Homogeneous polynomials with isomorphic milnor algebras

We recall first Mather’s Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.     

Calculating the parabolic Chern character of a locally abelian parabolic bundle

We calculate the parabolic Chern character of a bundle with locally abelian parabolic structure on a smooth strict normal crossings divisor, using the definition in terms of Deligne–Mumford stacks. We obtain explicit formulas for ch ₁, ch ₂ and ch ₃, and verify that these correspond to the formulas given by Borne for ch ₁ and Mochizuki for ch ₂.     

Green rings of Drinfeld doubles of Taft algebras

Abstract

In this article, we investigate the representation rings (or Green rings) of the Drinfeld doubles of the Taft algebras. It is shown that these Green rings are commutative rings generated by infinitely many elements subject to certain relations. The generators together with the subjecting relations are given. The stable Green rings of of the Drinfeld doubles of the Taft algebras are also described.     

Assessment of the natural radioactivity using two techniques for the measurement of radionuclide concentration in building materials used in Japan

The specific activities of ²³⁸U, ²³²Th, and ⁴⁰K in selected building materials used in Japan were measured using a high-purity germanium detector. The uranium and thorium concentrations were determined from same samples using inductively coupled plasma mass spectrometry. There was a good agreement between the measurement of uranium and thorium with both methods (R ² = 0.94, and 0.97, respectively). Based on the specific activities, we have estimated some hazard indexes such as radium equivalent activities (Ra _eq), external hazard index (H _ex), internal hazard index (H _in), annual gonadal equivalent dose (AGED), internal alpha dose, mass exhalation rate and emanation coefficient of radon.     

Study of optoelectronic energy bands and molecular energy levels of tris (8-hydroxyquinolinate) gallium and aluminum organometallic materials from their spectroscopic and electrochemical analysis

For the purpose of investigating electro-molecular absorption bands, energy gaps, E_g and molecular energy levels (ionization potential, IP and electron affinity, EA) of tris (8-hydroxyquinolinate) gallium and aluminum, spectral analysis in conjunction with electrochemical measurements was carried out. UV-Vis-NIR and FTIR spectroscopic measurements were used to assign the electronic and molecular absorption bands in both of the materials. The XRD and scanning electronic microscopy (SEM) technique showed the amorphous nature. From the recorded data of cyclic voltammetry (CV) and materials absorption coefficient, HOMO, LUMO energy levels and energy gaps for Gaq3 and Alq3 were calculated. A bit smaller value of energy gap for Gaq3 (2.80 eV) compared to that of Alq3 (2.86 eV) has been ascribed to the differences in electronic configuration and coordinated bond lengths related to the central metal atom with respect to the quinolinate ligands. A higher value of HOMO energy level for the Alq3 (IP = 6.3 eV) revealed the need of higher potentials to oxidize its molecules comparing to that of Gaq3 (IP = 5.8 eV). It was observed that cationic metals have a direct effect on the physical and chemical behaviors of such organometallic materials that can be exploited to be used in tuning their properties to match the desired application in OSC and/or OLED technologies.     

Total synthesis of (+)-roxaticin via C-C bond forming transfer hydrogenation: a departure from stoichiometric chiral reagents, auxiliaries, and premetalated nucleophiles in polyketide construction

A total synthesis of the oxo-polyene macrolide (+)-roxaticin is achieved in 20 steps from 1,3-propanediol. In this approach, 9 of 10 C-C bonds formed in the longest linear sequence are made via metal catalysis, including 7 C-C bonds formed by iridium catalyzed alcohol C-C coupling. Notably, the present synthesis, which represents the most concise preparation of any oxo-polyene macrolide reported to date, is achieved in the absence of chiral reagents and chiral auxiliaries with minimal use of premetalated C-nucleophiles.     

Microwave assisted synthesis of substituted furan-2-carboxaldehydes and their reactions

A series of 5-unsubstituted and 5-substituted furfurylidenes have been prepared, under thermal and non-thermal microwave irradiation methods, via condensation of furfural and its derivatives with some of active methylene compounds. Furthermore, various condensate products from these furfurylidenes, which contain halogen or sulpher atoms, were also prepared. Structural elucidation of the synthesized compounds were determined on the basis of various spectroscopic methods.     

Preparation, structure and spasmolytic activities of some derivatives of harmine series of alkaloids

Keeping in view the interesting chemistry and pharmacological importance of harmine series of bases -- the beta-carboline alkaloids, a number of new derivatives of tetrahydroharmine and harmalol have been prepared and characterized through spectral studies. Some of these derivatives showed spasmolytic activity. It was observed that all the N-acyl tetrahydroharmine derivatives are stable, not labile and no ring opening occurs in these compounds, as reported recently.     

Nanocatalysis on tailored shape supports: Au and Pd nanoparticles supported on MgO nanocubes and ZnO nanobelts

Active gold and palladium nanoparticles supported on MgO nanocubes and ZnO nanobelts and transition-metal-containing MgO nanobelts were synthesized by combining evaporation and deposition-precipitation techniques. The high activity and stability of the Au/CeO2 and Pd/CeO2 nanoparticle catalysts deposited on the MgO cubes are remarkable and imply that a variety of efficient catalysts can be designed and tested using this approach. The significant increase in the concentration of corner and edge sites in MgO nanocubes make them well-defined supports to study the detailed mechanism of the catalytic activity enhancement.