In statistics , an expectationmaximization EM algorithm is an iterative method for finding maximum likelihood ... in generalized expectationmaximization GEM algorithm, in which one only seeks an increase in the objective ...&type pdf The ExpectationMaximizationAlgorithm , by Frank Dellaert, gives an easier explanation of EM algorithm in terms of lowerbound maximization. http www.seanborman.com publications EM algorithm.pdf The ExpectationMaximizationAlgorithm A short tutorial , A self contained derivation of the EM ... hierarchy in C GPL including Gaussian Mixtures DEFAULTSORT ExpectationmaximizationAlgorithm Category ... Leibler divergence . Then the steps in the EM algorithm may be viewed as Expectation step ... and its faster variant Ordered subset expectationmaximization is also widely used in medical ... EM can be utilised with constrained estimation techniques. Expectation conditional maximization ECM ... depends on unobserved latent variable s. The EM iteration alternates between performing an expectation E step, which computes the expectation of the Likelihood function Log likelihood log likelihood evaluated using the current estimate for the parameters, and a maximization M step, which computes ... algorithm was explained and given its name in a classic 1977 paper by Arthur P. Dempster Arthur Dempster ... Rubin title Maximum Likelihood from Incomplete Data via the EM Algorithm journal Journal of the Royal ... Properties of the EM Algorithm journal Annals of Statistics volume 11 issue 1 month Mar. year 1983 .... The EM algorithm seeks to find the MLE of the marginal likelihood by iteratively applying the following two steps Expectation step E step Calculate the expected value of the log likelihood function ... theta t left log L boldsymbol theta mathbf X , mathbf Z right , math Maximization step M step Find the parameter ... simply by iterating over math mathbf Z math or through an algorithm such as the Viterbi algorithm ... an iterative algorithm, in the case where both math boldsymbol theta math and math mathbf Z math ... more details
about an algorithm Israeli food corporation Osem company In mathematical optimization , the ordered subset expectationmaximization OSEM method NOT algorithm is an iterative method that is used in computed tomography . In applications in medical imaging , the OSEM method is used for positron emission tomography , for single photon emission computed tomography , and for Computed tomography X ray computed tomography . The OSEM method is related to the expectationmaximization EM method of statistics. The OSEM method is also related to methods of filtered back projection . References Hudson, H.M., Larkin, R.S. 1994 Accelerated image reconstruction using ordered subsets of projection data , IEEE Trans. Medical Imaging , 13 4 , 601&ndash 609 doi 10.1109 42.363108 Hutton, Brian F., Hudson, H. Malcolm, Beekman, Freek J. 1997 A clinical perspective of accelerated statistical reconstruction , European Journal of Nuclear Medicine and Molecular Imaging , 24 7 , 797&ndash 808 doi 10.1007 BF00879671 Ing Tsung Hsiao and Hsuan Ming Huang 2010 An accelerated ordered subsets reconstruction algorithm using an accelerating power factor for emission tomography , Physics in Medicine and Biology 55 599. doi 10.1088 0031 9155 55 3 003 External links http osem.s pla.net Home page with IEEE paper and more information http osem.s pla.net Software Category Optimization algorithms and methods Category Medical statistics Category Medical imaging statistics stub ... more details
Maximization or maximisation can refer to Exaggeration Maximization in the sense of exaggeration Entropy maximizationMaximization economics Profit maximization Utility maximization problem Budget maximizing model Shareholder value maximization Optimization mathematics Expectationmaximizationalgorithm statistics See also Minimization disambig ... more details
wiktionary expectationExpectation may refer to Expectation epistemic Expected value , in mathematical probability theory Expectation value quantum mechanics Expectationmaximizationalgorithm , in statistics Great Expectations , a 1860 61 novel serial by Charles Dickens Expectations album , a 1971 album by Keith Jarrett disambig Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. de Erwartung nl Verwachting tr Beklenti ... more details
Expert subject Mathematics date November 2008 An entropy maximization problem is a convex optimization problem of the form maximize math f 0 vec x sum i 1 n x i log x i math subject to math A vec x leq b, quad mathbf 1 T vec x 1 math where math vec x in mathbb R n math is the optimization variable, math A in mathbb R m times n math and math b in mathbb R m math are problem parameters, and math mathbf 1 math denotes a vector whose components are all 1. See also Principle of maximum entropy External links cite book last Boyd first Stephen coauthors Lieven Vandenberghe title Convex Optimization publisher Cambridge University Press date 2004 pages p. 362 isbn 0521833787 url http www.stanford.edu boyd cvxbook bv cvxbook.pdf accessdate 2008 08 24 Category Mathematical optimization Category Convex optimization mathapplied stub ... more details
