On the range of the sum of monotone operators in general Banach spaces

The purpose of this paper is to generalize the Brézis-Haraux theorem on the range of the sum of monotone operators from a Hilbert space to general Banach spaces. The result obtained provides that the range is topologically almost equal to the sum where is a compatible topology in as proposed by Gossez. To illustrate the main result we consider some basic properties of densely maximal monotone operators.

     

Self-magnetism and Persistent Photoconductivity

Persistent photoconductivity has been investigated by various models, among which the Macroscopic Barrier model, Large-Lattice-Relaxation model, and Random Local Potential Fluctuations model are mostly well known. Although the three well-known models have played important roles in describing the persistent photoconductivity, they are not the principal cause of persistent photoconductivity. In this paper a classical model originated from ＂selfmagnetism of electron gas＂ is proposed to illustrate the persistent photoconductivity phenomenon. This classical model is based on electron gas pulsation, which depends on the charge density. Different concentrations of current carriers create different frequencies in the system, and thus the system is sensitive to different wave lengths of incident light. Then the construction of different detectors can be possible for different wave lengths of incident light.     

On non-linear magneto convection in a mushy layer with joule heating

This paper studies the flow pattern of non-linear magneto convection that can be realized in a horizontal mushy layer and in the presence of joule heating, which is the amount of heat produced by the induced magnetic field. We consider the appropriate system of equations and the associated boundary conditions for the flow in the mushy layer subjected to a vertical magnetic field of uniform strength. Under certain assumptions and conditions, we determine the stable finite-amplitude solutions of the resulting system using a perturbation approach and stability analysis. We find, in particular, that for a wide range of values of the joule heating parameter and sufficiently small amplitude of the flow, the only stable convective flow is in the form of subcritical down-hexagons with down-flow at the cells' centers and up-flow at the cells' boundaries. This result is in sharp contrast to the case in the absence of joule heating where instead the subcritical up-hexagons with up-flow at the cells' centers and down-flow at the cells' boundaries can be stable. In the presence of joule heating the stable subcritical down-hexagons were found to be enhanced with increasing the strength of the externally imposed magnetic field.     

On Perturbation and Marginal Stability Analysis of Magneto-Convection in Active Mushy Layer

This present study considers the problem of steady magneto-convection in a horizontal mushy layer with variable permeability and an impermeable mush–liquid interface during directional solidification of binary alloys. We model the flow by introducing a uniform magnetic field in the mushy layer which is considered as a porous medium where Darcy’s law holds and the permeability is a function of the local solid volume fraction. Basic-state solutions are obtained analytically using the no-flow condition. With the help of multiple shooting techniques, we obtain numerical solutions to the linear perturbation system for non-magnetic and magnetic cases. Numerical results are presented showing the effects of the magnetic field and the permeability of the layer. These results demonstrate that the application of an external magnetic field has stabilizing effects on the convection and can reduce the tendency for chimney formation in the mushy layer. In addition, variable permeability, which corresponds to an active mushy layer, indicates more stable and realizable flow system as compared to the case of constant permeability.     

Self-magnetism and Persistent Photoconductivity

Persistent photoconductivity has been investigated by various models, among which the Macroscopic Barrier model, Large-Lattice-Relaxation model, and Random Local Potential Fluctuations model are mostly well known. Although the three well-known models have played important roles in describing the persistent photoconductivity, they are not the principal cause of persistent photoconductivity. In this paper a classical model originated from “self-magnetism of electron gas” is proposed to illustrate the persistent photoconductivity phenomenon. This classical model is based on electron gas pulsation, which depends on the charge density. Different concentrations of current carriers create different frequencies in the system, and thus the system is sensitive to different wave lengths of incident light. Then the construction of different detectors can be possible for different wave lengths of incident light.     

H NMR Measurements of Wet/Dry Ratio andT1,T2Distributions in Lung

Proton-magnetic-resonance measurements have been carried out on juvenile porcine peripheral lung parenchyma. The free-induction-decay signal contained a motionally restricted component which decayed in a few tens of microseconds and a mobile component with aT₂time greater than 1 ms. The average second moment,M₂, for the motionally restricted signal was found to be 3.42 ± (0.25) × 10⁹s⁻². TheT₂distribution for the mobile signal consistently showed four resolvable components ofT₂range: 2–6, 10–40, 80–110, and 190–400 ms. The 2–6 ms component was present in a fully dehydrated preparation and was therefore assigned to a nonaqueous lung constituent. The motionally restricted FID component had aT₁= 0.772 ± 0.11 s and the mobile component had aT₁= 0.967 ± 0.02 s. The hydrogen content per unit mass for lung parenchyma and water were estimated in two ways: (1) on the basis of chemical content and (2) on the basis of comparison of restricted and mobile signals to the gravimetric (G) water content for a lung sample studied at a wide range of water contents. Lung wet/dry weight ratios were estimated from the free-induction decays and compared with gravimetric measurement. The ratio of (wet/dry)_NMR/(wet/dry)_Gwas 1.00 ± 0.08 and 1.00 ± 0.05 for the two methods of estimation.     

Ultra-long carbon nanotube growth on catalyst

Ultra-long carbon nanotube growth with Fe particles sitting at tip end as a function of reaction time, reaction temperature, diameter of the carbon nanotube, damping factor of the system, and the type of catalyst in chemical vapor deposition is investigated by using a theoretical analysis on the phonon vibration of the system. Simulations demonstrate that metal cluster makes and keeps the carbon atoms at tip end reactive. So carbon nanotube grows more than 4 cm. In addition, results show carbon nanotubes with larger diameter grow lesser owing to higher damping factors. In addition, effect of temperature on growth is discussed and it is shown that there is an optimum temperature for growth process. Lastly, dependence of type of catalyst on growth process is investigated.     

Ultrasound-promoted solvent-free aza-Michael addition of p-toluenesulfonamide to fumaric esters by potassium carbonate: Synthesis of p-toluenesulfonamide derivatives

An efficient, mild, inexpensive and eco-friendly protocol for the synthesis of p-toluenesulfonamide derivatives by aza-Michael addition reaction of p-toluenesulfonamide to fumaric esters using potassium carbonate under ultrasound irradiation was developed. This method is simple, convenient and the desired compounds are produced in good to excellent yield. The bulkiness of alkoxy group (–OR) of fumaric esters did not affect significantly on the yields and reaction times. This reaction worked well on linear and nonlinear alkyl fumarates. The reaction, surprisingly, was not successful on methyl fumarate. In this case methyl fumarate has been hydrolyzed to fumaric acid under reaction conditions.     

Sonodisruption of re-assembled casein micelles at different pH values

Casein solutions with different pH values were sonicated at a frequency of 35 kHz and increasing acoustic powers. As the sonication power increased, turbidity of solutions and particle diameter decreased at any given pH value, suggesting particles disruption due to the ultrasonic treatment. The magnitude of decrease in re-assembled micelles diameter was greater at a higher pH, indicating an interaction between pH and sonication power in sonodissociation. This interaction is attributed to a looser structure of micelles at higher pH values which increases the efficiency of ultrasonic disruption and not directly to the increased cavitation efficiency. We argue that increased cavitation efficiency with increasing sonication power, which enhances shear forces is the most likely reason for sonodisruption of re-assembled casein micelles.