A reduction method for semilinear elliptic equations and solutions concentrating on spheres

We show that any general semilinear elliptic problem with Dirichlet or Neumann boundary conditions in an annulus A⊆R^2m$A\subseteq {\mathbb{R}}^{2m}$, m?2$m?2$, invariant by the action of a certain symmetry group can be reduced to a nonhomogeneous similar problem in an annulus D⊂R^m+1$D\subset {\mathbb{R}}^{m+1}$, invariant by another related symmetry. We apply this result to prove the existence of positive and sign changing solutions of a singularly perturbed elliptic problem in A   which concentrate on one or two (m−1)$(m-1)$ dimensional spheres. We also prove that the Morse indices of these solutions tend to infinity as the parameter of concentration tends to infinity.     

A computational investigation of the thermodynamics of the Stillinger-Weber family of models at supercooled conditions

The existence of metastable liquid-liquid phase transitions (LLPTs) in tetrahedral liquids such as water, silicon, and silica has been the subject of vigorous scientific debate. Because high crystallization rates hinder experimental investigation at deeply supercooled conditions, computer simulation has been widely employed to investigate the existence of LLPTs in molecular models of tetrahedral liquids. The Stillinger-Weber (SW) model of silicon (and more generally, the SW family of models) has been actively studied along these lines. Whereas some studies observe evidence of an LLPT in this model, others report that only a single metastable liquid exists under deeply supercooled conditions. Here, we perform extensive state-of-the-art free energy calculations to investigate the possibility of an LLPT in the SW model of silicon. A similar analysis is also presented for the generalized SW family of models constructed by varying the strength of the three-body energetic term. Our analysis does not show any evidence of an LLPT in SW silicon nor in the generalized family of SW models over the parameter ranges studied. Explanations for the aforementioned discrepancies between previous studies are provided, along with explicit demonstrations of how these discrepancies may have occurred. Outstanding ambiguities and directions for future work are also discussed.     

Transition‐metal‐free N‐arylation: A general approach to aza‐fused poly‐heteroaromatics

A new and efficient method for the synthesis of various aza‐fused poly‐hetero aromatics has been described. This protocol includes an intermolecular condensation followed by metal‐free base‐promoted intramolecular C―N coupling reaction. The advantage of this one‐pot transformation lies in the use of simple cyclic amidines‐like compounds without prefunctionalization of the starting heterocycles.     

Structure-based virtual screening to identify inhibitors against Staphylococcus aureus MurD enzyme

Structural Chemistry - The MurD enzyme of Staphylococcus aureus is an attractive drug target as it is essential and ubiquitous in bacteria but absent in mammalian cells. In the present study, we...     

Critical age-dependent branching Markov processes and their scaling limits

This paper studies: (i) the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of agedependent critical branching Brownian motions.     

Finite generation of Hochschild homology algebras

We prove converses of the Hochschild-Kostant-Rosenberg Theorem, in particular: If a commutative algebra S is flat and essentially of finite type over a noetherian ring , and the Hochschild homology HH _* (S|) is a finitely generated S-algebra for shuffle products, then S is smooth over . Oblatum 27-V-1999 & 27-IX-1999 / Published online: 24 January 2000     

PIXE analysis of blood serum of breast cancer patients undergoing successive chemotherapy

Journal of Radioanalytical and Nuclear Chemistry - Particle induced X-ray emission technique was used to obtain the serum elemental profile of healthy subjects and breast cancer patients (BCPs)...     

Ion atmosphere relaxation controlled electron transfers in cobaltocenium polyether molten salts

A room-temperature redox molten salt for the study of electron transfers in semisolid media, based on combining bis(cyclopentadienyl)cobalt with oligomeric polyether counterions, [Cp2Co](MePEG350SO3), is reported. The transport properties of the new molten salt can be varied (plasticized) by varying the polyether content. The charge transport rate during voltammetric reduction of the ionically conductive [Cp2Co](MePEG350SO3) molten salt exceeds the actual physical diffusivity of [Cp2Co]+ because of rapid [Cp2Co](+/0) electron self-exchanges. The measured [Cp2Co](+/0) electron self-exchange rate constants (k(EX)) are proportional to the diffusion coefficients (D(CION)) of the counterions in the melt. The electron-transfer activation barrier energies are also close to those of ionic diffusion but are larger than those derived from optical intervalent charge-transfer results. Additionally, the [Cp2Co](+/0) rate constant results are close to those of dissimilar redox moieties in molten salts where D(CION) values are similar. All of these characteristics are consistent with the rates of electron transfers of [Cp2Co](+/0) (and the other donor-acceptor pairs) being controlled not by the intrinsic electron-transfer rates but by the rate of relaxation of the ion atmosphere around the reacting pair. In the low driving force regime of mixed-valent concentration gradients, the ion atmosphere relaxation is competitive with electron transfer. The results support the generality of the recently proposed model of ionic atmosphere relaxation control of electron transfers in ionically conductive, semisolid materials.     

Interaction of Cd and Zn with biologically important ligands characterized using solid-state NMR and ab initio calculations

For the first time, coordination geometry and structure of metal binding sites in biologically relevant systems are studied using chemical shift parameters obtained from solid-state NMR experiments and quantum chemical calculations. It is also the first extensive report looking at metal-imidazole interaction in the solid state. The principal values of the (113)Cd chemical shift anisotropy (CSA) tensor in crystalline cadmium histidinate and two different cadmium formates (hydrate and anhydrate) were experimentally measured to understand the effect of coordination number and geometry on (113)Cd CSA. Further, (13)C and (15)N chemical shifts have also been experimentally determined to examine the influence of cadmium on the chemical shifts of (15)N and (13)C nuclei present near the metal site in the cadmium-histidine complex. These values were then compared with the chemical shift values obtained from the isostructural bis(histidinato)zinc(II) complex as well as from the unbound histidine. The results show that the isotropic chemical shift values of the carboxyl carbons shift downfield and those of amino and imidazolic nitrogens shift upfield in the metal (Zn,Cd)-histidine complexes relative to the values of the unbound histidine sample. These shifts are in correspondence with the anticipated values based on the crystal structure. Ab initio calculations on the cadmium histidinate molecule show good agreement with the (113)Cd CSA tensors determined from solid-state NMR experiments on powder samples. (15)N chemical shifts for other model complexes, namely, zinc glycinate and zinc hexaimidazole chloride, are also considered to comprehend the effect of zinc binding on (15)N chemical shifts.