Spinorial field and Lyra geometry

The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum and spin tensors. Such scale relation is an intrinsic property for matter fields in Lyra background.

Gauge groups from brane-anti-brane systems at angles

We discuss a system formed by two pairs of brane-anti-brane that form an arbitrary angle in a plane. We identify the gauge groups from this system which presumably could be used to construct gauge theories.

Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl's ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.

Aprendizagem de conceitos geométricos pelo futuro professor das séries iniciais do Ensino Fundamental e as novas tecnologias

Com o movimento da Matemática Moderna, a partir de 1950, o ensino da matemática passou a enfatizar o simbolismo e a exigir dos alunos grandes abstrações, distanciando a matemática da vida real. O que se percebe é que o aluno formado por este currículo aprendeu muito pouco de geometria e não consegue perceber a relação deste conteúdo com sua realidade. Por outro lado, o professor que não conhece geometria não consegue perceber a beleza e a importância que a mesma possui para a formação do cidadão. A geometria estimula a criança a observar, perceber semelhanças, diferenças e a identificar regularidades. O objetivo deste trabalho é identificar o nível de conhecimento dos alunos do Centro Específico de Formação e Aperfeiçoamento ao Magistério (CEFAM), futuros professores da 1ª a 4ª séries do Ensino Fundamental do Estado de São Paulo, quanto aos conceitos de ponto, reta, plano, ângulos, polígonos e circunferências e também verificar as contribuições do computador para a construção de conceitos geométricos. Para atingir esses objetivos, foi desenvolvida uma pesquisa com 30 alunos do CEFAM de Presidente Prudente-SP, na qual, com base no diagnóstico das dificuldades de aprendizagem, organizaram e desenvolveram-se os momentos de formação, que utilizaram o computador como ferramenta de aprendizagem e projetos de trabalho tendo como aporte teórico a abordagem construcionista. O futuro professor que não dominar a geometria e não perceber sua relação com a natureza não conseguirá contribuir para o desenvolvimento do pensamento geométrico da criança. Esse pensamento é que permite a criança observar, compreender, descrever e representar, de forma organizada, o mundo em que vive.

Dichloro(cyclohexilidene-1-methylene)(phenyl)Te(IV). Looking for the theoretical treatment

C(13)H(16)Cl(2)Te,M(r)=370.76,P2(1)/a, a = 8.1833(8), b = 8.4163(8), c = 20.787(2) A, beta = 99.52(1)degrees, Z = 4, R(1) = 0,0275. The primary coordination around the Te(IV) atom is consistent with a pseudo-trigonal bipyramidal bond configuration with two Cl atoms occupying axial positions while the C atoms and the lone pair of electrons occupy the equatorial positions. The Te(IV) atom is involved in an intermolecular secondary interaction resulting in the self assembly of zigzag-chains supramolecular array. In order to determine the theoretical basis set for the Te atom which leads to the best agreement with the experimental data, a large series of geometry optimizations were performed on dichloro dimethyl Te(IV), as a model compound, and the results compared with the mean distances and angles obtained from 45 X-ray structures. The Ahlrichs basis set plus the Hay & Wadt ECP was selected and used for a series of calculations performed on the title compound.

Molecular structures and vibrational frequencies for cis-[PdCl2(tmen)] and cis-[Pd(N-3)(2)(tmen)]: A DFT study

Theoretical molecular structures of the complexes cis-[PdCl2(tmen)] and cis-[Pd(N-3)(2)(tmen)] (tmen = N,N,N',N'-tetramethylethylenediamine) were investigated using B3LYP/DFT method. The calculated molecular parameters, bond distances and angles, revealed a square-planar geometry around the metallic center for both compounds with the azide being linear. The theoretical infrared spectra of C, symmetry (electronic state (1)A) of the compounds are in agreement with the experimental data. (C) 2007 Elsevier B.V. All rights reserved.

Numerical simulation of magnetic-field-enhanced plasma immersion ion implantation in cylindrical geometry

Recent studies have demonstrated that the sheath dynamics in plasma immersion ion implantation (PIII) is significantly affected by an external magnetic field. In this paper, a two-dimensional computer simulation of a magnetic-field-enhanced PHI system is described. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded vacuum chamber filled with uniform molecular nitrogen plasma. A static magnetic field is created by a small coil installed inside the target holder. The vacuum chamber is filled with background nitrogen gas to form a plasma in which collisions of electrons and neutrals are simulated by the Monte Carlo algorithm. It is found that a high-density plasma is formed around the target due to the intense background gas ionization by the magnetized electrons drifting in the crossed E x B fields. The effect of the magnetic field intensity, the target bias, and the gas pressure on the sheath dynamics and implantation current of the PHI system is investigated.

