We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine’s 2φ1 transformation formula and Sears’ 3φ2 transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator T (bDq). Using this operator, we obtain extensi...

We study the Cauchy problem for the Aw-Rascle-Zhang model for traffic flow with a flux constraint at x = 0. More precisely we consider the Riemann solver, conserving the number of cars at x = 0 but not the generalized momentum, introduced in [9] for the problem with flux constrained. For such a Riemann solver, we prove existence of a solution for the Cauchy problem. The proof is based on the wa...

In this paper, we introduce the notion order quasi-Cauchy se-quences, downward and upward quasi-cauchy sequences, half Cauchy sequences. Next consider associated idea of continuity namely, ward continuous functions [2] investigated certain intersting results. The entire investigation is perform in (l)-group setting.

We consider a flagged form of the Cauchy determinant, for which we provide a combinatorial interpretation in terms of nonintersecting lattice paths. In combination with the standard determinant for the enumeration of nonintersecting lattice paths, we are able to give a new proof of the Cauchy identity for Schur functions. Moreover, by choosing different starting and end points for the lattice p...

We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Rosén. These are constructed through functional calculus and are in general beyond the scope of singular integrals. More precisely, we establish such Cauchy formulas for solutions u with gradient in weighted L2(R 1+...

— A meshfree computational scheme is developed to study the compressive deformation of single-walled carbon nanotubes (SWCNTs). The continuum constitutive relationship is based on an extended Cauchy-Born rule, the higher order Cauchy-Born rule, in which the atomic-scale deformed lattice vectors are calculated with both the first and second order deformation gradients. The compression of CNTs is...

We invenstigate a local analysis of the Lavrentiev regularization method applied to the ill-posed Cauchy problem. A convergence analysis of the approximated solution is carried out in a sub region away from the incomplete boundary, which is the source of the instability of the Cauchy solution. The use of a Carleman estimate with boundary condition by D.Tataru (see [4]) brings about super-conver...

We introduce the poly-Cauchy polynomials which generalize the classical Cauchy polynomials, and investigate their arithmetical and combinatorial properties. These polynomials are considered as analogues of the poly-Bernoulli polynomials that generalize the classical Bernoulli polynomials. Moreover, we investigate the zeta functions which interpolate the poly-Cauchy polynomials. The values of th...