Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Continuity and discontinuity: illuminating and interlacing the adventures of Viviane and Merlin in the 'Prose Merlin'

La rareté des miniatures consacrées à l'histoire amoureuse de Merlin et Viviane, dont le développement est à la fois épisodique et structuré par le recours au procédé de l'entrelacement, souligne son caractère marginal au sein de la narration. Les artistes et concepteurs de ces ouvrages manifestent une certaine réticence à l'égard d'aventures qui peuvent affecter l'autorité morale de Merlin, même si elles sont étroitement liées à la disparition du personnage et à la clôture du récit.

A sustainable agricultural landscape for Australia: A review of interlacing carbon sequestration, biodiversity and salinity management in agroforestry systems

Transformation of the south-western Australian landscape from deep-rooted woody vegetation systems to shallow-rooted annual cropping systems has resulted in the severe loss of biodiversity and this loss has been exacerbated by rising ground waters that have mobilised stored salts causing extensive dry land salinity. Since the original plant communities were mostly perennial and deep rooted, the model for sustainable agriculture and landscape water management invariably includes deep rooted trees. Commercial forestry is however only economical in higher rainfall (>700 mm yr−1) areas whereas much of the area where biodiversity is threatened has lower rainfall (300–700 mm yr−1). Agroforestry may provide the opportunity to develop new agricultural landscapes that interlace ecosystem services such as carbon mitigation via carbon sequestration and biofuels, biodiversity restoration, watershed management while maintaining food production. Active markets are developing for some of these ecosystem services, however a lack of predictive metrics and the regulatory environment are impeding the adoption of several ecosystem services. Nonetheless, a clear opportunity exists for four major issues – the maintenance of food and fibre production, salinisation, biodiversity decline and climate change mitigation – to be managed at a meaningful scale and a new, sustainable agricultural landscape to be developed.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems Of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.

Patterns, mathematics and culture : the search for symmetry in Azorean sidewalks and traditional crafts

In the hustle and bustle of daily life, how often do we stop to pay attention to the tiny details around us, some of them right beneath our feet? Such is the case of interesting decorative patterns that can be found in squares and sidewalks beautified by the traditional Portuguese pavement. Its most common colors are the black and the white of the basalt and the limestone used; the result is a large variety and richness in patterns. No doubt, it is worth devoting some of our time enjoying the lovely Portuguese pavement, a true worldwide attraction. The interesting patterns found on the Azorean handicrafts are as fascinating and substantial from the cultural point of view. Patterns existing in the sidewalks and crafts can be studied from the mathematical point of view, thus allowing a thorough and rigorous cataloguing of such heritage. The mathematical classification is based on the concept of symmetry, a unifying principle of geometry. Symmetry is a unique tool for helping us relate things that at first glance may appear to have no common ground at all. By interlacing different fields of endeavor, the mathematical approach to sidewalks and crafts is particularly interesting, and an excellent source of inspiration for the development of highly motivated recreational activities. This text is an invitation to visit the nine islands of the Azores and to identify a wide range of patterns, namely rosettes and friezes, by getting to know different arts and crafts and sidewalks.

Molecular Analysis of the PTEN Gene in a Choroidal Schwannoma in the Context of a Hamartomatous Syndrome

