Search results for "mathematical analysis"

Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation

2018

The paper deals with the generalization of Fourier-type relations in the context of fractional-order calculus. The instantaneous temperature-flux equation of the Fourier-type diffusion is generalized, introducing a self-similar, fractal-type mass clustering at the micro scale. In this setting, the resulting conduction equation at the macro scale yields a Caputo's fractional derivative with order [0,1] of temperature gradient that generalizes the Fourier conduction equation. The order of the fractional-derivative has been related to the fractal assembly of the microstructure and some preliminary observations about the thermodynamical restrictions of the coefficients and the state functions r…

Approximate analytic and numerical solutions to Lane-Emden equation via fuzzy modeling method

2012

Published version in the journal: Mathematical Problems in Engineering. Also available from the publisher: http://dx.doi.org/10.1155/2012/259494 A novel algorithm, called variable weight fuzzy marginal linearization VWFML method, is proposed. Thismethod can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

Nonstandard Uniserial Modules Over Valuation Domains

1987

One-dimensional nonlinear boundary value problems with variable exponent

2018

In this paper, a class of nonlinear differential boundary value problems with variable exponent is investigated. The existence of at least one non-zero solution is established, without assuming on the nonlinear term any condition either at zero or at infinity. The approach is developed within the framework of the Orlicz-Sobolev spaces with variable exponent and it is based on a local minimum theorem for differentiable functions.

Macro-elements in the mixed boundary value problems

2000

The symmetric Galerkin boundary element method (SGBEM), applied to elastostatic problems, is employed in defining a model with BE macro-elements. The model is governed by symmetric operators and it is characterized by a small number of independent variables upon the interface between the macro-elements.

A comparison of three recent selection theorems

2007

We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with the Schrader theorem based on bounded oscillation and with the Di Piazza-Maniscalco theorem based on bounded ${\cal A},\Lambda$-oscillation.

Holder continuity of solutions for a class of nonlinear elliptic variational inequalities of high order

2001

A method of desingularization for analytic two-dimensional vector field families

1991

It is well known that isolated singularities of two dimensional analytic vector fields can be desingularized: after a finite number of blowing up operations we obtain a vector field that exhibits only elementary singularities. In the present paper we introduce a similar method to simplify the periodic limit sets of analytic families of vector fields. Although the method is applied here only to reduce to families in which the zero set has codimension at least two, we conjecture that it can be used in general. This is related to the famouss Hibert's problem about planar vector fields.

A second strain gradient elasticity theory with second velocity gradient inertia – Part I: Constitutive equations and quasi-static behavior

2013

Abstract A multi-cell homogenization procedure with four geometrically different groups of cell elements (respectively for the bulk, the boundary surface, the edge lines and the corner points of a body) is envisioned, which is able not only to extract the effective constitutive properties of a material, but also to assess the “surface effects” produced by the boundary surface on the near bulk material. Applied to an unbounded material in combination with the thermodynamics energy balance principles, this procedure leads to an equivalent continuum constitutively characterized by (ordinary, double and triple) generalized stresses and momenta. Also, applying this procedure to a (finite) body s…

QSPR Modeling of Hydrocarbon Dipole Moments by Means of Correlation Weighting of Local Graph Invariants

2003

Hydrocarbon dipole moments are calculated by means of correlation weighting of local graph invariants within the context of QSPR theory. This sort of flexible topological descriptor is used for several parameters: local invariants of k th vertex in the labeled hydrogen filled graph extended connectivity of zero-, first- and second-orders, number of paths of length 2 at k th vertex and valence shell of the k th vertex. The models predict hydrocarbon dipole moments in a quite sensible way. The best model is that one based upon numbers of path length 2 correlation weighting.