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Technical Papers
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On the Computation of Semivalues for TU Games
(University of Texas at ArlingtonDepartment of Mathematics, 200812)In an earlier paper, [Dragan,2006a] , we proved that every Least Square Value is the Shapley Value of a game obtained by rescaling from the given game. In the paper where the Least Square Values were introduced by Ruiz, ... 
Particle Simulation in Contact Mechanics of a Bouncing Elastic Ball
(University of Texas at ArlingtonDepartment of Mathematics, 199905)An elastic ball is simulated by considering lumped mass molecular sets called particles. Particles are allowed to interact only locally in a fashion similar to that employed in molecular mechanics. Under local and gravity ... 
Molecular Mechanics Simulations of the Three Dimensional Cavity Problem
(University of Texas at ArlingtonDepartment of Mathematics, 199903)The rapid development of computer technology has resulted in broad interest in three dimensional fluid simulation, which is known to have more complex force interactions than occur in two dimensions (see, e.g., refs. [16], ... 
Tennis, Geometric Progression, Probability and Basketball
(University of Texas at ArlingtonDepartment of Mathematics, 199903)The following problem about a tennis match is well—known. See Halmos [1, 2]. Consider 2n tennis players playing a single elimination match. Ask the question: what are the number of games played? The answer can be obtained ... 
System Identification Problems and the Method of Moments
(University of Texas at ArlingtonDepartment of Mathematics, 197705)Let X(t) and W(t) be vectors of dimension N > 0. We are concerned with the problem of computing an N x N matrix A such that [see pdf for notation](1.1) where X'(t) is the rate of change of X(t) with respect to time t. ... 
New Mathematical Properties of the Least Square Value
(University of Texas at ArlingtonDepartment of Mathematics, 199603)The Least Square Values for cooperative TU games (briefly, LSvalues) represent a family of solutions of the following family of optimization problems associated with a cooperative TU game: minimize the sum of weighted ... 
Programs for Vortex Street Generation
(University of Texas at ArlingtonDepartment of Mathematics, 1987) 
CRAY XMP/24 Fortran Programs for Capillarity
(University of Texas at ArlingtonDepartment of Mathematics, 1987)This technical report contains the FORTRAN programs used in generating capillary action. They are provided so that the computations described elsewhere can be reproduced by the interested reader. Without this availability, ... 
Computer Files for Drop Formation
(University of Texas at ArlingtonDepartment of Mathematics, 1987) 
Zeros of BouligandNagumo Fields, FlowInvariance and the Bouwer Fixed Point Theorem
(University of Texas at ArlingtonDepartment of Mathematics, 1987)Mainly, in this paper we prove that if D is a convex compact of Rn, then the Brouwer fixed point property of D is equivalent to the fact that every BouligandNagums vector field on D, has a zero in D. Using a version of ... 
Supercomputer Simulation of Sessile and Pendent Drops
(University of Texas at ArlingtonDepartment of Mathematics, 1987)A intermolecular approach is developed for the modeling of sessile and pendent drops. Fundamental mechanisms of drop formation are formulated in terms of gravity and classical intermolecular type forces. CRAY XMP/24 ... 
Absolute Minimization by Supercomputer Computation
(University of Texas at ArlingtonDepartment of Mathematics, 1987)Numerical methodology is developed for approximating the absolute minimum of a function or a functional. Only simplistic numerical techniques are introduced and explored. CRAY X—MP/24 computer examples are described and discussed. 
Estimating Transition Probabilities from Aggregate Samples Augmented by Haphazard Recaptures
(University of Texas at ArlingtonDepartment of Mathematics, 1995)Transition probabilities provide a convenient summary of changes in a categorical trait over time in a population. The difficulties of estimating such probabilities based on only aggregate data from repeated sampling are ... 
Conservative Difference Formulations of Calogero and Toda Hamiltonian Systems
(University of Texas at ArlingtonDepartment of Mathematics, 1988)Calogero and Toda Hamiltonian systems are reformulated using only differences. The formulations prove to have the same fundamental invariants as the continuous systems and, in addition, are readily implementable on modern ... 
Particle Simulation of Biological Sorting on a Supercomputer
(University of Texas at ArlingtonDepartment of Mathematics, 1988)Cell sorting, or, self reorganization, is modelled by means of particles which obey classical molecular dynamical equations. A system of N second order, nonlinear, ordinary differential equations results when the number ... 
Heron's Problem in the Minkowski Plane
(University of Texas at ArlingtonDepartment of Mathematics, 1995)Heron's problem in the Euclidean plane is that of minimizing the length of a path that joins two points on one side of a line and intersects the line. A generalization in the Minkowski plane is given and used to discuss ... 
Supercomputer, Simulation of Liquid Drop Formation, Fall, and Collision
(University of Texas at ArlingtonDepartment of Mathematics, 1988)A generic molecular type model of liquid drops is developed and studied. Drop formation, fall, and collision are simulated on a CRAY XMP/24 and associated modes of oscillation are described. Methods for application to ... 
A TemperatureAdjusted Ozone Attainment Criterion Based on Extreme Value Regression Analysis
(University of Texas at ArlingtonDepartment of Mathematics, 1993)We propose a new statistical methodology to adjust observed peak ozone levels to "normal" meteorology (say, temperatures) across the year for a given site. The adjusted ozone levels can be used to establish a yearly ozone ... 
Particle Simulation of Large Carbon Dioxide Bubbles in Water
(University of Texas at ArlingtonDepartment of Mathematics, 1993)A method which can be applied to simulate the motion of fluid drops within fluids is described through a detailed study of a prototype problem, that is, the motion of carbon dioxide bubbles in water. The mathematical ... 
Covariant Computation in Special Relativistic Dynamics
(University of Texas at ArlingtonDepartment of Mathematics, 1988)The motion of a particle in a special relativistic framework is studied numerically. Difference equations which are covariant are developed first. It is then shown how computations can be done in both the lab and rocket ...