946 resultados para Fundamentals in linear algebra


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Some atomic multipoles (charges, dipoles and quadrupoles) from the Quantum Theory of Atoms in Molecules (QTAIM) and CHELPG charges are used to investigate interactions between a proton and a molecule (F2, Cl2, BF, AlF, BeO, MgO, LiH, H2CO, NH3, PH3, BF3, and CO2). Calculations were done at the B3LYP/6-311G(3d,3p) level. The main aspect of this work is the investigation of polarization effects over electrostatic potentials and atomic multipoles along a medium to long range of interaction distances. Large electronic charge fluxes and polarization changes are induced by a proton mainly when this positive particle approaches the least electronegative atom of diatomic heteronuclear molecules. The search for simple equations to describe polarization on electrostatic potentials from QTAIM quantities resulted in linear relations with r-4 (r is the interaction distance) for many cases. Moreover, the contribution from atomic dipoles to these potentials is usually the most affected contribution by polarization what reinforces the need for these dipoles to a minimal description of purely electrostatic interactions. Finally, CHELPG charges provide a description of polarization effects on electrostatic potentials that is in disagreement with physical arguments for certain of these molecules. (c) 2012 Wiley Periodicals, Inc.

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Objective: To estimate the frequency of anaemia in pregnant women before and after the fortification of flours with Fe. Design: Retrospective study developed from secondary data obtained from medical records. Setting: Two health units in Rio de Janeiro, Brazil. Subjects: Socio-economic, demographic, obstetric and Hb concentration data were collected of 778 pregnant women attending prenatal care. Two study groups were created: the first referred to the period before fortification (G1, n 391), including women whose parturition happened before June 2004; and the second referred to the period after fortification (G2, n 387), including women whose last menstrual cycle happened after June 2005. The Hb cut-off point adopted for anaemia diagnosis was <11.0 g/dl. Results: In linear regression models, when Hb concentration was expressed as a dependent variable, women in G2 presented Hb concentration 0.26 g/dl and 0.36 g/dl higher during the second and third trimesters of pregnancy, respectively, compared with G1. In logistic regression models where the dependent variable was anaemia during the second and third trimesters, it was verified that being a member of G2 was a protective factor against anaemia in the third trimester. Regarding the presence of anaemia at any gestational moment, it was verified that being a member of G2 represented a protective factor against anaemia during pregnancy. Conclusions: Results indicate the protective effect of the fortification of flours with Fe in the fight against gestational anaemia, contributing to prevention and control of this nutritional disorder among pregnant women.

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A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved.

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Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous statement for semilinear operators. (C) 2011 Elsevier Inc. All rights reserved.

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This research aimed to describe the macroscopic and microscopic liver of tambaqui, Colossoma macropomum, Teleost freshwater Family Characidae, of great economic interest for the Amazon basin. We used six juveniles aged between six month and one year, from the small holding Esteio, Alta Floresta/MT, that develops mainly fish farming. The body was photographed in situ, described macroscopically, and fragments were removed and processed by routine histological techniques through paraffin embedding and HE staining. The liver, located ventrally to the swim bladder and craniodorsally to the stomach, is brownish red and consisted of three lobes, the right lateral, the left lateral and the ventral lobe. Microscopically, the parenchyma consists of hepatocytes varying from irregular rounded hexagonal to round forms with a large and central nucleus, and arranged in linear strings limited by sinusoids and radiating to central veins, but with absence of liver lobules. The central veins are distributed throughout the parenchyma, while the portal space consists in most cases only of a hepatic vein and bile duct; elsewhere exist artery and duct. Formation of portal triads was not founde. Melano macrophages were frequently seen dispersed throughout the central parenchyma. The morphofunctional study of the digestive system of fishes of the Amazon basin is important to obtain knowledge about their weight gain, large scale production for human consumption and preservation of the species, and has also its importance for being used as bioindicators today.

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Because of its electronic properties, sulfur plays a major role in a variety of metabolic processes and, more in general, in the chemistry of life. In particular, S-S bridges between cysteines are present in the amino acid backbone of proteins. Protein disulfur radical anions may decay following different paths through competing intra and intermolecular routes, including bond cleavage, disproportionation, protein-protein cross linking, and electron transfer. Indeed, mass spectrometry ECD (electron capture dissociation massspectroscopy) studies have shown that capture of low-energy (<0.2 eV) electrons by multiply protonated proteins is followed by dissociation of S-S bonds holding two peptide chains together. In view of the importance of organic sulfur chemistry, we report on electron interactions with disulphide bridges. To study these interactions we used as prototypes the molecules dimethyl sulfide [(CH3)2S] and dimethyl disulfide [(H3C)S2(CH3)]. We seek to better understand the electron-induced cleavage of the disulfide bond. To explore dissociative processes we performed electron scattering calculations with the Schwinger Multichannel Method with pseudopotentials (SMCPP), recently parallelized with OpenMP directives and optimized with subroutines for linear algebra (BLAS) and LAPACK routines. Elastic cross sections obtained for different S-S bond lengths indicate stabilization of the anion formed by electron attachment to a σ*SS antibonding orbital, such that dissociation would be expected.

