levitation. In the past‚ magnetic levitation was attempted by using permanent magnets. Earnshaw’s theorem however‚ proves that this is mathematically impossible. There exists no arrangement of static magnets of charges that can stably levitate an object. There are however means of circumventing this theorem by altering its basic assumptions. The following conditions are exceptions to Earnshaw’s theorem: • Diamagnetism: occurs in materials which have a relative permeability less than one. The result
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Algebra is one of the broad parts of mathematics‚ together with number theory‚ geometry and analysis. For historical reasons‚ the word "algebra" has several related meanings in mathematics‚ as a single word or with qualifiers. • As a single word without article‚ "algebra" names a broad part of mathematics (see below). • As a single word with article or in plural‚ "algebra" denotes a specific mathematical structure. See algebra (ring theory) and algebra over a field. • With a qualifier‚ there
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treatment is unified in the sense that these probabilistic quantities are well defined for both ergodic and nonergodic Markov chains‚ and all results are valid for both approximation methods. Our proofs are simple in the sense that they only depend on one theorem from analysis: Weierstrass’ M-test. Our results include the convergence of stationary probability distributions when the Markov chain is ergodic. This work was directly motivated by the need to compute stationary probabilities for infinite-state Markov
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m∠ABC + m∠CBD = m∠ABD Linear Pair Postulate: ∠1 and ∠2 are linear pair → ∠1 and ∠2 are supplementary Theorems: Vertical Angles Theorem (V.A.T. or V.A.C): ∠1 and ∠2 are vertical angles → ∠1 ∠2 Right Angle Congruence Theorem (R.A.C): ∠1 and ∠2 are right angles → ∠1 ∠2 Congruent Supplements Theorem (C.S.T.): ∠1 and ∠2 are supp and ∠1 and ∠3 are supp → ∠2 ∠3 Congruent Complements Theorem (C.C.T): ∠1 and ∠2 are comp and ∠1 and ∠3 are comp → ∠2 ∠3 Corresponding ∠ Thm (C.A.T.): if a ⃦ b
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Measures of Risk Aversion Financial Economics Martín Solá October 2010 Martín Solá (FE) Measures of Risk Aversion 08/10 1 / 41 Introduction In this …rst stage we will study the individual decisions of optimal portfolio choice under uncertainty and its consequences in the valuation of risky assets. In short‚ the Financial Theory rests on the no-arbitrage principle. The idea behind this principle is that it is not possible to make pro…ts without risk‚ without initial investment
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Digital Logic •Introduction‚ Truth Tables and Boolean expressions •Logic Gates •Combination of Logic Gates •Circuit tracing and Boolean expressions •Creating Truth Table from a circuit •Creating a Circuit from a Truth Table •Basic Boolean Algebra •Using Boolean Algebra for Circuit Simplification •Practical Considerations Digital Circuit versus an analog circuit •Digital systems operate based on discrete information or signals‚ were as an analog system relies on continuous information
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All the Mathematics You Missed Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge‚ but few have such a background. This book will help students see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of the most important undergraduate topics in mathematics‚ emphasizing the intuitions behind the subject. The topics include linear
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4/24/2013 Microeconomics Introduction to General Equilibrium and Welfare Economics 1 Welfare Economics • Are market allocations of resources socio-economically efficient? • Welfare Economics: “The branch of economic theory concerned with the social desirability of alternative economic states.” • The theory is used to distinguish circumstances under which markets can be expected to perform well • It also helps define some circumstances under which we might want government
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Niels Henrik Abel On August 5th‚ 1802‚ Soren George Abel and Marie Simonsen gave birth to their son Niels Henrik Abel. Niels Able was born in Nedstrand‚ Norway (Encyclopedia Britannica). Niels grew up in a very religious family. His father‚ Soren had a degree in theology and philosophy. Soren was a pastor at Finnoy. As well as his father being a pastor‚ Niels’ grandfather‚ Hans Mathias Abel was a pastor at Gjerstad; where Niels’ father Soren was a chaplain during his childhood (WOLFRAM RESEARCH)
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Assignment 7: Mean-Variance Portfolio Theory ------------------------------------------------- Top of Form 1 . Consider‚ as in Lecture 7.1‚ a portfolio of two risky assets‚ with expected returns rˉ1‚rˉ2‚ variances σ21‚σ22 and covariance σ1‚2. No other assets are available. You have to allocate $1 mln of investment in the portfolio of the two assets in order to minimize total portfolio variance. What is the optimal amount of investment in asset 1 (in mln dollars)? Assume expected returns are
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