495 research outputs found
The Natural Logarithm on Time Scales
We define an appropriate logarithm function on time scales and present its
main properties. This gives answer to a question posed by M. Bohner in [J.
Difference Equ. Appl. {\bf 11} (2005), no. 15, 1305--1306].Comment: 6 page
Second cohomology groups and finite covers
For D an infinite set, k>1 and W the set of k-sets from D, there is a natural
closed permutation group G_k which is a non-split extension of \mathbb{Z}_2^W
by \Sym(D). We classify the closed subgroups of G_k which project onto
\Sym(D)$. The question arises in model theory as a problem about finite covers,
but here we formulate and solve it in algebraic terms.Comment: Typos corrected; change of title to 'Second cohomology groups and
finite covers of infinite symmetric groups' in published versio
Noether's Theorem on Time Scales
We show that for any variational symmetry of the problem of the calculus of
variations on time scales there exists a conserved quantity along the
respective Euler-Lagrange extremals.Comment: Partially presented at the 6th International ISAAC Congress, August
13 to August 18, 2007, Middle East Technical University, Ankara, Turke
Noether's symmetry theorem for nabla problems of the calculus of variations
We prove a Noether-type symmetry theorem and a DuBois-Reymond necessary
optimality condition for nabla problems of the calculus of variations on time
scales.Comment: Submitted 20/Oct/2009; Revised 27/Jan/2010; Accepted 28/July/2010;
for publication in Applied Mathematics Letter
The Second Euler-Lagrange Equation of Variational Calculus on Time Scales
The fundamental problem of the calculus of variations on time scales concerns
the minimization of a delta-integral over all trajectories satisfying given
boundary conditions. In this paper we prove the second Euler-Lagrange necessary
optimality condition for optimal trajectories of variational problems on time
scales. As an example of application of the main result, we give an alternative
and simpler proof to the Noether theorem on time scales recently obtained in
[J. Math. Anal. Appl. 342 (2008), no. 2, 1220-1226].Comment: This work was partially presented at the Workshop in Control,
Nonsmooth Analysis and Optimization, celebrating Francis Clarke's and Richard
Vinter's 60th birthday, Porto, May 4-8, 2009. Submitted 26-May-2009; Revised
12-Jan-2010; Accepted 29-March-2010 in revised form; for publication in the
European Journal of Contro
The decline and rise of neighbourhoods: the importance of neighbourhood governance
There is a substantial literature on the explanation of neighbourhood change. Most of this literature concentrates on identifying factors and developments behind processes of decline. This paper reviews the literature, focusing on the identification of patterns of neighbourhood change, and argues that the concept of neighbourhood governance is a missing link in attempts to explain these patterns. Including neighbourhood governance in the explanations of neighbourhood change and decline will produce better explanatory models and, finally, a better view about what is actually steering neighbourhood change
Short-range oscillators in power-series picture
A class of short-range potentials on the line is considered as an
asymptotically vanishing phenomenological alternative to the popular confining
polynomials. We propose a method which parallels the analytic Hill-Taylor
description of anharmonic oscillators and represents all our Jost solutions
non-numerically, in terms of certain infinite hypergeometric-like series. In
this way the well known solvable Rosen-Morse and scarf models are generalized.Comment: 23 pages, latex, submitted to J. Phys. A: Math. Ge
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