Joint Fractional Time Allocation and Beamforming for Downlink Multiuser MISO Systems

It is well-known that the traditional transmit beamforming at a base station (BS) to manage interference in serving multiple users is effective only when the number of users is less than the number of transmit antennas at the BS. Non-orthogonal multiple access (NOMA) can improve the throughput of users with poorer channel conditions by compromising their own privacy because other users with better channel conditions can decode the information of users in poorer channel state. NOMA still prefers that the number of users is less than the number of antennas at the BS transmitter. This paper resolves such issues by allocating separate fractional time slots for serving the users with similar channel conditions. This enables the BS to serve more users within the time unit while the privacy of each user is preserved. The fractional times and beamforming vectors are jointly optimized to maximize the system's throughput. An efficient path-following algorithm, which invokes a simple convex quadratic program at each iteration, is proposed for the solution of this challenging optimization problem. Numerical results confirm its versatility.Comment: IEEE Communications Letters (To Appear

Robust Beamforming for Secrecy Rate in Cooperative Cognitive Radio Multicast Communications

In this paper, we propose a cooperative approach to improve the security of both primary and secondary systems in cognitive radio multicast communications. During their access to the frequency spectrum licensed to the primary users, the secondary unlicensed users assist the primary system in fortifying security by sending a jamming noise to the eavesdroppers, while simultaneously protect themselves from eavesdropping. The main objective of this work is to maximize the secrecy rate of the secondary system, while adhering to all individual primary users' secrecy rate constraints. In the case of passive eavesdroppers and imperfect channel state information knowledge at the transceivers, the utility function of interest is nonconcave and involved constraints are nonconvex, and thus, the optimal solutions are troublesome. To address this problem, we propose an iterative algorithm to arrive at a local optimum of the considered problem. The proposed iterative algorithm is guaranteed to achieve a Karush-Kuhn-Tucker solution.Comment: 6 pages, 4 figures, IEEE ICC 201

Modeling Error of α-Models of Turbulence on a Two-Dimensional Torus

This paper is devoted to study the rate of convergence of the weak solutions u α of α-regularization models, namely the Leray-α, Navier-Stokes-α, modified Leray-α and simplified Bardina models, to the weak solution u of the Navier-Stokes equations in the two-dimensional case with subjecting to the periodic boundary conditions as the regularization parameter α goes to zero

On asymptotic properties of solutions to σ\sigma-evolution equations with general double damping

In this paper, we would like to consider the Cauchy problem for semi-linear $\sigma$-evolution equations with double structural damping for any $\sigma\ge 1$. The main purpose of the present work is to not only study the asymptotic profiles of solutions to the corresponding linear equations but also describe large-time behaviors of globally obtained solutions to the semi-linear equations. We want to emphasize that the new contribution is to find out the sharp interplay of ``parabolic like models" corresponding to $\sigma_1 \in [0,\sigma/2)$ and ``$\sigma$-evolution like models" corresponding to $\sigma_2 \in (\sigma/2,\sigma]$, which together appear in an equation. In this connection, we understand clearly how each damping term influences the asymptotic properties of solutions.Comment: 29 page

Effect of chromium substituted on structural and magnetic characterization lithium ferrite nanoparticles

In this work, we present a structural, morphology and magnetic study of the Li0.5Fe2.5-xCrxO4 spinel nanoparticles (x = 0, 0.5, 0.75, 1, and 1.25) with mean particle size of 20-30 nm prepared by sol-gel method. The lattice constants and the size of particle decrease with increasing Cr concentration. In these samples, the preference of Cr3+ and Li+ ions in the octahedral sites and a small degree of site-interchange between Li+ in the octahedral sites and Fe3+ in the tetrahedral sites were found which increases with increasing the Cr content. A decrease of magnetization due to the spin disorder in the surface layer of the particles was observed. The spontaneous magnetization at 5K suggests the Néel type of magnetic ordering in these samples. The magnetic coercivity is discussed in terms of particle size, morphology and chromium substitution. Keywords. Chromium substitution, sol-gel method, nanoparticles, lithium ferrite

Catalytic Dye Oxidation over CeO2 Nanoparticles Supported on Regenerated Cellulose Membrane

A novel regenerated cellulose (RC) membrane containing cerium oxide (CeO2) nanoparticles is described in detail. In this work, CeO2 nanoparticles with high surface area and mesoporosity were prepared by a modified template-assisted precipitation method. Successful synthesis was achieved using cerium nitrate as a precursor, adjusting the final pH solution to around 11 by ammonium hydroxide and ethylene diamine, and annealing at 550 °C for 3 hours under a protective gas flow. This resulted in a surface area of 55.55 m².g–1 for the nanoparticles. The regenerated cellulose membrane containing CeO2 particles was synthesized by the novel and environmentally friendly method. The catalyst CeO2 and cellulose/CeO2 membrane were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), Electron paramagnetic resonance (EPR), and Brunauer-Emmett-Teller (BET) measurements. The g-value of 2.276 has confirmed the presence of the surface superoxide species of CeO2 nanoparticles in EPR. The photocatalytic activity of the catalyst and the membrane containing the catalyst was evaluated through the degradation of methylene blue under visible light irradiation by UV-VIS measurements. The cellulose/CeO2 membrane degraded 80% of the methylene blue solution in 120 minutes, showing a better photocatalytic activity than the CeO2 catalyst, which degraded approximately 62% in the same period. It has been proven that the RC membrane is not only a good transparent supporting material but also a good adsorption for high-performance of CeO2 catalyst. Copyright © 2022 by Authors, Published by BCREC Group. This is an open access article under the CC BY-SA License (https://creativecommons.org/licenses/by-sa/4.0).

Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming

We prove a version of Lagrange multipliers theorem for nonsmooth functionals defined on normed spaces. Applying these results, we extend some results about saddle point optimality criteria in mathematical programming