A new approach to the cascade theory

The cascade theory of cosmic rays is investigated from a new point of view; we deal with the number of particles produced in a certain thickness of matter, the energy of each particle being greater than E at the point of its production. This new approach leads to an elegant asymptotic theory for large thicknesses and it is better adapted to the interpretation of experiments in nuclear emulsions.     

1,10-Phenanthroline catalysis of the chromium(VI) oxidation of alcohols: a kinetic and mechanistic study

Several primary, secondary and tertiary alcohols are oxidised in acidic solutions using Cr^VIas an oxygen donor and 1,10-phenanthroline (Phen) as catalyst. A large primary kinetic isotope effect, kie(k _H/k _D 10) suggests a linear transition state in the noncatalytic system, whereas a moderate kinetic isotope effect observedin the catalytic pathway can be associated with a cyclic transition state. The k _D2O/k _H2Oratio does not seem to indicate any significant solvent isotope effect. Cr^III inhibition, reflected in the firstorder plots, can be explained by exchange reactions. PhCH₂OH reacts ca. 7 times faster than MeOH. Moderately negative ^* values indicate ahydride abstraction mechanism. Imperfect correlation is observed in the LFER between catalytic and noncatalytic reaction systems.Enhanced reactivity has been observed in the presence of 2,2-bipyridyl, whereas the catalytic activity is insignificant with picolinicacid, imidazole and oxalic acid. Consideration of the kinetic behaviour of catalytic and noncatalytic reaction pathways provides valuable mechanistic insight into the systems studied.     

Changes in spectral features with varying mole fractions of anisaldehyde in binary mixtures

Raman and IR spectra of neat anisaldehyde (4‐methoxybenzaldehyde (4MeOBz)) and its binary mixtures (in polar and nonpolar solvents) with varying mole fraction of 4MeOBz were investigated. The concentration dependence of the wavenumber position and line width (full width at half maximum, FWHM) was analyzed to study the interaction of the solute vibrational modes with the microscopic solvent environment. The wavenumbers of Raman modes of 4MeOBz, namely, the carbonyl stretching, aldehydic δ (C H) and ring‐breathing modes, showed a linear variation in the peak position for varying concentrations of 4MeOBz in the different solvents. The dependence of Raman line width with concentration of 4MeOBz of these modes was also taken into account. The solute–solvent interaction is stronger in 2‐propanol and acetonitrile because of the formation of hydrogen bonds between them, whereas in benzene the interaction is too weak to affect the Raman modes. The modes, ν (CO) in 2‐propanol and aldehydic δ (C H) in acetonitrile, gave a Gaussian‐type line width variation, which was explained by the concentration fluctuation model, and the linear variation of the line widths was also interpreted by solute–solvent interactions. IR spectra were taken for these binary mixtures, which also give further support to these data. Copyright © 2006 John Wiley & Sons, Ltd.     

Novel effects of localization due to intrinsic disorder in manganites

We discuss the effects of a novel ‘intrinsic’ disorder in hole-doped rare-earth manganites. Using effective field theory as well as direct numerical simulations, we show that this disorder can have dramatic effects in terms of the transition from ferromagnetic insulator to ferromagnetic metal upon hole-doping, including an Anderson localized regime where variable range hopping may be observed.     

Multi-fuzzy sets: An extension of fuzzy sets

In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic fuzzy set theory and L-fuzzy set theory.     

Stability criteria with less LMI variables for linear system with additive time-delays

In this technical note, equivalent stability criterion with minimal number of variables for three recently reported stability criteria is proposed for a class of linear systems with additive time-varying delays. The existing delay-dependent stability criteria for additive time-delay systems have more number of matrix variables in the LMI; and hence, they require more computational cost. The proposed equivalent criteria, unlike the original ones, encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criteria mathematically less complex and computationally more attractive. The complexity involved in the existing stability criteria is attributed to the fact the cross-terms that emanate from the time-derivative of the Lyapunov-Krasovskii functional are dealt with free-weighting matrices. Hence, apart from the matrix variables that are associated in the corresponding Lyapunov-Krasovskii functional, the existing criteria also have additional matrix variables in them. In this paper, we have devised techniques to eliminate the free-weighting matrices in the existing stability criteria without sacrificing the conservatism. The resulting equivalent stability criteria, therefore, have least possible number of variables in the LMI; and hence, have minimum computational burden. The effectiveness of the proposed equivalent criteria is validated on a numerical example.     

Normal state resistivity and Tç studies of superconducting Ti1−xSbx system

The superconducting transition temperature (T_c) and the temperature dependence of the normal state resistivity of the Ti_1?xSb_x system between T_c and 300 K have been studied. The T_c values are found to depend on the heat treatment of the samples. Below 40 K, all alloys show a T² dependence of the resistivity. However, the sample with x = 0.53 is not superconducting and shows a different behaviour of the resistivity.