DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Problems with geoengineering schemes to combat climate change

The accelerated rate of increase in atmospheric CO2 concentration in recent years has revived the idea of stabilizing the global climate through geoengineering schemes. Majority of the proposed geoengineering schemes will attempt to reduce the amount of solar radiation absorbed by our planet. Climate modelling studies of these so called 'sunshade geoengineering schemes' show that global warming from increasing concentrations of CO2 can be mitigated by intentionally manipulating the amount of sunlight absorbed by the climate system. These studies also suggest that the residual changes could be large on regional scales, so that climate change may not be mitigated on a local basis. More recent modelling studies have shown that these schemes could lead to a slow-down in the global hydrological cycle. Other problems such as changes in the terrestrial carbon cycle and ocean acidification remain unsolved by sunshade geoengineering schemes. In this article, I review the proposed geoengineering schemes, results from climate models and discuss why geoengineering is not the best option to deal with climate change.

Estimation of mineral-adhered biomass of Thiobacillusferrooxidans by protein assay-some problems and remedies

Enumeration of adhered cells of Thiobacillus ferrooxidans on sulphide minerals through protein assay poses problems due to interference from dissolved mineral constituents. The manner in which sulphide minerals such as pyrite, chalcopyrite, sphalerite, arsenopyrite and pyrrhotite interfere with bacterial protein estimation is demonstrated. Such interferences can be minimised either through dilution or addition of H2O2 to the filtrate after hot alkaline digestion of the biotreated mineral samples.

Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Influence of Elastic-Constants on Mode-I Stress-Intensity Factors in 3-Dimensional Crack Problems

Plates with V-through edge notches subjected to pure bending and specimens with rectangular edge-through-notches subjected to combined bending and axial pull were investigated (under live-load and stress-frozen conditions) in a completely nondestructive manner using scattered-light photoelasticity. Stress-intensity factors (SIFs) were evaluated by analysing the singular stress distributions near crack-tips. Improved methods are suggested for the evaluation of SIFs. The thickness-wise variation of SIFs is also obtained in the investigation. The results obtained are compared with the available theoretical solutions.

Ant Colony Optimization Algorithms for Shortest Path Problems

We propose four variants of recently proposed multi-timescale algorithm in [1] for ant colony optimization and study their application on a multi-stage shortest path problem. We study the performance of the various algorithms in this framework. We observe, that one of the variants consistently outperforms the algorithm [1].

Hantzsch 1,4-dihydropyridine esters and analogs: candidates for generating reproducible one-dimensional packing motifs

Examination of the symmetric Hantzsch 1,4-dihydropyridine ester derivatives of the prototypical nifedipine molecule indicates the tendency of this class of molecule to form a common packing motif. Crystal structure analysis of 2,6-dimethyl-1,4-dihydropyridine-3,5-dicarboxylic diesters and analogs reveals that they form extended chains, characterized as the C(6) packing motif, via intermolecular (amine) N-H...O=C (C3,C5 carbonyl) hydrogen bonds. In addition, all the prepared derivatives also satisfy the basic structural requirements for their high binding efficiency to the receptor. The reproducible C(6) packing motif observed among these compounds has a use in the design of solid-state materials.

Problems Connected with the Rhombus

Abstract is not available.

Bottleneck assignment problems under categorization

This paper considers two special cases of bottleneck grouped assignment problems when n jobs belong to m distinct categories (m < n). Solving these special problems through the available branch and bound algorithms will result in a heavy computational burden. Sequentially identifying nonopitmal variables, this paper provides more efficient methods for those cases. Propositions leading to the algorithms have been established. Numerical examples illustrate the respective algorithms.

Aircraft pursuit-evasion problems with variable speeds

Aircraft pursuit-evasion encounters in a plane with variable speeds are analysed as a differential game. An engagement-dependent coordinate system confers open-loop optimality on the game. Each aircraft's optimal motion can be represented by extremel trajectory maps which are independent of role, adversary and capture radius. These maps are used in two different ways to construct the feedback solution. Some examples are given to illustrate these features. The paper draws on earlier results and surveys several existing papers on the subject.

Fuel cells: Problems and prospects

n recent years, fuel cell technology has advanced significantly. Field trials on certain types of fuel cells have shown promise for electrical use. This article reviews the electrochemistry, problems and prospects of fuel cell systems.

Low temperature Properties of glasses-unsolved problems

Glasses show very interesting behavior well below the glass transition temperature. Inspite of various experimental observations, even simple quantitative explanations relating these relaxation phenomena to structural properties are absent. In this paper we have tried to point out a phenomenological approach to this problem by identifying certain parameters which we think can be used to characterize these relaxations.

Handpumps: problems and search for remedies

This paper gives a brief survey of research and development work done on hand pumps in India as well as elsewhere and sets out the approach adopted by ASTRA Working Group. Ten ways in which a hand pump breakdown in practice have been identified. The physical reasons behind each type of breakdown analysed. Remedial measures have been developed from this analysis. Laboratory test rigs fabricated to evaluate these measures have been described and some experimental results presented. The course of further work has been charted.