Random assignment problems

Analysis of random instances of optimization problems provides valuable insights into the behavior and properties of problem’s solutions, feasible region, and optimal values, especially in large-scale cases. A class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems, and many important problems in operations research and computer science can be formulated as assignment problems. This paper presents an overview of the recent results and developments in the area of probabilistic assignment problems, including the linear and multidimensional assignment problems, quadratic assignment problem, etc.     

Integrated modelling and numerical treatment of freeway flow

The effectiveness of macroscopic dynamic freeway flow models at both uninterrupted and interrupted flow conditions is tested. Model implementation is made by finite difference methods developed here for solving the system's governing equations. These schemes are more effective than existing numerical methods, particularly when generation terms are introduced. The modelling alternatives and numerical solution algorithms are compared by employing a data base generated through microscopic simulation. Despite the effectiveness of the proposed numerical treatments, substantial deviations from the data at interrupted flows are still noticeable. In order to improve performance when flow is interrupted, we develop a modelling methodology that takes into account the ramp-freeway interactions so that all freeway components are treated as a system. We show that the coupling effects of the merging traffic streams are significant. Finally, the incremental benefits of using the more sophisticated high-order continuum models are assessed.     

Efficiency Conditions and Duality for a Class of Multiobjective Fractional Programming Problems

A class of constrained multiobjective fractional programming problems is considered from a viewpoint of the generalized convexity. Some basic concepts about the generalized convexity of functions, including a unified formulation of generalized convexity, are presented. Based upon the concept of the generalized convexity, efficiency conditions and duality for a class of multiobjective fractional programming problems are obtained. For three types of duals of the multiobjective fractional programming problem, the corresponding duality theorems are also established.     

The harmonic oscillator energy level spacing for neutrons and protons in nuclei

Approximate expressions of?ω for neutrons and protons separately, as functions of the neutron numberN and the proton numberZ respectively, are derived. The dependence ?ω_n(?ω_p) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of?ω show “discontinuities in the slope” at the closed shells throughout the periodic table. The difference ?ω_n — {ie17-01} is also discussed.     

Quadratic problems defined on a convex hull of points

In this paper we consider an algorithm for a class of quadratic problems defined on a polytope which is described as the convex hull of a set of points. The algorithm is based on simplex partitions using convex underestimating functions.     

Dynamics of energy transport in ternary molecular solids. II. Time evolution of naphthalene fluorescence

The spectrally resolved time-evolution of free and trapped singlet excitons was obtained at liquid-helium temperature for ternary crystals of perdeuteronaphthalene/naphthalene/betamethylnaphthalene (host/guest/supertrap). The naphthalene guest (donor) concentration varied between 0.30 and 0.99 mole fraction, while the supertrap (acceptor) concentrations were 10^?4–10^?5. At the lower guest concentrations (0.50 and below) the naphthalene-exciton decay time approaches the natural lifetime (≈ 122 ns). At higher concentrations, the decay is much shorter and extremely non-exponential. This behavior is inconsistent with simple homogeneous kinetics schemes that use a time-independent rate constant for energy transport. Above the percolation concentration (0.60 naphthalene) we fitted the experimental results with a random-flight-kinetic model, incorporating correlated random walks on the percolating guest cluster. The best fit was obtained for a “coherence length” (mean free path) of ≈ 10² lattice units. These results are in good agreement with previous steady-state studies on the same samples, and seem to indicate a partial coherence of the exciton transport in both pure and substitutionally disordered crystals at these low temperatures.     

Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A-->0 and A+B-->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A+A) and the segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A+A reaction) and of mixed A and B (A+B reaction) around the hubs of the network. Only at the limit of very sparse networks is the usual behavior recovered.     

Preface

Preface

Preface