Analysis of γ-ray production in neutral-current neutrino-oxygen interactions at energies above 200 MeV

It has long been recognized that the observation of γ rays originating from nuclear deexcitation can be exploited to identify neutral-current neutrino-nucleus interactions in water-Cherenkov detectors. We report the results of a calculation of the neutrino- and antineutrino-induced γ-ray production cross section for the oxygen target. Our analysis is focused on the kinematical region of neutrino energy larger than ～200 MeV, in which a single-nucleon knockout is known to be the dominant reaction mechanism. The numerical results have been obtained using for the first time a realistic model of the target spectral function, extensively tested against electron-nucleus scattering data. We find that at a neutrino energy of 600?MeV the fraction of neutral-current interactions leading to emission of γ?rays of energy larger than 6?MeV is ～41%, and that the contribution of the p_{3/2} state is overwhelming.     

Series solutions of confluent Heun equations in terms of incomplete Gamma-functions

We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having indefinite integral representation. The approach employs an auxiliary equation involving only the derivatives of a solution of the equation under consideration. Using power-series expansions of the solutions of this auxiliary equation, we construct several expansions of the four confluent Heun equations'' solutions in terms of the incomplete Gamma-functions. In the cases of single- and double-confluent Heun equations the coefficients of the expansions obey four-term recurrence relations, while for the bi- and tri-confluent Heun equations the recurrence relations in general involve five terms. Other expansions for which the expansion coefficients obey recurrence relations involving more terms are also possible. The particular cases when these relations reduce to ones involving less number of terms are identified. The conditions for deriving closed-form finite-sum solutions via right-hand side termination of the constructed series are discussed.     

Mean growth and geometric zero distribution of solutions of linear differential equations

The aim of this paper is to consider certain conditions on the coefficient A of the differential equation f″ + Af = 0 in the unit disc which place all normal solutions f in the union of Hardy spaces or result in the zero-sequence of each non-trivial solution being uniformly separated. The conditions on the coefficient are given in terms of Carleson measures.     

On the regularization of conservative maps

We show that smooth maps are C ¹-dense among C ¹ volume-preserving maps.     

Infinitely Many Local Higher Symmetries without Recursion Operator or Master Symmetry: Integrability of the Foursov–Burgers System Revisited

We consider the Burgers-type system studied by Foursov,

Stimulated four-photon mixing and efficient polychromatic visible light generation in SiO2-based single-mode optical fibers pumped at 1.319 μm

The generation of near-infrared and intense visible light through stimulated multi-wave mixing processes in single-mode silica-based optical fibers pumped by a Q-switched and mode-locked Nd:YAG laser operated at 1.319 μm is described. The experimental results show that intense infrared light around 1.2 μm is produced via selp-hase-matched four-photon mixing at the minimum group velocity dispersion region of pure SiO₂-core and P₂O₅-doped silica fibers. In the visible spectral region, from 580 nm to 600 nm, 20 W peak power 100-ps pulses were generated by pumping single spans of single-mode P₂O₅-doped and undoped SiO₂-core fibers with 1.319-μm laser pulses. The signal light generated in such fibers propagated in the LP₀₂ fiber mode and exhibited a threshold power that depended upon the fiber length and a critical length that was power dependent. Also, it exhibited an asymmetrical spectrum of a few nanometers bandwidth, with a long tail toward high frequencies. For GeO₂-doped silica-based fibers, a multiple-wavelength visible signal propagating in several high-order fiber modes was generated.     

New enantioselective method for hydration of alkenes using cyclodextrins as phase transfer catalyst

A new enantioselective/inverse phase transfer catalysis (IPTC) reaction for the Markovnikov hydration of double bounds by an oxymercuration-demercuration reaction with cyclodextrins as catalysts was disclosed. Moderate ee (up to 32%) and yields (14-60%) were obtained for allylic amines and protected allylic alcohols as starting materials.     

Intermolecular cycloaddition of nonstabilized azomethine ylides generated from 1,3-thiazolidine-4-carboxylic acids: synthesis of 5,7a-dihydro-1H,3H-pyrrolo[1,2-c]thiazoles

The 1,3-dipolar cycloaddition of dimethyl acetylenedicarboxylate with nonstabilized azomethine ylides, generated via the decarboxylative condensation of 1,3-thiazolidine-4-carboxylic acids with aldehydes, afforded 5,7a-dihydro-1H,3H-pyrrolo[1,2-c]thiazole derivatives. 2-Substituted-1,3-thiazolidine-4-carboxylic acids led to the stereoselective formation of 5,7a-dihydro-1H,3H-pyrrolo[1,2-c]thiazoles. Quantum-chemistry calculations were carried out allowing the rationalization of the observed stereoselective formation of the anti-dipole.     

Error analysis and improvements of coupled-cluster theory

Summary The error in the energy of the traditional coupled-cluster (TCC) approach and of several variants is analyzed in terms of the error of the cluster operatorS. A key feature of this analysis is that TCC can be based on an energy functional (asymmetric inS andS ) that is made stationary with respect to variation ofS . The error of TCC scales with the particle numbern, but it is not quadratic in . An improved coupled-cluster method (ICC) is presented that is the next step in a hierarchy from TCC to an exact variational theory. An alternative hierarchy is possible that leads to the extended coupled-cluster (ECC) method of Arponen. Variational (VCC) and unitary (UCC) coupled cluster theories and their stationary conditions and errors are analyzed along similar lines and practicable VCC or UCC approaches are presented. An infinite summation of certain terms in the VCC expectation value is shown to lead to a coupled-pair functional of the type proposed by Ahlrichs. The various CC schemes discussed here are compared on the CC-D, CC-SD and CC-SDT levels and beyond this. Special aspects referring to properties are also discussed.     

Structure-function relationships in glutathione and its analogues

The results are presented of measurements of protonation constants (potentiometry and NMR), UV spectroscopic properties and redox potentials of GSH and its five analogues, which are modified at the C-terminal glycine residue (gammaGlu-Cys-X, X = Gly, Gly-NH2, Gly-OEt, Ala, Glu, Ser). Strong linear correlations were found between various properties of the thiol and other functions of these peptides. These results allow discussion of the relationships between the structures and properties in glutathione and its analogues, and provide a novel chemical background for the issue of control of GSH reactivity.