Search results for "integral"
showing 10 items of 902 documents
Mellin transform approach for the solution of coupled systems of fractional differential equations
2015
In this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized form.
Partial differential equations governed by accretive operators
2012
The theory of nonlinear semigroups in Banach spaces generated by accretive operators has been very useful in the study of many nonlinear partial differential equations Such a theory is fundamentally based in the Crandall-Liggett Theorem and in the contributions of Ph. Benilan. In this paper, after outlining some of the main points of this theory, we present some of the applications to some nonlinear partial differential equations that appear in different fields of Science.
General theory for cross-ply laminated beams
1997
We present a general formulation of the elasticity theory of the cross-ply composite laminated beam subjected to various loadings such as axial load, bending moment, shear/bending, and torsion. The formulation is based on the integral equation theory, and a direct approach is employed to obtain the boundary integral equations for the analysis of the laminated beam. The integral equations governing the elasticity problem are directly deduced from the reciprocity theorem, by using the singular solutions of the orthotropic elasticity explicitly derived. The numerical solution is achieved by the boundary element method, which gives, once the traction free boundary conditions and the interfacial…
Reflection and Refraction of Singularities for Wave Equations with Interface Conditions given by Fourier Integral Operators
1992
Cauchy problems for hyperbolic operators often have the property, that the singularities of the initial data propagate along the bicharacteristic strips of the operator (cf. e.g. [13]). We consider, in the linear case, the situation where the bicharacteristics hit transversally a spacelike interface, which is ‘active’ in the sense that the interface condition is given via certain Fourier integral operators. Taking the identity, we obtain classical transmission conditions. A suitable functional analytic setting is furnished by the interaction concept [3], [6], [7], which covers very general mutual influences of evolution phenomena on different domains.
3D-2D dimensional reduction for a nonlinear optimal design problem with perimeter penalization
2012
A 3D-2D dimension reduction for a nonlinear optimal design problem with a perimeter penalization is performed in the realm of $\Gamma$-convergence, providing an integral representation for the limit functional.
Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem
2016
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we prove some estimates on the rate of convergence to the exact solution.
Indefinite integrals of some special functions from a new method
2015
A substantial number of indefinite integrals of special functions are presented, which have been obtained using a new method presented in a companion paper [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. The method was originally derived from the Euler–Lagrange equations but an elementary proof is also presented in [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. Sample results are presented here for Bessel functions, Airy functions and hypergeometric functions. More extensive results are given for th…
Pseudo-Abelian integrals along Darboux cycles
2008
We study polynomial perturbations of integrable, non-Hamiltonian system with first integral of Darboux-type with positive exponents. We assume that the unperturbed system admits a period annulus. The linear part of the Poincare return map is given by pseudo-Abelian integrals. In this paper we investigate analytic properties of these integrals. We prove that iterated variations of these integrals vanish identically. Using this relation we prove that the number of zeros of these integrals is locally uniformly bounded under generic hypothesis. This is a generic analog of the Varchenko-Khovanskii theorem for pseudo-Abelian integrals. Finally, under some arithmetic properties of exponents, the p…
Kirkwood-Buff Integrals for Finite Volumes.
2012
Exact expressions for finite-volume Kirkwood−Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.
P-adic Henstock integral in the theory of series over systems of characters of zero-dimensional groups.
2006
We introduce a path integral of Henstock type and use it to obtain inversion formulas for multiplicative integral transformations. The problem considered is a generalization of the problem of reconstruction of coefficients of a convergent orthogonal series from its sum.