Application of dynamical Lie algebraic method to atom-diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational-vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom-anharmonic oscillator scattering.

Qualitative Analysis of MOS Circuits

With the push towards sub-micron technology, transistor models have become increasingly complex. The number of components in integrated circuits has forced designer's efforts and skills towards higher levels of design. This has created a gap between design expertise and the performance demands increasingly imposed by the technology. To alleviate this problem, software tools must be developed that provide the designer with expert advice on circuit performance and design. This requires a theory that links the intuitions of an expert circuit analyst with the corresponding principles of formal theory (i.e. algebra, calculus, feedback analysis, network theory, and electrodynamics), and that makes each underlying assumption explicit.

Natural Language Input for a Computer Problem Solving System

The STUDENT problem solving system, programmed in LISP, accepts as input a comfortable but restricted subset of English which can express a wide variety of algebra story problems. STUDENT finds the solution to a large class of these problems. STUDENT can utilize a store of global information not specific to any one problem, and may make assumptions about the interpretation of ambiguities in the wording of the problem being solved. If it uses such information or makes any assumptions, STUDENT communicates this fact to the user. The thesis includes a summary of other English language questions-answering systems. All these systems, and STUDENT, are evaluated according to four standard criteria. The linguistic analysis in STUDENT is a first approximation to the analytic portion of a semantic theory of discourse outlined in the thesis. STUDENT finds the set of kernel sentences which are the base of the input discourse, and transforms this sequence of kernel sentences into a set of simultaneous equations which form the semantic base of the STUDENT system. STUDENT then tries to solve this set of equations for the values of requested unknowns. If it is successful it gives the answers in English. If not, STUDENT asks the user for more information, and indicates the nature of the desired information. The STUDENT system is a first step toward natural language communication with computers. Further work on the semantic theory proposed should result in much more sophisticated systems.

Zoneamento agroecológico do Município de Aquidauana - MS.

A Embrapa Solos, em parceria com a Secretaria de Estado de Desenvolvimento Agrário, da Produção, da Indústria, do Comércio e do Turismo - SEPROTUR, realizou o Zoneamento Agroecológico do Estado do Mato Grosso do Sul - Fase II - com objetivo de contribuir na indicação de áreas passíveis de exploração agrícola sustentável. No desenvolvimento desse trabalho foram considerados aspectos legais, restrições ambientais, potencial das culturas, aspectos do clima, de geomorfologia e dos solos, todos integrados em ambiente de sistema de informação geográfica com apoio de algebra de mapas, no intuito de avaliar a adequabilidade de uso das terras e apresentar uma proposição de planejamento de uso e ocupação das terras. Os foram consolidados por município e dão origem a esse boletim de pesquisa. No município de Aquidauana, as terras indicadas para o uso com lavouras somam cerca de 870 km², o que equivale a aproximadamente 23% da área total do município, sendo que, destas, 92% apresentam declividade inferior a 8%. As áreas recomendadas para pastagem equivalem a 54% e as áreas recomendadas para pastagem especial a aproximadamente 8% da área do município que corresponde a algo como 294 km². Nestas unidades é fundamental avaliar-se criteriosamente a utilização de pastagens nestas terras quando essas ainda se encontram sob cobertura vegetal, visto que, praticamente 40% destas terras ainda permanecem com vegetação natural em seus diversos graus de conservação. As terras recomendadas para conservação dos recursos naturais e/ou recuperação ambiental equivalem a menos de 475 km², as quais constituem áreas de alta fragilidade ambiental e/ou apresentam restrições legais de uso como áreas de preservação permanente. As áreas identificadas como zonas recomendadas para recuperação ambiental equivalem a 112 km² e constituem áreas de moderada a alta fragilidade ambiental e/ou que apresentam restrições legais de uso e que já foram desmatadas para o uso com pastagens/agricultura. Desconsiderando as terras de Pantanal, a área do município de Aquidauana apresenta um alto grau de ação antrópica das terras, onde mais de 75% das terras sendo utilizadas com pastagens e/ou com agricultura, enquanto que apenas 25% ainda apresentam certo grau de preservação.

Zoneamento agroecológico do Município de Anastácio - MS.

