Automorphisms and holomorphic differentials in characteristic p

Let G be a group of automorphisms of a function field F of genus g_F over an algebraically closed field K. The space $\text{Ω}{}_{\mathrm{F}}$ of holomorphic differentials of F is a g_F^? dimensional K-space. In response to a query of Hecke, Chevalley and Weil (Abh. Math. Sem. Univ. Hamburg, 10 (1934), 358–361) completely determined the structure of $\text{Ω}{}_{\mathrm{F}}$ as representation space for G in the classical case. They carried out the proof for the special case in which F is unramified over the fixed field of G. The case of cyclic ramified extensions had been previously considered by Hurwitz (Math. Ann., 41 (1893), 37–45). Weil (Abh. Math. Sem. Univ. Hamburg, 11 (1935), 110–115) gave a proof in the general case. The treatment in the last two papers is analytical. In characteristic p, the problem is open. If G is cyclic and F is unramified over the fixed field E of G, Tamagawa (Proc. Japan Acad., 27 (1951), 548–551) proved that the representation is the direct sum of one identity representation of degree 1 and g_E ? 1 regular representations. The principal object of this paper is an extension of Tamagawa's result to arbitrary cyclic extensions of p-power degree. The number of times an indecomposable representation of given degree occurs in the representation of G on $\text{Ω}{}_{\mathrm{F}}$ is explicitly determined in terms of g_E and the Witt vector characterizing the extension $\text{F}\text{E}$. The paper also contains a purely algebraic proof of the result of Chevalley and Weil for arbitrary cyclic extensions of degree relatively prime to p. Using character theory, it can be extended to arbitrary groups of order relatively prime to the characteristic.     

Mo-ZrO2 Solid Acid Catalyst For Transesterification of β-Ketoesters

An efficient and mild method for transesterification of β-ketoester catalyzed by Mo-Z1O₂ solid acid catalyst is described.     

Isotope shift measurement of high-lying atomic levels by multi-step photoionization

A new technique has been developed to measure isotope shifts of high-lying atomic levels using multi-step photoionization. This technique has been demonstrated with the measurement of isotope shift between²³⁵U and²³⁸U isotopes in the energy level at 34372.992 cm⁻¹. The value of isotope shift thus measured matches well with the value reported in literature.     

Chemical synthesis of PEDOT nanofibers

A one-step, room-temperature method is described to chemically synthesize bulk quantities of microns long, 100-180 nm diameter nanofibers of electrically conducting poly(3,4-ethylenedioxythiophene)(PEDOT) in the form of powders, or as optically transparent, substrate-supported films using a V2O5 seeding approach.     

Liquid Phase Friedel‐Crafts Alkylation over Mixed Metal Oxide Catalyst

Liquid phase Friedel‐Crafts alkylation of benzene with benzyl chloride was carried out over various ferrites viz. CuFe₂O₄, NiFe₂O₄, CoFe₂O₄, ZnFe₂O₄, and MgFe₂O₄. Among the various ferrites ZnFe₂O₄ showed the highest activity. These ferrites were prepared by co‐precipitation technique. The effect of variation of catalyst, speed of agitation and reaction temperature has been studied. Benzylation of other substrates such as toluene, anisole and chlorobenzene was also studied. The catalyst ZnFe₂O₄ was found to be reusable. The acid base properties of the catalyst were studied by cyclohexanol dehydration reaction and the data was correlated with activity.     

Absolute molecular weight of polyaniline

The absolute molecular weight of polyaniline in the pernigraniline, emeraldine, and leucoemeraldine oxidation states has been measured by light scattering and the exact number of aniline repeat units determined for the first time. Using potential-time profiling to monitor the chemical oxidative polymerization of aniline using ammonium peroxydisulfate oxidant, all three oxidation states of polyaniline can be synthesized in one step and the evolution of polymer molecular weight monitored. The pernigraniline intermediate formed during the chemical oxidative polymerization of aniline increases by 17-20% when it is converted to emeraldine, which is consistent with a two-step polymerization mechanism. These findings establish a solid experimental framework to chemically synthesize block copolymers of polyaniline by using different monomers to intercept the reaction at the pernigraniline oxidation state.     

Radiochemical studies on charge and mass distribution in medium energy fission

Present status of work on charge and mass distribution in medium energy fission of compound nuclei produced using various target projectile combinations is reviewed. Systematics of charge distribution parameters and their dependence on excitation energy of the fissioning nucleus is presented. Variation of mass distribution with excitation energy and mass and charge of the fissioning nucleus is discussed. Qualitative explanation of the data has been sought in terms of existing theories of fission. The importance of charge and mass distribution studies in identifying the different reaction mechanisms in heavy ion induced reaction is highlighted.This article is dedicated to the memory of our beloved friend and colleague Dr. Tarun Datta who passed away on April 2, 1995.