Algumas técnicas de construção de alguns poliedros e suas aplicações no ensino

Pós-graduação em Matemática em Rede Nacional - IBILCE

Uma Proposta de utilização de um software educacional para o ensino de poliedros

This paper presents an educational proposal to use an educational software for the teaching of mathematics, following in the conduct of activities, the main aspects of sociocultural theory of Vygotsky. For this, it chose the Poly educational software, with which were developed teaching and learning activities for the polyhedra content provided in the São Paulo State Mathematics curriculum for the 7th year of elementary school. The objectives of this pedagogical proposal are to stimulate situations of social interaction among students and between students and the teacher, using an educational software as a mediator instrument and present a different way of using digital technology in math classes, aiming production of mathematical knowledge

Algumas técnicas de construção de alguns poliedros e suas aplicações no ensino

Pós-graduação em Matemática em Rede Nacional - IBILCE

Synthesis and Characterization of the Europium(III) Pentakis(picrate) Complexes with Imidazolium Countercations: Structural and Photoluminescence Study

Six new lanthanide complexes of stoichiometric formula (C)(2)[Ln(Pic)(5)]-where (C) is a imidazolium cation coming from the ionic liquids 1-butyl-3-methylimidazolium picrate (BMIm-Pic), 1-butyl-3-ethylimidazolium picrate (BEIm-Pic), and 1,3-dibutylimidazolium picrate (BBIm-Pic), and Ln is Eu(III) or Gd(III) ions-have been prepared and characterized. To the best of our knowledge, these are the first cases of Ln(III) pentakis(picrate) complexes. The crystal structures of (BEIm)(2)[Eu(Pic)(5)] and (BBIm)(2)[Eu(Pic)(5)] compounds were determined by single-crystal X-ray diffraction. The [Eu(Pic)(5)](2-) polyhedra have nine oxygen atoms coordinated to the Eu(III) ion, four oxygen atoms from bidentate picrate, and one oxygen atom from monodentate picrate. The structures of the Eu complexes were also calculated using the sparkle model for lanthanide complexes, allowing an analysis of intramolecular energy transfer processes in the coordination compounds. The photoluminescence properties of the Eu(III) complexes were then studied experimentally and theoretically, leading to a rationalization of their emission quantum yields.

Carlosbarbosaite, ideally (UO2)(2)Nb2O6(OH)(2)center dot 2H(2)O, a new hydrated uranyl niobate mineral with tunnels from Jaguaracu, Minas Gerais, Brazil: description and crystal structure

Carlosbarbosaite, ideally (UO2)(2)Nb2O6(OH)(2)center dot 2H(2)O, is a new mineral which occurs as a late cavity filling in albite in the Jaguaracu pegmatite, Jaguaracu municipality, Minas Gerais, Brazil. The name honours Carlos do Prado Barbosa (1917-2003). Carlosbarbosaite forms long flattened lath-like crystals with a very simple orthorhombic morphology. The crystals are elongated along [001] and flattened on (100); they are up to 120 mu m long and 2-5 mu m thick. The colour is cream to pale yellow, the streak yellowish white and the lustre vitreous. The mineral is transparent (as individual crystals) to translucent (massive). It is not fluorescent under either long-wave or short-wave ultraviolet radiation. Carlosbarbosaite is biaxial(+) with alpha = 1.760(5), beta = 1.775(5), gamma = 1.795(5), 2V(meas) = 70(1)degrees, 2V(calc) = 83 degrees. The orientation is X parallel to a, Y parallel to b, Z parallel to c. Pleochroism is weak, in yellowish green shades, which are most intense in the Z direction. Two samples were analysed. For sample I, the composition is: UO3 54.52, CaO 2.07, Ce2O3 0.33, Nd2O3 0.49, Nb2O5 14.11, Ta2O5 15.25, TiO2 2.20, SiO2 2.14, Fe2O3 1.08, Al2O3 0.73, H2O (calc.) 11.49, total 104.41 wt.%; the empirical formula is (square 0.68Ca0.28Nd0.02Ce0.02)(Sigma=1.00)[U-1.44 square O-0.56(2.88)(H2O)(1.12)](Nb0.80Ta0.52Si0.27Ti0.21Al0.11Fe0.10)(Sigma=2.01) O-4.72(OH)(3.20)(H2O)(2.08). For sample 2, the composition is: UO3 41.83, CaO 2.10, Ce2O3 0.31, Nd2O3 1.12, Nb2O5 14.64, Ta2O5 16.34, TiO2 0.95, SiO2 3.55, Fe2O3 0.89, Al2O3 0.71, H2O (calc.) 14.99, total 97.43 wt.%; the empirical formula is (square 0.67Ca0.27Nd0.05Ce0.01)(Sigma=1.00)[U-1.04 square O-0.96(2.08)(H2O)(1.92)] (Nb0.79Ta0.53Si0.42Ti0.08Al0.10Fe0.08)(Sigma=2.00)O-4.00(OH)(3.96)(H2O)(2.04). The ideal endmember formula is (UO2)(2)Nb2O6(OH)(2)center dot 2H(2)O. Calculated densities are 4.713 g cm(-3) (sample 1) and 4.172 g cm(-3) (sample 2). Infrared spectra show that both (OH) and H2O are present. The strongest eight X-ray powder-diffraction lines [listed as d in angstrom(I)(hkl)] are: 8.405(8)(110), 7.081(10)(200), 4.201(9)(220), 3.333(6)(202), 3.053(8)(022), 2.931(7)(420), 2.803(6)(222) and 2.589(5)(040,402). The crystal structure was solved using single-crystal X-ray diffraction (R = 0.037) which gave the following data: orthorhombic, Cmem, a = 14.150(6), b = 10.395(4), c = 7.529(3) angstrom, V = 1107(1) angstrom(3), Z = 4. The crystal structure contains a single U site with an appreciable deficiency in electron scattering, which is populated by U atoms and vacancies. The U site is surrounded by seven 0 atoms in a pentagonal bipyramidal arrangemet. The Nb site is coordinated by four 0 atoms and two OH groups in an octahedral arrangement. The half-occupied tunnel Ca site is coordinated by four 0 atoms and four H2O groups. Octahedrally coordinated Nb polyhedra share edges and comers to form Nb2O6(OH)(2) double chains, and edge-sharing pentagonal bipyramidal U polyhedra form UO5 chains. The Nb2O6(OH)(2) and UO5 chains share edges to form an open U-Nb-phi framework with tunnels along [001] that contain Ca(H2O)(4) clusters. Carlosbarbosaite is closely related to a family of synthetic U-Nb-O framework tunnel structures, it differs in that is has an (OH)-bearing framework and Ca(H2O)(4) tunnel occupant. The structure of carlosbarbosaite resembles that of holfertite.

Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.

Synthesis and Structural Elucidation of Triazolylmolybdenum(VI) Oxide Hybrids and Their Behavior as Oxidation Catalysts

A large family of bifunctional 1,2,4-triazole molecular tectons (tr) has been explored for engineering molybdenum(VI) oxide hybrid solids. Specifically, tr ligands bearing auxiliary basic or acidic groups were of the type amine, pyrazole, 1H-tetrazole, and 1,2,4-triazole. The organically templated molybdenum(VI) oxide solids with the general compositions [MoO3(tr)], [Mo2O6(tr)], and [Mo2O6(tr)(H2O)2] were prepared under mild hydrothermal conditions or by refluxing in water. Their crystal structures consist of zigzag chains, ribbons, or helixes of alternating cis-{MoO4N2} or {MoO5N} polyhedra stapled by short [N–N]-tr bridges that for bitriazole ligands convert the motifs into 2D or 3D frameworks. The high thermal (235–350 °C) and chemical stability observed for the materials makes them promising for catalytic applications. The molybdenum(VI) oxide hybrids were successfully explored as versatile oxidation catalysts with tert-butyl hydroperoxide (TBHP) or aqueous H2O2 as an oxygen source, at 70 °C. Catalytic performances were influenced by the different acidic–basic properties and steric hindrances of coordinating organic ligands as well as the structural dimensionality of the hybrid.

Cretaceous radiolarians of the North Atlantic Ocean

Radiolarians form a remarkable part of the fossil plankton for Cretaceous sediments of the North Atlantic. Selected sites with long-term sedimentary successions of deep facies were studied (ODP Leg 103 and DSDP Site 398 off northwest Spain and DSDP Site 603 off the east coast of the United States). Preservation of the radiolarian faunas is generally poor, and the faunal abundance and diversity reflect the diagenetic history of the host sediment rather than the original faunal productivity. Several exceptions include abundant and some well-preserved radiolarian faunas from lower Campanian, Cenomanian/Turonian boundary, upper Albian, lower Albian, and Barremian sediments. These increases in radiolarian abundance and preservation coincide with well-established Cretaceous oceanic events in the North Atlantic. Typical faunal associations of these sections are described, and faunal associations from the Cenomanian/Turonian Boundary Event are documented for the first time in the North Atlantic. The relationship of the radiolarian blooms with coeval oceanic events in the North Atlantic is also discussed.

Convex polytopes and quantization of symplectic manifolds

Quantum mechanics associate to some symplectic manifolds M a quantum model Q(M), which is a Hilbert space. The space Q(M) is the quantum mechanical analogue of the classical phase space M. We discuss here relations between the volume of M and the dimension of the vector space Q(M). Analogues for convex polyhedra are considered.

