An extended technicolour model for grand unification

An extended technicolour grand unification model based on the gauge groupE ₆×SU(7) extended technicolour is presented. The symmetry-breaking based on extended technicolour theory is discussed. It is shown that the existing phenomenology is well explained by the model. The strangeness changing neutral currents may not be a problem with this model.     

THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Electrochemically generated super-hydrophilic surfaces

The control of surface wettability of indium tin oxide (In2O3-SnO2) coated glass surfaces is studied. We report here the first observation of purely electrochemical generation of super-hydrophilic surfaces at In2O3-SnO2 electrodes in the absence of an ultraviolet illumination source. This is achieved by the application of high anodic potentials for a prolonged period. Such surfaces are reversibly converted back to their original hydrophobic state on storage in air (one or two days) or water (a week)(and vice versa). The unique character of these surfaces can be attributed to the surface structure of the hydrophilic phase.     

Divalent transition metal complexes of 3,5-pyrazoledicarboxylate

New divalent transition metal 3,5-pyrazoledicarboxylate hydrates of empirical formula Mpz(COO)₂(H₂O)₂, where M=Mn, Co, Ni, Cu, Zn and Cd (pz(COO)₂=3,5-pyrazoledicarboxylate), metal hydrazine complexes of the type Mpz(COO)₂N₂H₄ where M=Co, Zn or Cd and Mpz(COO)₂nN₂H₄·H₂O, where n=1 for M=Ni and n=0.5 for M=Cu have been prepared and characterized by physico-chemical methods. Electronic spectroscopic data suggest that Co and Ni complexes adopt an octahedral geometry. The IR spectra confirm the presence of unidentate carboxylate anion (Δν=ν_asy(COO^–)–ν_sym(COO^–)>215 cm^–1) in all the complexes and bidentate bridging hydrazine (ν_N–N=985–950 cm^–1) in the metal hydrazine complexes. Both metal carboxylate and metal hydrazine carboxylate complexes undergo endothermic dehydration and/or dehydrazination followed by exothermic decomposition of organic moiety to give the respective metal oxides as the end products except manganese pyrazoledicarboxylate hydrate, which leaves manganese carbonate. X-ray powder diffraction patterns reveal that the metal carboxylate hydrates are isomorphous as are those of metal hydrazine complexes of cobalt, zinc and cadmium.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.