1,471 research outputs found
Multipeakons and a theorem of Stieltjes
A closed form of the multi-peakon solutions of the Camassa-Holm equation is
found using a theorem of Stieltjes on continued fractions. An explicit formula
is obtained for the scattering shifts.Comment: 6 page
Acoustic Scattering and the Extended Korteweg deVries hierarchy
The acoustic scattering operator on the real line is mapped to a
Schr\"odinger operator under the Liouville transformation. The potentials in
the image are characterized precisely in terms of their scattering data, and
the inverse transformation is obtained as a simple, linear quadrature. An
existence theorem for the associated Harry Dym flows is proved, using the
scattering method. The scattering problem associated with the Camassa-Holm
flows on the real line is solved explicitly for a special case, which is used
to reduce a general class of such problems to scattering problems on finite
intervals.Comment: 18 page
Study of mechanical properties of uranium compounds
Study determines the mechanical properties, including brittleness and ductility of several uranium compounds. These include uranium dioxide, uranium sulfide, and uranium phosphide
Non-Linear Evolution Equations with Non-Analytic Dispersion Relations in 2+1 Dimensions. Bilocal Approach
A method is proposed of obtaining (2+1)-dimensional non- linear equations
with non-analytic dispersion relations. Bilocal formalism is shown to make it
possible to represent these equations in a form close to that for their
counterparts in 1+1 dimensions.Comment: 13 pages, to be published in J. Phys.
Exact quantum query complexity of
In the exact quantum query model a successful algorithm must always output
the correct function value. We investigate the function that is true if exactly
or of the input bits given by an oracle are 1. We find an optimal
algorithm (for some cases), and a nontrivial general lower and upper bound on
the minimum number of queries to the black box.Comment: 19 pages, fixed some typos and constraint
Pyloric Stenosis Leading to Sinus Venous Thrombosis; A Case Report
Pyloric stenosis is typically diagnosed early and repaired after resuscitation and electrolyte correction in a timely manner. Delay in diagnosis or presentation of patient can lead to significant morbidity and even mortality. Here we present a case of pyloric stenosis leading to dehydration severe enough to lead to venous sinus thrombosis. This case highlights the importance of early detection of pyloric stenosis with timely correction of fluid status and electrolytes. Venous sinus thrombosis is a serious complication associated with our patient’s pyloric stenosis that has not yet been reported in literature
On the Caudrey-Beals-Coifman System and the Gauge Group Action
The generalized Zakharov-Shabat systems with complex-valued Cartan elements
and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their
gauge equivalent are studies. This includes: the properties of fundamental
analytical solutions (FAS) for the gauge-equivalent to CBC systems and the
minimal set of scattering data; the description of the class of nonlinear
evolutionary equations solvable by the inverse scattering method and the
recursion operator, related to such systems; the hierarchies of Hamiltonian
structures.Comment: 12 pages, no figures, contribution to the NEEDS 2007 proceedings
(Submitted to J. Nonlin. Math. Phys.
Secondary Scoliosis from a Retroperitoneal Ganglioneuroma in a 9-year-old Female: Case Report
Ganglioneuromas are rare benign tumors that tend to be asymptomatic until large enough to compress adjacent structures. These tumors are often found during childhood during evaluations for other pathologies. Retroperitoneal ganglioneuromas may be a secondary cause of scoliosis. Here, we present a case of a child who was found to have a retroperitoneal ganglioneuroma during an evaluation for scoliosis.
The Cauchy two-matrix model
We introduce a new class of two(multi)-matrix models of positive Hermitean
matrices coupled in a chain; the coupling is related to the Cauchy kernel and
differs from the exponential coupling more commonly used in similar models. The
correlation functions are expressed entirely in terms of certain biorthogonal
polynomials and solutions of appropriate Riemann-Hilbert problems, thus paving
the way to a steepest descent analysis and universality results. The
interpretation of the formal expansion of the partition function in terms of
multicolored ribbon-graphs is provided and a connection to the O(1) model. A
steepest descent analysis of the partition function reveals that the model is
related to a trigonal curve (three-sheeted covering of the plane) much in the
same way as the Hermitean matrix model is related to a hyperelliptic curve.Comment: 34 pages, 2 figures. V2: changes only to metadat
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