Matrix infrared measurement of TiN

Gas-phase reaction of active nitrogen with TiCl₄ produces TiN, which has been stabilized in a Kr matrix at 10 K and measured by FTIR. The vibrational frequency of 1037 cm^?1 in the matrix confirms the newest gas-phase analysis giving 1039.6 cm^?1.     

First synthesis of chiral 3-vinylindoles as 4π-components for diels-alder reactions

The first syntheses of chiral 3- and 2-vinylindoles bearing sulfoxide or (-)-menthyloxy functional groups at the β-vinyl positions by way of procedures based on the Horner-Wadsworth-Emmons and Wittig reactions, respectively, are described. Some Diels-Alder reactions demonstrating the 4π-reactivity of these compounds are reported.     

Asymptotic expansions in the conditional central limit theorem

Let X_n, n , be i.i.d. with mean 0, variance 1, and E(¦X_n¦^r) < ∞ for some r 3. Assume that Cramér's condition is fulfilled. We prove that the conditional probabilities P(1/√n Σ_{i = 1}ⁿ X_i t¦B) can be approximated by a modified Edgeworth expansion up to order o(1/n^{(r − 2)/2)}), if the distances of the set B from the σ-fields σ(X₁, …, X_n) are of order O(1/n^{(r − 2)/2)}(lg n)^β), where β < −(r − 2)/2 for r and β < −r/2 for r . An example shows that if we replace β < −(r − 2)/2 by β = −(r − 2)/2 for r (β < −r/2 by β = −r/2 for r ) we can only obtain the approximation order O(1/n^{(r − 2)/2)}) for r (O(lg lgn/n^{(r − 2)/2)}) for r ).     

Reactions of 1,1-bis(dimethylamino)-1,3-butadiene with olefins – (4 + 2) cycloadditions and zwitterion formation

1,1-Bis(dimethylamino)-1,3-butadiene ( 1 ) as a strong donor diene (E_1/2 = 0.03 V vs. SCE, 1st IP_v = 6.94 eV) is treated with acrylonitrile, dimethyl dicyanofumarate, and tetracyanoethylene. Cycloaddition with acrylonitrile is slow and requires elevated temperatures at which elimination of dimethylamine with formation of 1-cyano-2-(dimethylamino)-1,3-cyclohexadiene occurs. The reaction of 1 with TCNE at −40°C in acetonitrile is very fast and leads to the zwitterion 5 . At T ⩾ −20°C, 5 eliminates hydrogen cyanide to give a highly colored (λ_max = 489 nm, lgϵ = 4.716) merocyanine. A zwitterion 9 generated from 1 and dimethyl dicyanofumarate can be isolated in crystalline form. The structural analysis shows that the zwitterions are produced by attack of the olefin at the antiperiplanar conformation of 1 . Both zwitterions which can be trapped as crystalline picrates cannot be converted to cycloadducts. These results suggest that cycloaddition is observed if zwitterion formation becomes energetically unfavorable.     

On projections and monotony in Lp -spaces

In this paper we investigate the connection between the range of nearest point projections in L_p -spaces and monotony properties of the projection operator. We show e.g. that a nearest point projection onto a closed convex subset of an L_p -space (1相似文献   

Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index

Composite indicators (CIs) are often used for benchmarking countries' performance, but they frequently stir controversies about the unavoidable subjectivity in their construction. Data Envelopment Analysis helps to overcome some key limitations, as it does not need any prior information on either the normalization of sub-indicators or on an agreed unique set of weights. Still, subjective decisions remain, and such modelling uncertainty propagates onto countries' CI scores and rankings. Uncertainty and sensitivity analysis are therefore needed to assess the robustness of the final outcome and to analyse how much each source of uncertainty contributes to the output variance. The current paper reports on these issues, using the Technology Achievement Index as an illustration.     

Compactness and domination

It is well known that each dominated family of probability measures is compact in the sense of Pitcher. In this paper the converse direction is investigated. It is shown that a family of probability measures on a-field is dominated if it is compact with respect to each sub- -field. If is only compact with respect to the basic-field settheoretical assumptions are needed to obtain domination.     

Optical model analysis of proton-carbon elastic scattering in the range 20 to 50 MeV

The differential cross-sections for the elastic scattering of protons from¹²C with incident energies ranging in approximately 2 MeV steps between 20 and 50 MeV, are analyzed using a standard optical model.     

Experimental and theoretical study of the elastic break-up of the alpha particle on58Ni nuclei atE α=172.5 MeV

The triton-proton angular correlation function has been measured for the⁵⁸Ni(α, t p)⁵⁸Ni reaction leading to the ground state of the target nucleus. The obtained experimental data have been interpreted in terms of the direct break-up (fragmentation) of the alpha particle on the target nucleus potential. It is shown that the main features of the measured double differential cross section are well predicted by the DWBA theory of the break-up. The dependence of the elastic and inclusive break-up cross sections upon the fragment-target interaction potentials is discussed.