Fluctuating commutative geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number n of points. The spectral principle of Connes and Chamseddine is used to define dynamics. We show that this simple model has two phases. The expectation value , the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2. We also address another discrete model defined on a fixed d = 1 dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology.

Experimental and theoretical study of the compound [Pd(dmba)(NCO)(imz)]

The compound [Pd(dmba)(NCO)(imz)] (dmba = N,N-dimethylbenzilamine; NCO = cyanate; imz = imidazole) was studied through experimental and theoretical methods. The complex was synthesized and characterized by IR and NMR spectroscopy. To an appropriate representation of the molecular environment, Gaussian basis sets for the constituent atoms of the compound were built and, after adequate supplementation with polarization and diffuse functions, they were used to study the molecule. Calculations of electronic and vibrational structure of two possible isomers were carried out, showing that the compound, which contains the NCO GROUP trans to the Pd-C bond, is 4.29 kcal/mol more stable than the analogous one, where the imz ligand is trans to the Pd-C bond. The calculated molecular parameters, bond distances, and bond angles showed that the geometry around the metallic center is square-planar with the cyanate being linear. The theoretical infrared spectrum of C(1) symmetry (electronic state (1)A) is in accordance with the experimental one. It also verified the contribution of Pd (4d(xz) + 4d(yz)) and Pd (4d(xy)) in the HOMO and LUMO orbitals, respectively. (c) 2006 Elsevier B.V. All rights reserved.

Study of plasma immersion ion implantation into silicon substrate using magnetic mirror geometry

The effect of magnetic field enhanced plasma immersion ion implantation (PIII) in silicon substrate has been investigated at low and high pulsed bias voltages. The magnetic field in magnetic bottle configuration was generated by two magnetic coils installed outside the vacuum chamber. The presence of both, electric and magnetic field in PIII creates a system of crossed E x B fields, promoting plasma rotation around the target. The magnetized electrons drifting in crossed E x B fields provide electron-neutral collision. Consequently, the efficient background gas ionization augments the plasma density around the target where a magnetic confinement is achieved. As a result, the ion current density increases, promoting changes in the samples surface properties, especially in the surface roughness and wettability and also an increase of implantation dose and depth. (C) 2012 Elsevier B. V. All rights reserved.

Quantum geometry of chiral bosons on a circle

We extend the geometric treatment done for the Majorana-Weyl fermions in two dimensions by Sanielevici and Semenoff to chiral bosons on a circle. For this case we obtain a generalized Floreanini-Jackiw Lagrangian density, and the corresponding gravitational (or Virasoro) anomalies are found as expected. © 1989 The American Physical Society.

On the geometry of non-classical curves

In this paper we relate the numerical invariants attached to a projective curve, called the order sequence of the curve, to the geometry of the varieties of tangent linear spaces to the curve and to the Gauss maps of the curve. © 1992 Sociedade Brasileira de Matemática.

Synthesis, structure, and electronic and EPR spectra of copper(II) complexes containing the [CuBr4]2- anion and triphenylarsine oxide

The preparation and characterization of (Ph3AsOH)2[CuBr4] and [Cu(Ph3AsO)4][CuBr4] are reported (Ph3AsO = triphenylarsine oxide). Crystallographic analysis of the monoclinic crystals of (Ph3AsOH)2[CuBr4] (space group C2/c, a = 17.569 (3) Å, b = 13.090 (2) Å, c = 16.933 (2) Å, and β = 105.64 (2)°, R = 0.055 and Rw = 0.057) revealed the presence of compressed [CuBr4]2- tetrahedra of C2 symmetry with Cu-Br distances of 2.340 (1) and 2.437 (1) Å and trans-Br-Cu-Br angles of 139.2 (1) and 122.4 (1)°. The oxonium cations hydrogen bond to the bromine atoms involved in the longer Cu-Br bonds and the smaller trans-Br-Cu-Br angle. Single-crystal electronic and EPR spectra are interpreted in terms of the observed [CuBr4]2- geometry. Analysis of the electronic and EPR spectra of [Cu(Ph3AsO)4][CuBr4] led to the postulation of the presence of planar [Cu(Ph3AsO)4]2+ cations and distorted tetrahedral [CuBr4]2- anions. © 1992 American Chemical Society.