The multi-mode approximation is presented to compute the interior wave function of Schrödinger equation. This idea is necessary to handle the multi-barrier and high dimensional resonant tunneling problems where multiple eigenvalues are considered. The accuracy and efficiency of this algorithm is demonstrated via several numerical examples.

In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one...

The problem of reducing the deviation from a desired transfer function caused by the coefficient quantization errors is investigated for a three-dimensional (3D) separable in denominator digital filter. To begin with, a 3-D transfer function with separable denominator is represented with the cascade connection of three one-dimensional (1-D) transfer functions by applying a minimal decomposition...

In most DHT-based peer-to-peer systems, objects are totally declustered since such systems use a hash function to distribute objects evenly. However, such an object de-clustering can result in significant inefficiencies in advanced access operations such as multi-dimensional range queries, continuous updates, etc, which are common in many emerging peer-to-peer applications. In this paper, we pr...

This paper examines critically the contributions of Cournot, Jevons and Walras as the founders of classical mathematical economics from a methodological standpoint. Advances in different economic schools and doctrines in the 19th century produced an environment of multi-dimensionality in economic analysis which was regarded by the pioneers of classical mathematical economists as a chaotic state...

In this paper, experimentally derived correlations of heat transfer and pressure drop are used in a Pareto based Multi-Objective Optimization (MOO) approach to find the best possible combinations of heat transfer and pressure drop of TiO2-water nanofluid flow in tubes fitted with multiple twisted tape inserts in different arrangement. In this study there are four independent design variables: t...

The contribution of this paper is the formulation of the wind farm power maximization problem as a multi-stage dynamic programming problem. This formulation is made possible by introducing a state-space model to describe the evolution of the wind velocity profile as a function of the free-stream wind velocity and the wind turbine control variables. This state-space model is coupled with a multi...

Function approximation can improve the ability of a reinforcement learner. Tile coding and Kanerva coding are two classical methods for implementing function approximation, but these methods may give poor performance when applied to large-scale, high-dimensional instances. In the paper, we evaluate a collection of hard instances of the predator-prey pursuit problem, a classic multi-agent reinfo...

There are limitations to the current BRep based “model then animate” paradigm when animating time-dependent (dynamic) objects. This paper describes an approach to modeling dynamic objects directly in space-time or even higher dimensional space. The use of the function representation (FRep) is proposed due to the ease with which it handles higher dimensions. After creating a multidimensional FRe...