The Bass di®usion model is a well-known parametric approach to estimating new product demand trajectory over time. This paper generalizes the Bass model by allowing for a supply constraint. In the presence of a supply constraint, potential customers who are not able to obtain the new product join the waiting queue, generating backorders, and potentially reversing their adoption decision, result...

The Bass di®usion model is a well-known parametric approach to estimating new product demand trajectory over time. This paper generalizes the Bass model by allowing for a supply constraint. In the presence of a supply constraint, potential customers who are not able to obtain the new product join the waiting queue, generating backorders, and potentially reversing their adoption decision, result...

A stainless steel grid baked by a propane±air premixed ¯ame had iron, chromium and nickel oxide deposits on the grid surface. With this grid, entangled and curved shape multi-walled carbon nanotubes (MWNTs) were harvested from an ethylene±air di€usion ¯ame with yield rate of 3 mg/min. Nitrogen addition to the ¯ame was found to straighten the entangled tubes probably by lowering the ¯ame tempera...

In this paper we develop local and global estimates for the solution of advection-di usion problems. We then study the convergence properties of a Time Marching Algorithm solving advection-di usion problems on two domains using incompatible discretizations. This study is based on a DeGiorgi-Nash maximum principle. This work has been supported by the Hermes Research program under grant number RD...

Consequences of long-range hopping in one-dimensional tight-binding models are studied. A hopping term proportional to 1=r ij is used, where rij denotes the distance between atoms i and j and determines the range of the interactions within the system. Calculations of the di usion of an electron along the lattice yield interesting e ects of nonextensivity. In particular, we nd that the mean squa...

We study a queueing model of customer service chat (CSC) systems. A unique feature of these queueing systems is that a single agent can serve multiple customers simultaneously. We prove the convergence of the queueing process to di↵erent di↵usion processes in a many server heavy-tra c regime in three di↵erent cases. Using this result, we are able o↵er approximations for the steady state perform...

Shock wave theory was studied in literature by many authors. This article presents a survey with references about various topics related to shock waves: Hyperbolic conservation laws, Well-posedness theory, Compactness theory, Shock and reaction-di¤usion wave, The CJ and ZND theory, Existence of detonation in Majda’s model, Premixed laminar ‡ame, Multidimensional gas ‡ows, Multidimensional Riema...

We develop a discontinuous ®nite element method for advection±di€usion equations arising in contaminant transport problems, based on the Local Discontinuous Galerkin (LDG) method of Cockburn B and Shu CW. (The local discontinuous Garlerkin method for time-dependent convection±di€usion systems. SIAM J Numer Anal 1998;35:2440±63). This method is de®ned locally over each element, thus allowing for...

We present the mathematical analysis for the convergence of an h version Finite Element Method (FEM) with piecewise polynomials of degree p ≥ 1, de ned on an exponentially graded mesh. The analysis is presented for a singularly perturbed reaction-di usion and a convection-di usion equation in one dimension. We prove convergence of optimal order and independent of the singular perturbation param...

In this work, we apply quantum cellular automata (QCA) to study pattern formation and image processing in quantum-di usion Schrodinger systems (QDSS) with generalized complex di usion coe cients. Generalized complex numbers have the real part and imaginary part with the imaginary unit i = −1 (classical case), i = +1 (double numbers) and i = 0 (dual numbers). They form three 2-D complex algebras...