Estimation of parameters in the discrete distributions of order k

This paper considers estimating parameters in the discrete distributions of order k such as the binomial, the geometric, the Poisson and the logarithmic series distributions of order k. It is discussed how to calculate maximum likelihood estimates of parameters of the distributions based on independent observations. Further, asymptotic properties of estimators by the method of moments are investigated. In some cases, it is found that the values of asymptotic efficiency of the moment estimators are surprisingly close to one.     

?rganometallischer Komplex mit Lewis-Base. 3. Mitt. Polymerisationsmechanismen von Vinylverbindungen durch Al-Alkyl-Lewis-Basen-Komplex

Ohne Zusammenfassung     

Effect of sonication on the photo-catalytic mineralization of some chlorinated organic compounds

Effects of the irradiation of ultrasound (US) on the photo-catalytic mineralization of some chlorinated organic compounds such as dichloroethane, tri- and tetrachloroethylenes, chloroacetic acids and chloromethanes were examined in oxygen saturated aqueous solutions suspended titanium dioxide (P25) particles. The yields of the sonochemical mineralization for these compounds were found to be extremely low compared to the photo-catalysis. However, the pre-sonication, US irradiation on the sample solution before the photo-irradiation, enhanced significantly the following photo-catalytic degradation to the complete oxidation. The effect was investigated in detail and it was found that the effect was mainly owing to the increase in the capability of the catalysis of which particles were sparsely dispersed by the sonication. The other contribution of the pre-sonication effect was found to be "pre-sonolysis", the initial formation of some intermediated products sonochemically, which are oxidizable more rapidly further to carbon dioxide than the original compound by the following photo-catalytic reactions. The pre-sonolysis effect was observed remarkably for trichloroacetic acid and tetrachloromethane, both of which are known to be hardly reactive to the photo-catalytic degradation. The photo-catalytic degradation with simultaneous sonication were also carried out for these compounds. The synergetic effect in the mineralization was observed both for carbontetrachloride and for trichloroacetic acid, the higher carbon dioxide yield being obtained in the simultaneous reaction than the sum of the yields in the photo-catalysis and the sonolysis each alone, while no significant synergetic effect was observed in the mineralization of other compounds.     

<Emphasis Type="Italic">In Situ</Emphasis> Synthesis of Field-responsive Nanocrystalline BaTiO<Subscript>3</Subscript> Particles Modified with Functional Organics

Nanocrystalline BaTiO₃ particles modified with polarizable ligands were synthesized through hydrolysis of modified metal–organics below 100°C. BaTiO₃ precursor was synthesized from barium metal, titanium isopropoxide and polarizable ligands in a mixture of ethanol and 2-ethoxyethanol. The modified Ba–Ti complex alkoxide was hydrolyzed yielding BaTiO₃ particles modified with organics. The crystallinty of nanometer-sized particles was dependent upon the hydrolysis conditions, and increased with increasing water amount and time. The nanocrystalline particles were identified to be BaTiO₃ by X-ray diffraction (XRD) and electron diffraction. A fluid consisting of modified BaTiO₃ particles and silicone oil revealed a typical electrorheological (ER) behavior on applying DC field. The ER behavior was found to depend upon the kind of ligand. 4-Fluorobenzyloxy modifier revealed the highest yield stress in the ER measurement among 4-substitued benzyloxy ligands examined.     

3 dB squeezing by single-pass parametric amplification in a periodically poled KTiOPO4 crystal

We present the experimental observation of pulsed squeezed light from a degenerate optical parametric amplifier pumped by a second harmonic of a continuous-wave mode-locked Nd:YVO4 laser. With a single pass through a 10 mm long periodically poled KTiOPO4 crystal, the classical parametric gain of 11 is observed. The measured noise reduction in the quiet quadrature is 3.2 dB below the shot-noise level.     

Copper-catalyzed direct sulfoximination of azoles and polyfluoroarenes under ambient conditions

The direct dehydrogenative C-N coupling of azoles or polyfluoroarenes with N-H sulfoximines proceeds effectively in the presence of a copper catalyst at room temperature under air to afford the corresponding N-arylsulfoximines in good to high yields.     

Palladium-catalyzed stereo- and regiospecific allylation of aryl halides with homoallyl alcohols via retro-allylation: selective generation and use of sigma-allylpalladium

Treatment of tertiary homoallyl alcohol with aryl halide under palladium catalysis resulted in the transfer of the allyl moiety of the homoallyl alcohol to aryl halide and yielded the corresponding cross-coupling product stereo- and regiospecifically. The transfer process includes retro-allylation, which proceeds via a conformationally regulated six-membered transition state. The retro-allylation can be regarded as a method for the stereo- and regiospecific preparation of sigma-allylpalladium.     

Rhodium-catalyzed allyl transfer from homoallyl alcohols to aldehydes via retro-allylation followed by isomerization into ketones

Retro-allylation of homoallyl alcohol by rhodium catalysis occurs to generate allylrhodium species. This allylrhodium reacts with aldehydes to give the corresponding secondary alcohols in situ. Isomerization of these alcohols proceeds in the same pots to furnish the corresponding saturated ketones in good yields. [reaction: see text]     

The Renner effect in triatomic molecules with application to CH+, MgNC and NH2

We have developed a computational procedure, based on the variational method, for the calculation of the rovibronic energies of a triatomic molecule in an electronic state that become degenerate at the linear nuclear configuration. In such an electronic state the coupling caused by the electronic orbital angular momentum is very significant and it is called the Renner effect. We include it, and the effect of spin-orbit coupling, in our program. We have developed the procedure to the point where spectral line intensities can be calculated so that absorption and emission spectra can be simulated. In order to gain insight into the nature of the eigenfunctions, we have introduced and calculated the overall bending probability density function f(p) of the states. By projecting the eigenfunctions onto the Born-Oppenheimer basis, we have determined the probability density functions f+(rho) and f-(rho) associated with the individual Born-Oppenheimer states phi(-)elec and phi(+)elec. At a given temperature the Boltzmann averaged value of the f(p) over all the eigenstates gives the bending probability distribution function F(rho), and this can be related to the result of a Coulomb Explosion Imaging (CEI) experiment. We review our work and apply it to the molecules CH2+, MgNC and NH2, all of which are of astrophysical interest.