Analysis of compatibility between interdependent matrices in ANP

Analytic network process (ANP) addresses multi-attribute decision-making where attributes exhibit dependencies. A principal characteristic of such problems is that pairwise comparisons are needed for attributes that have interdependencies. We propose that before such comparison matrices are used—in addition to a test that assesses the consistency of a pairwise comparison matrix—a test must also be conducted to assess ‘consistency’ across interdependent matrices. We call such a cross-matrix consistency test as a compatibility test. In this paper, we design a compatibility test for interdependent matrices between two clusters of attributes. We motivate our exposition by addressing compatibility in Sinarchy, a special form of ANP where interdependency exists between the last and next-to-last level. The developed compatibility test is applicable to any pair of interdependent matrices that are a part of an ANP.     

Lateral connections for asymptotic solutions around higher order turning points

Asymptotic expansions as ε → 0⁺ or x → ∞ for fundamental systems of solutions for ε²u″(x) − p(x) u(x) = 0 were obtained by Evgrafov and Fedoryuk on unbounded canonical domains with neighborhoods deleted around turning points. When p(x) is a polynomial, lateral connection formulas were found by Evgrafov and Fedoryuk, and Leung for two fundamental systems of solutions with known expansions in the interior of two different unbounded overlapping canonical regions with common first or second order turning point at their boundaries. In this paper, lateral connection formulas are found when the turning points are of any higher order. Recent result of uniform simplification by Sibuya around higher order turning point is used.     

Ein Satz über lokal normale Varietäten

Ohne Zusammenfassung     

Plasma confinement by a picket-fence

A current produced line cusp field is shown to confine both plasma and primary ionizing electrons.     

The -indices of Tsirelson type spaces

If and are countable ordinals such that , denote by the completion of with respect to the implicitly defined norm

where the supremum is taken over all finite subsets of such that and . It is shown that the Bourgain -index of is . In particular, if \alpha =\omega^{\alpha_{1}}\cdot m_{1}+\dots+\omega^{\alpha_{n}}\cdot m_{n}$"> in Cantor normal form and is not a limit ordinal, then there exists a Banach space whose -index is .

     

Time-resolved resonance Raman and density functional study of an azirine intermediate in the 2-fluorenylnitrene ring-expansion reaction to form a dehydroazepine product

We report time-resolved resonance Raman spectra for the azirine intermediate produced in the 2-fluorenylnitrene ring-expansion reaction to form a dehydroazepine product. The Raman bands obtained with a 252.7 nm probe wavelength and 500 ns delay time exhibit reasonable agreement with predicted vibrational frequencies from density functional calculations for two isomers of azirine intermediates that may be formed from a 2-fluorenylnitrene precursor. The Raman bands observed for delay times of 15 ns and 10 micros were consistent with predicted vibrational frequencies from density functional calculations for the 2-fluorenylnitrene and dehydroazepine product species as well as previously reported 416 nm time-resolved Raman spectra obtained on the ns and micros time scales. Our results demonstrate that the 2-fluorenylnitrene ring-expansion reaction to produce dehydroazepine products proceeds via relatively long-lived 2-fluorenylnitrene and azirine intermediates. Substitution of a phenyl ring para to the nitrene group of phenylnitrene appears to lead to significant changes in the ring-expansion reaction so that longer lived arylnitrene and azirine intermediates can be observed. This should enable the chemical reactivity of azirine intermediates formed from arylnitrenes to be examined more readily.     

A novel synthesis of metallogermacyclopropane and molybdenum bis(iminophosphorano)carbene complexes from bisgermavinylidene

The reaction of bisgermavinylidene [(Me3SiN=PPh2)2C=Ge-->Ge=C(PPh2=NSiMe3)2] (1) with M(CO)5(THF) ( M = Cr, W, Mo) afforded the metallagermacyclopropane [(Me-3SiN=PPh2)2CGeM(CO)3[M(CO)5]] [M = W (2), Cr (3), Mo (4)]; in one of the reactions, compound 4 reacts further to give a "pincer" carbene complex [(CO)3Mo[C(Ph2P=NSi Me3)2]] (5); the X-ray structures of compounds 2 and 5 have been determined.     

Diphenylamino group as an effective handle to conjugated donor-acceptor polymers through electropolymerization

[reaction: see text] The diphenylamino group is an effective handle for electropolymerization to give electron donor-acceptor conjugated polymers. In addition, interesting electrochromic and photoresponsive behavior of 13 has been investigated.     

Photon emission from rare gas ion bombardment of metal surfaces

Metal surfaces (Mg, Cu, Zr, Mo) are bombarded with He⁺, Ne⁺ and Ar⁺ in the energy range of 400 eV to 8 keV. Radiation from scattered projectiles and sputtered target particles is observed between 200 and 700 nm. It is shown that most of the radiating particles originate from surface collisions. Auger neutralization, resonance tunneling and direct electron transitions are the important electronic processes involved.