Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem
2020
Abstract We consider the Laplace equation in a domain of R n , n ≥ 3 , with a small inclusion of size ϵ . On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For ϵ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.
Inversion formulae for the integral transform on a locally compact zero-dimensional group
2009
Abstract Generalized inversion formulae for multiplicative integral transform with a kernel defined by characters of a locally compact zero-dimensional abelian group are obtained using a Kurzweil-Henstock type integral.
On continua comparable with all continua
1999
Abstract A collection of continua is described such that each continuum either is incomparable with some element of the collection, or it is a continuous image of the harmonic fan. As a consequence, a characterization of continua comparable with all continua is obtained.
Iterative approach to the exponential representation of the time–displacement operator
2005
An iterative method due to Voslamber is reconsidered. It provides successive approximations for the logarithm of the time–displacement operator in quantum mechanics. The procedure may be interpreted, a posteriori, as an infinite re-summation of terms in the so-called Magnus expansion. A recursive generator for higher terms is obtained. From two illustrative examples, a detailed comparative study is carried out between the results of the iterative method and those of the Magnus expansion.
Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee
2020
In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted wi…
Abriss der Algebra der Logik, Teil 1. Elementarlehre
1909
Bearbeitet im Auftrag der Deutschen Mathematiker-Vereinigung von Eugen Müller.
A second-order differential equation for the two-loop sunrise graph with arbitrary masses
2011
We derive a second-order differential equation for the two-loop sunrise graph in two dimensions with arbitrary masses. The differential equation is obtained by viewing the Feynman integral as a period of a variation of a mixed Hodge structure, where the variation is with respect to the external momentum squared. The fibre is the complement of an elliptic curve. From the fact that the first cohomology group of this elliptic curve is two-dimensional we obtain a second-order differential equation. This is an improvement compared to the usual way of deriving differential equations: Integration-by-parts identities lead only to a coupled system of four first-order differential equations.
De Rham–Hodge–Kodaira Operator on Loop Groups
1997
AbstractWe consider a based loop group Le(G) over a compact Lie groupG, endowed with its pinned Wiener measureν(the law of the Brownian bridge onG) and we shall calculate the Ricci curvature for differentialn-forms over Le(G). A type of Bochner–Weitzenböck formula for general differentialn-forms (or Shigekawa identity) will be established.
Theory of Differential Inclusions and Its Application in Mechanics
2017
The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work, three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torqu…
Invariant varieties of discontinuous vector fields
2004
We study the geometric qualitative behaviour of a class of discontinuous vector fields in four dimensions around typical singularities. We are mainly interested in giving the conditions under which there exist one-parameter families of periodic orbits (a result that can be seen as one analogous to the Lyapunov centre theorem). The focus is on certain discontinuous systems having some symmetric properties. We also present an algorithm which detects and computes periodic orbits.