Sharif Digital Repository

We present a linear programming based algorithm for a class of optimization problems with a multi-linear objective function and affine constraints. This class of optimization problems has only one objective function, but it can also be viewed as a class of multi-objective optimization problems by decomposing its objective function. The proposed algorithm exploits this idea and solves this class of optimization problems from the viewpoint of multi-objective optimization. The algorithm computes an optimal solution when the number of variables in the multi-linear objective function is two, and an approximate solution when the number of variables is greater than two. A computational study... 

This brief deals with finding the necessary conditions which should be met by the polynomials appeared in the admittance functions passively realizable by using RLC components and two fractional elements. These conditions include structurally necessary equalities/specifications and positive-realness-based inequalities which should be satisfied by the involved polynomials. In the realizable cases, the acceptable region for choosing the pseudo inductances/capacitances of fractional elements is found from the obtained conditions. © 2004-2012 IEEE  

The Legendre polynomial expansion method (LPEM), which has been successfully applied to homogenous and longitudinally inhomogeneous gratings [J. Opt. Soc. Am. B 24, 2676 (2007)], is now generalized for the efficient analysis of arbitrary-shaped surface relief gratings. The modulated region is cut into a few sufficiently thin arbitrary-shaped subgratings of equal spatial period, where electromagnetic field dependence is now smooth enough to be approximated by keeping fewer Legendre basis functions. The R-matrix propagation algorithm is then employed to match the Legendre polynomial expansions of the transverse electric and magnetic fields across the upper and lower interfaces of every slice.... 

In this brief, a generalized expression for the popular ultra wideband waveforms is derived. It is shown that all three waveforms used in ultra wideband (Gaussian, modified Hermite, and prolate spheroidal waveforms) fulfill the Sturm–Liouville differential equation. By using this unified structure, characteristics of the waveforms such as orthogonality, finite duration in time and frequency spectrum are explained. © 2008 IEEE  

The deformation inhomogeneity in flattened wire produced by the wire flat rolling process is studied. Utilizing the combined Finite and Slab Element Method (FSEM), the effective strain fields in the flattened wire are calculated at different reductions in height and frictional conditions and compared with experiment. The calculated and experimental results exhibit that the deformation is inhomogeneous and macroscopic shear bands are appeared in the cross section of flattened wire. Using the results of the analysis, it is shown that the deformation inhomogeneity, introduced by an Inhomogeneity Factor (IF), is different on the x-axis and y-axis in the cross section of the flattened wire. By... 

In this paper, a parallel algorithm for computing the roots of a given polynomial of degree n on a ring of processors is proposed. The algorithm implements Durand-Kerner's method and consists of two phases: initialisation, and iteration. In the initialisation phase all the necessary preparation steps are realised to start the parallel computation. It includes register initialisation and initial approximation of roots requiring 3n - 2 communications, 2 exponentiation, one multiplications, 6 divisions, and 4n - 3 additions. In the iteration phase, these initial approximated roots are corrected repeatedly and converge to their accurate values. The iteration phase is composed of some iteration... 

A polynomial expansion approach to the extraction of guided and leaky modes in layered structures including dielectric waveguides and periodic stratified media is proposed. To verify the method we compared the results of analysis of a typical test case with those reported in the literature and found good agreement. Polynomial expansion is a nonharmonic expansion and does not involve harmonic functions or intrinsic modes of homogenous layers. This approach has the benefit of leading to algebraic dispersion equations rather than to a transcendental dispersion equation; therefore, it will be easier to use than other methods such as the argument principle method, the reflection pole method, and... 

We conduct a study on the problem of fair allocation of indivisible goods when maximin share [1] is used as the measure of fairness. Most of the current studies on this notion are limited to the case that the valuations are additive. In this paper, we go beyond additive valuations and consider the cases that the valuations are submodular, fractionally subadditive, and subadditive. We give constant approximation guarantees for agents with submodular and XOS valuations, and a logarithmic bound for the case of agents with subadditive valuations. Furthermore, we complement our results by providing close upper bounds for each class of valuation functions. Finally, we present algorithms to find... 

Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes and have an important role in the mixing process. In this work, the linear stability analysis in the temporal framework is used to study the stability characteristics of a particle-laden stratified two-layer flow for two different background density profiles: smooth (hyperbolic tangent) and piecewise linear. The effect of parameters, such as bed slope, viscosity, and particle size, on the stability is also considered. The pseudospectral collocation method employing Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, there are some differences in the... 