refimprove date October 2006 In economics , profit maximization is the short run process by which a firm determines the price and input economics output level that returns the greatest Profit economics profit . There are several approaches to this problem. The total revenue&ndash total cost method relies on the fact that profit equals revenue minus cost, and the marginal revenue &ndash marginal cost method is based on the fact that total profit in a perfectly competitive market reaches its maximum point where marginal revenue equals marginal cost. Basic definitions Any costs incurred by a corporation firm may be classed into two groups fixed costs and variable costs . Fixed costs are incurred by the business at any level of output, including zero output. These may include equipment maintenance, rent, wages, and general upkeep. Variable costs change with the level of output, increasing as more product is generated. Materials consumed during production often have the largest impact on this category. Fixed cost and variable cost, combined, equal total cost . Revenue is the amount of money ... right thumb 250px Profit Maximization The Totals Approach To obtain the profit maximising output ... max marginal small.svg right thumb 250px Profit maximization using the marginal approach An alternative ... complicated profit maximization solutions involve the use of game theory . Maximizing revenue method ... the math Pi max math conditions by maximizing revenues. Changes in total costs and profit maximization ... a firm s optimal level of output, a firm can also set price to maximize profit. Profit maximization .... ref name pindyck Pindyck, R and Rubinfeld, D 2001 p. 333. ref Fortunately the profit maximization .... ref MPL, MRPL and profit maximization The general rule is that firm maximizes profit by producing that quantity of output where marginal revenue equals marginal costs. The profit maximization issue ... Profit Maximization in Perfect Competition by Fiona Maclachlan, Wolfram Demonstrations Project ... more details
Distinguish Expected utility Unreferenced date December 2009 Context date October 2008 A qualification introduced by Jeremy Bentham , to distinguish between two different types of utility utilities , or, rather, sources of utility for utility, being identical to hedonism pleasure , remains always qualitatively the same . Expectation utilities are future regarding, and thus imply desires and beliefs natural utilities are not. Expectation utilities allow for long term projects, which provide a higher proportion of utility than the natural utilities favored by those agents that can only pursue their immediate interest. DEFAULTSORT Expectation Utilities Category Utility Econ theory stub ... more details
Unreferenced stub auto yes date December 2009 Contract law Expectation damages are damages recoverable from a breach of contract breach of contract by the non breaching party. It originates from an injured party s interest in realizing the value of the expectancy that was created by the promise of the other party. The purpose of expectation damages is to put the non breaching plaintiff party in the position he would have occupied had the contract been fulfilled. Expectation damages can be contrasted to reliance damages and restitution restitution damages , which are remedies that address other types of interests of parties involved in contract enforceable promises . Expectation damages are measured by the diminution in value, coupled with consequential damages consequential and incidental damages incidental damages. Measuring Expectation Damages In expectation damages, the measure of damages is the difference between what was given and what was promised, along with consequential and incidental expenses. The proper amount is that which gives the non breaching party the benefit of the bargain. However, it is important to note that expectation damages are not punitive its theoretical purpose is to place the injured, non breaching party in the same position that they would have occupied had there been full performance of the contract. In other words, it is the amount that makes the injured party indifferent to the breach. See also Smith v. Bolles , 132 U.S. 125 1889 , limiting expectation damages from fraudulent conduct to those legitimately attributable to defendant s misrepresentation, and precluding awards based on unrealized speculation. Compensatory damages Loss of chance in English law Punitive damages DEFAULTSORT Expectation Damages Category Contract law Law stub ... more details
For the 2006 South Korean television drama Great Inheritance Infobox Korean film name The Greatest Expectation image Greatest Expectation movie poster.jpg caption Theatrical poster hangul hanja rr Widaehan yusan mr director Oh Sang hoon producer writer Lee Won hyeong br Lee Won jae br Oh Sang hoon starring Lim Chang jung br Kim Seon ah br Kim Soo mi music Jo Seong woo cinematography editing Kyeong Min ho distributor CJ Entertainment released 24 October 2003 runtime 115 min. country South Korea language Korean budget The Greatest Expectation is a 2003 South Korea n romantic comedy film. External links http www.hancinema.net korean movie The Greatest Expectation.php?ac 1 The Greatest Expectation at HanCinema Cinema of Korea DEFAULTSORT Greatest Expectation, The Category 2003 films Category Korean language films Category South Korean films Korea film stub ... more details
