正则乘子Hopf代数上Yetter-Drinfel''d模范畴中的自同构代数

本文研究了正则乘子Hopf代数上Yetter-Drinfel''d模范畴中自同构代数的问题.利用乘子Hopf代数以及同调代数理论中的方法,获得了Yetter-Drinfel''d模范畴中两个自同构代数是同构的结果,推广了Panaite等人在Hopf代数中的结果.     

具有特殊坐标曲线网的B\''ezier曲面

在计算机辅助几何设计中, B\''ezier曲面是一类重要的参数曲面.在微分几何中,坐标曲线网也是重要的研究内容.本文中,我们对具有特殊坐标曲线网(如正交曲线网、曲率曲线网、共轭曲线网等)的B\''ezier曲面进行研究.此外,我们还构造了满足能量约束的特殊B\''ezier曲面,给出了基于控制结构的充分条件并给出具体实例.     

一类广义Li\'enard方程周期正解的存在性

本文证明一类广义Li\''enard方程周期正解的存在性及渐近稳定性. 我们讨论的非自治函数可满足超线性条件,克服了连续定理讨论超线性条件的困难. 文章的最后,我们给出两个例子和数值解以及对应的相图和时间序列图来验证我们的结论.     

Hom-Hopf代数的对极和Drinfel'd偶

本文证明了带有等价Hom- 范畴的Hom- 双代数是Hom-Hopf 代数, 在基本结构定理成立的前提下, 构造了对极使其成为Hom-Hopf 代数. 研究了拟三角Hom-Hopf 代数的对极, 并给出了Hom-Hopf 代数的Radford 公式. 最后, 对有限维Hom-Hopf 代数, 引入了Drinfel''d 偶的概念, 同时证明了Drinfel''d 偶是拟三角Hom-Hopf 代数.     

受L\''evy噪声扰动的Logistic方程的全局吸引性

本文考虑了受L\''evy噪声扰动的Logistic方程. 在合适的条件下, 我们得到了解的全局存在性与唯一性; 我们证明了当初始值小于环境的容纳量时, 唯一的正的平衡态具有全局吸引性.     

平面三次Pythagorean-Hodograph Hyperbolic曲线

本文基于Pythagorean-hodograph (PH)曲线和代数双曲线的良好几何特性,构造了Pythagorean-Hodograph Hyperbolic (PH-H)曲线,并给出了PH-H曲线的定义以及相应性质.同时,分别利用Hyperbolic基函数和Algebraic Hyperbolic (AH) B\''ezier基函数,得到了平面三次AH B\''ezier曲线为PH曲线的两个不同的充要条件.此外,三次PH-H曲线也被用于求解具有确定解的$G^1$ Hermite插值问题.文中给出了具体实例来说明我们的方法.     

扰动Fej\'{e}r点上复Hermite插值的联合逼近

$D$是复平面中由闭Jordan曲线$\Ga$围成的单连区域. 考虑在$\Ga$上扰动Fej\''er点的 Hermite插值一致逼近、平均逼近和联合逼近于函数$f\in A^{(q)}(\o D)$. 该文中的逼近阶一般说来是不可再改进的, 区域的边界限制条件到目前为止是最少的. 以往的全部同类结果都包括在该文中作为特殊情形, 由于该文方法上的改进, 简化和省去了以往 某些证明过程.     

二部图形式的Erd\H{O}s-S\''{o}s猜想

二部图形式的Erd\H{O}s-S\''{o}s猜想     

线性超图的边染色

超图$H$的一个$k$-边染色是用$k$种颜色的边染色, 使得相交的边染不同的颜色. Erd\H{o}s-Faber-Lov\''asz猜想认为任一$n$个顶点的无环线性超图都有一个$n$-边染色. 2021年, Kang, Kelly, K\"uhn, Methuku和Osthus对充分大的$n$确认了该猜想成立. 在本文中, 我们证明该猜想对弱冲突的超图是成立的. 这严格拓展了Bretto, Faisant 和Hennecart在2020年的两个相关结果.     

非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的双行波解

本文提出了一种全新复合$(\frac{G''}{G})$展开方法,运用这种新方法并借助符号计算软件构造了非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的多种双行波解,包括双双曲正切函数解,双正切函数解,双有理函数解以及它们的混合解. 复合$(\frac{G''}{G})$展开方法不但直接有效地求出了两类非线性偏微分方程的双行波解,而且扩大了解的范围.这种新方法对于研究非线性偏微分方程具有广泛的应用意义.     

A more accurate multidimensional Hardy-Hilbert''s inequality

In this paper, by the use of the weight coefficients, the transfer formula, Hermite-Hadamard''s inequality and the technique of real analysis, a more accurate multidimensional Hardy-Hilbert''s inequality with multi-parameters and a best possible constant factor is given, which is an extension of some published results. Moreover, the equivalent forms and the operator expressions are considered.     

EXISTENCE OF PERIODIC SOLUTIONS OF A CLASS OF SECOND-ORDER NON-AUTONOMOUS SYSTEMS

In this paper, we are concerned with the existence of periodic solutions of second-order non-autonomous systems. By applying the Schauder''s fixed point theorem and Miranda''s theorem, a new existence result of periodic solutions is established.     

Vectorial Ekeland's Variational Principle with a W-Distance and its Equivalent Theorems

By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristi's fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland's variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9–16[ are weakened or even completely relieved.     

On sampling theory and basic Sturm–Liouville systems

We investigate the sampling theory associated with basic Sturm–Liouville eigenvalue problems. We derive two sampling theorems for integral transforms whose kernels are basic functions and the integral is of Jackson's type. The kernel in the first theorem is a solution of a basic difference equation and in the second one it is expressed in terms of basic Green's function of the basic Sturm–Liouville systems. Examples involving basic sine and cosine transforms are given.     

Fej\''{e}r type inequalities for Harmonically-convex functions with applications

In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic convexity and some auxiliary results, some new Fej\''{e}r type integral inequalities are presented. Applications to special means of positive real numbers are given as well.     

The classical version of Stokes' theorem revisited

Using only fairly simple and elementary considerations–essentially from first year undergraduate mathematics–we show how the classical Stokes' theorem for any given surface and vector field in ?³ follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. However, the main point in the present article is first, that this latter fact usually does not get within reach for students in first year calculus courses and second, that calculus textbooks in general only just hint at the correspondence alluded to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well-known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of this article uses only integration in 1, 2 and 3 variables together with a ‘fattening’ technique for surfaces and the inverse function theorem.     

Visualizing and understanding l'hopital's rule‡

This article uses dynamic software in Excel to demonstrate several ways in which graphical and numerical approaches can be introduced both to enhance student understanding of l'Hopital's Rule and to explain why the Rule actually works to give the ‘right’ answers. One of the approaches used is to visualize what is happening by examining the limits with both l'Hopital's Rule and the associated Taylor approximation to the function. The dynamic software allows students to experiment with the ideas.     

拟常曲率黎曼流形中子流形的几何不等式的一些注记

本文研究了拟常曲率黎曼流形中子流形的Chen不等式.利用代数技巧,建立了Chen广义不等式、Chen-Ricci不等式和关于卷积函数和平均曲率平方的不等式,推广了Özgür和Chen的一些结果.     

带有加权Hardy-Sobolev临界指数的非齐次Neumann边界奇异的多解问题

主要研究了非齐次Neumann边界奇异的问题,利用Ekeland变分原理、山路引理和一些分析技巧,证明了正解的存在性.