Aurifeuillian factorization

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we can partially factor 24k+2+1. In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definition of what “such an identity” is. We then develop our theme to similarly factor f(bn) for any given polynomial f, using deep results of Faltings from algebraic geometry and Fried from the classification of finite simple groups.

Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions

Solvation. pressure due to adsorption of fluids in porous materials is the cause of elastic deformation of an adsorbent, which is accessible to direct experimental measurements. Such a deformation contributes to the Helmholtz free energy of the whole adsorbent-adsorbate system due to accumulation of compression or tension energy by the solid. It means that in the general case the solid has to be considered as not solely a source of the external potential field for the fluid confined in the pore volume, but also as thermodynamically nonmert component of the solid-fluid system. We present analysis of nitrogen adsorption isotherms and heat of adsorption in slit graphitic pores accounting for the adsorption deformation by means of nonlocal density functional theory. (c) 2006 Elsevier Ltd. All rights reserved.

Strong electronic correlations in superconducting organic charge transfer salts

We review the role of strong electronic correlations in quasi-two-dimensional organic charge transfer salts such as (BEDT-TTF)(2)X, (BETS)(2)Y, and beta'-[Pd(dmit)(2)](2)Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerized and is described by a half-filled Hubbard model; the second class is not strongly dimerized and is described by a quarter-filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include parameterizing minimal models, the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments, superconductors with low critical temperatures and extremely small superfluid stiffnesses, the possible spin- liquid states in kappa-(ET)(2)Cu-2(CN)(3) and beta'-[Pd(dmit)(2)](2)Z, and the need for high quality large single crystals.

The chemistry of ceramic glazes

The development of ideas and theories concerning the structure of glazes, as one of the glassy materials, are reviewed in the general introduction. The raw materials and the manufacturing process for glazes are described (Chapter One). A number of new vanadyl(IV) dipyridylamine and tripyrldylamine complexes have been prepared, various spectroscopic techniques are used in the investigation of the vanadyl ion in a weak ligand field, the situation of those found in a glaze environment (Chapter Three). In glaze recipes containing silica, potash feldspar, china clay, MO(M= Ca, Sr, Sa, Ti and Zn) and NiO, the ligand field theory is used in the elucidation of the effect of M (in MO) on the absorption spectra and coordination behaviour of Ni(II) in glazes. The magnetic and visible spectral results are reviewed in terms of Dietzel's idea of field strength of M and also in terms of Shteinberg's theory of glaze structure. X-ray diffraction is used for the identification of various species that formed after the firing process of glazes (Chapter Four). In Chapter Five, [] Mossbauer spectroscopy, supplemented by E.S.R., X-ray and visible spectral measurements are used in the investigation of iron in a glaze composition similar to that used in Chapter Four. The Mossbauer results are used in following the influence of; M in MO (M= Sr, Ca and Ba), oxides of titanium(IV) and vanadium(V ), and firing conditions on the chemistry of iron. Generally the iron(II) and iron(III) in the fired glazes are in octahedral sites although there are a range of similar, though not identical environments. A quite noticable influence of M (in MO) on the resonance line width is seen. In one case evidence is found for iron(IV) in an iron/vanadium glaze. E.S.R. of vanadium containing glazes indicate that vanadium is present as V02+ in a highly distorted tetragonal environment .

The missing link:Analogous human and primate cortical gamma oscillations

Recent animal studies highlighting the relationship between functional imaging signals and the underlying neuronal activity have revealed the potential capabilities of non-invasive methods. However, the valuable exchange of information between animal and human studies remains restricted by the limited evidence of direct physiological links between species. In this study we used magnetoencephalography (MEG) to investigate the occurrence of 30-70 Hz (gamma) oscillations in human visual cortex, induced by the presentation of visual stimuli of varying contrast. These oscillations, well described in the animal literature, were observed in retinotopically concordant locations of visual cortex and show striking similarity to those found in primate visual cortex using surgically implanted electrodes. The amplitude of the gamma oscillations increases linearly with stimulus contrast in strong correlation with the gamma oscillations found in the local field potential (LFP) of the macaque. We demonstrate that non-invasive magnetic field measurements of gamma oscillations in human visual cortex concur with invasive measures of activation in primate visual cortex, suggesting both a direct representation of underlying neuronal activity and a concurrence between human and primate cortical activity. © 2005 Elsevier Inc. All rights reserved.

