Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving tensor products over semisimple and semiprimary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work. (C) 2013 Elsevier B.V. All rights reserved.

Enhanced electro-oxidation resistance of carbon electrodes induced by phosphorus surface groups

The electro-oxidation of carbon materials enormously degrades their performance and limits their wider utilization in multiple electrochemical applications. In this work, the positive influence of phosphorus functionalities on the overall electrochemical stability of carbon materials has been demonstrated under different conditions. We show that the extent and selectivity of electroxidation in P-containing carbons are completely different to those observed in conventional carbons without P. The electro-oxidation of P-containing carbons involves the active participation of phosphorus surface groups, which are gradually transformed at high potentials from less-to more-oxidized species to slow down the introduction of oxygen groups on the carbon surface (oxidation) and the subsequent generation of (C*OOH)-like unstable promoters of electro-gasification. The highest-oxidized P groups (–C–O–P-like species) seem to distribute the gained oxygen to neighboring carbon sites, which finally suffer oxidation and/or gasification. So it is thought that P-groups could act as mediators of carbon oxidation although including various steps and intermediates compared to electroxidation in P-free materials.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Structure, bonding state and in-vitro study of Ca–P–Ti film deposited on Ti6Al4V by RF magnetron sputtering

Experimental investigation of functionally graded calcium phosphate-based bio-active films on Ti-6A1-4V orthopaedic alloy prepared in an RF magnetron sputtering plasma reactor is reported. The technique involves concurrent sputtering of Hydroxyapatite (HA) and Ti targets, which results in remarkably enhanced adhesion of the film to the substrate and stability of the interface. The films have been characterized using X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The XPS data show that the films are composed of O, Ca, P and Ti, and reveal the formation of O=P groups and hybridization of O-Ca-P. The XRD pattern shows that the Ca-P thin films are of crystalline calcium oxide phosphate (4CaO·P2O5) with preferred orientation varying with processing parameters. High-resolution optical emission spectra show that the emission of CaO is dominant. The CaO, PO and CaPO species are strongly influenced by deposition conditions. The introduction of Ti element during deposition provides a stable interface between bio-inert substrates Ti-6A1-4V and bioactive HA coating. In-vitro cell culturing tests suggest excellent biocompatibility of the Ca-P-Ti films.

Secure Computation in a Bidirectional Relay

Bidirectional relaying, where a relay helps two user nodes to exchange equal length binary messages, has been an active area of recent research. A popular strategy involves a modified Gaussian MAC, where the relay decodes the XOR of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes. In this work, we consider the Gaussian MAC in bidirectional relaying with an additional secrecy constraint for protection against a honest but curious relay. The constraint is that, while the relay should decode the XOR, it should be fully ignorant of the individual messages of the users. We exploit the symbol addition that occurs in a Gaussian MAC to design explicit strategies that achieve perfect independence between the received symbols and individual transmitted messages. Our results actually hold for a more general scenario where the messages at the two user nodes come from a finite Abelian group G, and the relay must decode the sum within G of the two messages. We provide a lattice coding strategy and study optimal rate versus average power trade-offs for asymptotically large dimensions.

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

The subvarieties of a field

Number systems which satisfy part but not all of the postulates for a field are called subvarieties of a field. The purpose of this paper is the determination of as great as possible a number of such varieties by suitable definitions of the class of elements and of the two operations involved.

Two postulate systems are considered. The first gives rise to 284 varieties, instances of all of which are given for infinite classes of elements, and of all except three for finite classes.

Of the 8192 combinations of postulates arising from the second system, not more than 1146 can be consistent. Instances are given of 1054 of these. As the postulates of this system are not independent, no conclusion has been reached regarding the remaining cases.

Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

On an embedding property of generalized Carter subgroups

If E and F are saturated formations, we say that E is strongly contained in F if for any solvable group G with E-subgroup, E, and F-subgroup, F, some conjugate of E is contained in F. In this paper, we investigate the problem of finding the formations which strongly contain a fixed saturated formation E.

Our main results are restricted to formations, E, such that E = {G|G/F(G) ϵT}, where T is a non-empty formation of solvable groups, and F(G) is the Fitting subgroup of G. If T consists only of the identity, then E=N, the class of nilpotent groups, and for any solvable group, G, the N-subgroups of G are the Carter subgroups of G.

We give a characterization of strong containment which depends only on the formations E, and F. From this characterization, we prove:

If T is a non-empty formation of solvable groups, E = {G|G/F(G) ϵT}, and E is strongly contained in F, then

(1) there is a formation V such that F = {G|G/F(G) ϵV}.

