4,587 research outputs found
Blow-up of solutions of nonlinear Schr\"odinger equations with oscillating nonlinearities
The finite time blow-up of solutions for 1-D NLS with oscillating
nonlinearities is shown in two domains: (1) the whole real line where the
nonlinear source is acting in the interior of the domain and (2) the right
half-line where the nonlinear source is placed at the boundary point. The
distinctive feature of this work is that the the initial energy is allowed to
be non-negative and the momentum is allowed to be infinite in contrast to the
previous literature on the blow-up of solutions with time dependent
nonlinearities. The common finite momentum assumption is removed by using a
compactly supported or rapidly decaying weight function in virial identities -
an idea borrowed from Ogawa-Tsutsumi (1991). At the end of the paper, a
numerical example satisfying the theory is provided.Comment: 19 page
Finite-parameter feedback control for stabilizing the complex Ginzburg-Landau equation
In this paper, we prove the exponential stabilization of solutions for
complex Ginzburg-Landau equations using finite-parameter feedback control
algorithms, which employ finitely many volume elements, Fourier modes or nodal
observables (controllers). We also propose a feedback control for steering
solutions of the Ginzburg-Landau equation to a desired solution of the
non-controlled system. In this latter problem, the feedback controller also
involves the measurement of the solution to the non-controlled system.Comment: 20 page
Structure of conflict graphs in constraint alignment problems and algorithms
We consider the constrained graph alignment problem which has applications in
biological network analysis. Given two input graphs , a pair of vertex mappings induces an {\it edge conservation} if
the vertex pairs are adjacent in their respective graphs. %In general terms The
goal is to provide a one-to-one mapping between the vertices of the input
graphs in order to maximize edge conservation. However the allowed mappings are
restricted since each vertex from (resp. ) is allowed to be mapped
to at most (resp. ) specified vertices in (resp. ). Most
of results in this paper deal with the case which attracted most
attention in the related literature. We formulate the problem as a maximum
independent set problem in a related {\em conflict graph} and investigate
structural properties of this graph in terms of forbidden subgraphs. We are
interested, in particular, in excluding certain wheals, fans, cliques or claws
(all terms are defined in the paper), which corresponds in excluding certain
cycles, paths, cliques or independent sets in the neighborhood of each vertex.
Then, we investigate algorithmic consequences of some of these properties,
which illustrates the potential of this approach and raises new horizons for
further works. In particular this approach allows us to reinterpret a known
polynomial case in terms of conflict graph and to improve known approximation
and fixed-parameter tractability results through efficiently solving the
maximum independent set problem in conflict graphs. Some of our new
approximation results involve approximation ratios that are function of the
optimal value, in particular its square root; this kind of results cannot be
achieved for maximum independent set in general graphs.Comment: 22 pages, 6 figure
Halide Edip kimdir?
Taha Toros Arşivi, Dosya No: 41-Halide Edip-A. Adnan Adıva
Toprak uyanırsa
Taha Toros Arşivi, Dosya No: 476-Şevket Süreyya Aydemir. Not: Gazetenin "Yeni Yayınlar" köşesinde yayımlanmıştır
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