BiHamiltonian Formulations of the Bateman Equation

We discuss a class of evolution equations equivalent to the simplest Universal Field Equation, the so--called Bateman equation, and show that all of them possess (at least) biHamiltonian structure. The first few conserved charges are calculated.Comment: 10 pages, LaTeX article, to appear in Phys. Lett.

Nonlocal symmetries of integrable two-field divergent evolutionary systems

Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each evolutionary system. Zero curvature representations for some new nonevolution systems are presented

Properties of the Scalar Universal Equations

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The Euler hierarchy itself is given a new interpretation in terms of the formal complex of variational calculus, and is shown to be related to the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl

Neuronal Activity in the Subthalamic Cerebrovasodilator Area under Partial-Gravity Conditions in Rats

The reduced-gravity environment in space is known to cause an upward shift in body fluids and thus require cardiovascular adaptations in astronauts. In this study, we recorded in rats the neuronal activity in the subthalamic cerebrovasodilator area (SVA), a key area that controls cerebral blood flow (CBF), in response to partial gravity. -Partial gravity{norm of matrix} is the term that defines the reduced-gravity levels between 1 g (the unit gravity acceleration on Earth) and 0 g (complete weightlessness in space). Neuronal activity was recorded telemetrically through chronically implanted microelectrodes in freely moving rats. Graded levels of partial gravity from 0.4 g to 0.01 g were generated by customized parabolic-flight maneuvers. Electrophysiological signals in each partial-gravity phase were compared to those of the preceding 1 g level-flight. As a result, SVA neuronal activity was significantly inhibited by the partial-gravity levels of 0.15 g and lower, but not by 0.2 g and higher. Gravity levels between 0.2-0.15 g could represent a critical threshold for the inhibition of neurons in the rat SVA. The lunar gravity (0.16 g) might thus trigger neurogenic mechanisms of CBF control. This is the first study to examine brain electrophysiology with partial gravity as an experimental parameter

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

A Young Adult Patient with Nonalcoholic Steatohepatitis Developed Severe Gastroesophageal Varices Associated with Severe Obesity and Diabetes Mellitus

Obesity is a major contributor to insulin resistance and nonalcoholic fatty liver disease, which is the most common cause of chronic liver diseases. Nonalcoholic steatohepatitis (NASH) can progress to liver cirrhosis and end-stage liver diseases. Some cases already show severe liver fibrosis at the time of diagnosis. We present the case of a 44-year-old male with overt obesity who was admitted with hematemesis due to the rupture of gastric varices. We diagnosed him with NASH with severe liver fibrosis. This case shows that we should be concerned about the progression of liver fibrosis due to NASH associated with severe obesity even in young patients