On Some Families of Modules for the Current Algebra

Given a finite-dimensional module V for a finite-dimensional, complex semi-simple Lie algebra \(\mathcal {g}\), and a positive integer m, we construct a family of graded modules for the current algebra \(\mathcal {g}[t]\) indexed by simple C \(\mathcal {S}_{m}\)-modules. These modules are free of finite rank for the ring of symmetric polynomials and so can be localized to give finite-dimensional graded \(\mathcal {g}[t]\)-modules. We determine the graded characters of these modules and show that these graded characters admit a curious duality.     

Buffers for the Physiological pH Range: Studies of 4-(N-Morpholino)butanesulfonic Acid (MOBS) from 5 to 55 °C

In this study, we report the pH values of two buffer solutions without chloride ion and eight buffer solutions with NaCl with an ionic strength I=0.16 mol?kg^?1. Electromotive force (emf) techniques have been used to get the cell potentials at 12 temperatures from 5 to 55?°C, including 37?°C. An extended form of the Bates-Guggenheim convention is used in the entire ionic strength range, 0.04 to 0.16?mol?kg^?1. The residual liquid junction potentials (??E _j ) of the buffer solutions of MOBS have been estimated from previous measurements with a flowing junction cell. These values of ??E _j have been used for correction in order to ascertain the operational pH values of four buffer solutions of MOBS at 25 and 37?°C. These solutions are recommended as pH standards for physiological application in the pH range 7.4 to 7.7.     

Synthesis of melicodenines C,D and E

A synthesis of the unusual cyclobutane-quinolinone alkaloids melicodenines C, D and E by intermolecular [2+2] cycloaddition is described.     

An antimicrobial zinc based molecule for cross linking poly-acrylic acid

A system for incorporating antimicrobial zinc into polymeric materials, in particular hydrogel type polymers has been developed. Zn(Bipy-(MMOES)₂) a zinc carboxylate monomer was designed with the purpose of mimicking commercial cross linking agents such as ethylene glycol diacrylate, as well as containing antimicrobial zinc ions (Zn²⁺), with the intention that it can be used to cross link into any polymeric material, the example here being polyacrylic acid. Two systems were studied: a homopolymer of the Zn(Bipy-(MMOES)₂) and copolymers of Zn(Bipy-(MMOES)₂) with acrylic acid (AA). The AA – Zn(Bipy-(MMOES)₂) produced water swellable polymers which retained antimicrobial activity. The ability of the polymers to release the zinc ions was shown to be pH responsive and the leachate analysed to give a proposed mechanism of action. The Zn(Bipy-(MMOES)₂) monomer and polymers have shown antibacterial activity against both gram positive Methicillin susceptible staphylococcus aureus (MSSA 476) and gram negative Pseudomonas aeruginosa (PA01).     

An explanation of the unusual strength of the hydrogen bond in small water clusters

We seek to explain why the hydrogen bond possesses unusual strength in small water clusters that account for many of the complex behaviors of water. We have investigated and visualized the donation of covalent character from covalent (sigma) to hydrogen bonds by calculating the eigenvector coupling properties of quantum theory of atoms in molecules (QTAIM), stress tensor σ ( r ), and Ehrenfest Force F ( r ) on the F ( r ) molecular graph. The next-generation three-dimensional (3-D) bond-path framework sets are presented, and only the F ( r ) bond-path framework sets reproduce the earlier finding on the coupling between covalent (sigma) and hydrogen bonds that possess a degree of covalent character. Exploration of the bond-path between the covalent (sigma) and hydrogen bond's critical points provides an explanation for the previously obtained coupling results. The directional character of the covalent (sigma) and hydrogen bonds' 3-D bond-path framework sets for the F ( r ) explains differences found in the earlier results from QTAIM and the stress tensor σ ( r ).     

On the local behavior of certain homeomorphisms. II

In the previous paper by the authors, it is shown that a sense-preserving homeomorphism, absolutely continuous on lines (ACL), under certain integral conditions on the complex dilation is conformal at a point. This result includes the Teichmüller-Wittich-Belinski theorem. In the present paper, it is shown that under weakened conditions the local behavior of such a homeomorphism is similar to that of a quasiconformal mapping. Bibliography: 2 titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 11–20.Dedicated to the 90th anniversary of G. M. Goluzin's birth.     

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes–Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions.     

Quantum topology phase diagrams for molecules,clusters, and solids

The need to make more quantitative use of the total electronic charge density distribution is demonstrated in this short perspective. This is framed in the perspective of the ground breaking early work of Bader and coworkers, along with mathematicians who captured the essential nature of a molecule in a suitably compact form in real space. We see that this simple form is the Poincaré–Hopf relation for molecules and clusters and the Euler–Hopf relation in solids. Thom's theory of elementary catastrophes combined with the Poincaré–Hopf relation provides the inspiration for the new quantum topology. An alternative use of the Poincaré–Hopf relation, molecular recognition, is discussed. Quantum topology is then used to create a topology phase diagram for both molecules and solids. The author adds their perspectives of the huge potential of the quantum topology approach by demonstrating the ease with which new theoretical ideas can be generated. © 2013 Wiley Periodicals, Inc.