Search results for "Mathematical Analysis"

Multiplicity results for systems of asymptotically linear second order equations

2002

Abstract We prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.

Multiplicity results for asymptotically linear equations, using the rotation number approach

2007

By using a topological approach and the relation between rotation numbers and weighted eigenvalues, we give some multiplicity results for the boundary value problem u′′ + f(t, u) = 0, u(0) = u(T) = 0, under suitable assumptions on f(t, x)/x at zero and infinity. Solutions are characterized by their nodal properties.

Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance

2007

Abstract Estimations of the number of solutions are given for various resonant cases of the boundary value problem 𝑥″ + 𝑔(𝑡, 𝑥) = 𝑓(𝑡, 𝑥, 𝑥′), 𝑥(𝑎) cos α – 𝑥′(𝑎) sin α = 0, 𝑥(𝑏) cos β – 𝑥′(𝑏) sin β = 0, where 𝑔(𝑡, 𝑥) is an asymptotically linear nonlinearity, and 𝑓 is a sublinear one. We assume that there exists at least one solution to the BVP.

The Monotone Area-preserving Flux-Form Advection Algorithm: Reducing the Time-splitting Error in Two-Dimensional Flow Fields

1993

Inverse problem for tripotential measures in the study of buried cavities

1996

This paper presents a solution to the inverse electrical problem for the interpretation of apparent resistivity anomalies due to empty buried cavities of quasi-spherical shape when tripotential measures are carried out. The anomalies of the apparent resistivities ra,rb andrg,and the composed resistivitiesrmand rt were previously calculated for a sufficient class of spherical models of resistivity anomalies. Then, for the whole class of models, some functionals of spatial distribution of the apparent and composed resistivity were identified and analyzed. They represent the average characteristics of the anomalies and, depending in a simple way on the fundamental parameters of the sources of …

An attempt to realise the constrained search approach in the density functional theory

2001

Abstract The problem of reconstruction of wave functions from a given electron density is considered. A reformulation of the problem is proposed which is based on the Fourier transform. Arising mathematical problems are studied, namely, the properties of reduced spatial densities and their Fourier images are obtained, which follow from known properties of the wave functions. The proposed approach may provide a practical implementation of the Constrained Search Approach to the DFT.

A bending theory of thermoelastic diffusion plates based on Green-Naghdi theory

2017

Abstract This article is concerned with bending plate theory for thermoelastic diffusion materials under Green-Naghdi theory. First, we present the basic equations which characterize the bending of thin thermoelastic diffusion plates for type II and III models. The theory allows for the effect of transverse shear deformation without any shear correction factor, and permits the propagation of waves at a finite speed without energy dissipation for type II model and with energy dissipation for type III model. By the semigroup theory of linear operators, we prove the well-posedness of the both models and the asymptotic behavior of the solutions of type III model. For unbounded plate of type III…

Integration of a Dirac comb and the Bernoulli polynomials

2016

Abstract For any positive integer n , we consider the ordinary differential equations of the form y ( n ) = 1 − Ш + F where Ш denotes the Dirac comb distribution and F is a piecewise- C ∞ periodic function with null average integral. We prove the existence and uniqueness of periodic solutions of maximal regularity. Above all, these solutions are given by means of finite explicit formulae involving a minimal number of Bernoulli polynomials. We generalize this approach to a larger class of differential equations for which the computation of periodic solutions is also sharp, finite and effective.

Computation of the area in the discrete plane: Green’s theorem revisited

2017

International audience; The detection of the contour of a binary object is a common problem; however, the area of a region, and its moments, can be a significant parameter. In several metrology applications, the area of planar objects must be measured. The area is obtained by counting the pixels inside the contour or using a discrete version of Green's formula. Unfortunately, we obtain the area enclosed by the polygonal line passing through the centers of the pixels along the contour. We present a modified version of Green's theorem in the discrete plane, which allows for the computation of the exact area of a two-dimensional region in the class of polyominoes. Penalties are introduced and …

Exponential Relaxation out of Nonequilibrium

1989

Simulation results are presented for a quench from a disordered state to a state below the coexistence curve. The model which we consider is the Ising model but with the dynamics governed by the Swendsen-Wang transition probabilities. We show that the resulting domain growth has an exponential instead of a power law behaviour and that the system is non-self-averaging while in nonequilibrium. The simulations were carried out on a parallel computer with up to 128 processors.