Unreferenced date December 2009 In English law , the concept of legitimate expectation arises from administrative law , a branch of public law . In proceedings for judicial review , it applies the principles of fairness and reasonableness to the situation where a person has an expectation or interest in a public body retaining a long standing practice or keeping a promise. Discussion The traditional constraint on a public body has been the test of irrationality , also known as Wednesbury unreasonableness ..., when faced with claims of a legitimate expectation, the courts have begun to require public officials ... expectation to protect the public interest in consistency and certainty through a test of proportionality ... a decision is taken if he or she has a legitimate expectation of being heard. But the fact that a person ... expectation unless fairly specific representations as to policies affecting future conduct ... any change is finally decided and, if the citizen s expectation is real, the courts might require the public body to identify an overriding public interest to trump the particular expectation. This supplements ... or irrational. The idea of legitimate expectation has received sufficient mention both academically and in case law so as to effectively merit being referred to as the doctrine of legitimate expectation. Legitimate expectation has been said to be a new category of fairness, with the dicta of Bingham ... for a public authority to do so, with Legitimate expectation thus being the public law equivalent ... 2000 showed that legitimate expectation is recognized in cases where the relevant authority had made ... with contract and the doctrine of estoppel. The clearest mention of the doctrine of legitimate expectation ... on its own. Reference to legitimate expectation is also made in the early and famous GCHQ case ... expectation as being Legitimate or reasonable expectation may arise either from an express promise ... See also Legitimate expectation in Singapore Category English administrative law de Vertrauensschutz ... more details
About the concept of expectation as a thought or belief expectation in the context of probability theory and statistics expected value In the case of uncertainty , expectation is what is considered the most likely to happen. An expectation, which is a belief that is centered on the future , may or may not be realistic. A less advantageous result gives rise to the emotion of disappointment . If something happens that is not at all expected it is a surprise emotion surprise . An expectation about the behavior or performance of another person, expressed to that person, may have the nature of a strong request, or an order. Expectations of well being Richard Lazarus asserts that people become accustomed to positive or negative life experiences which lead to favorable or unfavorable expectations of their present and near future circumstances. Lazarus notes the widely accepted philosophical principle that happiness depends on the background psychological status of the person...and cannot be well predicted without reference to one s expectations. ref name Lazarus Lazarus, Richard. Emotion and Adaptation . Oxford University Press, 1991. ref With regard to happiness or unhappiness, Lazarus notes that people whose objective conditions of life are those of hardship and deprivation often make a positive assessment of their well being, while people who are objectively well off...often make a negative assessment of their well being. Lazarus argues that the most sensible explanation of this apparent ... that a person s expectation is directly linked to the Self fulfilling prophecy Self fulfilling Prophecy . Whether or not such an expectation was truthful or not has little or no effect on the outcome ... will see the expectation to its inevitable conclusion. There is an inherent danger in this kind ... of in terms of causality or cause and effect, the higher a person s expectation and the lower ... expectation div style column count 3 moz column count 3 webkit column count 3 Collective belief Delusion ... more details
In music cognition melodic expectation is the tendency for a person listening to a melody to have a feeling or Expectation epistemic expectation for what might come next in the melody. For example, if the ascending musical partial octave do re mi fa sol la ... is heard, listeners familiar with Western music will have a strong expectation to hear one more note, ti , to complete the octave. Leonard Meyer Leonard Meyer s Emotion and Meaning in Music 1956 is the classic text in music expectation. Meyer s starting point is the belief that the experience of music as a listener is derived from one s emotions and feelings about the music, which themselves are a function of relationships within the music itself. Meyer writes that listeners bring with them a vast body of musical experiences that, as one listens to a piece, conditions one s