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 work, using the concept of natural density, we introduce $\left(
 p,q\right) $-analogue Stancu-beta operators rough $\lambda$%
 -statistically $\rho$-Cauchy convergence on triple sequence spaces. We define
 set Bernstein Stancu beta opeators statistical limit points of
 a spaces and obtain to $\lambda-$statistical convergence
 criteria associated with set. Also,...

In this paper, we define several ideal versions of Cauchy sequences and completeness in quasimetric spaces. Some examples are constructed to clarify their relationships. We also show that: (1) if a quasi-metric space (X, ?) is I-sequentially complete, for each decreasing sequence {Fn} nonempty I-closed sets with diam{Fn} ? 0 as n ?, then ?n?N Fn single-point set; (2) let I be P-ideal, every pre...

‎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...

In this article, we consider a Cauchy problem of heat equation, that is, determining the unknown temperature and heat flux at an inaccessible boundary from scattered temperature measurements on an accessible boundary or in some interior locations. This method is similar to the boundary control approach proposed by Leevan Ling and Tomoya Takeuchi in [1] where the authors considered a Cauchy prob...