Inductive Theorem Proving and Computer Algebra in the Mathweb Software Bus

Reasoning systems have reached a high degree of maturity in the last decade. However, even the most successful systems are usually not general purpose problem solvers but are typically specialised on problems in a certain domain. The MathWeb SOftware Bus (Mathweb-SB) is a system for combining reasoning specialists via a common osftware bus. We described the integration of the lambda-clam systems, a reasoning specialist for proofs by induction, into the MathWeb-SB. Due to this integration, lambda-clam now offers its theorem proving expertise to other systems in the MathWeb-SB. On the other hand, lambda-clam can use the services of any reasoning specialist already integrated. We focus on the latter and describe first experimnents on proving theorems by induction using the computational power of the MAPLE system within lambda-clam.

An Afriat theorem for the collective model of household consumption

We provide a nonparametric 'revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and sufficient condition for data consistency with collective rationality. Our main result takes the form of a ‘collective’ version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

“Unintended effects”: A theorem for complex systems

Unintended effects are well known to economists and sociologists and their consequences may be devastating. The main objective of this article is to formulate a mathematical theorem, based on Gödel's famous incompleteness theorem, in which it is shown, that from the moment deontical modalities (prohibition, obligation, permission, and faculty) are introduced into the social system, responses are allowed by the system that are not produced, however, prohibited responses or unintended effects may occur.

A structural theorem for co-commutative Hopf algebras

Lo scopo di questa tesi è studiare alcune proprietà di base delle algebre di Hopf, strutture algebriche emerse intorno agli anni ’50 dalla topologica algebrica e dalla teoria dei gruppi algebrici, e mostrare un collegamento tra esse e le algebre di Lie. Il primo capitolo è un’introduzione basilare al concetto di prodotto tensoriale di spazi vettoriali, che verrà utilizzato nel secondo capitolo per definire le strutture di algebra, co-algebra e bi-algebra. Il terzo capitolo introduce le definizioni e alcune proprietà di base delle algebre di Hopf e di Lie, con particolare attenzione al legame tra le prime e l’algebra universale inviluppante di un’algebra di Lie. Questo legame sarà approfondito nel quarto capitolo, dedicato allo studio di una particolare classe di algebre di Hopf, quelle graduate e connesse, che terminerà con il teorema di Cartier-Quillen-Milnor-Moore, un teorema strutturale che fornisce condizioni sufficienti affinché un’algebra di Hopf sia isomorfa all’algebra universale inviluppante dei suoi elementi primitivi.

Phylogenetics, Ancestral State Reconstruction, And A New Infrafamilial Classification Of The Pantropical Ochnaceae (medusagynaceae, Ochnaceae S.str., Quiinaceae) Based On Five Dna Regions.

Ochnaceae s.str. (Malpighiales) are a pantropical family of about 500 species and 27 genera of almost exclusively woody plants. Infrafamilial classification and relationships have been controversial partially due to the lack of a robust phylogenetic framework. Including all genera except Indosinia and Perissocarpa and DNA sequence data for five DNA regions (ITS, matK, ndhF, rbcL, trnL-F), we provide for the first time a nearly complete molecular phylogenetic analysis of Ochnaceae s.l. resolving most of the phylogenetic backbone of the family. Based on this, we present a new classification of Ochnaceae s.l., with Medusagynoideae and Quiinoideae included as subfamilies and the former subfamilies Ochnoideae and Sauvagesioideae recognized at the rank of tribe. Our data support a monophyletic Ochneae, but Sauvagesieae in the traditional circumscription is paraphyletic because Testulea emerges as sister to the rest of Ochnoideae, and the next clade shows Luxemburgia+Philacra as sister group to the remaining Ochnoideae. To avoid paraphyly, we classify Luxemburgieae and Testuleeae as new tribes. The African genus Lophira, which has switched between subfamilies (here tribes) in past classifications, emerges as sister to all other Ochneae. Thus, endosperm-free seeds and ovules with partly to completely united integuments (resulting in an apparently single integument) are characters that unite all members of that tribe. The relationships within its largest clade, Ochnineae (former Ochneae), are poorly resolved, but former Ochninae (Brackenridgea, Ochna) are polyphyletic. Within Sauvagesieae, the genus Sauvagesia in its broad circumscription is polyphyletic as Sauvagesia serrata is sister to a clade of Adenarake, Sauvagesia spp., and three other genera. Within Quiinoideae, in contrast to former phylogenetic hypotheses, Lacunaria and Touroulia form a clade that is sister to Quiina. Bayesian ancestral state reconstructions showed that zygomorphic flowers with adaptations to buzz-pollination (poricidal anthers), a syncarpous gynoecium (a near-apocarpous gynoecium evolved independently in Quiinoideae and Ochninae), numerous ovules, septicidal capsules, and winged seeds with endosperm are the ancestral condition in Ochnoideae. Although in some lineages poricidal anthers were lost secondarily, the evolution of poricidal superstructures secured the maintenance of buzz-pollination in some of these genera, indicating a strong selective pressure on keeping that specialized pollination system.

