Classification of numerical 3-semigroups by means of L-shapes

We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate L-shapes to each numerical 3-semigroup and we describe some main invariants of numerical 3-semigroups in terms of their associated L-shapes. Finally, we give a characterization of the parameters of the L-shapes associated with a numerical 3-semigroup in terms of its generators, and we use it to classify the numerical 3-semigroups of interest in curve singularity.     

Average densities of frequency bands of wavelets

A function is called a wavelet if its integral translations and dyadic dilations form an orthonormal basis for L ²(?). The support of the Fourier transform of a wavelet is called its frequency band. In this paper, we study the relation between diameters and measures of frequency bands of wavelets, precisely say, we study the ratio of the measure to the diameter. This reflects the average density of the frequency band of a wavelet. In particular, for multiresolution analysis (MRA) wavelets, we do further research. First, we discuss the relation between diameters and measures of frequency bands of scaling functions. Next, we discuss the relation between frequency bands of wavelets and the corresponding scaling functions. Finally, we give the precise estimate of the measure of frequency bands of wavelets. At the same time, we find that when the diameters of frequency bands tend to infinity, the average densities tend to zero.     

The value of foresight

Suppose you have one unit of stock, currently worth 1, which you must sell before time $T$. The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see $a$ units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information? The optimal solution to this problem will never be found, but in this paper we establish remarkably close bounds on the value of the problem, and we derive a fairly simple exercise rule that manages to extract most of the value of foresight.     

On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind

Orthogonal polynomials satisfy a recurrence relation of order two defined by two sequences of coefficients. If we modify one of these recurrence coefficients at a certain order, we obtain the so-called perturbed orthogonal sequence. In this work, we analyse perturbed Chebyshev polynomials of second kind and we deal with the problem of finding the connection coefficients that allow us to write the perturbed sequence in terms of the original one and in terms of the canonical basis. From the connection coefficients obtained, we derive some results about zeros at the origin. The analysis is valid for arbitrary order of perturbation.     

Optimal control of nonlinear evolution inclusions

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688.     

Existence of solutions of the nonautonomous abstract Cauchy problem of second order

In this paper the existence of solutions of a nonautonomous abstract Cauchy problem of second order is considered. Assuming appropriate conditions on the operator of the equation, we establish the existence of mild solutions and, in some cases, we construct an evolution operator associated to the homogeneous equation. Using this evolution operator we obtain existence of solutions for the inhomogeneous equation. Finally, we apply our results to study the existence of solutions of the nonautonomous wave equation.     

Nonnegativity of solutions of nonlinear fractional differential-algebraic equations

Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method.     

Classification of quintic eutactic forms

From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.

     

Forecasting the integration of immigrants

In this research, we develop and introduce a theoretical and mathematical forecasting framework of immigrant integration using immigrant density as a single driver. First, we introduce the integration concepts we aim at forecasting. Thereafter, we introduce a theoretical and mathematical model of the relationship between integration and immigrant density. Based on this model, we develop a methodological forecasting framework. We test the framework using immigrant integration data from Spain. We produce the forecasts, and conduct the proper evaluation of them. Finally, we conclude with a brief discussion of the wider implications of our results.     

Fractal properties of number systems

In this paper we study properties of the fundamental domain F of number systems in the n-dimensional real vector space. In particular we investigate the fractal structure of its boundary F. In a first step we give upper and lower bounds for its box counting dimension. Under certain circumstances these bounds are identical and we get an exact value for the box counting dimension. Under additional assumptions we prove that the Hausdorf dimension of F is equal to its box counting dimension. Moreover, we show that the Hausdorf measure is positive and fnite. This is done by applying the theory of graphdirected self similar sets due to Falconer and Bandt. Finally, we discuss the connection to canonical number systems in number felds, and give some numerical examples.     

