Boundary Control Problems for 2 ×2 Cooperative Hyperbolic Systems with Infinite Order Operators

In this study, boundary control problems with Neumann conditions for 2 × 2 cooperative hyperbolic systems involving infinite order operators are considered. The existence and uniqueness of the states of these systems are proved, and the formulation of the control problem for different observation functions is discussed.

Distributed Control for <i>n</i>×<i>n</i>Cooperative Systems Governed by Hyperbolic Operator of Infinite Order

In this study, a distributed optimal control problem for n × n cooperative hyperbolic systems with infinite order operators and Dirichlet conditions are considered. The existence and uniqueness of the state of these systems are proved. The necessary and sufficient conditions for optimality of distributed control with constraints are found, and the set of equations and inequalities that defining the optimal control of these systems is also obtained. Finally, some examples for the control problem without constraints are given.

Uniqueness on Difference Operators of Meromorphic Functions of Infinite Order

We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of Jank-Mues-Volkmann.Our method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding vectors.This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the functions.Furthermore,the idea in this paper can also be applied to the case for several variables.

On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators

This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes,where the kernels are PF densities.Moreover,the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVAL(Ⅰ)

In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare examined, where are constants, and i=0,1.

ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.

THE COMPLEX OSCILLATION OF NON－HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH INFINITE ORDER ENTIRE COEFFICIENTS

In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite order of growth, and the others Aj(j≠d) satisfy m(r,Aj) = 0{m(r,Ad)}, F≠0 is an entire function, and obtain some precise estimates of the exponent of convergence of the zero-sequence of its solutions.

一种具有分形结构的弹黏塑性材料建模及其求解方法

本文建立了一种具有分形结构的元件模型,用于描述材料弹粘塑性特性,并可以在无需求解相应的无限阶微分方程的情况下获得各载荷作用下模型的力学反应.首先,基于这种建模方法,建立了表征具有复杂无限阶分形结构材料弹黏塑性特性的混联元件模型(L-R模型).然后,利用MATLAB/Simulink,借助弹簧(弹性)、黏壶(黏性)和塑性体(塑性)单元的本构关系来描述材料的基本力学性能.之后,将宾厄姆模型作为基本模型按照分形理论进行迭代,通过求解得到描述材料在各种载荷作用下的力学(弹黏塑性)反应.最后,为了验证该建模方法及其求解结果的可靠性,在钢、板岩、煤、红砂岩和盐岩五种不同分形结构的材料上进行了循环载荷实验.将实验结果与求解结果进行比较,表明所建立的模型能够有效地描述材料的弹黏塑性性能.

随机Richlet级数的增长性(英文)

For a known random Dirichlet series of infinite order on the whole plane, the authors construct a Dirirchlet series such that the growth of both series referring to the type function is the same. Thus one can study the growth of the former by studying the coefficient and exponent of the latter.