We present a surface Cauchy-Born approach to modeling FCC metals with nanometer scale dimensions for which surface stresses contribute significantly to the overall mechanical response. The model is based on an extension of the traditional Cauchy-Born theory in which a surface energy term that is obtained from the underlying crystal structure and governing interatomic potential is used to augmen...

Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the original Cauchy problem. Fractional Cauchy problems are useful in physics to model anomalous diffus...

Chruściel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons are generic. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence o...

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.

The Fueter–Sce–Qian theorem provides a way of inducing axial monogenic functions in $$\mathbb {R}^{m+1}$$ from holomorphic intrinsic one complex variable. This result was initially proved by Fueter and Sce for the cases where dimension m is odd using pointwise differentiation, while extension to even Qian corresponding Fourier multipliers. In this paper, we provide an alternative description te...

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

It is shown how the extended conformal Einstein field equations and a gauge based on properties of geodesics can be used to analyse non-linear stability spaces with negative scalar curvature. This class spacetimes admits smooth extension spacelike boundary. Central analysis use Gaussian systems obtain hyperbolic reduction for which standard Cauchy results symmetric employed. The methods allows ...

Nous étudions des matrices dont les entrées sont variables libres ou échangeables d’un W*-espace de probabilités tracial. Plus précisément, nous considérons Wigner et Wishart avec à valeurs opérateurs montrons la convergence quantitative, vers semi-circulaires sur une certaine sous-algèbre, en termes transformées Cauchy distance Kolmogorov. Comme applications directes, obtenons taux explicites ...