辛普生公式的推广

推广了数值积分中著名的辛普生公式,讨论了中值点的渐近性.     

Generalization of the Plana Formula

We obtain an analog of the Plana formula, which is essential in obtaining the functional equation for the classical Riemann zeta-function.     

校正梯形公式的推广

对数值积分中的校正梯形公式作出推广并讨论了中间值的渐近性.     

Generalization of the Cramer Formula

We apply the method of parametrized continued fractions to the solution of systems of linear algebraic equations on the basis of their Liouville–Neumann formal power series. We construct an analog of the Cramer formula, which is also applicable to the cases of singular, ill-posed, and rectangular matrices.     

一个积分等式的推广与应用

从积分限和积分次数两方面推广关系式∫0^xf（t）（x-t）dt=∫0^x（∫0^tf（u）du） dt,其中f（x）为连续函数,并举例说明所得结论在累次积分计算中的应用.     

Lefschetz–Verdier Trace Formula and a Generalization of a Theorem of Fujiwara

The goal of this paper is to generalize a theorem of Fujiwara (Deligne’s conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also give a proof of the Lefschetz–Verdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially self-contained. The work was supported by the Israel Science Foundation (Grant No. 555/04) Received: May 2005 Accepted: August 2005     

On a Generalization of Injective Rings

Abstract

A ring R is called left IP-injective if every homomorphism from a left ideal of R into R with principal image is given by right multiplication by an element of R. It is shown that R is left IP-injective if and only if R is left P-injective and left GIN (i.e., r(I ∩ K) = r(I) + r(K) for each pair of left ideals I and K of R with I principal). We prove that R is QF if and only if R is right noetherian and left IP-injective if and only if R is left perfect, left GIN and right simple-injective. We also show that, for a right CF left GIN-ring R, R is QF if and only if Soc(R _R ) ? Soc( _R R). Two examples are given to show that an IP-injective ring need not be self-injective and a right IP-injective ring is not necessarily left IP-injective respectively.     

关于Widder定理的推广

利用解析函数理论及改进了的Holder不等式,并借助于Hardy的技巧建立了广义的Widder不等式,当p=q=2时,得到Widder定理的一个改进.     

On a Generalization of Equilogical Spaces

We use the theory of triposes to prove that every (non-degenerate) locale H is the set of truth values of a complete and co-complete quasi-topos into which the category of topological spaces embeds and the topos of sheaves over H reflectively embeds.     

半交换环的一个推广研究

In this paper, a generalization of the class of semicommutative rings is investigated.A ring R is called left GWZI if for any a ∈ R, l(a) is a GW-ideal of R. We prove that a ring R is left GWZI if and only if S3(R) is left GWZI if and only if Vn(R) is left GWZI for any n ≥ 2.     

On a Generalization of Szemeredi's Theorem

Let N be a natural number and A [1, ..., N]² be a set of cardinalityat least is an absolute constant. We prove that A contains a triple {(k, m), (k+d, m), (k, m+d)},where d > 0. This theorem is a two-dimensional generalizationof Szemerédi's theorem on arithmetic progressions. 2000Mathematics Subject Classification 35J25, 37A15.     

F.H.Jackson超几何级数公式_8φ_7的推广

将 C.Krattenthaler的矩阵反演恰当地用于初文昌的恒等式得到了 F.H.Jackson的超几何级数公式 87的推广 .     

Generalization of the Berezin Formula to the Noncommutative Case

With the help of functional integrals in Fock space, under some analytical assumptions, we construct representations for exponents of quadratic functions of creation and annihilation operators with noncommuting coefficients.     

Cauchy中值定理与Leibniz公式的推广

引入辅助函数的方法可将Cauchy中值定理推广到高阶形式,即两函数n阶Taylor展开误差的比值等于在某点两函数(n+1)阶导数比值的形式;用数学归纳法可将Leibniz公式中函数的个数推广至任意有限多个.     

Euler求和公式的一种推广和应用

将只适用于有限区间上具有连续微商的函数的Eu ler求和公式推广到一般的连续函数,并应用此公式推出对于满足L ipsch itz条件的函数普通数值积分的梯形法、矩形法与S im pson法.     

On a Generalization for Tribonacci Quaternions

Let \(V_{n}\) denote the third order linear recursive sequence defined by the initial values \(V_{0}\), \(V_{1}\) and \(V_{2}\) and the recursion \(V_{n}=rV_{n-1}+sV_{n-2}+tV_{n-3}\) if \(n\ge 3\), where r, s, and t are real constants. The \(\{V_{n}\}_{n\ge 0}\) are generalized Tribonacci numbers and reduce to the usual Tribonacci numbers when \(r=s=t=1\) and to the 3-bonacci numbers when \(r=s=1\) and \(t=0\). In this study, we introduced a quaternion sequence which has not been introduced before. We show that the new quaternion sequence that we introduced includes the previously introduced Tribonacci, Padovan, Narayana and third order Jacobsthal quaternion sequences. We obtained the Binet formula, summation formula and the norm value for this new quaternion sequence.