Subspaces of Maximal Operator Spaces

We explore subspaces of maximal operator spaces ( submaximal spaces) and give a new characterization of such spaces. We show that the set of n-dimensional submaximal spaces is closed in the topology of c.b. distance, but not compact. We also investigate subspaces of MAX(L ) and prove that any homogeneous Hilbertian subspace of MAX(L ₁) is completely isomorphic to R + C.     

Velocity and velocity-difference distributions in Burgers turbulence

We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and velocity-difference probability density functions and confirm the results with high-resolution numerical simulations.     

Three-dimensional relativistic electromagnetic subcycle solitons

Three-dimensional (3D) relativistic electromagnetic subcycle solitons were observed in 3D particle-in-cell simulations of an intense short-laser-pulse propagation in an underdense plasma. Their structure resembles that of an oscillating electric dipole with a poloidal electric field and a toroidal magnetic field that oscillate in phase with the electron density with frequency below the Langmuir frequency. On the ion time scale, the soliton undergoes a Coulomb explosion of its core, resulting in ion acceleration, and then evolves into a slowly expanding quasineutral cavity.     

Direct Sums of Operator Spaces

It is proved that if X and Y are operator spaces such that everycompletely bounded operator from X into Y is completely compactand Z is a completely complemented subspace of X Y, then thereexists a completely bounded automorphism : X Y X Y with completelybounded inverse such that Z = X₀ Y₀, where X₀ and Y₀ are completelycomplemented subspaces of X and Y, respectively. If X and Yare homogeneous, the existence is proved of such a under aweaker assumption that any operator from X to Y is strictlysingular. An upper estimate is obtained for ||||_cb||^–1||_cbif X and Y are separable homogeneous Hilbertian operator spaces.Also proved is the uniqueness of a ‘completely unconditional’basis in X Y if X and Y satisfy certain conditions.     

Modification of polysulfones by click chemistry: Amphiphilic graft copolymers and their protein adsorption and cell adhesion properties

Well‐defined amphiphilic graft copolymer with hydrophobic polysulfone (PSU) backbone and hydrophilic poly(acrylic acid) (PAA) side chains were synthesized and characterized. For this purpose, commercially available PSU was converted to azido‐functionalized polymer (PSU‐N₃) by successive chloromethylation and azidation processes. Independently, poly(tert‐butyl acrylate) (PtBA) with an alkyne‐end‐group is obtained by using suitable initiator in atom transfer radical polymerization (ATRP). Then, this polymer was successfully grafted onto PSU‐N₃ by click chemistry to yield polysulfone‐graft‐poly(tert‐butyl acrylate), (PSU‐g‐PtBA). Finally, amphiphilic polysulfone‐graft‐poly(acrylic acid), (PSU‐g‐PAA), membranes were obtained by hydrolyzing precursor the PSU‐g‐PtBA membranes in trifluoroacetic acid. The final polymer and intermediates at various stages were characterized by ¹H NMR, FTIR, GPC, and SEM analyses. Protein adsorption and eukaryotic and prokaryotic cell adhesion on PSU‐g‐PAA were studied and compared to those of PSU‐g‐PtBA and unmodified PSU. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Complex pole approach in thermodynamic description of fluid mixtures with small number of molecules

The subject matter of classical thermodynamics is the asymptotic behavior of equilibrium systems in thermodynamic limit, for small molecular systems, when transition to thermodynamic limit is impossible, the extension of thermodynamics is required. This work studies novel approach for the evaluation of partition functions of small systems by complex pole analysis. Several cases for molecular systems in small cavities are studied numerically. In particular size-dependent additional pressure for small systems is evaluated analytically and numerically. Similar approach was developed earlier in nuclear physics for finite systems of nucleons. The obtained results correspond to published experimental data and molecular dynamics simulations.     

A DFT,X- and W-band EPR and ENDOR Study of Nitrogen-Centered Species in (Nano)Hydroxyapatite

Incorporation of the nitrogen-containing impurities in hydroxyapatite (HAp) powders with the sizes of the crystallites of (20–50) nm was studied using first-principles modeling combined with the multi-frequency (9 and 94 GHz) electron paramagnetic resonance (EPR) methods. It is shown that the observed EPR spectra are undoubtedly due to the presence of the bulk radiation-induced NO₃ ^2? radicals. This conclusion is based on spin-polarized density functional theory calculations of spectroscopic parameters within gauge-including projector augmented wave framework followed by the exact comparison of the simulated EPR and electron–nuclear double resonance spectra with the experimental findings. In addition, a comprehensive analysis of the simulated properties allows us to suggest that the paramagnetic centers preferably occupy PO₄ ^3? sites in the HAp structure.     

Syntheses,Characterizations, Crystal structures,and Antitumor Activities of Arenetelluronic Triorganotin Esters

Six new arenetelluronic triorganotin esters, namely (R₃Sn)₄[ArTe(μ‐O)(OH)O₂)]₂ (Ar = Ph, R = Me: 1 , R = Ph: 2 ; Ar = 3‐Me‐Ph, R = Me: 3 , R = Ph: 4 , Ar = 3‐Cl‐Ph, R = Me: 5 , R = Ph: 6 ), were prepared by treating arenetelluronic acids with the corresponding R₃SnCl (R = Me, Ph) with potassium hydroxide in methanol. All complexes were characterized by elemental analysis, FT‐IR, NMR (¹H, ¹³C, ¹¹⁹Sn) spectroscopy, and X‐ray crystallography. The structural analyses indicate that these complexes are isostructural as Sn₄Te₂ moiety, in which the Te₂(μ₂‐O)₂ units are situated in the center and each Te atom is coordinated with two OSnR₃ groups on the side. Complexes 1 , 3 , and 5 show one‐dimensional chain and two‐dimensional network supramolecular structures by intermolecular C H···O or C H···Cl interactions. The antitumor activities of these complexes reveal that most arenetelluronic triorganotin esters have powerful antitumor activities with certain regularity.     

Synthesis and binding ability of mono- and tetrasubstituted aminophosphonate Zn-tetraarylporphyrins towards N- and O-containing organic substrates

The 1,6-addition of mono- and tetra-amino 5,10,15,20-tetraphenylporphyrins with dimethyl-(3,5-di-tert-butyl-4-oxocyclohexa-2,5-dienylidenemethyl)phosphonate leads to the corresponding mono- and tetrasubstituted aminophosphonate porphyrin derivatives. The binding ability of their Zn(II)-complexes towards 1,4-diazabicyclo[2,2,2]octane, imidazole, 4-(1H-imidazole-1-yl)benzyl alcohol and 4-(1H-imidazole-1-ylmethyl)benzyl alcohol in toluene was investigated by spectrophotometric and ¹H NMR titration. It has been determined that the monosubstituted Zn-tetraarylporphyrin is involved in a two-point selective binding of 4-(1H-imidazole-1-ylmethyl)benzyl alcohol. Taking into account the fact that this binding is accompanied by a clear and easily identifiable response in the UV–vis spectra of the reaction mixture, this metalloporphyrin could be considered as a molecular optical sensing device for selected bidentate N- and O-containing substrates.