...Logarithms and Levels Logarithms are used to compare two quantities to one another quickly with an easy frame of reference. It is particularly useful if there is a large difference in orders of magnitude between quantities as in acoustic pressure or acoustic energy calculations. We will see how useful logarithms can be in our next lesson. For now, let's concentrate on review of some of the basic principles leading up to our use of logarithms. Unless otherwise stated, we will be working solely with logarithms that are in base 10 (Briggsian) . Some useful relationships to remember when working with logarithms are: 1. y = 10x then log10 ( y ) = x 2. log ( xy ) = log ( x ) + log ( y ) ⎛x⎞ 3. log ⎜ ⎟ = log ( x ) − log ( y ) ⎝ y⎠ ( ) 4. 10 log x n = n10 log( x ) Intensity Level In the last lesson, we defined the time average intensity in relation to the time average or rms pressure as well as the maximum acoustic pressure. p2 p2 I = = max 2ρc ρc The intensity is a useful quantity because it quantifies the power in an acoustic wave, but because of the large variation in magnitudes of Intensity, it is more useful to use logarithms to compare intensities. The below table demonstrates the wide variation in Intensity for typical sounds in air. We will start by defining a new quantity, L, the intensity level, which has units of dB. I L ≡ 10 log I0 where: is the time average intensity of the sound wave. I0 is the reference level used for comparison...
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...The Market 4 2 Budget Constraint 8 3 Preferences 10 4 Utility 14 5 Choice 18 6 Demand 24 7 Revealed Preference 27 8 Slutsky Equation 30 9 Buying and Selling 33 10 Intertemporal Choice 37 12 Uncertainty 39 14 Consumer Surplus 43 15 Market Demand 46 18 Technology 48 19 Profit Maximization 52 20 Cost Minimization 54 21 Cost Curves 57 22 Firm Supply 59 23 Industry Supply 62 24 Monopoly 64 2 25 Monopoly Behavior 67 26 Factor Market 72 27 Oligopoly 76 28 Game Theory 80 30 Exchange 85 3 Ch. 1. The Market I. Economic model: A simplified representation of reality A. An example – Rental apartment market in Shinchon: Object of our analysis – Price of apt. in Shinchon: Endogenous variable – Price of apt. in other areas: Exogenous variable – Simplification: All (nearby) Apts are identical B. We ask – How the quantity and price are determined in a given allocation mechanism – How to compare the allocations resulting from different allocation mechanisms II. Two principles of economics – Optimization principle: Each economic agent maximizes its objective (e.g. utility, profit, etc.) – Equilibrium principle: Economic agents’ actions must be consistent with each other III. Competitive market A. Demand – Tow consumers with a single-unit demand whose WTP’s are equal to r1 and r2 (r1 < r2 ) p r2 r1 1 2 – Many people ...
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...Course Title | BTEC Level 3 Nationals in Business | Unit Title | Unit 2 – Business Resources (60 hour unit) | Level | 3 | Unit Number | 2 | Unit Credit | 10 | Assignment Title | Describing Recruitment documents | Part Unit | P1, P2 & M2 | Whole Unit | n/a | Learner Name | | Signature | | Assessor | Mark Grant | Signature | | Start Date | 22/10/14 | Submission Date | 12/11/14 | Feedback Date | 26/11/14 | | | | | | | Vocational Context | It is important to understand the purpose and format of different types of documents that are used in the recruitment process, as you will be coming across them when you apply for jobs. This assignment will allow you to develop a good understanding of these documents. Additionally you will possibly need to create them if you are involved with recruiting staff during your career. | The Brief | ------------------------------------------------- (P1, P2 and M2) A family friend has been operating his own small fashion clothing business (KH Fashions) that has been trading for five years. He has decided to expand the business and has asked you to research different businesses.------------------------------------------------- He wishes to take on staff from outside the family, and because he wants to do this in a professional way, has asked you specifically to research how human and non-human (such as technological and physical) resources are used within organisations. | Grading Criteria. | Evidence | What...