In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass.... 

Analyzing the features of the chromosomes can be very useful for diagnosis of many genetic disorders or prediction of the possible abnormalities that may occur in the future generations. For this purpose, karyotype is often used which to make it, there is necessary to identify each one of the 24 chromosomes from the microscopic images. Definition and extraction of the morphological and band pattern based features for each chromosome is the first step to identify them. An important class of the morphological features is the location of the chromosome's centromere. Thus, centromere localization is an initial step in designing an automatic karyotyping system. In this paper, a novel algorithm... 

In General, there are two methods to analyse the inverse kinematic of manipulators, one of which can be selected with respect to the conditions and the type of the manipulator. One of the methods is the closed solution which is based on the analytical expressions or forth degree or less polynomial solution in which the calculations are non-repetitive. The other method is the numerical solution. In the numerical solutions, the numbers are repeated and generally it is much slower than the closed solutions. The slowness of this method is so noticeable in such a way that principally there is no interest to use the numerical solutions to solve kinematic equations. The purpose of the present paper... 

An efficient ray tracing technique for channel modeling of an ultrawideband signal in 60 GHz band is introduced. In the usual method, field calculations at many frequencies must be done where has a high computational cost. We have introduced a novel method using Chebyshev polynomials interpolation to reduce the computational cost. Some propagation parameters such as gain and root mean square (RMS) delay spread are obtained and compared to the other method  

Key pre-distribution algorithms have recently emerged as efficient alternatives of key management in today's secure communications landscape. Secure routing techniques using key pre-distribution algorithms require special algorithms capable of finding optimal secure overlay paths. To the best of our knowledge, the literature of key pre-distribution systems is still facing a major void in proposing optimal overlay routing algorithms. In the literature work, traditional routing algorithms are typically used twice to find a NETWORK layer path from the source node to the destination and then to find required cryptographic paths. In this paper, we model the problem of secure routing using... 

Dynamic Flows were introduced by Ford and Fulkerson in 1958 to model flows over time. They define edge capacities to be the total amount of flow that can enter an edge in one time unit. Each edge also has a length, representing the time needed to traverse it. Dynamic Flows have been used to model many problems including traffic congestion, hop-routing of packets and evacuation protocols in buildings. While the basic problem of moving the maximal amount of supplies from sources to sinks is polynomial time solvable, natural minor modifications can make it NP-hard. One such modification is that flows be confluent, i.e., all flows leaving a vertex must leave along the same edge. This corresponds... 

Given a triangulation of a point set on the plane, dilation of any pair of the points is the ratio of their shortest path length to their Euclidean distance. The maximum dilation over all pairs of points is called the dilation of this triangulation. Minimum dilation triangulation problem seeks a triangulation with the least possible dilation of an input point set. For this problem no polynomial time algorithm is known. We present an exact algorithm based on a branch and bound method for finding minimum dilation triangulations. This deterministic algorithm after generating an initial solution, iteratively computes a lower bound for the answer and then applies a branch and bound method to find... 

In this work1, we consider the problem of secure multi-party computation (MPC), consisting of F sources, each has access to a large private matrix, N processing nodes or workers, and one master. The master is interested in the result of a polynomial function of the input matrices. Each source sends a randomized functions of its matrix, called as its share, to each server. The workers process their shares in interaction with each other, and send some results to the master such that it can derive the final results. There are several constraints: (1) each worker has a constraint on its storage, such that it can store equivalent of displaystyle rac{1}{m} fraction of size of each input matrices... 

The exact nature of the induced coupled-fields of anisotropic magneto-electro-elastic ellipsoidal inclusions, multi-inclusions, and inhomogeneities with non-uniform eigenfields under polynomial magneto-electro-elastic far-field loadings is of particular interest. For the sake of prediction of the induced coupled-fields of magneto-electro-elastic multi-inclusions due to piecewise polynomial generalized eigenfields several theorems and corollaries are stated and proved. Some classes of impotent generalized eigenfields associated with encapsulated ellipsoidal multi-inclusion result in vanishing generalized disturbance strains within the innermost ellipsoidal domain. On the other hand, it is...