response to that piece as it unfolds. Meyer argued that music s evocative power derives from its capacity to generate, suspend, prolongate, or violate these expectations. Meyer models listener expectation in two levels. On a perceptual level, Meyer draws on Gestalt psychology to explain how listeners build mental representations of auditory phenomena. Above this raw perceptual level, Meyer argues that learning shapes and re shapes one s expectations over time. Implication Realization Model main Implication Realization Narmour s 1992 Implication Realization I R Model is a detailed formalization based on Meyer s work on expectation. The theory focuses on how implicative intervals set up expectations for certain realizations to follow. Extensions to the Implication ... an expectation , Margulis attempts to model intervalic local expectation as well as more deeply schematic global expectation. For this, Margulis relies on Lerdahl s and Jackendoff s GTTM 1983 ... is explicit and realizable, and yields quantitative output. The output melodic expectation at each ... Press. ISBN 0 19 505834 8. Margulis, E. H. 2005 . A Model of Melodic Expectation . Music Perception ... more details
Infobox Album See Wikipedia WikiProject Albums Name Experiments In Expectation Album Experiments in Expectation Cover Type Album Artist Kill Sadie Released 2001 Genre Post hardcore Label Dim Mak Records Reviews AbsolutePunk.net 91 http www.absolutepunk.net showthread.php?t 334751 link Allmusic rating 3 5 Allmusic class album id r655102 pure url yes link This album Experiments In Expectations br 2001 Experiments in Expectation was the final full length release album by Seattle based band Kill Sadie . It was released on Dim Mak Records in 2001. Band Photography by Shawn Brackbill . Track listing The Ivy League Donor Prescription Epidemic 6 21 The Laugh Track for Contemporary Music 2 46 Rebirth Through Adaptation 2 07 Erf The Place You Live 4 49 The Quieting Function of Mouth 3 50 The Surgeon s Muse 3 31 Untitled Number Three Hundred and Three 2 07 The Cocktail Party Effect 3 35 A Ride in the Contrifuge 3 38 An Antiquated Bluff 8 33 2000s punk album stub Category 2001 albums Category Kill Sadie albums ... more details
Expectation propagation EP is a technique in Bayesian machine learning , developed by Thomas Minka . EP finds approximations to a probability distribution . It uses an iterative approach that leverages the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as Variational Bayesian methods . Reference Minka, T. 2001 Expectation Propagation for Approximate Bayesian Inference http research.microsoft.com en us um people minka papers ep minka ep uai.pdf Corrected pdf In Jack S. Breese, Daphne Koller Eds. UAI 01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, University of Washington, Seattle, Washington, USA, August 2 5, 2001. pages 362&ndash 369 External links http research.microsoft.com minka papers ep Minka s EP papers http research.microsoft.com en us um people minka papers ep roadmap.html List of papers using EP . Category Machine learning Category Bayesian statistics compsci stub ... more details
, one cannot have a reasonable expectation of privacy in things held out to the public. A well known ... car. While a person may have a subjective expectation of privacy in his her car , it is not always ... do not have an objective expectation of privacy. ref See, e.g., Oliver v. United States . ref Privacy and search The expectation of privacy is crucial to distinguishing a legitimate, reasonable ... expectation of privacy 2 and that expectation of privacy must be reasonable, in the sense ... expectation that the evidence obtained would not be available to the public. In other words, the person ... , then no subjective expectation of privacy is assumed. ref Mark Tunick 1998 Practices and Principles ... Objectivity philosophy objectively would society at large deem a person s expectation of privacy to be reasonable ... reasonable expectation of privacy and thus no search when officers hovering ... a reasonable expectation of privacy in the contents of their e mail in United States v. Warshak , although ... more details
Infobox Album See Wikipedia WikiProject Albums Name Annihilation of Expectation Type ep Longtype Split album Artist The Knife Trade Through the Eyes of the Dead Cover Released 2005 Recorded November 2004 Genre Metalcore Deathcore Length 36 17 Label Lovelost Records Producer Jamie King Reviews Chronology Through the Eyes of the Dead Last album The Scars of Ages EP br 2004 This album Annihilation of Expectation br 2005 Next album Bloodlust album Bloodlust br 2005 Annihilation of Expectation was a split recorded by melodic death metal band The Knife Trade who contributed the first five tracks and deathcore act Through the Eyes of the Dead who contributed the final five tracks . Track listing tracklist title1 Intro length1 1 21 title2 The Silent Life length2 3 47 title3 Mortification Under Scarlet Skies length3 3 53 title4 Resurrection length4 3 23 title5 Off With Their Heads length5 4 51 title6 Intro length6 0 53 title7 Abyssal Creation length7 4 10 title8 Reconstruction Of The Female Anatomy length8 3 50 title9 Erratic Perception length9 4 11 title10 Truest Shade Of Crimson length10 6 02 total length 36 17 Credits The Knife Trade Joey Stiletto Vocals Ryan Knight Guitar Ryan McCullough Guitar Daniel Shroyer Bass Nate Lumbra Drums Through The Eyes Of The Dead Anthony Gunnells Vocals Justin Longshore Guitar Chris Anderson Guitar Jeff Springs Bass Dayton Cantley Drums Trivia Ryan Knight, guitarist for The Knife Trade, would go on to join Arsis , and later go on to join The Black Dahlia Murder . This album is Through The Eyes of The Dead s last album released on Lovelost Records. DEFAULTSORT Annihilation Of Expectation Category Through the Eyes of the Dead albums Category Split EPs Category 2005 EPs 2000s metalcore album stub 2000s death metal album stub ... more details
