In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.

The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function.

We describe in brief some aspects of the Langlands program, focussing on Euler products, and also some new constructions, where Euler products are replaced by twisted Euler products. The twisted Euler products are related to automorphic forms on metaplectic groups. 2000 Mathematics Subject Classification: 11F66, 11F55, 11F70, 11M41, 22E55.

1 Euler Characteristics and Infinitesimal Characters 4 1.1 The unitary duals of SL2(R) and SL4(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Euler characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Euler-Poincaré functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Euler characteristics in t...

The main goal of this paper is to present the basis for a heterogeneous Euler/Venn diagram and First Order Logic (FOL) reasoning system. We will begin by defining a homogeneous reasoning system for Euler/Venn diagrams including named constants and show this system to be sound and complete. Then we will propose a heterogeneous rule of inference allowing the extraction of formulas of FOL from an ...

Abstract Based on the Euler-Euler-Lagrangian framework, Euler-Euler two-fluid model coupled with population balance (PBM) and Discrete Phase Model (DPM) were used to simulate gas-liquid-solid three phase dynamic behavior in laboratory bubble column. The non-Newtonian properties of liquid was considered numerical simulation, cases different models discussed. It is found that peak value velocity ...

A linear complementarity formulation for dynamic multi-rigid-body contact problems with Coulomb friction is presented. The formulation, based on explicit Euler integration and polygonal approximation of the friction cone, is guaranteed to have a solution for any number of contacts and contact con guration. A model with the same property is formulated for impact problems with friction and nonzer...