Transient solution of anM/M/1 queue with balking

An infinite capacityM/M/1 queue with balking is discussed. Defining the generating function in an unusual and direct way, the time-dependent solution for the system size is obtained elegantly.     

t-structures in the derived category of representations of quivers

Given a finite quiver without oriented cycles, we describe a family of algebras whose module category has the same derived category as that of the quiver algebra. This is done in the more general setting oft-structures in triangulated categories. A completeness result is shown for Dynkin quivers, thus reproving a result of Happel [H].     

A class of stochastic games with ordered field property

It is shown that discounted general-sum stochastic games with two players, two states, and one player controlling the rewards have the ordered field property. For the zero-sum case, this result implies that, when starting with rational data, also the value is rational and that the extreme optimal stationary strategies are composed of rational components.     

QSAR studies of 2-substituted 2,3-dihydro-1h-naphtho[1,8-de]-1,3,2-diazaphosphorine 2-oxides and sulphides

A quantitative structure activity relationship (QSAR) study of 2-substituted 2,3-dihydro-1H-naphtho[1,8,de]-1,3,2-diazaphosphorine 2-oxides and sulphides (DND), examines the extent of the contribution by various physicochemical parameters with respect to their antimicrobial activity. Simple bivariant regression analysis, based on the least squares method, is applied in order to predict models. The predicted models reveal that the steric factor, MR, is the major contributor influencing antimicrobial activity. Bulky groups at the C-19 (C=0 group) position positively influence the potency of the compounds     

Stochastic dilations of uniformly continuous completely positive semigroups

For an arbitrary uniformly continuous completely positive semigroup ( _t :t0) on the space of bounded operators on a Hilbert space, we construct a family (U(t)t0) of unitary operators on a Hilbert space and a conditional expectation from to, such that, for arbitraryt0,. The unitary operatorsU(t) satisfy a stochastic differential equation involving a noncommutative generalisation of infinite dimensional Brownian motion. They do not form a semigroup.Part of this work was completed when the first author was visiting research associate at the Center for Relativity, Physics Department, The University of Texas at Austin, Austin, TX 78712, U.S.A., supported in part by NSF PHY 81-01381.     

Synthesis of 4-β-D-arabinofuranosyl-5,6-dihydro-2H-1,2,4-thiadiazin-3-one 1,1-dioxide and x-ray diffraction analysis of its 2′,3-anhydro precursor

Reaction of 2-amino-3′,5′-bis(O-tert-butyldimethylsilyl)-β- D -arabinofuran[1′,2′:4,5]-2-oxazoline with 2-chloroethylsulfonyl chloride in the presence of sodium bicarbonate followed by removal of the protecting groups gave 2′,3-anhydro-4-β- D -arabinofuranosyl-5,6-dihydro-2H-1,2,4-thiadiazin-3-one 1,1-dioxide ( 5 ), which by treatment with ammonia was converted to 4-β- D -arabinofuranosyl-5,6-dihydro-2H-1,2,4-thiadiazin-3-one 1,1-dioxide ( 6 ). The structure of compound 5 was unequivocally established by means of an x-ray diffraction analysis. The compound crystallized in the space group P2₁2₁2₁ with unit cell dimensions a = 5.883(3), b = 9.352(2), c = 18.769(7) Å, Z = 4. Its structure was established by direct multisolution techniques and refined by the full matrix least squares method to a final R value of 0.058 for the 1515 reflections observed.     

Electrostatically driven spatial patterns in lipid membrane composition

To explore the physical mechanisms that can guide spatial organization at biological membranes, we have constructed simple, cell-free intermembrane junctions. We find that the mechanically driven patterning of proteins uncovered in our earlier work can electrostatically generate spatial patterns in the distribution of charged membrane lipids. Tuning the magnitude of the interaction as a function of composition and ionic strength, and analyzing the interplay between thermodynamics and electrostatics via a Poisson-Boltzmann approach, we are able to determine the charge density and surface potential of the junction components. Surprisingly, the electrostatic potential of the proteins is a minor factor in the lipid reorganization; the protein size and its modulation of the junction topography play the dominant role in driving the electrostatic patterns.