Uniqueness of a cycle with discounting that is optimal with respect to the average time profit

For cyclic processes modeled by periodic motions of a continuous control system on a circle, we prove the uniqueness of a cycle maximizing the average one-period time profit in the case of discounting provided that the minimum and maximum velocities of the system coincide at some points only and the profit density is a differentiable function with a finite number of critical points. The uniqueness theorem is an analog of Arnold’s theorem on the uniqueness of such a cycle in the case when the profit gathered along the cycle is not discounted.     

An uniqueness result with some density theorems with interior transmission eigenvalues

Given a set of transmission eigenvalues, we apply Cartwright’s theory to show the density function inversely determines the indicator function. This indicator function gives a Weyl’s type of asymptotics on the transmission eigenvalues. The inverse uniqueness problem on the refraction index is reduced to identifying a parameter of an entire function. We use a Carlson’s type of theorem to prove the uniqueness as in entire function theory. Taking advantage of the uniqueness of rod density problem, we prove an uniqueness result with interior transmission eigenvalues.     

EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTION TO PRESSURELESS EULER SYSTEM WITH A FLOCKING DISSIPATION

We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang's energy condition is also necessary for our nonhomogeneous system.     

A uniqueness theorem on the eigenvalues of spherically symmetric interior transmission problem in absorbing medium

We study the asymptotic distribution of the eigenvalues of interior transmission problem in absorbing medium. We apply Cartwright’s theory and the technique from entire function theory to find a Weyl’s type of density theorem in absorbing medium. Given a sufficient quantity of transmission eigenvalues, we obtain limited uniqueness on the refraction index as a uniqueness problem in entire function theory.     

Uniqueness of periodic solutions of a nonautonomous density-dependent predator–prey system

In this present paper, we investigate the uniqueness of periodic solutions of a nonautonomous density-dependent and ratio-dependent predator–prey system, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator–prey system conforms to the realistically biological environment. We start with a sufficient condition for the permanence of the system and then construct a weaker sufficient condition by introducing a specific set, denoted as Γ. Based on this Γ and the Brouwer fixed-point theorem, we obtain the existence condition of positive periodic solutions. Moreover, since the uniqueness of positive periodic solutions can be ensured by global attractiveness, we alternatively introduce a sufficient condition for global attractiveness. Similarly, we also provide a sufficient condition for the uniqueness of non-negative periodic solutions.     

UNIQUENESS OF MINIMIZATION PROBLEMS

In this paper we give a uniqueness theorem for a minimization problem.Meanwhile weprovide a uniform uniqueness theorem for L_p(1≤p≤∞)simultaneous approximationsincluding mean simultaneous approximation and Chebyshev simultaneous approximation.     

CHEBYSHEV APPROXIMATION BY FUNCTIONS HAVING RESTRICTED RANGES WITH EQUALITIES

In this paper, we establish a new type of alternation theory for more general restricted ranges Chebyshev approximation with equalities. The uniqueness and strong uniqueness theorems are given. Applying the results, we obtain the alternation theorem and uniqueness theorem for best coposilive approximation.     

A parabolic–hyperbolic system modeling the tumor growth with angiogenesis

In this paper, we study the parabolic–hyperbolic system about the growth of a tumor. The model is a coupled system of PDEs with Robin boundary, which involves nutrient density, extracellular matrix and matrix degrading enzyme. By transforming the free boundary into a fixed boundary and using strict mathematical analysis, we can prove the existence and uniqueness of the radially symmetric stationary solution. By the fixed point theorem, we obtain the existence and uniqueness of the radially symmetric solution globally in time.     

An existence and uniqueness result for a strain-adaptive bone remodeling problem

In this paper we prove an existence and uniqueness result for a strain-adaptive bone remodeling model that couples the displacements and the apparent density (the porosity) of the bone. The rate of this density at a particular location is described as an objective function, which depends on a particular stimulus at that location. Then, a new version of this problem is considered, based on a regularization on the bone remodeling law by using convolution operators. The existence and uniqueness result is proved by applying classical results for nonlinear parabolic differential inclusions, Gronwall’s inequality and the Banach fixed point theorem.     

