A generalized Weyl—Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators

By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.     

二元混合型指数分布的识别性及其应用

对新提出的一类二元混合型指数分布和其他三类二元混合型指数分布,讨论了它们的分布识别问题,即记z=min（x1,x2）,I=i,当z=xi;记U-max（＆,x2）,J=j,当U=Xi;已知（Z,I）或（U,J）的分布,求（X1,X2）分布的唯一性问题．给出了（x1,x2）服从Marshall-Olkin型指数分布时,有关寿险中Z及u的精算现值的2个公式．     

二维连续信号的近似采样定理

利用加细方程的面具,给出该方程的一个近似解,并根据这个近似解构造出二维连续信号的近似采样定理.其近似采样函数是所求加细方程的近似解,它是由加细方程的面具唯一确定的逐段线性函数,且有显示的计算公式.因此可以根据需要选择加细方程的面具,从而达到控制近似采样函数的衰减速度.     

Coordinate-Momentum Intermediate Representation and Marginal Distributions of Quantum Mechanical Bivariate Normal Distribution

We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜.ψ〉｜^2, where ｜x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.     

On nonlinear bivariate singular integral operators

In this paper, we give some pointwise convergence and Fatou type convergence theorems for a family of nonlinear bivariate singular integral operators in the following form: where m₁,m₂ ≥ 1 are fixed natural numbers, and ω ∈ Ω, Ω denotes a nonempty set of indices endowed with a topology. Here, denotes a family of kernel functions and f belongs to the space of Lebesgue integrable functions . Some numerical examples and graphical illustrations supporting the results are also given.     

Bivariate Metal–Organic Frameworks with Tunable Spin-Crossover Properties

In this work, pyrazine ( A ), aminopyrazine ( B ), quinoxaline ( C ), and 5,6,7,8-tetrahydroquinoxaline ( D ) have been screened out among a large number of pyrazine derivatives to construct Hofmann-type metal–organic frameworks (MOFs) Fe(L)[M(CN)₄] (M=Pt, Pd) with similar 3D pillared-layer structures. X-ray single-crystal diffraction reveals that the alternate linkage between M and Fe^II ions through cyano bridges forms the 2D extended metal cyanide sheets, and ligands A – D acted as vertical columns to connect the 2D sheets to give 3D pillared-layer structures. Subsequently, a series of bivariate MOFs were constructed by pairwise combination of the four ligands A–D , which were confirmed by ¹H NMR, PXRD, FTIR, and Raman spectroscopy. The results demonstrated that ligand size and crystallization rate play a dominant role in constructing bivariate Hofmann-type MOFs. More importantly, the spin-crossover (SCO) properties of the bivariate MOFs can be finely tuned by adjusting the proportion of the two pillared ligands in the 3D Hofmann-type structures. Remarkably, the spin transition temperatures, T_c↑ and T_c↓ of Fe( A )_x( B )_1−x[Pt(CN)₄] (x=0 to 1) can be adjusted from 239 to 254 K and from 248 to 284 K, respectively. Meanwhile, the width of the hysteresis loops can be widened from 9 to 30 K. Changing Pt to Pd, the hysteresis loops of Fe( A )_x( B )_1−x[Pd(CN)₄] can be tuned from 9 (T_c↑=215 K, T_c↓=206 K) to 24 K (T_c↑=300 K, T_c↓=276 K). This research provides wider implications in the development of advanced bistable materials, especially in precisely regulating SCO properties.     

On two families of bivariate distributions with exponential marginals: Aggregation and capital allocation

In this paper, we consider two main families of bivariate distributions with exponential marginals for a couple of random variables $(X_1,X_2)$. More specifically, we derive closed-form expressions for the distribution of the sum $S=X_1+X_2$, the TVaR of $S$ and the contributions of each risk under the TVaR-based allocation rule. The first family considered is a subset of the class of bivariate combinations of exponentials, more precisely, bivariate combinations of exponentials with exponential marginals. We show that several well-known bivariate exponential distributions are special cases of this family. The second family we investigate is a subset of the class of bivariate mixed Erlang distributions, namely bivariate mixed Erlang distributions with exponential marginals. For this second class of distributions, we propose a method based on the compound geometric representation of the exponential distribution to construct bivariate mixed Erlang distributions with exponential marginals. Notably, we show that this method not only leads to Moran–Downton’s bivariate exponential distribution, but also to a generalization of this bivariate distribution. Moreover, we also propose a method to construct bivariate mixed Erlang distributions with exponential marginals from any absolutely continuous bivariate distributions with exponential marginals. Inspired from Lee and Lin (2012), we show that the resulting bivariate distribution approximates the initial bivariate distribution and we highlight the advantages of such an approximation.     

二元Freund型指数分布的特征及参数估计

利用分布密度分拆的思想,导出了二元Freund型指数分布的一个特征,利用该特征,获得了二元Freund型指数分布参数的最大似然估计及矩估计,还给出了强度服从二元Freund型指数分布时并联结构系统的可靠度估计及模拟.