Recurrence relations for orthogonal rational functions

It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arbitrary prescribed real or complex conjugate poles. The number of terms in the recursion relation is shown to be related to the structure of the orthogonal rational functions.     

1-Ethoxycarbonyl-3-ferrocenyl-propan-1,3-dion und Ferrocen-1,1'bis(2,4-dioxobutansäureethylester) als Liganden für Übergangsmetallionen. Kristallstruktur von Bis(1-ethoxycarbonyl-3-ferrocenyl-propan-1,3dionato)kupfer(II)

1-Ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and Ferrocene-1,1′bis(2,4-dioxobutanoic acid ethylester) as Ligands for Transition Metal Ions. Crystal Structure of Bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3dionato)copper(II) The ligands 1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and ferrocene-1,1′-bis(2,4-dioxo-butanoic acid ethylester) have been prepared by reaction of acetylferrocene or 1,1′-diacetylferrocene and diethyl oxalate. They yield neutral chelates with Cu^II, Ni^II, Zn^II, Co^II, and Mn^II. The acid dissociation constants of the ligands and the stability constants of their metal complexes including Fe^II complexes are reported. The structure of bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dionato)copper(II) was determined by X-ray structure analysis. A cis arrangement with a nearly square planar coordination sphere at the Cu atom is found.     

Ab initio studies of structural features not easily amenable to experiment: Part 20. Structural aspects of ethyl groups

The molecular structures of a number of stable conformations of ethanol, ethylamine, methylethyl ether, methylethylamine and of the ethyl anion have been determined by ab initio geometry optimizations using Pulay's Force method on the 4–21G level. The calculated geometries characterize the extent to which structural groups in a molecule are sensitive to asymmetries in their environment. Characteristic structural trends are consistently found for the CH bond distances and CCH angles in the C₂H₅ groups of trans-ethanol, trans-methylethyl ether and in the ethyl anion. They differ from those previously found for C₂H₅ groups in hydrocarbons. There is qualitative disagreement between the trends calculated for CH bond distances in trans-ethanol and trans-methylethyl ether and those found in the microwave substitution structures of these compounds. Since the substitution parameters are unresolved because of relatively large experimental or model uncertainties, it is presently impossible to decide whether this discrepancy is the result of computational or experimental deficiency. The methyl groups in methylethyl ether and methylethylamine exhibit the characteristic structural distortions which are usually found for CH₃ groups adjacent to electron lone pairs. The CC bond distances in C₂H₅ in the systems studied here are sensitive to the conformational arrangement of ethyl relative to the rest of a system in a way which can be rationalized by orbital interactions involving antibonding orbitals on sp³-hybridized carbon atoms. The calculated conformational stabilities agree qualitatively with experimental trends, except in the case of ethanol where the trans — gauche energy difference is small (about 0.1 kcal mol^?1) and within the uncertainties of the calculations. Our conformational energies for CH₃CH₂NH₂ are in disagreement with a previous ab initio investigation based on a comparison of unoptimized standard geometries. In general, the agreement between calculated structural parameters and corresponding reliable experimental values is very good in all comparable cases.     

In vivo study of the inflammatory modulating effects of low-level laser therapy on iNOS expression using bioluminescence imaging

This study was designed to demonstrate that bioluminescence imaging (BLI) can be used as a new tool to evaluate the effects of low-level laser therapy (LLLT) during in vivo inflammatory process. Here, the efficacy of LLLT in modulating inducible nitric oxide synthase (iNOS) expression using different therapeutic wavelengths was determined using transgenic animals with the luciferase gene under control of the iNOS gene expression. Thirty transgenic mice, FVB/N-Tg(iNOS-luc)Xen, were allocated randomly to one of four experimental groups treated with different wavelengths (lambda = 635, 785, 808 and 905 nm) or a control group (nontreated). Inflammation was induced by intra-articular injection of zymosan A in both knee joints. Laser treatment (25 mW cm(-2), 200 s, 5 J cm(-2)) was applied to the knees 15 min after inflammation induction. Measurements of iNOS expression were performed at various times (0, 3, 5, 7, 9 and 24 h) by measuring the bioluminescence signal using a highly sensitive charge-coupled device (CCD) camera. The results showed a significant increase in BLI signal after irradiation with 635 nm laser when compared to the nonirradiated animals and the other LLLT-treated groups, indicating wavelength dependence of LLLT effects on iNOS expression during the inflammatory process, and thus demonstrating an action spectrum of iNOS gene expression following LLLT in vivo that can be detected by BLI. Histological analysis was also performed and demonstrated the presence of fewer inflammatory cells in the synovial joints of mice irradiated with 635 nm compared with nonirradiated knee joints.     

Multinuclear NMR Studies of Ligand-Exchange Reactions on Analogous Technetium(V) and Rhenium(V) Complexes. Relevance to nuclear medicine

The kinetics of pyridine exchange on trans-[MO₂(py)₄]⁺ have been followed by ¹H-NMR in CD₃NO₂ for M = Re, Tc: k²⁹⁸S^?1 = (5.5 ± 0.1) × 10^?6, 0.04 ± 0.02; ΔH^≠/kJmol^?1 = 111 ± 3, 101 ± 9; ΔS^≠/JK^?1mol^?1 = +28 ± 10, +68 ± 35. For the Re^v complex, pyridine and oxygen exchanges have been measured simultaneously by ¹H- and ¹⁷O-NMR in deuterated water: k²⁹⁸/s^?1 = (8.6 ± 0.2) × 10^?6 (py), (14.5 ± 0.3) × 10^?6 (oxygen); ΔH^≠/kJmol^?1 = 111 ± 1, 91 ± 1; ΔS /JK^?1mol^?1 = +32 ± 3, ?32 ± 4. For both complexes, the rate law for pyridine exchange is first-order in complex and zero-order in pyridine; together with the activation parameter values, and the fact that the rate does not depend significantly on the nature of the solvent, this strongly implies the operation of a dissociative mechanism. The ratio of pyridine exchange rates for the Tc and Re complexes at room temperature is ca. 8000. The consequences of these observations for radiopharmaceutical synthesis are discussed.