The gamma-core and coalition formation

This paper reinterprets the γ-core (Chander and Tulkens in Int Tax Pub Financ 2:279–293, 1995; in Int J Game Theory 26:379–401, 1997) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition formation theory. The problem of coalition formation is formulated as an infinitely repeated game in which the players must choose whether to cooperate or not. It is shown that a certain equilibrium of this game corresponds to the γ-core assumption that when a coalition forms the remaining players form singletons, and that the grand coalition is an equilibrium coalition structure. An earlier version of this paper was presented at the conference on Game Theory and Its Applications held in Mumbai in 2003 and was subsequently circulated as CORE Discussion Paper 2003/46.     

2,4,5-trinitroimidazole-based energetic salts

2,4,5-Trinitroimidazolate (TNI) salts with "high-nitrogen" cations tend to be highly hydrogen bonded and have heats of formation ranging up to 616 kJ mol(-1). Density, oxygen balance, and thermostability are enhanced by the presence of TNI. Based on theoretical calculations, all of the new salts are potential propellants.     

Synergic effect of multi-walled carbon nanotubes and gold nanoparticles towards immunosensing of ricin with carbon nanotube-gold nanoparticles-chitosan modified screen printed electrode

An amperometric immunosensor for the specific detection of Ricinus communis is reported. Screen printed electrodes (SPEs) were modified with gold nanoparticles (GNPs) loaded multiwalled carbon nanotubes (MWCNTs)-chitosan (Ch) film. The ratio of MWCNT and GNP was optimised to get best electrochemically active electrode. Sandwich immunoassay format was used for the immunosensing of ricin. The revealing antibodies tagged with the enzyme alkaline phosphatase (ALP) converts the substrate 1-naphthyl phosphate into 1-naphthol that was determined with the amperometric technique. The amperometric current obtained was correlated with the concentration of ricin. The prepared GNP-MWCNT-Ch-SPE showed high stability due to the Ch film, short response time with good reproducibility and increased shelf life of the electrodes immobilised with antibodies. The electrochemical activity of the electrode improved because of optimization of composition of CNTs and gold nanoparticles. Under the optimal conditions, the modified electrode showed a wide linear response to the concentration of ricin in the range of 2.5-25 ng mL(-1) with a limit of detection of 2.1 ng mL(-1) and with a relative standard deviation of 5.1% and storage life of 32 days.     

An analytic algorithm for time fractional nonlinear reaction–diffusion equation based on a new iterative method

A new analytic algorithm for highly nonlinear time fractional reaction–diffusion equations is proposed in this paper. The proposed method is an amalgamation of variational iteration method (VIM), Adomian decomposition method (ADM) and further refined by introducing a new correction functional. This new correction functional is obtained from the standard correction functional of VIM by introducing an auxiliary parameter γ and an auxiliary function H(x) in it. Further, a sequence G_n(x, t), with suitably chosen support, is also introduced in the new correction functional. The algorithm is easy to implement and only four to six iterations are sufficient for fairly accurate solutions. The algorithm is tested on Fitzhugh – Nagumo and generalized Fisher equations with nonlinearity ranging from 2 to 5.     

Fractional optimal control of a 2-dimensional distributed system using eigenfunctions

This paper presents an eigenfunctions expansion based scheme for Fractional Optimal Control (FOC) of a 2-dimensional distributed system. The fractional derivative is defined in the Riemann–Liouville sense. The performance index of a FOC problem is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) containing two space parameters and one time parameter. Eigenfunctions are used to eliminate the terms containing space parameters and to define the problem in terms of a set of generalized state and control variables. For numerical computation Grünwald–Letnikov approximation is used. A direct numerical technique is proposed to obtain the state and the control variables. For a linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for different number of eigenfunctions and time discretization. Numerical results show that only a few eigenfunctions are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced.     

Second-order doppler-free spectroscopy

The observation of second-order Doppler-free optical resonances with a width of 50 Hz are reported for the first time. It was achieved due to the use of optical selection of cold particles from an absorbing gas. The experiments have been carried out by using a new laser spectrometer, supposed to obtain the saturated absorption resonances with a relative width 10^–13–10^–14. The results of experimental and theoretical studies of second-order Doppler-free effect influence on the shape of nonlinear optical resonances in transit-time conditions are considered.     

Quaternary trialkyl(polyfluoroalkyl)ammonium salts including liquid iodides

New quaternary ammonium salts that contain polyfluorinated alkyl substituents were prepared by the polyfluoroalkylation of tertiary amines with polyfluorinated alkyl iodides. Metathesis reactions of the iodide salts with fluorine-containing anions resulted in new low melting salts. The iodide salts of the tri(isooctyl)polyfluoroalkyl amines are also liquids at 25°C.     

Lanthanum(III) and praseodymium(III) complexes with isatin thiosemicarbazones

Ten new lanthanum(III) and praseodymium(III) complexes of the general formula Na[La(L)2H2O] (Ln=La(III) or Pr(III); LH2=thiosemicarbazones) derived from the condensation of isatin with 4-phenyl thiosemicarbazide, 4-(4-chlorophenyl) thiosemicarbazide, 4-(2-nitrophenyl) thiosemicarbazide, 4-(2-bromophenyl) thiosemicarbazide and 4-(2-methylphenyl) thiosemicarbazide, have been synthesized in methanol in presence of sodium hydroxide. The XRD spectra of the complexes were monitored to verify complex formation. The complexes have also been characterized by elemental analysis, molar conductance, electronic absorption and fluorescence, infrared, far infrared, 1H and 13C NMR spectral studies. Thermal studies of these complexes have been carried out in the temperature range 25-800 degrees C using TG, DTG and DTA techniques. All these complexes decompose gradually with the formation of Ln2O3 as the end product. The Judd-ofelt intensity parameter, oscillator strength, transition probability, stimulated emission cross section for different transitions of Pr3+ for 4-phenyl thiosemicarbazones have been calculated.