2,929 research outputs found
Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations
We consider the focusing nonlinear Schr\"odinger equations in dimension and for slightly
supercritical nonlinearities p_c
with and 0<\e\ll 1. We prove the existence and stability in the energy space of a self similar finite time blow up dynamics and provide a qualitative description of the singularity formation near the blow up tim
Characteristics of bound modes in coupled dielectric waveguides containing negative index media
We investigate the characteristics of guided wave modes in planar coupled
waveguides. In particular, we calculate the dispersion relations for TM modes
in which one or both of the guiding layers consists of negative index media
(NIM)-where the permittivity and permeability are both negative. We find that
the Poynting vector within the NIM waveguide axis can change sign and
magnitude, a feature that is reflected in the dispersion curves
An interior point algorithm for minimum sum-of-squares clustering
Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds
National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec
General Conditions for Lepton Flavour Violation at Tree- and 1-Loop Level
In this work, we compile the necessary and sufficient conditions a theory has
to fulfill in order to ensure general lepton flavour conservation, in the
spirit of the Glashow-Weinberg criteria for the absence of flavour-changing
neutral currents. At tree-level, interactions involving electrically neutral
and doubly charged bosons are investigated. We also investigate flavour changes
at 1-loop level. In all cases we find that the essential theoretical
requirements can be reduced to a few basic conditions on the particle content
and the coupling matrices. For 1-loop diagrams, we also investigate how exactly
a GIM-suppression can occur that will strongly reduce the rates of lepton
flavour violating effects even if they are in principle present in a certain
theory. In all chapters, we apply our criteria to several models which can in
general induce lepton flavour violation, e.g. LR-symmetric models or the MSSM.
In the end we give a summarizing table of the obtained results, thereby
demonstrating the applicability of our criteria to a large class of models
beyond the Standard Model.Comment: 31 pages, 2 figure
Why a splitting in the final state cannot explain the GSI-Oscillations
In this paper, I give a pedagogical discussion of the GSI anomaly. Using two
different formulations, namely the intuitive Quantum Field Theory language of
the second quantized picture as well as the language of amplitudes, I clear up
the analogies and differences between the GSI anomaly and other processes (the
Double Slit experiment using photons, scattering, and
charged pion decay). In both formulations, the conclusion is reached that the
decay rate measured at GSI cannot oscillate if only Standard Model physics is
involved and the initial hydrogen-like ion is no coherent superposition of more
than one state (in case there is no new, yet unknown, mechanism at work).
Furthermore, a discussion of the Quantum Beat phenomenon will be given, which
is often assumed to be able to cause the observed oscillations. This is,
however, not possible for a splitting in the final state only.Comment: 10 pages, 3 figures; matches published version (except for some
stylistic ambiguities
Stable self-similar blow-up dynamics for slightly -supercritical generalized KdV equations
In this paper we consider the slightly -supercritical gKdV equations
, with the nonlinearity
and . We will prove the existence and
stability of a blow-up dynamic with self-similar blow-up rate in the energy
space and give a specific description of the formation of the singularity
near the blow-up time.Comment: 38 page
Measurement of Vegetation and Terrain Characteristics On Small Scale Vertical Aerial Photographs
Few events in recent years have stirred public imagination and interest to the degree occasioned by the uses made of aerial photographs in the Cuban affair. The average earth scientist, however, was not taken by surprise since the basic methods, materials and principles involved were not new to him. As a matter of fact, since World War II, aerial photography has become an everyday, virtually indispensable tool to most earth feature and natural resource analysts. In order better to understand the application of aerial photographs to such civil pursuits, it would be well at this point to differentiate the two basic levels of use:
(1). Photogrammetry involves use of highly precise measurements and complicated instrument systems. Among the products of photogrammetry, to list a very few, are highway design, topographic maps, bridge and dam site surveys.
(2). Photo Interpretation involves the extraction of both subjective information and the performance of measurements at a lower level of precision than that essential to the photogrammetrist. Photo interpretation work is usually done by the skilled professional ( e.g., archeologist, forester, geographer, geologist) who utilizes this information to formulate decisions pertinent to his professional activity.
Admittedly, this a gross over-simplification of the distinction between the two levels of activity and precision since there is a certain degree of overlap between the two . As a matter of fact, there are some individuals who are fully qualified to perform both functions. Nevertheless, these basic categories must be recognized in order to indicate to the average subject matter specialist the photo interpretation applications which are available to him directly.
Although the photo interpretation process is basically subjective, both in nature and by definition, a useful degree of quantification is possible. Crude though these measurements and controlled estimates may appear to be to the photogrammetric engineer, they are still suitable and often fully adequate for the purposes of the interpreter. It is doubtful, however, whether these techniques are being put to sufficient use since it is generally estimated that not more than 60% of the useful capabilities of currently-available photo interpretation systems are being realized. It is the purpose of this paper, therefore, to briefly describe some of these measurement techniques, give a few examples in current use and suggest some possibilities for the future
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