The paper deals with a fluid dynamic model for supply chains. A mixed continuum-discrete model is proposed and possible choices of solutions at nodes guaranteeing the conservation of fluxes are discussed. Fixing a rule a Riemann solver is defined and existence of solutions to Cauchy problems is proved.

We establish elliptic regularity for nonlinear, inhomogeneous Cauchy-Riemann equations under weak assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the solution set can be explicitly calculated. The methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost c...

Consider a strictly hyperbolic nn system of conservation laws in one space dimension: u t + F(u) x = 0: () Relying on the existence of the Standard Riemann Semigroup generated by (), we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of u along space-like segments.

In this paper, we study the local Cauchy-Riemann embeddability of strictly pseudoconvex real hyperboloids M2n+1 into spheres. By solving a CR analogue of the Gauss equation, we prove that M2n+1 is CR-embeddable into spheres with a CR co-dimension < n− 1 if and only if it is spherical.

• Pre-Hilbert spaces: definition • Cauchy-Schwarz-Bunyakowski inequality • Example: spaces ` • Triangle inequality, associated metric, continuity issues • Hilbert spaces, completions, infinite sums • Minimum principle • Orthogonal projections to closed subspaces • Orthogonal complements W⊥ • Riesz-Fischer theorem on linear functionals • Orthonormal sets, separability • Parseval equality, Bessel...

The present work has the scope to show the relationship between four three-dimensional waves. This fact will be made in the form of coupling, using for it the Cauchy-Riemann conditions for quaternionic functions [1], through certain Laplace’s equation in [2]. The coupling will relate those functions that determine the wave as well as their respective propagation speeds. AMS Subject Classificati...

We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy–Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated.

This paper researches properties of a regular function defined on a domain in Clifford analysis. Also, the paper investigates properties of extensions for a regular function with values in DH and the corresponding Cauchy-Riemann system for a regular function of dual quaternionic variables.

We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables. c ©2016 all rights reserved.