Applied Mathematics Commons^™

Monotone Iterations For Differential Equations With A Parameter, Tadeusz Jankowski, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

Consider the problem {y′(t)=f(t,y(t),λ),t∈J=[0,b],y(0)=k0,G(y,λ)=0. Employing the method of upper and lower solutions and the monotone iterative technique, existence of extremal solutions for the above equation are proved.

Some Properties Of Hereditarily Indecomposable Chainable Continua, Thomas John Kacvinsky

Masters Theses

"In 1920, B. Knaster and C. Kuratowski raised the question of whether each homogeneous plane continuum is a simple closed curve. In 1921, S. Mazurkiewicz raised the question of whether each subcontinuum of Euclidean n-space which is homeomorphic to each of its subcontinua is necessarily an arc. In that same year, B. Knaster and C. Kuratowski raised the question of whether there exists a nondegenerate hereditarily indecomposable continuum.

The third question was answered in the affirmative in 1922 by B. Knaster, when he constructed a nondegenerate hereditarily indecomposable subcontinuum of the plane.

The second question was answered in 1947 by …

Collected Papers, Vol. 2, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

An Invariance Property Of Common Statistical Tests, N. Rao Chaganty, A. K. Vaish

Mathematics & Statistics Faculty Publications

Let A be a symmetric matrix and B be a nonnegative definite (nnd) matrix. We obtain a characterization of the class of nnd solutions Σ for the matrix equation AΣA = B. We then use the characterization to obtain all possible covariance structures under which the distributions of many common test statistics remain invariant, that is, the distributions remain the same except for a scale factor. Applications include a complete characterization of covariance structures such that the chisquaredness and independence of quadratic forms in ANOVA problems is preserved. The basic matrix theoretic theorem itself is useful in other characterizing …

Limiting Spheroid Size As A Function Of Growth Factor Source Location, J. A. Adam, K. Y. Ward

Mathematics & Statistics Faculty Publications

Solutions C(r) of the time-independent nonhomogeneous diffusion equation for three different piecewise-uniform source terms are used to examine the limiting size of multicell spheroids using a simple model which reproduces concentration-dependent mitotic behavior. A condition is derived under which nontrivial solutions do not exist (in all three cases), and a condition for the existence of a unique nontrivial solution is established for the case of growth-modifying factor (GMF) production throughout the spheroid. Qualitative behavior of the limiting size is established as a function of various physiological parameters. Of fundamental importance is the assumed GMF concentration threshold θ, …

Continuities Of Metric Projection And Geometric Consequences, Robert Huotari, Wu Li

Mathematics & Statistics Faculty Publications

We discuss the geometric characterization of a subset K of a normed linear space via continuity conditions on the metricprojection onto K. The geometric properties considered includeconvexity, tubularity, and polyhedral structure. The continuityconditions utilized include semicontinuity, generalized stronguniqueness and the non-triviality of the derived mapping. Infinite-dimensional space with the uniform norm we show thatconvexity is equivalent to rotation-invariant almost convexityand we characterize those sets every rotation of which has continuousmetric projection. We show that polyhedral structure underliesgeneralized strong uniqueness of the metric projection.

Convolution And Fourier-Feynman Transforms, Chull Park, David Skough

Department of Mathematics: Faculty Publications

In this paper, for a class of funtionals on Wiener space of the form F(x) = exp{∫^T₀ f(t, x(t)) dt}, we show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms. This allows us to compute the transform of the convolution product without computing the convolution product.

Hoffman’S Error Bounds And Uniform Lipschitz Continuity Of Best L(P) -Approximations, H. Berens, M. Finzel, W. Li, Y. Xu

Mathematics & Statistics Faculty Publications

In a central paper on smoothness of best approximation in 1968 R. Holmes and B. Kripke proved among others that on ℝⁿ, endowed with the l_ρ-norm, 1< p < ∞, the metric projection onto a given linear subspace is Lipschitz continuous where the Lipschitz constant depended on the parameter p. Using Hoffman’s Error Bounds as a principal tool we prove uniform Lipschitz continuity of best l_ρ -ap- proximations. As a consequence, we reprove and prove, respectively, Lipschitz. continuity of the strict best approximation (sba, p = ∞ and of the natural best approximation (nba, p = 1.

Superconvergence Of The Iterated Collocation Methods For Hammerstein Equations, Hideaki Kaneko, Richard D. Noren, Peter A. Padilla

Mathematics & Statistics Faculty Publications

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].

A Dual Approach To Constrained Interpolation From A Convex Subset Of Hilbert Space, Frank Deutsch, Wu Li, Joseph D. Ward

Mathematics & Statistics Faculty Publications

Many interesting and important problems of best approximationare included in (or can be reduced to) one of the followingtype: in a Hilbert spaceX, find the best approximationPK(x) to anyx∈Xfrom the setK≔C∩A−1(b),whereCis a closed convex subset ofX,Ais a bounded linearoperator fromXinto a finite-dimensional Hilbert spaceY, andb∈Y. The main point of this paper is to show thatPK(x)isidenticaltoPC(x+A*y …

Global Attractors From The Explosion Of Singular Cycles, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Résumé:

Nous présentons dans cette Note des résultats récents concernant l’existence et les bifurcations d’un nouvel attracteur global chaotique.

Antiplane Shear Of A Strip Containing A Staggered Array Of Rigid Line Inclusions, G. Kerr, G. Melrose, J. Tweed

Mathematics & Statistics Faculty Publications

Motivated by the increased use of fibre-reinforced materials, we illustrate how the effective elastic modulus of an isotropic and homogeneous material can be increased by the insertion of rigid inclusions. Specifically we consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing two sets of ribbon-like, rigid inclusions perpendicular to the faces of the strip. The strip is then subjected to a prescribed uniform displacement difference between its faces, see Figure 1. it should be noted that the problem posed is equivalent to that of the uniform antiplane shear problem for an infinite …

The Laws Of Complexity & The Complexity Of Laws: The Implications Of Computational Complexity Theory For The Law, Eric Kades

Faculty Publications

No abstract provided.