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.     

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。     

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.     

From shape to randomness: A classification of Langevin stochasticity

The Langevin equation–perhaps the most elemental stochastic differential equation in the physical sciences–describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation’s stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from “infra-mild” to “ultra-wild”. We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation’s stochastic output–based on the shape of the Langevin equation’s potential field.     

Image characterization and classification by physical complexity

We present a method for estimating the complexity of an image based on Bennett's concept of logical depth. Bennett identified logical depth as the appropriate measure of organized complexity, and hence as being better suited to the evaluation of the complexity of objects in the physical world. Its use results in a different, and in some sense a finer characterization than is obtained through the application of the concept of Kolmogorov complexity alone. We use this measure to classify images by their information content. The method provides a means for classifying and evaluating the complexity of objects by way of their visual representations. To the authors' knowledge, the method and application inspired by the concept of logical depth presented herein are being proposed and implemented for the first time. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Random fuzzy differential equations under generalized Lipschitz condition

We present the studies on two kinds of solutions to random fuzzy differential equations (RFDEs). The different types of solutions to RFDEs are generated by the usage of two different concepts of fuzzy derivative in the formulation of a differential problem. Under generalized Lipschitz condition, the existence and uniqueness of both kinds of solutions to RFDEs are obtained. We show that solutions (of the same kind) are close to each other in the case when the data of the equation did not differ much. By an example, we present an application of each type of solutions in a population growth model which is subjected to two kinds of uncertainties: fuzziness and randomness.     

Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements

While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of 2log23 random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit a device-independent method for certification of the full Weyl–Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states.     

ADSORPTION OF 1,2,4-ACID BY WEAKLY BASIC RESIN： ISOTHERMS, THERMODYNAMICS AND KINETICS

The adsorption properties, including the adsorption isotherms, thermodynamics and kinetics, of l-amino-2-naphthol-4-sulfonic acid (1,2,4-acid) onto weakly basic resin ND900 are investigated. Both the Langmuir and Freundlich equations can give a good fit to the adsorption isotherms, which indicates an endothermic and a favorable adsorption in our study range. A high yield in elimination of about 45.21%-97.28% is obtained for the tested adsorption systems. The capacity and affinity of the adsorption increase with temperature, due to the phenomena of “solvent-motivated” effects. The value of ΔH is 51.59 kJ/mol, which indicates a chemical adsorption and then expects the poor desorption property of ND900. The negative value of ΔG indicates the spontaneous nature of the adsorption process, and the positive value of ΔS shows the increased randomness at the solid/solution interface during the adsorption process. The value of the adsorption rate constant lower than 0.013 min^-1 is indicative of a slow adsorption rate. The intra-particle diffusion must be one of the rate limiting steps.     

Synthesis and Characterization of Block Copolymers of Poly(Butylenes Terephthalate-Co-Adipate)

The block copolyesters of poly(butylene terephthalate)(PBT) and poly(butylene adipate)(PBA) were prepared by a novel two-stage method. In the first stage, high molecular weight PBT and PBA were melt mixed in the presence of 1,4-butanediol at 275 °C. In the second stage, vacuum was applied to raise the molecular weight. The extent of transesterification was controlled by the proportion of 1,4-butanediol. The sequence distribution and the thermal properties of the block copolyesters were characterized by NMR and DSC respectively.