Isomorphous substitutions of rare earth elements for calcium in synthetic hydroxyapatites

Polycrystalline hydroxyapatites Ca(10-x)REE(x)(PO(4))(6)(OH)(2-x)O(x) were synthesized and studied by X-ray powder diffraction, infrared absorption, diffuse-reflectance spectroscopy, and thermogravimetry. The solubility limits x(max) of rare earth elements (REE) in Ca hydroxyapatites decreases with an increasing REE atomic number from x(max) = 2.00 for La, Pr, and Nd to x(max) = 0.20 for Yb at 1100 °C. Refinements of X-ray diffraction patterns by the Rietveld method show that REE atoms substitute for Ca preferentially at the Ca(2) sites of the apatite structure. The substitution decreases the Ca(2)-O(4) atomic distances in the calcium coordination polyhedra and increases the Ca(2)-O(1,2,3) distances. This observation shows that interatomic distances depend not only on radii of the ions involved in the substitution but also on their charges.     

On the sectionwise connectedness of a contingent

Let X be a real normed space and let f: ? → X be a continuous mapping. Let T _f (t ₀) be the contingent of the graph G(f) at a point (t ₀, f(t ₀)) and let S ⁺ ? (0,∞) × X be the “right” unit hemisphere centered at (0, 0 _X ). We show that

1. 1.
   If dimX < ∞ and the dilation D(f, t ₀) of f at t ₀ is finite then T _f (t ₀) ∩ S ⁺ is compact and connected. The result holds for \(T_f (t_0 ) \cap \overline {S^ + } \) even with infinite dilation in the case f: [0,∞) → X.
    
2. 2.
   If dimX = ∞, then, given any compact set F ? S ⁺, there exists a Lipschitz mapping f: ? → X such that T _f (t ₀) ∩ S ⁺ = F.
    
3. 3.
   But if a closed set F ? S ⁺ has cardinality greater than that of the continuum then the relation T _f (t ₀) ∩ S ⁺ = F does not hold for any Lipschitz f: ? → X.
    

     

*-Representations of Twisted Generalized Weyl Constructions

We study bounded and unbounded *-representations of Twisted Generalized Weyl Algebras and algebras similar to them for different choices of involutions.     

Simple weith modules over twisted generalized weyl algebras

We introduce a twisted higher rank generalization of generalized Weyl algebras and study simple weight modules over such algebras.     

Spectroscopic,structural and theoretical studies of 2‐methyl‐4‐nitroaniline (MNA) crystal. Electronic transitions in IR

Polarized FT‐IR, Raman, neutron scattering (IINS), and UV‐Vis‐NIR spectra of 2‐methyl‐4‐nitroaniline (MNA) crystal plates, powder, and solutions were measured in the 10–50 000 cm⁻¹ range. The FT‐IR spectrum of deuterated MNA (DMNA) in KBr pellet, the Raman spectrum of the DMNA powder as well as the EPR spectrum of the MNA powder were also recorded. Complete assignments of bands to normal vibrations have been proposed. Density functional theory (DFT) calculations of wavenumbers and potential energy distribution (PED) have been performed to strengthen the assignments. The analysis of vibrational and electronic spectra has revealed vibronic couplings in MNA molecules in solutions and in crystals. In the polarized FT‐IR spectra of the crystal five unusually large bands are observed in MIR and NIR regions. Their origin is discussed in terms of N H···O, C H···O, C H···H N hydrogen bonds, intermolecular charge transfers, electrostatic interactions, and ion radicals formation in the crystal. The role of a methyl group introduction to 4‐nitroaniline is analyzed. The crystal structure of MNA at the room temperature was re‐investigated. Copyright © 2008 John Wiley & Sons, Ltd.     

Lipschitz mappings,contingents, and differentiability

The main purpose of the paper is to show that, for each real normed space Y of infinite dimension, each number L > 0, and each at most countable set Q ? ?, there exists a Lipschitz mapping ?: ? → Y, with constant L, whose graph has a tangent everywhere, whereas ? is not differentiable at any point of Q.     

Synthesis,Anticancer, and QSAR Studies of 2‐Alkyl(aryl,hetaryl)quinazolin‐4(3H)‐thione's and [1,2,4]Triazolo[1,5‐c]quinazoline‐2‐thione's Thioderivatives

Considering the frightening high level of mortality from cancer, studies of anticancer agents are vital nowadays. The 24 thioderivatives of 2‐alkyl(aryl)‐quinazolin‐4(3H)‐thiones and 20 thioderivatives of [1,2,4]triazolo[1,5‐c]quinazoline‐2‐thiones were synthesized and evaluated for preliminary in vitro anticancer activity with subsequent in silico QSAR analysis. The substance 18 had the best results inhibiting growth of eight cancer cell lines: CCRF‐CEM of leukemia; SF‐539, SNB‐75, and U251 of CNS cancer; 786, RXF393, and UO‐31 of renal cancer; and MDA‐MB‐231/ATCC of breast cancer (?31.50 – 47.41% of cell growth) with low procancer effect. Calculated QSAR‐models for CCRF‐CEM of leukemia, T‐47D and HS 578T of breast cancer, and mean cell growth demonstrated good rate of anticancer activity prediction (r² = 0.7 – 0.8,  = 0.5 – 0.7).     

Minimum contrast estimation of stationary processes based on the squared periodogram?

We present a class of minimum contrast estimators based on the objective function that is composed using the squared periodogram. We prove the consistency and asymptotic normality of the proposed estimators.