A Remark on a Paper of Banerjee, Lardy and Lutoborski

The paper that may be worthy of remark is entitled "Asymptotic Expansions of Integrals of Certain Rapidly Oscillating Functions" and appeared in Mathema tics of Computation, Vol. 49, No. 179(1987), 243—249.What we would like to mention is that the main result of the paper, namely an asymptotic expansion formula with a remainder estimate (cf.§3), is actually a special consequence     

关于Kumar和Mathur一文的注记

1°记T_n(x)=cosθ(x=cosθ)为多项式,x_k=cosθ_k=cos(2k-1/2n)π(k=1,…,n)是它的n个零点。以(1-x~2)T_n(x)的零点为节点的Lagrange插值多项式有如下形式:     

关于A.Menezes和S.Vanstone一文的注记

1987年,R.Schoof对于有限域Fq上的椭圆曲线的同构类数目得出了一个公式.1990年,A.M enezes和S.V anstone对此当q为偶数时给出了一个初等证明.本文利用Burnside引理对q为偶数时给出一个更简单的证明.     

关于《关于一类单叶函数》一文的注记

Let T be the class of functions of the form f(z)=z sum from n=2 to∞a_nz~n which are analytic inthe unit disc U={z:|z|<1}.A function f(z)∈T is said to be a member of the classR(a,b)if and only if it satisfies     

关于“广义模糊软集”一文的注记

In this paper,we point out that several assertions（Propositions 3.15 and 5.2（v）） in a previous paper by Majumdar and Samanta are not true in general,by counterexamples.     

关于《Multi—Dimensionae Q-Processes》一文的注记

本文指出了[1]中定理3(ⅱ)条件R′=∞只是一个充分条件,必要性并不成立。给出了一个反例;进一步,对全稳定保守Q矩阵Q=(q_(irj))i,j∈Z+,存在有限子集H(?)Z+使得: ⅰ)q_i,j(=)0,i∈H,j(?)H; ⅱ)q_i,i+1>0,i(?)H; q_i,j=0,i(?)H,j>i+1。给出了Q过程是唯一的充要条件。     

关于“改进Huang族算法”一文的注记

J.Flach,在文[1]中对Huang族算法的迭代式这里引进新的参数争φ_k和σ_k,令得到“改进Huang”族算法的迭代公式并在文献[1]的主要定理中证明了这一改进Huang族算法类中,所有算法产生的序列{x_k}只依赖于ρ_k、φ_k和σ_k,与其他参数无关.本文指出,J.Flaohs引进的独立参数仅仅是σ_k,这样[1]的主要结论可改为:改进Huang族算法产生的{x_k}只依赖于ρ_k和σ_k,与其他参数无关.考虑迭代公式     

Remark on a Paper of Sababheh and Khalil

We show that any Banach space X that has a sequence of unit vectors weakly converging to 0 has a closed and bounded convex set that is not remotal. This extends the main result of Sababheh and Khalil, (Numer. Funct. Anal. Optim. 2008; 29:1166–1170).     

关于Srinivasan一个问题的一点注记

本文的目的是用Ｂｒｕｎ筛法证明Ｓ．Ｓｒｉｎｉｖａｓａｎ提出的一个计数函数的渐近公式并纠正了他的一个错误．     

A Remark on a Problem of Rolf Nevanlinna

Let T ( f ) and N ( r,c ) denote the usual Nevanlinna characteristic and the counting function for the c -points of a meromorphic function f , respectively. Using a result of Miles and Shea ( Quart. J. Math. Oxford , 24 (2), (1973), 377-383) and two simple estimates for trigonometric functions, we show in connection with a 1929 problem of Nevanlinna for meromorphic functions f of finite order 1 < u < X $$ \limsup\limits_{r\rightarrow \infty } { N(r, 0)+N(r, \infty ) \over T(r, \,f)}\ge {2\sqrt 2 \over \pi} {|\sin \pi \lambda | \over D(\lambda )}\ge (0.9)\, {{|\sin \pi \lambda | \over {D(\lambda )}, }} $$ with D ( u ) = q +|sin ~ u | for $ q\le \lambda \le q + \fraca {1}{2} $ and D ( u ) = q + 1 for $ q + {\fraca {1} {2}} \le \lambda \lt q + 1 $ , where $ q = \lfloor \lambda \rfloor $ .     

A Remark on a Theorem by Kodama and Shimizu

We prove a characterization theorem for the unit polydisc Δ ⁿ ⊂ℂ ⁿ in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group Aut (M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) Aut (M) and Aut (Δ ⁿ ) are isomorphic as topological groups equipped with the compact-open topology, then M is holomorphically equivalent to Δ ⁿ .      

关于余逼近的一点注记

本文证明了１－维子空间和余１－维子空间是余可逼近的，且余度量射影有线性的选择，并举出例子对任何维数不小于２的有限维子空间未必是可余逼近的。     

A Remark on Steinness

In this paper, the authors prove that if Mn is a complete noncompact Kahler manifold with a pole p, and its holomorphic bisectional curvature is asymptotically non-negative to p, then it is a Stein manifold.