Thec logc contribution to the electrolyte conductance and Onsager's reciprocal relation

The differential equations and the boundary conditions for the nonequilibrium binary distribution function of an unsymmetrical binary electrolyte are derived from the Ebeling-Falkenhagen continuity equation. The connection between the Onsager reciprocal relation and the binary distribution functions is shown. Further, Feistel's result for thec logc contribution to the conductance is extended to unsymmetrical binary electrolytes. The reason for the difference between Feistel's and Chen'sc logc term is explained, and the significance of Onsager's reciprocal relation for the calculation ofc logc and higher-concentration contributions of the conductance is discussed.     

Chromatographic study of the thermodynamics of solutions of hydrocarbons in liquid crystal solvents. Evidence for order disturbance by the solutes

Gas-chromatographic experiments were carried out in various phases of the solvents 4-acetoxy-N-[4-methoxy-benzylidene]-aniline, dibutoxyazoxybenzene, lithium stearate, dihexoxyazoxybenzene, and diheptoxyazoxybenzene. The solutes were linear, branched and cyclic alkanes, and substituted benzenes. Excess enthalpies, entropies, and free entropies were calculated from net retention volumes. In the nematic liquid crystalline phases the effect of order disturbance was significant in and but it was, by enthalpy-entropy compensation, not demonstrable in . Differences in flexibility and degree of expansion of the solutes did not result in significantly different values of the excess quantities.     

Preservation of transform orders under a semiparametric model and its mixture

In this paper, sufficient conditions for preservation of several transform orders under a typical family of semiparametric distributions are made. The preservation properties are developed to compare mixture semiparametric distributions. Possible applications of the achieved results to compare scale family of distributions and also compare coherent systems with dependent but identical components and series and parallel systems with randomized number of components are provided.     

Schrödinger方程的连续时空有限元方法

本文讨论Schr?dinger方程的连续时空有限元方法,通过引入相应的时空投影算子,利用实部虚部分离技巧,得到了变量u在时间节点处的L²范数,以及u和u_t的全局L²(H¹)和L²(L²)范数意义下的最优误差估计结果.该文的结论对进一步探索和设计Schr?dinger方程的数值算法是有益的.     

Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).     

Characterizations based on conditional expectations of the doubled truncated distribution

The expression of the continuous distribution function F(x) is obtained whenever % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGaa8xBaiaabIcacaWG4bGaaiilaiaadMha% caqGPaGaa8hiaiaab2dacaWFGaGaa8xraiaa-HcacaWFybGaa8hiai% aa-XhacaWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bca% cqGHKjYOcaWFGaGaa8xEaiaa-Lcaaaa!53EE!\[m{\rm{(}}x,y{\rm{)}} {\rm{ = }} E(X | x \le X \le y)\]is known. Moreover, we obtain the necessary and sufficient conditions so that any function m: ² is the conditional expectation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGOaGaamiwaerbhv2BYDwAHbacfiGaa8hiaiaacYha% caWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bcacqGHKj% YOcaWFGaGaa8xEaiaacMcaaaa!4D0D!\[E(X | x \le X \le y)\]of a random variable X with continuous distribution function. Furthermore, we relate m(x,y) to order statistics.     

Mass shifting roles of negative kernel mass in density estimation

f(x) is a univariate density in C ⁴ with bounded support. For any n and sufficiently small kernel bandwidths, the symmetric appendage of any negative mass, –U, to any smooth unimodal symmetric kernel of order p=2 shifts expected estimator mass from regions where f(x)>0 to regions where f(x)<0. For large n, the mean automatic kernel adaptation induced by –U is analyzed in the simplest MISE reduction scenario: The symmetric appendage of –U to the uniform kernel K(x, X) over MISE-optimal bandwidths reduces MISE by shifting K(x, X) mass asymmetrically across the observation X in the direction of decreasing |f(x)|.     

An analysis of cubic approximation schemes for conic sections

In this paper a piece of a conic section is approximated by a cubic or piecewise cubic polynomial. The main tool is to define the two inner control points of the cubic as an affine combination, defined by [0, 1], of two control points of the conic. If is taken to depend on the weightw of the latter, a function (w) results which is used to distinguish between different algorithms and to analyze their properties. One of the approximations is a piecewise cubic havingG ⁴ continuity at the break points.     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).