In probability theory , a conditional expectation also known as conditional expected value or conditional ... distribution . The concept of conditional expectation is extremely important in Andrey Kolmogorov Kolmogorov ... of conditional probability itself is actually defined in terms of conditional expectation. Introduction Let X and Y be discrete random variable s, then the conditional expectation of X given the event ... to define both conditional expectation, and conditional probability. Formal definition Let math ... B subseteq mathcal A math . Then a conditional expectation of X given math scriptstyle mathcal ... E X mathcal B math is simply the name of the conditional expectation function. Discussion A couple ... the required property that a conditional expectation must satisfy. The required property has the same form as the last expression in the Introduction section. Existence of a conditional expectation ... of the same conditional expectation will only differ on a null set set of probability zero . The ... expectation math scriptstyle E X mathcal B math over a finer grained algebra math scriptstyle ... the conditional expectation using the pre image of with respect to Y math mathcal B sigma Y Y 1 left Sigma right Y 1 S S in Sigma math This suffices to ensure that the conditional expectation is &sigma Y measurable. Although conditional expectation is defined to condition on events in the underlying ... with respect to the Borel algebra Borel algebra on 0,1 . Note that the expectation of this random ... operatorname P A mathcal B math is the conditional expectation of the indicator function for A math ... for all &omega &Omega . An expectation of a random variable with respect to a regular conditional probability is equal to its conditional expectation. For the trivial sigma algebra math ... of conditional expectation that we provided above, the fact that Y is a real random variable is irrelevant ... of with respect to Q. The defining condition of conditional expectation then is the equation math ... more details
The Expectations Hypothesis of the term structure of interest rates also known as Term structure Yield Curve is the proposition that the long term rate is determined by the market s expectation for the short term rate plus a constant risk premium Sarno et al., 2007 . It has been found that the expectation hypothesis has been tested and rejected using a wide variety of interest rates, over a variety of time periods and monetary policy regimes Guidolin et al., 2008 . This analysis is supported in a study conducted by Sarno, where it is concluded that while conventional bivariate procedure provides mixed results, the more powerful testing procedures, for example expanded Vector Autoregression test, suggest rejection of the EH throughout the maturity spectrum examined. A common reason given for the failure of the EH is that the risk premium is not constant as the expectation hypothesis requires, but is time varying. However, research by Guidolin and Thornton 2008 suggest otherwise. It is postulated that the expectation hypothesis fails because short term interest rates are not predictable to any significant degree. While traditional term structure tests mostly indicate that expected future interest rates are ex post inefficient forecasts, Froot 1989 has an alternative take on it. At short maturities, the expectation hypothesis fails. At long maturities, however, changes in the yield curve reflect changes in expected future rates one for one. 1 i lt n 1 i st year 1 1 i st year 2 cdots 1 i st year n This hypothesis assumes that the various maturities are perfect substitutes and suggests that the shape of the yield curve depends on market participants expectations of future interest rates. These expected rates, along with an assumption that arbitrage opportunities will be minimal, is enough information to construct a complete yield curve. For example, if investors have an expectation of what 1 year interest rates will be next year, the 2 year interest rate can be calculate ... more details
Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team should have won based on the number of run baseball runs they scored and allowed. Comparing a team s actual and Pythagorean winning percentage can be used to evaluate how lucky that team was by examining the variation between the two winning percentages . The term is derived from the formula s resemblance to the Pythagorean theorem . The basic formula is math mathrm Win frac text runs scored 2 text runs scored 2 text runs allowed 2 frac 1 1 text runs allowed text runs scored 2 . math where Win is the winning ratio generated by the formula. The expected number of wins would be the expected winning ratio multiplied by the number of games played. Empirical origin Empirically, this formula correlates fairly well with how baseball teams actually perform, although an exponent of 1.81 is slightly more accurate. This correlation is one justification for using run baseball runs as a unit of measurement for player performance. Efforts have been made to find the ideal exponent for the formula, the most widely known being the Pythagenport formula ref http www.baseballprospectus.com article.php?articleid 342 Baseball Prospectus Articles Revisiting the Pythagorean Theorem Bot generated title ref developed by Clay Davenport of Baseball Prospectus 1.5 log r ra g 0.45 and the less well known but equally if not more effective Pythagenpat formula r ra g sup 0.287 sup , developed by David Smyth. ref http gosu02.tripod.com id69.html W Estimators Bot generated title ref Davenport expressed his support for the latter of the two, saying blockquote After further ... via James Pythagorean expectation. The formula says that a team s win percentage equals the following ... James Pythagorean expectation to professional basketball while a researcher at STATS, Inc. . He ... cgi bin pointspread.cgi?league mlb Current Major League Baseball Pythagorean expectation. http ... more details
200px thumb lright Flow chart of an algorithm Euclid s algorithm for calculating the greatest common divisor g.c.d. of two numbers a and b in locations named A and B. The algorithm proceeds by successive ... B is less than or equal to the number a in location A THEN the algorithm specifies B B A meaning ... of B is 0, yielding the g.c.d. in A. Algorithm derived from Scott 2009 13 symbols and drawing style from Tausworthe 1977 . In mathematics and computer science , an algorithm IPAc en audio en ... mathematical algorithm, for example, can be described in a finite number of English words Rogers ... the algorithm There is a computing agent, usually human, which can react to the instructions and carry ... an algorithm is a procedure for computing a function with respect to some chosen notation for integers ... an algorithm is a step by step procedure for calculations. Starting from an initial state and initial input perhaps null string empty , ref An algorithm has zero or more inputs, i.e., quantity quantities which are given to it initially before the algorithm begins Knuth 1973 5 . ref the instructions ... A procedure which has all the characteristics of an algorithm except that it possibly lacks finiteness ..., eventually producing output ref An algorithm has one or more outputs, i.e. quantities which have a specified ... not including the input is an algorithm is debatable. Rogers opines that a computation is carried ... chapter What is an algorithm? title Mathematics Unlimited &mdash 2001 and beyond editor1 first B ... the definition of algorithm see Algorithm characterizations . For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations , see Algorithm examples . While there is no generally accepted formal definition of algorithm, an informal definition ... people, a program is only an algorithm if it stops eventually for others, a program is only an algorithm ... terminate in a finite number of steps Stone 1973 7 8 . ref A prototypical example of an algorithm ... more details
In microeconomics , the utility maximization problem is the problem consumer consumers face how should I spend my money in order to maximize my utility ? It is a type of Optimal decision optimal decision problem . Basic setup Suppose their consumption set , or the enumeration of all possible consumption bundles that could be selected if there are no budget constraints, has L commodities and is limited to positive amounts of consumption of each commodity. Let x be the vector x x sub i sub i 1,... L containing the amounts of each commodity, then math x in textbf R L . math Suppose also that the prices p of the L commodities are positive math p in textbf R L , math and that the consumer s wealth is w , then the set of all affordable packages, the budget set , is math B p, w x in textbf R L langle p , x rangle leq w , math where math langle p , x rangle math is the Inner product inner product of p and x , or the total cost of consuming x of the products at price level p math langle p , x rangle sum i 1 L p i x i . math The consumer would like to buy the best package of commodities it can afford. Suppose that the consumer s utility function u is a real valued function with domain of the commodity bundles, or math u textbf R L rightarrow textbf R . math Then the consumer s optimal choices x p , w are the utility maximizing bundle that is in the budget set, or math x p, w operatorname argmax x in B p, w u x math . Finding x p , w is the utility maximization problem . If u is continuous and no commodities are free of charge, then x p, w exists. Citation needed date August 2010 If there is always a unique maximizer, then it is called the Marshallian demand function . The relationship between the utility function and Marshallian demand in the Utility Maximization Problem mirrors the relationship ... Choice Modelling Utility function Expenditure minimization problem Linear programming Profit maximization ... of Cobb Douglas Type Utility Functions in 3D DEFAULTSORT Utility Maximization Problem Category ... more details
