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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 ...
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 ...
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 ...
The depth of the associated graded ring of ideals with any reduction number
(2002)
Let R be a local Cohen-Macaulay ring, let I be an R-ideal, and let G be the associated graded ring of I. We give an estimate for the depth of G when G is not necessarily Cohen-Macaulay. We assume that I is either equimultiple, ...
A Variant of NTRU with Non-Invertible Polynomials
(2002)
We introduce a generalization of the NTRU cryptosystem and describe its advantages and disadvantages as compared with the original NTRU protocol. This extension helps to avoid the potential problem of finding “enough” ...
Extension of weakly and strongly F-regular rings by flat maps
(2002)
Throughout this paper all rings will be Noetherian of positive characteristic p. Hence
tight closure theory [HH1-4] takes a prominent place (see §2 for tight closure definitions
and terminology). The purpose of this note ...
On the Number of Sparse RSA Exponents
(2002)
An RSA modulus is a product M = pl of two primes p and l. We show that for almost all RSA moduli M, the number of sparse exponents e (which allow for fast RSA encryption) with the property that gcd(e,φ(M)) = 1 (hence RSA ...
The F-signature and strong F-regularity
(2002)
We show that the F-signature of a local ring of characteristic p, defined by Huneke and Leuschke, is positive if and only if the ring is strongly F-regular.
Character Sums over Integers with Restricted g-ary Digits
(2002)
We establish upper bounds for multiplicative character sums and exponential sums over sets of integers that are described by various
properties of their digits in a fixed base g ≥ 2. Our main tools are the Weil and ...
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.