The generalized Thomas–Fermi singular boundary value problems for neutral atoms

This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above‐mentioned upper–lower solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

An algorithm for a class of nonlinear fractional problems using ranking of the vertices

In this note we consider an algorithm for quasiconcave nonlinear fractional programming problems, based on ranking the vertices of a linear fractional programming problem and techniques from global optimization.     

Step‐by‐Step Growth of Complex Oxide Microstructures

The synthesis of complex and hybrid oxide microstructures is of fundamental interest and practical applications. However, the design and synthesis of such structures is a challenging task. A solution‐phase process to synthesize complex silica and silica–titania hybrid microstructures was developed by exploiting the emulsion‐droplet‐based step‐by‐step growth featuring shape control. The strategy is robust and can be extended to the preparation of complex hybrid structures consisting of two or more materials, with each having its own shape.     

A modified active set algorithm for transportation discrete network design bi-level problem

Transportation discrete network design problem (DNDP) is about how to modify an existing network of roads and highways in order to improve its total system travel time, and the candidate road building or expansion plan can only be added as a whole. DNDP can be formulated into a bi-level problem with binary variables. An active set algorithm has been proposed to solve the bi-level discrete network design problem, while it made an assumption that the capacity increase and construction cost of each road are based on the number of lanes. This paper considers a more general case when the capacity increase and construction cost are specified for each candidate plan. This paper also uses numerical methods instead of solvers to solve each step, so it provides a more direct understanding and control of the algorithm and running procedure. By analyzing the differences and getting corresponding solving methods, a modified active set algorithm is proposed in the paper. In the implementation of the algorithm and the validation, we use binary numeral system and ternary numeral system to avoid too many layers of loop and save storage space. Numerical experiments show the correctness and efficiency of the proposed modified active set algorithm.     

Tumor Biochemical Heterogeneity and Cancer Radiochemotherapy: Network Breakdown Zone-Model

Breakdowns of two-zone random networks of the Erdős–Rényi type are investigated. They are used as mathematical models for understanding the incompleteness of the tumor network breakdown under radiochemotherapy, an incompleteness that may result from a tumor’s physical and/or chemical heterogeneity. Mathematically, having a reduced node removal probability in the network’s inner zone hampers the network’s breakdown. The latter is described quantitatively as a function of reduction in the inner zone’s removal probability, where the network breakdown is described in terms of the largest remaining clusters and their size distributions. The effects on the efficacy of radiochemotherapy due to the tumor micro-environment (TME)’s chemical make-up, and its heterogeneity, are discussed, with the goal of using such TME chemical heterogeneity imaging to inform precision oncology.     

On complexity of unconstrained hyperbolic 0-1 programming problems

Single- and multiple-ratio unconstrained hyperbolic 0-1 programming problems are considered. We prove that checking whether these problems have a unique solution is NP-hard. Furthermore, we show that finding the global maximizer of problems with unique solution remains NP-hard. We also discuss complexity of local search and approximability for multiple-ratio problems.     

Absolute reaction rate of chlorine atoms with neopentane

The reaction of atomic chlorine with neopentane was studied in the gas phase with the Very Low Pressure Reactor (VLPR) technique over the temperature range 273–333 K. The absolute reaction rate was found to be temperature-independent, and the average rate constant was k₁ = (1.11± 0.13) × 10^?10 cm³ molecule^?1 s^?1 within experimental error. The reaction proceeds via metathesis of a hydrogen atom with no activation energy, and leads to the formation of HCl and neopentyl radical. © 1995 John Wiley & Sons, Inc.     

Generating quadratic assignment test problems with known optimal permutations

The quadratic assignment problem (QAP) is a well-known combinatorial optimization problem of which the travelling-salesman problem is a special case. Although the QAP has been extensively studied during the past three decades, this problem remains very hard to solve. Problems of sizes greater than 15 are generally impractical to solve. For this reason, many heuristics have been developed. However, in the literature, there is a lack of test problems with known optimal solutions for evaluating heuristic algorithms. Only recently Paulubetskis proposed a method to generate test problems with known optimal solutions for a special type of QAP. This paper concerns the generation of test problems for the QAP with known optimal permutations. We generalize the result of Palubetskis and provide test-problem generators for more general types of QAPs. The test-problem generators proposed are easy to implement and were also tested on several well-known heuristic algorithms for the QAP. Computatinal results indicate that the test problems generated can be used to test the effectiveness of heuristic algorithms for the QAP. Comparison with Palubetskis' procedure was made, showing the superiority of the new test-problem generators. Three illustrative test problems of different types are also provided in an appendix, together with the optimal permutations and the optimal objective function values.