We consider some geometric aspects of regular Sturm-Liouville problems. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of Sturm-Liouville eigenvalues on the boundary condition, and reveals many new properties of these eigenvalues. In particular, the eigenvalues for separated boundary conditions and thos...

We show that for a continuous map of a closed interval to itself, if the set of periodic points is closed, then every recurrent point is periodic. If, furthermore, the set of least periods of the periodic points is finite, then every nonwandering point is periodic. This answers a question of L. Block [Proc. Amer. Math. Soc. 67 (1977), 357-360]. Introduction. In [1] and [2], L. Block studied con...

We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin-spin couplings are the same in both directions. The exact ...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

Abstract We study the periodic cosmic transit behavior of accelerated universe in framework symmetric teleparallelism. The exact solution field equations is obtained by employing a well-known deceleration parameter (DP) called varying DP, q = m</mml:mi...

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

Received 16 March 2008; accepted 4 May 2008 Abstract: We classify the maximal irreducible periodic subgroups of PGL(q,F) , where F is a field of positive characteristic p transcendental over its prime subfield, q 6= p is prime, and F× has an element of order q . That is, we construct a list of irreducible subgroups G of GL(q,F) containing the centre F×1q of GL(q,F) , such that G/F×1q is a maxim...

for each t ∈R. When convergence in (1.1) and (1.2) is uniform in t ∈ R, f is said to be (Bochner) almost periodic. Almost periodic functions are characterized by the following so-called Bochner’s criterion. f : R→ X is almost periodic if and only if for every sequence of real numbers (s′ n), there exists a subsequence (sn) such that (f (t+sn)) is uniformly convergent in t ∈R. For more informati...