The main purpose of this paper is to study normed hypervector spaces. We generalize some definitions such as basis, convexity, operator norm, closed set, Cauchy sequences, and continuity in such spaces and prove some theorems about them.

In this paper we first give a unified method by introducing the concept of admissible triplets to study local and global Cauchy problems for semi-linear parabolic equations with a general nonlinear term in different Sobolev spaces. In particular, we establish the local well-posedness and small global well-posedness of the Cauchy problem for semi-linear parabolic equations without the homogeneou...

Evolution strategies are a class of general optimisation algorithms which are applicable to functions that are multimodal, non-diierentiable, or even discontinuous. Although recombination operators have been introduced into evolution strategies, their primary search operator is still mutation. Classical evolution strategies rely on Gaussian mutations. A new mutation operator based on the Cauchy...

equations as something "which Cauchy never even wrote" is obviously a wrong translation, what was meant being something like "which Cauchy did not write here". I have kept a list of dozens of lesser errors, but at least this translator does not fall to the depths of rendering Abel's famous statement "Cauchy est 'fou' " by "Cauchy is a fool" [3, p. 25]. The presentation of the book is scandalous...

Cauchy-Characteristic Matching (CCM), the combination of a central 3 + 1 Cauchy code with an exterior characteristic code connected across a timelike interface, is a promising technique for the generation and extraction of gravitational waves. While it provides a tool for the exact specification of boundary conditions for the Cauchy evolution, it also allows to follow gravitational radiation al...

In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.

This is the rst of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the pro...

We propose a new O(n)-space implementation of the GKO-Cauchy algorithm for the solution of linear systems with Cauchy-like matrix. Despite its slightly higher computational cost, this new algorithm makes a more efficient use of the processor cache memory. Thus, for matrices of size larger than n ≈ 500− 1000, it outperforms the existing algorithms. We present an applicative case of Cauchy-like m...

The behaviour of test fields near a compact Cauchy horizon is investigated. It is shown that solutions of nonlinear wave equations on Taub spacetime with generic initial data cannot be continued smoothly to both extensions of the spacetime through the Cauchy horizon. This is proved using an energy method. Similar results are obtained for the spacetimes of Moncrief containing a compact Cauchy ho...