Invertible point transformations,Painlevé test,and the second Painlevé transcendent

The techniques of invertible point transformations and the Painlevé analysis can be used to construct integrable ordinary differential equations. We compare both techniques for the second Painlevé transcendent.     

An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

Lie-symmetry vector fields for linear and nonlinear wave equations

We derive the Lie symmetry vector fields for the linear wave equation u=0 and nonlinear wave equation u=u ³. The conformal vector fields for the underlying metric tensor fieldg are also given. We construct the conservation laws and derive similarity solutions. Furthermore, we perform a Painlevé test for the nonlinear wave equation and discuss whether Lie-Bäcklund vector fields exist.     

Animal models for treatment of unresectable liver tumours: a histopathologic and ultra-structural study of cellular toxic changes after electrochemical treatment in rat and dog liver

INTRODUCTION: Electrochemical treatment (EChT) has been taken under serious consideration as being one of several techniques for local treatment of malignancies. The advantage of EChT is the minimal invasive approach and the absence of serious side effects. Macroscopic, histopathological and ultra-structural findings in liver following a four-electrode configuration (dog) and a two-electrode EChT design (dog and rat) were studied. MATERIALS AND METHODS: 30 female Sprague-Dawley rats and four female beagle dogs were studied with EChT using Platinum:Iridium electrodes and the delivered dose was 5, 10 or 90 C (As). After EChT, the animals were euthanized. RESULTS: The distribution of the lesions was predictable, irrespective of dose and electrode configuration. Destruction volumes were found to fit into a logarithmic curve (dose-response). Histopathological examination confirmed a spherical (rat) and cylindrical/ellipsoidal (dog) lesion. The type of necrosis differed due to electrode polarity. Ultra-structural analysis showed distinct features of cell damage depending on the distance from the electrode. Histopathological and ultra-structural examination demonstrated that the liver tissue close to the border of the lesion displayed a normal morphology. CONCLUSIONS: The in vivo dose-planning model is reliable, even in species with larger tissue mass such as dogs. A multi-electrode EChT-design could obtain predictable lesions. The cellular toxicity following EChT is clearly identified and varies with the distance from the electrode and polarity. The distinct border between the lesion and normal tissue suggests that EChT in a clinical setting for the treatment of liver tumours can give a reliable destruction margin.     

On Planar Toeplitz Graphs

We describe several classes of finite, planar Toeplitz graphs and present results on their chromatic number. We then turn to counting maximal independent sets in these graphs and determine recurrence equations and generating functions for some special cases.     

First integrals and reduction of a class of nonlinear higher order ordinary differential equations

We propose a method for constructing first integrals of higher order ordinary differential equations. In particular third, fourth and fifth order equations of the form are considered. The relation of the proposed method to local and nonlocal symmetries are discussed.     

Literatur

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