Standard tensor and its applications in problem of singular values of tensors

In this paper, first we give the definition of standard tensor. Then we clarify the relationship between weakly irreducible tensors and weakly irreducible polynomial maps by the definition of standard tensor. And we prove that the singular values of rectangular tensors are the special cases of the eigen-values of standard tensors related to rectangular tensors. Based on standard tensor, we present a generalized version of the weak Perron-Frobenius Theorem of nonnegative rectangular tensors under weaker conditions. Furthermore, by studying standard tensors, we get some new results of rectangular tensors. Besides, by using the special structure of standard tensors corresponding to nonnegative rectangular tensors, we show that the largest singular value is really geometrically simple under some weaker conditions.     

一类非线性发展方程的动力学行为

本文通过引入一类Frechet空间,证明了一类与流体力学有关的非线性发展方程的弱解存在着整体吸引子．     

Agent-based interpretations of classic network models

The paper is aimed at developing agent-based variants of traditional network models that make full use of concurrency. First, we review some classic models of the static structure of complex networks with the objective of developing agent-based models suited for simulating a large-scale, technology-enabled social network. Secondly, we outline the basic properties that characterize such networks. Then, we briefly discuss some classic network models and the properties of the networks they generate. Finally, we discuss how such models can be converted into agent-based models (i) to be executed more easily in heavily concurrent environments and (ii) to serve as basic blocks for more complex agent-based models. We evidence that many implicit assumptions made by traditional models regarding their execution environment are too expensive or outright impossible to maintain in concurrent environments. Consequently, we present the concurrency issues resulting from the violation of such assumptions. Then, we experimentally show that, under reasonable hypothesis, the agent-based variants maintain the main features of the classic models, notwithstanding the change of environment. Eventually, we present a meta-model that we singled out from the individual classic models and that we used to simplify the agent-oriented conversion of the traditional models. Finally, we discuss the software tools that we built to run the agent-based simulations.     

非线性积分方程解的指数与解的个数

本文对型非线性积分方程,给出了一个由Fredholm行列式表示其解的指数的公式,并且讨论了利用Fredholm行列式判断其解的个数的方法。 引理1 设线性积分算子A:C(G)→C(G) (Au)(x)=integral from G (K(x,y)u(y)dy) (1) 其中GR~N为有界闭域,K(x,y)在G×G上连续。从而A全连续,相应于A的Fredholm行列式F-det[I-A]为     

ISOMORPHISMS OF CIRCULANT DIGRAPHS OF DEGREE 3

Abstract. In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine the isomorphic classes of circulant digraphs of degree 3. In psrticular, we characterize those circulant digraphs of degree 3 which don‘‘t satisfy JkdAm‘‘s conjectttre.     

Classification of Krasner Hyperfields of Order 4

In this paper, first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism. Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4. Moreover, we propose a hyperfield of order 4 which is not as a quotient hyperfield F/G. Finally, some programs written in MATLAB which are based on obtained results compute the number of polygroups, weak polygroups and Krasner hyperfields of order 4 up to isomorphism.     

Uniform proofs of q-Series-product identities

In this paper we give a simple proof of the Jacobi triple product identity by using basic properties of cube roots of unity. Then we give a new proof of the quintuple product identity, the septuple product identity and Winquist’s identity by using the Jacobi triple product identity and basic properties of cube and fifth roots of unity. Furthermore, we derive some new product identities by this uniform method. Later, we give some generalizations of those identities. Lastly, we derive some modular equations.     

An Approach to the Optimization and Approximation of Solutions of any Operator Inclusion

In this paper we shall present the optimization problem in a set of solutions of operator inclusion with the maximal monotone operator. Then we treat optimization problem by Galerkin method and we prove convergence of optimal values of approximated optimization problems to the one for the original problem. Finally, we apply the results to give a simple example.     

一类lpp-半群的结构

本文研究含左正则lpp-断面的lpp-半群的结构．特别地，给出了合右理想左正则lpp-断面的lpp-半群的一个结构．另外，还把这个结构用于一些特殊情况。     

Towards a self-consistent theory of volatility

In this paper, we propose a new theory for the formation of volatility which takes into account the influence of option hedging on the assets price dynamics. By analogy with statistical mechanics, we build a self-consistent equation for the volatility, we show it is well-posed and we explain how it can be solved.