Filtrations on G1T-Modules

Let G be an almost simple algebraic group defined over F_p forsome prime p. Denote by G₁ the first Frobenius kernel in G andlet T be a maximal torus. In this paper we study certain Jantzentype filtrations on various modules in the representation theoryof G₁T. We have such filtrations on the baby Verma modules Z,where is a character of T. They are obtained via a certaindeformation of the natural homomorphism from Z into its contravariantdual Z. Using the same deformation we construct for each projectiveG₁T-module Q a filtration of the vector space . We then prove that this filtration may also bedescribed in terms of the above-mentioned homomorphism Z() Z() and this leads us to a sum formula for our filtrations.When Q is indecomposable with highest weight in the bottom alcove(with respect to some special point) we are able to computethe filtrations on F(Q) explicitly for all . This is then thestarting point of an induction which proceeds via wall crossingsto higher alcoves. If our filtrations behave as expected undersuch wall crossings then we obtain a precise relation betweenthedimensions of the layers in the filtrations of F(Q) for an arbitraryindecomposable projective Q and the coefficients in the correspondingKazhdan–Lusztig polynomials. We conclude the paper byproving that the above results in the G₁T theory have some analoguesin the representation theory of G (where, however, we have towork with representations of bounded highest weights) and thecorresponding theory for quantum groups at roots of unity. Theseresults extend previous work by the first author. 2000 MathematicsSubject Classification: 20G05, 20G10, 17B37.     

A bound for the theorem of de Franchis

We give a bound on the number of nonconstant holomorphic maps between compact Riemann surfaces of genera .

     

Magnetic property and structural study of nickel supported on reduced graphene oxide prepared by chemical vapor deposition

Nickel supported on reduced graphene oxide was synthesized by chemical vapor deposition technique. The crystal structure and magnetic properties of the prepared sample were studied by means of Raman spectrometry, X-ray photoelectron spectroscopy (XPS), transmission electron microscopy (TEM), inductively coupled plasma optical emission spectrometry (ICP-OES), and vibrating sample magnetometry (VSM). The result of Raman spectroscopy revealed the structure of few-layer graphene as the support for Ni nanoparticles. XP spectrum confirmed the presence of metallic Ni on the a few-layer graphene surface. TE micrograph showed that the nickel nanoparticles were sphere shaped and the mean particle size is about 20 nm deposited on the reduced graphene oxide. The magnetic study showed the ferromagnetic behavior of 3.2 wt% nickel over reduced graphene oxide at room temperature.     

Indium-catalyzed 2-alkenylation of 1,3-dicarbonyl compounds with unactivated alkynes

1,3-Dicarbonyl compounds add to unactivated alkynes in the presence of a catalytic amount of indium(III) trifluoromethanesulfonate in high to excellent yield to give 2-alkenylated 1,3-dicarbonyl compounds with exclusive regioselectivity as to the position of C-C bond formation on the acetylene moiety. In most of the cases, the reaction requires less than 1-mol % loading of the catalyst and does not require solvent. The reaction tolerates a wide variety of functional groups including ester, ether, allylic halide, furan, thiophene, and protected amine. Experimental and theoretical studies suggested that the reaction proceeds via a concerted carbometalation reaction of an indium(III) enolate with the acetylene, where indium-acetylene interaction is important.     

Tandem phospha-Friedel-Crafts reaction toward curved π-conjugated frameworks with a phosphorus ring junction

The tandem phospha-Friedel-Crafts reaction transforms dichloro(m-teraryl)phosphine to the corresponding triarylphosphine derivatives containing curved π-conjugated frameworks with a phosphorus ring junction. The rigid molecular frameworks enable these unprecedented phosphine compounds to hold an extended π-conjugation spread over the whole molecule.     

Whole-body counter surveys of Miharu-town school children for four consecutive years after the Fukushima NPP accident

Comprehensive whole-body counter surveys of Miharu-town school children have been conducted for four consecutive years, in 2011–2014. This represents the only long-term sampling-bias-free study of its type conducted after the Fukushima Dai-ichi accident. For the first time in 2014, a new device called the Babyscan, which has a low ^134/137Cs MDA of <50 Bq/body, was used to screen the children shorter than 130 cm. No child in this group was found to have detectable level of radiocesium. Using the MDAs, upper limits of daily intake of radiocesium were estimated for each child. For those screened with the Babyscan, the upper intake limits were found to be ≲1 Bq/day for ¹³⁷Cs. Analysis of a questionnaire filled out by the children’s parents regarding their food and water consumption shows that the majority of Miharu children regularly consume local and/or home-grown rice and vegetables. This however does not increase the body burden.     

Novel Synthesis of Optically Active 2‐Ethylhexanoic Acid, 2‐Ethylhexanol,and 2‐Ethylhexylamine via the Asymmetric Favorskii Rearrangement

The asymmetric Favorskii rearrangement of optically active α‐haloketones, which are easily prepared from chiral menthyl‐4‐toluenesulfoxide in several steps using primary or secondary amines, yields their corresponding secondary or tertiary chiral amides. The secondary chiral amides were converted to acids or amines using acylation followed by hydrolysis or reduction. In addition, the tertiary amides were directly reduced to alcohol with Super‐Hydride^®.     

Heavy element stable isotope ratios : analytical approaches and applications

Continuous developments in inorganic mass spectrometry techniques, including a combination of an inductively coupled plasma ion source and a magnetic sector-based mass spectrometer equipped with a multiple-collector array, have revolutionized the precision of isotope ratio measurements, and applications of inorganic mass spectrometry for biochemistry, geochemistry, and marine chemistry are beginning to appear on the horizon. Series of pioneering studies have revealed that natural stable isotope fractionations of many elements heavier than S (e.g., Fe, Cu, Zn, Sr, Ce, Nd, Mo, Cd, W, Tl, and U) are common on Earth, and it had been widely recognized that most physicochemical reactions or biochemical processes induce mass-dependent isotope fractionation. The variations in isotope ratios of the heavy elements can provide new insights into past and present biochemical and geochemical processes. To achieve this, the analytical community is actively solving problems such as spectral interference, mass discrimination drift, chemical separation and purification, and reduction of the contamination of analytes. This article describes data calibration and standardization protocols to allow interlaboratory comparisons or to maintain traceability of data, and basic principles of isotope fractionation in nature, together with high-selectivity and high-yield chemical separation and purification techniques for stable isotope studies.

Coherent and Incoherent Excitations of Electron-Doped SrTiO3

Resonant photoemission at the Ti 2p and O 1s edges on a Nb-doped SrTiO(3) thin film revealed that the coherent state (CS) at the Fermi level (E(F)) had a mainly Ti 3d character whereas the incoherent in-gap state (IGS) positioned approximately 1.5 eV below E(F) had a mixed character of Ti 3d and O 2p states. This indicates that the IGS is formed by a spectral-weight transfer from the CS and subsequent spectral-weight redistribution through d-p hybridization. We discuss the evolution of the excitation spectrum with 3d band filling and rationalize the IGS through a mechanism similar to that proposed by Haldane and Anderson.