Some results related to the Bombieri type generalisation of Bessel's inequality in 2-inner product spaces are given. The corresponding versions for Selberg and Heilbronn inequalities for 2-inner products and applications for determinantal integral inequalities are also pointed out

A first principles analysis of an open system thermodynamical Carnot cycle is provided, and the results are compared to those proposed by Gibbs for open systems. The Kelvin-Clausius statement concerning heat transfer for reversible cycles is taken as an axiom, from which several rigorous...

Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided

The goal of the paper is to present a new method (similar to phase-integral method) for hnding approximation of the eigenfunctions and eigenvalues of the one-dimensional Schrödinger operator with asymmetric double-well potential

Let := () be defined over an algebraically closed field of prime characteristic . Put and let { = − , = } be a base of the root system Φ of . For a Weyl group element and for a character λ ∈ (), we put where = λ, mod and denotes a Borel subalgebra of generated by positive root vectors...

The goal of this paper is to present a new method for hnding approximation of eigenfunctions and eigenvalues of the one-dimensional Schrödinger operator. The novelty of the method is that it is based on construction of exponentially increasing solutions. This approach has some advantages...

Let ∈ ℂ be a nontrivial involution; i.e., = ≠ ± We say that ∈ ℂ is -symmetric (-skew symmetric) if = ( = − ).There are positive integers and with + = and matrices ∈ ℂ and ∈ ℂ such that = , = , = , and = −. We give an explicit representation of an arbitrary -symmetric...

We strengthen a theorem of Kuijlaars and Serra Capizzano on the distribution of zeros of a sequence of orthogonal polynomials for which the coefficients in the three term recurrence relation are clustered at finite points. The proof uses a matrix argument motivated by a theorem of Tyrtyshnikov

Let be the Fourier coefficients of ∈ [−, ] and consider the Toeplitz matrices {()}, where ; thus, {()} is generated by the symbol . There are many results on asymptotic properties of {()} as → ∞. If is a positive integer and , then where is easily obtained from . Hence, known results on...

In this paper, we study the existence of multiple stationary solutions of Generalized Kadomtsev-Petviashvili (Abbr. GKP) equation with asymptotically linear term at infinity. In this case, the well-known Ambrosetti-Rabinowtz type condition doesn't hold, hence it is difficult to verify the...