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 In a marginal case, this result is superseded by a result of Lev.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.     

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.     

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.     

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.     

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.     

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).

     

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.     

On Green’s functions for positive,elliptic differential operators on closed,Riemannian manifolds and some consequences for semi-linear PDE

In this article, we establish the non-negativity of Green’s functions for a class of elliptic differential operators on closed, Riemannian manifolds. The method used is the calculus of variations with a unilateral constraint. Consequences of this result are then explored, with a maximum principle-type result established for a broad class of semi-linear elliptic PDE as a result. Finally, a result regarding the positivity of the principal eigenfunction of an operator in this class is proven as well.     

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.     

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.     

Homogenization and corrector for the wave equation with discontinuous coefficients in time

In this paper we analyze the homogenization of the wave equation with bounded variation coefficients in time, generalizing the classical result, which assumes Lipschitz-continuity. We start showing a general existence and uniqueness result for a general sort of hyperbolic equations. Then, we obtain our homogenization result comparing the solution of a sequence of wave equations to the solution of a sequence of elliptic ones. We conclude the paper making an analysis of the corrector. Firstly, we obtain a corrector result assuming that the derivative of the coefficients in the time variable is equicontinuous. This result was known for non-time dependent coefficients. After, we show, with a counterexample, that the regularity hypothesis for the corrector theorem is optimal in the sense that it does not hold if the time derivative of the coefficients is just bounded.     

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．     

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.     

An example of stability for the minima of a sequence of dc functions: Homogenization for a class of nonlinear Sturm-Liouville problems

Combining the Clarke-Ekeland dual least action principle and the epi-convergence, we state an existence result and study the asymptotic behaviour for the periodic solution of a nonlinear Sturm-Liouville problem deriving from a convex subquadratic potential, when the data are perturbed in a suitable sense. The result appears like a stability result for the minimizers of a sequence of DC functions.     

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.     

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.     

Well-posedness and stability for a mixed order system arising in thin film equations with surfactant

The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated, but also of mixed orders. To the best of our knowledge the only well-posedness result for a capillary driven thin film with surfactant is provided in [4] by the same author, where a severe smallness condition on the surfactant concentration is assumed to prove the result. Thus, in spite of an intensive analytical study of thin film equations with surfactant during the last decade, a proper well-posedness result is still missing in the literature. It is the aim of the present paper to fill this gap. Furthermore, we apply a recently established result on asymptotic stability in interpolation spaces [15] to prove that the flat equilibrium of our system is asymptotically stable.     

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.     

Asymptotic behaviour of a nonlinear equation and its application

In this paper, we study the asymptotic behaviour of a second order nonlinear differential equation arising in a constrained optimal stopping problem. Two examples are considered to illustrate our main result. The present result extends and supplements a recent result of the author [5].     

Linearization of class C for contractions on Banach spaces

In this work we prove a C¹-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations.