On the gaps between non-zero Fourier coefficients of cusp forms of higher weight

We show that if a modular cuspidal eigenform f of weight 2k is 2-adically close to an elliptic curve \(E/\mathbb {Q}\), which has a cyclic rational 4-isogeny, then n-th Fourier coefficient of f is non-zero in the short interval \((X, X + cX^{\frac{1}{4}})\) for all \(X \gg 0\) and for some \(c > 0\). We use this fact to produce non-CM cuspidal eigenforms f of level \(N>1\) and weight \(k > 2\) such that \(i_f(n) \ll n^{\frac{1}{4}}\) for all \(n \gg 0\).     

A wavelet cross-spectral analysis of solar–ENSO–rainfall connections in the Indian monsoons

The possible connections between the El Nino-Southern Oscillation (ENSO) phenomenon and Indian monsoon rainfall have been widely discussed in the meteorological literature. We show strong statistical evidence here for connections of ENSO with solar activity. This is particularly evident in a comparison between the two contrasting test periods of 1878–1913 and 1933–1964, representing three complete cycles of lowest and highest solar activity respectively since 1850. Wavelet statistical analysis reveals that the link between solar activity and ENSO is generally stronger than that between ENSO and rainfall but only slightly weaker than that between solar activity and rainfall. Over the two test periods an increase in solar activity is associated with a decrease in ENSO indices and an increase in the monsoon rainfall in the 8–16 y period band. In the 2–7 y period band the effects vary with region. The net effect of solar processes on rainfall thus appears to be the result of counteracting or cooperating influences on shorter (about 5–6 y) and longer (about 11–12 y) time scales, the latter on the whole dominating over the former. The present analysis thus suggests that the influence of solar processes on Indian rainfall operates in part indirectly through ENSO, but on more than one time scale.     

Effect of acids on the gamma-radiolysis of frozen aqueous systems of some organic compounds

Abstract

ESR spectra of γ-irradiated frozen aqueous solutions of a number of organic compounds such as alcohols, ether, acetone and tetrahydrofurans have been examined in the presence and absence of mineral acids such as H₂SO₄. The presence of the acid is found to cause an intensification of the organic radical ESR spectra as compared with the acid free solutions. Also, the presence of the organic compounds in frozen aqueous H₂SO₄ suppresses the formation of both H-atoms and SO₄ ^? radical ions. These results have been explained on the basis of reactions of the electrons and holes, or excitons, primarily formed by the action of radiation on the substrate ice.     

A simple chemosensor for Hg2+ and Cu2+ that works as a molecular keypad lock

A new chemosensor which can detect Hg(2+) in water and Hg(2+)/Cu(2+) in acetonitrile and its application as a molecular keypad lock using Cu(2+) and F(-) as ionic inputs are demonstrated.     

Modified o-methyl-substituted IBX: room temperature oxidation of alcohols and sulfides in common organic solvents

o-Methyl-substituted Me-IBX is the first modified analog of IBX that oxidizes alcohols in common organic solvents at room temperature, due to a composite of two factors, that is, low solubility and hypervalent twisting-promoted rate enhancement. Furthermore, the reagent is efficient for selective oxidation of sulfides to sulfoxides, a transformation that otherwise occurs only sluggishly with standard IBX. The facile synthetic accessibility and its mild as well as non-hazardous nature render Me-IBX a stable equivalent of Dess-Martin periodinane reagent in organic oxidations.     

First example of the carbon-Ferrier rearrangement of glycals with isocyanides: a novel synthesis of C-glycosyl amides

Glycals undergo smooth carbon-Ferrier rearrangement with isocyanides in the presence of a catalytic amount of FeCl₃ under mild reaction conditions to provide C-glycosyl amides in good yields with high α-selectivity. The use of FeCl₃ makes this method simple, convenient and cost-effective. This is the first report on carbon-Ferrier rearrangement using isonitriles as nucleophiles.     

InX3-catalyzed haloamidation of vinyl arenes: a facile synthesis of α-bromo- and α-fluoroamides

A variety of alkenes are converted into the corresponding α-fluoroamides in high yields by selectfluor^TM in the presence of 10 mol % of InF₃ in nitrile solution. α-Bromoamides are obtained with NBS in the presence of 10 mol % InBr₃ under similar conditions. The use of Lewis acid in haloamidation significantly improved the yields and reaction rates.     

Structural characterization of Th-doped TiO2 photocatalyst and its extension of response to solar light for photocatalytic oxidation of oryzalin pesticide: a comparative study

The degradation efficiency of Th-doped TiO₂ / TiO₂ photocatalysts were investigated under UV and solar light illumination. The model compound chosen for the study was Oryzalin (OZ). Doping of inner transition metal ion Th was intended to modify the electronic properties of TiO₂. The Th-doped TiO₂ were synthesized by incorporating 0.02, 0.04, 0.06, and 0.1 atom percentage of Th into the TiO₂ lattice by solid-state reaction. The stochiometry of the prepared samples is Ti_1−xTh_xO₂, where ‘x’ is the percentage of Th. The samples were characterized by UV-Visible absorption, UV-Visible -Diffused reflectance spectra, Scanning Electron Microscopy (SEM), Energy Dispersive X-ray Analysis (EDX) and X-ray Diffraction (XRD). The pore size and surface area of these samples were studied by Brunauer, Emmett and Teller (BET) adsorption method. It was found that metal ion doping at various percentage compositions enables a large shift in the absorption band of the TiO₂ towards visible light region. This is due to the formation of various mid band gaps at 2.84 eV, 2.804 eV, 2.66 eV, and 2.55 eV. The extent of degradation of the pesticide was followed by UV-Visible spectroscopy and GC-MS methods. Based on the spectral analysis, the probable degradation reaction mechanism for OZ is proposed. These results indicate that Th-doped TiO₂ with the modified electronic properties is a good catalyst under solar light irradiation. But these particles show marginal variation in rates under UV-illumination. All the photodegradation reactions follow the first order kinetics.      

On the order of a non-abelian representation group of a slim dense near hexagon

In this paper we study the possible orders of a non-abelian representation group of a slim dense near hexagon. We prove that if the representation group R of a slim dense near hexagon S is non-abelian, then R is a 2-group of exponent 4 and |R|=2 ^β , 1+NPdim(S)≤β≤1+dimV(S), where NPdim(S) is the near polygon embedding dimension of S and dimV(S) is the dimension of the universal representation module V(S) of S. Further, if β=1+NPdim(S), then R is necessarily an extraspecial 2-group. In that case, we determine the type of the extraspecial 2-group in each case. We also deduce that the universal representation group of S is a central product of an extraspecial 2-group and an abelian 2-group of exponent at most 4. This work was partially done when B.K. Sahoo was a Research Fellow at the Indian Statistical Institute, Bangalore Center with NBHM fellowship, DAE Grant 39/3/2000-R&D-II, Govt. of India.