Rational Solutions of the H3 and Q1 Models in the ABS Lattice List

In the paper we present rational solutions for the H3 and Q1 models in the Adler-Bobenko-Suris lattice list. These solutions are in Casoratian form and are generated by considering difference equation sets satisfied by the basic Casoratian column vector

A Harmonic Extension Approach for Collaborative Ranking

We present a new perspective on graph-based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank approximation methods using convex optimization and the nuclear norm, we formulate matrix completion as a series of semi-supervised learning problems, and propagate the known ratings to the missing ones on the user-user or item-item graph globally. The semi-supervised learning problems are expressed as Laplace-Beltrami equations on a manifold, or namely, harmonic extension, and can be discretized by a point integral method. We show that our approach does not impose a low-rank Euclidean subspace on the data points, but instead minimizes the dimension of the underlying manifold. Our method, named LDM (low dimensional manifold), turns out to be particularly effective in generating rankings of items, showing decent computational efficiency and robust ranking quality compared to state-of-the-art methods

Growth rate and superconducting properties of Gd-Ba-Cu-O bulk superconductors melt processed in air

A generic Mg-doped Nd-Ba-Cu-O seed crystal has been developed recently for the fabrication of any type of rare earth (RE) based (RE)-Ba-Cu-O single grain bulk superconductor in air. The new generic seed simplifies significantly the top seeded melt growth (TSMG) process for light rare earth based (Nd, Sm, Gd, or mixed rare earth elements) bulk superconductors, in particular. GdBCO single grains have been fabricated successfully in air using the new seed in a cold-seeding process. In this study, precursor powders were enriched with different amounts of BaO2 to investigate the extent of substitution of Gd for Ba in the Gd1+xBa2-xCu3O7-delta solid solution phase. The growth process of large single grains in air was investigated at various growth temperatures under isothermal processing conditions. Crystal growth rate as a function of under-cooling and BaO2 content has been determined from these experiments. The spatial variation of Tc and transition temperature width for applied field aligned along the a/b and c-axis of grains fabricated with different BaO2 content has also been investigated in order to understand the extent of the formation of Gd/Ba solid solution with varying growth temperature and precursor composition. These results have been used to establish the optimum conditions for fabricating solid solution-free, large single grains of GdBCO in air

On the first place antitonicity in QL-implications

To obtain a demanded fuzzy implication in fuzzy systems, a number of desired properties have been proposed, among which the first place antitonicity, the second place isotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, R- and QL-implications all satisfy the second place isotonicity and the boundary conditions. However, not all the QL-implications satisfy the first place antitonicity as S- and R-implications do. In this paper we study the QL-implications satisfying the first place antitonicity. First we establish the relationship between the first place antitonicity and other required properties of QL-implications. Second we work on the conditions under which a QL-implication generated by different combinations of a t-conorm S, a t-norm T and a strong fuzzy negation N satisfy the first place antitonicity, especially in the cases that both S and T are continuous. We further investigate the interrelationships between S- and R-implications generated by left-continuous t-norms on one hand and QL-implications satisfying the first place antitonicity on the other

Darboux and binary Darboux transformations for discrete integrable systems 1. Discrete potential KdV equation

The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equations, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations

High-frequency Light Reflector via Low-frequency Light Control

We show that the momentum of light can be reversed via the atomic coherence created by another light with one or two orders of magnitude lower frequency. Both the backward retrieval of single photons from a timed Dicke state and the reflection of continuous waves by high-order photonic band gaps are analysed. The required control field strength scales linearly with the nonlinearity order, which is explained by the dynamics of superradiance lattices. Experiments are proposed with $^{85}$Rb atoms and Be$^{2+}$ ions. This holds promise for light-controllable X-ray reflectors.Comment: 5 pages, 5 figure