Pooling in tandem queueing networks with non-collaborative servers

This paper considers pooling several adjacent stations in a tandem network of single-server stations with finite buffers. When stations are pooled, we assume that the tasks at those stations are pooled but the servers are not. More specifically, each server at the pooled station picks a job from the incoming buffer of the pooled station and conducts all tasks required for that job at the pooled station before that job is placed in the outgoing buffer. For such a system, we provide sufficient conditions on the buffer capacities and service times under which pooling increases the system throughput by means of sample-path comparisons. Our numerical results suggest that pooling in a tandem line generally improves the system throughput—substantially in many cases. Finally, our analytical and numerical results suggest that pooling servers in addition to tasks results in even larger throughput when service rates are additive and the two systems have the same total number of storage spaces.     

Titanium imido complexes of cyclooctatetraenyl ligands

Reaction of [Ti(NR)Cl2(py)3] (R=tBu or 2,6-iPr2C6H3) with K(2)[COT] (COT=C8H8) or Li2[COT'] (COT'=1,4-C8H6(SiMe3)2) gave the monomeric complexes [Ti(NR)(eta8-COT)] or [Ti(NR)(eta8-COT')], respectively. The pseudo-two coordinate, "pogo stick" geometry for these complexes is unique in both early transition-metal and cyclooctatetraenyl ligand chemistry. In contrast, reaction of [Ti(N-2,6-Me2C6H3)Cl2(py)3] with K2[COT] gave the mu-imido-bridged dimer [Ti2(mu-N-2,6-Me2C6H3)2(eta8-COT)2]. It appears that as the steric bulk of the imido and C8 ring substituents are decreased, dimerisation becomes more favourable. Aryl imido COT complexes were also prepared by imido ligand exchange reactions between anilines and [Ti(NtBu)(eta(8)-COT)] or [Ti(NtBu)(eta(8)-COT')]. The complexes [Ti(NtBu)(eta(8)-COT)], [Ti(N-2,6-iPr2C6H3)2(eta8-COT)] and [Ti2(mu-N-2,6-Me2C6H3)2(eta8-COT)2] have been crystallographically characterised. The electronic structures of both the monomeric and dimeric complexes have been investigated by using density functional theory (DFT) calculations and gas-phase photoelectron spectroscopy. The most striking aspect of the bonding is that binding to the imido nitrogen atom is primarily through sigma and pi interactions, whereas that to the COT or COT' ring is almost exclusively through delta symmetry orbitals. A DFT-based comparison between the bonding in [Ti(NtBu)(eta8-COT)] and the bonding in the previously reported late transition-metal "pogo stick"complexes [Os(NtBu)(eta6-C6Me6)], [Ir(NtBu)(eta5-C5Me5)] and [Ni(NO)(eta5-C5H5)] has also been undertaken.     

Thermal deformation thermodynamics of a smectite mineral

A method has been purposed to calculate some of the thermodynamic quantities for the thermal deformation of a smectite without using any basic thermodynamic data. The Hanç?l? (Keskin, Ankara, Turkey) bentonite containing a smectite of 88% by volume was taken as material. Thermogravimetric (TG) and differential thermal analysis (DTA) curves of the sample were obtained. Bentonite samples were heated at various temperatures between 25–900°C for the sufficient time (2 h) until to establish the thermal deformation equilibrium.Cation-exchange capacity (CEC) of heated samples was determined by using the methylene blue standard method. The CEC was used as a variable of the equilibrium. An arbitrary equilibrium constant (K _a) was defined similar to chemical equilibrium constant and calculated for each temperature by using the corresponding CEC-value. The arbitrary changes in Gibbs energy (ΔG _a ⁰ ) were calculated from K _a-values. The real change in enthalpy (ΔH ⁰) and entropy (ΔS ⁰) was calculated from the slopes of the lnK vs. 1/T and ΔG vs. T plots, respectively. The real changes in Gibbs energy (ΔG ⁰) and real equilibrium constant (K) were calculated by using the ΔH ⁰ and ΔS ⁰ values. The results at the two different temperature intervals are summarized as below: ΔG ₁ ⁰ =ΔH ₁ ⁰ ?ΔS ₁ ⁰ T=?RTlnK ₁=47000?53t, (200–450°C), and ΔG ₂ ⁰ =ΔH ₂ ⁰ -ΔS ₂ ⁰ T=?RTlnK ₂=132000?164T, (500–800°C).     

