Littlewood-Richardson Coefficients via Yang-Baxter Equation

The purpose of this paper is to present an interpretation for the decomposition of the tensor product of two or more irreducible representations of GL(N) in terms of a system of quantum particles. Our approach is based on a certain scattering matrix that satisfies a Yang-Baxter type equation. The corresponding piecewise-linear transformations of parameters give a solution to the tetrahedron equation. These transformation maps are naturally related to the dual canonical bases for modules over the quantum enveloping algebra $U_q(sl_n)$. A byproduct of our construction is an explicit description for the cone of Kashiwara's parametrizations of dual canonical bases. This solves a problem posed by Berenstein and Zelevinsky. We present a graphical interpretation of the scattering matrices in terms of web functions, which are related to honeycombs of Knutson and Tao.Comment: 24 page

Semigroups of sl3(C)sl_3(\mathbb{C}) tensor product invariants

We compute presentations for a family of semigroup algebras related to the problem of decomposing $sl_3(\mathbb{C})$ tensor products. Along the way we find new toric degenerations of the Grassmannian variety $Gr_3(\mathbb{C}^n)$ which $T-$invariant for $T \subset GL_n(\mathbb{C})$ the diagonal torus.Comment: 12 pages, 13 figure

Low speed crack propagation via kink formation and advance on the silicon (110) cleavage plane

We present density functional theory based atomistic calculations predicting that slow fracturing of silicon is possible at any chosen crack propagation speed under suitable temperature and load conditions. We also present experiments demonstrating fracture propagation on the Si(110) cleavage plane in the ~100 m/s speed range, consistent with our predictions. These results suggest that many other brittle crystals could be broken arbitrarily slowly in controlled experiments

Functional methods in the theory of magnetoimpurity states of electrons in quantum wires

Functional methods are used to study magnetoimpurity states of electrons in nanostructures. The Keldysh formalism is applied to these states. The theory is illustrated using a quantum wire sample with impurity atoms capable of localizing electrons in a magnetic field. The characteristics of magnetoimpurity states of electrons in the wire are calculated using the model of a Gaussian separable potential.Comment: 15 pages, 1 figur

Teaching Sciences in Virtual Worlds with Mastery Learning: A Case of Study in Elementary School

Virtual worlds are 3D environments that provide a feeling of immersion and a high degree of interaction, collaboration, communication between users. Its applicability can be focused on the educational scope, in which theories can be integrated as the basis to didactic activities carried out in the 3D environment, being its area of interdisciplinary comprehension. In this context, this article presents the use of a Virtual World built to assist in the teaching of Science for students of the middle school, whose articulation of the activities performed in the course are based on the precepts of the educational theory Mastery Learning. Tests were carried out in the subject of science, being divided into two periods with different groups for comparative purposes and realized evaluations during the period of the experiments. Kruskal-Wallis and Wilcoxon-Mann-Whitney non-parametric test were applied to the results of the assessments to ascertain the performance of each group. It was verified in the general analyzis that the participants who used the Virtual World had a growing performance, with high medians and adequate distribution of the results, being predominant of a smaller variability and amplitude. Thus, was possible to conclude that the results obtained with the approach were positive, which led to the validation of this research and presented a clear contribution to the academic environment

Saving and Real Interest Rates in Brazil

This paper presents a critical analysis of governments' attempts to increase national and private savings by raising the real rate of return on financial assets. Using the Brazilian economy as a case study, the paper argues that successes in increasing the savings rate can be traced to the fiscal reforms that accompanied the process of financial system redesign that sought to free interest rates from administrative controls. Two types of econometric exercises are performed to offer evidence of the responsiveness of savings to changes in the expected real interest rate. The first one uses a standard saving function approach in evaluating the magnitude of the interest elasticity of savings. The second test addresses the issue by using the Euler equation technique and measuring the rate of intertemporal substitution in consumption. The results obtained in both sections point to a negligible effect of real interest rates on aggregate and private sector saving. These results have important implications for the design of stabilization and structural reform programs and they contradict the fundamental behavioral hypothesis underlying the savings policy advice most often given to developing economies by international organizations like the World Bank and the IMF.Este artigo apresenta uma análise crítica do esforço do governo em aumentar a poupança nacional e a poupança privada através do aumento da taxa de retorno real dos ativos financeiros. Usando a economia brasileira como estudo de caso, argui-se que o sucesso em aumentar a taxa de poupança tem sua origem na reforma fiscal que acompanhou o processo de reforma do sistema financeiro que procurou liberar as taxas de juros de controles administrativos. Dois tipos de exercícios econométricos são realizados para estudar a sensibilidade da poupança a mudanças na taxa de juros real esperada. O primeiro exercício faz uso de uma função de poupança clássica para avaliar a magnitude da elasticidade da poupança em relação a taxa de juros. O segundo teste aborda o problema através da equação de Euler e mede a taxa de substituição intertemporal do consumo. Os resultados obtidos em ambas as seções mostram que o efeito da taxa de juros real sobre a poupança agregada privada é negligível. Estes resultados tem implicações profundas para os programas de estabilização e de reforma estrutural pois contradizem a hipótese comportamental fundamental subjacente à política de poupança recomendada para os países em desenvolvimento por organizações internacional tais como o Banco Mundial e o FMI