(2) If for each prime p, we assume that T does not contain the class, S_p’, of all solvable p’-groups, then either E = F, or F contains all solvable groups.

This solves the problem for the Carter subgroups.

We prove the following result to show that the hypothesis of (2) is not redundant:

If R = {G|G/F(G) ϵS_r’}, then there are infinitely many formations which strongly contain R.

Estudos dos efeitos antioxidantes e anti-inflamatórios da própolis sobre as células RAW 264.7 e na resposta inflamatória pulmonar aguda causada pela exposição à fumaça de cigarro em camundongos

A doença pulmonar obstrutiva crônica (DPOC) causa a redução da capacidade respiratória e seu desenvolvimento é associado à fumaça de cigarro. O cigarro possui mais de 4800 substâncias tóxicas e causa a morte de seis milhões de pessoas por ano no mundo. Estudos buscam meios de reverter os males causados pela fumaça de cigarro. A própolis (P) é um produto produzido por abelhas que possui várias propriedades. O objetivo deste trabalho foi avaliar os efeitos antioxidantes da P em macrófagos murinos e na inflamação pulmonar aguda induzida pela fumaça de cigarro (CS) em camundongos. A análise dos compostos fitoquímicos do extrato alcóolico da P (EAP) foi feita por cromatografia gasosa acoplada à espectrometria de massa (GC-MS). Células da linhagem RAW 264.7 foram tratadas em diversas concentrações de P durante 24 horas. Após tratamento, as seguintes análises foram realizadas: polifenóis totais; viabilidade celular (MTT); potencial redutor (DPPH); espécies reativas de oxigênio totais (ROS) e de malondialdeído (MDA). Trinta camundongos C57BL/6 foram divididos em 3 grupos (n=10/grupo): Controle+P, CS e CS+P. Ambos os grupos CS foram expostos a 6 cigarros/dia durante 5 dias. O grupo CS foi tratado com veículo. O pulmão e o lavado broncoalveolar (BAL) foram coletados para análise histológica e contagem diferencial de células. As análises para mieloperoxidase (MPO), superóxido dismutase (SOD), catalase (CAT), glutationa peroxidase (GPx), glutationa reduzida (GSH) e oxidada (GSSG), MDA, nitrito e western blotting para TNF-alfa foram realizadas. A análise fitoquímica do EAP mostrou a presença dos ácidos hidrocinâmicos e coumárico, a artepilina C e a drupanina. Foi observado o aumento concentração-dependente dos níveis de polifenóis totais (p<0,001), do MTT (p<0,001) e do DPPH (p<0,001), e o inverso com o MDA (p<0,001). Os níveis de ROS diminuem nas concentrações de 15,6 e 31,2 mg/mL (p<0,05, ambos). A histologia pulmonar do grupo Controle+P foi similar ao do CS+P e foi observado um influxo de macrófagos e neutrófilos no grupo CS (p<0,01 e p<0,001, respectivamente). Os níveis de MPO foram aumentados no grupo CS (526,534,72 mU/mg ptn, p<0,01), mas houve uma redução no grupo CS+P (385,127,64 mU/mg ptn, p<0,05) comparável ao Controle+P (13412,99 mU/mg ptn, p<0,001), o mesmo aconteceu com as enzimas antioxidantes: SOD (Controle+P: 523,529,6 U/mg ptn; CS: 523,529,6 U/mg ptn, p<0,001; CS+P: 246,815,69 U/mg ptn, p<0,001); CAT (Controle+P: 37,383,39 U/mg ptn; CS: 92,686,24 U/mg ptn, p<0,001; CS+P: 59,844,55 U/mg ptn, p<0,05); GPx (Controle+P: 2,230,17 (M/min/mg ptn) x 10-1; CS: 4,510,31 (M/min/mg ptn) x 10-1, p<0,001; CS+P: 2,640,19 (M/min/mg ptn) x 10-1, p<0,05). O inverso ocorreu com a relação GSH/GSSG (Controle+P: 1,0880,17; CS: 0,7360,07, p<0,05; CS+P: 1,2580,10, p<0,05). Os níveis de MDA (Controle+P: 0,2660,05 nMol/mg ptn; CS: 0,940,076 nMol/mg ptn, p<0,001; CS+P: 0,4980,06 nMol/mg ptn, p<0,01) e de nitrito (Controle+P: 50,014,19 Mol/mg ptn; CS: 108,77,73 Mol/mg ptn, p<0,001; CS+P: 58,843,42 nMol/mg ptn, p<0,01) estavam aumentados no CS que em outros grupos. A expressão de TNF-α foi observada no grupo CS. O tratamento da P apresentou ação anti-inflamatória e antioxidante em macrófagos e em camundongos expostos à fumaça de cigarro, possivelmente pela ação dos polifenóis presentes nela