A Embrapa Solos, em parceria com a Secretaria de Estado de Desenvolvimento Agrário, da Produção, da Indústria, do Comércio e do Turismo - SEPROTUR, realizou o Zoneamento Agroecológico do Estado do Mato Grosso do Sul - Fase II - com objetivo de contribuir na indicação de áreas passíveis de exploração agrícola sustentável. No desenvolvimento desse trabalho foram considerados aspectos legais, restrições ambientais, potencial das culturas, aspectos do clima, de geomorfologia e dos solos, todos integrados em ambiente de sistema de informação geográfica com apoio de algebra de mapas, no intuito de avaliar a adequabilidade de uso das terras e apresentar uma proposição de planejamento de uso e ocupação das terras. Os resultados foram consolidados por município e dão origem a esse boletim de pesquisa. No município de Anastácio, as terras indicadas para o uso com lavouras somam 1.425 km², o que equivale a aproximadamente 50% da área total do município, enquanto que as recomendadas para pastagem equivalem a 26,5% e as áreas recomendadas para pastagem especial ou cultivo de arroz correspondem a cerca de 20% da área do município que corresponde a algo como 578 km². Nestas unidades é fundamental avaliar criteriosamente a utilização de pastagens nestas terras quando essas ainda se encontram sob cobertura vegetal, visto que, praticamente 20% destas terras ainda permanecem com vegetação natural em seus diversos graus de conservação. As terras recomendadas para conservação dos recursos naturais equivalem a menos de 80 km², as quais constituem áreas de alta fragilidade ambiental e/ ou apresentam restrições legais de uso como áreas de preservação permanente. As áreas identificadas como zonas recomendadas para recuperação ambiental equivalem a 80 km² e constituem áreas de moderada a alta fragilidade ambiental e/ou que apresentam restrições legais de uso e que já foram desmatadas para o uso com pastagens/agricultura. A área do município de Anastácio apresenta alto grau de ação antrópica das terras, onde mais de 75% das terras sendo utilizadas com pastagens e/ou com agricultura, enquanto que apenas 25% ainda apresentam certo grau de preservação.

Zoneamento agroecológico do Município de Coxim - MS.

A Embrapa Solos, em parceria com a Secretaria de Estado de Desenvolvimento Agrário, da Produção, da Indústria, do Comércio e do Turismo - SEPROTUR, realizou o Zoneamento Agroecológico do Estado do Mato Grosso do Sul - Fase II - com objetivo de contribuir na indicação de áreas passíveis de exploração agrícola sustentável. No desenvolvimento desse trabalho foram considerados aspectos legais, restrições ambientais, potencial das culturas, aspectos do clima, de geomorfologia e dos solos, todos integrados em ambiente de sistema de informação geográfica com apoio de algebra de mapas, no intuito de avaliar a adequabilidade de uso das terras e apresentar uma proposição de planejamento de uso e ocupação das terras. As terras indicadas para o uso com lavouras somam cerca de 1.040 km², o que equivale a aproximadamente 16% da área total zoneada. As áreas recomendadas para pastagem equivalem a 47% e as áreas recomendadas para pastagem especial a menos de 1,5% da área do município que corresponde a algo como 80 km². Nestas unidades é fundamental avaliar criteriosamente a utilização de pastagens nestas terras quando essas ainda se encontram sob cobertura vegetal, visto que, praticamente 82% destas terras ainda permanecem com vegetação natural em seus diversos graus de conservação. As terras recomendadas para conservação dos recursos naturais e/ou recuperação ambiental equivalem a 210 km², as quais constituem áreas de alta fragilidade ambiental e/ou apresentam restrições legais de uso como áreas de preservação permanente. As áreas identificadas como zonas recomendadas para recuperação ambiental equivalem a 123 km² e constituem áreas de moderada a alta fragilidade ambiental e/ou que apresentam restrições legais de uso e que já foram desmatadas para o uso com pastagens/agricultura. O do município de Coxim apresenta um alto grau de ação antrópica das terras, onde cerca de 60% das terras são utilizadas com pastagens e/ou com agricultura, enquanto que apenas 40% ainda apresentam certo grau de preservação. O município de Coxim apresenta um bom potencial para o desenvolvimento da agropecuária, porém, devidos às características edafoclimáticas e de topografia, a recomendação preferencial é a utilização com pastagens.