In mathematics , the Regiomontanus angle maximization problem , is a famous Maxima and minima optimization problem posed by the 15th century German mathematician Johannes M ller ref Eli Maor , Trigonometric Delights , Princeton University Press , 2002, pages 46&ndash 48 ref also known as Regiomontanus . The problem is as follows Image Regiomontanus.problem.png right thumb 550px The two dots at eye level are possible locations of the viewer s eye. A painting hangs from a wall. Given the heights of the top and bottom of the painting above the viewer s eye level, how far from the wall should the viewer stand in order to maximize the angle subtended angle subtended by the painting and whose vertex is at the viewer s eye? If the viewer stands too close to the wall or too far from the wall, the angle is small somewhere in between it is as large as possible. The same approach applies to finding the optimal place from which to kick a ball in rugby. ref citation title Rugby and Mathematics A Surprising Link among Geometry, the Conics, and Calculus first1 Troy last1 Jones first2 Steven last2 Jackson journal Mathematics Teacher volume 94 issue 8 pages 649 654 year 2001 url http wesclark.com rrr rugby and math.pdf . ref For that matter, it is not necessary that the alignment of the picture be at right angles we might be looking at a window of the Leaning Tower of Pisa or a realtor showing off the advantages of a sky light in a sloping attic roof. Solution by elementary geometry Image Regiomontanus.solution.png right thumb 550px There is a unique circle passing through the top and bottom of the painting and tangent to the eye level line. By elementary geometry, if the viewer s position were to move along the circle, inscribed angle the angle subtended by the painting would remain constant . All positions on the eye level line except the point of tangency are outside of the circle, and therefore the angle subtended by the painting from those points is smaller. By Euclid s Elements ... more details
The Feast of the Expectation of the Blessed Virgin Mary was a Catholic Feast that was originally celebrated in Spain, but started to be celebrated in other Catholic countries. ref CathEncy title Feast of the Expectation of the Blessed Virgin Mary url http www.newadvent.org cathen 05712a.htm ref References reflist RC stub Category Roman Catholic Church ... more details
Unreferenced date October 2009 Quantum field theory cTopic Tools In quantum field theory the vacuum expectation value also called condensate or simply VEV of an Operator physics operator is its average, expected value in the Vacuum The quantum mechanical vacuum vacuum . The vacuum expectation value of an operator var O var is usually denoted by math langle O rangle math . One of the best known examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect . This concept is important for working with Correlation function quantum field theory correlation functions in quantum field theory . It is also important in spontaneous symmetry breaking . Examples are The Higgs field has a vacuum expectation value of 246 GeV . This nonzero value allows the Higgs mechanism to work. The chiral condensate in Quantum chromodynamics gives a large effective mass to quark s, and distinguishes between phases of quark matter . The gluon condensate in Quantum chromodynamics may be partly responsible for masses of hadrons. The observed Lorentz invariance of space time allows only the formation of condensates which are Lorentz scalar s and have vanishing charge physics charge . Thus fermion condensates must be of the form math langle overline psi psi rangle math , where var var is the fermion field. Similarly a tensor field, var G var sub var var sub , can only have a scalar expectation value such as math langle G mu nu G mu nu rangle math . In some Vacuum The quantum mechanical vacuum vacua of string theory , however, non scalar condensates are found. If these describe our universe , then Lorentz symmetry Lorentz violation Lorentz symmetry violation may be observable. See also Wightman axioms and Correlation function quantum field theory vacuum energy or dark energy Spontaneous symmetry breaking DEFAULTSORT Vacuum Expectation Value Category Quantum field theory Category Standard Model Quantum stub ko it Valore di aspettazione ... more details
Orphan date February 2009 Expectation of the Millennium Shi ism in History is a book on Shia Islam co written by Seyyed Hossein Nasr , Hamid Dabashi and Seyyed Vali Reza Nasr . External links http search.barnesandnoble.com booksearch isbnInquiry.asp?userid hJ7lQUWCY9&isbn 088706843X&itm 1 Book description at Barnes & Nobel Category Works by Hossein Nasr Islam book stub ... more details
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