The spectrum of the S^5 compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4)

The authors calculate the spectrum of the S^5 compactification of the chiral N=2, D=10 supergravity theory. The modes on S^5 fall into unitary irreducible representations of the D=5, N=8 anti-de Sitter supergroup U(2,2/4). These unitary supermultiplets involve field of spin <or=2 with quantised 'mass' eigenvalues. The massless multiplet contains fifteen vector fields, six self-dual and six anti-self-dual anti-symmetric tensor fields. The fields of the massless multiplet are expected to be those of a gauged N=8 theory in D=5 with a local gauge group SU(4)

Photochemical Studies in Flash Photolysis. II. Photolysis of Acetone with Filtered Light

Flash photolysis was studied in the absence of wavelengths below 200 mμ. Effects of acetone pressure, light intensity, added biacetyl, temperature, and wavelength were investigated. The results are consistent with primary acts postulated previously on the basis of low‐intensity studies, but with the absence of complicating first‐order secondary reactions at these high radical concentrations. Deactivation of excited molecules explains the pressure effect on the C_2H_6/CO ratio, for wall effects are absent under flash conditions. A hot radical mechanism is suggested by the data for methane formation. The effect of wavelength on C_2H_6/CO ratio in regions centered near 260, 280, and 295 mμ is rather striking, and the results are compared with trends in low‐intensity studies in the same pressure region

Bimolecular Recombination Reactions: Low Pressure Rates in Terms of Time-Dependent Survival Probabilities, Total J Phase Space Sampling of Trajectories, and Comparison with RRKM Theory

We consider the bimolecular formation and redissociation of complexes using classical trajectories and the survival probability distribution function P(E,J,t) of the intermediate complexes at time t as a function of the energy E and total angular momentum quantum number J. The P(E,J,t) and its deviation from single exponential behavior is a main focus of the present set of studies. Together with weak deactivating collisions, the P(E,J,t) and a cumulative reaction probability at the given E and J can also be used to obtain the recombination rate constant k at low pressures of third bodies. Both classical and quantum expressions are given for k in terms of P(E,J,t). The initial conditions for the classical trajectories are sampled for atom−diatom reactions for various (E,J)’s using action-angle variables. A canonical transformation to a total J representation reduces the sampling space by permitting analytic integration over several of the variables. A similar remark applies for the calculation of the density of states of the intermediate complex ρ and for the number of states N* of the transition state as a function of E and J. The present approach complements the usual approach based on the rate of the reverse reaction, unimolecular dissociation, and the equilibrium constant. It provides results not necessarily accessible from the unimolecular studies. The formalism is applied elsewhere to the study of nonstatistical aspects of the recombination and redissociation of the resulting ozone molecules and comparison with RRKM theory

Esthetic rehabilitation with ultra-thin ceramic veneers and direct mock-up in the treatment of dental erosion – Case report

Indexación: Scopus.Dental erosion is a high prevalence condition characterized by the loss of dental substance due to chemical agents. It can also be associated with �physical wear, affecting function and aesthetics. Ceramic veneers can provide effective solutions to patients affected by erosive disorders, by means of an indirect approach and minimal intervention. Recent advances in cementation techniques and ceramic materials have allowed their use in reduced thicknesses, known as "dental contact lenses" or "ultra-thin veneers". They contribute significantly to the preservation of the dental structures, having excellent models or mock ups in order to preview the final outcome. Case: The aim of this report is to communicate the use of this technique for the treatment and successful 12-months follow-up of a patient affected by dental erosion of the maxillary central incisors. Special interest was placed on direct mock-up, which is a simple technique not requiring laboratory steps. Luting of the lithium disilicate veneers was carried out with a light-curing resin cement and try-in pastes, yielding a very satisfactory result. Conclusion: Diagnosis and early treatment of this disorder allows the application of conservative techniques, such as ultra-thin veneers, which are seen as a promising alternative treatment to full coverage restorations and traditional ceramic veneers. © 2018, Universidad de Concepcion. All rights reserved.http://joralres.com/index.php/JOR/article/view/481/45

Stability of barycentric interpolation formulas

The barycentric interpolation formula defines a stable algorithm for evaluation at points in [−1, 1] of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside [−1, 1], the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or "first barycentric" formula dating to Jacobi in 1825. This difference in stability confirms the theory published by N. J. Higham in 2004 (IMA J. Numer. Anal., v. 24) and has practical consequences for computation with rational functions

Three-Loop Leading Singularities and BDS Ansatz for Five Particles

We use the leading singularity technique to determine the planar three-loop five-particle amplitude in N=4 super Yang-Mills in terms of a simple basis of integrals. We analytically compute the integral coefficients for both the parity-even and the parity-odd parts of the amplitude. The parity-even part involves only dual conformally invariant integrals. Using the method of obstructions we numerically evaluate two previously unfixed coefficients which appear in the three-loop BDS ansatz.Comment: 20 pages, 2 figures, v2: very minor change

Patterns versus Characters in Subword-aware Neural Language Modeling

Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed. Thus, in order to build a proper word representation one must take into account its internal structure. From a corpus of texts we extract a set of frequent subwords and from the latter set we select patterns, i.e. subwords which encapsulate information on character $n$-gram regularities. The selection is made using the pattern-based Conditional Random Field model with $l_1$ regularization. Further, for every word we construct a new sequence over an alphabet of patterns. The new alphabet's symbols confine a local statistical context stronger than the characters, therefore they allow better representations in ${\mathbb{R}}^n$ and are better building blocks for word representation. In the task of subword-aware language modeling, pattern-based models outperform character-based analogues by 2-20 perplexity points. Also, a recurrent neural network in which a word is represented as a sum of embeddings of its patterns is on par with a competitive and significantly more sophisticated character-based convolutional architecture.Comment: 10 page