Deformed Harry Dym and Hunter-Zheng Equations

We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same Hamiltonian structures. They are integrable and belong to the same hierarchy corresponding to positive and negative flows. We present the Lax pair description for both the systems and construct the conserved charges of negative order from the Lax operator. For the deformed Harry Dym equation, we construct the non-standard Lax representation for two special classes of values of the deformation parameters. In general, we argue that a non-standard description will involve a pseudo-differential operator of infinite order.Comment: Latex file, 15 page

A Nonliearly Dispersive Fifth Order Integrable Equation and its Hierarchy

In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges. We construct two compatible Hamiltonian structures as well as their Casimir functionals. One of the structures has a single Casimir functional while the other has two. This allows us to extend the flows into negative order and clarifies the meaning of two different hierarchies of positive flows. We study the behavior of these systems under a hodograph transformation and show that they are related to the Kaup-Kupershmidt and the Sawada-Kotera equations under appropriate Miura transformations. We also discuss briefly some properties associated with the generalization of second, third and fourth order Lax operators.Comment: 11 pages, LaTex, version to be published in Journal of Nonlinear Mathematical Physics, has expanded discussio

On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy

Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 44:4756--4767 (2003)], are transformed into previously known integrable systems: one--into a pair of decoupled KdV equations, the other one--into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.Comment: 7 page

On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy

A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.Comment: to appear in Journal of Mathematical Physics, 17 pages, Late

Anterior mitral valve aneurysm is an uncommon complication of aortic valve infective endocarditis. A case report

Objective: Rare disease Background: Mitral valve aneurysms (MVAs) are uncommon conditions frequently associated with aortic valve endocarditis. They may be complicated by perforation and severe mitral regurgitation (MR). Optimal treatment of MVA, and in particular the best timing for surgery, are uncertain. Case Report: A 62-year-old man with a recent history of dental surgery presented to the Emergency Department complaining relapsing fever. A first echocardiogram demonstrated infective endocarditis of the aortic valve. The patient was primarily managed with specific antibiotic therapy. Despite this, a few days later he suffered from splen-ic embolization and an MVA with MR was detected. Surgical replacement of the mitral and aortic valves was therefore performed. Conclusions: MVAs are infrequent but potentially severe complications of AV endocarditis. In the absence of definite treatment indication, the correct time for surgery should depend on concomitant clinical and infective features

Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models

New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics behaviour are presented as an example. The special attention is paid for the singular case $(\gamma=1)$ for which we found new non homogenious solutions expressed in terms of the elementary functions.Comment: 11 pages, 1 figur

Identification of single nucleotide polymorphisms from the transcriptome of an organism with a whole genome duplication

BACKGROUND: The common ancestor of salmonid fishes, including rainbow trout (Oncorhynchus mykiss), experienced a whole genome duplication between 20 and 100 million years ago, and many of the duplicated genes have been retained in the trout genome. This retention complicates efforts to detect allelic variation in salmonid fishes. Specifically, single nucleotide polymorphism (SNP) detection is problematic because nucleotide variation can be found between the duplicate copies (paralogs) of a gene as well as between alleles. RESULTS: We present a method of differentiating between allelic and paralogous (gene copy) sequence variants, allowing identification of SNPs in organisms with multiple copies of a gene or set of genes. The basic strategy is to: 1) identify windows of unique cDNA sequences with homology to each other, 2) compare these unique cDNAs if they are not shared between individuals (i.e. the cDNA is homozygous in one individual and homozygous for another cDNA in the other individual), and 3) give a “SNP score” value between zero and one to each candidate sequence variant based on six criteria. Using this strategy we were able to detect about seven thousand potential SNPs from the transcriptomes of several clonal lines of rainbow trout. When directly compared to a pre-validated set of SNPs in polyploid wheat, we were also able to estimate the false-positive rate of this strategy as 0 to 28% depending on parameters used. CONCLUSIONS: This strategy has an advantage over traditional techniques of SNP identification because another dimension of sequencing information is utilized. This method is especially well suited for identifying SNPs in polyploids, both outbred and inbred, but would tend to be conservative for diploid organisms

Identification of potential leafhoppers vectors of phytoplasmas (16SrIII group) associated with broccoli stunt disease in Brazil.

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