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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar
Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of …
Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan
Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new …
The Terwilliger Algebra Of An Almost-Bipartite P- And Q-Polynomial Association Scheme, John S. Caughman Iv, Mark S. Maclean, Paul M. Terwilliger
The Terwilliger Algebra Of An Almost-Bipartite P- And Q-Polynomial Association Scheme, John S. Caughman Iv, Mark S. Maclean, Paul M. Terwilliger
Mathematics and Statistics Faculty Publications and Presentations
Let Y denote a D-class symmetric association scheme with D≥3, and suppose Y is almost-bipartite P- and Q-polynomial. Let x denote a vertex of Y and let T=T(x) denote the corresponding Terwilliger algebra. We prove that any irreducible T-module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the isomorphism class of W as a T-module is determined by two parameters, the dual endpoint and diameter of W. We find a recurrence which gives the multiplicities with which the …
Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We introduce a method that gives exactly incompressible velocity approximations to Stokes ow in three space dimensions. The method is designed by extending the ideas in Part I (http://archives.pdx.edu/ds/psu/10914) of this series, where the Stokes system in two space dimensions was considered. Thus we hybridize a vorticity-velocity formulation to obtain a new mixed method coupling approximations of tangential velocity and pressure on mesh faces. Once this relatively small tangential velocity-pressure system is solved, it is possible to recover a globally divergence-free numerical approximation of the fluid velocity, an approximation of the vorticity whose tangential component is continuous across …
Modeling The Evolution Of Inhomogeneities, Marek Elźanowski, Serge Preston
Modeling The Evolution Of Inhomogeneities, Marek Elźanowski, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
A model of an anelastic evolution law of a defective continuum is discussed, emphasizing the role of the Clausius-Duhem inequality in selecting admissible processes.
Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we introduce a new and efficient way to compute exactly divergence-free velocity approximations for the Stokes equations in two space dimensions. We begin by considering a mixed method that provides an exactly divergence-free approximation of the velocity and a continuous approximation of the vorticity. We then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique. This novel formulation bypasses the difficult task of constructing an exactly divergence-free basis for velocity approximations. Moreover, the discrete system resulting from our method has fewer degrees …
Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz
Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz
Mathematics and Statistics Faculty Publications and Presentations
In this note, we provide a conveniently implementable basis for simplicial Nédélec spaces of any order in any space dimension. The main feature of the basis is that it is expressed solely in terms of the barycentric coordinates of the simplex.
Curvature Of The Weinhold Metric For Thermodynamical Systems With 2 Degrees Of Freedom, Manuel Santoro, Serge Preston
Curvature Of The Weinhold Metric For Thermodynamical Systems With 2 Degrees Of Freedom, Manuel Santoro, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work the curvature of Weinhold (thermodynamical) metric is studied in the case of systems with two thermodynamical degrees of freedom. Conditions for the Gauss curvature R to be zero, positive or negative are worked out. Signature change of the Weinhold metric and the corresponding singular behavior of the curvature at the phase boundaries are studied. Cases of systems with the constant Cv, including Ideal and Van der Waals gases, and that of Berthelot gas are discussed in detail.