THE NOTE ON MATRIX-VALUED RATIONAL INTERPOLATION

In [3], a kind of matrix-valued rational interpolants （MRIs） in the form of Rn（x） = M（x）/D（x） with the divisibility condition D（x） ｜ ｜｜M（x）｜｜^2, was defined, and the characterization theorem and uniqueness theorem for MRIs were proved. However this divisibility condition is found not necessary in some cases. In this paper, we re- move this restricted condition, define the generalized matrix-valued rational interpolants （GMRIs） and establish the characterization theorem and uniqueness theorem for GMRIs. One can see that the characterization theorem and uniqueness theorem for MRIs are the special cases of those for GMRIs. Moreover, by defining a kind of inner product, we succeed in unifying the Samelson inverses for a vector and a matrix.     

Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations

In this article, we study a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations. We obtain sufficient conditions for existence and uniqueness of positive solutions. We use the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem for uniqueness and existence results. As in application, we provide an example to illustrate our main results.     

Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles

We construct cumulant (semi-invariant) representations for a solution of the initial-value problem for the Bogolyubov hierarchy for quantum systems of particles. In the space of sequences of trace-class operators, we prove a theorem on the existence and uniqueness of a solution. We study the equivalence problem for various representations of a solution in the case of the Maxwell-Boltzmann statistics. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1175–1191, September, 2006.     

On the uniqueness problem of harmonic quasiconformal mappings

In this paper, we give an affirmative answer to Sheretov's problem on the uniqueness of harmonic mappings and improve the unique minimal mapping theorem of Reich and Strebel. Meanwhile, we also solve a problem posed by Reich and obtain the uniqueness theorem on related weight functions.

     

On a uniqueness problem

We prove a uniqueness theorem for series which are a broad generalization of Dirichlet series. In particular, we obtain a uniqueness theorem for series solutions of differential equations.Translated from Matematicheskie Zametki, Vol. 16, No. 6, pp. 871–878, December, 1974.     

一类捕食者-食饵系统的全局结构

本文中我们证明了关于一般捕食者-食饵系统不存在闭轨线的定理,即文中定理2.应用这一定理和关于捕食者-食饵系统极限环的存在唯一性定理[1],我们完成了在各种参数条件对一个具体的捕食者-食饵系统模型[2]的研究.     

非线性一阶常微分方程解的存在惟一性

讨论了一类非线性一阶常微分方程边值问题解的存在惟一性.得到了当参数在一定的范围取值时解存在惟一的充分条件,并包含了一些已知结果.主要结果基于Leray-Schauder非线性抉择理论和Banach不动点定理.     

带梯度算子二阶方程的渐近概周期解

利用渐近概周期函数的性质得到带梯度算子二阶方程的渐近概周期解在C（R^-）中的存在性．同时利用迭代法和线性常微分方程的概周期解的存在性和唯一性,得到R上此方程渐近概周期解的存在和唯一性．     

The Tychonoff uniqueness theorem for the G-heat equation

In this paper we shall investigate a uniqueness result for solutions of the G-heat equation. We obtain the Tychonoff uniqueness theorem for the G-heat equation.     

一类奇异拟线性椭圆型方程组的可解性

研究了一类P-Laplacian方程组边值问题正径向整体解的存在性和唯一性.首先,利用隐函数定理证明了该问题的局部解的存在性与唯一性,以及解对初值的连续依赖性.最后,证明了该问题存在唯一的正径向整体解.     

输液管非线性运动方程弱解的存在唯一性

本文利用Faedo-Galerkin法证明了一简支且两端不可移动的细长输液直管非线性运动方程弱解的存在唯一性。