Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose ?? is the shift acting on Bernoulli space X={1,2,??,d}^?, and, consider a fixed continuous cost function c:X×X???. Denote by ?? the set of all Borel probabilities ?? on X×X, such that, both its x and y marginals are ??-invariant probabilities. We are interested in the optimal plan ?? which minimizes ??c? d?? among the probabilities in ??. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan ?? by convex combinations of plans such that the support projects in periodic orbits.     

Dynamic hyperfine interactions in In(Cd)-doped ZnO semiconductor: PAC results supported by ab initio calculations

In this work, we present results of Time-Differential γ–γ Perturbed-Angular-Correlations (PAC) experiments performed in ¹¹¹Cd-doped ZnO semiconductor. The PAC technique has been applied in order to characterize the electric-field-gradient (EFG) tensor at (¹¹¹In (EC)→) ¹¹¹Cd nuclei located, as was later demonstrated, at defect-free cation sites of the ZnO host structure. The PAC experiments were performed in the temperature range of 77–1075 K. At first glance, the unexpected presence of low-intensity dynamic hyperfine interactions was observed, which were analyzed with a perturbation factor based on the Bäverstam and Othaz model. The experimental EFG results were compared with ab initio calculations performed with the Full-Potential Augmented Plane Wave plus local orbital (FP-APW+lo) method, in the framework of the Density Functional Theory (DFT), using the Wien2K code. The presence of the dynamic hyperfine interactions has been analyzed enlightened by the FP-APW+lo calculations of the EFG performed as a function of the charge state of the cell. We could correlate the large strength of the dynamic hyperfine interaction with the strong variation of the EFG due to changes in the electronic charge distribution in the Cd vicinity during the time-window of the PAC measurement. It was also revealed that the Cd impurity decays to a final stable neutral charge state (Cd²⁺) fast enough (in few ns) to produce the nearly undamped observed PAC spectra.     

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.