Analysis Commons^™

The Phillips Properties, Walden Freedman, Ali Ülger

Walden Freedman

A Banach space  has the Phillips property if the canonical projection  is sequentially weak-norm continuous, and has the weak Phillips property if  is sequentially weak-weak continuous. We study both properties in connection with other geometric properties, such as the Dunford-Pettis property, Pelczynski's properties  and (V), and the Schur property.

Uniform Convergence Of N-Dimensional Trigonometric Fourier Series., Ushangi Goginava

Ushangi Goginava

No abstract provided.

On The Convergence And Summability Of $N$-Dimensional Fourier Series With Respect To The Walsh-Paley Systems In The Spaces $L\Sp P([0,1]\Sp N)$, $P\In[1,+\Infty]$, Ushangi Goginava

Ushangi Goginava

No abstract provided.

On The Uniform Summability Of Multiple Walsh-Fourier Series, Ushangi Goginava

Ushangi Goginava

No abstract provided.

An Electromagnetic Inverse Problem In Chiral Media, Stephen R. Mcdowall

Mathematics Faculty Publications

We consider the inverse boundary value problem for Maxwell's equations that takes into account the chirality of a body in R³ . More precisely, we show that knowledge of a boundary map for the electromagnetic fields determines the electromagnetic parameters, namely the conductivity, electric permittivity, magnetic permeability and chirality, in the interior. We rewrite Maxwell's equations as a first order perturbation of the Laplacian and construct exponentially growing solutions, and obtain the result in the spirit of complex geometrical optics.

Total Determination Of Material Parameters From Electromagnetic Boundary Information, M. S. (Mark Suresh) Joshi, Stephen R. Mcdowall

Mathematics Faculty Publications

In this paper we complete the proof that the material parameters can be obtained for a chiral electromagnetic body from the boundary admittance map. We prove that from the admittance map, the parameters are uniquely determined to infinite order at the boundary. This removes the assumption of such knowledge in the result of the second author regarding interior determination for chiral media.

Multigrid For The Mortar Finite Element Method, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

A multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic boundary value problems is described and analyzed. These problems are posed on domains partitioned into subdomains, each of which is independently triangulated in a multilevel fashion. The multilevel mortar finite element spaces based on such triangulations (which need not align across subdomain interfaces) are in general not nested. Suitable grid transfer operators and smoothers are developed which lead to a variable Vcycle preconditioner resulting in a uniformly preconditioned algebraic system. Computational results illustrating the theory are also presented.

Mortar Estimates Independent Of Number Of Subdomains, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

The stability and error estimates for the mortar finite element method are well established. This work examines the dependence of constants in these estimates on shape and number of subdomains. By means of a Poincar´e inequality and some scaling arguments, these estimates are found not to deteriorate with increase in number of subdomains.

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench

William F. Trench

No abstract provided.