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.     

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.

     

Is Bitcoin’s Carbon Footprint Persistent? Multifractal Evidence and Policy Implications

The Bitcoin mining process is energy intensive, which can hamper the much-desired ecological balance. Given that the persistence of high levels of energy consumption of Bitcoin could have permanent policy implications, we examine the presence of long memory in the daily data of the Bitcoin Energy Consumption Index (BECI) (BECI upper bound, BECI lower bound, and BECI average) covering the period 25 February 2017 to 25 January 2022. Employing fractionally integrated GARCH (FIGARCH) and multifractal detrended fluctuation analysis (MFDFA) models to estimate the order of fractional integrating parameter and compute the Hurst exponent, which measures long memory, this study shows that distant series observations are strongly autocorrelated and long memory exists in most cases, although mean-reversion is observed at the first difference of the data series. Such evidence for the profound presence of long memory suggests the suitability of applying permanent policies regarding the use of alternate energy for mining; otherwise, transitory policy would quickly become obsolete. We also suggest the replacement of ‘proof-of-work’ with ‘proof-of-space’ or ‘proof-of-stake’, although with a trade-off (possible security breach) to reduce the carbon footprint, the implementation of direct tax on mining volume, or the mandatory use of carbon credits to restrict the environmental damage.     

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...     

Surface Modification of Smectite Clay Induced by Non-thermal Gliding Arc Plasma at Atmospheric Pressure

Smectite clay from Sabga (west-Cameroon) was treated in aqueous suspension by gliding arc plasma to modify its surface properties. The evolution of the modifications was followed with the exposure time and post-discharge duration using Fourier transformed infra red spectroscopy and scanning electron microscopy. X-ray diffraction and nitrogen physisorption analyses were also performed to evaluate if both crystalline and textural properties of the material are affected by the treatment. The results obtained show that the plasma treatment causes the breakdown of structural bounds at the clay surface and induces the formation of new hydroxyl groups (Si–OH and Al–OH) on the clay edges. Crystallinity, sheet structure and textural properties are not significantly affected by the plasma treatment. However, it should be noted that an intensive treatment of the clay lowers the pH of the suspension, which subsequently induces an acid attack of the clay. In such case, the specific surface area of the clay increases. This study demonstrates that gliding arc plasma treatments can be used to activate clay minerals for environmental application.     

Acetylene Derivatives of Cationic Diazaoxatriangulenes and Diaza [4]Helicenes - Access to Red Emitters and Planar Chiral Stereochemical Traits

Cationic triangulenes, and related helicenes, constitute a rich class of dyes and fluorophores, usually absorbing and emitting light at low energy, in the orange to red domains. Recently, to broaden the scope of applications, regioselective late-stage functionalizations on these core moieties have been developed. For instance, with the introduction of electron-donating groups (EDGs), important bathochromic shifts are observed pushing absorptions towards or in the near-infrared (NIR) spectral domain while emissive properties disappear essentially completely. Herein, to upset this drawback, acetylene derivatives of cationic diazaoxa triangulenes (DAOTA) and [4]helicenes are prepared (16 examples). Contrary to other EDG-functionalized derivatives, C≡C− functionalized products remain broadly fluorescent, with red-shifted absorptions (Δλ_abs up to 25 nm) and emissions (Δλ_em up to 73 nm, Φ_PL up to 51 %). Quite interestingly, a general dynamic stereoisomerism phenomenon is evidenced for the compounds derived from achiral DAOTA cores. At low temperature in ¹H NMR spectroscopy (218 K), N−CH₂ protons become diastereotopic with chemical shifts differences (Δδ) as high as +1.64 ppm. The signal coalescence occurs around 273 K with a barrier of ∼12 kcal mol⁻¹. This phenomenon is due to planar chiral conformations (S_p and R_p configurations), induced by the geometry of the alkyl (n-propyl) side-chains next to the acetylenic substituents. Ion pairing studies with Δ-TRISPHAT anion not only confirm the occurrence of the chiral conformations but evidence a moderate but definite asymmetric induction from the chiral anion onto the cations. Finally, DFT calculations offer a valuable insight on the geometries, the corresponding stereodynamics and also on the very large difference in NMR for some of the diastereotopic protons.