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.     

23 excitation of Li+ by electron impact

The 1¹S→2³S excitation of Li⁺ has been studied in the Coulomb-Born-Oppenheimer approximation. The differential and the total cross sections are given at double the threshold energy.     

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.     

Deterministic inventory models for variable production

This paper presents two deterministic inventory models for a single item, where for the first model, the production rate at any instant depends on the on-hand inventory and for the second one, it is demand dependent. However, in both cases, the demand rate at any moment of time is a linear function of time for the scheduling period. Both the models are formulated and solved without allowing shortages. Two numeric examples have been added to illustrate the results.     

Mechanisms of the aquation of tris-(substituted) malonatochromate(III) complexes

Summary Investigations on the aquation of tris-(substituted)malonatochromate(III)ion, between 25°–40° in the presence of acid (I=1.0M) show that the mono- and dimethyl substituted complexes aquate by a two term rate law, only one of which is acid dependent. All other complexes aquate by a one term rate law which is first-order with respect to acid concentration; the unsubstituted malonato complex behaves in this way. Aquation of the first two complexes is dissociative, while for others appreciable associative character has been observed.     

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.     

Synthesis of bisindolylmaleimides related to GF109203x and their efficient conversion to the bioactive indolocarbazoles

From a structure-activity relationship perspective, the new indolocarbazoles 11 and 12 have been synthesized and evaluated biologically as novel Chk1 inhibitors. Compounds 11 and 12 were synthesized in high yield from indole via bisindolylmaleimides 18 and 24.     

Bionomic exploitation of a ratio-dependent predator–prey system

The present article deals with the problem of combined harvesting of a Michaelis–Menten-type ratio-dependent predator–prey system. The problem of determining the optimal harvest policy is solved by invoking Pontryagin's Maximum Principle. Dynamic optimization of the harvest policy is studied by taking the combined harvest effort as a dynamic variable. Computer simulations are carried out to illustrate our analytical findings. Biological and bioeconomical interpretations of the results are explained critically.     

Classes of graphs with minimum skew rank 4

The minimum skew rank of a simple graph G   is the smallest possible rank among all real skew-symmetric matrices whose (i,j)$(i,j)$-entry is nonzero if and only if the edge joining i and j is in G. It is known that a graph has minimum skew rank 2 if and only if it consists of a complete multipartite graph and some isolated vertices. Some necessary conditions for a graph to have minimum skew rank 4 are established, and several families of graphs with minimum skew rank 4 are given. Linear algebraic techniques are developed to show that complements of trees and certain outerplanar graphs have minimum skew rank 4.     

Optical and structural properties of lead iodide thin films prepared by vacuum evaporation method

Thermally processed lead iodide (PbI₂) thin films were prepared by the vacuum evaporation method in a constant ambient. Measured thickness of the film was verified analytically from the optical transmittance data in a wavelength range between 300 and 1600 nm. From the Tauc relation for the non‐direct inter band transition, the optical band gap of the film was found to be 2.58 eV for film thickness 300 nm. X‐ray diffraction analysis confirmed that PbI₂ films are polycrystalline, having hexagonal structure. The low fluctuation in Urbach energy indicates that the grain size is quite small. The present findings are in agreement with the other results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)