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Dichotomy theorems for evolution equations
(University of Missouri--Columbia, 2008)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In the first part of this work, under minimal assumptions, we characterize the Fredholm property and compute the Fredholm index of abstract differential ...
The implicit function theorem for Lipschitz functions and applications
(University of Missouri--Columbia, 2008)
The subject matter of this thesis is the classical Implicit Function Theorem and its generalizations. Dictated by practical applications, it is of interest to relax the hypothesis of the standard Implicit Function Theorem ...
Surface to surface changes of variables and applications
(University of Missouri--Columbia, 2008)
The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration ...
Orlicz-Lorentz Spaces
(2011)
The purpose of this article is to summerize some recent results of the author about Orlicz-Lorentz spaces - function spaces that provide a common generalization of Orlicz spaces and Lorentz spaces.
Evolutionary semigroups and Lyapunov theorems in Banach spaces
(2011)
We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from ...
Temperature and heat flux estimation from sampled transient sensor measurements
(2011)
Laplace transform is used to solve the problem of heat conduction over a finite slab. The temperature and heat flux on the two surfaces of a slab are related by the transfer functions. These relationships can be used to ...
Analytic measures and Bochner measurability
(2011)
Many authors have made great strides in extending the celebrated F. and M. Riesz
Theorem to various abstract settings. Most notably, we have, in chronological order,
the work of Bochner, Helson and Lowdenslager, de Leeuw ...
Gravitomagnetic Jets
(arXiv, 2010)
We present a family of dynamic rotating cylindrically symmetric Ricci-flat gravitational fields whose geodesic motions have the structure of gravitomagnetic jets. These correspond to helical motions of free test particles ...
Some conjectures about integral means of ∂f and ∂¯f
(2011)
We discuss some conjectural inequalities concerning a problem from the calculus of variations, namely that rank 1 convex functions are quasi-convex. An affirmative answer would also give the best constants for the ...
Measures on Hilbert spaces and applications to hydrodynamics
(University of Missouri--Columbia, 2010)
Homogeneous and isotropic statistical solutions of the Navier-Stokes equations are produced. These are shown to be approximated by Galyerkin statistical solutions on finite dimensional subspaces. Homogeneous and isotropic ...
Gravitomagnetic Accelerators
(arXiv, 2010)
We study a simple class of time-dependent rotating Ricci-flat cylindrically symmetric spacetime manifolds whose geodesics admit gravitomagnetic jets. The helical paths of free test particles in these jets up and down ...
Measuring the magnitude of sums of independent random variables
(2011)
This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Lévy property. We then give ...
Concrete representation of martingales
(2011)
Let (fn) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (dn) from [0,1]n such that ∫01 dn(x1,...,xn) dxn = 0 for almost all x1,...,xn-1, and such that the law of (fn) is the same ...
A transference theorem for ergodic H1
(2011)
In this paper, we extend the basic transference theorem for convolution operators on Lp spaces of Coifman and Weiss to H1 spaces.
Mathematical problems from cryobiology
(University of Missouri--Columbia, 2009)
Cryobiology is the study of life anddeath at low temperatures and provides a fascinating setting for applied mathematics. The interdisciplinary nature of cryobiology mirrors the diversity of applications ranging from animal ...
Inequalities of correlation type for symmetric stable random vectors
(2011)
We point out a certain class of functions f and g for which random variables f(X1,...,Xm) and g(Xm+1,...,Xk) are non-negatively correlated for any symmetric jointly stable random variables Xi. We also show another result ...
Comparison of sums of independent identically distributed random variables
(2011)
Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ∥Sk∥ with that of ∥Sj∥, and deduce some tail distribution maximal ...
A free boundary gas dynamic model as a two-body field theory problem
(University of Missouri--Columbia, 2009)
Motivated by the two-body problem in the classical field theories of electrodynamics and gravitation, in which finite propagation speeds lead to radiation reaction and runaway solutions, we develop a free boundary problem ...
Hahn's embedding theorem for orders and harmonic analysis on groups with ordered duals
(2011)
Let G be a locally compact abelian group whose dual group Γ contains a Haar measurable order P. Using the order P we define the conjugate function operator on Lp(G), 1 ≤ p < ∞, as was done by Helson. We will show how to ...
Delay equations and radiation damping
(arXiv, 2001)
Starting from delay equations that model field retardation effects, we study the origin of runawaymodes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation ...