Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros

In this paper we study the neighbourhood of 15-variable Patterson-Wiedemann (PW) functions, i.e., the functions that differ by a small Hamming distance from the PW functions in terms of truth table representation. We exploit the idempotent structure of the PW functions and interpret them as Rotation Symmetric Boolean Functions (RSBFs). We present techniques to modify these RSBFs to introduce zeros in the Walsh spectra of the modified functions with minimum reduction in nonlinearity. Our technique demonstrates 15-variable balanced and 1-resilient functions with currently best known nonlinearities 16272 and 16264 respectively. In the process, we find functions for which the autocorrelation spectra and algebraic immunity parameters are best known till date.     

On stochastic games,II

In this paper, we consider positive stochastic games, when the state and action spaces are all infinite. We prove that, under certain conditions, the positive stochastic game has a value and that the maximizing player has an -optimal stationary strategy and the minimizing player has an optimal stationary strategy.The authors are grateful to Professor David Blackwell and the referee for some useful comments.     

A previously unrecognised hydronium di-cation in the crystal structure of a cucurbituril derivative

Examination of the crystal structure of the adduct of hydronium tetrachloroferrate dichloride with cucurbituril resulted in the discovery that the hydronium cation present therein is not the well known H7O3+ species; rather, it is an unprecedented cyclic species of composition (H14O6)2+, templated by the formation of five hydrogen bonds to cucurbituril.     

Spin state selective coherence transfer: a method for discrimination and complete analyses of the overlapped and unresolved 1H NMR spectra of enantiomers

In general, the proton NMR spectra of chiral molecules aligned in the chiral liquid crystalline media are broad and featureless. The analyses of such intricate NMR spectra and their routine use for spectral discrimination of R and S optical enantiomers are hindered. A method is developed in the present study which involves spin state selective two dimensional correlation of higher quantum coherence to its single quantum coherence of a chemically isolated group of coupled protons. This enables the spin state selective detection of proton single quantum transitions based on the spin states of the passive nuclei. The technique provides the relative signs and magnitudes of the couplings by overcoming the problems of enantiomer discrimination, spectral complexity and poor resolution, permitting the complete analyses of the otherwise broad and featureless spectra. A non-selective 180 degrees pulse in the middle of MQ dimension retains all the remote passive couplings. This accompanied by spin selective MQ-SQ conversion leads to spin state selective coherence transfer. The removal of field inhomogeneity contributes to dramatically enhanced resolution. The difference in the cumulative additive values of chemical shift anisotropies and the passive couplings, between the enantiomers, achieved by detecting Nth quantum coherence of N magnetically equivalent spins provides enhanced separation of enantiomer peaks. The developed methodology has been demonstrated on four different chiral molecules with varied number of interacting spins, each having a chiral centre.     

Correlation between photophysical properties and lasing performances of Rhodamine-19 in three types of sol–gel glass hosts

Rhodamine-19 (Rh-19) incorporated three types of sol–gel samples (mentioned as dope route-I, dope route-II and dip method) were prepared by using two different methods of dye impregnation. The photophysical properties of all the three types of Rh-19 incorporated sol–gel solids were studied by using the UV–Visible absorption and the fluorescence spectroscopy. A single photon counting technique was used to estimate the lifetime of fluorescent species. From the study of fluorescence spectra, the coexistence of dimers (fluorescent and non-fluorescent both) and monomer of Rh-19 was observed. The photophysical properties of Rh-19 were found to be the best in dip sample, medium in dope route-II sample and low in dope route-I sample. After studying photophysical properties, the samples were subjected to laser study under nitrogen laser pumping at 337.1 nm at the rate of 1.5 Hz in transverse dye laser cavity. The highest laser efficiency and photostability of the dye were observed in dip sample, medium in dope route-II sample and small in dope route-I sample. A comparison between photophysical properties and laser performance of these materials showed a very good correlation.     

Enantiomeric discrimination by double quantum excited selective refocusing (DQ-SERF) experiment

The differences in chemical shift anisotropies, dipolar couplings, and quadrupolar couplings of two enantiomers in the chiral liquid crystalline media are employed to visualize enantiomers. In spite of the fact that proton has high magnetic moment and is abundantly present in all the chiral molecules, 1H NMR is not exploited to its full potential because of severe overlap of unresolved transitions arising from long- and short-distance couplings. Furthermore, the two spectra from R and S enantiomers result in doubling of the number of observable transitions. The present study demonstrates the application of the selectively excited homonuclear double quantum (DQ) coherence correlated to its single quantum coherence of an isolated methyl group in a chiral molecule. The DQ dimension retains only the passive couplings within the protons of the methyl group while the long-distance passive couplings are refocused, removing the overlap of central transitions, and each enantiomer displays a doublet instead of a triplet unlike in regular selective refocusing experiment. The doublet separation being different for each enantiomer results in their discrimination. The cross section taken along the single quantum dimension pertaining to each transition in the DQ dimension provides the one-dimensional spectra for each individual enantiomer with the complete removal of the overlapped transitions from the other enantiomer. The experiment is robust, the pulse sequence is easy to implement, and the methodology has been demonstrated on different chiral molecules.     

57Fe Mössbauer spectroscopy predicts superstructure for K0.08[Cu(II)(N,N'app)Cl]2[Fe(III)(CN)6].0.92H3O.3H2O

The compound [Cu(N,N'app)Cl](2)[Fe(CN)(6)].xH(2)O, with N,N'app being bis(N,N'-3-aminopropylpiperazine), was prepared and its structure determined by single crystal X-ray analysis, confirming a ratio of two copper complexes to one iron complex; (57)Fe M?ssbauer spectra showed three quadrupole doublets typical of iron(iii) low spin species which call for the presence of a superstructure.     

Effect of cusps in time-dependent quantum mechanics

Within nonrelativistic quantum mechanics, spatial cusps in initial wave functions can lead to nonanalytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time analytic.