On the uniqueness of motion of viscous gaseous stars

The existence of solutions of the evolutionary equations of motion of a star regarded as a compressible viscous fluid with self-gravitation, bounded by a free surface, has recently been considered [3, 4]. In this paper I study the uniqueness of the above solutions.     

High-performance liquid chromatographic assay of bacterial collagenase

Summary The activity of bacterial collagenase Clostridiopeptidase A was estimated using a labelled synthetic peptide, 4-phenylazobenzyloxycarbonyl-L-Pro-L-Leu-Gly-L-Pro-D-Arg, as substrate. The N-protected dipeptide obtained after enzymatic hydrolysis of Leu-Gly peptide bond was quantified by reversed-phase, high-performance liquid chromatography using 4-phenylazobenzyloxycarbonyl-L-Pro-L-Phe as internal standard. The time dependence of the appearance of the hydrolysis product and the dependence of rates of hydrolysis on collagenase concentration were linear. Kinetic parameters for collagenase were determined to test the suitability of the described procedure.     

N-Person stochastic games with upper semi-continuous payoffs

Every n-person stochastic game with a countable state space, finite action sets for the players and bounded, upper semi-continuous payoffs has an ε-equilibrium for every ε>0.     

Stay-in-a-set games

There exists a Nash equilibrium (ε-Nash equilibrium) for every n-person stochastic game with a finite (countable) state space and finite action sets for the players if the payoff to each player i is one when the process of states remains in a given set of states G _i and is zero otherwise. Received: December 2000     

Purification to homogeneity of bovine prolactin by high-performance ion-exchange chromatography

Homogeneous bovine prolactin (bPRL) has been obtained using a procedure based on high-performance anion-exchange chromatography. The procedure enables up to 6 mg of 99.4% pure bPRL to be obtained per hour, with a recovery of 32.4%. The purity of the protein was checked by N-terminal sequencing and sodium dodecyl sulphate-polyacrylamide gel electrophoresis. The highly purified bPRL obtained with this method is suitable for complete structural and immunochemical studies.     

Self-assembly of a double calix[6]arene pseudorotaxane in oriented channels

A synthetic study to disclose the more appropriate manner by which two calix[6]arene units could be connected for the construction of an extended tubular structure was undertaken. As a result, a head-to-tail double calix[6]arene having the structure of an oriented nanotube that is about 2.6 nm long and 1.6 nm wide was prepared and characterized. This molecule is able to act as a wheel-type host and forms a supramolecular complex with an axle-type molecule, derived from 4,4'-bipyridinium (viologen), through very efficient self-assembly in solution. The properties of such a pseudorotaxane-type complex, which is stabilized by a combination of noncovalent interactions, were investigated in solution by UV/Vis absorption spectroscopy and voltammetric methods. These observations provide a clue about the location of the bipyridinium unit along the nanotube. In the solid state, the complex undergoes a further stage of self-assembly, thereby initiating extended oriented tubular structures. Crystallographic studies revealed that the positioning of the viologen dication in this asymmetric wheel is addressed by a complicated pattern of cooperative noncovalent intermolecular interactions that involve only one half of the host, whereas the remaining (more polar) half of the host is exploited to create long-range structural order that leads to a "secondary" structure of extended supramolecular channels that, in turn, self-assemble in the lattice, thus giving rise to a "tertiary" structure of parallel sandwiches of nanotubes.     

On the existence of good stationary strategies for nonleavable stochastic games

This paper discusses the problem regarding the existence of optimal or nearly optimal stationary strategies for a player engaged in a nonleavable stochastic game. It is known that, for these games, player I need not have an -optimal stationary strategy even when the state space of the game is finite. On the contrary, we show that uniformly -optimal stationary strategies are available to player II for nonleavable stochastic games with finite state space. Our methods will also yield sufficient conditions for the existence of optimal and -optimal stationary strategies for player II for games with countably infinite state space. With the purpose of introducing and explaining the main results of the paper, special consideration is given to a particular class of nonleavable games whose utility is equal to the indicator of a subset of the state space of the game.