Purpose: To investigate the molecular involvement of PTEN, a tumor suppressor gene, in a case of cellular pigmented choroidal Schwannoma in a patient with hamartomatous syndrome due to heterozygous PTEN germline mutation. Methods: Histopathological, immunohistochemical, and electron microscopy analyses were performed by standard procedures. Paraffin-embedded samples of normal and tumor eye tissues were collected and DNA was extracted. A 145 bp region flanking the heterozygous c.406T>C mutation in exon 5 of PTEN was amplified by PCR and sequenced. To evaluate the allelic status of PTEN in the tumor sample, we cloned different PCR products in E. coli using a TA cloning procedure. Results: Histopathology demonstrated a posterior choroidal mass measuring 1.3 x 1.6 x 1.4 cm. The tumor was composed by fascicles of spindle cells with wavy cytoplasm. No Verrocay bodies could be identified. Scattered histiocytes with clear cytoplasm were present. By immunohistochemistry, the cells were expressing S100 and focally Melan A proteins. Pericellular type IV collagen could be demonstrated. Interlacing cytoplasmic processes covered by thick basement membrane could be found by electron microscopy as well as few premelanosomes. Moderate PTEN expression by immunohistochemistry was identified in some cells. As expected, the germline mutation could be detected by DNA sequencing in both the paraffin-embedded normal and tumor eye tissues. Analysis of 33 E. coli colonies bearing clones from the tumor eye tissue DNA surprisingly revealed that most of them contained the PTEN wild-type allele (29 vs. 4, Fisher's test p-value = 0.002). Conclusions: This is the first reported case of choroidal cellular Schwannoma arising in the context of a PTEN hamartomatous syndrome. Allelic analysis of PTEN in the tumor suggests a statistically-significant partial loss of heterozygozity in favor of the wild-type allele. Our findings are in clear contrast with what is usually observed in cancer tissues, for which mutated alleles of tumor suppressor genes are usually brought to homozygosity. Similar results were previously reported in human non-Hodgkin's lymphomas, displaying an overexpression of the wild-type form of the tumor suppressor gene p53. We are in the process of investigating additional DNA derived from other fresh and paraffin-embedded tissues from the patient, in order to gain insights on the molecular bases of PTEN involvement in this rare choroidal Schwannoma.

Capital investments planning and life cycle simulations for the new valves manufacturing facility in Russia

The focus of the research is on the derivation of the valid and reliable performance results regarding establishment and launching of the new full-scale industrial facility, considering the overall current conditions for the project realization in and out of Russia. The study demonstrates the process of the new facility concept development, with following perfor-mance calculation, comparative analyzes conduction, life-cycle simulations, performance indicators derivation and project`s sustainability evaluation. To unite and process the entire input parameters complexity, regards the interlacing between the project`s internal technical and commercial sides on the one hand, and consider all the specifics of the Russian conditions for doing business on the other hand, was developed the unique model for the project`s performance calculation, simulations and results representation. The complete research incorporates all corresponding data to substantiate the assigned facility`s design, sizing and output capacity for high quality and cost efficient ferrous pipe-line accessories manufacturing, as well as, demonstrates that this project could be suc-cessfully realized in current conditions in Russia and highlights the room for significant performance and sustainability improvements based on the indexes of the derived KPIs.

Les sciences sociales devraient-elles être neutres? : le rôle des chercheurs(ses) face à la normativité du discours éthique et politique, de Weber à Putnam.

L'objectif de ce mémoire est de comprendre la neutralité axiologique non pas comme une exigence épistémologique, mais plutôt comme un idéal éducationnel. Max Weber propose une science basée sur la description factuelle, de laquelle on exclut la formulation de jugements de valeur. Pour l'auteur, il est préférable de séparer les jugements descriptifs des jugements évaluatifs dans le but de préserver l'autonomie intellectuelle des étudiants. Comme il serait contraire au principe d'autonomie de laisser le professeur influencer et convaincre ses étudiants, de façon partisane, d'adhérer à certaines thèses normatives, Weber propose un mécanisme pour éviter que le professeur n'influence ses étudiants de manière illégitime. Les critiques contemporaines de la neutralité axiologique, en particulier celles de Sen et Putnam, voient dans le critère de neutralité un rejet de l'entrelacement logique des faits et des valeurs. Ils critiquent la supposée subjectivité des valeurs et, ce faisant, défendent une conception enrichie de la science où les valeurs éthiques sont présentes. Weber n'a jamais défendu qu'il était impossible de mener une analyse à la fois descriptive et normative. Seulement, on doit s'interroger sur les lieux où s'exprime la normativité, et s'assurer que toutes les conditions sont présentes pour qu'une discussion normative tende réellement à l'objectivité.