The charge effect on the hindrance factors for diffusion and convection of a solute in pores II

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e.the Debye-Hückel equation. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Charge effects on hindrance factors for diffusion and convection of solute in pores I

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

Charge effects on the hindered transport of macromolecules across the endothelial surface glycocalyx layer

A fluid mechanical and electrostatic model for the transport of solute molecules across the vascular endothelial surface glycocalyx layer (EGL) was developed to study the charge effect on the diffusive and convective transport of the solutes. The solute was assumed to be a spherical particle with a constant surface charge density, and the EGL was represented as an array of periodically arranged circular cylinders of like charge, with a constant surface charge density. By combining the fluid mechanical analyses for the flow around a solute suspended in an electrolyte solution and the electrostatic analyses for the free energy of the interaction between the solute and cylinders based on a mean field theory, we estimated the transport coefficients of the solute across the EGL. Both of diffusive and convective transports are reduced compared to those for an uncharged system, due to the stronger exclusion of the solute that results from the repulsive electrostatic interaction. The model prediction for the reflection coefficient for serum albumin agreed well with experimental observations if the charge density in the EGL is ranged from approximately -10 to -30 mEq/l.

Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic field, and obtain an asymptotic expansion of the resonances as the coupling constant ϰ of the perturbation tends to zero. Further, under the assumption that the Fermi Golden Rule holds true, we deduce estimates for the time evolution of the resonance states with and without analyticity assumptions; in the second case we obtain these results as a corollary of suitable Mourre estimates and a recent article of Cattaneo, Graf and Hunziker [11]. Next, we describe sets of perturbations V for which the Fermi Golden Rule is valid at each embedded eigenvalue of H; these sets turn out to be dense in various suitable topologies. Finally, we assume that V decays fast enough at infinity and is of definite sign, introduce the Krein spectral shift function for the operator pair (H+V, H), and study its singularities at the energies which coincide with eigenvalues of infinite multiplicity of the unperturbed operator H.

Non-thermal transitions in a model inspired by moral decisions

This work introduces a model in which agents of a network act upon one another according to three different kinds of moral decisions. These decisions are based on an increasing level of sophistication in the empathy capacity of the agent, a hierarchy which we name Piaget's ladder. The decision strategy of the agents is non-rational, in the sense they are arbitrarily fixed, and the model presents quenched disorder given by the distribution of its defining parameters. An analytical solution for this model is obtained in the large system limit as well as a leading order correction for finite-size systems which shows that typical realisations of the model develop a phase structure with both continuous and discontinuous non-thermal transitions.

Otimização da síntese do AlSBA-15 para produção de biodiesel por transesteri-ficação do óleo de coco

Stimulus encouraging the production and consumption of biodiesel favors the policy of pre-serving the environment, contributing to the reduction of greenhouse gas reducing climate change. The current trend of research in this field focuses on improving these processes with the use of heterogeneous catalysts, seeing has significant advantages such as: low contamination of products, ease of separation of the catalyst from the reaction medium, possibili-ty of reuse of the catalyst, decreased corrosion problems. The objective of this research was to optimize the synthesis of AlSBA-15 for the production of biodiesel through transesterification process via ethyl route. For the optimization of hydrothermal synthesis of type AlSBA-15 catalyst has assembled a 23 factorial experimental matrix with eleven trials. The stoichiometric amounts of starting materials were varied according to different ratios Si / Al which is a factor in the experimental design, in addition to the time and temperature of aging of the synthesis gel. The material showed the best results of characterization (SBET = 591.7 (m2 / g), Vp = 0.83 (cm3 / g), Dp = 5.59 (nm), w = 6.48 (nm) was synthesized at 100 ° C for 24 hours, with a ratio Si / Al = 10.This material was applied as a heterogeneous catalyst in the reaction of ethyl transesterification as raw coconut oil in natura. Coconut oil presented suitable for obtaining biodiesel via ethyl route.The visual aspects and physical-chemical characteristics of the reaction products show that AlSBA-15 catalyst favored the reaction. According to physical-chemical analysis the order of oxidative stability of the product of the transesterification reaction was: catalytic reaction at 1500 ° C> non-catalytic reaction at 100 ° C> 100 ° C catalytic> catalytic reaction at 200 ° C Reaction. The results of oxidative stability and kinematic viscosity shows that the biodiesel produced in the catalytic sandblasting held at 150 ° C which was maintained within the ABNT NBR 7148, ABNT NBR 10441 and EN 14112.

Das "zweite Leben" Erwin Chargaffs : kritische Essayistik zwischen den "Two cultures"

Magdalena Bachmann

State sum models for quantum gravity

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.