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...1. Deadlock (“deadly embrace”) is a system-wide tangle of resource requests that begins when 2 or more jobs are put on hold. • Each job is waiting for a vital resource to become available. • Needed resources are held by other jobs also waiting to run but can’t because they’re waiting for other unavailable resources. • The jobs come to a standstill. • The deadlock is complete if remainder of system comes to a standstill as well. • The resources can be categorized into physical and logical resources. The physical resources are printer, disk drive, cpu, memory, scanner etc. The logical resources are files. • Deadlock is more serious than indefinite postponement or starvation because it affects more than one job. • Because resources are being tied up, the entire system (not just a few programs) is affected. • Requires outside intervention (e.g., operators or users terminate a job) to resolved the deadlock. 2. Seven Cases of Deadlocks Case 1 Deadlocks on file requests Case 2 Deadlocks in databases Case 3 Deadlocks in dedicated device allocation Case 4 Deadlocks in multiple device allocation Case 5 Deadlocks in spooling Case 7 Deadlocks in disk sharing Case 8 Deadlocks in a network Case 1: Deadlocks on File Requests | |If jobs can request and hold files for duration of their...
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...is lower than that of its trading partner. 1.1 Technology and markets The Ricardian model assumes that production uses only 1 input (labor), with constant returns to scale. This assumption means that the technology in each country and each sector is entirely determined by the labor requirement per unit of output. The other assumptions are that (a) labor moves freely between sectors within a country, but (b) labor cannot move between countries. Assumption (a) implies that in a particular country, the wage must be the same in both sectors; assumption (b) means that the wage need not be the same (and typically is not the same) in the two countries. In addition, all agents are price takers, i.e. there is perfect competition. In my example, the unit labor requirements are unit labor requirement Corn (good 1) US Canada au = 1 1 Umbrellas (good 2) au = 1 2 ac = 3 ac = 6 1 2 Table 1, Labor requirements 1 (Corn is good 1, umbrellas are good 2. Subscripts indicate commodity, superscripts indicate country.) I assume that both goods require one unit of labor to produce one unit of output in the US. This assumption is without loss of generality; it merely amounts to a choice of units....
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...------------------------------------------------- Level 3 Sub Dip/Extended Diploma in Business - Academic Year 2013-14 Candidate | | | Unit No. | Unit 5 ; Unit 2 ; Unit 18 | | Unit Name | Business accounting, Business resources and managing a business event | * | Qualification | Btec Level 3 | | Start Date | September 2013 | | Deadline | November 2013 | | Assessor | Maria Pillay | | Unit 5 – Business accounting | | | Criteria | To achieve the criteria the evidence must show that the student is able to: | Page No. | Achieved? | P1 | Describe the purpose of accounting for an organisation | | | P2 | Explain the difference between capital and revenue items of expenditure and income | | | P3 | Prepare a 12 month cash flow forecast to enable an organisation to manage its cash | | | P4 | Prepare a profit and loss account and balance sheet for a given organisation | | | P5 | Perform ration analysis to measure the profitability and liquidity and efficacy of a given organisation | | | M1 | Analyse the cash flow problems a business might experience | | | M2 | Analyse the performance of a business using suitable ratios | | | D1 | Justify actions a business might take when experiencing cash flow problems | | | D2 | Evaluate the financial performance ad position of a business using ratio analysis | | | Unit 2 – Business resources | | | Criteria | To...
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...curve and the budget line; (ii) a kink in an indifference curve; (iii) a “corner” where the consumer specializes in consuming just one good. Here is how you find a point of tangency if we are told the consumer’s utility function, the prices of both goods, and the consumer’s income. The budget line and an indifference curve are tangent at a point (x1 , x2 ) if they have the same slope at that point. Now the slope of an indifference curve at (x1 , x2 ) is the ratio −M U1 (x1 , x2 )/M U2 (x1 , x2 ). (This slope is also known as the marginal rate of substitution.) The slope of the budget line is −p1 /p2 . Therefore an indifference curve is tangent to the budget line at the point (x1 , x2 ) when M U1 (x1 , x2 )/M U2 (x1 , x2 ) = p1 /p2 . This gives us one equation in the two unknowns, x1 and x2 . If we hope to solve for the x’s, we need another equation. That other equation is the budget equation p1 x1 + p2 x2 = m. With these two equations you can solve for (x1 , x2 ).∗ Example: A consumer has the utility...