Estudo da cinética de crescimento de células de inseto Sf21 e infecção por baculovírus Anticarsia gemmatalis (AgMNPV) para a produção de bioinseticida.

O interesse em estudar o cultivo das células de inseto está relacionado entre outros usos a sua utilização na produção de biopesticidas. Há muitos anos os pesticidas químicos vêm contribuindo no controle de pragas na agricultura. Entretanto, o uso desses compostos prolongadamente tem resultado na seleção de insetos resistentes e em poluição ambiental. Diante disso, torna-se necessário o desenvolvimento e aprimoramento dos bioinseticidas. No Brasil, o baculovírus Anticarsia gemmatalis multiple nucleopolyhedrovirus (AgMNPV) foi o principal agente de controle biológico da praga da soja Anticarsia gemmatalis. Assim, estudos que viabilizem a produção desses vírus in vitro possibilitariam uma produção mais controlada e de melhor qualidade desses biopesticidas. Neste trabalho, investigou-se a suscetibilidade à infecção por AgMNPV de diferentes linhagens celulares de Sf21 e o crescimento dessas células em diferentes sistemas: cultivos em schotts, em spinner e em biorreator, variando-se a idade do inóculo (IA) e a concentração celular inicial (X0). Constatou-se variação no perfil de infecção das linhagens, sendo as linhagens mais adequadas para a produção de bioinseticida as linhagens de Sf21 denominadas EMBRAPA, UFRN e GibcoG, uma vez que estas apresentaram mais do que 40 % das células com poliedros em cultivos em suspensão, enquanto a linhagem denominada GibcoSF teve menos de 2 % das células infectadas com poliedros. Ao se estudar o efeito do número de subcultivos na morfologia e crescimento celular, foi averiguado um aumento no diâmetro de 10 % e no volume de 26 % das células UFRN em relação às células GibcoSF. Além disso, o crescimento das células UFRN foi 49% menor do que das células GibcoSF. Quando realizado o Delineamento Composto Central Rotacional (DCCR) para se analisar o efeito da IA e a X0 na taxa de crescimento específica máxima (?max) e na concentração celular máxima (Xvmax) em cultivos em schott com células UFRN, obteve-se um modelo empírico. Quando analisadas as variáveis IA e X0 separadamente, não foram encontradas diferenças significativas para as respostas Xvmax e ?max em relação a X0. Para a IA, entretanto, obteve-se os resultados mais satisfatórios para os inóculos com IA de 72 e 96 horas: Xvmax de 5,97.106 cel/mL e 5,99.106 cel/mL, e ?max de 0,70 dia-1 e 0,63 dia-1, respectivamente. Nos cultivos em spinner com células UFRN, foi observada a formação de grumos, o que levou a Xvmax de 2,00.106 cel/mL. No cultivo em biorreator com células UFRN, foi obtido um Xvmax de 6,21.106 cel/mL, ?max de 0,70 dia-1, Qo2 na fase exponencial de 67,3 ± 3,6 .10-18 molO2/cel/s, rendimento de glicose em célula igual a 1,0.109 cel/g de glicose e um rendimento de glutamina em células de 3,0.109 cel/mL. Comprovou-se, portanto, a existência de alterações na infecção entre diferentes linhagens de Sf21; a importância do estado fisiológico da célula nos subcultivos, a ocorrência de mudanças no crescimento celular de acordo com os sistemas de cultivo e o efeito do número de subcultivos na morfologia e crescimento de células Sf21.

Development of exfoliated layered stannosilicate for hydrogen adsorption

The use of hydrogen as an energy vector leads to the development of materials with high hydrogen adsorption capacity. In this work, a new layered stannosilicate, UZAR-S3, is synthesized and delaminated, producing UZAR-S4. UZAR-S3, with the empirical formula Na4SnSi5O14·3.5H2O and lamellar morphology, is a layered stannosilicate built from SnO6 and SiO4 polyhedra. The delamination process used here comprises three stages: protonation with acetic acid, swelling with nonylamine and the delamination itself with an HCl/H2O/ethanol solution. UZAR-S4 is composed of sheets a few nanometers thick with a high aspect ratio and a surface area of 236 m2/g, twenty times higher than that of UZAR-S3. At −196 °C for UZAR-S4, H2 adsorption reached remarkable values of 3.7 and 4.2 wt% for 10 and 40 bar, respectively, the latter value giving a high volumetric H2 storage capacity of 26.2 g of H2/L.

A solution to the hidden line problem.

"Supported in part by the Advanced Research Projects Agency ... under Contract no. US AF 30(602)4144."