Applications of the Category of Linear Complexes of Tilting Modules Associated with the Category

We use the category of linear complexes of tilting modules for the BGG category \mathfrakg\mathfrak{g}, to reprove in purely algebraic way several known results about obtained earlier by different authors using geometric methods. We also obtain several new results about the parabolic category .     

A lattice approach to narrow operators

It is known that if a rearrangement invariant function space E on [0,1] has an unconditional basis then each linear continuous operator on E is a sum of two narrow operators. On the other hand, the sum of two narrow operators in L₁ is narrow. To find a general approach to these results, we extend the notion of a narrow operator to the case when the domain space is a vector lattice. Our main result asserts that the set N_r(E, F) of all narrow regular operators is a band in the vector lattice L_r(E, F) of all regular operators from a non-atomic order continuous Banach lattice E to an order continuous Banach lattice F. The band generated by the disjointness preserving operators is the orthogonal complement to N_r(E, F) in L_r(E, F). As a consequence we obtain the following generalization of the Kalton-Rosenthal theorem: every regular operator T : E → F from a non-atomic Banach lattice E to an order continuous Banach lattice F has a unique representation as T = T_D + T_N where T_D is a sum of an order absolutely summable family of disjointness preserving operators and T_N is narrow. Supported by Ukr. Derzh. Tema N 0103Y001103.     

One‐electron Optical Properties of a Nanorice with a Nonconcentric Core

We investigate optical properties of nanoshells (small composite clusters composed of a dielectric core and a metal shell; contribution of the shell dominates in the optical properties of the whole cluster) far from plasmon resonance. In particular, nanoshells with the shape of a stretched rotation ellipsoid (nanorice) are considered. For such shell‐type particle the electron wavefunction, the electron energy, the wavenumber spectrum, and the matrix elements of corresponding optical transitions were found. Using these quantities, the classical optical conductivity of such shells (the quantum effects are not considered) and the quantum optical conductivity (relevant addendums for the classical conductivity that are caused by the quantum effects like the electron spectrum discreteness) were found. Oscillating nature of the dependence of these addendums on the incident light frequency is established. The optical conductivity expressions are generalized for the case of a nanorice particle with a weak nonconcentricity.     

New members of ternary rare-earth metal boride carbides containing finite boron-carbon chains: RE25B14C26 (RE=Pr, Nd) and Nd25B12C28

New ternary rare-earth metal boride carbides RE₂₅B₁₄C₂₆ (RE=Pr, Nd) and Nd₂₅B₁₂C₂₈ were synthesized by co-melting the elements. Nd₂₅B₁₂C₂₈ is stable up to 1440 K. RE₂₅B₁₄C₂₆ (RE=Pr, Nd) exist above 1270 K. The crystal structures were investigated by means of single-crystal X-ray diffraction. Nd₂₅B₁₂C₂₈: space group P, a=8.3209(7) Å, b=8.3231(6) Å, c=29.888(2) Å, α=83.730(9)°, β=83.294(9)°, γ=89.764(9)°. Pr₂₅B₁₄C₂₆: space group P2₁/c, a=8.4243(5) Å, b=8.4095(6) Å, c=30.828(1) Å, β=105.879(4)°, V=2100.6(2) Å³, (R1=0.048 (wR2=0.088) from 2961 reflections with I_o>2σ(I_o)); for Nd₂₅B₁₄C₂₆ space group P2₁/c, Z=2, a=8.3404(6) Å, b=8.3096(6) Å, c=30.599(2) Å, β=106.065(1)°. Their structures consist of a three-dimensional framework of rare-earth metal atoms resulting from the stacking of slightly corrugated and distorted square nets, leading to cavities filled with cumulene-like molecules [B₂C₄]⁶⁻ and [B₃C₃]⁷⁻, nearly linear [BC₂]⁵⁻ and bent [BC₂]⁷⁻ units and isolated carbon atoms. Structural and theoretical analysis suggests the ionic formulation for RE₂₅B₁₄C₂₆: (RE³⁺)₂₅[B₂C₄]⁶⁻([B₃C₃]⁷⁻)₂([BC₂]⁵⁻)₄([BC₂]⁷⁻)₂(C⁴⁻)₄·5e⁻ and for Nd₂₅B₁₂C₂₈: (Nd³⁺)₂₅([B₂C₄]⁶⁻)₃([BC₂]⁵⁻)₄([BC₂]⁷⁻)₂(C⁴⁻)₄·7e⁻. Accordingly, extended Hückel tight-binding calculations indicate that the compounds are metallic in character.     

Virtual Computational Chemistry Laboratory – Design and Description

Internet technology offers an excellent opportunity for the development of tools by the cooperative effort of various groups and institutions. We have developed a multi-platform software system, Virtual Computational Chemistry Laboratory, http://www.vcclab.org, allowing the computational chemist to perform a comprehensive series of molecular indices/properties calculations and data analysis. The implemented software is based on a three-tier architecture that is one of the standard technologies to provide client-server services on the Internet. The developed software includes several popular programs, including the indices generation program, DRAGON, a 3D structure generator, CORINA, a program to predict lipophilicity and aqueous solubility of chemicals, ALOGPS and others. All these programs are running at the host institutes located in five countries over Europe. In this article we review the main features and statistics of the developed system that can be used as a prototype for academic and industry models.     