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In linearen Paulfallen gespeicherte und lasergekühlte Ionen stellen in weiten Bereichen der Physik ideale Objekte hinsichtlich störungsfreier und präziser Messungen atomarer Übergangsfrequenzen und der gezielten Manipulation von Quantenzuständen dar. Eine Einschränkung dieser optimalen Bedingungen erfolgt durch Heizmechanismen, die aus Abweichungen des Speicherpotentials von der idealen Quadrupolform resultieren. Höhere Potentialordnungen führen zu einer Kopplung der radialen Bewegungsmoden und bei bestimmten Speicherparametern zu nichtlinearen Resonanzen. Hierbei werden die Ionenbahnen durch eine Energieaufnahme aus dem Speicherfeld destabilisiert. Dieses kann zu Linienverbreiterungen, einer Limitierung der Kohärenzzeiten und unter Umständen zu einem Ionenverlust führen. Die systematische Untersuchung dieser Instabilitäten in einer linearen Paulfalle erfolgt durch Spektroskopie an einer kleinen Anzahl lasergekühlter ^40Ca^+ - Ionen. Der experimentell zugängliche Speicherbereich wird mit hoher Auflösung abgetastet. Durch eine eingehende Quantifizierung der Falleneigenschaften werden die nichtlinearen Resonanzen eindeutig den erzeugenden Potentialtermen zugeordnet. Die Resonanzlinien zeigen eine charakteristische Aufspaltung, deren Größe vom angelegten Axialpotential bestimmt wird. Diese zusätzliche Kopplung der Radialbewegung an die Axialbewegung führt zu einer modifizierten Resonanzbedingung. Nichtlineare Resonanzen treten massenspezifisch auf. Da eine präzise Kontrolle der Axialpotentiale sehr einfach ist, könnten die beobachteten radial-axial koppelnden Resonanzen eine Anwendung in der Massenspektrometrie finden.

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The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

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Fluorescence correlation spectroscopy (FCS) is a powerful technique to determine the diffusion of fluorescence molecules in various environments. The technique is based on detecting and analyzing the fluctuation of fluorescence light emitted by fluorescence species diffusing through a small and fixed observation volume, formed by a laser focused into the sample. Because of its great potential and high versatility in addressing the diffusion and transport properties in complex systems, FCS has been successfully applied to a great variety of systems. In my thesis, I focused on the application of FCS to study the diffusion of fluorescence molecules in organic environments, especially in polymer melts. In order to examine our FCS setup and a developed measurement protocol, I first utilized FCS to measure tracer diffusion in polystyrene (PS) solutions, for which abundance data exist in the literature. I studied molecular and polymeric tracer diffusion in polystyrene solutions over a broad range of concentrations and different tracer and matrix molecular weights (Mw). Then FCS was further established to study tracer dynamics in polymer melts. In this part I investigated the diffusion of molecular tracers in linear flexible polymer melts [polydimethylsiloxane (PDMS), polyisoprene (PI)], a miscible polymer blend [PI and poly vinyl ethylene (PVE)], and star-shaped polymer [3-arm star polyisoprene (SPI)]. The effects of tracer sizes, polymer Mw, polymer types, and temperature on the diffusion coefficients of small tracers were discussed. The distinct topology of the host polymer, i.e. star polymer melt, revealed the notably different motion of the small tracer, as compared to its linear counterpart. Finally, I emphasized the advantage of the small observation volume which allowed FCS to investigate the tracer diffusions in heterogeneous systems; a swollen cross-linked PS bead and silica inverse opals, where high spatial resolution technique was required.

