Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: critical analysis of various approaches and application to a Gd(III)-based contrast agent

The time correlation functions (TCFs) G(alphaalpha(t)[triple bond](Salpha(t)Salpha(0)) (alpha = x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron. These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution. When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs. We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results. We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times. This method is applied for various values of the magnetic field taken to be along the z direction. At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF GII(t) [triple bond] G(zz)(t) has a monoexponential decay with an electronic relaxation time T1e different from 1/(2D(r)), D(r) being the rotational diffusion coefficient of the complex. At intermediate and high field, the simulation results show that GII (t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail. These results are illustrated for spins S = 1, 3/2, and 5/2 in axial and rhombic symmetries. Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760-Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging.     

Dialkyl formyl-1 methylphosphonates α-fonctionnels—II : Preparation par voie thermique et transformation en heterocycles α-phosphoniques

The thermal condensation of functional phosphonates bearing strongly withdrawing groups (RO)₂P(O)CH₂Z1 with dimethylformamide dimethyl acetal gives corresponding β-functional, β-phosphonic enamines (RO)₂P(O)C(Z)=CHNMe₂2. Acid or basic hydrolysis of the enamines frequently gives the free aldehyde (RO)₂P(O)CH(Z)—CHO 3. We show that the enamines can be used with success for the synthesis of heterocycles like, pyrazoles 4, pyrimidines 5, benzodiazepine 6 or indole 7, all of them substituted with a phosphonate group.     

Ab initio calculations of all-trans octatetraene and eight isoelectronic conjugated chains: Semiempirical heats of formation and stabilization energies

In the framework of our study of the changes of the electric polarizability upon substituting heteroatomic linkages in conjugated hydrocarbon backbones, we have been led to examine the relative stability of eight compounds isoelectronic to the all-trans octatetraene using the Cox and Pilcher concept of stabilization energy (SE ), SE = ΔH_a – ΣN_ABE_AB, where ΔH_a is the heat of atomization of the species under consideration and the E_AB's are bond-energy terms. Full geometry optimizations at the 4-31G level have been performed to obtain the equilibrium geometries needed to deduce reliable semiempirical heats of formation from appropriate isodesmic processes. Some of the compounds containing the ? CH?N? and ? N?N ? groups have electric polarizabilities and stabilization energies comparable to octatetrene.     

Gas-liquid chromatographic method for the measurement of plasma levels of d-7,8-dimethoxy-3-methyl-phenyl-2,3,4,5-tetrahydro-1h-3-benzazepine acid maleate (SCH-12679) and its major metabolites in aggressive mental retardites

A sensitive gas-liquid chromatographic technique for the quantitative analysis of SCH-12679 (d-7,8-dimethoxy-3-methyl-phenyl-2,3,4,5-tetrahydro-1H-3-benzazepine acid maleate) and its major metabolites in plasma of aggressive mental retardates receiving therapeutic doses of the medicament has been developed. The lower limits of detection are 20 ng/ml for SCH-12679, 0.5 ng/ml for 3-desmethyl SCH-12679 and 0.4 ng/ml for 7-desmethyl plus 8-desmethyl SCH-12679. SCH-12679 is estimated with a flame ionization detector. Its metabolites are quantitated using an electron-capture detector after conversion of the compounds to their heptafluorobutyryl derivatives by reaction with the appropriate anhydride. Data on plasma levels of unchanged SCH-12679, 3-desmethyl SCH-12679 and a combination of 7-desmethyl and 8-desmethyl SCH-12679 in fifteen patients treated with the medicament are presented.     

Synthesis of substituted 4H-thieno[2,3-b][1]benzothiopyran-4-ones as possible schistosomicidal agents

Summary A new series of thiophenic isosters of thioxanthones, namely: 2-substituted-4H-thieno[2,3-b][1]benzothiopyran-4-ones and 5-substituted-2-nitro-8-methyl-4H-thieno[2,3-b][1]benzothiopyran-4-ones were synthesized as potential schistosomicidal agents. The synthesized compounds were characterized by their¹H-NMR data.

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Synthese von substituierten 4H-Thieno[2,3-b][1]benzothiopyran-4-onen als mögliche schistosomicide Wirkstoffe

Zusammenfassung Es wurde eine neue Serie von thiophenischen Isosteren des Thioxanthons, nämlich 2-substituierte 4H-Thieno[2,3-b][1]benzothiopyran-4-one und 5-substituierte 2-Nitro-8-methyl-4H-thieno[2,3-b][1]benzothiopyran-4-one als potentielle schistosomicide Wirkstoffe synthetisiert. Die synthetisierten Verbindungen wurden mittels ihrer¹H-NMR Daten charakterisiert.

     

Hydroxyalkylation of α-Phosphonylated α-Silylated Allylic Carbanions. An Unexpected Cyclization Reaction

Abstract

When reacted with aldehydes, in situ generated title carbanions 2 can give phosphonodienes (4 or 6), phosphonolactones (5 or 8) or phosphonoalcohols 7, depending on structure of reagents and on reaction conditions.     

Motion analysis of two-link nonholonomic swimmers

Nonlinear Dynamics - This paper presents a tool for analyzing the motion of two-link nonholonomic swimmers. We refer to these systems as Land-sharks, which are a generalization of the well known...     

A new methodology for studying the equity premium

This paper provides a new framework for the derivation and estimation of consumption and equity premium functions. Applying duality in a dynamic context, we show that equity premium and consumption functions can be easily obtained from the indirect utility function. Our new framework, therefore, does not require explicit specification of underlying consumer preferences. Using aggregate US data (1929–2000) we estimate the consumption and equity premium functions using a nonparametric technique. We find that the model does well in explaining the observed smooth consumption patterns and does reasonably well in explaining the high mean and volatility of equity premia.