具组合型非线性项与调和位势的非线性Schr(o)dinger方程

讨论了一类带有组合型非线性项与调和位势的非线性Schr(o)dinger方程.通过构造变分问题,引入位势井方法.给出了位势井的结构和位势井深度函数的性质.得到了问题的相关集合在流之下的不变性.揭示了只要问题的初值属于位势井内或位势井外,则问题在今后所有时间内的解都存在于位势井内或井外.结合凹性方法,给出了解的整体存在性的最佳条件.     

具组合型非线性项与调和位势的非线性Schrdinger方程

讨论了一类带有组合型非线性项与调和位势的非线性Schrdinger方程.通过构造变分问题,引入位势井方法.给出了位势井的结构和位势井深度函数的性质.得到了问题的相关集合在流之下的不变性.揭示了只要问题的初值属于位势井内或位势井外,则问题在今后所有时间内的解都存在于位势井内或井外.结合凹性方法,给出了解的整体存在性的最佳条件.     

具有多个非线性源项的波动方程

利用位势井方法研究在有界区域上具有多个非线性源项的波动方程初边值问题．给出了位势井的结构和位势井深度函数的性质．通过引进位势井族得到了在这些问题的流之下的一些集合不变性以及解的真空隔离,揭示了只要问题的初值属于位势井内或位势井外,则问题在今后所有时间内的解都存在于位势井内或井外,同时存在一个没有解的空间区域．进而给出了解的整体存在和不存在的门槛结果．最后,利用相同的方法讨论了具有临界初始条件的问题．     

关于位势井及其对强阻尼非线性波动方程的应用

本文研究强阻尼非线性波动方程的初边值问题其中f(u)u≥0.首先用新的方法再次得到了位势井深度d的值,并首次得到了位势井内外结构.而后用位势井方法得到了问题的整体弱解,整体强解的存在性.最后证明了位势井W及井外集合V在问题(1)-(3)的流之下的不变性.     

控制论在现代物理中应用伪位势理论与孤粒子理论

§1 引言本文系应用 Galilean 度规变换及 Galilean 度规微分算子变换,将 KDV方程、SG 方程和 NLS 方程化为广义的牛顿近似方程;从而引出了各种类型的伪位势函数.给出了伪位势函数与孤粒子解之间的明确关系,它说明了孤粒子解的出现是由位势所确定的.这可能意味着孤粒子解的真正物理意义!同时,我们还将证明位势与谱在数学结构上的明确形式.另外,我们还讨论由位势的作用,求出高斯分布的广义力学体系以及黑体辐射的 Planck公式的黑体辐射空间中的广义力学体系.这里的“势”可以看作是宇宙里的存在的控制.     

控制论在现代物理中应用伪位势理论与孤粒子理论

§1 引言 本文系应用Galilean度规变换及Galilean度规微分算子变换,将KDV方程、SG方程和NLS方程化为广义的牛顿近似方程;从而引出了各种类型的伪位势函数。给出了伪位势函数与孤粒子解之间的明确关系,它说明了孤粒子解的出现是由位势所确定的。这可能意味着孤粒子解的真正物理意义!同时,我们还将证明位势与谱在数学结构上的明确形式。另外,我们     

拓扑序列复杂性和混合

本文给出动力系统的拓扑序列复杂函数和族.F-扩散的概念,利用序列复杂函数给出一致刚性、等度连续性和F-混合的特征,并讨论了族F-混合与一致刚性、相关族扩散、混沌及序列等度连续点存在性的关系.     

拓扑序列复杂性和混合

本文给出动力系统的拓扑序列复杂函数和族F-扩散的概念,利用序列复杂函数给出一致刚性、等度连续性和F-混合的特征,并讨论了族F-混合与一致刚性、相关族扩散、混沌及序列等度连续点存在性的关系.     

函数一致连续的比较判别法

在一般教材上对无穷区间上的函数,通常都采用定义的方法判别其一致连续性,对于复杂的函数,判别其是否一致连续一般来说常常比较困难.本文给出了判别无穷区间上函数一致连续性的一种比较判别法.     

