Characterization of mean transformations

The mean transformations M(A,?B) are linear mappings and they are analogues of the matrix means of A,?B?≥?0. They are defined by operator monotone functions. In this article several properties are described and a part of them characterize the concept.     

A Volume Inequality for Quantum Fisher Information and the Uncertainty Principle

Let A ₁,…,A _N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

The exposed points of the set of invariant means on an ideal

Let be a -compact locally compact nondiscrete group and let be a -invariant ideal of . We denote the set of left invariant means on that are zero on (i.e. for all ) by . We show that, when is amenable as a discrete group and the closed -invariant subset of the spectrum of corresponding to is a -set, is very large in the sense that every nonempty -subset of contains a norm discrete copy of , where is the Stone- compactification of the set of positive integers with the discrete topology. In particular, we prove that has no exposed points in this case and every nonempty -subset of the set of left invariant means on contains a norm discrete copy of .

     

Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues

We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian,

     

Characterizations of classes of risk measures by dispersive orders

In this paper, a class C₁ of risk measures, which generalizes the class of risk measures for the right-tail deviation suggested by Wang [Wang, S., 1998. An actuarial index of the right-tail risk. North Amer. Actuarial J. 2, 88–101], is characterized in terms of dispersive order. If dispersive order does not hold, unanimous comparisons are still possible by restricting our attention to a subclass C₂C₁ and then the criterion is the excess-wealth order. Sufficient conditions for stochastic equivalence of excess-wealth ordered random variables are derived in terms of some particular measures of C₂.     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.     

DIRECT AND INVERSE THEOREMS FOR JACKSON MEANS OF ENTIRE EXPONENTIAL TYPE IN Ba SPACES

This paper presents a new type of interpolation of B_a spaces, with which a new characterization of B_a spaces by the Jackson means of entire exponential type is given.     

热注射法合成Cu2 SnSe3纳米晶及其光电转换性能

以乙酰丙酮铜、无水氯化亚锡为金属源,Se/OLA悬浊液为硒源,在油胺溶剂中热注射合成了Cu2 SnSe3纳米晶.采用TEM、XRD、EDS分别对典型纳米晶产物的形貌、物相和组成做了分析表征.通过不同反应温度的条件实验,研究了反应温度对最终产物的影响,探讨了相关规律.采用光电化学池评价了纳米晶的光电转换性能,结果表明Cu2 SnSe3纳米晶光电转换性能优良,表现出较好的应用前景.