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.     

Identification of a K isomer in 252No

A K isomer with a half-life of (110±10) ms at an excitation energy of 1254keV has been identified in the nucleus ²⁵²No . The isomer is interpreted as a two-quasineutron state with K ^π = 8^- . The isotope ²⁵²No was produced in the fusion-evaporation reaction ²⁰⁶Pb(⁴⁸Ca, 2n)²⁵²No . The experiment has been performed at the velocity filter SHIP of GSI Darmstadt.     

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.     

A catalytic one-step process for the chemo- and regioselective acylation of monosaccharides

An organocatalytic method for the chemo- and regioselective acylation of monosaccharides has been developed. Treatment of octyl beta-D-glucopyranoside with isobutyric anhydride in the presence of 10 mol % of a C2-symmetric chiral 4-pyrrolidinopyridine catalyst (1) at -50 degrees C gave the 4-O-isobutyryl derivative as the sole product in 98% yield. Thus, chemoselective acylation, favoring a secondary hydroxyl group in the presence of a free primary hydroxyl group, and regioselective acylation, favoring one of three secondary hydroxyl groups, took place with perfect selectivity. A competitive acylation between octyl beta-D-glucopyranoside and a primary alcohol (2-phenylethanol) with 1.1 equiv of isobutyric anhydride in the presence of 1 gave the 4-O-isobutyrate of octyl beta-D-glucopyranoside with 99% regioselectivity in 98% yield, which indicates that acylation of the secondary hydroxyl group at C(4) of the carbohydrate proceeds in an accelerative manner. A possible mechanism, involving multiple hydrogen-bonding between 1 and the monosaccharide, is proposed for the chemo- and regioselective acylation.     

Domains in multiband superconductors

Multiband superconductors can have several types of domains that are inhibited in conventional single-band superconductors. These domains are phase domains and chiral domains and their domain wall are an interband phase difference soliton. In a superconductor with an odd number of electronic bands (five or more) and with positive interband Josephson interactions, we find other types of domains with different interband phase differences. We call these domains configuration domains because pseudo-order parameters for each band are dispersed in the complex plain and several configurations, which have several local minima. Fractional vortices serve as hubs for phase difference solitons (configuration domain walls). The divergence of the number of configurations with local minima would pose a serious problem for the stability of superconductivity.     

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.