Control Policies for Inventory with Service Time

Abstract

This article introduces an additional control policy—the N-policy–into (s, S) inventory system with positive service time. Under specified interarrival and service time distributions, which are independent of each other, we obtain the necessary and sufficient condition for the system to be stable. We also obtain the optimal values of the control variables s, S, and N; it is seen that the cost function attains the minimum value at s = 0. It is also shown that the cost function is separately convex in the variables S and N. Numerical illustrations are provided. Several measures of performance of the system are evaluated.     

The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service

Customers arriving according to a Markovian arrival process are served at a single server facility. Waiting customers generate priority at a constant rate γ$\gamma$; such a customer waits in a waiting space of capacity 1 if this waiting space is not already occupied by a priority generated customer; else it leaves the system. A customer in service will be completely served before the priority generated customer is taken for service (non-preemptive service discipline). Only one priority generated customer can wait at a time and a customer generating into priority at that time will have to leave the system in search of emergency service elsewhere. The service times of ordinary and priority generated customers follow PH-distributions. The matrix analytic method is used to compute the steady state distribution. Performance measures such as the probability of n consecutive services of priority generated customers, the probability of the same for ordinary customers, and the mean waiting time of a tagged customer are found by approximating them by their corresponding values in a truncated system. All these results are supported numerically.     

Vanadium(V)-substituted Keggin-type heteropolyoxotungstophosphates as electron transfer and antimicrobial agents: oxidation of glutathione and sensitization of MRSA towards β-lactam antibiotics

Glutathione (GSH) undergoes facile electron transfer with vanadium(V)-substituted Keggin-type heteropolyoxometalates, [ \textPV^\textV \textW _{1 1} \textO _{4 0} ] ^{4 -} [ {\text{PV}}^{\text{V}} {\text{W}}_{ 1 1} {\text{O}}_{ 4 0} ]^{{ 4 { - }}} (HPA1) and [ \textPV^\textV \textV^\textV \textW _{1 0} \textO _{4 0} ] ^{5 -} [ {\text{PV}}^{\text{V}} {\text{V}}^{\text{V}} {\text{W}}_{ 1 0} {\text{O}}_{ 4 0} ]^{{ 5 { - }}} (HPA2). The kinetics of these reactions have been investigated in phthalate buffers spectrophotometrically at 25 °C in aqueous medium. One mole of HPA1 consumes one mole of GSH and the product is the one-electron reduced heteropoly blue, [ \textPV^\textIV \textW _{1 1} \textO ₄₀ ] ^5- [ {\text{PV}}^{\text{IV}} {\text{W}}_{ 1 1} {\text{O}}_{ 40} ]^{ 5- } . But in the GSH-HPA2 reaction, one mole of HPA2 consumes two moles of GSH and gives the two-electron reduced heteropoly blue [ \textPV^\textIV \textV^\textIV \textW ₁₀ \textO ₄₀ ] ^7- [ {\text{PV}}^{\text{IV}} {\text{V}}^{\text{IV}} {\text{W}}_{ 10} {\text{O}}_{ 40} ]^{ 7- } . Both reactions show overall third-order kinetics. At constant pH, the order with respect to both [HPA] species is one and order with respect to [GSH] is two. At constant [GSH], the rate shows inverse dependence on [H⁺], suggesting participation of the deprotonated thiol group of GSH in the reaction. A suitable mechanism has been proposed and a rate law for the title reaction is derived. The antimicrobial activities of HPA1, HPA2 and [ \textPV^\textV \textV^\textV \textV^\textV \textW ₉ \textO _{4 0} ] ^{6 -} [ {\text{PV}}^{\text{V}} {\text{V}}^{\text{V}} {\text{V}}^{\text{V}} {\text{W}}_{ 9} {\text{O}}_{ 4 0} ]^{{ 6 { - }}} (HPA3) against MRSA were tested in vitro in combination with vancomycin and penicillin G. The HPAs sensitize MRSA towards penicillin G.     

The Minimal Polynomial of Some Matrices Via Quaternions

This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete determination of the Jordan structure of skew-Hamiltonian matrices and the computation of the Cayley transform are given. Some new classes of matrices are uncovered, whose behaviour insofar as minimal polynomials are concerned, is remarkably similar to those of skew-Hamiltonian and Hamiltonian matrices. The main technique is the invocation of the associative algebra isomorphism between the tensor product of the quaternions with themselves and the algebra of real 4 × 4 matrices. Extensions to higher dimensions via Clifford Algebras are discussed.     

Synthesis of 2-substituted 3-ethyl-3H-imidazo[4,5-b]pyridines catalyzed by Al-exchanged K10 clay as solid acids

A series of imidazopyridine derivatives have been synthesized efficiently via intramolecular cyclization in excellent yields using Al³⁺-exchanged on K10 montmorillonite clay (Al³⁺-K10 clay) as a reusable heterogeneous catalyst. To the best of our knowledge, this is the first report to utilize Al³⁺-K10 as a catalyst for imidazopyridine synthesis. Many functional groups are tolerated during the synthesis of targeted compounds. The catalyst is reused at least five times with a slight decrease in the yield. This catalyst is environmentally benign, cost-effective, and also provides other advantages such as nontoxicity, operational/experimental simplicity, and mild reaction conditions.     

Protein polymer conjugates: improving the stability of hemoglobin with poly(acrylic acid)

The synthesis, characterization, and evaluation of a novel polymer-protein conjugate are reported here. The covalent conjugation of high-molecular weight poly(acrylic acid) (PAA) to the lysine amino groups of met-hemoglobin (Hb) resulted in the covalent conjugation of Hb to PAA (Hb-PAA conjugate), as confirmed by dialysis and electrophoresis studies. The retention of native-like structure of Hb in Hb-PAA was established from Soret absorption, circular dichroism studies, and the redox activity of the iron center in Hb-PAA. The peroxidase-like activities of the Hb-PAA conjugate further confirmed the retention of Hb structure and biological activity. Thermal denaturation of the conjugate was investigated by differential scanning calorimetry and steam sterilization studies. The Hb-PAA conjugate indicated an improved denaturation temperature (T(d)) when compared to that of the unmodified Hb. One astonishing observation was that polymer conjugation significantly enhanced the Hb-PAA storage stability at room temperature. After 120 h of storage at room temperature in phosphate-buffered saline (PBS) at pH 7.4, for example, Hb-PAA retained 90% of its initial activity and unmodified Hb retained <60% of its original activity under identical conditions of buffer, pH, and temperature. Our conjugate demonstrates the key role of polymers in enhancing Hb stability via a very simple, efficient, general route. Water-swollen, lightly cross-linked, stable Hb-polymer nanogels of 100-200 nm were produced quickly and economically by this approach for a wide variety of applications.     

Rhodium catalysed coupling reaction of myrcene with ethyl acetoacetate in the ionic liquid 1-ethyl-3-methylimidazolium triflimide

The ionic liquid 1-ethyl-3-methylimidazolium triflimide was used successfully as the reaction medium to carry out the rhodium catalysed coupling of myrcene with the active methylene compound ethyl acetoacetate in the presence of TPPMS as the ligand. Coupling product was obtained in 93% isolated yield without any side product formation when a 1:50 ratio of rhodium catalyst/TPPMS was used.     

Effect of Titanium Substrate Surface on the Titanium Oxide Membrane Pore Diameter,Formed upon Anodization in the Presence of Fluoride Ions

Theoretical and Experimental Chemistry - This is the first report of the dependence of the pore diameter in a titania membrane prepared by anodizing a titanium substrate in the presence of fluoride...     

Synthesis and characterization of polycholesteryl methacrylate–polyhydroxyethyl methyacrylate block copolymers

We report the synthesis and characterization of a series of novel diblock copolymers, poly(cholesteryl methacrylate‐b‐2‐hydroxyethyl methacrylate) (PCMA‐b‐PHEMA). Monomers, cholesteryl methacrylate (CMA) and 2‐(trimethylsiloxy)ethyl methacrylate (HEMA‐TMS), were prepared from methyacryloyl chloride and 2‐hydroxyethyl methacrylate, respectively. Homopolymers of CMA, PCMA, with well‐defined molecular weights and polydispersity indices (PDI), were prepared by reversible addition fragmentation and chain transfer (RAFT) method. Precursor diblock copolymers, PCMA‐b‐P(HEMA‐TMS), were synthesized using PCMA as macromolecular chain transfer agent and monomer, HEMA‐TMS. Product diblock copolymers, PCMA‐b‐PHEMA, were prepared by deprotecting trimethylsilyl units in the precursor diblock copolymers using acid catalysts. Detailed molecular characterization of the precursor diblock copolymers, PCMA‐b‐P(HEMA‐TMS), and the product diblock copolymers, PCMA‐b‐PHEMA, confirmed the composition and structure of these polymers. This versatile synthetic strategy can be used to prepare new amphiphilic block copolymers with cholesterol in one block and hydrogen‐bonding moieties in the second block. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6801–6809, 2008