Generalized gauge fields and applications to weak interactions

Yang-Mills' field is generalized to possess a nontrivial scalar part. The most general transformations for such a field under the 3-parameter isotopic gauge transformation is obtained. Using this generalized gauge field, a gauge invariant Lagrangian is constructed within the framework of the quark model. Interactions for spin-1 as well as for spin-0 are generated. As a further application a weak interaction theory mediated by the generalized gauge (boson) field is formulated. The entire weak interactions are generated in two halfs; the hadron-boson interaction is generated according to Yang-Mills' trick using the generalized gauge field and the other half (boson-lepton, etc.) is then generated by making use of the scalar part of the gauge fields according to the conventional pion gauge principle. The effective Lagrangian is then found to be mediated by the effective propagators which fall off as p⁻² at high momenta; the unitarity of the theory can thereby be insured. Universality in weaker sense than the usual one is applied to the intermediate bosons; our theory for β-decay then reduces to Cabibbo's at low energy.     

Vibrational spectroscopic studies of (3-mercaptopropyl)trimethoxylsilane sol-gel and its coating

Organosilane sol-gels have been prepared under different conditions from mercaptopropyltrimethoxysilane (MPTMS) and mercaptopropyltriethoxysilane (MPTES). These sol-gels were applied for the thin film coating on aluminum. Vibrational spectroscopy has been employed to trace and to study the proceeding of the sol-gel formation and the curing of the coated films on Al. Based on the group frequencies as well as their spectral behavior under different conditions, vibrational assignments have been made for most of the observed bands. Surface enhanced Raman scattering has revealed the chemical adsorption of MPTMS sol-gel on silver particles. Recorded reflection and absorption infrared (RAIR) spectra of coated tiles cured at different temperatures have indicated that surface reaction may occur at high temperature. The anticorrosion characters of the coated metals have been evaluated with the measured electrochemical data. Results from cyclic voltammographs have indicated that each layer of sol-gel coating would reduce the redox current across the electrode/electrolyte solution interface. Tafel plots have shown that the anodic current of the coated electrode decreases significantly and the corrosion potentials shift to the positive side.     

On the Asymptotic Behavior of Solutions of Differential Systems

There are many studies on the asymptotic behavior of solutions of differential equations. In the present paper, we consider another aspect of this problem, namely, the rate of the asymptotic convergence of solutions. Let ϕ (t) be a scalar continuous monotonically increasing positive function tending to ∞ as t → ∞. It is established that if all solutions of a differential system satisfy the inequality

Laser excited luminescence of coronene in a shpolskii matrix

The luminescence spectrum of coronene in n-heptane at 77°K has been studied using both xenon lamp and argon ion laser excitation. The results illustrate the Shpolskii theory of different emitting sites. With xenon excitation the emission spectrum consists of two similar slightly shifted subspectra. With laser excitation at 3511 Å only the longer wavelength subspectrum is observed. Fluorescence and phosphorescence excitation spectra show that this laser line is absorbed by the longwave component of the S₂←S₀ doublet.     

Generalizing some properties of short range classical solutions to Yang-Mills theory

We extend a theorem which states that for classical solutions of Yang-Mills theory, the field G_μν has to decrease at least as fast as the source S_μ at spatial infinity, provided G_μν decreases exponentially [G_μν ～ exp(?Mr)]. This generalization encompasses all decreases G_μν ～ exp(?Mr^η) with η > 0, r→∞. This is done by assuming an integral representation for A_μ, the vector potential, and imposing some regularity conditions on A_μ, valid as r→∞.     

Spectroscopic studies of trimetoxypropylsilane and bis(trimethoxysilyl)ethane sol-gel coatings on aluminum and copper

Trimethoxypropylsilane (TMPS) and bis(trimethoxysilyl)ethane (BTMSE) were used as surface modifiers of metal vie the sol-gel process and dip coating. In addition to the single coating of Al, Cu and Sn, double treatments of Al were also conducted by combining coatings with these sol-gels in different sequences. Reflection and absorption infrared spectroscopy (RAIR) was employed to characterize and to trace the proceeding of the sol-gel process of the films. It was found that the silanol condensation occurs in the coating films on Al and the covalent linkage exists between the TMPS film and copper surface. From the assigned vibration modes, two conformers were identified in pure TMPS, TMPS sol-gel and coated film. A series of dip coating experiments with different concentrations of TMPS sol-gel was conducted, and the results from the collected RAIR spectra of the coated samples suggested that the coated Cu consistently has a better RAIR spectrum than that of the coated Al. The TMPS sol-gel appeared to have a better affinity to Cu than to Al. The temperature effect and the aging effect in the coating films were studied. X-ray photoelectronic spectroscopy (XPS) was employed to characterize the coated film, and the XPS data confirm the formation of the siloxane film from the silane coupling agents (SCA). Electrochemical impedance spectra (EIS) have been collected for bare Al and Cu, BTMSE sol-gel coated Al, and TMPS sol-gel coated Cu in 0.15M NaCl solution. The corresponding electronic circuit parameters have been determined to match the experimental EIS data.     

On a backward problem for fractional diffusion equation with Riemann-Liouville derivative

In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L² and H^τ norms is considered and illustrated by numerical example.     

A discrete convolution involving Fourier sine and cosine series and its applications

ABSTRACT

In this paper, we introduce a discrete convolution involving both the Fourier sine and cosine series. We study Young's type inequality and a discrete transform related to this convolution and solve in closed form a class of discrete Toeplitz plus Hankel equations.     

New Convolutions for Quadratic-Phase Fourier Integral Operators and their Applications

We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann–Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.