Adjugates in Banach algebras

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

     

Fractal strings as an alternative justification for El Naschie''s cantorian spacetime and the fine structure constant

Beginning with the most general fractal strings/sprays construction recently expounded in the book by Lapidus and Frankenhuysen, it is shown how the complexified extension of El Naschie's cantorian-fractal spacetime model belongs to a very special class of families of fractal strings/sprays whose scaling ratios are given by suitable pinary (pinary, p prime) powers of the Golden Mean. We then proceed to show why the logarithmic periodicity laws in Nature are direct physical consequences of the complex dimensions associated with these fractal strings/sprays. We proceed with a discussion on quasi-crystals with p-adic internal symmetries, von Neumann's Continuous Geometry, the role of wild topology in fractal strings/sprays, the Banach-Tarski paradox, tesselations of the hyperbolic plane, quark confinement and the Mersenne-prime hierarchy of bit-string physics in determining the fundamental physical constants in Nature.     

Electrochemical impedance spectroscopy and linear polarization applied to evaluation of porosity of phosphate conversion coatings on electrogalvanized steels

In this work, electrochemical impedance spectroscopy and linear polarization are used in determining porosity of zinc phosphates, and of nickel and manganese modified zinc phosphates on electrogalvanized steel. The porosity of the phosphate layers ranges from 0.1% for the manganese-modified hopeite to 8% for hopeite, using the linear polarization and the electrochemical impedance spectroscopy techniques. The porosity values measured using the two techniques were in agreement. All impedance spectra of coated samples showed two steps, with two capacitive arcs and an inductive looping.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

Area orthogonality in normed linear spaces

A new concept of orthogonality in real normed linear spaces is introduced. Typical properties of orthogonality (homogeneity, symmetry, additivity, ...) and relations between this orthogonality and other known orthogonalities (Birkhoff, Boussouis, Unitary-Boussouis and Diminnie) are studied. In particular, some characterizations of inner product spaces are obtained.     

Alloy model for high-temperature superconductors

An alloy model is proposed for the electronic structure of high-temperature superconductors. It is based on the assumption that holes and extra electrons are localized in small copper-oxygen clusters, that would be the components of such an alloy. This model, when used together with quantum chemical calculations on small clusters, can explain the structure observed in the experimental densities of states of both hole and electron superconductors close to the Fermi energy. The main point is the strong dependence of the energy level distribution and composition on the number of electrons in a cluster. The alloy model also suggests a way to correlate T_c with the number of holes, or extra electrons, and the number of adequate clusters to locate them.     

One‐step synthesis of aminopyrimidines from 5‐Oxo‐4H‐benzopyrans

Novel 4‐amino‐6‐aryl‐2‐phenylpyrimidine‐5‐carbonitriles have been prepared in one step procedure from the readily available 4‐aryl‐2‐amino‐3‐cyano‐5,6,7,8‐tetrahydro‐7,7‐dimethyl‐5‐oxo‐4H‐benzopyrans. The mass spectroscopy study under EI conditions shows molecular peaks with high intensity corresponding to the loss of benzonitrile from the C2 position of the pyrimidine ring. Semiempirical (AMI and PM3) and ab initio HF/6–31G* calculations reveal a favored distorted geometry where the three rings are not in the same plane.     

Lie point symmetries of the Lane-Emden systems

It is shown that a Lie point symmetry of the Lane-Emden system is a Noether symmetry if and only if its parameters belong to the critical hyperbola.