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Turing-type instabilities in a mathematical model of notch and retinoic acid pathways
(2006)
In this paper we employ Turing Theory to study the effects of Notch and Retinoic Acid (RA) pathways on neuronal differentiation. A mathematical model consisting of two reaction-diffusion subsystems is presented such that ...
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 ...
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 ...
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 ...
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 ...
Explicit Fermi coordinates and tidal dynamics in de Sitter and Gödel spacetimes
(American Physical Society, 2006)
Fermi coordinates are directly constructed in de Sitter and Gödel spacetimes and the corresponding exact coordinate transformations are given explicitly. The quasi-inertial Fermi coordinates are then employed to discuss ...
Gravitational induction
(Institute of Physics, 2008)
We study the linear post-Newtonian approximation to general relativity known as gravitoelectromagnetism (GEM); in particular, we examine the similarities and differences between GEM and electrodynamics. Notwithstanding ...
Extension theorems in vector spaces over finite fields
(University of Missouri--Columbia, 2008)
We study the L[superscript p] - L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. ...
Tidal dynamics in Kerr spacetime
(Institute of Physics, 2006)
The motion of free nearby test particles relative to a stable equatorial circular
geodesic orbit about a Kerr source is investigated. It is shown that the nonlinear
generalized Jacobi equation can be transformed in this ...
Seiberg-Witten invariants on 3-manifolds with an orientation reversing involution
(University of Missouri--Columbia, 2009)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This work is devoted to the study of Seiberg-Witten theory for three dimensional manifolds in the presence of involutions. G. Tian and S.Wang explored ...
Acceleration-induced nonlocality: uniqueness of the kernel
(arXiv, 2002)
We consider the problem of uniqueness of the kernel in the nonlocal theory of accelerated observers. In a recent work, we showed that the convolution kernel is ruled out as it can lead to divergences for nonuniform accelerated ...
Significance of c /sqrt2 in relativistic physics
(American Institute of Physics, 2004)
In the description of relative motion in accelerated systems and gravitational fields, inertial and tidal accelerations must be taken into account, respectively. These involve a critical speed that in the first approximation ...
Ultrarelativistic motion: inertial and tidal effects in Fermi coordinates
(Institute of Physics, 2004)
Fermi coordinates are the natural generalization of inertial Cartesian
coordinates to accelerated systems and gravitational fields. We study themotion
of ultrarelativistic particles and light rays in Fermi coordinates ...
Acceleration-induced nonlocality: kinetic memory versus dynamic memory
(arXiv, 2001)
The characteristics of the memory of accelerated motion in Minkowski spacetime are discussed within the framework of the nonlocal theory of accelerated observers. Two types of memory are distinguished: kinetic and dynamic. ...
Tidal acceleration of ultrarelativistic particles
(EDP Sciences, 2005)
We investigate the motion of free relativistic particles relative to the ambient medium around a gravitationally
collapsed system. If the relative speed exceeds a critical value given by c/√2, the gravitational tidal ...
Existence and construction of real-valued equiangular tight frames
(University of Missouri--Columbia, 2009)
This paper presents results on real-valued equiangular tight frames (ETFs) and related topics. Some geometric theorems are developed, and aspects of frame theory are used to gain insight into ETFs. We develop a projection ...
Approximate isometries and distortion energy functionals
(University of Missouri--Columbia, 2009)
A fundamental problem in Riemannian Geometry and related areas is to determine whether two diffeomorphic compact Riemannian manifolds (M, [subscript g][subscript M]) and (N, [subscript g][subscript N]) are isometric; that ...
Asymptotic unconditionality in Banach spaces
(University of Missouri--Columbia, 2009)
We show that a separable real Banach space embeds almost isometrically in a space [Upsilon] with a shrinking 1-unconditional basis if and only if lim [subscript n] [subscript arrow] [subscript infinity] [norms] [chi] [group ...