Higher order supersymmetries and fermionic conservation laws of the supersymmetric extension of the KdV equation

By the introduction of nonlocal basonic and fermionic variables we construct a recursion symmetry of the super KdV equation, leading to a hierarchy of bosonic symmetries and one of fermionic symmetries. The hierarchies of bosonic and fermionic conservation laws arise in a natural way in the construction

The harmonic map and Killing fields for self-dual SU(3) Yang-Mills equations

Using symbolic computations, the unique metric in the space of fields, required to describe self-dual SU(3) Yang-Mills equations by a harmonic map, is determined. Moreover the complete Lie algebra of Killing fields for this metric is established

A geometric study of the dispersionless Boussinesq type equation

We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney-Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in . The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators that send conservation laws and symmetries to each other but are neither Hamiltonian, nor symplectic. These operators give rise to a noncommutative infinite-dimensional algebra of recursion operators

The Lie algebra of infinitesimal symmetries of nonlinear diffusion equations

By using developed software for solving overdetermined systems of partial differential equations, the authors establish the complete Lie algebra of infinitesimal symmetries of nonlinear diffusion equations

On the integrability conditions for some structures related to evolution differential equations

Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.htm), we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp., symplectic).Comment: 5 pages, AMS-LaTeX. v2: minor correction

On integrability of the Camassa-Holm equation and its invariants. A geometrical approach

Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local and nonlocal).Comment: 24 page

Mechanisms of Volatile Anesthetic-Induced Myocardial Protection

Volatile anesthetics protect myocardium against reversible and irreversible ischemic injury. Experimental evidence from several in vitro and in vivo animal models demonstrates that volatile agents enhance the recovery of stunned myocardium and reduce the size of myocardial infarction after brief or prolonged coronary artery occlusion and reperfusion, respectively. This protective effect persists after the anesthetic has been discontinued, a phenomenon known as anesthetic-induced preconditioning (APC). Recent clinical data also demonstrates evidence of APC in patients during cardiac surgery. Thus, administration of volatile anesthetics may represent a novel therapeutic approach that reduces morbidity and mortality associated with perioperative myocardial ischemia and infarction. The mechanisms responsible for APC appear to be similar to those implicated in ischemic preconditioning, but nonetheless have subtle differences. Accumulating evidence indicates that APC is characterized by complex signal transduction pathways that may include adenosine receptors, G proteins, protein kinase C, reactive oxygen species, and sarcolemmal or mitochondrial KATP channels. Opioid analgesics may further enhance APC as well. This article will review recent advances in the understanding of mechanisms responsible for volatile anesthetic-induced myocardial protection

Microfocal X-Ray Computed Tomography Post-Processing Operations for Optimizing Reconstruction Volumes of Stented Arteries During 3D Computational Fluid Dynamics Modeling

Restenosis caused by neointimal hyperplasia (NH) remains an important clinical problem after stent implantation. Restenosis varies with stent geometry, and idealized computational fluid dynamics (CFD) models have indicated that geometric properties of the implanted stent may differentially influence NH. However, 3D studies capturing the in vivo flow domain within stented vessels have not been conducted at a resolution sufficient to detect subtle alterations in vascular geometry caused by the stent and the subsequent temporal development of NH. We present the details and limitations of a series of post-processing operations used in conjunction with microfocal X-ray CT imaging and reconstruction to generate geometrically accurate flow domains within the localized region of a stent several weeks after implantation. Microfocal X-ray CT reconstruction volumes were subjected to an automated program to perform arterial thresholding, spatial orientation, and surface smoothing of stented and unstented rabbit iliac arteries several weeks after antegrade implantation. A transfer function was obtained for the current post-processing methodology containing reconstructed 16 mm stents implanted into rabbit iliac arteries for up to 21 days after implantation and resolved at circumferential and axial resolutions of 32 and 50 μm, respectively. The results indicate that the techniques presented are sufficient to resolve distributions of WSS with 80% accuracy in segments containing 16 surface perturbations over a 16 mm stented region. These methods will be used to test the hypothesis that reductions in normalized wall shear stress (WSS) and increases in the spatial disparity of WSS immediately after stent implantation may spatially correlate with the temporal development of NH within the stented region

Furfural to Cyclopentanone – a Search for Putative Oligomeric By-products

We report here on the reductive rearrangement of biomass-derived furfural to cyclopentanone, a promising non-fossil feedstock for fuels and chemicals. An underreported aspect of this reaction is the inevitable formation of heavy byproducts. To mitigate its formation, process condition such as, solvent, catalyst, temperature, acidity, and feed concentration were varied to unravel the chemistry and improve the reaction performance. Water medium was confirmed to play a crucial role, as organic solvents were unable to deliver cyclopentanone or heavy by products. Copper-based catalyst showed the highest selectivity for ring-rearrangement, reaching 50 mol % under the conditions investigated. The main factor influencing the yields of cyclopentanone (CPO), and promote oligomer formation, are the feed concentration and the pH, as high feed concentrations and high acidity facilitate the self-polymerization of furfuryl alcohol (FALC). This was confirmed by dedicated experiments using FALC and the hydroxypentenone intermediate as feed. The concentration challenge could be mitigated by slowly dosing the feed, which increased the desired product yields by 4–12 mol %. Nevertheless, most oligomers appeared to fall in the range of common liquid fuels and could be converted to diesel by hydrodeoxygenation.</p