Non-catalytic bromination of benzene: a combined computational and experimental study

The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable

Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method of uniformization: We assign to the nonlocal problem a pseudodifferential operator with the same index, acting in sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah-Singer index theorem.Comment: 16 pages, no figure

Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.Comment: 14 pages, corrected typos, references and comments adde

Brominated Porous Nitrogen-Doped Carbon Materials for Sodium-Ion Storage

Chemical modification improves the performance of the carbon anode in sodium-ion batteries (SIBs). In this work, porous nitrogen-doped carbon (PNC) was obtained by removing template nanoparticles from the thermal decomposition products of calcium glutarate and acetonitrile vapor. The treatment of PNC with a KOH melt led to the etching of the carbon shells at the nitrogen sites, which caused the replacement of some nitrogen species by hydroxyl groups and the opening of pores. The attached hydroxyl groups interacted with Br2 molecules, resulting in a higher bromine content in the brominated pre-activated sample (5 at%) than in the brominated PNC (3 at%). Tests of the obtained materials in SIBs showed that KOH activation has little effect on the specific capacity of PNC, while bromination significantly improves the performance. The largest gain was achieved for brominated KOH-activated PNC, which was able to deliver 234 and 151 mAh g−1 at 0.05 and 1 A g−1, respectively, and demonstrated stable long-term operation at 0.25 and 0.5 A g−1. The improvement was related to the separation of graphitic layers due to Br2 intercalation and polarization of the carbon surface by covalently attached functional groups. Our results suggest a new two-stage modification strategy to improve the storage and high-rate capability of carbon materials in SIBs

Elliptic operators on manifolds with singularities and K-homology

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.Comment: revised version; 25 pages; section with applications expande

Detailed balance in Horava-Lifshitz gravity

We study Horava-Lifshitz gravity in the presence of a scalar field. When the detailed balance condition is implemented, a new term in the gravitational sector is added in order to maintain ultraviolet stability. The four-dimensional theory is of a scalar-tensor type with a positive cosmological constant and gravity is nonminimally coupled with the scalar and its gradient terms. The scalar field has a double-well potential and, if required to play the role of the inflation, can produce a scale-invariant spectrum. The total action is rather complicated and there is no analog of the Einstein frame where Lorentz invariance is recovered in the infrared. For these reasons it may be necessary to abandon detailed balance. We comment on open problems and future directions in anisotropic critical models of gravity.Comment: 10 pages. v2: discussion expanded and improved, section on generalizations added, typos corrected, references added, conclusions unchange

Next stage of search for 2K(2ν\nu)-capture of 78^{78}Kr

A technique to search for 2K-capture of $^{78}$Kr with large low-background proportional counter filled with an enriched in $^{78}$Kr up to 99.8% sample of Krypton at a pressure of 4.51 is described in this paper. The results of first measurements are presented. Analysis of data collected during 159 hours yielded new limit to the half-life of $^{78}$Kr with regard to 2K-capture (T$_{1/2}\geq6\cdot10^{21}$ yr (90% C.L.)). Sensitivity of the facility to the process for one year of measurement was evaluated to be $\texttt{S}=1.0\cdot10^{22}$ yr (90% C.L.).Comment: 4 pages, 5 figures; talk at the NANP'05 Conference; submitted to Phys. At. Nuc

Algebraic Geometry Approach to the Bethe Equation for Hofstadter Type Models

We study the diagonalization problem of certain Hofstadter-type models through the algebraic Bethe ansatz equation by the algebraic geometry method. When the spectral variables lie on a rational curve, we obtain the complete and explicit solutions for models with the rational magnetic flux, and discuss the Bethe equation of their thermodynamic flux limit. The algebraic geometry properties of the Bethe equation on high genus algebraic curves are investigated in cooperationComment: 28 pages, Latex ; Some improvement of presentations, Revised version with minor changes for journal publicatio

Construction of Polymeric Antigenic Diagnosticum Based on <i>Vibrio cholera</i> О1 Lipopolysaccharide

Representatives of the genus Vibrio cholerae differ in the structure of lipopolysaccharide, in particular, its O-polysaccharide chains (O-antigen), which determines the serological specificity of vibrios. Currently, the water-phenolic method is used to obtain the lipopolysaccharide preparation. However, this technique relates to harsh chemical methods, leads to a change in original molecular organization of biopolymer, violating its structure and biological properties. Modern technologies in the development of diagnostic kits for the immunosuspension reaction of volume agglomeration allow for obtaining synthetic carriers with different reaction groups on the particle surface capable to bind antigens/antibodies. The aim of this study was to construct cholera antigenic polymeric diagnostic kit based on the lipopolysaccharide of Vibrio cholerae O1 serogroup. Materials and methods. The lipopolysaccharide was used as a sensitizer obtained through the author's modification of enzymatic purification from the cell membranes of Vibrio cholerae using ultrasonic disintegration. Results and discussion. The resulting sensitin contains small impurities of protein (1.5 %) and nucleic acids (0.1 %). Diagnosticum is characterized by high analytical sensitivity in agglomeration reaction with commercial and experimental rabbit serum to Vibrio cholerae O1 serogroup (1:640 - 1:5120) and analytical specificity (the diagnosticum does not interact with heterologous sera, with serums to pathogens of acute intestinal infections, as well as with sera from healthy donors). A polymeric antigenic cholera diagnosticum designed to detect antibodies to lipopolysaccharide of Vibrio cholerae in the blood serum of patients who were ill, suspected of the disease or vaccinated people has been constructed