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.     

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.     

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.     

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.     

High sensitivity (1 ppm) hydrogen detection using an unconventional Pd/n-InP Schottky device

Hydrogen is detected using a Pd/n-InP Schottky diode in which the elongated, very thin Pd electrode is of greater resistance than the underlying semiconductor substrate. Four-probe measurements of the device resistance, as a function of hydrogen concentration, are made by contacting only the Pd electrode, with a sensitivity of 1 ppm being achieved. On hydrogen exposure the device resistance drops from an initial high value, characteristic of the Pd electrode alone, to a lower value due to a hydrogen-induced lowering of the Schottky barrier that opens up the InP substrate as a parallel current carrying channel.     

ZEOLITE-SUPPORTED CHROMIUM(VI) OXIDE: A MILD,EFFICIENT, AND INEXPENSIVE REAGENT FOR OXIDATIVE DEPROTECTION OF TRIMETHYLSILYL ETHERS UNDER MICROWAVE IRRADIATION

Primary and secondary trimethylsilyl ethers are effeciently converted to the corresponding carbonyl compounds using HZSM-5 zeolite-supported CrO ₃ under microwave irradiation in solventless system.