Two storage inventory model in a mixed environment

Multi-item inventory models with two storage facility and bulk release pattern are developed with linearly time dependent demand in a finite time horizon under crisp, stochastic and fuzzy-stochastic environments. Here different inventory parameters—holding costs, ordering costs, purchase costs, etc.—are assumed as probabilistic or fuzzy in nature. In particular cases stochastic and crisp models are derived. Models are formulated as profit maximization principle and three different approaches are proposed for solution. In the first approach, fuzzy extension principle is used to find membership function of the objective function and then it’s Graded Mean Integration Value (GMIV) for different optimistic levels are taken as equivalent stochastic objectives. Then the stochastic model is transformed to a constraint multi-objective programming problem using Stochastic Non-linear Programming (SNLP) technique. The multi-objective problems are transferred to single objective problems using Interactive Fuzzy Satisfising (IFS) technique. Finally, a Region Reducing Genetic Algorithm (RRGA) based on entropy has been developed and implemented to solve the single objective problems. In the second approach, the above GMIV (which is stochastic in nature) is optimized with some degree of probability and using SNLP technique model is transferred to an equivalent single objective crisp problem and solved using RRGA. In the third approach, objective function is optimized with some degree of possibility/necessity and following this approach model is transformed to an equivalent constrained stochastic programming problem. Then it is transformed to an equivalent single objective crisp problem using SNLP technique and solved via RRGA. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

Inventory of differential items selling at two shops under single management

Inventory of differential (both good and defective) items purchased in a lot for two shops under a single management is considered here. In the primary shop, the lot is received and separated, only good units are sold and shortages are allowed which are backlogged from the good units specially purchased at the beginning of the next cycle. The separated defective units are continuously trasnsferred and sold at a reduced price from the secondary shop. This inventory model is formulated and illustrated numerically for three scenarios depending upon the time periods of the shops.     

Kinetic studies on the formation of ternary complexes in the reaction of diaquonitrilotriacetatonickelate(II) with amino acids in aqueous solution

Summary Kinetics of formation of ternary complexes in the reaction of Ni(NTA)(H₂O) ₂ ^– with several amino acids, LH^± (glycine, -alanine, -alanine, L-valine and L-phenylalanine) have been studied by a pH indicator method using stopped-flow spectrophotometry. The results conform to 1/k_obs = 1/k + [H⁺]/ kKT_L where K is the equilibrium constant for formation of Ni(NTA)(–L)(H₂O)^2–, and k is the specific rate constant for the subsequent rate-determining ring-closure step leading to Ni(NTA)(=L)^2–. For the different amino acids studied, the k values decrease in the sequence: glycine > -alanine > L-phenylalanine > L-valine > -alanine. These k values areca. 1000 times lower than the values for complexation of Ni(NTA)(H₂O) ₂ ^– with NH₃ and imidazole and the spread in k values is much less than the pK_a values of the amino acids. The relative rates are enthalpy controlled and the S values are highly negative in conformity with ring closure as the rate determining step.     

Interlayer force constants in high symmetry layer crystals

Symmetry adapted linear chain model has been used for the evaluation of compressional and shear interlayer force constants in MnCl₂ and GaSe from the observed zone centre and zone edge frequencies. The method is applicable to two major groups of high symmetry layer crystals having XAX and XAAX type layers.     

Synthesis,reduction, and reductive alkylation of a few tricyclic α,β-unsaturated ketones

Reduction and reductive alkylation of the tricyclic α,β-unsaturated ketones 9–12 afforded the saturated ketones 13–21 in high yields.     

Viscous fluid in static spherically symmetric space-time

The paper presents a static spherically symmetric viscous fluid solution of Einstein field equation, assuming an equation of statep=(γ?1)ρ. Though static, the solution has expansion, shear, and acceleration and can explain cosmological red shift. Also it has a particle horizon. The singularity at the origin and larger viscosity make it unfit to represent a real universe.     

Kinetics and mechanism for the aquation of bismalonatoethylenediaminecobaltate(III) ion in acid perchlorate media

Summary The title complex aquates in acid media, first to [Co(mal)-(H₂O)₂(en)]⁺ (1) (Step 1) and subsequently to [Co(H₂O)₄(en)]³⁺ (2) (Step 2). Complex species (1) has been separated and characterised in solution. While Step 1 involves only a second-order acid catalysed path, Step 2 involves both a first-order acid independent path and a second-order acid catalysed path. The rate constants and activation parameters evaluated for these reaction paths have been compared with those for similar carboxylato-cobalt(III) complexes. This, together with an observed isokinetic relation, indicates that the rate-determining step involves opening of the unprotonated (in the spontaneous acid independent path) or the protonated (for the acid catalysed path) chelate ring of the malonate ligand and insignificant solvation of the central metal ion.     

Elasticity from the force network ensemble in granular media

Transmission of forces in static granular materials is studied within the framework of the force network ensemble, by numerically evaluating the mechanical response of hexagonal packings of frictionless grains and rectangular packings of frictional grains. In both cases, close to the point of application of the overload, the response is nonlinear and displays two peaks, while at larger length scales, it is linear and elasticlike. The crossover between these two behaviors occurs at a depth that increases with the magnitude of the overload and decreases with increasing friction.