Inscriptions d’un legs littéraire : analyse comparatiste des inscriptions funéraire et amoureuse dans Premier amour de Samuel Beckett

L'œuvre à l'étude dans cet essai est la nouvelle intitulée Premier Amour de Samuel Beckett. À travers l'analyse de deux mises en scène de l’acte d'inscription présentes dans cette courte fiction, ce mémoire traite de la question que nous posent les inscriptions lorsque nous les lisons et lorsque nous les inscrivons. Il se divise donc en deux chapitres : le premier déploie l'étude de l'inscription linguistique en tant qu'inscription visible et lisible; le second se concentre sur l'inscription en tant qu'elle est marquée par le concept de legs. En caractérisant et en comparant ces deux inscriptions, d’une part funéraire (l'épitaphe que compose le narrateur pour lui-même suite à la mort de son père) et d’autre part amoureuse (le nom que trace le narrateur au moment où il « tombe amoureux »), ce mémoire expose comment Premier Amour peut être envisagé comme un premier pas dans une compréhension générale de la constitution écrite d'un « legs littéraire ». Surtout, il explicite comment s’orchestre l'imbrication conceptuelle de l’inscription et du legs qu'elle véhicule et présuppose, puisque cette imbrication est inhérente à la compréhension de notre monde et de la littérature. En conclusion, cette étude mène à considérer le rapport conflictuel entre la contemporanéité rêvant d’un monde sans inscriptions et l’inévitabilité de l’inscription.

O sindicalismo e a administração publica

A dissertação aqui apresentada versa sobre uma temática nova, quer vista sob a ótica do nascimento do fato sociológico analisado - O Sindicalismo e a Administração Pública quer se considere a quase inexistência de fontes nas quais se possa abeberar, para que fosse possível estabelecer o fio condutor no desenvolvimento do tema. A temática foi analisada em dois planos: primeiro, fêz-se uma apreciação crítica da história do associativismo no Brasil, em sua simbiose com o aspecto social, com o lado econômico e com o lastro jurídico, ao ser analisado o caminho percorrido desde o primeiro clarão do Brasil até os dias presentes. Em segundo estágio, perquiriu-se a questão sindical, no que diz respeito à sua etiologia, o seu despertar mais consciente na década de 80 do nosso século, perpassando pela criação das Centrais Sindicais, ao serem detectados os desvios ideológicos, as contradições, a sua fisiologia em função de sua organização, ideário e ação na direção do que se propõem em nome de seus afiliados. Com efeito, o núcleo do trabalho se cinge à arregimentação do corpo de funcionários públicos com vistas a um eficaz - hoje, ainda muito incipiente - congraçamento, ao se deparar com uma forte resistência institucional, de vez que só a partir da Constituição de 1988, é que se abriu caminho para o direito de associação sindical a esse estamento dos agentes públicos. As disfunções são, aí, analisadas em relação ao despreparo dos Recursos Humanos no exercício de liderança e em confronto com a estrutura institucional anacrônica e de feitio autoritário, para fazer valer, de forma eficaz e efetiva, um bom desempenho da ação sindical, que se deseja genuína, autônoma e autógena, em função dos interesses de classe e a ter em vista a excelência dos serviços públicos; o fenômeno estudado, inversamente, mostra o processamento de uma luta sindical radicada em estrutura antidemocrática, em que o Estado financia os sindicatos e todo o aparelhamento sindical vertical, via contribuição sindical e a considerar que esse lastro sustentador da luta sindical é decalque de uma época de predominância de valores chauvinistas, exaltados no Brasil - e em outros países -, nas décadas de 30 e 40. Ainda foi feito um estudo comparativo com três modelos de sindicalismo, quais sejam: o francês, o alemão e o português. Os dois primeiros por razões de se constituirem em paradigmas de países centrais, tendo em vista que: (1) a França é modelo inspirador das instituições ocidentais, em sede político-jurídico-social, haja vista a sua História prenhe de fatos solapadores do statu quo ante; e (2) a Alemanha, por ter uma classe eficazmente institucionalizada de agentes públicos, tendo tradição araigada desde a burocracia prussiana, o que dá o toque de elevado profissionalismo a esses agentes públicos, os quais contam com uma agremiação sindical que guarda independência com relação ao movimento sindical do trabalhador privado, este, também consolidado em poderosa organização sindical naquele país. Portugal aparece no trabalho como o ascendente cultural do Brasil, o que implica em ser mostrado o nascedouro sindical desse país, dentro do clima cultural em que viveu e vive a península lusitana, e com isso se tenta elucidar o estágio de seu sindicalismo, as suas disfunções e auto funções , as suas semelhanças com o modelo brasileiro, as suas inclinações e natureza. As conclusões aferidas registram alguns aspectos relevantes: 1º) o Brasil nasceu de uma Administração centralizadora, marcada por uma máquina administrativa ineficaz, ineficiente, com a marca do Estato-império e sem a presença da construção concomitante de uma nação que é retardatária no assentar a viga da cidadania, o que levou a delongar a formação dos anseios e do espírito genuinamente autóctones. A repressão ao desenvolvimento das letras foi um entrave à criação de um espírito de povo, com a variante de ser uma maioria inculta, massacrantemente iletrada, em meio a uma pirâmide social em que se registrava apenas uma base desmesurada e um vértice acanhado, sem ter de permeio outras classes sociais que pudessem ser ou vir a ser estratificadas. Na esteira desses elementos, concluiu-se que: 2º) o movimento associativo é uma realidade incipiente e adormecido durante séculos, o que desbordou em uma apatia que só hoje começa a ser sacudida, através dos movimentos associativistas e sindical, este último nascido no meio das fábricas e estendido a algumas capitais de maior relevância política ou de maior peso econômico. o aspecto de maior magnitude para o trabalho foi a sinalização aberta aos servidores públicos para que se sindicalizassem, do que decorreu a conclusão de que essa ação precisa ser tangenciada e carreada a ser um movimento mais autenticamente ligado aos interesses da classe, pois por desvirtuamento contingencial em face da iniciante pouca expressão e inexperiência desse estamento, a ação sindical desses servidores sempre esteve à ilharga do movimento sindical do trabalhador privado, o qual tem outra linha de ação direcionada a interesses mais ligados ao conflito trabalho vs. capital, interesses esses que não se coadunam e nem se identificam com as aspirações e necessidades do funcionalismo público, mesmo que, muitas vezes, a questão do conflito desses agentes tenha uma interface no conjunto da pauta de reivindicação dos trabalhadores privados, ou seja, a questão salarial. O imperativo maior - e esta é a base da recomendação mais substancial - é conduzir a ação dos agentes públicos de forma heterodoxa na direção de se independentizar o movimento sindical desses agentes, a ser impulsionado pelas suas peculiaridades e por sua essencialidade ditada pela sua ontologia de servidores da coisa pública e tendo o público como sua clientela. Este é, em síntese, o caminho aqui trilhado.

