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.

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 …

Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles. Among the interesting aspects are that even if the affine contraction underlying the iterated function system is not conjugated to a similarity we obtain an upper- and and lower-bound for its Hausdorff dimension. In fact, we obtain the exact value for the dimension if the moduli of the eigenvalues of the underlying affine contraction are all equal (this includes Jordan blocks). The tiles we discuss play an important role in the theory of wavelets. We calculate the dimension for a …

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 …

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

Faculty Publications

No abstract provided.

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.

The Effect Of Three-Dimensional Freestream Disturbances On The Supersonic Flow Past A Wedge, Peter W. Duck, D. Glenn Lasseigne, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al. [P W. Duck, D. G. Lasseigne, and M. Y. Hussaini, ''On the interaction between the shock wave attached to a wedge and freestream disturbances,'' Theor. Comput. Fluid Dyn. 7, 119 (1995) (also ICASE Report No. 93-61)] through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of …

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].

Scattering From Stellar Acoustic-Gravity Potentials: Ii. Phase Shifts Via The First Born Approximation, J. A. Adam, I. Mckaig

Mathematics & Statistics Faculty Publications

Using the first Born approximation, properties of the scattering phase shift are investigated for waves that are scattered by a schematic representation of a large-scale “stellar potential,” i.e., one for which the star itself is viewed as the potential inducing a phase shift in an incoming wave. In particular, the phase shift properties are examined as functions of the relative wavenumber (α) and the azimuthal wavenumber (l), high l-values being of interest in helioseismology.

Time-Optimal Tree Computations On Sparse Meshes, D. Bhagavathi, V. Bokka, H. Gurla, S. Olariu, J. L. Schwing

Computer Science Faculty Publications

The main goal of this work is to fathom the suitability of the mesh with multiple broadcasting architecture (MMB) for some tree-related computations. We view our contribution at two levels: on the one hand, we exhibit time lower bounds for a number of tree-related problems on the MMB. On the other hand, we show that these lower bounds are tight by exhibiting time-optimal tree algorithms on the MMB. Specifically, we show that the task of encoding and/or decoding n-node binary and ordered trees cannot be solved faster than Ω(log n) time even if the MMB has an infinite …

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.

Collected Papers, Vol. 2, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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.