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...Mobile Communications Department, Institute Eur´ com, e 06560 Sophia-Antipolis, France, Email: {gesbert, kiani}@eurecom.fr maximize the network capacity for the case of individual link power constraints [8] and a sum power constraint [9]. In [10] it is assumed that each base station, when it transmits, transmits with maximum power Pmax . Which base stations that should be active at each time slot is decided according to a rate maximization objective. However, no proof of optimality is given for the on/off power allocation. In [11] transmit power allocation for a downlink two-user interference channel is studied under a sum transmit power constraint and the assumption of symmetric interference. The derived power allocation depends on the level of interference; when the inference is above a certain threshold the total power is allocated to the best user. For interference less than the threshold, the available power is divided among the two users according to a water-filling principle. However, due to the sum power constraint and symmetry of interference assumption these results are not readily applicable for two-cell power allocation, where it is more reasonable to assume individual power constraints and that the received interference will be different for different users. In this paper we tackle the problem of analytically finding a closed form solution for power allocation in a simple two-cell network, without resorting to the restricting assumptions of interference limiting or...
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...Demand and Supply: The Basics 21 FUNDAMENTALS OF ECONOMICS FOR BUSINESS - (Second Edition) © World Scientific Publishing Co. Pte. Ltd. http://www.worldscibooks.com/economics/6794.html Chapter 2 Introduction The most basic, and in many ways the most lasting, lesson to be learnt from “Economics 101” relates to the fundamental concepts of demand and supply and their interaction. These are usually presented in a simple graphical format involving demand and supply “curves”. The word is in quotes because in this chapter, for simplicity, we will actually assume only straightline relationships between price and quantities demanded and supplied. The main issue that is important in reality is the direction of the relationship between prices and quantities. Will a reduction in price lead to an increase in the quantity demanded of any particular product or service? Will an increase in price lead to an increase in supply? And so on. The principal technical tools for analyzing demand and supply conditions in particular markets, then, are the demand and supply schedules or curves. The demand curve shows an estimate or conjecture about the relationship between the price of any particular product or service and the quantity of that product that will be demanded by consumers. It is usually assumed to slope downward, in the general case, for most products and services. In other words, the lower the price of the item, the greater the quantity of it that will be demanded. Technically, this...
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...European Journal of Operational Research 224 (2013) 507–519 Contents lists available at SciVerse ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Production, Manufacturing and Logistics Pricing decisions for complementary products with firms’ different market powers Jie Wei a,⇑, Jing Zhao b, Yongjian Li c a General Courses Department, Military Transportation University, Tianjin 300161, PR China School of Science, Tianjin Polytechnic University, Tianjin 300160, PR China c Business School, Nankai University, Tianjin 300071, PR China b a r t i c l e i n f o Article history: Received 25 July 2011 Accepted 5 September 2012 Available online 11 September 2012 Keywords: Pricing Complementary products Market power Stackelberg game a b s t r a c t This article reports the results of a study that explores the pricing problems with regard to two complementary products in a supply chain with two manufacturers and one common retailer. The authors establish five pricing models under decentralized decision cases, including the MS-Bertrand, MS-Stackelberg, RS-Bertrand, RS-Stackelberg, and NG models, with consideration of different market power structures among channel members. By applying a game-theoretical approach, corresponding analytic solutions are obtained. Then, by comparing the maximum profits and optimal pricing decisions obtained in different decision cases, interesting and valuable managerial...
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...exacerbation in global economic competition, more and more electronic products possess a very short lifespan prior to becoming outdated. For example, electronic products including mobile phones, MP3-players, digital cameras, tablets and laptops often have a lifespan being no more than one year. In the meanwhile, the shortage in global resources and deterioration of ecological environment makes remanufacturing a popular alternative to the sustainable development of many electronic manufacturers. Most electronic products have the remanufacturing potential so as to receive additional revenues. Products to be remanufactured can be collected actively and deliberately by the manufacturer through the choice of remanufactured ability level or quality control, or passively with various causes such as regulatory and environmental concerns, warranty reasons, purchase...
