Wave simulations of Gray‐Scott reaction‐diffusion system

In this work, we study the numerical simulation of the one‐dimensional reaction‐diffusion system known as the Gray‐Scott model. This model is responsible for the spatial pattern formation, which we often meet in nature as the result of some chemical reactions. We have used the trigonometric quartic B‐spline (T4B) functions for space discretization with the Crank‐Nicolson method for time integration to integrate the nonlinear reaction‐diffusion equation into a system of algebraic equations. The solutions of the Gray‐Scott model are presented with different wave simulations. Test problems are chosen from the literature to illustrate the stationary waves, pulse‐splitting waves, and self‐replicating waves.     

Effects of productivity definition and measurement on performance evaluation

Productivity has often been cited as a key factor in industrial performance, and actions to increase it are said to improve profitability and the wage earning capacity of employees. Experimental studies have shown, however, that the ultimate effects of such actions are dependent on the choice of productivity measure.Productivity has traditionally been measured in relation to a single input factor at a time, often with consequences to other factors. For example, attempts to increase the productivity of labour may eventually lead to over-investment in capital inputs and hence to high capital costs. Alternatively, observed increases in, say, value added per head, which appears to be a common measure of labour productivity, may reflect increases in material productivity rather than in the productivity of labour itself, and should, therefore, be treated with caution in any productivity-linked payment schemes.In this paper some commonly used measures of productivity, relating to both physical and financial inputs and outputs are reviewed. Adopting a modelling approach, they are compared in terms of their implications for performance evaluation and highlight their differences and similarities, strengths and weaknesses.     

Valuation of Resources

This paper presents an overview of results of research into problems of financial reporting faced by an average manufacturing company. The paper demonstrates how Linear Programming can be used to overcome some of the shortcomings encountered by standard accounting procedures. However, the widespread occurrence of degenerate solutions to such LP corporate models requires a fundamental revision to our interpretation of the economic meaning of the dual variables: a revision that may be extended to the dual of non-degenerate optimal solutions.     

Expected Distances in Distribution Problems

In many problems in distribution management it is necessary to take account of the expected distances that result from dispatching vehicles to meet customer demand. For example, in mathematical models for determining the optimal location of depots, the sum of radial distances (between customers and the depot), or the sum of the weighted distances, is used as a measure of the delivery "costs". Since actual delivery operations from the depot usually consist of truck-routes with each truck delivering to more than one customer at a time, it is important to know to what extent the above simplification is valid, namely to find a relationship between the actual route-distances and the sum of the radial distances.This paper makes use of an algorithm which plans optimal or near optimal routes to estimate this relationship by solving a large number of randomly generated problems. The discrepancies between the two methods are shown to be significant under certain circumstances.     

Synthesis and X-ray crystal structure determination of N-p-methylphenyl-4-benzoyl-3,4-diphenyl-2-azetidinone

The title compound, C₂₉H₂₃NO₂, has been characterized by single-crystal X-ray diffraction at two different temperatures (303 K and 120 K) and wavelengths (MoK _α and CuK _α). The non-centrosymmetric hexagonal crystal structure contains four-membered planar β-lactam ring with an unusually long C-C bond. The β-lactam ring is almost planar.     

Towards molecular computers that operate in a biological environment

Even though electronic computers are the only computer species we are accustomed to, the mathematical notion of a programmable computer has nothing to do with electronics. In fact, Alan Turing’s notional computer [L.M. Turing, On computable numbers, with an application to the entcheidungsproblem, Proc. Lond. Math. Soc. 42 (1936) 230-265], which marked in 1936 the birth of modern computer science and still stands at its heart, has greater similarity to natural biomolecular machines such as the ribosome and polymerases than to electronic computers. This similarity led to the investigation of DNA-based computers [C.H. Bennett, The thermodynamics of computation — Review, Int. J. Theoret. Phys. 21 (1982) 905-940; A.M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021-1024]. Although parallelism, sequence specific hybridization and storage capacity, inherent to DNA and RNA molecules, can be exploited in molecular computers to solve complex mathematical problems [Q. Ouyang, et al., DNA solution of the maximal clique problem, Science 278 (1997) 446-449; R.J. Lipton, DNA solution of hard computational problems, Science 268 (1995) 542-545; R.S. Braich, et al., Solution of a 20-variable 3-SAT problem on a DNA computer, Science 296 (2002) 499-502; Liu Q., et al., DNA computing on surfaces, Nature 403 (2000) 175-179; D. Faulhammer, et al., Molecular computation: RNA solutions to chess problems, Proc. Natl. Acad. Sci. USA 97 (2000) 1385-1389; C. Mao, et al., Logical computation using algorithmic self-assembly of DNA triple-crossover molecules, Nature 407 (2000) 493-496; A.J. Ruben, et al., The past, present and future of molecular computing, Nat. Rev. Mol. Cell. Biol. 1 (2000) 69-72], we believe that the more significant potential of molecular computers lies in their ability to interact directly with a biochemical environment such as the bloodstream and living cells. From this perspective, even simple molecular computations may have important consequences when performed in a proper context. We envision that molecular computers that operate in a biological environment can be the basis of “smart drugs”, which are potent drugs that activate only if certain environmental conditions hold. These conditions could include abnormalities in the molecular composition of the biological environment that are indicative of a particular disease. Here we review the research direction that set this vision and attempts to realize it.