Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Continuous Selectors of Fixed Point Sets of Multifunctions with Decomposable Values

Existence theorems of continuous selectors whose values are fixed points of multivalued contractions are proved. As an application, the existence of continuous selectors to generalized solution sets of partial differential inclusions, depending on a parameter, is obtained.     

关于E-凸函数及E-凸规划几个错误结论的修正

本文研究Youness在1999年建立的有关E凸函数和E规划的结论.利用E凸函数和E凸规划的基本性质和优化分析技术,获得了有关E凸函数E凸规划的几个错误结论的修正..     

Self-organized critical pinball machine

The nature of self-organized criticality (SOC) is pin-pointed with a simple mechanical model: a pinball machine. Its phase space is fully parameterized by two integer variables, one describing the state of an on-going game, the other describing the state of the machine. This is the simplest possible SOC system, having only two degrees of freedom and no spatial correlations, yet is not solvable by analytical means.     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.     

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON-PISOT NUMBERS

1　IntroductionForany 0 <λ <1 ,letνλ　denotethedistributionof ∞n=0 εnλn wherethecoefficientsεnareeither0or1 ,chosenindependentlywithprobability12 foreach .Itistheinfiniteconvo lutionproductofthedistributions 12 (δ0 +δλn) ,givingrisetotheterm“infiniteBernoulliconvolution”orsimply“Bernoulliconvolution” .TheBernoulliconvolutioncanbeexpressedasaself similarmeasureνλsatisfyingtheequationνλ =12 νλ φ- 10 + 12 νλ φ- 11,( 1 .1 )whereφ0 (x) =λxand φ1(x) =λx + 1 .Thisme…     

Reformulation of the support set selection problem in the logical analysis of data

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed.     

VECTOR-VALUED RANDOM POWER SERIES ON THE UNIT BALL OF C^n

In this article, the authors study the vector-valued random power series on the unit ball of Cn and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.