Hydrodynamical limit for a Hamiltonian system with weak noise

Starting from a general hamiltonian system with superstable pairwise potential, we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles. We prolve that, in the scaling limit, the time conserved quantities, energy, momenta and density, satisfy the Euler equation of conservation laws up to a fixed timet provided that the Euler equation has a smooth solution with a given initial data up to timet. The strength of the noise term is chosen to be very small (but nonvanishing) so that it disappears in the scaling limit.Research partially supported by U.S. National Science Foundation grants DMS 89001682, DMS 920-1222 and a grant from ARO, DAAL03-92-G-0317Research partially supported by U.S. National Science Foundation grants DMS-9101196, DMS-9100383, and PHY-9019433-A01, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship     

Invariant interpolation formulas for higher-order derivatives of functions of a vector argument

Interpolation formulas for higher-order derivatives which guarantee the invariance of the results under changes of coordinates are obtained for functions of a vector argument.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 22–25, 1987.     

Echo planar imaging of perfluorocarbons

Emulsions of perfluorotributylamine (FTBA) and perflubron were evaluated for their utility in ¹⁹F echo planar imaging. Fluorine images of the emulsions were obtained in a phantom and two mice that had been predosed. Both agents, but particularly perflubron, show potential for fluorine echo planar studies because of the long spin-spin relaxation times of the CF₃ resonances. High resolution thin slice images obtained in as little as 26.6 ms are presented.     

1H and13C nuclear magnetic relaxation and local dynamics of lysozyme and synthetic polypeptides

The combined analysis of¹H and¹³C NMR relaxation data in solid lysozyme and some typical homopolypeptides was carried out by using “model-free” approach. Three types of relaxation transitions (γ’, γ and β) were revealed in the temperature range investigated. The microdynamical parameters of these motions were determined. From the comparison of these parameters with those of selected synthetic polymers it follows that the molecular motions in proteins and synthetic polymers are of the same nature. All these motions show pronounced anisotropic character. In the investigated temperature range no molecular motions corresponding to α-relaxation (liquid-like) transition were revealed. The hydration effects on parameters of the motions in proteins were considered. The most pronounced effect takes place for β-transition. The effect of Brownian rotation of protein molecule in solution on measured correlation function of local motions was also discussed.     

Plant polysaccharides I. Polysaccharides ofLagochilus and their biological activity

Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (3712) 89 14 75. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 313–314, March–April, 1995. Original article submitted November 7, 1994.     

Invariants of chaotic Hamiltonian systems

The invariants of chaotic bounded Hamiltonian systems and their relation to the solutions of the first variational equations of the equations of motion are studied. We show that these invariants are characterized by the fact that they either lose the property of differentiability as functions on phase space or that a certain formal power series defined in terms of the derivatives of the invariants has zero radius of convergence. For a specific example, we show that the former possibility appears to apply.     

A concept of fuzzy transition probabilities

Starting from fuzzy real numbers with an arbitrary lattice of belief and following the extension principle, we develop concepts of fuzzy probabilities, transition probabilities and random variables and of their combinations, and show that these concepts are consistent. We derive some results on fuzzy real numbers, on the expectation of fuzzy random variables and on fuzzy stochastic processes. To sketch the range of applications of fuzzy stochastics, we give two examples that show how real-world problems may be modeled by means of fuzzy probabilities and that give small numerical examples. Moreover, we give a brief outlook for a possible expansion of our theory to fuzzy Markovian decision processes by means of a partial order on the set of all fuzzy real numbers.     

A high performance liquid chromatographic assay for AMP-deaminase activity in the erythrocytes of healthy subjects and patients with inherited purine disorders

A novel method for measuring AMP-deaminase activity in human erythrocytes is presented, based on the determination of the reaction product, IMP, using high performance liquid chromatography. IMP formation was found to be proportional both to the incubation time and the amount of haemolysate over a wide range. The minimal detectable AMP-deaminase activity was more than 1000 times lower than the mean activity found in healthy controls (1083 nmol/h/mg Hb). No marked difference of activity was found in the patients with the following inherited purine disorders: familial juvenile gouty nephropathy and deficiencies of adenosine deaminase, hypoxanthine-guanine phosphoribosyltransferase or adenine phosphoribosyltransferase. The activity in the erythrocytes of patients with chronic renal failure was also similar to controls. The existence of subjects with low erythrocyte AMP-deaminase activity in the population has been confirmed.