The complexity and randomness of linear multi-secret sharing schemes with non-threshold structures

In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi- secret sharing scheme is measured by means of the complexity a and the randomness . Informally, the com- plexity a is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness is the ratio between the amount of information distributed to the set of users U = {1, …, n} and the minimum of information corresponding to every key. In this paper, we discuss a and of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make a and to be the minimum, respectively. That is, they are optimal.     

回归函数的混合型递归核估计的强相合性

本文讨论了把最小二乘估计和一类递归核估计结合起来所得回归函数的混合型递归核估计的强相合性.     

A Note on Closed Degrees of Difficulty of the Medvedev Lattice

We consider some nonprincipal filters of the Medvedev lattice. We prove that the filter generated by the nonzero closed degrees of difficulty is not principal and we compare this filter, with respect to inclusion, with some other filters of the lattice. All the filters considered in this paper are disjoint from the prime ideal generated by the dense degrees of difficulty. Mathematics Subject Classification: 03D30.     

Computable Real-Valued Functions on Recursive Open and Closed Subsets of Euclidean Space

In this paper we study intrinsic notions of “computability” for open and closed subsets of Euclidean space. Here we combine together the two concepts, computability on abstract metric spaces and computability for continuous functions, and delineate the basic properties of computable open and closed sets. The paper concludes with a comprehensive examination of the Effective Riemann Mapping Theorem and related questions.     

离散时间风险模型的递推公式

在本文中,我们研究了含有投资和通货膨胀因素的离散时间风险模型,通过递推的方法,得到了有限时间内的破产概率、破产时间的分布、破产持续时间的分布的递推公式.     

用类同余法产生随机数及其检验

模拟随机过程的各种模型都需要用到大量随机数 ,而各种分布的随机样本又可以由U(0 ,1)来产生 ,所以如何产生性能好、成本低、使用方便的随机数具有重要意义。本文介绍了一种随机数的产生方法并对其进行了严格的检验。     

Convergence Rates of Digital Diffusion Network Algorithms for Global Optimization with Applications to Image Estimation

Motivated by the recent developments in digital diffusion networks, this work is devoted to the rates of convergence issue for a class of global optimization algorithms. By means of weak convergence methods, we show that a sequence of suitably scaled estimation errors converges weakly to a diffusion process (a solution of a stochastic differential equation). The scaling together with the stationary covariance of the limit diffusion process gives the desired rates of convergence. Application examples are also provided for some image estimation problems.     

Recursive formulas for discrete distributions

We apply power series techniques for differential equations on probability generating functions to derive recursive formulas for discrete compound distributions. Such formulas are computationally effective and useful in risk theory.     

Spin quantum number in the ground state of the Mattis-Heisenberg model

Total spin quantum number is rigorously calculated for a quantum version of the Mattis model of random spin systems. Crossover between three universality classes of the Ising model, theXY model, and the Heisenberg model is explicitly worked out in the presence of randomness. The randomness of the type of the Mattis model is shown to have no thermodynamic effects even in quantum systems.     

K-moment problem for recursive sequences of order ∞: Application to the zeros of analytic functions

In this paper we solve the K-moment problem for a family of sequences defined by linear recursive relations of order ∞ indexed by Z. Extension of some known properties are studied and others results are established. Moreover, we paraphrase a fundamental application on the existence of zeros of an analytic function, in terms of the support of the representing measure of the former sequences.