Putnam’s Inequality for log-Hyponormal Operators

Let T be a bounded linear operator on a complex Hilbert space H. T $/in$ B(H) is called a log-hyponormal operator if T is invertible and log (TT ^*) log (T ^* T). Since a function log : (0,) (-,) is operator monotone, every invertible p-hyponormal operator T, i.e., (TT ^*) ^p (T ^* T ^p is log-hyponormal for 0 < p 1. Putnams inequality for p-hyponormal operator T is the following:$ \| (T^*T)^p-(TT^*)^p \|\leq\frac{p}{\pi}\int\int_{\sigma(T)}r^{2p-1}drd\theta $.In this paper, we prove that if T is log-hyponormal, then$ \| log(T^*T)-log(TT^*) \|\leq\frac{1}{\pi}\int\int_{\sigma(T)}r^{-1}drd\theta $.     

Synthesis of 3-acyl-1-alkyl-2-alkylseleno-1-cyclobutene using alkyneselenolate

The reaction of lithium alkyneselenolate with alpha,beta-unsaturated ketone and then alkyl or acyl halide afforded 3-acyl-1-alkyl-2-alkylseleno-1-cyclobutene. The structure of the cyclobutene was elucidated by IR, MS, (1)H, (13)C, and (77)Se NMR, COSY, HMQC, and HMBC data and X-ray analysis.     

Enantio- and stereocontrolled formation of the bisspiroacetal core of spirolide B

The bisspiroacetal core of spirolide B, a marine natural toxin, was synthesized from triketone 10 via one-step bisspiroacetalization, methylation, and silylation accompanied by isomerization of the C-15 spirocenter. The equilibrium of two isomers under acidic conditions was also examined.     

Highly diastereoselective reductive coupling of 2-bromo-2,3,3,3-tetrafluoropropanamide with aldehydes promoted by triphenylphosphine-titanium(IV) isopropoxide. An efficient route to the synthesis of erythro-alpha-fluoro-alpha-(trifluoromethyl)-beta-hydroxy amides

The reductive coupling reaction of N-methoxy-N-methyl-2-bromo-2,3,3,3-tetrafluoropropanamide (Weinreb amide) with various aldehydes under the influence of the combined reagent, 1.2 equiv each of triphenylphosphine and titanium(IV) isopropoxide, took place smoothly at ambient temperature to give the corresponding alpha-fluoro-alpha-(trifluoromethyl)-beta-hydroxy amides in a highly erythro-selective manner. The high erythro selectivity was also obtained even by employing a combination of triphenylphosphine (1.2 equiv) and a catalytic amount of titanium(IV) isopropoxide.     

Magic number 7+/-2 in networks of threshold dynamics

Information processing by random feed-forward networks consisting of units with a sigmoidal input-output response is studied by focusing on the dependence of its outputs on the number of parallel paths M. It is found that the system leads to a combination of on-off outputs when M less or similar to 7, while for M greater or similar to 7, chaotic dynamics arises, resulting in a continuous distribution of outputs. This universality of the critical number M approximately 7 is explained by a combinatorial explosion, i.e., the dominance of factorial over exponential increase. The relevance of the result to biological problems is briefly discussed.     

Search for coherent charged pion production in neutrino-carbon interactions

We report the result from a search for charged-current coherent pion production induced by muon neutrinos with a mean energy of 1.3 GeV. The data are collected with a fully active scintillator detector in the K2K long-baseline neutrino oscillation experiment. No evidence for coherent pion production is observed, and an upper limit of is set on the cross section ratio of coherent pion production to the total charged-current interaction at 90% confidence level. This is the first experimental limit for coherent charged pion production in the energy region of a few GeV.     

Mössbauer study of mechanically alloyed powders

Using the⁵⁷Fe Mössbauer spectroscopy, the microscopic behavior of Fe powders has been investigated during and after the mechanical alloying (MA) process for Al?Fe and Ag?Fe systems. A repeated rolling method as well as a conventional ball-milling method are employed in order to understand the microscopic process of the kneading of Al and Fe powders during their MA and the resultant powders show quite similar Mössbauer spectra suggesting that the kneading by an impact between colliding balls is the same process as that of the thickness reduction by cold rolling. Mössbauer spectra show clearly the occurrence of the mutual atomic dispersion for the thermodynamically immiscible Ag?Fe system.     

Dimensional reduction in an oscillatory Kaluza-Klein cosmology

We study the dynamical evolution of a seven-dimensional, homogeneous, cosmological model. Anisotropy is prevailed all over the spatial dimensions with the topology S³ × S³, and leads to repetitious (nonchaotic) oscillations of the scale factors. The universe evolves from an initial Kasner phase to a final one, from which the dimensional reduction results. We pay attention to the effect of radiation-energy density and discuss the isotropization of ordinary dimensions through the stabilization of extra dimensions at the Kaluza-Klein radius.