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."

A procedure for detecting intersections and its application.

Bibliography: p. 72-74.

Ausgewählte capitel aus der darstellenden geometrie zum gebrauch bei constructionsübungen,

No more published?

Effects of cation substitutions on the physical properties of M2M1T2O6 pyroxenes

In this PhD study, the effects of the cation substitutions on the physical properties of pyroxenes have been discussed. The results of this work extend the knowledge on pyroxenes with different chemical compositions. These properties might be used in the development of ceramic pigments, advanced materials and for the mineralogical phase identification. First of all, the crystallographic differences between Ge and Si pyroxenes have been examined. The structure of C2/c Ca rich Ge clinopyroxenes is very close to the low pressure C2/c structural configuration found in Ca-rich Si-pyroxenes. The shear of the unit cell is very similar, and the difference between a Ge end member and the corresponding Si-rich one is less than 1°. Instead, a remarkable difference exists between Ca-poor Si and Ge clinopyroxenes. First, Ca-poor Ge pyroxenes do not display a P21/c symmetry, but retain the C2/c symmetry; second, the observed C2/c structure shows, at room pressure, the configuration with highly kinked tetrahedral chains characteristic of the high pressure C2/c symmetry of Si Ca-poor pyroxenes. In orthopyroxenes, with Pbca symmetry, Ge-pyroxenes have volume larger than Si-pyroxenes. Samples along the system CaCoGe2O6 - CoCoGe2O6 have been synthesized at three different temperatures: 1050 °C, 1200 °C and 1250 °C. The aim of these solid state syntheses was to obtain a solid solution at ambient pressure, since the analogues Si-system needs high pressure. Unfortunately, very limited solution occurs because the structure forms of the two end member (high temperature for CaCoGe2O6 and high pressure CoCoGe2O6) are incompatible. The phase diagram of this system has been sketched and compared to that of Si. The cobalt end member (CoCoGe2O6) is stable at ambient pressure in two symmetries: at 1050 °C C2/c and 1200 °C Pbca. The impurity phase formed during these experiments is cobalt spinel. Raman spectroscopy has been used to investigate the vibrational properties of Ca-pyroxenes CaCoGe2O6, CaMgGe2O6, CaMgSi2O6 and CaCoSi2O6. A comparison between silicate and germanate pyroxenes shows significant changes in peak positions of the corresponding modes caused mainly by the difference of the Ge-Si atomic weight along with the distortion and compression of the coordination polyhedra. Red shift in Raman spectra of germanates has been calculated by a rough scale factor calculated by a simple harmonic oscillator model, considering the different bond lengths for 4-coordinated Si ~ 1.60- 1.65 Å vs Ge–O distance ~1.70 - 1.80 Å. The Raman spectra of CaMgGe2O6 and CaCoGe2O6 have been classified, in analogy with silicate (Wang et al., 2001) counterparts, in different ranges: - R1 (880-640 cm-1): strong T-O stretching modes of Ge and non-bridging O1 and O2 atoms within the GeO4 tetrahedron; - R2 (640-480 cm-1): stretching/bending modes of Ge-Obr-Ge bonds (chain stretching and chain bending); - R4 (480-360 cm-1): O-Ge-O vibrations; - R3 (360-240 cm-1): motions of the cations in M2 and M1 sites correlated with tetrahedral chain motion and tilting tetrahedra; - R5 (below 240 cm-1): lattice modes. The largest shift with respect to CaMgSi2O6 - CaCoSi2O6 is shown by the T-O stretching and chain modes. High-pressure Raman spectroscopy (up to about 8 GPa) on the same samples of Ca-pyroxenes using an ETH-type diamond anvil cell shows no phase transition within the P-ranges investigated, as all the peak positions vary linearly as a function of pressure. Our data confirm previous experimental findings on Si-diopside (Chopelas and Serghiou, 2000). In the investigated samples, all the Raman peaks shift upon compression, but the major changes in wavenumber with pressure are attributed to the chain bending (Ge-Obr-Ge bonds) and tetrahedra stretching modes (Ge-Onbr). Upon compression, the kinking angle, the bond lengths and T-T distances between tetrahedra decrease and consequently the wavenumber of the bending chain mode and tetrahedra stretching mode increases. Ge-pyroxenes show the higher P-induced peak-position shifts, being more compressible than corresponding silicates. The vibrational properties of CaM2+Ge2O6 (M2+ =Mg, Mn, Fe, Co, Ni, Zn) are reported for the first time. The wavenumber of Ge-Obr-Ge bending modes decreases linearly with increasing ionic radius of the M1 cation. No simple correlation has been found with M1 atomic mass or size or crystallographic parameters for the peak at ~850 cm-1 and in the low wavenumber regions. The magnetic properties of the system CaCoSi2O6 - CoCoSi2O6 have been investigated by magnetometry. The join is always characterized by 1 a.p.f.u. of cobalt in M1 site and this causes a pure collinear antiferromagnetic behaviour of the intra-chain superexchange interaction involving Co ions detected in all the measurements, while the magnetic order developed by the cobalt ions in M2 site (intra-chain) is affected by weak ferromagnetism, due to the non-collinearity of their antiferromagnetic interaction. In magnetically ordered systems, this non-collinearity effect promotes a spin canting of anti-parallel aligned magnetic moments and thus is a source of weak ferromagnetic behaviour in an antiferromagnetic. The weak ferromagnetism can be observed only for the samples with Co content higher than 0.5 a.p.f.u. in M2, when the concentration is sufficiently high to create a long range order along the M2 chain which is magnetically independent of M1 chain. The ferromagnetism was detected both in the M(T) at 10 Oe and M(H).

