Generalized Cohomologies and the Physical Subspace of the SU(2) WZNW Model

The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that being the height of the current algebra representation) acts in -dimensional indefinite metric space of quantum group invariant vectors. The generalized cohomologies Ker are 1-dimensional. Their direct sum spans the physical subquotient of .     

QUASI: a novel method for simultaneous superposition of multiple flexible ligands and virtual screening using partial similarity

The structure of many receptors is unknown, and only information about diverse ligands binding to them is available. A new method is presented for the superposition of such ligands, derivation of putative receptor site models and utilization of the models for screening of compound databases. In order to generate a receptor model, the similarity of all ligands is optimized simultaneously taking into account conformational flexibility and also the possibility that the ligands can bind to different regions of the site and only partially overlap. Ligand similarity is defined with respect to a receptor site model serving as a common reference frame. The receptor model is dynamic and coevolves with the ligand alignment until an optimal self-consistent superposition is achieved. When ligand conformational flexibility is permitted, different superposition models are possible and consistent with the data. Clustering of the superposition solutions is used to obtain diverse models. When the models are used to screen a database of compounds, high enrichments are obtained, comparable to those obtained in docking studies.     

Analytical Linear Inequality Systems and Optimization

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.     

Bimodules over nest algebras and Deddens' theorem

We generalize Deddens' theorem for nest algebras in the case of w*-closed nest algebras bimodules. For each such bimodule, we introduce a norm closed sub-bimodule of it, which corresponds to the radical of a nest algebra and describe it in a number of ways, generalizing known facts about nest algebras.

     

Sediment Assessment of the Pchelina Reservoir,Bulgaria

The temporal dynamics of anthropogenic impacts on the Pchelina Reservoir is assessed based on chemical element analysis of three sediment cores at a depth of about 100–130 cm below the surface water. The ¹³⁷Cs activity is measured to identify the layers corresponding to the 1986 Chernobyl accident. The obtained dating of sediment cores gives an average sedimentation rate of 0.44 cm/year in the Pchelina Reservoir. The elements’ depth profiles (Ti, Mn, Fe, Zn, Cr, Ni, Cu, Mo, Sn, Sb, Pb, Co, Cd, Ce, Tl, Bi, Gd, La, Th and U_nat) outline the Struma River as the main anthropogenic source for Pchelina Reservoir sediments. The principal component analysis reveals two groups of chemical elements connected with the anthropogenic impacts. The first group of chemical elements (Mn, Fe, Cr, Ni, Cu, Mo, Sn, Sb and Co) has increasing time trends in the Struma sediment core and no trend or decreasing ones at the Pchelina sampling core. The behavior of these elements is determined by the change of the profile of the industry in the Pernik town during the 1990s. The second group of elements (Zn, Pb, Cd, Bi and U_nat) has increasing time trends in Struma and Pchelina sediment cores. The increased concentrations of these elements during the whole investigated period have led to moderate enrichments for Pb and U_nat, and significant enrichments for Zn and Cd at the Pchelina sampling site. The moderately contaminated, according to the geoaccumulation indexes, Pchelina Reservoir surface sediment samples have low ecotoxicity.     

K6Pb8Cd: A Zintl Phase with Oligomers of Pb4 Tetrahedra Interconnected by Cd Atoms

Unprecedented (Pb ₄ )Cd(Pb ₄ )Cd(Pb ₄ )Cd(Pb ₄ ) tetramers (see picture) are present in the structure of the title compound, in which they coexist with isolated Pb₄ tetrahedra. Since Cs₆Ge₈Zn has the same stoichiometry as K₆Pb₈Cd but contains exclusively (Ge₄)₂Zn dimers, this can be viewed as a disproportionation reaction of the type (a).     

Synthesis of novel aminophosphonic acids with hydantoin structure

The novel α‐aminophosphonic acids with hydantoin structure have been synthesized reacting 5,5‐dimetylhydantoin with formaldehyde and phosphorus trichloride, or via Kabachnik–Fields reaction. Their structures were proved by means of IR, ¹H, ¹³C{¹H}, and ³¹P NMR spectroscopy. © 2009 Wiley Periodicals, Inc. Heteroatom Chem 20:87–90, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20515     

Kinetics of solubilization of n-decane and benzene by micellar solutions of sodium dodecyl sulfate

We observed the diminishing of single microscopic oil drops to study the kinetics of solubilization of n-decane and benzene by micellar solutions of sodium dodecyl sulfate (SDS). Each drop is located in a horizontal glass capillary of inner diameter 0.06 cm filled with a thermostated surfactant solution; the small vertical dimension of the cell prevents the appearance of uncontrollable thermal convections. The experiments show that the radius of an n-decane drop decreases linearly with time, whereas for benzene this dependence is nonlinear. To interpret the data, a kinetic model of solubilization is developed. It accounts for the diffusion and capturing of dissolved oil molecules by the surfactant micelles, as well as for the finite rate of oil dissolution at the oil-water interface. By processing the data, we determined the rate constant of solubilization for a given oil and surfactant. It turns out that the elementary act of catching a dissolved oil molecule by a surfactant micelle occurs under a barrier (rather than diffusion) control. The effective rate of solubilization is greater for the oil, which exhibits a higher equilibrium solubility in pure water (benzene), despite the lower value of the solubilization rate constant for this oil.     

Relaxation methods for solving linear inequality systems: converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In González-Gutiérrez and Todorov (Optim. Lett. doi:10.1007/s11590-010-0244-4, 2011), an algorithm, called extended relaxation method, for solving the feasibility problem has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we consider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.