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...CPU SCHEDULINGCPU scheduling in UNIX is designed to benefit interactive processes. Processes are given small CPU time slices by a priority algorithm that reduces to round-robin scheduling for CPU-bound jobs.The scheduler on UNIX system belongs to the general class of operating system schedulers known as round robin with multilevel feedback which means that the kernel allocates the CPU time to a process for small time slice, preempts a process that exceeds its time slice and feed it back into one of several priority queues. A process may need much iteration through the "feedback loop" before it finishes. When kernel does a context switch and restores the context of a process. The process resumes execution from the point where it had been suspended.Each process table entry contains a priority field. There is a process table for each process which contains a priority field for process scheduling. The priority of a process is lower if they have recently used the CPU and vice versa.The more CPU time a process accumulates, the lower (more positive) its priority becomes, and vice versa, so there is negative feedback in CPU scheduling and it is difficult for a single process to take all the CPU time. Process aging is employed to prevent starvation.Older UNIX systems used a 1-second quantum for the round- robin scheduling. 4.33SD reschedules processes every 0.1 second and recomputed priorities every second. The round-robin scheduling is accomplished by the -time-out mechanism, which tells...
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...Qualification suite covered | Edexcel BTEC Level 3 Diploma/Extended Diploma, Health and Social Care | Assignment title | Life Stages | Unit number and title | Unit 4:Development Through the Life Stages | Assessor | Kelly Ocloo | Learning aims covered | On completion of this unit a learner should:1. Know the stages of growth and development throughout the human lifespan 2. Understand the potential effects of life factors and events on the development of the individual 3. Understand the physical and psychological changes of ageing | Context | The study of lifespan development is about understanding the way we change over time. In this unit you will be able to identify some patterns in the course of human development and a range of factors that will influence how your life turns out. You will also need to make up your own mind about some very deep questions. Will you have a fixed life course where you can predict much of what will happen to you? How far is your life fixed for you by your genetics or by the social and economic environment you grow up in? How far can you choose to control your own life and can you try to ensure a happy old age? | Overall Scenario | As part of your work experience you have been asked to produce a fact file to show your understanding of the different life stages. You have been asked to discover as much information as possible about a family member (Parent, Aunt, Uncle, Grandparents) or a high profile person, to describe the...
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...will arrive in a five-minute period? The expected number is of 0.4*5 = 2 customer is a five-minute period. b) Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. The probabilities of the described scenarios are as follows: P0=20e-20! P0=0.135335283 P1=21e-21! P1=0.270670566 P2=22e-22! P2=0.270670566 P3=23e-23! P3=0.180447044 c) Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? This probability can be expressed as the probability of more than 3 customers arriving during the five-minute period, which can be computed as following: P(x > 3) = 1 – P(x ≤ 3) P (x > 3) = 1 – 0.85712346 P(x > 3) = 0.14287654 Thus, there is a 14, 29% probability of expected delays in five-minute period. Problem 3 Use the single-server drive-up bank teller operation referred to in Problems 1 and 2 to determine the following characteristics for the system: Using arrival rate and service rate PER MINUTE a) The probability that no customers are in the system P0=1- 0.40.6 P0=0.3333 b) The average number of customers waiting Lq=0.420.6(0.6-0.4) Lq=1.3333 c) The average number of customers waiting L = 1.3333 + 0.40.6 L = 2 d) The average time a customer’s spends waiting Wq= 1.33330.4 ...
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...inputs – the nature of the contractual relationship between the providers of inputs to a firm may be quite complicated 2 Contractual Relationships • Some contracts between providers of inputs may be explicit – may specify hours, work details, or compensation • Other arrangements will be more implicit in nature – decision-making authority or sharing of tasks 3 Modeling Firms’ Behavior • Most economists treat the firm as a single decision-making unit – the decisions are made by a single dictatorial manager who rationally pursues some goal • usually profit-maximization 4 Profit Maximization • A profit-maximizing firm chooses both its inputs and its outputs with the sole goal of achieving maximum economic profits – seeks to maximize the difference between total revenue and total economic costs 5 Profit Maximization • If firms are strictly profit maximizers, they will make decisions in a “marginal” way – examine the marginal profit obtainable from producing one more unit of hiring one additional laborer 6 Output Choice • Total revenue for a firm is given by R(q) = p(q)q • In the production of q, certain economic costs are incurred [C(q)] • Economic profits () are the difference between total revenue and total costs (q) = R(q) – C(q) = p(q)q –C(q) 7 Output Choice • The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the function with respect to q equal to zero ...
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