与中心数相关的一类级数求和公式

This paper provides a pair of summation formulas for a kind of combinatorial series involvingak＋b m as a factor of the summand. The construction of formulas is based on a certain series transformation formula [2, 7, 9] and by making use of the C-numbers [3]. Various consequences and examples including several remarkable classic identities are presented to illustrate some applications of the formulas obtained.     

双参数有限q指数算子及其应用

本文构造两个双参数有限q指数算子,得到了几个算子恒等式;应用这些算子恒等式到著名的q-Chu-Vandermonde求和恒等式,求导了若干奇异的q-级数恒等式,包含著名的Jackson恒等式的一个推广.     

一个组合恒等式的推广(Ⅱ)

用母函数方法获得了一个组合恒等式的更一般的形式.借助这一结果,又给出了若干个有趣的组合恒等式.是作者以前的一篇文章的继续.     

一个组合恒等式的推广

本文推广了文[1]中的一个组合恒等式.     

关于一个普遍本源公式及其应用

Here presented is a further investigation on a general source formula(GSF) that has been proved capable of deducing more than 30 special formulas for series expansions and summations in the author's recent paper [On a pair of operator series expansions implying a variety of summation formulas.Anal.Theory Appl.,2015,31(3):260–282].It is shown that the pair of series transformation formulas found and utilized by He,Hsu and Shiue [cf.Disc.Math.,2008,308:3427–3440] is also deducible from the GSF as consequences.Thus it is found that the GSF actually implies more than 50 special series expansions and summation formulas.Finally,several expository remarks relating to the(Σ?D) formula class are given in the closing section.     

A Nonlinear Expression for Fibonacci Numbers and Its Consequences

Here investigated is a kind of nonlinear combinatorial expression involving Fibonacci numbers defined on the set of integers.A number of particular consequences will bepresented as examples.     

由广义微分算子定义的某些解析函数类的优化性质

本文首先引入了由广义微分算子定义的某些$p$叶解析函数新子类$S_{p,q,\lambda}^{m,j,l}[A,B;\gamma]$ 和 $H_{p,q,\lambda}^{m,j,l}(\alpha,\beta)$, 然后研究了该子类的优化性质, 所得结果推广了某些已知结论.     

由算法分析引出的一类差分方程的解及其相应的求和公式——悼念游兆永教授

感谢会议对我的邀请并提供发言的机会，此时此地，此会此际，本来游兆永教授当应居东道的首席，不幸不久前逝世了，令人不胜悲痛和惆怅。     

Reflexivity of Weighted Shifts

Let {β（n）}n be a sequence of positive numbers such that β（0） = 1 and let 1 ≤ p 〈 ≤. We will investigate the reflexivity of all integer powers of the multiplication operator on the Banach spaces of formal Laurent series, L^P（β）.     

Ferenc Lukács type theorems in terms of the Abel-Poisson mean of conjugate series

A theorem of Ferenc Lukács determines the generalized jumps of a periodic, Lebesgue integrable function in terms of the partial sum of the conjugate series to the Fourier series of . The main aim of this paper is to prove an analogous theorem in terms of the Abel-Poisson mean. We also prove an estimate of the partial derivative (with respect to the angle) of the Abel-Poisson mean of an integrable function at those points at which is smooth. Finally, we reveal the intimate relation between these two results.

     

Near-symmetry in and refined Jones factorization

We use variants of the Hardy-Littlewood maximal and the Cruz-Uribe-Neugebauer minimal operators to give direct characterizations of and that clarify their near symmetry and yield elementary proofs of various known results, including Cruz-Uribe and Neugebauer's refinement of the Jones factorization theorem.

     

Banach空间中含$(H,\eta)$单调算子变分包含组解的迭代法

In this paper, we introduce and study a new system of variational inclusions involving （H, η）-monotone operators in Banach space. Using the resolveut operator associated with （H, η）- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.     

2一致凸Banach空间中均衡问题、变分不等式问题和不动点问题的一个弱收敛定理

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.     

A High-Order Kernel-Free Boundary Integral Method for Incompressible Flow Equations in Two Space Dimensions

This paper presents a fourth-order kernel-free boundary integral method for the time-dependent, incompressible Stokes and Navier-Stokes equations defined on irregular bounded domains. By the stream function-vorticity formulation, the incompressible flow equations are interpreted as vorticity evolution equations. Time discretization methods for the evolution equations lead to a modified Helmholtz equation for the vorticity, or alternatively, a modified biharmonic equation for the stream function with two clamped boundary conditions. The resulting fourth-order elliptic boundary value problem is solved by a fourth-order kernel-free boundary integral method, with which integrals in the reformulated boundary integral equation are evaluated by solving corresponding equivalent interface problems, regardless of the exact expression of the involved Green's function. To solve the unsteady Stokes equations, a four-stage composite backward differential formula of the same order accuracy is employed for time integration. For the Navier-Stokes equations, a three-stage third-order semi-implicit Runge-Kutta method is utilized to guarantee the global numerical solution has at least third-order convergence rate. Numerical results for the unsteady Stokes equations and the Navier-Stokes equations are presented to validate efficiency and accuracy of the proposed method.     

${[\ell_p]}_{e.r}$ Euler-Riesz Difference Sequence Spaces

Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$.     

An Expansion Formula for q-Series and Applications

In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers–Fine identity, the nonterminating ₆₅ summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed.     

Cobordism,Relative Indices and Stein Fillings

In this article we build on the framework developed in Ann. Math. 166, 183–214 ([2007]), 166, 723–777 ([2007]), 167, 1–67 ([2008]) to obtain a more complete understanding of the gluing properties for indices of boundary value problems for the Spin _ℂ-Dirac operator with sub-elliptic boundary conditions. We extend our analytic results for sub-elliptic boundary value problems for the Spin _ℂ-Dirac operator, and gluing results for the indices of these boundary problems to Spin _ℂ-manifolds with several pseudoconvex (pseudoconcave) boundary components. These results are applied to study Stein fillability for compact, 3-dimensional, contact manifolds. This material is based upon work supported by the National Science Foundation under Grant No. 0603973, and the Francis J. Carey term chair. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.     

Some families of combinatorial and other series identities and their applications

The main object of this presentation is to show how some simple combinatorial identities can lead to several general families of combinatorial and other series identities as well as summation formulas associated with the Fox-Wright function _pΨ_q and various related generalized hypergeometric functions. At least one of the hypergeometric summation formulas, which is derived here in this manner, has already found a remarkable application in producing several interesting generalizations of the Karlsson-Minton summation formula. We also consider a number of other combinatorial series identities and rational sums which were proven, in recent works, by using different methods and techniques. We show that much more general results can be derived by means of certain summation theorems for hypergeometric series. Relevant connections of the results presented here with those in the aforementioned investigations are also considered.     

Abel's method on summation by parts and theta hypergeometric series

Abel's lemma on summation by parts is reformulated to investigate systematically terminating theta hypergeometric series. Most of the known identities are reviewed and several new transformation and summation formulae are established. The authors are convinced by the exhibited examples that the iterating machinery based on the modified Abel lemma is powerful and a natural choice for dealing with terminating theta hypergeometric series.