复微分方程组及复微分-差分方程解的级

利用Zalcman关于正规族的方法,研究了两类复高阶微分方程组的亚纯解的增长级问题;同时,利用Nevanlinna值分布理论,讨论了两类复微分-差分方程的超越整函数解的增长级.所得结论推广和改进了一些文献的结果,并举例说明本文的结论精确.     

复高阶代数微分方程组的亚纯解

利用亚纯函数的Nevanlinna值分布理论,研究了一类高阶代数微分方程组亚纯允许解的存在性问题,得到了一个主要结果.     

A mathematical model for Babesiosis disease in bovine and tick populations

In this paper, we analyze the Babesiosis transmission dynamics on bovine and tick populations. Ticks play a role of infectious agents and vector of the protozoan Babesia hemo‐parasite. In this sense, we set out a mathematical model with constant size population for the evolution of the infected bovines with Babesiosis and analyze its qualitative dynamics. Statistical data are used to estimate some of the parameters of the model. Numerical simulations of the model varying the parameters show different scenarios about the spread of the disease. Copyright © 2011 John Wiley & Sons, Ltd.     

A brief account of Klein’s icosahedral extensions

We present an alternative relatively easy way to understand and determine the zeros of a quintic polynomial whose Galois group is isomorphic to the group of rotational symmetries of a regular icosahedron. The extensive algebraic procedures of Klein in his famous Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade are here shortened via Heymann’s theory of resolvents. Also, we give a complete explanation of the so-called icosahedral equation and its solution in terms of Gaussian hypergeometric functions. As an innovative element, we construct this solution by using algebraic transformations of hypergeometric series.     

Semicontinuous Mappings into T.V.S. with Applications to Mixed Vector Variational-Like Inequalities

Let (X, Z) be the space of continuous linear mappings between topological vector spaces, where Z is Hausdorff and preordered by a closed convex cone C. In this paper, we introduce a notion of semicontinuity to any function from a topological space into X. A notion of semicontinuity is also introduced to any function from a topological space into (X, Z). These two notions of semicontinuity are related by the embedding of X into (X, Z). Their basic properties are given. As an application, we derive some existence results for the mixed vector variational-like inequality. This work was partially supported by grants from the National Science Council of the Republic of China.     

Feedback control variables to restrain the Babesiosis disease

In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations.     

Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves

We study the relationship between the growth and decrease of the sum of the entire Dirichlet series of finite order (in the sense of Ritt) on arbitrary curves going to infinity. For a class of exponents having a regular distribution (in a certain sense), we obtain a test for the logarithm of the maximal term to be equivalent to the logarithm of the absolute value of the sum of the Dirichlet series on at least one unbounded sequence of points of the curve.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 37–51.Original Russian Text Copyright © 2005 by A. M. Gaisin, I. D. Latypov.     

Fronts,traveling fronts,and their stability in the generalized Swift-Hohenberg equation

The generalized Swift-Hohenberg equation with an additional quadratic term is studied. Time-stable localized stationary solutions of the pulse and front types are found. It is shown that stationary fronts give rise to traveling fronts, whose branches are also obtained. This study combines theoretical methods for dynamical systems (in particular, the theory of homo-and heteroclinic orbits) and numerical simulation.     

Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active Constraints

We consider parametric semi-infinite optimization problems without the usual asssumptions on the continuity of the involved mappings and on the compactness of the index set counting the inequalities. We establish a characterization of those optimization problems which have a unique or strongly unique solution and which are stable under small pertubations. This result generalizes a well-known theorem of Nürnberger. The crucial roles in our investigations are a new concept of active constraints, a generalized Slater's condition, and a Kuhn—Tucker-type theorem. Finally, we give some applications in vector optimization, for approximation problems in normed spaces, and in the stability of the minimal value. Accepted 5 August 1996     

Systems of diagonal Diophantine inequalities

We treat systems of real diagonal forms of degree , in variables. We give a lower bound , which depends only on and , such that if holds, then, under certain conditions on the forms, and for any positive real number , there is a nonzero integral simultaneous solution of the system of Diophantine inequalities for . In particular, our result is one of the first to treat systems of inequalities of even degree. The result is an extension of earlier work by the author on quadratic forms. Also, a restriction in that work is removed, which enables us to now treat combined systems of Diophantine equations and inequalities.