Oriented immobilized anti‐hIgG via Fc fragment‐imprinted PHEMA cryogel for IgG purification

Antibodies are used in many applications, especially as diagnostic and therapeutic agents. Among the various techniques used for the purification of antibodies, immunoaffinity chromatography is by far the most common. For this purpose, oriented immobilization of antibodies is an important step for the efficiency of purification step. In this study, F_c fragment‐imprinted poly(hydroxyethyl methacrylate) cryogel (MIP) was prepared for the oriented immobilization of anti‐hIgG for IgG purification from human plasma. Non‐imprinted poly(hydroxyethyl methacrylate) cryogel (NIP) was also prepared for random immobilization of anti‐hIgG to compare the adsorption capacities of oriented (MIP/anti‐hIgG) and random (NIP/anti‐hIgG) cryogel columns. The amount of immobilized anti‐hIgG was 19.8 mg/g for the NIP column and 23.7 mg/g for the MIP column. Although the amount of immobilized anti‐hIgG was almost the same for the NIP and MIP columns, IgG adsorption capacity was found to be three times higher than the NIP/anti‐hIgG column (29.7 mg/g) for the MIP/anti‐hIgG column (86.9 mg/g). Higher IgG adsorption capacity was observed from human plasma (up to 106.4 mg/g) with the MIP/anti‐hIgG cryogel column. Adsorbed IgG was eluted using 1.0 m NaCl with a purity of 96.7%. The results obtained here are very encouraging and showed the usability of MIP/anti‐hIgG cryogel prepared via imprinting of Fc fragments as an alternative to conventional immunoaffinity techniques for IgG purification. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic control of a flexible server in an assembly-type queue with setup costs

We consider a queueing system with multiple stations attended by a single flexible server. An order arriving at this system needs to go through each station only once but there is no particular precedence relationship among these stations. One can also think of this system as an assembly system where each station processes a different component of an order and once all the components associated with an order are processed they are assembled instantaneously. A holding cost is charged for keeping the orders in the system and there is a penalty associated with the switches of the server between stations. Our objective is to minimize the long-run average costs by dynamically assigning the server to stations based on the system state. Using sample-path arguments, we provide partial characterizations of the optimal policy and provide sufficient conditions under which a simple state-independent policy that works on one order at a time is optimal. We also propose three simple threshold policies and present a numerical study that provides supporting evidence for the superior performance of our double-threshold heuristic.     

Valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints

Stochastic dominance relations are well studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second order stochastic dominance constraints can be solved by linear programming. However, problems involving first order stochastic dominance constraints are potentially hard due to the non-convexity of the associated feasible regions. In this paper we consider a mixed 0–1 linear programming formulation of a discrete first order constrained optimization model and present a relaxation based on second order constraints. We derive some valid inequalities and restrictions by employing the probabilistic structure of the problem. We also generate cuts that are valid inequalities for the disjunctive relaxations arising from the underlying combinatorial structure of the problem by applying the lift-and-project procedure. We describe three heuristic algorithms to construct feasible solutions, based on conditional second order constraints, variable fixing, and conditional value at risk. Finally, we present numerical results for several instances of a real world portfolio optimization problem. This research was supported by the NSF awards DMS-0603728 and DMI-0354678.     

An Unusual Example of Hypervalent Silicon: A Five‐Coordinate Silyl Group Bridging Two Palladium or Nickel Centers through a Nonsymmetrical Four‐Center Two‐Electron Bond

Pd and Ni dimers supported by PSiP ligands in which two hypervalent five‐coordinate Si atoms bridge the two metal centers are reported. Crystallographic characterization revealed a rare square‐pyramidal geometry at Si and an unusual asymmetric M₂Si₂ core (M=Pd or Ni). DFT calculations showed that the unusual structure of the core is also found in a model in which the phosphine and Si centers are not part of a pincer group, thus indicating that the observed geometry is not imposed by the PSiP ligand. NBO analysis showed that an asymmetric four‐center two‐electron (4c‐2e) bond stabilizes the hypervalent Si atoms in the M₂Si₂ core.     

A numerical approach to solve the model of an electromechanical system

In this paper, the model of an electromechanical system, which is a system of linear differential equations, is studied. Haar wavelet collocation method (HWCM) is applied for finding the approximate solution of the model. HWCM reduces the system of the model into a matrix‐vector form that contains the unknown Haar coefficients, and these coefficients are easily calculated. To demonstrate the validity and applicability of HWCM, numerical solutions of the system for different parameter values in the system are presented. The obtained results demonstrate the efficiency and accuracy of the method. All of the computations are performed via a program written in Mathematica.