# constrained

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**First class constraint**— In Hamiltonian mechanics, consider a symplectic manifold M with a smooth Hamiltonian over it (for field theories, M would be infinite dimensional). Poisson bracketsSuppose we have some constraints : f i(x)=0, for n smooth functions :{ f i } {i=… …52

**Lagrange multiplier**— Figure 1: Find x and y to maximize f(x,y) subject to a constraint (shown in red) g(x,y) = c …53

**Newtonian dynamics**— In physics, the Newtonian dynamics is understood as the dynamics of a particle or a small body according to Newton s laws of motion. Contents 1 Mathematical generalizations 2 Newton s second law in a multidimensional space 3 Euclidean structure …54

**Linear least squares (mathematics)**— This article is about the mathematics that underlie curve fitting using linear least squares. For statistical regression analysis using least squares, see linear regression. For linear regression on a single variable, see simple linear regression …55

**Economic Affairs**— ▪ 2006 Introduction In 2005 rising U.S. deficits, tight monetary policies, and higher oil prices triggered by hurricane damage in the Gulf of Mexico were moderating influences on the world economy and on U.S. stock markets, but some other… …56

**Mathematical optimization**— For other uses, see Optimization (disambiguation). The maximum of a paraboloid (red dot) In mathematics, computational science, or management science, mathematical optimization (alternatively, optimization or mathematical programming) refers to… …57

**Lagrange multipliers**— In mathematical optimization problems, the method of Lagrange multipliers, named after Joseph Louis Lagrange, is a method for finding the extrema of a function of several variables subject to one or more constraints; it is the basic tool in… …58

**constrain**— 01. Too many women s lives have been [constrained] by the sexist views held by some people in society. 02. The boss has turned down our request to expand the Research and Development Department due to financial [constraints]. 03. We had to… …59

**Degrees of freedom (statistics)**— In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.[1] Estimates of statistical parameters can be based upon different amounts of information or data. The number… …60

**Loot system**— A Loot System refers to a system of distributing items ( loot ) amongst a group of players in a game, most commonly in a Massively Multiplayer Online Role Playing Games (MMORPG). The Premise of a Loot System Loot Systems exist solely because of… …