     

The method of lower and upper solutions for damped elastic systems in Banach spaces

In this paper, we are concerned with the initial value problem of a class of damped elastic systems in an order Banach spaces $E$. By employing the method of lower and upper solutions, we discuss the existence of extremal mild solutions between lower and upper mild solutions for such problem with the associated semigroup is equicontinuous. In addition, two examples are given to illustrate our results.     

Ladder operators for Szego polynomials and related biorthogonal rational functions

We find the raising and lowering operators for orthogonal polynomials on the unit circle introduced by Szego and for their four parameter generalization to biorthogonal rational functions on the unit circle.

     

Generalized fuzzy set systems and particularization

It is suggested that there exists many fuzzy set systems, each with its specific pointwise operations for union and intersection. A general law of compound possibilities is valid for all these systems, as well as a general law for representing marginal possibility distributions as unions of fuzzy sets. Max-min fuzzy sets are a special case of a fuzzy set system which uses the pointwise operations of max and min for union and intersection respectively. Probabilistic fuzzy sets are another special case which uses the operations of addition and multiplication. Probably there exists an infinite number of fuzzy set operations and systems. It is shown why the law of idempotency for intersection is not required for such systems. An essential difference between the meaning of the operations of union and intersection in traditional measure theory as compared with their meaning in the theory of possibility is pointed out. The operation of particularization is used to illustrate that the two distinct classical theories of nonfuzzy relations and of probability are merely two aspects of a more generalized theory of fuzzy sets. It is shown that we must distinguish between particularization of conditional fuzzy sets and of joint fuzzy sets. The concept of restriction of nonfuzzy relations is a special case of particularization of both conditional and joint fuzzy sets. The computation of joint probabilities from conditional and marginal ones is a special case of particularization of conditional probabilistic fuzzy sets. The difference between linguistic modifiers of type 1 and particulating modifiers is pointed out, as well as a general difference between nouns and adjectives.     

Systems with nonextendable convergence of quasipolynomials

The system , where Λ={λ _n } is the set of zeros (of multiplicitiesm _n ) of the Fourier transform

Critical Points and Error Rank in Best H 2 Matrix Rational Approximation of Fixed McMillan Degree

This paper deals with best rational approximation of prescribed McMillan degree to matrix-valued functions in the real Hardy space of the complement of the unit disk endowed with the Frobenius L ₂ -norm. We describe the topological structure of the set of approximants in terms of inner-unstable factorizations. This allows us to establish a two-sided tangential interpolation equation for the critical points of the criterion, and to prove that the rank of the error F-H is at most k-n when F is rational of degree k , and H is critical of degree n . In the particular case where k=n , it follows that H=F is the unique critical point, and this entails a local uniqueness result when approximating near-rational functions. January 23, 1996. Date revised: September 16, 1996.     

非线性中立型控制系统的镇定与控制

本文利用Riccati矩阵方程的对称正定解构造正定二次型V函数,运用L yapunov分解等价法,给出了非线性中立型定常控制系统的镇定与次优控制。同时得到了滞后量与非线性项的界限的估计公式。     

On some iterated weighted spaces

It is proved that the Hörmander and spaces (Ω₁⊂Rn, Ω₂⊂Rm open sets, 1?p<∞, ki Beurling-Björck weights, k=k₁⊗k₂) are isomorphic whereas the iterated spaces and are not if 1<p≠q<∞. A similar result for weighted Lp-spaces of entire analytic functions is also obtained. Finally a result on iterated Besov spaces is given: and are not isomorphic when 1<q≠2<∞.