207 research outputs found
One-line γ ray spectroscopic investigation of the 180Hg(T 1/2 = 3 s) decay chain
With the rebuilt ISOLDE 2 facility we have investigated on-line the 18080Hg decay products. The decay half-lives, the energies and intensities of the main γ lines of both 180Hg(T 1/2 = 3.0 ± 0.3 s) and 18079Au(T1/2 = 8.1 ± 0.3 s) , and a tentative decay scheme of 18078Pt are given
Selmer Groups in Twist Families of Elliptic Curves
The aim of this article is to give some numerical data related to the order
of the Selmer groups in twist families of elliptic curves. To do this we assume
the Birch and Swinnerton-Dyer conjecture is true and we use a celebrated
theorem of Waldspurger to get a fast algorithm to compute . Having
an extensive amount of data we compare the distribution of the order of the
Selmer groups by functions of type with small. We discuss how the
"best choice" of is depending on the conductor of the chosen elliptic
curves and the congruence classes of twist factors.Comment: to appear in Quaestiones Mathematicae. 16 page
L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields
The goal of this paper is to explain how a simple but apparently new fact of
linear algebra together with the cohomological interpretation of L-functions
allows one to produce many examples of L-functions over function fields
vanishing to high order at the center point of their functional equation. The
main application is that for every prime p and every integer g>0 there are
absolutely simple abelian varieties of dimension g over Fp(t) for which the BSD
conjecture holds and which have arbitrarily large rank.Comment: To appear in Inventiones Mathematica
Integral closure of rings of integer-valued polynomials on algebras
Let be an integrally closed domain with quotient field . Let be a
torsion-free -algebra that is finitely generated as a -module. For every
in we consider its minimal polynomial , i.e. the
monic polynomial of least degree such that . The ring consists of polynomials in that send elements of back to
under evaluation. If has finite residue rings, we show that the
integral closure of is the ring of polynomials in which
map the roots in an algebraic closure of of all the , ,
into elements that are integral over . The result is obtained by identifying
with a -subalgebra of the matrix algebra for some and then
considering polynomials which map a matrix to a matrix integral over . We
also obtain information about polynomially dense subsets of these rings of
polynomials.Comment: Keywords: Integer-valued polynomial, matrix, triangular matrix,
integral closure, pullback, polynomially dense set. accepted for publication
in the volume "Commutative rings, integer-valued polynomials and polynomial
functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 201
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
Schur duality decomposes many copies of a quantum state into subspaces
labeled by partitions, a decomposition with applications throughout quantum
information theory. Here we consider applying Schur duality to the problem of
distinguishing coset states in the standard approach to the hidden subgroup
problem. We observe that simply measuring the partition (a procedure we call
weak Schur sampling) provides very little information about the hidden
subgroup. Furthermore, we show that under quite general assumptions, even a
combination of weak Fourier sampling and weak Schur sampling fails to identify
the hidden subgroup. We also prove tight bounds on how many coset states are
required to solve the hidden subgroup problem by weak Schur sampling, and we
relate this question to a quantum version of the collision problem.Comment: 21 page
Eta invariants for flat manifolds
Using H. Donnelly result from the article "Eta Invariants for G-Spaces" we
calculate the eta invariants of the signature operator for almost all
7-dimensional flat manifolds with cyclic holonomy group. In all cases this eta
invariants are an integer numbers. The article was motivated by D. D. Long and
A. Reid article "On the geometric boundaries of hyperbolic 4-manifolds, Geom.
Topology 4, 2000, 171-178Comment: 18 pages, a new version with referees comment
Generating uniform random vectors in \QTR{bf}{Z}_{p}^{k}: the general case
This paper is about the rate of convergence of the Markov chain
(mod ), where is an integer matrix with nonzero
eigenvalues and is a sequence of independent and identically
distributed integer vectors, with support not parallel to a proper subspace of
invariant under . If for all eigenvalues
of , then steps are sufficient and
steps are necessary to have sampling from a nearly uniform
distribution. Conversely, if has the eigenvalues that are
roots of positive integer numbers, and for
all , then steps are necessary and sufficient.Comment: The published version is to appear in the Journal of Theoretical
Probabilit
On Proper Polynomial Maps of
Two proper polynomial maps are said to be \emph{equivalent} if there exist such that .
We investigate proper polynomial maps of arbitrary topological degree up to equivalence. Under the further assumption that the maps are Galois
coverings we also provide the complete description of equivalence classes. This
widely extends previous results obtained by Lamy in the case .Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi
Supersymmetric Heterotic Action out of M5 Brane
Generalizing the work by Cherkis and Schwarz [1], we carry out the double
dimensional reduction of supersymmetric M5 brane on K3 to obtain the
supersymmetric action of heterotic string in 7-dimensional flat space-time.
Motivated by this result, we propose the supersymmetric heterotic action in
10-dimensional flat space-time where the current algebra is realized in a novel
way. We explicitly verify the kappa-symmetry of the proposed action.Comment: 27 page
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