A parallel clustering technique for the vehicle routing problem with split deliveries and pickups

In this paper, a parallel clustering technique and route construction heuristic have been developed for the vehicle routing problem (VRP) with split deliveries and pickups. An MILP formulation for determining the exact solution to the problem has also been included. It has been shown through extensive experimentation that the algorithm proposed in this paper statistically produces better results than the only heuristic existing for this class of problems in literature. We also form a basis of comparison between this class of problems and the VRP with simultaneous deliveries and pickups. We note that while heuristics for simultaneous deliveries and pickups cannot be applied in situations where customers' delivery or pickup demands exceed the vehicle capacity, heuristics allowing split deliveries and pickups can, in fact, be applied in every situation, even producing superior results under the combined objective of minimization of the fixed charge and mileage associated with vehicle routes. A guideline as to which heuristic could be used under what parametric conditions and objective functions, has also been provided.     

New coupled Liouville system: Prolongation structure,soliton solution,and complete integrability

We suggest a new coupled Liouville equation which is exactly solvable. We obtain the Lax pair through a prolongation analysis and also obtain the exact one-soliton-like solution by a direct procedure. We confirm our result through a Painlevé analysis of the similarity reduced systems.     

On further application of r as a metric for validation of QSAR models

Validation is a crucial aspect for quantitative structure–activity relationship (QSAR) model development. External validation is considered, in general, as the most conclusive proof of predictive capacity of a QSAR model. In the absence of truly external data set, external validation is usually performed on test set compounds, which are members of the original data set but not used in model development exercise. In the case of small data sets, QSAR researchers experience problem in model development due to the fact that the developed models may be less reliable on account of the small number of training set compounds and such models may also show poor external predictability because the models may not have captured all necessary features required for the particular structure–activity relationships. The present paper attempts to show that ‘true r_(LOO)’ statistic calculated based on the model derived from the undivided data set with application of variable selection strategy at each cycle of leave‐one‐out (LOO) validation may reflect external validation characteristics of the developed model thus obviating the requirement of splitting of the data set into training and test sets. This approach may be helpful in the case of small data sets as it uses all available data for model development and validation thus making the resulting model more reliable. Copyright © 2009 John Wiley & Sons, Ltd.     

Methane preconcentration in a microtrap using multiwalled carbon nanotubes as sorbents

The GC monitoring of green house gases is a challenging task because the concentration of organic species such as methane are relatively low (ppm to ppb) and their analysis requires some level of preconcentration. Since methane is highly volatile, it is not easily retained on conventional sorbents. In this paper we present multiwalled carbon nanotubes (MWNTs) as an effective sorbent for a microtrap designed for methane preconcentration. Its performance was compared to other commercially available carbon based sorbents, and it was found to be the most effective sorbent in terms of breakthrough volume and enthalpy of adsorption.     

Syntheses,characterization, X-ray crystal structures and emission properties of copper(II), zinc(II) and cadmium(II) complexes of pyridyl–pyrazole derived Schiff base ligand – Metal selective ligand binding modes

The varying coordination modes of the title ligand, L [5-methyl-1-(pyridin-2-yl)-N′-[pyridin-2-ylmethylidene]pyrazole-3-carbohydrazide] towards the different metal centers is reported by preparation and characterization of Cu(II), Zn(II) and Cd(II) complexes, [Cu(L)NO₃.H₂O](NO₃) (1) [Zn(L)₂](ClO₄)₂·2DMF (2) and [Cd(L)(I)₂] (3) respectively. In 1, the neutral ligand serves as tetradentate 4 N donor where both pyridine and pyrazole nitrogen atoms of pyridyl–pyrazole part are coordinatively active, leaving the carbonyl oxygen of the carbohydrazide part inactive. The same pyridine and pyrazole N atoms remain abstained from the coordination process towards the Zn(II) and Cd(II) metal centers. For 2 and 3 the ligand behaves as a tridentate NNO donor where the two nitrogen atoms come from azomethine, pyridine of pyridine-2-carbaldehyde parts and O from carbonyl oxygen atoms (carbohydrazide part). The complex 1 and 2 are distorted octahedral while complex 3 adopts distorted square pyramidal geometry. All the complexes are X-ray crystallographically characterized.     

Synthesis and reactivity of N-aryl substituted N-heterocyclic silylenes

The synthesis of two N-aryl substituted 2-silaimidazolidenes 9a, b by metal-reduction of the appropriate silicon(IV) heterocycles is reported. Structural as well as spectroscopic data obtained for the N-aryl substituted N-heterocyclic silylenes (NHSi) are very close to those obtained previously for their N-alkyl substituted counterparts. NHSis 9a, b are used as starting materials for the synthesis of a series of dichalcogenadisiletanes 19-24 and for of a mono silylene tungsten complex 29. The reactivity studies revealed only marginally differences between the N-aryl substituted NHSis 9a, b and previously described N-alkyl substituted silylenes.     

Macroscopic Form of the First Law of Thermodynamics for an Adibatically Evolving <Emphasis Type="Italic">Non-singular</Emphasis> Self-gravitating Fluid

We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve proper volume element rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation as well as particle number conservation equation. It is also emphasized that we are considering here a non-singular fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum gravity which apparently suggests thermodynamical properties even for a (singular) black hole. Having made such a clarification, we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified that such a global first law of thermodynamics, for a non-singular fluid, has not been formulated earlier.     

Dynamic multiscaling in two-dimensional fluid turbulence

We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with air-drag-induced friction. We show that different ways of extracting time scales from these time-dependent structure functions lead to different dynamic-multiscaling exponents, which are related to equal-time multiscaling exponents by different classes of bridge relations; for a representative value of the friction we verify that, given our error bars, these bridge relations hold.     

Persistence problem in two-dimensional fluid turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Λ to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent θ=2.9±0.2.