Development of double cylindrical dielectric barrier discharge ion source

This paper deals with the dielectric barrier discharge (DBD) ion source composed of the outer cylindrical dielectric tube and the inner grounded metallic tube electrode. The sample gas is supplied through the inner ceramic tube. In this ion source, the DBD plasma is localized in the DBD tube so that the sample gases can be ionized just outside of the ceramic tube by the DBD excited helium gas without being exposed in the plasma jet. Besides, ambient air does not take part in the ionization of the sample vapor because ionization takes place inside the DBD ion source. Thus, this method is totally free from contaminants in ambient air. It was found that this ion source is capable of soft, high-sensitivity, and reproducible ionization. Application of this technique to the analysis of methamphetamine, carbaryl and basil leaf was given.     

Nano Molecular‐Platform: A Protocol to Write Energy Transmission Program Inside a Molecule for Bio‐Inspired Supramolecular Engineering

In a coded self‐assembly, a simple code is written in the molecule, which self‐assembles the molecules into a fractal like structure, which acts as a seed for the next step. As the molecule turns into a complex seed, the code transforms into another form and several seeds self‐assemble into another structure, which acts as a seed for the next step. Until now, this technology was considered as a prerogative of nature. Here, a dendritic network is used to write a basic code by synthetically attaching 32 molecular rotors and doping two controller molecules in its cavity. The code live, which is an energy transmission path in the molecule, is imaged. When the energy transmission path or code is triggered, a series of products generate one after another spontaneously. Two examples are: i) dendritic seed (5–6 nm)→paired nanowire (≈12 nm)→nanowire (≈200 nm)→microwire (500 nm)→wire like rod (1–2 μm)→jelly→rectangular sheet (5 μm). ii) dendritic seed→nano‐sphere (20 nm)→micro‐sphere (500 nm)→large balls(1 μm)→oval shape rod (5–10 μm)→Y, L or T shaped rod assembly. The energy level interactions are tracked using spectroscopy how exactly a directed energy transfer code generates multi‐step synthesis from nano to the visible scale.     

A zero sum differential game in a Hilbert space

We study a zero sum differential game of fixed duration in a separable Hilbert space. We prove a minimax principle and establish the equivalence between the dynamic programming principle and the existence of a saddle point equilibrium. We also prove sufficient conditions for optimality.     

SnCl2 mediated efficient N,N-dialkylation of azides to tertiary-amine via potential stannaimine intermediate

A base free one-pot conversion of azides to N,N-dialkylamine is described. A two-step reaction pathway has been postulated invoking the intermediacy of stannaimine. This new carbon-nitrogen bond formation strategy adds to the repertoire of tin(II) chemistry.     

A Generalization of Commutativity Degree of Finite Groups

The commutativity degree of a finite group is the probability that two arbitrarily chosen group elements commute. This notion has been generalized in a number of ways. The object of this article is to study yet another generalization of the same notion, which further extends some of the existing generalizations.     

Ergodic Control of Partially Degenerate Diffusions in a Compact Domain

The problem of ergodic control of a reflecting diffusion in a compact domain is analysed under the condition of partial degeneracy, i.e. when its transition kernel after some time is absolutely continuous with respect to the Lebesgue measure on a part of the state space. Existence of a value function and a “martingale dynamic programming principle” are established by mapping the problem to a discrete time control problem. Implications for existence of optimal controls are derived.     

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.     

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.     

Genetic evolutionary algorithm for optimal allocation of wavelength converters in WDM optical networks

In this article, a genetic evolutionary algorithm is proposed for efficient allocation of wavelength converters in WDM optical networks. Since wavelength converters are expensive, it is desirable that each node in WDM optical networks uses a minimum number of wavelength converters to achieve a near-ideal performance. The searching capability of genetic evolutionary algorithm has been exploited for this purpose. The distinguished feature of the proposed approach lies in handling the conflicting circumstances during allocation of wavelength converters considering various practical aspects (e.g., spatial problem, connectivity of a node with other nodes) rather than arbitrarily to possibly improve the overall blocking performance of WDM optical networks. The proposed algorithm is compared with a previous approach to establish its effectiveness and the results demonstrate the ability of the proposed algorithm to efficiently solve the problem of Optimal Wavelength Converters Allocation (OWCA) in practical WDM optical networks.