Structural,magnetic and Mössbauer spectral studies of nanosize aluminum substituted nickel zinc ferrites

Nanosize aluminum substituted nickel zinc ferrites were prepared through aerosol route and characterized using TEM, XRD, magnetic measurements and Mössbauer spectroscopy. The particle size of as obtained samples was found to be ∼10 nm which increases up to ∼85 nm upon annealing at 1200 °C. The unit cell parameter ‘a’ decreases linearly with concentration of aluminum due to the small ionic radius of aluminum. The saturation magnetization for all the samples after annealing at 1200 °C lies in the range 12.9–72.6 emu/g and decreases linearly with concentration of aluminum. Room temperature Mössbauer spectra of all as obtained samples of ferrite compositions exhibited a broad doublet suggesting super paramagnetic nature. This doublet is further resolved into two doublets and assigned to the surface region and internal region atoms of the particles. The samples annealed at 1200 °C show broad sextets, which were fitted with five sextets, indicating different local environment of both tetrahedrally and octahedrally coordinated Fe cation.     

Bounds on charged lepton mixing with exotic charged leptons

We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the process l⁺l⁻ →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s = Λ), we obtain bounds on light heavy charged lepton mixing parameter sin²(2θ _L ^a ) where θ _L ^a is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin² (2θ _L ^a ) form _E < 0.69 TeV. However, sin² (2θ _L ^a ) ≤ 1.52×10⁻⁵ form _E = 5 TeV, sin² (2θ _L ^a ) ≤ 2.41 ×10⁻⁷ form _E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin² (2θ _L ^a ) for m_E < 1.97 TeV and sin² (2θ _L ^a ) ≤ 0.15 form _E = 5 TeV and sin² (2θ _L ^a ) ≤ 3.88×10^-2 form _E = 10 TeV.     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Kinetics and mechanism of the oxidation of acetaldehyde by chromic acid in perchloric acid

Summary The oxidation of MeCHO by chromium(VI) has been studied in HClO₄ medium over a wide range of experimental conditions and has been found to obey the rate law;v=k[MeCHO][HCrO ₄ ^– ][H⁺]. The calculated H and-S values for the reaction are 30±2kJ mol^–1 and 171±7J mol^–1deg^–1, respectively. The mechanism is discussed in terms of carbon-hydrogen bond cleavage.     

Use of a chiral surfactant for enantioselective reduction of a ketone

The influence of a chiral surfactant and a polymer-supported chiral additive on reduction of ketones using sodium borohydride will be described. Initial preparations involved methylation of (S)-leucinol to give (2S)-N , N-dimethyl-2-amino-4-methyl-1-pentanol (1) (67%). The chiral surfactant (2) was synthesized by reacting (1) with bromohexadecane (71%). The functionalized styrene for the polymer-supported chiral additive (5) was synthesized by reacting (1) with 4-vinylbenzyl chloride. Polymerization was carried out with 10% of the functionalized monomer (4), 5% cross-linking agent divinylbenzene, and 85% styrene with AIBN as the initiator. The activity of the chiral surfactant and polymeric additive were examined by using them as additives in a standard reduction of 2-pentanone with sodium borohydride to yield (R)- and (S)-2-pentanol (3) (20%). The resulting alcohol was analyzed by polarimetry (ee 9.5%) and also esterified with (2S)-methylbutyric acid prior to characterization by NMR. 13C NMR indicated an enantiomeric excess of 5.2% when the chiral surfactant was used, and 7% when the polymeric additive was used.     

Structural features of some small carbonyls in the 1,3nπ states: An mcscf study

Structural features of a series of tetraatomic carbonyls in the ^1,3nπ* states are studied by using a recently proposed MCSCF algorithm at the INDO/2 level. The computed geometrical parameters and the inversion barrier heights agree quite well with the available experimental or ab initio theoretical data. The calculated transition energies turn out to be somewhat lower than the experimental counterparts. The specific MCSCF algorithm used is found to have excellent convergence properties.     

Stop times in fock space stochastic calculus

Summary A stop time S in the boson Fock space over L ₂()₊ is a spectral measure in [0,] such that {S([0,t])} is an adapted process. Following the ideas of Hudson [6], to each stop time S a canonical shift operator U ^Sis constructed in . When S({}) has the vacuum as a null vector U ^Sbecomes an isometry. When S({})=0 it is shown that admits a factorisation _S]{S where _{S is the range of U ^Sand _S] is a suitable subspace of called the Fock space upto time S. This, in particular, implies the strong Markov property of quantum Brownian motion in the boson as well as fermion sense and the Dynkin-Hunt property that the classical Brownian motion begins afresh at each stop time. The stopped Weyl and fermion processes are defined and their properties studied. A composition operation is introduced in the space of stop time to make it a semigroup. Stop time integrals are introduced and their properties constitute the basic tools for the subject.     

Substituent electronic effects on the persistence and absorption spectra of (Z)-o-xylylenols. A nanosecond laser flash photolysis study

[reaction: see text] A systematic investigation on a broad set of aldehydes reveals that the lifetimes of (Z)-photoenols can be modulated by variation of the substituents. We have found that the lifetimes of (Z)-enols (in benzene) can be varied by more than 1 order of magnitude with a judicious choice of the substituents that exert mesomeric and inductive effects as, for example, in the case of pentamethylbenzaldehyde (tau = 35 ns) and dicyanomesitaldehyde (tau = 760 ns). This study thus points to the fact that the electronic factors in conjunction with hydrogen bonding stabilization can considerably broaden the uni- as well as bimolecular chemistry based on photoenolization. Further, we have shown that the photoenols exhibit dramatic shifts in their absorption properties with variation of the substituents; although the photoenols have long been considered to be colored, their absorption properties have not been heretofore comprehensively examined.