Stable and superstable customer policies in queues with balking and priority options

We discuss decision-making in queueing systems where individual customers have one or both of two options: (1) option to join or balk, (2) option to choose priority through a payment made on arrival. Each customer's objective is to maximize the expected net gain, defined as 0 if he balks, and as R - b - hE(W) if he joins, where R is his reward, b is his payment, h is his unit time waiting loss, and E(W) is his expected waiting time. The models considered are: (A) a GI/M/s/N queue with either FIFO or LIFO rule, and a balking option, (B) an M/M/s/N queue with a priority option, (C) an M/M/s/N queue with balking and priority options. Rational customers will limit their choice to a certain subset of actions, derived by considering the actions of other customers. When the subset consists of just one action we call it optimal. The analysis focuses on policies, that is, decision rules selecting an action as a function of arrival state (customers in system), R and h. Stable (self-sustaining) and superstable (optimal) policies are of special interest. A stable policy may not exist and it is not necessarily unique. In model A a superstable policy exists except, possibly, for N = ∞ with LIFO rule. For model B we give necessary and sufficient conditions that a policy is stable and induces either FIFO or LIFO service order. Similar results are derived in special cases of model C.     

Controllability of stochastic Volterra integrodifferential systems

In this paper, sufficient conditions for the controllability of stochastic integrodifferential systems in Banach spaces are established. The results are obtained by using a fixed point theorem. An example is provided to illustrate the theory.     

Cobalt complexes of terpyridine ligands: Crystal structure and nuclease activity

Cobalt(II) (1) and cobalt(III) (2) complexes of tridentate ligand, imidazole terpyridine (Itpy), have been synthesized and characterized by both spectroscopic and electrochemical techniques. Single crystal X-ray diffraction studies of complexes 1 and 2 shows that the complexes belong to monoclinic crystal system, with the two Itpy ligands coordinated to the central metal ion. The binding behavior of both the cobalt complexes to calf thymus DNA has been investigated by UV–Vis, fluorescence spectroscopy, viscosity and electrochemical measurements. The results suggest that complexes 1 and 2 bind to DNA through intercalation. The intrinsic DNA binding constant values obtained from absorption spectral titration studies were found to be (5.07 ± 0.12) × 10³ M⁻¹ and (7.46 ± 0.16) × 10³ M⁻¹, respectively, for complexes 1 and 2. Gel electrophoresis studies with the cobalt complexes show that while complex 1 cleaves DNA in the presence of hydrogen peroxide, complex 2 cleaves DNA in the presence of ascorbic acid and hydrogen peroxide.     

Cytotoxic copper(II) complex of tripyridoquinoxaline with DNA hydrolase activity

A monomeric copper(II) complex, [Cu(tpq)₂(H₂O)₂](ClO₄)₂, (tpq = tripyridoquinoxaline), has been synthesized and characterized spectroscopically. This complex has been found to bind DNA intercalatively and the DNA binding constant, K_b, for this complex has been determined from absorption measurements and was found to be (5.7 ± 0.3) × 10³ M⁻¹. This complex successfully promotes hydrolytic cleavage of plasmid DNA, producing single and double DNA strand breaks in the absence of any added cofactor. The amount of conversion of the supercoiled form of plasmid to the nicked circular form depends on the concentration of the copper complex as well as the duration of the incubation of the complex with DNA. The rate of conversion of SC to NC has been determined to be 2.65 × 10⁻⁴ s⁻¹ at pH 7.2 in the presence of 80 μM of the complex. This complex has also been shown to be cytotoxic towards A549 lung adenocarcinoma cells. This complex has been shown to bring about apoptosis of the cancerous A549 cell line.     

Synthesis and biological evaluation of neopeltolide and analogs

The synthesis of neopeltolide analogues that contain variations in the oxazole-containing side chain and in the macrolide core are reported along with the GI(50) values for these compounds against MCF-7, HCT-116, and p53 knockout HCT-116 cell lines. Although biological activity is sensitive to changes in the macrocycle and the side chain, several analogues displayed GI(50) values of <25 nM. Neopeltolide and several of the more potent analogues were significantly less potent against p53 knockout cells, suggesting that p53 plays an auxiliary role in the activity of these compounds.     

Crystal Structure and Thermal Studies of Ruthenium(II) Bisimidazolylterpyridine Hexafluorophosphate Complex

Abstract  

A hexafluorophosphate salt of ruthenium(II) bis(4′-(1H-imidazol-2-yl)-2,2′:6′,2″-terpyridine) complex was synthesized. It crystallizes in the monoclinic space group C2₁/c with unit cell parameters, a = 18.5878(15) ?, b = 15.9546(11) ?, c = 16.1418(12) ?, β = 106.721(3)°, V = 4584.6(6) ?³ and Z = 4. The bond lengths, bond angles and torsional angles of hexafluorophosphate salt of the [Ru(itpy)₂]²⁺ cation show significant change from the nitrate salt of the same cation. Thermogravimetric analysis and differential scanning calorimetry confirm the loss of solvents of crystallization between 100 and 200 °C.     

Controllability of nonlinear fractional dynamical systems

In this paper we establish a set of sufficient conditions for the controllability of nonlinear fractional dynamical systems. The results are obtained by using the recently derived formula for solution representation of systems of fractional differential equations and the application of the Schauder fixed point theorem. Examples are provided to illustrate the results.     

Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces

In this paper approximate and exact controllability for semilinear stochastic functional integrodifferential systems are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the theory.     

Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces

In this paper sufficient conditions for the controllability of impulsive neutral integrodifferential systems with infinite delay are established. The results are obtained by using the Schauder fixed point theorem.