The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. equations motion and stress-energy-momentum tensor for hyperelastic body are derived the gauge-invariant action principle first considered by DeWitt. This natural extension single particle. central object in Lagrangian treatment Landau-Lifshitz radar metric, which version right Cauc...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

We introduce a class of independence relations, which include free, boolean and monotone independence, in operator-valued probability. show that this relations have matricial extension property so we can easily study their associated convolutions via Voiculescu's fully function theory. Based the property, many results be generalized to multi-variable cases. Besides additive convolutions, will f...

The research in the field of cardiovascular biomechanics is focused primarily on the heart and blood vessels, but the surrounding tissues, on the other hand, are often overlooked in the literature. This study shows that the human perivascular adipose tissue can significantly affect mechanical response of the human abdominal aorta. Analytical model of incompressible bilayer thick-walled closed c...

in this paper, we present legendre wavelet method to obtain numerical solution of a singular integro-differential equation. the singularity is assumed to be of the cauchy type. the numerical results obtained by the present method compare favorably with those obtained by various galerkin methods earlier in the literature.

We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes family. We also investigate when the domain of means can be extended beyond the ”natural domain”.

Recently, K. Kamano studied sums of products of Bernoulli numbers including poly-Bernoulli numbers. A relation among these sums was given, and an explicit expression of sums of two products was also given, reduced to the famous Euler’s formula. The concept of poly-Cauchy numbers is given by the author as a generalization of the classical Cauchy number and an analogue of poly-Bernoulli number. I...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

the main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $s$ to an arbitrary unitary complex banachalgebra and also $psi: s^{2}rightarrow [0,infty)$ is afunction. fur...

A generalized Cauchy-Kowalevski approach is proposed for flatness-based trajectory planning for boundary controlled semilinear systems of PDEs in a one-dimensional spatial domain. For this, the ansatz presented in [16] using formal integration is generalized towards a unified design framework, which covers linear and semilinear PDEs including rather broad classes of nonlinearities arising in ap...