Proof of the Projective Lichnerowicz Conjecture for Pseudo-Riemannian Metrics with Degree of Mobility Greater than Two

Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We prove that complete metrics on (n≥ 3)−dimensional manifolds with degree of mobility ≥ 3 do not admit complete metrics that are geodesically equivalent to them, but not affinely equivalent to them. As the main application we prove an important special case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting an essential group of projective transformations is the standard round sphere (up to a finite cover and multiplication of the metric by a constant).     

Phase separation in non-ionic surfactant Triton X-100 solutions in the presence of phenol

The influence of concentration conditions and acidity on the phase separation in non-ionic surfactants Triton X-100 solutions in the presence of phenol was investigated. It was shown that the addition of small amounts of phenol results in the decrease of the cloud point temperature of Triton X-100 solutions. On the other hand, the addition of phenol into the investigated system resulted in the decrease of the hydration values of surfactant-rich phases and the increase of their hydrophobicity. The extraction degree and distribution coefficient of phenol between the water and the surfactant-rich phases were studied. On the basis of data obtained the molar parts of water, phenol and Triton X-100 in the non-ionic surfactant-rich phases formed at different concentration conditions were calculated. Possibilities of the application of phenol-induced micellar extraction for microcomponents preconcentration were estimated.     

Novel heterometallic Schiff base complexes featuring unusual tetranuclear {Co(III)2Fe(III)2(μ-O)6} and octanuclear {Co(III)4Fe(III)4(μ-O)14} cores: direct synthesis, crystal structures, and magnetic properties

A one-pot reactions of cobalt powder with iron(II) chloride in dimethylformamide (DMF; 1) or dimethyl sulfoxide (DMSO; 2) solutions of polydentate salicylaldimine Schiff base ligands (H(2)L(1), 1; H(4)L(2), 2) based on 2-aminobenzyl alcohol (1) or tris(hydroxymethyl)aminomethane (2), formed in situ, yielded two novel heterometallic complexes, [Co(III)(2)Fe(III)(2)(L(1))(6)]·4DMF (1) and [Co(III)(4)Fe(III)(4)(HL(2))(8)(DMSO)(2)]·18DMSO (2). Crystallographic investigations revealed that the molecular structure of 1 is based on a tetranuclear core, {Co(III)(2)Fe(III)(2)(μ-O)(6)}, with a chainlike metal arrangement, while the structure of 2 represents the first example of a heterometallic octanuclear core, {Co(III)(4)Fe(III)(4)(μ-O)(14)}, with a quite rare manner of metal organization, formed by two pairs of {CoFe(HL(2))(2)} and {CoFe(HL(2))(2)(DMSO)} moieties, which are joined by O bridges of the Schiff base ligands. Variable-temperature (1.8-300 K) magnetic susceptibility measurements showed a decrease of the μ(B) value at low temperature, indicative of antiferromagnetic coupling (J/hc = -32 cm(-1) in 1; J/hc = -20 cm(-1) in 2) between the Fe(III) magnetic centers in both compounds. For 2, three J constants between Fe(III) centers were assumed to be identical. High-frequency electron paramagnetic resonance spectra allowed one to find spin Hamiltonian parameters in the coupled-spin triplet and quintet states of 1 and estimate them in 2. The "outer" and "inner" Fe atoms in 2 appeared separately in the M?ssbauer spectra.     

Heterocyclization of N-(1-chloro-2,2,2-trifluoroethylidene)carbamates with β-enaminoesters—a novel synthetic strategy to functionalized trifluoromethylated pyrimidines

A novel synthetic strategy to 4-trifluoromethyl substituted 2-oxo-1,2-dihydropyrimidine-5-carboxylates has been developed based on the cyclocondensation of β-enaminoesters with N-(1-chloro-2,2,2-trifluoroethylidene)carbamates.     

Dy5Ni0.66Bi2.34 and Lu5Ni0.56Sb2.44 – Substitution derivatives with the orthorhombic Yb5Sb3-type structure. Magnetocaloric effect of Dy5Ni0.66Bi2.34

Dy₅Ni_0.66Bi_2.34 and Lu₅Ni_0.56Sb_2.44 were synthesized by arc-melting and were found to adopt an orthorhombic Yb₅Sb₃-type structure. Cell parameters are a = 12.075(2), b = 9.165(2), c = 8.072(1) Å for Dy₅Ni_0.66Bi_2.34 and a = 11.6187(9), b = 8.933(1) and c = 7.8377(6) Å for Lu₅Ni_0.56Sb_2.44. Dy₅Ni_0.66Bi_2.34 undergoes a step-like ferromagnetic transition around 66 K. Magnetocaloric effect in terms of the magnetic entropy change, ΔS, reaches −3.73 J/kg K at 75 K for Dy₅Ni_0.66Bi_2.34.