The effect of zinc and titanium on the structure of calcium-sodium phosphate based glass

An array of different structural probes has been used to define the effect of adding Zn and Ti to a sodium-calcium phosphate glass. X-ray absorption spectroscopy at the Zn K-edge suggests that the Zn atoms occupy mixed (4- and 6-fold) sites within the glass matrix. X-ray diffraction reveals a feature at 2.03 angstrom that develops with the addition of Zn and Ti and is consistent with Zn-O and Ti-O near-neighbour distances. Neutron diffraction is used to resolve two distinct P-O distances and highlights the decrease in P center dot center dot center dot P coordination number from 2.0 to 1.7 as the Ti metal concentration rises, which is attributed to the O/P fraction moving away from the metaphosphate value of 3.0 to 3.1 with the addition of Ti. Other correlations, such as those associated with CaO(x) and NaO(x) polyhedra, remain largely unaffected. These results suggest that the network forming P center dot center dot center dot P correlation is most disrupted, with the disorder parameter rising from 0.07 to 0.10 angstrom with the additional modifiers. Zn appears to be introduced into the network as a direct replacement for Ca and causes no structural variation over the composition range studied.

Structure of dysprosium and holmium phosphate glasses by the method of isomorphic substitution in neutron diffraction

The relative distribution of rare-earth ions R3+ (Dy3+ or Ho3+) in the phosphate glass RAl0.30P3.05O9.62 was measured by employing the method of isomorphic substitution in neutron diffraction and, by taking the role of Al into explicit account, a self-consistent model of the glass structure was developed. The glass network is found to be made from corner sharing PO4 tetrahedra in which there are, on average, 2.32(9) terminal oxygen atoms, OT, at 1.50(1) Å and 1.68(9) bridging oxygen atoms, OB, at 1.60(1) Å. The network modifying R3+ ions bind to an average of 6.7(1) OT and are distributed such that 7.9(7) R–R nearest neighbours reside at 5.62(6) Å. The Al3+ ion also has a network modifying role in which it helps to strengthen the glass through the formation of OT–Al–OT linkages. The connectivity of the R-centred coordination polyhedra in (M2O3)x(P2O5)1−x glasses, where M3+ denotes a network modifying cation (R3+ or Al3+), is quantified in terms of a parameter fs. Methods for reducing the clustering of rare-earth ions in these materials are then discussed, based on a reduction of fs via the replacement of R3+ by Al3+ at fixed total modifier content or via a change of x to increase the number of OT available per network modifying M3+ cation.

