In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and condition on circle for generalized Cauchy-Riemann equation singular coefficient. To solve problem, conducted complete of the solvability theory analytic functions infinite due to number points special type vorticity. Based these results, have derived formula general solution studied existence soluti...

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...

The problems below are motivated by some of the works I did in the past. They deal with the dynamics of compressible fluids, either viscous or inviscid. They could be good questions for mathematicians having originality and technical strength. They are not worth a million dollars, even not a penny, but they are interesting in their own. 1 Global-in-time Cauchy problem for Euler–Fourier system P...

Cauchy-compact flat spacetimes with extreme BTZ are Lorentzian analogue of complete hyperbolic surfaces finite volume. Indeed, the latter 2-manifolds locally modeled on plane, group isometries $\mathrm{PSL}_2(\R)$, admitting finitely many cuspidal ends while regular part former 3-manifolds models 3 dimensionnal Minkowski space, $\mathrm{PSL}_2(\R)\ltimes \RR^3$, whose neighborhoods foliated by ...

‎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...

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.