Exact and approximate numerical solutions to steady-state single-server queues:M/G/1 — a unified approach

This paper presents a unified approach for the numerical solutions of anM/G/1 queue. On the assumption that the service-time distribution has a rational Laplace-Stieltjes transform (LST), explicit closed-form expressions have been obtained for moments, distributions of system length and waiting time (in queue) in terms of the roots of associated characteristic equations (c.e.'s). Approximate analyses for the tails of the distributions based on one or more roots are also discussed. Numerical aspects have been tested for a variety of complex service-time distributions including but not restricted to only mixed generalized Erlang and generalized hyperexponential. A sample of numerical computations is also included. It is hoped that the results obtained would prove to be beneficial to both practitioners and theorists dealing with bounds, inequalities, approximations, and other aspects.     

Hall mobility of degenerate semiconductors

The dependence ofHall mobility of carriers on impurity content has been theoretically investigated for degenerate semiconductors, taking scattering by lattice vibrations as well as ionized impurities into account. The scattering due to optical modes of lattice vibrations has been neglected, for the sake of simplicity of calculations. This omission is not serious at temperatures, when the impurity scattering is important.     

Fluctuation-dissipation theorems for systems in non-thermal equilibrium and applications

The linear response theory of systems obeying Fokker-Planck equations is discussed under the assumption that the principle of detailed balance is satisfied. This theory is used to obtain fluctuation-dissipation theorems for systems in a non-thermal equilibrium state corresponding to the steady state solution of the Fokker-Planck equation. Some of the aspects of the threshold region of a single mode laser (without detuning) are discussed. In particular it is shown that, contrary to the results established recently by others, the “linear susceptibility” χ(Ω) is acontinuous function of the pump parameterp. The results are then specialized to Gaussian Markov process in which case an alternate form of the fluctuation-dissipation theorems is also given. Finally few other generalizations of the fluctuation-dissipation theorems are also briefly discussed.     

On the motion of visco-elastic electrically conducting liquid in the presence of a magnetic field

Zusammenfassung Es wird die Strömung einer viskoelastischen, elektrisch leitenden Flüssigkeit untersucht auf Grund der elektromagnetischen Grundgleichung und der für solche Flüssigkeiten geltenden Bewegungsgleichungen. Im besonderen wird die Strömung zwischen parallelen Platten erörtert. Sie ist charakterisiert durch zwei dimensionslose Kennzahlen, die Hartmannsche Zahl und die Elastizitätszahl. Das elastische Verhalten bewirkt eine Verflachung des Geschwindigkeitsprofils und verändert auch den Druck und die Schubspannungen.

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Notations x ₁,x ₂,x ₃ space coordinates - B magnetic induction vector - E electric intensity - H magnetic field - D displacement vector - J current density vector - _e E electrostatic force - V×B current density due to the motion of the fluid - _e V convection current - _e excess charge density - electrical conductivity - magnetic permeability - dielectric constant - =1/ magnetic diffusivity - V=v ¹ i+v ² j+v ³ k velocity vector - v ₁= ₁/ kinematic viscosity - ₁ coefficient of viscosity - _c coefficient of cross-viscosity - v _c = _c / kinematic cross-viscosity - density of the fluid - relaxation time - S _j ⁱ stress-tensor - d _j ⁱ strain-tensor - x, y, z dimensionless coordinates - L spacing between the planes, taken as the characteristic length - U ₀ characteristic velocity - f non-dimensional velocity - H non-dimensionalx-component of the magnetic field.     

Effects of self-focusing on the selfdistortion of amplitude modulated microwaves in non-parabolic semiconductors

Omitting the dispersion of side bands, the self-distortion of an amplitude-modulated e.m. signal due to non-linear polarizability in nonparabolic semiconductors has been investigated. The distortion is basically due to self-focusing of the electromagnetic wave and is different from the resistive (absorption) type demodulation.In n-InSb and at average powers of 1 W the index of modulation is found to increase four times at a modulation frequency R~10⁸ s^–1.     

