Harmonic Cheeger–Simons characters with applications

We initiate the study of harmonic Cheeger–Simons characters, with applications to smooth versions of the Geometric Langlands program in the abelian case.     

A model for codependent reversible/irreversible growth processes

A model for codependent growth that combines reversible and irreversible bond formation is developed. The system is composed of two processes: A reversible process which is fast but does not lead to a stable growth by itself, while the irreversible process is stable but is too slow to occur by itself. Therefore, neither the reversible nor the irreversible growth processes will occur separately, but their combination is shown to yield a new type of stable, codependent growth. Using kinetic Monte Carlo techniques we simulate and analyze the general properties of this codependent growth. We discuss the general conditions for such growth and its applications to self-organization processes.     

Gas-phase nazarov cyclization of protonated 2-methoxy and 2-hydroxychalcone: An example of intramolecular proton-transport catalysis

Upon CA, ESI generated [M + H]⁺ ions of chalcone (benzalacetophenone) and 3-phenyl-indanone both undergo losses of H₂O, CO, and the elements of benzene. CA of the [M + H]⁺ ions of 2-methoxy and 2-hydroxychalcone, however, prompts instead a dominant loss of ketene. In addition, CA of the [M + H]⁺ ions of 2-methoxy-β-methylchalcone produces an analogous loss of methylketene instead. Furthermore, the [M + D]⁺ ion of 2-methoxychalcone upon CA eliminates only unlabeled ketene, and the resultant product, the [M + D − ketene]⁺ ion, yields only the benzyl-d ₁ cation upon CA. We propose that the 2-methoxy and 2-hydroxy (ortho) substituents facilitate a Nazarov cyclization to the corresponding protonated 3-aryl-indanones by mediating a critical proton transfer. The resultant protonated indanones then undergo a second proton transport catalysis facilitated by the same ortho substituents producing intermediates that eliminate ketene to yield 2-methoxy- or 2-hydroxyphenyl-phenyl-methylcarbocations, respectively. The basicity of the ortho substituent is important; for example, replacement of the ortho function with a chloro substituent does not provide an efficient catalyst for the proton transports. The Nazarov cyclization must compete with an alternate cyclization, driven by the protonated carbonyl group of the chalcone that results in losses of H₂O and CO. The assisted proton transfer mediated by the ortho substituent shifts the competition in favor of the Nazarov cyclization. The proposed mechanisms for cyclization and fragmentation are supported by high-mass resolving power data, tandem mass spectra, deuterium labeling, and molecular orbital calculations.     

Schottky diode characteristics: Aluminium with 500 and 1000 Å thicknesses on p type WSe2 crystal

The conduction properties of Al‐p WSe₂ Schottky barrier diodes prepared identically but with different metal thickness are reported here. The p type WSe₂ semiconducting crystals used in the present study was grown by direct vapour transport technique. The current‐voltage characteristics of these diodes were analyzed from 140 K to 300 K on the basis of thermionic emission theory applying Gaussian distribution. Below 200 K, deviations were observed in barrier height, ideality factor and Richardson plot. Hence at lower temperatures, a model has been considered where the total current is assumed to be the sum of thermionic emission, generation recombination and tunneling components. The observed deviations in the diode parameters were successfully interpreted in terms of the contribution of these multiple charge transport mechanisms across the interface of the fabricated diodes. The diode with a thickness of 500 Å Al showed more homogeneous nature than with 1000 Å. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology and Flux of T-Dual Manifolds with Circle Actions

We present an explicit formula for the topology and H-flux of the T-dual of a general type II, compactification, significantly generalizing earlier results. Our results apply to T-dualities with respect to any circle action on spacetime X. As before, T-duality exchanges type IIA and type IIB string theories. A new consequence is that the T-dual spacetime is a singular space when the fixed point set ${X^\mathbb{T}}$ is non-empty; the singularities correspond to Kaluza-Klein monopoles. We propose that the Ramond-Ramond charges of type II string theories on the singular dual are classified by twisted equivariant cohomology groups. We also discuss the K-theory approach.     