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A permutation is said to avoid a pattern if it does not contain any subsequence which is order-isomorphic to it. Donald Knuth, in the first volume of his celebrated book "The art of Computer Programming", observed that the permutations that can be computed (or, equivalently, sorted) by some particular data structures can be characterized in terms of pattern avoidance. In more recent years, the topic was reopened several times, while often in terms of sortable permutations rather than computable ones. The idea to sort permutations by using one of Knuth’s devices suggests to look for a deterministic procedure that decides, in linear time, if there exists a sequence of operations which is able to convert a given permutation into the identical one. In this thesis we show that, for the stack and the restricted deques, there exists an unique way to implement such a procedure. Moreover, we use these sorting procedures to create new sorting algorithms, and we prove some unexpected commutation properties between these procedures and the base step of bubblesort. We also show that the permutations that can be sorted by a combination of the base steps of bubblesort and its dual can be expressed, once again, in terms of pattern avoidance. In the final chapter we give an alternative proof of some enumerative results, in particular for the classes of permutations that can be sorted by the two restricted deques. It is well-known that the permutations that can be sorted through a restricted deque are counted by the Schrӧder numbers. In the thesis, we show how the deterministic sorting procedures yield a bijection between sortable permutations and Schrӧder paths.

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Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

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In the recent years, for oral care in general, both improving oral hygiene and tobacco use cessation have been identified as necessary measures to gain and maintain long-term periodontal health. This growing evidence has given the dental team a whole new task to tackle when achieving and maintaining oral health with their patients. In order to support dental patients to quit tobacco use, it is helpful for the clinician to have a clear understanding of the genesis of 'tobacco use disease' in general. At present, the evidence-based method for tobacco use cessation consists of professional counselling on behavioural change using the so called "5A Method" (Ask, Advise, Assess, Assist and Arrange") in combination with pharmacotherapy. A suitable model for behavioural support in tobacco use cessation would help patients to move from one stage to the next. People who want to quit the smoking habit do not always participate in carefully controlled nicotine withdrawal programs, e.g. in linear fashion and from start to finish. Nevertheless, simple instructions - like those offered in the "Assist" (to help) and "Arrange" (to organize follow-up visits) - can be valuable tools for dental professionals supporting their patients to quit smoking. On the basis of significant evidence on the recovery of the oral mucosa and the periodontal tissue following tobacco use cessation, a new task has been emerged in dentistry: the role of oral health professionals providing counselling for patients who ought to quit tobacco use.

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Subjective quality of life (SQOL) is an important outcome in the treatment of patients with schizophrenia. However, there is only limited evidence on factors influencing SQOL, and little is known about whether the same factors influence SQOL in patients with schizophrenia and other mental disorders. This study aimed to identify the factors associated with SQOL and test whether these factors are equally important in schizophrenia and other disorders. For this we used a pooled data set obtained from 16 studies that had used either the Lancashire Quality of Life Profile or the Manchester Short Assessment of Quality of Life for assessing SQOL. The sample comprised 3936 patients with schizophrenia, mood disorders, and neurotic disorders. After controlling for confounding factors, within-subject clustering, and heterogeneity of findings across studies in linear mixed models, patients with schizophrenia had more favourable SQOL scores than those with mood and neurotic disorders. In all diagnostic groups, older patients, those in employment, and those with lower symptom scores had higher SQOL scores. Whilst the strength of the association between age and SQOL did not differ across diagnostic groups, symptom levels were more strongly associated with SQOL in neurotic than in mood disorders and schizophrenia. The association of employment and SQOL was stronger in mood and neurotic disorders than in schizophrenia. The findings may inform the use and interpretation of SQOL data for patients with schizophrenia.

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Little is known about the magnetic resonance imaging (MRI) appearance of canine meniscal lesions. The aim of this study is to describe the MR appearance of meniscal lesions in dogs with experimentally induced cranial cruciate ligament (CCL) deficiency. The pilot study revealed dogs weighing approximately 10 kg to be too small for meniscal evaluation on low-field MRI. In the main study, dogs weighing approximately 35 kg were used. The left CCL was transected and low-field MRI was performed regularly until 13 months post-surgery. Normal menisci were defined as grade 0. Intrameniscal lesions not reaching any surface corresponded to grade 1 if focal and to grade 2 if linear or diffuse. Grade 3 lesions consisted in linear tears penetrating a meniscal surface. Grade 4 lesions included complex signal changes or meniscal distortion. Between 2 and 13 months post-surgery, all dogs developed grade 4 lesions in the medial meniscus. Most of them corresponded to longitudinal or bucket handle tears on arthroscopy and necropsy. Two dogs showed grade 3 lesions reaching the tibial surface of the lateral meniscus on MRI but not in arthroscopy. Such tears are difficult to evaluate arthroscopically; MRI provides more accurate information about the tibial meniscal surface. Grades 1 and 2 lesions could not be differentiated from presumably normal menisci with our imaging technique. An MRI grading system better adapted to canine lesions has yet to be developed. MRI is a helpful tool for the diagnosis of complete tears in the canine meniscus, especially in larger dogs.