Fundamentos geometricos e algebricos da calibração e reconstrução tridimensional : aplicação na analise cinematica de movimentos humanos

Universidade Estadual de Campinas . Faculdade de Educação Física

Efeitos do aparelho Jasper Jumper no tratamento da má oclusão de Classe II

OBJETIVO: o objetivo deste estudo foi avaliar os efeitos esqueléticos e dentoalveolares do tratamento de pacientes com má oclusão de Classe II com o aparelho Jasper Jumper associado ao aparelho ortodôntico fixo, comparados a um grupo controle não-tratado. MÉTODOS: a amostra foi constituída por 47 indivíduos, divididos em dois grupos: Grupo 1, contendo 25 pacientes com idade média de 12,72 anos, tratados com o aparelho Jasper Jumper por um tempo médio de 2,15 anos; Grupo 2 (controle), composto por 22 indivíduos com idade média de 12,67 anos, não-submetidos a tratamento ortodôntico e com má oclusão de Classe II, observados por um período médio de 2,12 anos. Foram avaliadas as telerradiografias ao início e ao final do tratamento ortodôntico para o Grupo 1 e do período de observação para o Grupo 2. As variáveis cefalométricas iniciais, finais e as alterações com o tratamento foram comparadas entre os grupos por meio do teste t independente. RESULTADOS: em comparação ao grupo controle, o grupo Jasper Jumper apresentou maior restrição do deslocamento anterior da maxila e maior retrusão maxilar, melhora da relação maxilomandibular, diminuição da convexidade facial, maior protrusão e intrusão dos incisivos inferiores e maior extrusão dos molares inferiores, além de maior diminuição dos trespasses horizontal e vertical e maior melhora da relação molar. CONCLUSÃO: a correção da Classe II no grupo tratado com o Jasper Jumper e aparelhagem fixa se deu principalmente devido à restrição do crescimento maxilar, protrusão e intrusão dos incisivos inferiores e extrusão dos molares inferiores.

Avaliação dos fatores determinantes da estética do perfil facial

OBJETIVO: avaliar a influência da idade, do sexo, da relação oclusal sagital, do Padrão Facial e de 8 medidas do perfil facial sobre a estética do perfil. MÉTODOS: foram utilizadas tabelas de contingência, o Teste Qui-quadrado e o coeficiente de Cramér para avaliar a possível associação entre a nota dada por 32 avaliadores (14 ortodontistas, 12 leigos e 6 artistas) para a estética do perfil de 100 brasileiros - adultos, leucodermas, portadores de selamento labial passivo - e a idade, o sexo, a relação oclusal sagital, o Padrão Facial e as variáveis da análise facial numérica do perfil. RESULTADOS: não foi observada associação entre a idade, o sexo e a relação oclusal sagital e a estética do perfil facial. A associação foi observada entre a nota recebida para a estética do perfil e o Padrão Facial, o ângulo de convexidade facial e o ângulo do terço inferior da face. CONCLUSÃO: o Padrão Facial, definido na avaliação do perfil pela convexidade do perfil facial, e a projeção anterior do mento foram, entre os fatores avaliados, os determinantes para a estética do perfil facial.

Estudo das características cefalométricas em adolescentes brasileiros portadores de Padrão Face Longa

OBJETIVO: definir valores cefalométricos esqueléticos e dentários para adolescentes brasileiros com Padrão Face Longa. MÉTODOS: a amostra foi constituída de telerradiografias em norma lateral de 30 pacientes com Face Longa, sendo 17 do sexo feminino e 13 do masculino; e 30 pacientes face Padrão I, 15 do sexo masculino e 15 do feminino, no estágio de dentadura permanente durante a adolescência. As características do Padrão Face Longa foram definidas clinicamente, pela análise facial. As seguintes grandezas cefalométricas foram avaliadas: (1) Comportamento sagital das bases apicais (SNA, SNB, ANB, NAP, Co-A, Co-Gn); (2) Comportamento vertical das bases apicais (SN.PP, SN.PM, ângulo goníaco, AFAT, AFAI, AFAM, AFP, AFATperp, AFAIperp); (3) Comportamento dentoalveolar (1-PP, 6-PP, 1-PM, 6-PM, 1.PP, IMPA); e (4) Proporção entre as alturas faciais (AFAIPerp/AFATPerp, AFAI/AFAT, AFAM/AFAI). RESULTADOS E CONCLUSÕES: o erro vertical na Face Longa concentra-se no terço inferior. A maxila apresenta uma maior altura dentoalveolar e a mandíbula, com morfologia mais vertical, mostra maior rotação no sentido horário. Essas características morfológicas e espaciais acarretam alterações sagitais e verticais no esqueleto e alterações verticais dentoalveolares. No sentido sagital, os ângulos de convexidade facial estão aumentados. No sentido vertical, as alturas faciais anteriores total e inferior estão aumentadas. O componente dentoalveolar está mais longo.

Entropia, reversibilidade, irreversibilidade, equação de transporte e teorema H de Boltzmann e o teorema do retorno de Poincaré

Neste trabalho analisamos as conexões entre entropia, reversibilidade, irreversibilidade, teorema H e equação de transporte de Boltzmann e o teorema de retorno de Poincaré. Estes tópicos são estudados separadamente em muitos artigos e livros, mas não são em geral analisados em conjunto mostrando as relações entre eles como fizemos aqui. Procuramos redigir o artigo didaticamente seguindo um caminho que achamos ser o mais simples possível a fim de tornar o conteúdo acessível aos alunos de graduação de física.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Two dimensional analysis of inflatable structures by the positional FEM

This paper presents a, simple two dimensional frame formulation to deal with structures undergoing large motions due to dynamic actions including very thin inflatable structures, balloons. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions. Velocity, acceleration and strain are achieved directly from positions, not. displacements, characterizing the novelty of the proposed technique. A non-dimensional space is created and the deformation function (change of configuration) is written following two independent mappings from which the strain energy function is written. The classical New-mark equations are used to integrate time. Dumping and non-conservative forces are introduced into the mechanical system by a rheonomic energy function. The final formulation has the advantage of being simple and easy to teach, when compared to classical Counterparts. The behavior of a bench-mark problem (spin-up maneuver) is solved to prove the formulation regarding high circumferential speed applications. Other examples are dedicated to inflatable and very thin structures, in order to test the formulation for further analysis of three dimensional balloons.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.