A Recursive Algorithm for Order Cycle-time that Minimizes Logistics Cost

A firm's logistics cost, including shipping and inventory-carrying, is a substantial percentage of its sales. Nevertheless, typical inventory-control methods ignore or insufficiently represent the shipping cost. This paper describes a recursive algorithm that determines the reorder cycle-time that minimizes total logistics cost. It allows for a realistic accounting of shipping cost, which is modelled here as a function of shipping distance and weight. The algorithm uses a relaxation procedure to identify a suitable initial approximation to the optimal order cycle-time and then, through a series of recursive steps, moves to the optimal result. We demonstrate the algorithm with a single item, with a group of items that share a common order cycle, and with multi-items when item demands are random variables. Experience with this algorithm indicates that it converges to the optimal result in a very few steps.     

Polyhedral <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">2</Emphasis></Subscript>

 Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional case provides interesting classes of groups. Received: 13 December 2001 / Revised version: 24 June 2002 The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107 Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20     

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems for scalar-valued measures on rings of sets that are in general not σ-rings are presented. As a consequence, the rings of subsets of N with density zero and uniform density zero are shown to have the Nikodym property. In addition, vector measure generalizations of the Vitali–Hahn–Saks theorem are given.     

Synthesis of molecular imprinted organic-inorganic hybrid polymer binding caffeine

Random copolymers of poly{(methacrylamide)-co-(vinyl trimethoxysilane)} and poly{(methacrylic acid)-co-(vinyl trimethoxysilane)} were synthesized via a free radical polymerization reaction. Acid catalyzed sol-gel process of tetraethylorthosilicate (TEOS) with aforementioned polymers in the presence of methyl xanthine class of alkaloid like caffeine resulted in the formation of highly transparent monoliths. Solvent extraction of the template leaves behind the recognition sites intact with high selectivity towards the print molecule. The ionic and non-specific adsorptions, which are considered to be the main disadvantages of the molecularly imprinted polymers (MIP), are prevented to a considerable extent by the end capping of surface silanol groups. The template binding efficiencies of MIP were determined by HPLC analysis.     

A high‐resolution scheme for low Mach number flows

A method for computing low Mach number flows using high‐resolution interpolation and difference formulas, within the framework of the Marker and Cell (MAC) scheme, is presented. This increases the range of wavenumbers that are properly resolved on a given grid so that a sufficiently accurate solution can be obtained without extensive grid refinement. Results using this scheme are presented for three problems. The first is the two‐dimensional Taylor–Green flow which has a closed form solution. The second is the evolution of perturbations to constant‐density, plane channel flow for which linear stability solutions are known. The third is the oscillatory instability of a variable density plane jet. In this case, unless the sharp density gradients are resolved, the calculations would breakdown. Under‐resolved calculations gave solutions containing vortices which grew in place rather than being convected out. With the present scheme, regular oscillations of this instability were obtained and vortices were convected out regularly. Stable computations were possible over a wider range of sensitive parameters such as density ratio and co‐flow velocity ratio. Copyright © 2004 John Wiley Sons, Ltd.     

Separation and Determination of Chloroplast Pigments from Spinach by Thin-Layer Chromatography: a Student Laboratory Experiment

JPC – Journal of Planar Chromatography – Modern TLC -     

Comparative behavior of polybutadiene and polynorbornene‐based latices prepared by dispersion ring‐opening metathesis polymerization with a poly(ethylene oxide) macromonomer

This study critically examines the similarities and differences between poly(ethylene oxide) (PEO) stabilized latices of polynorbornene and polybutadiene. Features such as the kinetics of copolymerization of norbornene and cyclooctadiene with a macromonomer of PEO, the particles' size and morphology, the type of copolymer formed, and the stability of these latices were investigated and the results obtained are considered. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2705–2716, 2004     

Amphiphilic membranes crosslinked and reinforced by POSS

This article concerns the synthesis and characterization of novel tricomponent amphiphilic membranes consisting of hydrophilic poly(ethylene glycol) (PEG) and hydrophobic polydimethylsiloxane (PDMS) segments cocrosslinked and reinforced by octasilane polyhedral oligomeric silsesquioxane (octasilane‐POSS) cages. Rapid and efficient network synthesis was effected by cocrosslinking diallyl‐telechelic PEG (A‐PEG‐A) and divinyl‐telechelic PDMS (V‐PDMS‐V) with pentamethylpentacyclosiloxane (D₅H), using Karstedt's catalyst in conjunction with Et₃N cocatalyst and water. Films were prepared by pouring charges in molds and crosslinking by heating at 60 °C for several hours. The films were characterized by sol fractions and equilibrium swelling both in hexane and water, extent of crosslinking, contact angle hysteresis, oxygen permeability, thermogravimetric analysis, and mechanical properties. The crosslinking of octasilane‐POSS achieved by the same catalyst system was studied in separate experiments. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4337–4352, 2004     

The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.