult to fully grasp the effect and benefits of the full compliance or any levels of compliance with the IFRS in relation to developing or less developed countries because of the lack in data and the different perspectives followed between the IFRS and the local accounting system of a particular entity. The need to interpret the effects of the different levels of compliance with...
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...DISCUSSION PAPERThe determinants of Indigenous employment outcomes: the importance of education and training B. Hunter No. 115/1996 ISSN 1036-1774 ISBN 0 7315 1789 XSERIES NOTE The Centre for Aboriginal Economic Policy Research (CAEPR) was established in March 1990 under an agreement between The Australian National University (ANU) and the Aboriginal and Torres Strait Islander Commission (ATSIC). CAEPR operates as an independent research unit within the University's Faculty of Arts and is funded by ATSIC, the Commonwealth Department of Social Security and the ANU. CAEPR's principal objectives are to undertake research to: • investigate the stimulation of Aboriginal and Torres Strait Islander economic development and issues relating to Aboriginal and Torres Strait Islander employment and unemployment; • identify and analyse the factors affecting Aboriginal and Torres Strait Islander participation in the labour force; and • assist in the development of government strategies aimed at raising the level of Aboriginal and Torres Strait Islander participation in the labour market. The Director of the Centre is responsible to the Vice-Chancellor of the ANU and receives assistance in formulating the Centre's research priorities from an Advisory Committee consisting of five senior academics nominated by the Vice-Chancellor and four representatives nominated by ATSIC, the Department of Employment, Education, Training and Youth Affairs and the Department of Social...
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...FIN301 Module 2 Instructions for CASE and SLP Assignments 07-13-15 Module 2 - Home ------------------------------------------------- PRESENT VALUE Modular Learning Outcomes Upon successful completion of this module, the student will be able to satisfy the following outcomes: * Case * Explain the concept of present value. * Calculate the present value of a future stream of income. * Describe the determinants of the discount factor. * Explain the determinants of present value. * SLP * Explain the concept of present value. * Describe the determinants of the discount factor. * Explain the determinants of present value. * Discussion * Explain the concept of present value. * Describe the determinants of the discount factor. Module Overview In order to value assets such as stocks, bonds, or investment projects, you need to be able to place a value on payments that you will receive in the future. If you as a financial manager with to invest in some new equipment, you need to be able to place a value on the total amount of additional profits your company will receive over the next several years due to this new purchase. In general, people prefer to have money paid to them today rather than tomorrow. The value of one dollar today is exactly one dollar. But what about being paid one dollar exactly one year from now? Would you pay a dollar for the that dollar to be paid to you in one year? Definitely not! Of...
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