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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 ...
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 ...
Character varieties and harmonic maps to R-trees
(1998)
We show that the Korevaar-Schoen limit of the sequence of equivariant harmonic maps corresponding to a sequence of irreducible $SL_2({\mathbb C})$ representations of the fundamental group of a compact Riemannian manifold ...
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 ${\Bbb F}_q^{*}$ ...
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.
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 ...
On the Morgan-Shalen compactification of the SL(2,C) character varieties of surface groups
(1998)
A gauge theoretic description of the Morgan-Shalen compactification of the SL(2, C)
character variety of the fundamental group of a hyperbolic surface is given in terms of a natural compactification of the moduli space ...
How often is a permutation an n'th power?
(1997)
We give a short argument that for any fixed n, the probability that a permutation on m letters is an n'th power is asymptotically C m^{phi(n)/n - 1}.
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.
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 ...
Addendum: On the ionization of a Keplerian binary system by periodic gravitational radiation [J. Math. Phys. 37, 3997-4016 (1996)]
(American Institute of Physics, 1996)
Addendum: On the ionization of a Keplerian binary system by periodic gravitational radiation [J. Math. Phys. 37, 3997-4016 (1996)]
On the norm of an idempotent Schur multiplier on the Schatten class
(American Mathematical Society, 2004)
We show that if the norm of an idempotent Schur multiplier on the Schatten class Sp lies sufficiently close to 1, then it is necessarily equal to 1. We also give a simple characterization of those idempotent Schur multipliers ...
Coincidences in the values of the Euler and Carmichael functions
(Polish Academy of Sciences, Institute of Mathematics, 2006)
The Euler function has long been regarded as one of the most basic of the arithmetic functions. More recently, partly driven by the rise in importance of computational number theory, the Carmichael function has drawn an ...
On integers with a special divisibility property
(Masarykova Universita, 2006)
In this note, we study those positive integers n which are divisible by the Carmichael function.
Test ideals and flat base change problems in tight closure theory
(2002)
Test ideals are an important concept in tight closure theory and their behavior via flat base change can be very difficult to understand. Our paper presents results regarding this behavior under flat maps with reasonably ...
Average Normalisations of Elliptic Curves
(Australian Mathematical Society, 2002)
Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field Fp is isomorphic to a curve y2 = x3 +ax+b
with a and b of size O(p3/4). In this paper, we show that almost all elliptic curves ...
Towards Faster Cryptosystems, II
(American Mathematical Society, 2005)
We discuss three cryptosystems, NTRU, SPIFI , and ENROOT, that are based on the use of polynomials with restricted coefficients.
Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n
(European Mathematical Society, 2006)
For a positive integer n, we let φ(n) and λ(n) denote the Euler function and the Carmichael function, respectively. We define ξ(n) as the ratio φ(n)/λ(n) and study various arithmetic properties of ξ(n).
Distributional Properties of the Largest Prime Factor
(University of Michigan, 2005)
Let P(n) denote the largest prime factor of an integer n ≥ 2, and put P(1) = 1. In this paper, we study the distribution of the sequence {P(n) : n ≥ 1} over the set of congruence classes modulo an integer q ≥ 2, and we ...