283,081 research outputs found
Coherence Optimization and Best Complex Antipodal Spherical Codes
Vector sets with optimal coherence according to the Welch bound cannot exist
for all pairs of dimension and cardinality. If such an optimal vector set
exists, it is an equiangular tight frame and represents the solution to a
Grassmannian line packing problem. Best Complex Antipodal Spherical Codes
(BCASCs) are the best vector sets with respect to the coherence. By extending
methods used to find best spherical codes in the real-valued Euclidean space,
the proposed approach aims to find BCASCs, and thereby, a complex-valued vector
set with minimal coherence. There are many applications demanding vector sets
with low coherence. Examples are not limited to several techniques in wireless
communication or to the field of compressed sensing. Within this contribution,
existing analytical and numerical approaches for coherence optimization of
complex-valued vector spaces are summarized and compared to the proposed
approach. The numerically obtained coherence values improve previously reported
results. The drawback of increased computational effort is addressed and a
faster approximation is proposed which may be an alternative for time critical
cases
Generic absoluteness and boolean names for elements of a Polish space
It is common knowledge in the set theory community that there exists a
duality relating the commutative -algebras with the family of -names
for complex numbers in a boolean valued model for set theory . Several
aspects of this correlation have been considered in works of the late 's
and early 's, for example by Takeuti, and by Jech. Generalizing Jech's
results, we extend this duality so as to be able to describe the family of
boolean names for elements of any given Polish space (such as the complex
numbers) in a boolean valued model for set theory as a space
consisting of functions whose domain is the Stone space of , and
whose range is contained in modulo a meager set. We also outline how this
duality can be combined with generic absoluteness results in order to analyze,
by means of forcing arguments, the theory of .Comment: 27 page
A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems
In this article we propose a descent method for equality and inequality
constrained multiobjective optimization problems (MOPs) which generalizes the
steepest descent method for unconstrained MOPs by Fliege and Svaiter to
constrained problems by using two active set strategies. Under some regularity
assumptions on the problem, we show that accumulation points of our descent
method satisfy a necessary condition for local Pareto optimality. Finally, we
show the typical behavior of our method in a numerical example
Polynomial overrings of
We show that every polynomial overring of the ring of
polynomials which are integer-valued over may be considered as the
ring of polynomials which are integer-valued over some subset of
, the profinite completion of with respect to the
fundamental system of neighbourhoods of consisting of all non-zero ideals
of Comment: Final version, J. Commut. Algebra 8 (2016), no. 1, 1-28. Keywords:
Integer-valued polynomial, Pr\"ufer domain, Overring, Irredundant
representatio
Computing the number of certain Galois representations mod
Using the link between mod Galois representations of \qu and mod
modular forms established by Serre's Conjecture, we compute, for every prime
, a lower bound for the number of isomorphism classes of continuous
Galois representation of \qu on a two--dimensional vector space over \fbar
which are irreducible, odd, and unramified outside .Comment: 28 pages, 3 table
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