Heptairon bis(phosphate) tetrakis(hydrogenphosphate)

A new iron hydrogen phosphate, heptairon bis(phosphate) tetrakis(hydrogenphosphate), Fe-7(PO4)(2)(HPO4)(4), has been prepared hydrothermally and characterized by single-crystal X-ray diffraction. The compound has one Fe atom on an inversion centre and is isostructural with Mn-7(PO4)(2)(HPO4)(4) and Co-7(PO4)(2)(HPO4)(4). The structure is based on a framework of edge- and corner-sharing FeO6, Fe-5 and PO4 polyhedra, isotypic with that found in the mixed-valence iron phosphate Fe-7(PO4)(6). The Fe atoms in the title compound are purely in the divalent state, just like the Co atoms in Co-7(PO4)(2)(HPO4)(4), the necessary charge balance being maintained by the addition of H atoms in the form of bridging Fe-OH-P groups.

A NMR-STUDY OF THE INTERACTION OF SILICA WITH DIPALMITOYLPHOSPHATIDYLCHOLINE LIPOSOMES

The interaction of silica with dipalmitoylphosphatidylcholine (DPPC) liposomes has been studied by detecting H-1 and 2D NOESY NMR spectra and measuring proton spin-lattice relaxation time (T-1). The antagonistic effect of aluminium citrate on silica has also been studied by measuring the proton T-1 values, The results show that silica particles mainly bind to the phosphate moiety of the polar headgroup of DPPC bilayers through hydrogen bonds between Si-OH and O-P groups, but they have no significant effect on the conformation of the choline group of the polar headgroup, The addition of silica particles decreases the mobilities of the hydrocarbon chains slightly, Proton T-1 data also indicate that aluminium citrate reduces the effect of silica, A possible mechanism for the toxicity of silica and the antagonistic effect of aluminium titrate on silica is suggested. (C) 1995 Academic Press Inc.

Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel

Time-dependent density-functional theory is a rather accurate and efficient way to compute electronic excitations for finite systems. However, in the macroscopic limit (systems of increasing size), for the usual adiabatic random-phase, local-density, or generalized-gradient approximations, one recovers the Kohn-Sham independent-particle picture, and thus the incorrect band gap. To clarify this trend, we investigate the macroscopic limit of the exchange-correlation kernel in such approximations by means of an algebraical analysis complemented with numerical studies of a one-dimensional tight-binding model. We link the failure to shift the Kohn-Sham spectrum of these approximate kernels to the fact that the corresponding operators in the transition space act only on a finite subspace.

Nonequilibrium Quantum Landauer Principle

Using the operational framework of completely positive, trace preserving operations and thermodynamic fluctuation relations, we derive a lower bound for the heat exchange in a Landauer erasure process on a quantum system. Our bound comes from a nonphenomenological derivation of the Landauer principle which holds for generic nonequilibrium dynamics. Furthermore, the bound depends on the nonunitality of dynamics, giving it a physical significance that differs from other derivations. We apply our framework to the model of a spin-1/2 system coupled to an interacting spin chain at finite temperature.

Potassium nickel(II) gallium phosphate hydrate, K[NiGa2(PO4)(3)(H2O)(2)]

The title compound, potassium nickel(II) digallium tris-( phosphate) dihydrate, K[NiGa2(PO4)(3)(H2O)(2)], was synthesized hydrothermally. The structure is constructed from distorted trans-NiO4(H2O)2 octahedra linked through vertices and edges to GaO5 trigonal bipyramids and PO4 tetrahedra, forming a three-dimensional framework of formula [NiGa2(PO4)(3)(H2O)(2)](-). The K, Ni and one P atom lie on special positions (Wyckoff position 4e, site symmetry 2). There are two sets of channels within the framework, one running parallel to the [10 (1) over bar] direction and the other parallel to [001]. These intersect, forming a three-dimensional pore network in which the water molecules coordinated to the Ni atoms and the K+ ions required to charge balance the framework reside. The K+ ions lie in a highly distorted environment surrounded by ten O atoms, six of which are closer than 3.1 angstrom. The coordinated water molecules are within hydrogen-bonding distance to O atoms of bridging Ga-O-P groups.