Related papers: The mathematics of functional differentiation unde…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
We present a class of functions $\mathcal{K}$ in $C^0(\R)$ which is variant of the Knopp class of nowhere differentiable functions. We derive estimates which establish $\mathcal{K} \sub C^{0,\al}(\R)$ for $0<\al<1$ but no $K \in…
We propose three new discrete variational schemes that capture the conservative-dissipative structure of a generalized Kramers equation. The first two schemes are single-step minimization schemes while the third one combines a streaming and…
Fractional calculus of variation plays an important role to formulate the non-conservative physical problems. In this paper we use semi-inverse method and fractional variational principle to formulate the fractional order generalized…
Using the six parameters truncated Mittag-Leffler function, we introduce a convenient truncated function to define the so-called truncated $\mathcal{V}$-fractional derivative type. After a discussion involving some properties associated…
A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the…
The relationship between the refractive index decrement, $\delta$, and the real part of the atomic form factor, $f^\prime$, is used to derive a simple polynomial functional form for $\delta(E)$ far from the K-edge of the element. The…
To any left system of diagram categories or to any left pointed derivateur (in the sense of Grothendieck) a K-theory space is associated. This K-theory space is shown to be canonically an infinite loop space and to have a lot of common…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The derivative discontinuity of the exchange-correlation functional of density-functional theory is cast as the difference of two types of electron affinities. We show that standard Kohn-Sham calculations can be used to calculate both…
It is known that the dynamics of $f$ and $g$ vary to a large extent from that of its composite entire functions. Using Approximation theory of entire functions, we have shown the existence of entire functions $f$ and $g$ having infinite…
Given a function $f:(0,\infty)\rightarrow\RR$ and a positive semidefinite $n\times n$ matrix $P$, one may define a trace functional on positive definite $n\times n$ matrices as $A\mapsto \Tr(Pf(A))$. For differentiable functions $f$, the…
We address a classical open question by H.Brezis and R.Ignat concerning the characterization of constant functions through double integrals that involve difference quotients. Our first result is a counterexample to the question in its full…
In this paper we develop the theory of {\it polymorphisms} of measure spaces, which is a generalization of the theory of measure-preserving transformations; we describe the main notions and discuss relations to the theory of Markov…
The generalized Stokes theorem (connecting integrals of dimensions 3 and 4) is formulated in a curved space-time in terms of paths in Minkowski space (forming Path Group). A covariant integral form of the conservation law for the…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
The pairings between the cyclic cohomologies and the K-theories of separable $C^\ast$-algebras supply topological invariants that often relate to physical response coefficients of materials. Using three numerical simulations, we exemplify…
It is shown that one can obtain canonically-defined dynamical equations for non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel of the…