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We also prove that among all matrix functions with these properties, there exists a distinguished one that maximizes the entropy.


The ArovGrossman Model and the Burg Multivariate Entropy


In this article we deal with the ArovGrossman functional model to describe all the solutions of the Covariance Extension Problem for qvariate stationary stochastic processes and we find the density that maximizes the Burg Multivariate Entropy.


With this correspondence, the density that maximizes the Burg Multivariate Entropy corresponds to the function H\equiv0.


An asymptotic behavior of the corresponding entropy numbers is calculated.

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 The dependence of the entropy of a homogeneous system on the composition is investigated with the help of a reversible adiabatic process which allows the change of composition by means of a semipermeable wall. The conditions of equilibrinm for phase transition and for homogeneous chemical reaction are derived in a new way. Next the criterion of minimum energy for constant entropy and volume is derived from the principle of increase of entropy. This criterion is then applied to obtain the conditions... The dependence of the entropy of a homogeneous system on the composition is investigated with the help of a reversible adiabatic process which allows the change of composition by means of a semipermeable wall. The conditions of equilibrinm for phase transition and for homogeneous chemical reaction are derived in a new way. Next the criterion of minimum energy for constant entropy and volume is derived from the principle of increase of entropy. This criterion is then applied to obtain the conditions of equilibrium and stability with the help of Lagrange's multipliers. The conditions of stability are expressed in several alternative forms. Next the equilibrium properties of a binary system arc considered, and some types of phase diagram are explained by means of equations. The theory is extended to the general heterogeneous equilibrium of a system consisting of any number of independent components. A system of equations for the change of temperature, pressure, and composition are obtained and are solved by means of determinants. Next Planck's theory of a binary solution is extended to a solution consisting of several solnte components, with the same conclusion regarding the lowering of freezing point as for a binary solution. Finally Planck's theory on the number of coexisting phases for aonecomponent system is extended to a system consisting of k components with the result that a state with, σ coexisting phases is more stable than one with σ1 phases: where σ is an integer not greater than k + 2.  本文首述如何应用一半渗透之壁使一物体所包含各种分子之数改变,因之决定此物体之熵与其各种分子数之关系,由此关系极易推出一物体在改变其形态时,如汽化凝结等,所应适合之平衡条件。且若形态不变,而发生内部化学作用时,其平衡条件亦易推得。 次述如何由熵之增加原理推出能量最小之法则,然後应用此法则,辅以拉革兰氏之不定乘子,以求得一物体之普遍平衡与稳定之条件。其稳定之条件且以各种不同之形式表示之。 继讨论二元物体在平衡时之性质,随之以多元物体之性质,求得一组方程式以决定当此物体之性质改变时,其温度压力及各种分子之数如何改变。曾特别注意及溶液之性质,对於融点之降低与沸点之升高有一普遍之证明。 最後推广卜朗克氏关於并存形态之理论於多元物体,得与卜氏相似之结论。  This paper deals with a method of treating problems of Turbulence from a kinetic point of view. Turbulence "temperature", "pressure", and "entropy" are first defined as state functions, and then the pressure and temperature are incorporated into the equations of motion. Turbulent flows through a circular pipe and between parallel planes are considered in some detail, while the problems of turbulence decay, turbulence structure, and correlation characteristics are briefly discussed. Practically in all cases,... This paper deals with a method of treating problems of Turbulence from a kinetic point of view. Turbulence "temperature", "pressure", and "entropy" are first defined as state functions, and then the pressure and temperature are incorporated into the equations of motion. Turbulent flows through a circular pipe and between parallel planes are considered in some detail, while the problems of turbulence decay, turbulence structure, and correlation characteristics are briefly discussed. Practically in all cases, the constancy of the turbulence temperature is found to play an important role.  本文系用热性论之观点研讨激流之各项问题。先规定激流之情态函数,如温度压力,熵等,然後将激流温度纳入运行公式内,以求得流速之分布,激流之构造与消灭等情形。自各方面观之,本文之理论结果,大都与事实相符。  Until now there is no universally accepted formulation of the third law of thermodynamics. In this paper, a formulation appeared more general to the author is presented, viz. the derivation of Nernst's heat theorem from the principle of the unattainability of the absolute zero of temperature. Some controversal points, like the absolute value of entropy and the proof of the unattainability of absolute zero by means of Carnot cycle, are discussed.  热力学第三定律的说法至今还没有一致。本文提出一种作者认为较普遍的说法:以绝对零度不能达到为基础导出能氏定理。本文还讨论了一般所争论的问题,如熵的绝对值问题,利用卡诺循环证明绝对零度不能达到问题。   << 更多相关文摘 
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