Existence and uniqueness of the solution,separation for certain second order elliptic differential equation

In this paper, we study conditions under which Schrodinger type operators with a matrix potential is separated and Schrodinger equation has a unique solution in the weighted space L_2,k(Rⁿ)^l, where l is any natural number and k ε C¹(Rⁿ) is a positive function     

Low temperature,atmospheric pressure,direct current microplasma jet operated in air,nitrogen and oxygen

Micro-plasma jets in atmospheric pressure molecular gases (nitrogen, oxygen, air) were generated by blowing these gases through direct current microhollow cathode discharges (MHCDs). The tapered discharge channel, drilled through two 100 to 200 μm thick molybdenum electrodes separated by a 200 μm thick alumina layer, is 150 to 450 μm in diameter in the cathode and has an opening of 100 to 300 μm in diameter in the anode. Sustaining voltages are 400 to 600 V, the maximum current is 25 mA. The gas temperature of the microplasma inside the microhollow cathode varies between ~2000 K and ~1000 K depending on current, gas, and flow rate. Outside the discharge channel the temperature in the jet can be reduced by manipulating the discharge current and the gas flow to achieve values close to room temperature. This cold microplasma jet can be used for surface treatment of heat sensitive substances, and for sterilization of contaminated areas.     

Light reflection from finite conductors with a Gaussian random roughness using Kirchhoff and geometric optics approximations

A comparison between exact solutions and two approximate models, Kirchhoff approximation (KA) and geometric optics approximation (GOA), for reflection from random Gaussian rough conductive metallic surfaces for three regimes of correlation length in both cases of polarization TM and TE has been reported. The phenomenon of excitation of surface plasmons (SPs) has been shown only at TM polarization for KA. The domains of validity of both approximate models have been quantified. It is shown that accuracy and efficiency of any approximate method depended of various parameters: surface roughness, polarization, SPs effects, wavelength, and surface materials. KA is efficient for weakly rough surfaces with correlation length greater than wavelength, but when rms height increases GOA is more suitable than KA. Excitation of SPs is observed only at TM-polarized light, only for weakly rough surfaces with correlation length less than wavelength using KA and not GOA.     

Bifunctional-elementary relation algebras

A relation algebra is bifunctional-elementary if it is atomic and for any atom a, the element a;1;a is the join of at most two atoms, and one of these atoms is bifunctional (an element x is bifunctional if ’). We show that bifunctional-elementary relation algebras are representable. Our proof combines the representation theorems for: pair-dense relation algebras given by R. Maddux; relation algebras generated by equivalence elements provided corresponding relativizations are representable by S. Givant; and strong-elementary relation algebras dealt with in our earlier work. It turns out that atomic pair-dense relation algebras are bifunctional elementary, showing that our theorem generalizes the representation theorem of atomic pair-dense relation algebras. The problem is still open whether the related classes of rather elementary, functional-elementary, and strong functional-elementary relation algebras are representable. Received July 15, 2007; accepted in final form March 17, 2008.     

Suppression of hysteresis in a forced van der Pol–Duffing oscillator

This paper examines the suppression of hysteresis in a forced nonlinear self-sustained oscillator near the fundamental resonance. The suppression is studied by applying a rapid forcing on the oscillator. Analytical treatment based on perturbation analysis is performed to capture the entrainment zone, the quasiperiodic modulation domain and the hysteresis area as well. The analysis leads to a strategy for the suppression of hysteresis occurring between 1:1 frequency-locked motion and quasiperiodic response. This hysteresis suppression causes the disappearance of nonlinear effects leading to a smooth transition between the quasiperiodic and the frequency-locked responses. Specifically, it appears that a rapid forcing introduces additional apparent nonlinear stiffness which can effectively suppress hysteresis in a certain range of the rapid excitation frequency. This work was motivated by the important issue of controlling and eliminating hysteresis often undesirable in mechanical systems, in general, and in application to microscale devices, especially.     

Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction

An analysis is carried out to study the flow, chemical reaction and mass transfer of a steady laminar boundary layer of an electrically conducting and heat generating fluid driven by a continuously moving porous surface embedded in a non-Darcian porous medium in the presence of a transfer magnetic field. The governing partial differential equations are converted into ordinary differential equations by similarity transformation and are solved numerically by using the finite element method. The results obtained are presented graphically for velocity, temperature and concentration profiles, as well as the Sherwood number for various parameters entering into the problem.     

Schur operators and domination problem

In this paper we are concerned with developing generalizing concepts of Dunford–Pettis operators analogous to the generalization of compact operators by strictly singular operators. Also, we give some new results concerning the domination problem in the setting of positive operators between Banach lattices.     

Theoretical and experimental investigations of complexation with BF3.Et2O effects on electronic structures,energies and photophysical properties of Anil and tetraphenyl (hydroxyl) imidazol

The novel compounds (E)‐2‐(((4‐hydroxyphenyl)imino)methyl)phenol, Tetraphenyl (hydroxyl) imidazole and their corresponding Boron difluoride complexes were synthesized and characterized by spectroscopic techniques. Density functional theory calculations at B3LYP‐D3/6–311++G (d, p) level of theory were performed for the geometric parameters. The MEP surface studies were used to understand the behavior of molecules in terms of charge transfer and to determine how these molecules interact. We used the GIAO and the B3LYP‐D3 with a 6–311++ G (d, p) basis set to simulate the (¹H‐NMR and ¹⁹F‐NMR) and the IR spectra, respectively. The corresponding calculated results are in good agreement with the experimental data. The stability of the molecule arising from hyperconjugation interaction and charge delocalization were analyzed using NBO analysis. FMOs revealed the occurrence of charge transfer within the molecule. The complexation using BF₃.Et₂O was also found to have remarkable effects on the electrochemical properties of the studied molecules, where (b) and (d) present lower chemical stability, higher reactivity and higher polarizability than (a) and (c), respectively. Moreover, the energy gap of (a) and (c) decreased after complexation using BF₃.Et₂O, indicating the reliability of the electrochemical evaluation of LUMO and HOMO energy levels. These values are the factors explaining the possible charge transfer interaction within the molecule. The absorption and emission spectra of the model compound were also simulated and compared to experimental observations in the DMF solvent. The results of DFT calculations supported the structural and spectroscopic data and confirmed the structure modification of frontier molecular orbitals for BF₂ complexes as well as tunable potentials and energy levels.