Generalized set-valued mixed nonlinear quasi variational inequalities

In this paper we introduce and study a number of new classes of quasi variational inequalities. Using essentially the projection technique and its variant forms we prove that the generalized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations (normal maps). This equivalence enables us to suggest a number of iterative algorithms for solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational inequalities, we obtain a class of quasi variational inequalities studied by Siddiqi, Husain and Kazmi [35], but there are several inaccuracies in their formulation of the problem, the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of their results can be obtained as special cases from our main results.     

Generation of dark hollow beam by use of phase-only filtering

A simple but effective scheme to generate dark hollow beams is proposed by use of phase-only filtering and optical Fourier transform. A Gaussian beam of fundamental mode is modulated by a pre-designed phase mask, which is a piecewise modification of an axicon lens, and followed by a Fourier transform to generate an ideal dark hollow beam at the focal plane. This method has an advantage that the total energy of the beam is conserved under paraxial approximation. Numerical calculations are provided to show the validity of the proposed scheme.     

Entropy squeezing of an atom with a k-photon in the Jaynes--Cummings model

The entropy squeezing of an atom with a k-photon in the Jaynes-Cummings model is investigated. For comparison, we also study the corresponding variance squeezing and atomic inversion. Analytical results show that entropy squeezing is preferable to variance squeezing for zero atomic inversion. Moreover, for initial conditions of the system the relation between squeezing and photon transition number is also discussed. This provides a theoretical approach to finding out the optimal entropy squeezing.     

Optical Fiber Excitation of Fano Resonances in a Silicon Microsphere

In this article, Fano lineshape whispering gallery modes were observed in the light scattering spectrum of a silicon microsphere in near-infrared telecommunication wavelengths. A simple model is presented to explain the transition from Lorentzian lineshape to the Fano lineshape resonances with the coupled-mode theory of multiple whispering gallery modes. Polar mode spacing of 0.23 nm is observed in the spectra, which correlates well with the calculated value. The quality factor of the Lorentzian and Fano resonances are on the order of 10⁵. By using an appropriate interface design for the microsphere coupling geometries, Fano lineshape optical resonances herald novel device applications for silicon volumetric lightwave circuits.     

Transfer of radioactivity from soil to vegetation in Rechna Doab, Pakistan

In Rechna Doab, samples of the most common vegetation, perennial grass Desmostachya bipinnata (dab), were collected along with soil samples from 29 sites. Natural radioactivity of 22?Ra, 232Th/22?Ac and ??K was measured by using high purity germanium-based gamma ray spectrometer. Activity concentration levels of 22?Ra, 232Th/22?Ac and ??K in soil were found to be 46.8 ± 6.2 (36.0-57.6), 61.4 ± 5.9 (48.2-73.2) and 644.8 ± 73.9 (537.7-868.4) Bq kg?1 (dry mass), respectively, and those in vegetation were 2.74 ± 1.70 (1.00-6.39), 2.24 ± 0.59 (1.56-2.61) and 172.72±113.37 (53.14-469.24) Bq kg?1 (dry mass), respectively. The measured values of the activity concentration in vegetation are comparable with some other international data. Calculated soil to vegetation transfer factors of 22?Ra, 22?Ac and ??K were 0.06 ± 0.03 (0.02-0.14), 0.04 ± 0.01 (0.03-0.04) and 0.26 ± 0.16 (0.09-0.69). The mean outdoor absorbed dose rate in air for the area under study was determined as 8.22 nGy h?1 and the mean indoor absorbed dose rate in air was 11.52 nGy h?1. The total annual effective dose to the general public from the vegetation was found to be (0.02-0.16) mSv, which is below the recommended limit value of 1 mSv y?1 for the general public. The dab vegetation under study was found to be radiologically safe for the population and environment.     

Rician noise reduction in magnetic resonance images using adaptive non-local mean and guided image filtering

This paper proposes a Rician noise reduction method for magnetic resonance (MR) images. The proposed method is based on adaptive non-local mean and guided image filtering techniques. In the first phase, a guidance image is obtained from the noisy image through an adaptive non-local mean filter. Sobel operators are applied to compute the strength of edges which is further used to control the spread of the kernel in non-local mean filtering. In the second phase, the noisy and the guidance images are provided to the guided image filter as input to restore the noise-free image. The improved performance of the proposed method is investigated using the simulated and real data sets of MR images. Its performance is also compared with the previously proposed state-of-the art methods. Comparative analysis demonstrates the superiority of the proposed scheme over the existing approaches.     

Appraisal of radioactivity and associated radiation hazards in sand samples of four rivers of Punjab province, Pakistan

Natural and anthropogenic radioactivity of sand and water samples collected from the four big rivers of Punjab province, Pakistan, was measured using a high-purity germanium detector coupled with a high resolution multichannel analyser. The average concentration of the naturally occurring radionuclides (226)Ra, (232)Th and (40)K in all the sand samples from the rivers Jhelum, Chenab, Ravi and Indus was found to be 22±0.6, 36±1 and 287±10 Bq kg (-1), respectively, while the concentration of the anthropogenic radionuclide (137)Cs was found to be below the minimum detectable activity, i.e. ~1.2 Bq?kg (-1). All the sand samples have Ra(eq) concentrations lower than the limit of 370 Bq kg (-1). Indoor (H (in)) and outdoor (H (out)) radiation hazard indices were calculated for the samples to assess the radiation hazards arising due to the use of this sand in construction, and were found to be less than unity in the study area. Calculated values of the absorbed dose rate were less than the typical world average value of 59 nGy h (-1), and the annual effective dose rate was also less than the typical world value of 70 μSv, except in the Indus river, in which it is slightly higher then the world average. Results show that the measured values are comparable with other global radioactivity measurements. None of the studied riverbeds was considered a radiological hazard, and their sand can be safely used in construction.     

Projection algorithms for solving a system of general variational inequalities

In this paper, we introduce and consider a new system of general variational inequalities involving four different operators. Using the projection operator technique, we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving three operators, variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.     

Effect of Temperature Anisotropy on Various Modes and Instabilities for a Magnetized Non-relativistic Bi-Maxwellian Plasma

Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those modes whose magnetic-field perturbations are perpendicular to the ambient magnetic field, i.e., B ₁ $\bot $ B ₀, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them (i.e., the whistler mode, pure Alfvén mode, firehose instability, and whistler instability), and the O-mode are affected by thermal anisotropies, since they satisfy the required condition $\mathbf{B}_{1}\bot \mathbf{B}_{0}$ . By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfvén waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations. The threshold conditions for different instabilities are also obtained.     

Bounds for Shannon and Zipf‐Mandelbrot entropies

Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy.