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associates with an algebra Acl of classical observables an algebra Aq of quantum observables The algebra Acl is usually realized as a commutative Poisson algebra 13) of derivable functions on a symplectic (or phase) space X The algebra Aq is, however, noncommutative in general and the quantization procedure must provide a correspondence Acl Aq : f A f Various procedures of quantization exist, and minimally require the following conditions, which loosely parallel those listed in Section 123: With the constant function 1 is associated the unity of Aq , The commutation relations of Aq reproduce the Poisson relations of Acl Moreover, they offer a realization of the Heisenberg algebra Aq is realized as an algebra of operators acting in some Hilbert space Most physical quantum theories may be obtained as the result of a canonical quantization procedure However, the prescriptions for the latter appear quite arbitrary Moreover, it is dif cult, if not impossible, to implement it covariantly It is thus dif cult to generalize this procedure to many systems Geometrical quantization [175] exploits fully the symplectic structure of the phase space, but generally requires more structure, such as a symplectic potential, for example, the Legendre form on the cotangent bundle of a con guration space In this regard, the deformation quantization appears more general in the sense that it is based on the symplectic structure only and it preserves symmetries (symplectomorphisms) [176, 177] The coherent state quantization that is presented here is by far more universal since it does not even require a symplectic or Poisson structure The only structure that a space X must possess is a measure This procedure can be considered from different viewpoints: It is mostly genuine in the sense that it veri es all the requirements above, including those relative to the Poisson structure when the latter is present It may also be viewed as a fuzzy cation of X: an algebra Acl of functions on X is replaced by an algebra Aq of operators, which may be considered as the coordinates of a fuzzy version of X, even though the original X is not equipped with a manifold structure The term fuzzy manifold, where points have noncommutative coordinates, was proposed by Madore [178] in his presentation of noncommutative geometry of simple manifolds such as the sphere As a matter of fact, ordinary quantum mechanics may also be viewed as a noncommutative version of the geometry of the phase space, where position and momentum operators do not commute [179] In this regard, the quantization of a set of data makes a fuzzy or noncommutative geometry emerge.



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even simple hand-laundry required staggering amounts of human time and labor A typical preindustrial wash involved scrubbing, boiling, and rinsing One load required 400 gallons of water weighing 400 pounds moved from pump or well or faucet to stove and tub in buckets and wash boilers The innovation and spread of mechanical clothes washers in the last century put an end to these painful but necessary processes By 1940, already 60 percent of the 25,000,000 electrically wired homes in the United States had a washing machine* It has taken China another 40 years to come to this point China is currently the largest market for washing machines in the world Annual imports of clothes washers rose from 128 million in 1981 to 194 million in 2003 About 95 percent of urban Chinese families and more than 40 percent of rural families have one Currently washing machines require 1,600 kilowatt hours (kWh) of electricity per urban household in China As China continues to modernize, it aims to switch from the simpler but





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Usually, PowerShell will be asked to do some other processing with the file so the result of Get-Content will either be assigned to a variable or piped into another command. For example, if the file comes from a GPS logger it might be piped into the Where-Object Cmdlet to select only the lines that are tagged as the Recommend minimum Data which begin $GPRMC and drop all the other lines of diagnostic information.

13) A Poisson algebra A is an associative algebra together with a Lie bracket X , Y {X , Y } that also satis es the Leibniz law: for any X A the action D X (Y ) = {X , Y } on A is a derivation {X , Y Z } = {X , Y }Z + Y {X , Z }

As a matter of fact, the space of real-valued smooth functions over a symplectic manifold, when equipped with the Poisson bracket, forms a Poisson algebra

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Finally, this procedure is, to a certain extent, a change of point of view in considering the system X, not necessarily a path to quantum physics In this sense, it could be called a discretization or a regularization [180] It shows a similitude with standard procedures pertaining to signal processing, for instance, those involving wavelets, which are coherent states for the af ne group transforming the time-scale half-plane into itself In many respects, the choice of a quantization appears as the choice of a resolution in looking at the system

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*Answerscom Washing Machine, wwwanswerscom/topic/washingmachine Jiang Lin and Maithili Iyer, Cold or Hot Wash: Technological Choices, Cultural Change, and Their Impact on Clothes-Washing Energy Use in China, Energy Policy,Volume 35 (2007): 3046 3052

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