Convergent synthesis of carbonic anhydrase inhibiting bi-heterocyclic benzamides: Structure–activity relationship and mechanistic explorations through enzyme inhibition,kinetics, and computational studies

By using a convergent methodology, a novel series of N-arylated 4-yl-benzamides containing a bi-heterocyclic thiazole–triazole core was synthesized, and the structures of these hybrid molecules, 9a–k , were corroborated through spectral analyses. The in vitro studies of these multifunctional molecules demonstrated their potent carbonic anhydrase inhibition relative to the standard used. The kinetics mechanism was exposed by Lineweaver–Burk plots, which revealed that 9j inhibited carbonic anhydrase non-competitively by forming an enzyme-inhibitor complex. The inhibition constants K_i calculated from Dixon plots for this compound was 1.2 μM. The computational study was also persuasive with the experimental results, and these molecules disclosed good results of all scoring functions and interactions, which suggested a good binding to carbonic anhydrase. So, it was predicted from the inferred results that these molecules might be considered as promising medicinal scaffolds for various diseases related to the uncontrolled production of this enzyme.     

A formula for the powers of fractional order operators

We derive none some explicit formula for the power of fractional order (differential and integral) operators.     

Harnack’s inequality for a class of non-divergent equations in the Heisenberg group

We prove an invariant Harnack’s inequality for operators in non-divergence form structured on Heisenberg vector fields when the coe?cient matrix is uniformly positive definite, continuous, and symplectic. The method consists in constructing appropriate barriers to obtain pointwise-to-measure estimates for supersolutions in small balls, and then invoking the axiomatic approach developed by Di Fazio, Gutiérrez, and Lanconelli to obtain Harnack’s inequality.     

Recurrence Tracking Microscope Based on Two Magnetic Mirrors

We introduce a recurrence tracing microscope based on the reflection of cold atoms from two magnetic mirrors placed in parallel. A cantilever is attached perpendicularly to one of the two mirrors at the lower end that probes surface structures. The quantum dynamics in the system provides the matter waves to store information on the height and spacing between the nanostructures. We use the recurrence tracking microscope in static and dynamic modes to study arbitrary and periodic nanostructures.     

Effect of the acyl group and the dodecylsulfonate chain on the inclusion of pyrene inside the cavity of β-cyclodextrin

The solubilization of pyrene in aqueous solution of β-cyclodextrin (β-CD) or its derivatives such as β-CD-hexanoyl, β-CD-benzoyl and β-CD-dodecylsulfonate was investigated by spectrophotometry. Linear and non-linear regression methods were used to estimate the association constants (K₁). A 1:1 stoichiometric ratio and different effects of the hexanoyl, benzoyl and dodecylsulfonate groups on the association constant were observed for the binary inclusion complex between pyrene and β-CD. The formation constant was shown to decrease when β-CD was modified by a dodecylsulfonate chain. The value of K₁ was 190 ± 10 L mol⁻¹ for the [pyrene/β-CD] complex and 145 L mol⁻¹ for the [pyrene/β-CD-dodecylsulfonate] complex. Partitioning of the pyrene molecules between the dodecylsulfonate chains and cyclodextrin cavities can explain the decrease in the association constant value. In the cases of β-CD-hexanoyl and β-CD-benzoyl derivatives, no association constants were detected. Results suggest that the high hydrophobicity of the hexanoyl and benzoyl groups prevents the inclusion of pyrene molecules inside the cyclodextrin cavity.     

Space-Time Dynamics of?Gazeau-Klauder Coherent States in?Power-Law Potentials

Gazeau-Klauder coherent states are developed for power-law potentials and their evolution in space and time is analyzed. We show that these states follow classical dynamics as long as the underlying energy spectrum is linear, otherwise they follow a classical-like evolution upto a few classical periods and disperse thereafter, despite its special construction. Auto-correlation function and probability density as a function of space and time explain the spatio-temporal behavior of these states.     

Tracing Bose�CEinstein condensate effects in a recurrence tracking microscope

The recurrence tracking microscope for probing nanostructures on a surface is based on the quantum recurrence phenomenon. We report that condensed atoms bouncing off on the atomic mirror, connected to a cantilever, modify the quantum recurrences. The times at which the recurrences occur depend on the initial energy of the bouncing condensates above the atomic mirror, which change with the density of condensed atoms.     

Dosage des traces de magnésium dans l'aluminium par le para-nitrobenzène-azo-α-naphtol (magneson II)

Zusammenfassung Es wird ein Verfahren zur Extraktion und nachfolgenden spektrophotometrischen Bestimmung von Magnesiumspuren in hochgradig gereinigtem Aluminium beschrieben. Die mit Magneson II (p-Nitrobenzol-azo--naphthol) entwickelte Blaufärbung gelangt hierfür zur Anwendung. Es konnten so noch 0,00015% Magnesium mit einem ungefähren relativen Fehler von 5% bestimmt werden.

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Summary The author gives a procedure for the extraction of traces of magnesium in extra pure aluminum. He then determined these traces by a spectrophotometric method in which he used the blue coloration given with magneson II. He thus measured 1,5 p. p. m. of magnesium with a probable error of the order of 5% (Magneson II = para-nitrobenzene-azo--naphthol).

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Résumé L'auteur donne un procédé d'extraction des traces de magnésium dans l'aluminium extra-pur, puis, il dose ces traces par voie spectrophotométrique, en se servant de la coloration bleue donnée avec le magnéson II; il mesure ainsi 1,5 p. p. m. de magnésium avec une erreur probable de l'ordre de 5%.

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Résumé d'une Thèse soutenue devant la Faculté des Sciences de Paris, le 22 juin 1950.

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Avec 2 figures.     

Dynamic quantum revivals in phase space

We explain quantum revivals and fractional revivals in phase space of the Fermi?CUlam accelerator. We derive analytic expressions of the Wigner distribution function for the driven system describing quantum interferences in position and momentum space. We assume that the fractional revival times are nonrecurrent under certain conditions and display randomness in the occurrence of the phenomenon at these times.