A probabilistic index for completely positive maps and an application

Gohm, Rolf, (2003) 'A probabilistic index for completely positive maps and an application', Journal of Operator Theory 54(2) pp.339-361 RAE2008

The ‘Faust’ or ’Lucifer’ Sonata? On Liszt’s idea of programme music as exemplifi ed by his Piano Sonata in B minor

The musicological tradition places Liszt’s Sonata in B minor within the sphere of compositions inspired by the Faustian myth. Its musical material, its structure and its narrative exhibit certain similarities to the ‘Faust’ Symphony. Yet there has appeared a diff erent and, one may say, a rival interpretation of Sonata in B minor. What is more, it is well-documented from both a musical and a historical point of view. It has been presented by Hungarian pianist and musicologist Tibor Szász. He proposes the thesis that the Sonata in B minor has been in fact inspired by Milton’s Paradise Lost, with its three protagonists: Adam, Satan and Christ. He fi nds their illustrations and even some key elements of the plot in the Sonata’s narrative. But yet Milton’s Paradise Lost and Goethe’s Faust are both stories of the Fall and Salvation, of the cosmic struggle between good and evil. The triads of their protagonists – Adam and Eve, Satan, and Christ; Faust, Mephisto and Gretchen – are homological. Thus both interpretations of the Sonata, the Goethean and the Miltonian, or, in other words, the Faustian and the Luciferian, are parallel and complementary rather than rival. It is also highly probable that both have had their impact on the genesis of the Sonata in B minor.

Systematic Verification of Safety Properties of Arbitrary Network Protocol Compositions Using CHAIN

Formal correctness of complex multi-party network protocols can be difficult to verify. While models of specific fixed compositions of agents can be checked against design constraints, protocols which lend themselves to arbitrarily many compositions of agents-such as the chaining of proxies or the peering of routers-are more difficult to verify because they represent potentially infinite state spaces and may exhibit emergent behaviors which may not materialize under particular fixed compositions. We address this challenge by developing an algebraic approach that enables us to reduce arbitrary compositions of network agents into a behaviorally-equivalent (with respect to some correctness property) compact, canonical representation, which is amenable to mechanical verification. Our approach consists of an algebra and a set of property-preserving rewrite rules for the Canonical Homomorphic Abstraction of Infinite Network protocol compositions (CHAIN). Using CHAIN, an expression over our algebra (i.e., a set of configurations of network protocol agents) can be reduced to another behaviorally-equivalent expression (i.e., a smaller set of configurations). Repeated applications of such rewrite rules produces a canonical expression which can be checked mechanically. We demonstrate our approach by characterizing deadlock-prone configurations of HTTP agents, as well as establishing useful properties of an overlay protocol for scheduling MPEG frames, and of a protocol for Web intra-cache consistency.

Type Inference for Variant Object Types

Existing type systems for object calculi are based on invariant subtyping. Subtyping invariance is required for soundness of static typing in the presence of method overrides, but it is often in the way of the expressive power of the type system. Flexibility of static typing can be recovered in different ways: in first-order systems, by the adoption of object types with variance annotations, in second-order systems by resorting to Self types. Type inference is known to be P-complete for first-order systems of finite and recursive object types, and NP-complete for a restricted version of Self types. The complexity of type inference for systems with variance annotations is yet unknown. This paper presents a new object type system based on the notion of Split types, a form of object types where every method is assigned two types, namely, an update type and a select type. The subtyping relation that arises for Split types is variant and, as a result, subtyping can be performed both in width and in depth. The new type system generalizes all the existing first-order type systems for objects, including systems based on variance annotations. Interestingly, the additional expressive power does not affect the complexity of the type inference problem, as we show by presenting an O(n^3) inference algorithm.

The abelianization of the Johnson kernel

We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym H 1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of G. In this setup, we also obtain a precise nilpotence test. © European Mathematical Society 2014.

Consistent deformations of [p,p]-type gauge field theories

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p > 1. Under the assumptions of locality and Poincaré invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term. © SISSA/ISAS 2004.

No self-interaction for two-column massless fields

We investigate the problem of introducing consistent self-couplings in free theories for mixed tensor gauge fields whose symmetry properties are characterized by Young diagrams made of two columns of arbitrary (but different) lengths. We prove that, in flat space, these theories admit no local, Poincaré-invariant, smooth, selfinteracting deformation with at most two derivatives in the Lagrangian. Relaxing the derivative and Lorentz-invariance assumptions, there still is no deformation that modifies the gauge algebra, and in most cases no deformation that alters the gauge transformations. Our approach is based on a Becchi-Rouet-Stora-iyutin (BRST) -cohomology deformation procedure. © 2005 American Institute of Physics.

Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension 3$">n>3. Under the sole assumptions of Poincaré and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions 4$">n>4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed. © SISSA 2006.