On Noncentral Generalized Laplacianness of Quadratic Forms in Normal Variables

A general distribution which will be called the noncentral generalized Laplacian (NGL) is introduced and its properties studied. Then a set of results are obtained which will give the necessary and sufficient conditions for a bilinear expression or a quadratic expression to be distributed as a NGL.     

Diastereoselective self-condensation of dihydroxyfumaric Acid in water: potential route to sugars

Jack of all trades: Water-soluble salts of DHF underwent self-condensation to afford the threo diastereomer of pentulosonic acid, through differing reaction pathways contingent on the metal salt used. This transformation exemplifies the diverging roles of DHF as a nucleophile (a synthon for α-hydroxyacetyl anion) and an electrophile (an α-carboxyglycolaldehyde equivalent).     

Probing conformational variations at the ATPase site of the RNA helicase DbpA by high-field electron-nuclear double resonance spectroscopy

The RNA helicase DbpA promotes RNA remodeling coupled to ATP hydrolysis. It is unique because of its specificity to hairpin 92 of 23S rRNA (HP92). Although DbpA kinetic pathways leading to ATP hydrolysis and RNA unwinding have been recently elucidated, the molecular (atomic) basis for the coupling of ATP hydrolysis to RNA remodeling remains unclear. This is, in part, due to the lack of detailed structural information on the ATPase site in the presence and absence of RNA in solution. We used high-field pulse ENDOR (electron-nuclear double resonance) spectroscopy to detect and analyze fine conformational changes in the protein's ATPase site in solution. Specifically, we substituted the essential Mg(2+) cofactor in the ATPase active site for paramagnetic Mn(2+) and determined its close environment with different nucleotides (ADP, ATP, and the ATP analogues ATPγS and AMPPnP) in complex with single- and double-stranded RNA. We monitored the Mn(2+) interactions with the nucleotide phosphates through the (31)P hyperfine couplings and the coordination by protein residues through (13)C hyperfine coupling from (13)C-enriched DbpA. We observed that the nucleotide binding site of DbpA adopts different conformational states upon binding of different nucleotides. The ENDOR spectra revealed a clear distinction between hydrolyzable and nonhydrolyzable nucleotides prior to RNA binding. Furthermore, both the (13)C and the (31)P ENDOR spectra were found to be highly sensitive to changes in the local environment of the Mn(2+) ion induced by the hydrolysis. More specifically, ATPγS was efficiently hydrolyzed upon binding of RNA, similar to ATP. Importantly, the Mn(2+) cofactor remains bound to a single protein side chain and to one or two nucleotide phosphates in all complexes, whereas the remaining metal coordination positions are occupied by water. The conformational changes in the protein's ATPase active site associated with the different DbpA states occur in remote coordination shells of the Mn(2+) ion. Finally, a competitive Mn(2+) binding site was found for single-stranded RNA construct.     

Fractional integral operators in the complex matrix variate case

A formal definition of fractional integrals in the complex matrix variate case is given here. This definition will encompass all the various fractional integral operators introduced by various authors in the real scalar and matrix cases. The new definition is introduced in terms of M-convolutions of products and ratios of matrices in the complex domain. Their connections to statistical distribution theory, Mellin convolutions, M-transforms and Mellin transform are pointed out. Some basic properties are given and a pathway extension of the new definition is also given. The pathway extension will provide a switching mechanism to move among three different families of functions.     

Generalized Boltzmann factors induced by Weibull-type distributions

The inverse Mellin transform technique is utilized to obtain closed form representations of the generalized Boltzmann factors associated with several Weibull-type models such as the generalized gamma, Maxwell, Rayleigh and half-normal distributions. The results complement those already available in the Physics literature in connection with the distribution of certain variables affecting the behavior of nonequilibrium systems subject to complex dynamics, which include for instance computable expressions for the generalized Boltzmann factors induced by the gamma, F$F$, uniform and lognormal statistical models.