Sharif Digital Repository

We study the regularity of solutions of the following semilinear problemΔu=−λ+(x)(u+)q+λ−(x)(u−)qinB1,where B1 is the unit ball in ℝn, 0 < q < 1 and λ± satisfy a Hölder continuity condition. Our main results concern local regularity analysis of solutions and their nodal set {u = 0}. The desired regularity is C[κ],κ−[κ] for κ = 2/(1 − q) and we divide the singular points in two classes. The first class contains the points where at least one of the derivatives of order less than κ is nonzero, the second class which is named Sκ, is the set of points where all the derivatives of order less than κ exist and vanish. We prove that Sκ= ∅ when κ is not an integer. Moreover, with an example we show... 

We study the regularity of solutions of the following semilinear problem(Formula presented.)where B1 is the unit ball in ℝn, 0 < q < 1 and λ± satisfy a Hölder continuity condition. Our main results concern local regularity analysis of solutions and their nodal set {u = 0}. The desired regularity is C[κ],κ−[κ] for κ = 2/(1 − q) and we divide the singular points in two classes. The first class contains the points where at least one of the derivatives of order less than κ is nonzero, the second class which is named (Formula presented.), is the set of points where all the derivatives of order less than κ exist and vanish. We prove that (Formula presented.) when κ is not an integer. Moreover,... 

The singular sources method is given to detect the shape of a thin infinitely cylindrical obstacle from a knowledge of the TM-polarized scattered electromagnetic field in large distance. The basic idea is based on the singular behaviour of the scattered field of the incident point source on the cross-section of the cylinder. We assume that the scatterer is a perfect conductor which is possibly coated by a material and investigate two models with different boundary conditions. Also we give a uniqueness proof for the shape reconstruction. Copyright © 2006 John Wiley & Sons, Ltd  

Long-term evolution (LTE) is aimed to achieve the peak data rates in excess of 300 Mb/s for the next-generation wireless communication systems. Turbo codes, the specified channel-coding scheme in LTE, suffer from a low-decoding throughput due to its iterative decoding algorithm. One efficient approach to achieve a promising throughput is to use multiple maximum a posteriori (MAP) cores in parallel, resulting in a large area overhead. The two computationally challenging units in an MAP core are α and β recursion units. Although several methods have been proposed to shorten the critical path of these recursion units, their area-efficient architecture with minimum silicon area is still missing.... 

Long term evolution (LTE)-advanced aims the peak data rates in excess of 3 Gbps for the next generation wireless communication systems. Turbo codes, the specified channel coding scheme in LTE, suffers from a low-decoding throughput due to its iterative decoding algorithm. One efficient approach to achieve a promising throughput is to use multiple Maximum a Posteriori (MAP) cores in parallel, resulting in a large area overhead, a big drawback. The scaled Max-log MAP algorithm is a common approach to implement the MAP algorithm due to its efficient architecture with its acceptable performance. Although many works have been reported to reduce the area of the MAP unit, an efficient VLSI... 

5-th generation mobile networks aim the peak data rates in excess of few Gbs, which may appear to be challenging to achieve due to the existence of some blocks such as the turbo decoder. In fact, the interleaver is known to be a major challenging part of the turbo decoder due to its need to the parallel interleaved memory access. LTE uses Quadratic Permutation Polynomial (QPP) interleaver, which makes it suitable for the parallel decoding. In this paper, a new property of the QPP interleaver, called the correlated shifting property, is theoretically proved, leading to a fully scalable interleaver and a low-complexity address generator for an arbitrary order of parallelism. The proposed... 

The purpose of this paper is to provide a full analysis of the null controllability problem for the one dimensional degenerate/singular parabolic equation ut - (a(x)ux)x - λ/x βu = 0, (t,x) ∈ (0, T) × (0,1), where the diffusion coefficient a(·) is degenerate at x = 0. Also the boundary conditions are considered to be Dirichlet or Neumann type related to the degeneracy rate of a(·). Under some conditions on the function a(·) and parameters β, λ, we prove global Carleman estimates. The proof is based on an improved Hardy-type inequality  

We consider the homogenization of a Robin boundary value problem in a locally periodic perforated domain which is also time-dependent. We aim at justifying the homogenization limit, that we derive through asymptotic expansion technique. More exactly, we obtain the so-called corrector homogenization estimate that specifies the convergence rate. The major challenge is that the media is not cylindrical and changes over time. We also show the existence and uniqueness of solutions of the microscopic problem. © 2020 American Institute of Mathematical Sciences. All rights reserved  

The purpose of this paper is to address the question of well-posedness and spectral controllability of the wave equation perturbed by potential on networks which may contain unbounded potentials in the external edges. It has been shown before that in the absence of any potential, there exists an optimal time T∗ (which turns out to be simply twice the sum of all length of the strings of the network) that describes the spectral controllability of the system. We will show that this holds in our case too, i.e., the potentials have no effect on the value of the optimal time T∗. The proof is based on the famous Beurling-Malliavin’s Theorem on the completeness interval of real exponentials and on a... 

We study the semilinear problem Δu=λ+(x)(u+)q−1−λ−(x)(u−)q−1inB1, from a regularity point of view for solutions and the free boundary ∂{±u>0}. Here B1 is the unit ball, 1