Moments of first passage times in general birth–death processes

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In particular, we compute for some non-standard Markovian queues, the moments of the busy period duration, the busy cycle duration, and the state-dependent waiting time in queue.      

Hexagonal nanorods of tungsten trioxide: Synthesis, structure, electrochemical properties and activity as supporting material in electrocatalysis

Tungsten trioxide, unhydrated with hexagonal structure (h-WO₃), has been prepared by hydrothermal method at a temperature of 180 °C in acidified sodium tungstate solution. Thus prepared h-WO₃ has been characterized by X-ray diffraction (XRD) method and using electrochemical techniques. The morphology has been examined by scanning and transmission electron microscopies (SEM and TEM) and it is consistent with existence of nanorods of 50-70 nm diameter and up to 5 μm length. Cyclic voltammetric characterization of thin films of h-WO₃ nanorods has revealed reversible redox behaviour with charge-discharge cycling corresponding to the reversible lithium intercalation/deintercalation into the crystal lattice of the h-WO₃ nanorods. In propylene carbonate containing LiClO₄, two successive redox processes of hexagonal WO₃ nanorods are observed at the scan rate of 50 mV/s. Such behaviour shall be attributed to the presence of at least two W atoms of different surroundings in the lattice structure of h-WO₃ nanorods. On the other hand, in aqueous LiClO₄ solution, only one redox process is observed at the scan rate of 10 mV/s. The above observations can be explained in terms of differences in the diffusion of ions inside two types of channel cavities existing in the structure of the h-WO₃ nanorods. Moreover, the material can be applied as active support for the catalytic bi-metallic Pt-Ru nanoparticles during electrooxidation of ethanol in acid medium (0.5 mol dm⁻³ H₂SO₄).     

Efficient portfolios in financial markets with proportional transaction costs

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general multi-currency financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. We provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig (Rev Financ Stud 1:67–88, 1988) and Jouini and Kallal (J Econ Theory 66: 178–197, 1995). We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system that prices it. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading, and give a dual representation of it as the largest proportion of the market price necessary for all agents to reach the same expected utility level.     

Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.     

Crystal structure of pentakis ethylenediammonium bis undecachlorodiantimonate(III) tetrahydrate, (NH3(CH2)2NH3)5(Sb2Cl11)2·4H2O

The pentakis ethylenediammonium bis undecachlorodiantimonate(III) tetrahydrate salt is monoclinic with the following unit cell dimensions:a=16.271(5) Å,b=13.004(4) Å,c=13.932(4) Å, β=111.72(2)°, space groupP2₁/c withZ=2. The structure was solved by Patterson methods and refined to a finalR value of 0.023 for 4435 reflections withF ₀>4σ(F ₀). The structure shows a layer arrangement perpendicular to thea axis: planes of the [Sb₂Cl₁₁]⁵⁻ bioctahedra alternate with planes of [NH₃(CH₂)₂NH₃]²⁺ dications. The [Sb₂Cl₁₁]⁵⁻ bioctahedra are connected through O−H...Cl hydrogen bonds, such that infinite chains of composition [Sb₂Cl₁₁(H₂O]_n ⁵ⁿ⁻ are formed in the structure, parallel to the twofold axis. These chains are themselves interconnected by means of N−H...Cl and O−H...Cl bonds originating from the [NH₃(CH₂)₂NH₃]²⁺ entities and the water molecules, respectively, and form a threedimensional network.