Absolute bounds on optimal cost for a class of set covering problems

We study the class of (m constraint,n variable) set covering problems which have no more thank variables represented in each constraint. Letd denote the maximum column sum in the constraint matrix, letr=[m/d]?1, and letZ _g denote the cost of a greedy heuristic solution. Then we prove $$\begin{gathered} Zg \leqslant 1 + r + m - d - \left[ {mk \cdot MAX\left\{ {\frac{{2r}}{{2n - r - 1}},\ln \frac{n}{{n - r}}} \right\}} \right. \hfill \\ \left. { - kd \cdot MIN\left\{ {\frac{{r(r + 1)}}{{2(n - r)}},n \cdot \ln \frac{{n - 1}}{{n - r - 1}} - 1} \right\}} \right]. \hfill \\ \end{gathered} $$ This provides the firsta priori nontrivial upper bound discovered on heuristic solution cost (and thus on optimal solution cost) for the set covering problem. An example demonstrates that this bound is attainable, both for a greedy heuristic solution and for the optimal solution. Numerical examples show that this bound is substantially better than existing bounds for many problem instances. An important subclass of these problems occurs when the constraint matrix is a circulant, in which casem=n andk=d=[αη] for some 0<α<1. For this subclass we prove $$\mathop {\lim }\limits_{n \to \infty } Zg/n \leqslant \frac{{\alpha ^2 }}{2}[1/\alpha ][1/\alpha ].$$      

Pareto optimality and a class of set covering heuristics

The set covering problem has many diverse applications to problems arising in crew scheduling, facility location and other business areas. Since the problem is known to be hard to solve optimally, a number of approximate (heuristic) approaches have been designed for it. These approaches (with one exception) divide into two main groups, greedy heuristics and dual saturation heuristics. We use the concept of a Pareto optimal dual solution to show that an arbitrary dual saturation heuristic has the same worst-case performance guarantee as the two best known heuristics of that type. Moreover, this poor performance level is always attainable by those two heuristics.     

Ferroelectric properties of a series of core-fluorinated dopants containing the 2,3-difluoroalkoxy tail

Abstract

Previous reports from these laboratories [1] have discussed the synthesis and properties of core-fluorinated phenylpyridines with an attached difluoroalkoxy tail. This paper discusses core-fluorinated phenylpyridine difluoroalkoxides and compares their properties to those of the corresponding phenylpyrimidines. The pyridine and pyrimidine series are found to be remarkably similar in properties. They have similar high polarizations and fast rise times, attractive in surfacestabilized ferroelectric liquid crystal (SSFLC) applications, and in high concentration have pitch properties compatible with deformable helix FLC applications.     

Can Polymer Solar Cells Open the Path to Sustainable and Efficient Photovoltaic Windows Fabrication?

Sunlight is among the most abundant energy sources available on our planet. Finding adequate solutions to properly and efficiently harvest it is of major importance to potentially solve the global energy crisis. Polymer solar cells have been introduced in the late 20^th century as low‐cost and easily processed alternative to the state‐of‐the‐art silicon photovoltaics. Their power conversion efficiencies, which were initially rather low, are constantly improving and now reach values close to 15 %. As their optical properties can be easily tuned, designing active layer which absorb homogeneously throughout the visible spectrum is relatively simple. These peculiar characteristics enable the possibility to fabricate visibly transparent solar cells with high color rendering indices which can be employed as photovoltaic windows. After reviewing some of the most successful examples of polymer solar cell‐based transparent photovoltaic window fabrication, I will discuss the possibility to produce these devices in a sustainable and/or eco‐friendly manner while maintaining their performances.     

The madelung constant for the tetragonal distortion of the cscl lattice

The Madelung constant is calculated for the tetragonal distortion of the CsCl lattice using Ewald's method over a large $\text{c}\text{a}$ range. The results deviate considerably from the analytical expressions for the Madelung constant in the literature. As a checkpoint for our calculation, the Madelung constant for the ideal cubic AuCuI structure $\text{(}\text{c}\text{a}\text{= √2)}$ is also computed by direct lattice summation using Evjen's method.     

A new class of high birefringence smectic C liquid crystals. 3,3'-Difluorodiphenyldiacetylenes

Ferroelectric smectic C* liquid crystals have been shown to exhibit high speed, multistate electro-optic switching, particularly when incorporated into the surface stabilized ferroelectric liquid crystal (SSFLC) light valve. Certain applications utilizing IR modulation, waveguide, and fibre-optic devices can benefit from a birefringence higher than the value of Δn = 0·15 seen in typical FLC materials. By incorporating the highly conjugated diacetylene moiety into an FLC core, an increase in birefringence to greater than Δn = 0·3 is achieved. Fluorination of the core induces a strong preference for the tilted smectic C phase as compared to the unfluorinated materials which typically show the nematic phase. The effect of different tail substitutions is examined in the 3,3'-difluorodiphenyldiacetylene system.     

N-nitrosamines and differential pulse polarography

Differential pulse polarography is a versatile and sensitive technique which yields both qualitative and quantitative information about N-nitrosamines. The ability of the technique to carry out determinations in-situ permits the study of anchimeric, metabolic, and mechanistic properties in addition to phenomena such as kinetics and transnitrosation.     

Studies on the geochemical behaviour of uranium isotopes in Tuwa springs and Khari river sediments

High activities of radium were observed in the spring waters of Tuwa in Panchamahal district of Gujarat state. These determinations have led to further studies on geochemical behaviour of uranium in the surface sediments of this region. Labile uranium from the surface of the sediment particles is leached with saturated solution of ammonium carbonate. Uranium is chemically separated from the leachates by cellulose column chromatography. Unusually high activity ratios of²³⁴U/²³⁸U in the range of 2.3 to 2.77 were observed on the surface of the particles. The core of the particles exhibited a ratio of 1.00 indicating soluble²³⁴U fraction has migrated.     

Design analysis for optimal calibration of diffusivity in reactive multilayers

Calibration of the uncertain Arrhenius diffusion parameters for quantifying mixing rates in Zr–Al nanolaminate foils have been previously performed in a Bayesian setting [M. Vohra, J. Winokur, K.R. Overdeep, P. Marcello, T.P. Weihs, and O.M. Knio, Development of a reduced model of formation reactions in Zr–Al nanolaminates, J. Appl. Phys. 116(23) (2014): Article No. 233501]. The parameters were inferred in a low-temperature, homogeneous ignition regime, and a high-temperature self-propagating reaction regime. In this work, we extend the analysis to determine optimal experimental designs that would provide the best data for inference. We employ a rigorous framework that quantifies the expected information gain in an experiment, and find the optimal design conditions using Monte Carlo techniques, sparse quadrature, and polynomial chaos surrogates. For the low-temperature regime, we find the optimal foil heating rate and pulse duration, and confirm through simulation that the optimal design indeed leads to sharp posterior distributions of the diffusion parameters. For the high-temperature regime, we demonstrate the potential for increasing the expected information gain concerning the posteriors by increasing the sample size and reducing the uncertainty in measurements. Moreover, posterior marginals are also obtained to verify favourable experimental scenarios.