15,413 research outputs found
Evolution strategies in optimization problems
Evolution strategies are inspired in biology and form part of a larger research field known as evolutionary algorithms. Those strategies perform a random search in the space of admissible functions, aiming to optimize some given objective function. We show that simple evolution strategies are a useful tool in optimal control, permitting one to obtain, in an efficient way, good approximations to the solutions of some recent and challenging optimal control problems.CEOCFCTFEDER/POCI 201
The nuclear contacts and short range correlations in nuclei
Atomic nuclei are complex strongly interacting systems and their exact
theoretical description is a long-standing challenge. An approximate
description of nuclei can be achieved by separating its short and long range
structure. This separation of scales stands at the heart of the nuclear shell
model and effective field theories that describe the long-range structure of
the nucleus using a mean- field approximation. We present here an effective
description of the complementary short-range structure using contact terms and
stylized two-body asymptotic wave functions. The possibility to extract the
nuclear contacts from experimental data is presented. Regions in the two-body
momentum distribution dominated by high-momentum, close-proximity, nucleon
pairs are identified and compared to experimental data. The amount of
short-range correlated (SRC) nucleon pairs is determined and compared to
measurements. Non-combinatorial isospin symmetry for SRC pairs is identified.
The obtained one-body momentum distributions indicate dominance of SRC pairs
above the nuclear Fermi-momentum.Comment: Accepted for publication in Physics Letters. 6 pages, 2 figure
On F-Algebroids and Dubrovin's Duality
In this note we introduce the concept of F-algebroid, and give its elementary
properties and some examples. We provide a description of the almost duality
for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of
two anchor maps of a unique cotangent F-algebroid.Comment: 13 pages; v2 has small changes, it has improved exposition. Revised
version to appear in: "Archivum Mathematicum
Evolution Strategies in Optimization Problems
Evolution Strategies are inspired in biology and part of a larger research
field known as Evolutionary Algorithms. Those strategies perform a random
search in the space of admissible functions, aiming to optimize some given
objective function. We show that simple evolution strategies are a useful tool
in optimal control, permitting to obtain, in an efficient way, good
approximations to the solutions of some recent and challenging optimal control
problems.Comment: Partially presented at the 5th Junior European Meeting on "Control
and Information Technology" (JEM'06), Sept 20-22, 2006, Tallinn, Estonia. To
appear in "Proceedings of the Estonian Academy of Sciences -- Physics
Mathematics
A symmetric quantum calculus
We introduce the -symmetric difference derivative and the
-symmetric N\"orlund sum. The associated symmetric quantum
calculus is developed, which can be seen as a generalization of the forward and
backward -calculus.Comment: Submitted 26/Sept/2011; accepted in revised form 28/Dec/2011; to
Proceedings of International Conference on Differential & Difference
Equations and Applications, in honour of Professor Ravi P. Agarwal, to be
published by Springer in the series Proceedings in Mathematics (PROM
Fractional Newton-Raphson Method Accelerated with Aitken's Method
The Newton-Raphson (N-R) method is characterized by the fact that generating
a divergent sequence can lead to the creation of a fractal, on the other hand
the order of the fractional derivatives seems to be closely related to the
fractal dimension, based on the above, a method was developed that makes use of
the N-R method and the fractional derivative of Riemann-Liouville (R-L) that
has been named as the Fractional Newton-Raphson (F N-R) method.
In the following work we present a way to obtain the convergence of the F N-R
method, which seems to be at least linearly convergent for the case where the
order of the derivative is different from one, a simplified way to
construct the fractional derivative and fractional integral operators of R-L is
presented, an introduction to the Aitken's method is made and it is explained
why it has the capacity to accelerate the convergence of iterative methods to
finally present the results that were obtained when implementing the Aitken's
method in F N-R method.Comment: Newton-Raphson Method, Fractional Calculus, Fractional Derivative of
Riemann-Liouville, Method of Aitken. arXiv admin note: substantial text
overlap with arXiv:1710.0763
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