We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this paper, Lorentz Transformation(LT) is derived by an alternate method, using photon clocks, placed at the locations of the concerned events, which are initially synchronised using a light signal(Einstein synchrony). Then, it is shown that the second term in the time dilation equation of the LT, is the term responsible for time travel and further it is shown that this term arises merely du...

We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy– Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motiv...

We introduce a concept of Cauchy complete Császár frames and construct Cauchy completions of Császár frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

In this paper, we first study the material stability of nanostructured materials via the continuum linearized stability analysis technique with the temperature-related Cauchy–Born (TCB) rule. As a temperature-related homogenization technique, the TCB rule considers the free energy instead of the potential so that temperature effects on material stability can be investigated. In addition, we dev...

For an o-minimal expansion R of a real closed field and a set V of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to V . This is an elementary extension S of R generated by all completions of all the residue fields of the V ∈ V , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings u...

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC(&lambda1, &lambda2), that it has more flexible than the skew-Cauchy distribution (denoted by SC(&lambda)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC(&lambd...

Quasi-nearness biframes provide an asymmetric setting for the study of nearness; in [1] a completion (called a quasi-completion) was constructed for such structures and in [2] completeness was characterized in terms of the convergence of regular Cauchy bifilters. In this talk, questions of functoriality for this quasi-completion are considered and one sees that having enough regular Cauchy bifi...