Optimum acoustic wave second-harmonic generation in piezoelectric semiconductors

The phenomenological approach has been used to study analytically the acoustic wave second harmonic generation in piezoelectric semiconductors in the presence of the d.c. electric and an oscillating electromagnetic field (OEF). It has been suggested that the second harmonic acoustic flux (SHAF) can be enhanced considerably by the application of an OEF polarized in the direction of the propagating acoustic wave. The SHAF exhibits a maximum at Ω = ω, where Ω is the frequency of the OEF and ω is the frequency of the acoustic wave. The SHAF also shows a maximum at d.c. electric fields for which the average drift velocity of the carriers is equal to the velocity of sound. It is found that for a typical case of n-type nondegenerate InSb (77°K, n = 2·5 × 10¹⁴ cm^?3) that the SHAF is enhanced by a factor of 10³ over its value in the absence of OEF. The present analysis is valid in the low frequency region only (i.e. ql ? 1).     

Effect of magnesium substitution on dielectric and magnetic properties of Ni-Zn ferrite

The dielectric and magnetic properties of Mg incorporated Ni-Zn spinel ferrites have been investigated. Ni_0.5−xZn_0.5Mg_xFe₂O₄ ferrites have been prepared by sol-gel auto-combustion technique. The as prepared ferrites were annealed at 673, 873 and 1073 K. The X-ray diffraction studies reveal the spinel structure of annealed ferrites. The TEM results are in agreement with XRD results. FTIR study has also been carried out to get insight into the structure of these ferrites. The dielectric measurements show that the dielectric constant (ε′), dielectric loss (tan δ) and conductivity (σ_ac) increase on incorporation of Mg in the Ni-Zn ferrite. ε′, tan δ and σ_ac also show dependence on temperature, frequency of external applied electric field and microstructure of the samples. The magnetic moment measurements reveal that the saturation magnetization (M_s) increases and coercivity (H_c) decreases with the increase in concentration of Mg²⁺ ions. M_s and H_c also show dependence on the annealing temperature.     

Reporter protein-targeted probes for magnetic resonance imaging

Contrast agents for magnetic resonance imaging are frequently employed as experimental and clinical probes. Drawbacks include low signal sensitivity, fast clearance, and nonspecificity that limit efficacy in experimental imaging. In order to create a bioresponsive MR contrast agent, a series of four Gd(III) complexes targeted to the HaloTag reporter were designed and synthesized. HaloTag is unique among reporter proteins for its specificity, versatility, and the covalent interaction between substrate and protein. In similar systems, these properties produce prolonged in vivo lifetimes and extended imaging opportunities for contrast agents, longer rotational correlation times, and increases in relaxivity (r(1)) upon binding to the HaloTag protein. In this work we report a new MR contrast probe, 2CHTGd, which forms a covalent bond with its target protein and results in a dramatic increase in sensitivity. A 6-fold increase in r(1), from 3.8 to 22 mM(-1) s(-1), is observed upon 2CHTGd binding to the target protein. This probe was designed for use with the HaloTag protein system which allows for a variety of substrates (specific for MRI, florescence, or protein purification applications) to be used with the same reporter.     

Innovative synthesis of citrate-coated superparamagnetic Fe3O4 nanoparticles and its preliminary applications

In this study, we describe the development of a facile and effective route for the synthesis of Fe(3)O(4)-based T(1) contrast agent, which can be useful for in vivo magnetic resonance (MR) imaging. Citrate-coated Fe(3)O(4) nanoparticles (6 nm) with a narrow size distribution were synthesized by "one-pot green chemistry route" in diethylene glycol (DEG) solvent. The synthesized nanoparticles were characterized by different analytical techniques including XRD, TEM, HRTEM, and FTIR. At room temperature, nanoparticles exhibited superparamagnetic nature with high saturation magnetization. The longitudinal (r(1)) and transverse (r(2)) relaxivities were found to be 35.45 and 51.81 mM(-1)s(-1), respectively. Contrast agent developed by this method showed a relatively higher longitudinal relaxivity (r(1)) and the lowest relaxivity ratio (r(2)/r(1)=1.46) at 3T MR field. The anionic nature of citric acid facilitated non-specific internalization without impairment of cell viability and functionality. The in vitro studies showed both phagocitic and non-phagocytic uptake of these NPs. In vivo MR imaging of swine showed both T(1) and T(2) contrast effect.     

Glucosamine-based primary amines as organocatalysts for the asymmetric aldol reaction

Glucosamine derivatives have been synthesized starting from commercially available N-acetyl-D-glucosamine/glucosamine hydrochloride and have been employed successfully as efficient organocatalysts for the direct asymmetric aldol reaction between cyclohexanone and aryl aldehydes having diversified substituents. Furthermore, the anomeric effect of various groups present at the anomeric position on the catalytic activity of these organocatalysts was also studied.