函数一致连续性的判别新法

分别给出了各类区间上函数一致连续性的新的判定方法,使得一些复杂函数的一致连续性可以借助于较易判别出一致连续性的初等函数去判定.最后举例验证了方法的可行性和有效性.     

Two-sided estimate for the modulus of continuity of a convolution

We study the differential properties of the convolution of functions with a generalized Bessel-Macdonald kernel. The integral properties of a function are characterized in terms of its decreasing permutation. The differential properties of the convolution are described in terms of its modulus of continuity of arbitrary order in the uniform norm. We obtain order-sharp estimates for the modulus of continuity of the convolution. By way of application, we present two-sided estimates for the modulus of continuity of the classical Bessel potential.     

Nehari函数族的偏差性质与拟共形延拓

研究某一Nehari函数族的偏差性质,得到这类函数族的H?lder连续性及若干偏差定理,同时讨论了该函数类的拟共形延拓问题,并给出拟共形延拓的复伸张估计,推广了杨宗信等人相应的结论.     

关于随机解析算子函数的正族性质

该文在经典函数的正族理论基础上建立了随机解析算子函数的正族、一致有界和等度连续等概念，并在此意义下，给出了随机解析算子函数族内闭一致有界与等度连续、正族与一致有界的关系，以及随机解析算子函数族为正族的一个充分必要条件。     

Estimation of the uniform modulus of continuity of the generalized Bessel potential

We study generalized Bessel potentials constructed by means of convolutions of functions with kernels that generalize the classical Bessel-Macdonald kernels. In contrast to the classical case, nonpower singularities of kernels in a neighborhood of the origin are admitted. The integral properties of functions are characterized in terms of decreasing rearrangements. The differential properties of potentials are described by the kth-order moduli of continuity in the uniform norm. An order-sharp upper estimate is established for the modulus of continuity of a potential. Such estimates play an important role in the theory of function spaces. They allow one to establish sharp embedding theorems for potentials, find majorants of the moduli of continuity, and estimate the approximation numbers of embedding operators.     

Sobolev space properties of superharmonic functions on metric spaces

Our objective is to study regularity of superharmonic functions of a nonlinear potential theory on metric measure spaces. In particular, we are interested in the local integrability properties of a superharmonic function and its derivative. We show that every superharmonic function has a weak upper gradient and provide sharp local integrability estimates. In addition, we study absolute continuity of a superharmonic function.     

On the continuity of the minima for a family of constrained optimization problems ∗

We consider a family of problems Py dealing with the minimization of a given function on a constraint set, both depending on a parameter y. We study continuity properties, with respect to a parameter, of the value and of the solution set of the problems. Working with convex functions and convex constraint sets, we show how the well-posedness of the problem allows to avoid compactness hypotheses usually requested to get the same stability results.     

Optimal embedding and sharp estimates of the continuity envelope for generalized Bessel potentials

In the theory of function spaces it is an important problem to describe the differential properties for the convolution u = G * f in terms of the behavior of kernel near the origin, and at the infinity. In our paper the differential properties of convolution are characterized by their modulus of continuity of order k ∈ N in the uniform norm. The kernels of convolution generalize the classical kernels determining the Bessel and Riesz potential. They admit non-power behavior near the origin. The order-sharp estimates are obtained for moduli of continuity of the convolution in the uniform norm as well as for continuity envelope function of generalized Bessel potentials. Such estimates admit sharp embedding theorems into a Calderon space and imply estimates for the approximation numbers of the embedding operator.     

Characterization of a regular family of semimartingales by line integrals

A characterization of a regular family of semimatingales as a maximal fasmily of processes with respect of which one can define a stochastic line integral with natural continuity properties is given.     

Some approximation results involving the q‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization

The purpose of this paper is to introduce a family of q‐Szász–Mirakjan–Kantorovich type positive linear operators that are generated by Dunkl's generalization of the exponential function. We present approximation properties with the help of well‐known Korovkin's theorem and determine the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K‐functional, and the second‐order modulus of continuity. Furthermore, we obtain the approximation results for bivariate q‐Szász–Mirakjan–Kantorovich type operators that are also generated by the aforementioned Dunkl generalization of the exponential function. Copyright © 2017 John Wiley & Sons, Ltd.