The PRV-formula for tensor product decompositions and its applications

Let G be a semisimple algebraic group, V a simple finite-dimensional self-dual G-module, and W an arbitrary simple finite-dimensional G-module. Using the triple multiplicity formula due to Parthasarathy, Ranga Rao, and Varadarajan, we describe the multiplicities of W in the symmetric and exterior squares of V in terms of the action of a maximum-length element of the Weyl group on some subspace in V ^T , where T ? G is a maximal torus. By way of application, we consider the cases in which V is the adjoint, little adjoint, or, more generally, a small G-module. We also obtain a general upper bound for triple multiplicities in terms of Kostant’s partition function.     

On seaweed subalgebras and meander graphs in type D

In 2000, Dergachev and Kirillov introduced subalgebras of “seaweed type” in ${\mathfrak{gl}}_n$ and computed their index using certain graphs, which we call type-A meander graphs. Then the subalgebras of seaweed type, or just “seaweeds”, have been defined by Panyushev (2001) [9] for arbitrary reductive Lie algebras. Recently, a meander graph approach to computing the index in types B and C has been developed by the authors. In this article, we consider the most difficult and interesting case of type $\mathsf{D}$. Some new phenomena occurring here are related to the fact that the Dynkin diagram has a branching node.     

Polyelectrolyte nanoparticles based on functionalized silica and pillar[5]arene derivatives for recognition of model proteins

Russian Chemical Bulletin - The paper reports the first synthesis of positively charged hybrid organic-inorganic silicon dioxide nanoparticles with an average particle diameter of 28 nm modified...     

Nanoporous metal organic framework materials for hydrogen storage

Hydrogen is expected to play an important role in future transportation as a promising alternative clean energy source to carbon-based fuels.One of the key challenges to commercialize hydrogen energy is to develop appropriate onboard hydrogen storage systems,capable of charging and discharging large quantities of hydrogen with fast enough kinetics to meet commercial requirements.Metal organic framework (MOF) is a new type of inorganic and organic hybrid nanoporous particulate materials.Its diverse networks can enhance hydrogen storage through tuning the structure and property of MOFs.The MOF materials so far developed adsorb hydrogen through weak disperston interactions,which allow significant quantity of hydrogen to be stored at cryogenic temperatures with fast kinetics.Novel MOFs are being developed to strengthen the interactions between hydrogen and MOFs in order to store hydrogen under ambient conditions.This review surveys the development of such candidate materials,their performance and future research needs.     

A core level and valence band photoemission study of the (1 1 1) and ( ) surfaces of 3C–SiC

A core level and valence band photoemission study of thick 3C–SiC(1 1 1) and 3C–SiC( ) epilayers grown by sublimation epitaxy is reported. The as introduced samples show threefold 1×1 low-energy electron diffraction patterns. For the Si face and reconstructed surfaces develop after in situ heating to 1100°C and 1300°C, respectively. For the C face a 3×3 reconstruction form after heating to 980°C. A semiconducting behavior is observed for the and 3×3 reconstructed surfaces while the reconstruction show a Fermi edge and thus a metallic-like behavior. The surface state on the surface is investigated and found to have Λ₁ symmetry and a total band width of 0.10 eV within the first surface Brillouin zone. For the Si 2p and C 1s core levels binding energies and surface shifted components are extracted and compared to earlier reported results for 6H– and 4H–SiC.     

The effect of electron irradiation on the luminescence of cadmium and lead tungstates

It is shown that the intensity of luminescence of cadmium tungstate crystals changes nonmonotonically under electron irradiation. At low irradiation doses, an increase in the luminescence intensity can be observed. However, with an increase in the irradiation dose, the luminescence intensity decreases. The effect observed can be explained by the competition of two processes: increase in the number of luminescence centers and nonradiative recombination under the action of irradiation.     

Thiokols Based on Wastes from Epichlorohydrin Production as Components of Rail Lubricants

Preparation of solid polymers with varied content of sulfur by condensation of 1,2,3-trichloropropane-rich wastes from epichlorohydrin production with sodium polysulfide Na₂S_x (x = 1-4) generated by reductive dissolution of sulfur in the hydrazine hydrate-alkali system was studied.     

Self-assembled fractal hybrid dendrites from water-soluble anionic (thia)calix[4] arenes and Ag<Superscript>+</Superscript>

Novel water-soluble anionic p-tert-butylthiacalix[4]arene with propanesulfonate fragments has been synthesized. Alkylation of the lower rim of thiacalix[4]arene in the presence of NaH/THF led to cone conformation instead of the expected 1,3-alternate conformer due to metal template effect. The presence of supramolecular associates at the critical micelle concentration of 1.65 · 10^?5 M were investigated in aqueous solutions by a combination of different techniques (DLS and conductivity). It was observed that the macrocyclic platform decreases the CMC by tenfold as compared with non-macrocycle analogs. A simple approach for the design of stable monodisperse Ag-based nanoaggregates (near 95 nm) containing ionic Ag and organic ligand–thiacalix[4]arene sulfo derivative in water has been developed. Self-assembled fractal hybrid nanodendrites consisting of water-soluble anionic (thia)calix[4]arenes and Ag⁺ have been obtained in a single step under mild conditions.

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