Um olhar estético sobre o telespetáculo esportivo :contribuições para o ensino do esporte na escola

The sportive television spectacle shows up like a media phenomenon which evidence performances and techniques that further on the community realized in the quotidian sportive practices into a show and play mixer, that more and more, sensibility the viewers. In this scenery , this research is about the relation between sportive television spectacle and viewer by the aesthetics perspective, and discussed the sport in the Physical Education context with the focus in the contributions to teaching in the school. The research, to the methodological view, uses the discuss analysis and realizes a qualitative study in two interdependent moments. In the first, analysis the dada collated in the Education, sport and television workshop. In the second, turns about TV images of sportive television spectacle to appreciated, to support a discuss of these phenomenon s aesthetics elements, looking for the relation established between the sportive television spectacle and viewer. The analysis s emphasis is in the sensations by sportive television spectacle, as well in the aesthetic elements problems promoted by this experience, from the two basics concepts, to know: the aesthetic and the synaesthetic perception. The analysis s corpus is composed by Esporte Espetacular TV program. Identify, in the sportive television spectacle appreciation, four big discuss axis of great importance between sportive television spectacle and viewer understanding: the relation space and time, the belonging feeling, the language interlacing, and beauty models. Understand in the analysis that, in the sportive TV scenery, occurs a construction image that seduces and involves the viewer through the aesthetics elements. From that discuss axis reflect about teaching sport in the school, main concern to the materialization a sport model only. Aims unfolding about space and time construction yet, and about the multiplicity language for to work in the school. Positions that no absolute rules, but that check the TV sport by the seduction promoted in the viewers through the aesthetics elements transmit

Stabilizing a class of time delay systems using the Hermite-Biehler theorem

In this paper we use the Hermite-Biehler theorem to establish results for the design of fixed order controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. (C) 2003 Elsevier B.V. All rights reserved.

Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.