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Ubiquity of simplices in subsets of vector spaces over finite fields
(2007)
We prove that a sufficiently large subset of the $d$-dimensional vector space over a finite field with $q$ elements, $ {\Bbb F}_q^d$, contains a copy of every $k$-simplex. Fourier analytic methods, Kloosterman sums, and ...
Sums and products in finite fields: an integral geometric viewpoint
(2007)
We prove that if $A \subset {\Bbb F}_q$ is such that $$|A|>q^{{1/2}+\frac{1}{2d}},$$ then $${\Bbb F}_q^{*} \subset dA^2=A^2+...+A^2 d \text{times},$$ where $$A^2=\{a \cdot a': a,a' \in A\},$$ and where ${\Bbb F}_q^{*}$ ...
Distances sets that are a shift of the integers and Fourier basis for planar convex sets
(2007)
The aim of this paper is to prove that if a planar set $A$ has a difference set $\Delta(A)$ satisfying $\Delta(A)\subset \Z^++s$ for suitable $s$ than $A$ has at most 3 elements. This result is motivated by the conjecture ...
Some upper bounds on the number of resonances for manifolds with infinite cylindrical ends
(2002)
We prove some sharp upper bounds on the number of resonances associated with the Laplacian, or Laplacian plus potential, on a manifold with infinite cylidrical ends.
An electric charge has no screw sense—a comment on the twistfree formulation of electrodynamics by da Rocha & Rodrigues
(Wiley-Blackwell, 2010)
Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and ...
The resonance counting function for Schrödinger operators with generic potentials
(2005)
We show that the resonance counting function for a Schr¨odinger operator has maximal order of growth for generic sets of real-valued, or
complex-valued, L1-compactly supported potentials.
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 ...
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 ...
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 ...
Sustained resonance: a binary system perturbed by gravitational radiation
(American Institute of Physics, 2000)
The general phenomena associated with sustained resonance are studied in this paper in connection with relativistic binary pulsars. We represent such a system by two point masses in a Keplerian binary system that evolves ...
The generalized Jacobi equation
(American Institute of Physics, 2002)
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into ...
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 ...
Tidal Dynamics of Relativistic Flows Near Black Holes
(arXiv, 2003)
We point out novel consequences of general relativity involving tidal dynamics of ultrarelativistic relative motion. Specifically, we use the generalized Jacobi equation and its extension to study the force-free dynamics ...
A Gravitational Mechanism for the Acceleration of Ultrarelativistic Particles
(arXiv, 2005)
Imagine a swarm of free particles near a point P outside a gravitating mass M and a free reference particle at P that is on a radial escape trajectory away from M. Relative to this reference particle and in a Fermi normal ...
Dynamics of Relativistic Flows
(arXiv, 2004)
Dynamics of relativistic outflows along the rotation axis of a Kerr black hole is investigated using a simple model that takes into account the relativistic tidal force of the central source as well as the Lorentz force ...
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. ...
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 ...
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 ...
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 ...
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 ...