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.     

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.     

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.     

Cold N+NH collisions in a magnetic trap

We present an experimental and theoretical study of atom-molecule collisions in a mixture of cold, trapped N atoms and NH molecules at a temperature of ～600 mK. We measure a small N+NH trap loss rate coefficient of k(loss)(N+NH)=9(5)(3)×10(-13) cm(3)?s(-1). Accurate quantum scattering calculations based on ab initio interaction potentials are in agreement with experiment and indicate the magnetic dipole interaction to be the dominant loss mechanism. Our theory further indicates the ratio of N+NH elastic-to-inelastic collisions remains large (>100) into the mK regime.     

Examination of the dynamic software-supported learning environment in data analysis

The Fatih Project in Turkey has improved software in mathematics teaching such as data analysis software. As a result, the need to inquire into the efficiency of computer-supported learning environments has emerged. This study aims to examine the effect of dynamic data analysis software-supported learning environments on secondary school students’ achievement and attitude. The research method employs a quasi-experimental design with a pre-test, post-test control group. Basic topics related to data analysis were introduced through dynamic statistics software in the experimental group while the students were taught with the help of smart boards, course books and exercises in the control group. Data were collected with an achievement test, attitude scale and semi-structured interviews. Also, interviews were conducted with four students from the experimental group in order to get more detailed information from students. The data gained in the study were analysed both quantitatively and qualitatively. The findings revealed that statistics teaching through statistics software is more efficient than the one with the traditional method on achievement and attitudes. In accordance with this result, it is suggested that computer-supported statistics software should be used in statistics teaching.