On the Interpretation of Optimal Dual Solutions in Convex Programming

The relationships between multiple optimal dual solutions of a convex programming problem and the corresponding primal optimal value function are established by straightforward arguments on known results in duality theory. The subsequent discussion includes a demonstration that one-sided shadow prices can be found by solving a linear programming problem, conditions for the uniqueness and validity of the classical shadow price interpretation and a specialization of the results to the linear programming case.     

Diethyl-2,2′-bipyridyl-palladium(II), a case for the study of combination vs. disproportionation products.

Diethyl-2,2′-bipyridyl-palladium(II) is synthesized and its decomposition reactions in absence and presence of methyl acrylate are compared with those of the corresponding nickel and platinum complexes. Depending on the reaction conditions either CC-coupling or disproportionation can be induced.     

Selenium-77 NMR chemical shifts of five-membered selenium and sulphur heterocycles with CSe,CS,and CO groups

This paper reports the ⁷⁷Se NMR chemical shifts of 1,3-dithiole-, 1,3-thiaselenole- and 1,3-diselenole-2-ones, -thiones and -selones, of the corresponding saturated compounds 1,3-diselenolane-2-one, -thione and -selone, and the 1,3-thiaselenolium tetrafluoroborates, either unsubstituted or substituted by morpholino, ethylthio or ethylseleno groups in the 2-position. The ⁷⁷Se chemical shift values of the ring selenium and the C?Se groups are compared with the ¹³C chemical shift values of neighbouring carbon atoms. The relationships between the ⁷⁷Se chemical shifts of the C?Se groups and the wavelengths of their n→* absorption in the UV-visible spectrum are discussed with respect to the significance of the δE term in the contribution of the paramagnetic screening and the electron density distribution.     

Empirical additive parameter and automatic assignment of 13C NMR signals of some aryl and heteroaryl groups. A new criterion for a linear relationship between 13C chemical shifts and charge densities

The ¹³C NMR signals of some mono- and disubstituted aryl compounds were assigned by means of empirical additive substituent parameters and information taken from fully coupled spectra. This assignment was compared with that obtained with the help of the method of automatic assignment of the signals based on the linear relationship between ¹³C chemical shift and charge density. The results show that in the cases of XR substituents (X = O, NH and R = H, CH₃, CH₂CH₂OH) a good correlation is observed and the automatic assignment is correct. In contrast, in the cases of ? CH₂CH₂Y substituents (Y = OH, NH₂, Cl) a worsening of the correlation is observed and the automatic assignment is not correct. It is suggested that for compounds with a preliminarily known assignment, the automatic assignment can serve as an additional criterion for the reliability of the linear relationship between ¹³C chemical shift and charge density.     

Dynamics of current flow through the phase-boundary between a normal and a superconducting region

The time-dependent Bogoliubov Equations — which are derived in a slightly generalized form — are applied to the problem of quasiparticle reflection from the phaseboundary between a normal and a superconducting region. The momentum balance of current flow through the boundary is discussed. The supercurrent induced by a quasiparticle with excitation energy less than the maximum value of the pair-potential is calculated.     

Beitrag zur Theorie der Modulfunktionen 2. Grades. II

Ohne Zusammenfassung