Structure of lanthanum and cerium phosphate glasses by the method of isomorphic substitution in neutron diffraction

Neutron diffraction was used to measure the total structure factors for several rare-earth ion R3+ (La3+ or Ce3+) phosphate glasses with composition close to RAl0.35P3.24O10.12. By assuming isomorphic structures, difference function methods were employed to separate, essentially, those correlations involving R3+ from the remainder. A self-consistent model of the glass structure was thereby developed in which the Al correlations were taken into explicit account. The glass network was found to be made from interlinked PO4 tetrahedra having 2.2(1) terminal oxygen atoms, OT, at 1.51(1) Angstrom, and 1.8(1) bridging oxygen atoms, OB, at 1.60(1) Angstrom. Rare-earth cations bonded to an average of 7.5(2) OT nearest neighbors in a broad and asymmetric distribution. The Al3+ ion acted as a network modifier and formed OT-A1-OT linkages that helped strengthen the glass. The connectivity of the R-centered coordination polyhedra was quantified in terms of a parameter f(s) and used to develop a model for the dependence on composition of the A1-OT coordination number in R-A1-P-O glasses. By using recent 17 A1 nuclear-magnetic-resonance data, it was shown that this connectivity decreases monotonically with increasing Al content. The chemical durability of the glasses appeared to be at a maximum when the connectivity of the R-centered coordination polyhedra was at a minimum. The relation of f(s) to the glass transition temperature, Tg, was discussed.

One Application of the Informatics in the Descriptive Geometry

This work acquaints with a program for interactive computer training to students on the subject "Mutual intersecting of pyramids in axonometry ”. Our software is a set of three modules, which we call "student", "teacher" and "autopilot". It gives the final solution of the problem, the traceability of various significant moments in its solution and 3D-image of the finished composition of the two intersecting polyhedra, stripped of the working lines and subjected to rotation and translation.

Характеристични свойства на някои многостени

Plamen Penchev - The origin is a problem from the Canadian Mathematical Olympiad in 1980, which is solved in general and ended to similar variants. Certain characteristic properties of such polyhedra are investigated.

Reconsidering the Origins of Forsbergh Birefringence Patterns

In 1949, P. W. Forsbergh Jr. reported spontaneous spatial ordering in the birefringence patterns seen in flux-grown BaTiO3 crystals [1], under the transmission polarized light microscope [2]. Stunningly regular square-net arrays were often only found within a finite temperature window and could be induced on both heating and cooling, suggesting genuine thermodynamic stability. At the time, Forsbergh rationalized the patterns to have resulted from the impingement of ferroelastic domains, creating a complex tessellation of variously shaped domain packets. However, evidence for the intricate microstructural arrangement proposed by Forsbergh has never been found. Moreover, no robust thermodynamic argument has been presented to explain the region of thermal stability, its occurrence just below the Curie Temperature and the apparent increase in entropy associated with the loss of the Forsbergh pattern on cooling. As a result, despite decades of research on ferroelectrics, this ordering phenomenon and its thermodynamic origin have remained a mystery. In this paper, we re-examine the microstructure of flux-grown BaTiO3 crystals, which show Forsbergh birefringence patterns. Given an absence of any obvious arrays of domain polyhedra, or even regular shapes of domain packets, we suggest an alternative origin for the Forsbergh pattern, in which sheets of orthogonally oriented ferroelastic stripe domains simply overlay one another. We show explicitly that the Forsbergh birefringence pattern occurs if the periodicity of the stripe domains is above a critical value. Moreover, by considering well-established semiempirical models, we show that the significant domain coarsening needed to generate the Forsbergh birefringence is fully expected in a finite window below the Curie Temperature. We hence present a much more straightforward rationalization of the Forsbergh pattern than that originally proposed, in which exotic thermodynamic arguments are unnecessary.