Addendum to “Distribution of points on the circle” [J. Number Theory 127 (1) (2007) 127-135]

In an earlier paper we gave a result relating the value of an exponential sum with the distribution of summands in the arcs of the unit circle in the complex plane. In a marginal case, this result is superseded by a result of Lev. In this addendum we use an idea of Lev to give a new proof of our earlier result and to improve upon the marginal result.     

明目科研成果应用及其多元统计分析

本文简介了明目科研成果《易效明目功》的应用，并重点对易效明目功防治青少年近视的效用进行了多元统计分析，Ｐ＜０．０５，效果显著。     

An acceleration property of theE-algorithm for alternate sequences

We prove a convergence acceleration result by theE-algorithm for sequences whose error has an asymptotic expansion on the scale of comparison for which a determinantal relation holds. This result is generalized to the vector case. Moreover we prove a result which contains an acceleration property for columns and diagonals of theE array. This result is applied to some alternating series.     

Direct Result for a Summation-Integral Type Modification of Szász-Mirakjan Operators

In this paper, study of direct result for a summation-integral type modification of Szász-Mirakjan operators is carried out. Calculation of moments, density result and a Voronovskaja-type result are also obtained.     

Conditions on subgraphs,degrees, and domination for hamiltonian properties of graphs

Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties. In our first main result we relax the condition on claw-freeness and obtain a common generalization of the result of Ageev and a recent result due to Cai. Our other results deal with similar conditions that guarantee traceability, pancyclicity and hamiltonian-connectivity. We also leave some open problems.     

Duality for Multiobjective Optimization via Nonlinear Lagrangian Functions

In this paper, a strong nonlinear Lagrangian duality result is established for an inequality constrained multiobjective optimization problem. This duality result improves and unifies existing strong nonlinear Lagrangian duality results in the literature. As a direct consequence, a strong nonlinear Lagrangian duality result for an inequality constrained scalar optimization problem is obtained. Also, a variant set of conditions is used to derive another version of the strong duality result via nonlinear Lagrangian for an inequality constrained multiobjective optimization problem.     

Mazur-Ulam定理的一个注记

本文的主要结论是给出了一个更广泛形式的Mazur-Ulam定理.讨论的对象是实的赋准范空间,满等距算子被减弱成其像空间构成一个加法子群的算子.最后给出的推论推广了Skof的一个结果.     

A note on the analytic families of compact submanifolds of complex manifolds

In this paper, we prove a result of the deformation of the complex structure of a submanifold. Our result is a modification of the result of Kodaira (Ann. Math 75(1), 146-162, 1962).

     

A note on dentability, quasi-dentability and LUR renorming

In this work we prove a result that provides us an equivalent LUR norm in a normed space whenever it has the property of denting and compact faces in the unit ball; we obtain this result after applying the main result of [11]. In the last part of the paper we obtain our main result that gives us a universal map between dentability and quasi-dentability indices.Received: 29 July 2004; revised: 31 January 2005     

A polynomial Hutton theorem with applications

Extending a classical linear result due to Hutton to a nonlinear setting, we prove that a continuous homogeneous polynomial between Banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be approximated by finite rank linear operators. Among other consequences, we apply this result to generalize a classical result due to Aron and Schottenloher about the approximation property on spaces of polynomials and a recent result due to Çaliskan and Rueda about the quasi-approximation property on projective symmetric tensor products.     

Eulerian* -polynomial identities on matrix algebras

In this paper we considerably strengthen a result of Ribenboim on noetherian generalised power series rings. While Ribenboim proves his result under the restrictive assumption that the monoid occuring in the definition of the geralised power series ring in cancellative we prove a corresponding result for arbitrary ordered monoids.     

Non-existence of positive solution to a quasilinear elliptic system and blow-up estimates for a reaction-diffusion system

IntroductionIn these years, the reaction-diffusion systems of Fujita typea5 ttell as the related elliptic systemt'ith fl g RN, Tnl. n1 3 0, i = 1, 2. \vere studied by' a nu111ber of authors. The probiemsconcerning system (l) inc1ude globa1 existence and g1obal existen(.e numbers. b1ow-up. bloxv-uprates, and blow-up sets. uniqueness or nonuniqueness. et('. FOr s}'stem (2) there are problemssuch as existence or non-existence. uniqueness or nonllniqueI1ess. and so ol1. 1Ieanwhile. itseems that…     

Characterization of Totally Geodesic Totally Real 3-dimensional Submanifolds in the 6-sphere

In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li.     

An extension of Peleg's inequality

In this note, we prove an extension of a remarkable result due to B. Peleg. Peleg's result concerns the simultaneous validity of a set of inequalities for families of functions defined on a finite product of standard simplices in finite-dimensional spaces. The main result we prove here provides an extension of that result to the case of functions defined on a rather general product of simplices. Some topological requirements lead us to deal with this problem from a functional point of view.     

Minkowski空间中具有常值支持函数的子流形

在Mlinkowski空间中证明了完备连通且具有常值支持函数的子流形必为Finsler球面或者为一个平面．利用支持函数研究的两类子流形是Euclid空间中结果的推广，同时优化了Euclid空间中子流形的相应结果．     

Existence of solutions for nonlinear inequalities in locally convex separated space

An existence result for abstract nonlinear inequalities. As a consequence of our result, we obtain some further generalizations of recent known results. According to this result, we show the existence of g-saddle point and Aumann strong equilibrium for a constrained noncooperative game.     

AN ESTIMATE OF EIGENVALUES IN THE SYMMETRIC QR ALGORITHM*

The estimate of the eigenvalues is given when the off-diagonal elements in symmetric tridiagonal matrix are replaced by zero. The result can be applied to QR or QL algorithm. It is a generalization of Jiang' s result in 1987. This estimate is sharper than Hager's result in 1982 and could not fail     

On existence and asymptotic behaviour of solutions of a functional integral equation

The paper contains a result on the existence and asymptotic behaviour of solutions of a functional integral equation. That result is proved under rather general hypotheses. The main tools used in our considerations are the concept of a measure of noncompactness and the classical Schauder fixed point principle. The investigations of the paper are placed in the space of continuous and tempered functions on the real half-line. We prove an existence result which generalizes several ones concerning functional integral equations and obtained earlier by other authors. The applicability of our result is illustrated by some examples.     

ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.     

Concerning derivations of lie algebras

Schur showed that if the center of a group has finite index, then the commutator subgroup is finite. By replacing inner automorphisms by automorphisms, Hegarty obtained a variation of Schur's result. The Lie algebra analogue of Schur's result is well-known. We obtain a strong Lie algebra version of Hegarty's result.