Counting limit cycles with the help of the renormalization group

We use the renormalization group to set up an easy algorithm for finding the amplitude equation for an arbitrary two dimensional dynamical system of the Liénard type. This allows us to address the second part of Hilbert’s sixteenth problem, at least in the weak damping limit.     

A Pd-mediated intramolecular ketalization of alkynediols: construction of the central [3.2.1]-bicyclic ketal core of cyclodidemniserinol trisulfate

A preliminary study dealing with the Pd-mediated alkynediol cycloisomerization to construct the central bicyclic ketal core of cyclodidemniserinol trisulfate is documented.     

Contracting over multiple parameters: Capacity allocation in semiconductor manufacturing

This paper is a generalization of Mallik and Harker [Mallik, S., Harker, P.T., 2004. Coordinating supply chains with competition: Capacity allocation in semiconductor manufacturing. European Journal of Operational Research 159, 330–347] that presented an integrated model of incentive problems arising in forecasting and capacity allocation. In that model, multiple product managers and multiple manufacturing managers forecast the means of their respective demand and capacity distributions, and a central coordinator allocates capacities based on these forecasts. A mechanism that elicits truthful information from the managers was the main contribution of that paper. The objective of this paper is to generalize our previous results to multiple statistics reporting. This work assumes that the central coordinator can ask the managers to report multiple statistics (mean and variance, for example) about their respective distributions. We propose a game theoretic model and design a mechanism (a bonus scheme and an allocation rule) that elicits truthful reporting of all statistics by all managers. It turns out that the structure of the optimal bonus schemes are rather simple with easily calculable parameters. We also show that a large class of allocation rules are manipulable. A bonus is often required for elicitation of truthful information. We compare our results of multiple statistics reporting with those from Mallik and Harker (2004). We also characterize under what conditions the reporting of the extra information is of limited use.     

Inventory competition and allocation in a multi-channel distribution system

Consider a supply chain involving one manufacturer and one independent retailer. The manufacturer distributes her product to the end consumer through the independent retailer as well as through her direct channel. Each of the two channels faces a stochastic demand. If one channel is out of stock, a fraction of the unsatisfied customers visit the other channel, which induces inventory competition between the channels. Under the scenario described above, will the manufacturer ever undercut the retailer’s order when the capacity is infinite? What are the equilibria of the game? How does a capacity constraint affect the equilibrium outcome? What is the optimal inventory allocation strategy for the manufacturer? Using a game theoretic model we seek answers to the above questions. Both the capacitated and the infinite capacity games are considered. We establish the necessary condition for a manufacturer to undercut a retailer’s order and show that a manufacturer may deny the retailer of inventory even when the capacity is ample. We show that there can be an equilibrium in the capacitated game where a manufacturer might not use the entire capacity and still deny a retailer inventory. We also show that a mild capacity constraint may make both parties better off and thereby increase the total supply chain profit. We develop a simple yet practical contract called the reverse revenue sharing contract and show that along with a fixed franchise fee this contract can coordinates our decentralized supply chain.     

Gas chromatographic screening of cyclic alcohols as selective solvents for cyclohexane extraction

Summary Gas chromatography has been employed for screening cyclic alkanols as selective solvents for the extraction of cyclohexane from an aromatic-free cyclohexane-rich fraction (77–81°C). The relative volatilities for close boiling hydrocarbons in all three cyclic alcohol solvents have been compared. Activity coefficient data at infinite dilution for nine binary hydrocarbon systems at 25°C have also been presented.     

Crystallographic structure and defects in epitaxial bismuth films grown on mica

Atomic force microscopy is used to image the surface relief of epitaxial Bi films grown on mica substrates. Monatomic terrace steps are readily resolved, which provide detailed information on crystal growth and defect structures. The films grow from the coalescence of isolated three-dimensional islands, however, each island grows layer-by-layer. The islands are triangular in shape and when they coalesce to form a continuous film, their structures are either in-phase, and consequently large crystallites are formed, or they are out-of-phase and defect structures are formed. The most common defects observed are twinning and stacking faults. Images showing the microscopic details of stacking faults, twinning, and grain boundaries are observed as a result of islands coalescing to form a continuous film.     

Amperometric titration of mercury with a stationary platinum electrode in stirred solutions

Amperometric titration of mercury (in the range of 0-4 to 3.5 mg) has been carried out with 2-mercaptobenzoxazole with a stationary electrode in stirred solution in a sodium acetate-acetic acid medium.