An implicit function theorem for directionally differentiable functions

A new implicit function theorem for a class of nonsmooth functions is proved. It is used to improve the directional implicit function theorem of Demidova and Demyanov (Ref. 1).     

Service stage Petri net models with product form solution

A class of service stage Petri net models whose equilibrium probabilities satisfy local balance equations is presented. Examples of their applicability include bus oriented multiprocessor interconnections, the classical dining philosophers problem and the alternating bit protocol. The natural topological space for embedding the state transition lattice for this class of SSPN is shown to be a multidimensional toroidal manifold.     

Complex dynamical behavior in a new chemical oscillator: The chlorite–thiourea reaction in a CSTR

The reaction between chlorite ion and thiourea has been studied both in a closed (batch) system and in a flow reactor (CSTR). The principal stoichiometry is given by In batch, the reaction displays an induction period, whose length is proportional to [CS(NH₂)₂]/[ClO] [H⁺], followed by the rapid buildup and disappearance of a ClO₂ intermediate. At [ClO]/[CS(NH₂)₂] ratios between 2.5 and 3.5, a second peak in the ClO₂ absorbance is observed. In the CSTR, this iodine-free system displays simple and complex periodic oscillation, bistability, aperiodic oscillation, and birhythmicity.     

Linked cluster expansions for U(1) lattice gauge theory in 2 + 1 and 3 + 1 dimensions

Compact U(1) lattice gauge theory is studied in 2 + 1 and 3 + 1 dimensions using strong coupling series expansions and the recently proposed exact linled cluster expansion alborithm Results for the vacuum energy, specific heat and axial string tension in 2 + 1 dimensions are in agreement with previous finite lattice estimates. In 3 + 1 dimensions, we present new strong coupling series results (order g^?40) which together with the ELCE estimates show evidence of a continuous phase transition at x = 1/g⁴ = 0.72 ± 0.08. The associated critical index for the vanishing string tension is μ = 0.65 ± 0.12. The axial string tension in D = 3 + 1 appears to undergo a non-deconfining roughening transition at smaller x (0.56 ± 0.07).     

Orientational sampling and rigid-body minimization in molecular docking revisited: On-the-fly optimization and degeneracy removal

Summary Strategies for computational association of molecular components entail a compromise between configurational exploration and accurate evaluation. Following the work of Meng et al. [Proteins, 17 (1993) 266], we investigate issues related to sampling and optimization in molecular docking within the context of the DOCK program. An extensive analysis of diverse sampling conditions for six receptor-ligand complexes has enabled us to evaluate the tractability and utility of on-the-fly force-field score minimization, as well as the method for configurational exploration. We find that the sampling scheme in DOCK is extremely robust in its ability to produce configurations near to those experimentally observed. Furthermore, despite the heavy resource demands of refinement, the incorporation of a rigid-body, grid-based simplex minimizer directly into the docking process results in a docking strategy that is more efficient at retrieving experimentally observed configurations than docking in the absence of optimization. We investigate the capacity for further performance enhancement by implementing a degeneracy checking protocol aimed at circumventing redundant optimizations of geometrically similar orientations. Finally, we present methods that assist in the selection of sampling levels appropriate to desired result quality and available computational resources.     

Theorems on products of EPr matrices,II

This paper gives necessary and sufficient conditions that the product of EPr matrices with entries from an arbitrary field be EPr. Results about the Reverse Order Law for generalized inverses of products of these matrices are included.     

π−A1 interference in πN → ϱN

An estimate of the A₁NN coupling is made using axial vector meson dominance of weak form factors, PCAC and current algebra. We use this to predict a vanishingly small polarisation due to unnatural parity exchanges in πN → ?N near the forward direction. In contrast, the contribution to πN → ωN of the Z (the J^PC = 2^?? exchange degenerate partner of the A₁) is found to be significant as indeed indicated by experiment.