TRAVELING WAVE SOLUTIONS TO BEAM EQUATION WITH FAST-INCREASING NONLINEAR RESTORING FORCES

§ 1　IntroductionIthas been found by Mc Kenna and Walter[1 ] that traveling wave solutions to the fol-lowing nonlinear beam equation existutt uxxxx u -1 =0 .Equation (1 ) has been posed as a simple model of a nonlinearly suspended bridge,whereu =max{ u,0 } represents a one-sided restoring force and f(u) =u -1 is hence called therestoring force function.The strategy of finding the traveling wave solutions is to study the partial differentialequation on the real line,look for solutions of t…     

Generalized spanning trees

In this paper, we propose a definition for the Generalized Minimal Spanning Tree (GMST) of a graph. The GMST requires spanning at least one node out of every set of disjoint nodes (node partition) in a graph. The analysis of the GMST problem is motivated by real life agricultural settings related to construction of irrigation networks in desert environments. We prove that the GMST problem is NP-hard, and examine a number of heuristic solutions for this problem. Computational experiments comparing these heuristics are presented.     

A Topological Proof of Stability of N-Front Solutions of the FitzHugh–Nagumo Equations

Consideration is devoted to traveling N-front wave solutions of the FitzHugh–Nagumo equations of the bistable type. Especially, stability of the N-front wave is proven. In the proof, the eigenvalue problem for the N-front wave bifurcating from coexisting simple front and back waves is regarded as a bifurcation problem for projectivised eigenvalue equations, and a topological index is employed to detect eigenvalues.     

Traveling wave solutions for a non-monotone Logistic equation in a cylinder

The traveling wave solutions connecting two equilibria for a delayed Logistic equation in a cylinder are obtained for any delay $\tau >0$. We attain our goal by using the approach based on the combination of Schauder fixed point theory and the weak coupled upper–lower solutions method. Moreover, we prove that there is a constant $c^1$ that serves as the minimal wave speed of such traveling wave solutions.     

A new population seeding technique for permutation-coded Genetic Algorithm: Service transfer approach

Genetic Algorithm (GA) is a popular heuristic method for dealing complex problems with very large search space. Among various phases of GA, the initial phase of population seeding plays an important role in deciding the span of GA to achieve the best fit w.r.t. the time. In other words, the quality of individual solutions generated in the initial population phase plays a critical role in determining the quality of final optimal solution. The traditional GA with random population seeding technique is quite simple and of course efficient to some extent; however, the population may contain poor quality individuals which take long time to converge with optimal solution. On the other hand, the hybrid population seeding techniques which have the benefit of good quality individuals and fast convergence lacks in terms of randomness, individual diversity and ability to converge with global optimal solution. This motivates to design a population seeding technique with multifaceted features of randomness, individual diversity and good quality. In this paper, an efficient Ordered Distance Vector (ODV) based population seeding technique has been proposed for permutation-coded GA using an elitist service transfer approach. One of the famous combinatorial hard problems of Traveling Salesman Problem (TSP) is being chosen as the testbed and the experiments are performed on different sized benchmark TSP instances obtained from standard TSPLIB [54]. The experimental results advocate that the proposed technique outperforms the existing popular initialization methods in terms of convergence rate, error rate and convergence time.     

New generalized and improved (G′/G)-expansion method for nonlinear evolution equations in mathematical physics

In this article, new extension of the generalized and improved (G′/G)-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV) equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.     

Dynamic tabu search strategies for the traveling purchaser problem

Tabu search is a metastrategy for guiding known heuristics to overcome local optimality with a large number of successful applications reported in the literature. In this paper we investigate two dynamic strategies, the reverse elimination method and the cancellation sequence method. The incorporation of strategic oscillation as well as a combination of these methods are developed. The impact of the different methods is shown with respect to the traveling purchaser problem, a generalization of the classical traveling salesman problem. The traveling purchaser problem is the problem of determining a tour of a purchaser buying several items in different shops by minimizing the total amount of travel and purchase costs. A comparison of the tabu search strategies with a simulated annealing approach is presented, too.     

The minimum-area spanning tree problem

Motivated by optimization problems in sensor coverage, we formulate and study the Minimum-Area Spanning Tree (mast) problem: Given a set of n points in the plane, find a spanning tree of of minimum “area”, where the area of a spanning tree is the area of the union of the n−1 disks whose diameters are the edges in . We prove that the Euclidean minimum spanning tree of is a constant-factor approximation for mast. We then apply this result to obtain constant-factor approximations for the Minimum-Area Range Assignment (mara) problem, for the Minimum-Area Connected Disk Graph (macdg) problem, and for the Minimum-Area Tour (mat) problem. The first problem is a variant of the power assignment problem in radio networks, the second problem is a related natural problem, and the third problem is a variant of the traveling salesman problem.