A majorization inequality for Wright-convex functions revisited

We give an elementary proof of a majorization inequality concerning Wright-convex functions.     

An elementary proof of Rayleigh's principle

Rayleigh's principle states that the smallest eigenvalue of a regular Sturm-Liouville problem with regular boundary conditions is the minimum value of a certain functional, the so-called Rayleigh quotient, and that this value is attained at the corresponding eigenfunctions only. This can be proved by advanced methods. However, there is an elementary proof, which is presented in this note.     

A majorization principle forp-valent functions

A theorem augmenting the well-known Lindelöf principle (concerning Green functions) and the Mityuk inequality forp-valent maps is proved. Applications of this theorem and of the symmetrization method to the geometric theory of functions of a complex variable are given.     

An elementary proof of the principle of local reflexivity

We give an elementary proof of the principle of local reflexivity.

     

Decomposition of higher-order Wright-convex functions

In this paper we consider higher-order Wright-convex functions and prove that they are representable as the sum of a continuous higher-order convex function and a polynomial function.     

An elementary proof of the maximum principle for optimal control problems governed by a Volterra integral equation

An elementary proof of the maximum principle for optimal control problems whose states are governed by Volterra integral equations is given. Our proof is motivated by the work of Michel (Ref. 7) and utilizes only elementary results from analysis and mathematical programming. By appealing to Pontryagin-type perturbations of the controls, the above optimal control problem is effectively reduced to a mathematical programming problem. The results are then obtained by appealing to well-known mathematical programming results.     

An elementary proof of the Jordan-Kronecker theorem

This paper presents a proof of the Jordan-Kronecker theorem on the reduction to canonical form of a pair of skew-symmetric bilinear forms on a finite-dimensional linear space over an algebraically closed field.     

An elementary proof of Strauss conjecture

In this paper, we consider the Cauchy problem for semilinear wave equation in high dimensions. First we use a Morawetz energy estimate which is obtained by integrating on the light cone to get a weighted L²−L²$L^2-L^2$ estimate of the solution, and then give an elementary proof of the weighted Strichartz estimate in Georgiev et al. [3], hence the Strauss conjecture. We also obtain a variant of the weighted Strichartz estimates and give the sharp estimate of the lifespan for the semilinear wave equation with subcritical nonlinearity.     

An elementary proof of Lubeseder's theorem

Dedicated to Professor B. Huppert on his 60th birthday     

An elementary exclusion principle for Michell trusses

The exclusion optimality principle for Michell trusses established in Figueraoa et al. (2012) [2] is extended to frames which consist of countably many bars or rods. Furthermore, our extended exclusion principle can be applied to any point of the support of the frame under analysis.