36 instance of the satissability problem we associate a set of such matrices. The instance is called 1?semi?unitary if there is at least one 1?semi?unitary matrix in this set. Now 1 ? SEMI ? UNISAT is the satissability problem restricted to 1 ? semi ? unitary instances, KMb]. Given such parameters, 1 ? SEMI ? UNISAT can be solved in polynomial time. Problem 7.3 What is the complexity that we ca...

We extend the work of Letchford [Letchford, A. N. 2000. Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res. 25 443–454] by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the m...

The Boussinesq equations for Rayleigh–Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25 000, the axisymmetric flow becomes unstable to standing or travelling azi...

In this report, we aim to understand the key ideas and major techniques used in the assigned paper "Polynomial Time Approximation Schemes for Euclidean Traveling Salesman and Other Geometric Problems" by Sanjeev Arora. We also provide a review of related literature with an emphasis on the concurrent work by Joseph S. B. Mitchell. One presentation topic is selected from Arora’s paper and the oth...

For the Traveling Salesman Problem (TSP) on Halin graphs with three types of cost functions: sum, bottleneck and balanced and with arbitrary real edge costs we compute in polynomial time the persistency partition EAll, ESome, ENone of the edge set E, where: EAll = {e ∈ E, e belongs to all optimum solutions}, ENone = {e ∈ E, e does not belong to any optimum solution} and ESome = {e ∈ E, e belong...

We consider a simplified model of vertical non-static groundwater flow, resulting in a Burgers’ diffusive equation extended with a third order term with mixed derivatives in space and time. This model is motivated by previous work on the existence of travelling wave solutions on a more general model. We investigate stability of travelling wave solutions of the simplified model, for which we fir...

transfer matrix method (tmm) has been applied to analyze characteristics of semiconductor laser optical amplifiers. the input signal is sinusoidal modulating wave and we do not assume the modulating bias signal as well. we have shown that the distoration arises from gain modulation at low modulation frequencies, but in microwave modulation frequencies, the gain takes an average value and the re...

The travelling salesman problem with time windows is a difficult optimization problem that arises, for example, in logistics. This paper deals with the minimization of the travel-cost. For solving this problem, this paper proposes a Beam-ACO algorithm, which is a hybrid method combining ant colony optimization with beam search. In general, Beam-ACO algorithms heavily rely on accurate and comput...

The rapid progress of wireless technologies has made the information of real-time traffic available to vehicles. In this paper, the authors propose a dynamic path planning algorithm for vehicle navigation system which can adapt to changeable traffic and replan a better path with good travelling time for drivers within a reasonable computation time for large-scale road networks. Based on the hie...

This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion  ethod for  constructing exact travelling wave solutions of nonlinear partial  differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and  Derivat...