Sharif Digital Repository

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,... 

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... 

In this paper, the third order differential equation x‴ + ψ (x′)x″ + (κ2 +ø (x))x′ + f(t, x = e(t) is considered. Under certain conditions on the functions appearing in the differential equation, the existence of periodic solutions is proved. Similar problems have been treated by authors in [4,6,7]. However, the method employed here is used by Reissig [1] and the results obtained are, in fact, a generalization of those in [1-3]. The conditions imposed on the nonlinear terms do not require the ultimate boundedness of all solutions. © Sharif University of Technology  

A new methodology has been proposed to enhance inverse dynamics applications in the process of trajectory planning and optimization in Terrain Following Flights (TFF). The new approach uses least square scheme to solve a general two-dimensional (2D) Terrain Following Flight in a vertical plane. In the mathematical process, Chebyshev polynomials are used to model the geographical data of the terrain in a given route in a manner suitable for the aircraft at hand. The aircraft then follows the modeled terrain with sufficient clearance. In this approach the TF problem is effectively converted to an optimal tracking problem. Results show that. this method provides a flexible approach to solve the... 

The MAXQ hierarchical reinforcement learning method is computationally expensive in applications with deep hierarchy. In this paper, we propose a new learning algorithm for MAXQ method to address the open problem of reducing its computational complexity. While the computational cost of the algorithm is considerably decreased, the required storage of new algorithm is less than two times as the original learning algorithm requires storage. Our experimental results in the simple Taxi Domain Problem show satisfactory behavior of the new algorithm  

We propose a new method for estimating the mixing matrix, A, in the linear model x(t) = As(t),t = 1,...,T, for the problem of underdetermined Sparse Component Analysis (SCA). Contrary to most previous algorithms, there can be more than one dominant source at each instant (we call it a "multiple dominant" problem). The main idea is to convert the multiple dominant problem to a series of single dominant problems, which may be solved by well-known methods. Each of these single dominant problems results in the determination of some columns of A. This results in a huge decrease in computations, which lets us to solve higher dimension problems that were not possible before. © Springer-Verlag... 

Equity in distribution is one of the most controversial and essential concepts which for a long time has been the central concern of political philosophers when considering planning concerns of the societies. Transport is a key field by which politicians and decision-makers impose their intention on societies. Although there have been studies discussing equity in transport, yet there is no clear mathematical framework to utilize the equity concept in transportation planning. This study has reviewed equity in transportation, as well as in human science studies to investigate and determine how transportation advantages should be equitably distributed among society members. This review has led... 

The outcome of the classic percolation approach is several power-law curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical exponents, which control the global properties of a system, are independent of its details. Classic percolation considers the connectivity between two lines and two faces at opposite sides of a system in 2- and 3D problems, respectively; whereas, in practice (e.g. hydrocarbon formations), production and injection wells are represented by points (in 2D areal models) and lines (in 3D models). This study presents the results of Monte Carlo simulations of a 2D percolation model wherein the connection... 

The cutting stock problem is an important problem in the field of combinational optimization. In classic versions of this problem, the aim is to find a solution for cutting some equal-width mother rolls into smaller parts with given width so that the amount of trim-loss become as small as possible. There are plenty of works which addressed the classic cutting stock problem. However in real world applications there are usually some constraints which make the problem different form classical version and make it harder to solve. In this paper we investigate a special cutting stock problem in film industry and show that it can not be solved by using previous methods. We propose a new hybrid... 

Presented within this paper is the identification of impact force acting on a simply supported beam. The force identification is an inverse problem in which the measured response of the structure is used to determine the applied force. The identification problem is formulated as an optimization problem and genetic algorithm is utilized to solve the optimization problem. The objective function is calculated on the difference between analytical and measured responses and the decision variables are the location and magnitude of the applied force. The results from simulation show the effectiveness of the approach and its robustness to the measurement noise and sensor location  

A limiting problem for a stochastic evolution equation is studied in the paper. In the equation, the linear operator is non-positive with a pure point spectrum, the non-linearity is monotone, and the Brownian motion is cylindrical. It is shown that, in the limit, the mild solution to the evolution equation tends to the solution of an ordinary Ito equation. Copyright © Taylor & Francis, Inc  

The one-dimensional cutting stock problem has many applications in industries and during the past few years has been one of the centers of attention among the researchers in the field of applied operations research. In this paper, a revised version of Ant Colony Optimization (ACO) technique is presented to solve this problem. This paper is a sequel to the previous ACO algorithm presented by the authors. In this algorithm, according to some probabilistic rules, artificial ants will select cutting patterns and generate a feasible solution. Computational results show the high efficiency and accuracy of the proposed algorithm for solving one- dimensional cutting stock problem  

We study the optimal value of p for solvability of the problem [Equation not available: see fulltext.]Here λ, α> 0 , p> 1 , f is a non-negative measurable function and [InlineEquation not available: see fulltext.], N⩾ 3 , is an open bounded domain with smooth boundary such that 0 ∈ Ω. We find the critical threshold exponent p+(λ, α) for solvability of (1) and show that if [InlineEquation not available: see fulltext.], 1 < p< p+(λ, α) and [InlineEquation not available: see fulltext.] for some sufficiently small c0> 0 , then there exists a solution as a limit of solutions to approximating problems. Moreover, for p⩾ p+(λ, α) we show that a complete blow-up phenomenon occurs. © 2017, Springer... 

Given a 2.5D terrain and a query point p on or above it, we want to find the triangles of terrain that are visible from p. We present an approximation algorithm to solve this problem. We implement the algorithm and test it on real data sets. The experimental results show that our approximate solution is very close to the exact solution and compared to the other similar works, the computational cost of our algorithm is lower. We analyze the computational complexity of the algorithm. We consider the visibility testing problem where the goal is to test whether a given triangle of the terrain is visible or not with respect to p. We present an algorithm for this problem and show that the average... 

In this research, a maximal covering location problem (MCLP) with real-world constraints such as multiple types of facilities and vehicles with different setup costs is taken into account. An original mixed integer linear programming (MILP) model is constructed in order to find the optimal solution. Since the problem at hand is shown to be NP-hard, a constructive heuristic method and a meta-heuristic approach based on genetic algorithm (GA) are developed to solve the problem. To find the most effective solution technique, a set of problems of different sizes is randomly generated and solved by the proposed solution methods. Computational results demonstrate that the heuristic method is... 

Today there are many Internet sites which require only the entry by human users but unfortunately some computer softwares called bots are designed by some hackers to enter these sites and use their resources through false registration. As a result some systems named CAPTCHA have been introduced to tell apart human users and computer software. This paper introduces a new CAPTCHA method. In this method a simple mathematical problem is generated according to a predefined pattern but instead of some object's name, we put their images. Then the whole problem is saved and shown to the user inform of an image to be answered by him. But since answering this problem requires four abilities of... 

In this paper, we consider the solution of an nth order boundary-value problem. We solve this problem by changing the problem to a system of two integral-differential equations and using the variational iteration method. By giving three examples and comparing with the other methods, the efficiency of the method will be shown. © 2007 Elsevier Inc. All rights reserved  

How can we remove some interactions (generate shorter clauses) in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e., random K -satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will directly provide the solutions of the original problem. © 2006... 

This paper derives an estimated function made by simple Neural Network to find initial state of optimization parameters. It changes a system of differential equations with boundary values to a system of equations with initial values. So a lot of time would be saved to solve it. As a result, the system with differential equations will reach the desired final state. Copyright © 2006 by ASME  

A new method for global minimization of continuous functions has been proposed based on Ant Colony Optimization. In contrast with the previous researches on continuous ant-based methods, the proposed scheme is purely pheromone-based. The algorithm has been applied to several standard test functions and the results are compared with those of two other meta-heuristics. The overall results are compatible, in good agreement and in some cases even better than the two other methods. In addition the proposed algorithm is much simpler, which is mainly due to its simpler structure. Also it has fewer control parameters, which makes the parameter settings process easier than many other methods. © 2004...