3,523 research outputs found
Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy
It is well-known that the finite-gap solutions of the KdV equation can be
generated by its recursion operator.We generalize the result to a special form
of Lax pair, from which a method to constrain the integrable system to a
lower-dimensional or fewer variable integrable system is proposed. A direct
result is that the -soliton solutions of the KdV hierarchy can be completely
depicted by a series of ordinary differential equations (ODEs), which may be
gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is
constrained to a series of univariate integrable hierarchies. The key is a
special form of Lax pair for the AKNS hierarchy. It is proved that under the
constraints all equations of the AKNS hierarchy are linearizable.Comment: 12 pages, 0 figur
Some Applications of the Extended Bendixson-Dulac Theorem
During the last years the authors have studied the number of limit cycles of
several families of planar vector fields. The common tool has been the use of
an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this
work is to present an unified approach of some of these results, together with
their corresponding proofs. We also provide several applications.Comment: 19 pages, 3 figure
Spectral analysis and a closest tree method for genetic sequences
We describe a new method for estimating the evolutionary tree linking a collection of species from their aligned four-state genetic sequences. This method, which can be adapted to provide a branch-and-bound algorithm, is statistically consistent provided the sequences have evolved according to a standard stochastic model of nucleotide mutation. Our approach exploits a recent group-theoretic description of this model
Apolipoprotein AIV gene variant S347 is associated with increased risk of coronary heart disease and lower plasma apolipoprotein AIV levels
The impact of common variants in the apolipoprotein gene cluster (APOC3-A4-A5) on prospective coronary heart disease (CHD) risk was examined in healthy UK men. Of the 2808 men followed over 9 years, 187 had a clinically defined CHD event. Examination of 9 single nucleotide polymorphisms (SNPs) in this group revealed that homozygotes for APOA4 S347 had significantly increased risk of CHD [hazard ratio (HR) of 2.07 (95%CI 1.04 to 4.12)], whereas men homozygous for APOC3 1100T were protected [HR 0.28 (95%CI 0.09 to 0.87)]. In stepwise multiple regression analysis, after entering all the variants and adjusting for established risk factors APOA4 T347S alone remained in the model. Using all nine SNPs, the highest risk-estimate haplotypes carried APOA4 S347 and rare alleles of the two flanking intergenic markers. The protective effect of APOC3 1100T could be explained by negative linkage disequilibrium with these alleles. To determine the association of APOA4 T347S with apoAIV levels, the relationship was examined in 1600 healthy young European men and women. S347 homozygotes had significantly lower apoAIV plasma levels (13.64±0.59 mg/dL) compared with carriers of the T347 allele (14.90±0.12 mg/dL) (P=0.035). These results demonstrate that genetic variation in and around APOA4, independent of the effects of triglyceride, is associated with risk of CHD and apoAIV levels, supporting an antiatherogenic role for apoAIV
Spectral Statistics in the Quantized Cardioid Billiard
The spectral statistics in the strongly chaotic cardioid billiard are
studied. The analysis is based on the first 11000 quantal energy levels for odd
and even symmetry respectively. It is found that the level-spacing distribution
is in good agreement with the GOE distribution of random-matrix theory. In case
of the number variance and rigidity we observe agreement with the random-matrix
model for short-range correlations only, whereas for long-range correlations
both statistics saturate in agreement with semiclassical expectations.
Furthermore the conjecture that for classically chaotic systems the normalized
mode fluctuations have a universal Gaussian distribution with unit variance is
tested and found to be in very good agreement for both symmetry classes. By
means of the Gutzwiller trace formula the trace of the cosine-modulated heat
kernel is studied. Since the billiard boundary is focusing there are conjugate
points giving rise to zeros at the locations of the periodic orbits instead of
exclusively Gaussian peaks.Comment: 20 pages, uu-encoded ps.Z-fil
Casimir force on a piston
We consider a massless scalar field obeying Dirichlet boundary conditions on
the walls of a two-dimensional L x b rectangular box, divided by a movable
partition (piston) into two compartments of dimensions a x b and (L-a) x b. We
compute the Casimir force on the piston in the limit L -> infinity. Regardless
of the value of a/b, the piston is attracted to the nearest end of the box.
Asymptotic expressions for the Casimir force on the piston are derived for a <<
b and a >> b.Comment: 10 pages, 1 figure. Final version, accepted for publication in Phys.
Rev.
Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric t-J Model
We construct the Drinfeld twists (factorizing -matrices) for the
supersymmetric t-J model. Working in the basis provided by the -matrix (i.e.
the so-called -basis), we obtain completely symmetric representations of the
monodromy matrix and the pseudo-particle creation operators of the model. These
enable us to resolve the hierarchy of the nested Bethe vectors for the
invariant t-J model.Comment: 23 pages, no figure, Latex file, minor misprints are correcte
Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two
We consider the billiard dynamics in a non-compact set of R^d that is
constructed as a bi-infinite chain of translated copies of the same
d-dimensional polytope. A random configuration of semi-dispersing scatterers is
placed in each copy. The ensemble of dynamical systems thus defined, one for
each global realization of the scatterers, is called `quenched random Lorentz
tube'. Under some fairly general conditions, we prove that every system in the
ensemble is hyperbolic and almost every system is recurrent, ergodic, and
enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure
Quantum criticality, particle-hole symmetry, and duality of the plateau-insulator transition in the quantum Hall regime
We report new experimental data on the plateau-insulator transition in the
quantum Hall regime, taken from a low mobility InGaAs/InP heterostructure. By
employing the fundamental symmetries of the quantum transport problem we are
able to disentangle the universal quantum critical aspects of the
magnetoresistance data (critical indices and scaling functions) and the sample
dependent aspects due to macroscopic inhomogeneities. Our new results and
methodology indicate that the previously established experimental value for the
critical index (kappa = 0.42) resulted from an admixture of both universal and
sample dependent behavior. A novel, non-Fermi liquid value is found (kappa =
0.57) along with the leading corrections to scaling. The statement of
self-duality under the Chern Simons flux attachment transformation is verified.Comment: 4 pages, 2 figure
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