Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

Set-Valued and Variational Analysis - R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or...     

Corrigendum to “Liouvillian solutions of first order nonlinear differential equations” [J. Pure Appl. Algebra 221 (2) (2017) 411–421]

The purpose of this erratum is to provide a correct proof for the first part of Theorem 2.2 of the paper ([3]) referred to in the title.     

A generalization of sumset and its applications

Let A be a nonempty finite subset of an additive abelian group G and let r and h be positive integers. The generalized h-fold sumset of A, denoted by \(h^{(r)}A\), is the set of all sums of h elements of A, where each element appears in a sum at most r times. The direct problem for \(h^{(r)}A\) is to find a lower bound for \(|h^{(r)}A|\) in terms of |A|. The inverse problem for \(h^{(r)}A\) is to determine the structure of the finite set A for which \(|h^{(r)}A|\) is minimal with respect to some fixed value of |A|. If \(G = \mathbb {Z}\), the direct and inverse problems are well studied. In case of \(G = \mathbb {Z}/p\mathbb {Z}\), p a prime, the direct problem has been studied very recently by Monopoli (J. Number Theory, 157 (2015) 271–279). In this paper, we express the generalized sumset \(h^{(r)}A\) in terms of the regular and restricted sumsets. As an application of this result, we give a new proof of the theorem of Monopoli and as the second application, we present new proofs of direct and inverse theorems for the case \(G = \mathbb {Z}\).     

A convenient one-pot synthesis of 3,5-diarylisoxazoles via oxidative cyclisation using catalytic CuBr2 and oxone

A facile one-pot synthesis of 3,5-diarylisoxazoles from α,β-unsaturated ketones and hydroxylamine hydrochloride is reported. The reaction is efficiently promoted by catalytic CuBr₂ and Oxone to afford the desired products mostly in high yields and in relatively short time. The mild nature of the synthesis and short reaction time are notable advantages of the developed protocol. This protocol is effective toward various substrates having different functionalities.     

Nonlinear Optical Switching in Regioregular Porphyrin Covalent Organic Frameworks

Covalent organic frameworks (COFs) have garnered immense scientific interest among porous materials because of their structural tunability and diverse properties. However, the response of such materials toward laser‐induced nonlinear optical (NLO) applications is hardly understood and demands prompt attention. Three novel regioregular porphyrin (Por)‐based porous COFs—Por‐COF‐HH and its dual metalated congeners Por‐COF‐ZnCu and Por‐COF‐ZnNi—have been prepared and present excellent NLO properties. Notably, intensity‐dependent NLO switching behavior was observed for these Por‐COFs, which is highly desirable for optical switching and optical limiting devices. Moreover, the efficient π‐conjugation and charge‐transfer transition in ZnCu‐Por‐COF enabled a high nonlinear absorption coefficient (β=4470 cm/GW) and figure of merit (FOM=σ₁/σ_o, 3565) value compared to other state‐of‐the‐art materials, including molecular porphyrins (β≈100–400 cm/GW), metal–organic frameworks (MOFs; β≈0.3–0.5 cm/GW), and graphene (β=900 cm/GW).     

An Efficient Oxidative Difunctionalisation of 2-Amino-2H-chromene and Antimicrobial Activity of the Synthesized Tetrahydrochromene Derivatives

A novel series of 3-amino-2,2-dialcoxy-7,7-dimethyl-5-oxo-4-phenyl-3,4,5,6,7,8-hexahydro-2H-chromene-3-carbonitriles are synthesized by oxidative difunctionalization (geminal dialkoxylation and migration of the amino group) of 2-amino-4-aryl-7,7-dimethyyl-5-oxo-5,6,7,8-tetrahydro-4H-chromene-3-carbonitriles in the presence of iodobenzenediacetate in water medium with excellent yields. All the newly synthesized compounds are characterized by IR, ¹H and ¹³C NMR and Mass spectral data. The representative synthesized analogues are screened in vitro for antibacterial and antifungal activity using Gentamycin sulphate and Nystatin as standard drugs.

     

Methods and approaches for determination and enantioseparation of (RS)‐propranolol

Propranolol, a β‐adrenergic receptor antagonist, is a chiral compound that is marketed as a racemate, but only the (S)‐(?)‐enantiomer is responsible for the β‐adrenoceptor blocking activity. Different chromatographic methods have been applied for separation and determination of enantiomers of (RS)‐propranolol. In this article a review is presented on different liquid chromatographic methods used for enantioseparation of (RS)‐propranolol, using both HPLC and TLC. In addition, some aspects of enantioseparation under achiral phases of liquid chromatography have been briefly mentioned.     

Excited-State Dynamics of Thienoguanosine,an Isomorphic Highly Fluorescent Analogue of Guanosine

Thienoguanosine (^thG) is an isomorphic analogue of guanosine with promising potentialities as fluorescent DNA label. As a free probe in protic solvents, ^thG exists in two tautomeric forms, identified as the H1, being the only one observed in nonprotic solvents, and H3 keto–amino tautomers. We herein investigate the photophysics of ^thG in solvents of different polarity, from water to dioxane, by combining time-resolved fluorescence with PCM/TD-DFT and CASSCF calculations. Fluorescence lifetimes of 14.5–20.5 and 7–13 ns were observed for the H1 and H3 tautomers, respectively, in the tested solvents. In methanol and ethanol, an additional fluorescent decay lifetime (≈3 ns) at the blue emission side (λ≈430 nm) as well as a 0.5 ns component with negative amplitude at the red edge of the spectrum, typical of an excited-state reaction, were observed. Our computational analysis explains the solvent effects observed on the tautomeric equilibrium. The main radiative and nonradiative deactivation routes have been mapped by PCM/TD-DFT calculations in solution and CASSCF in the gas phase. The most easily accessible conical intersection, involving an out-of plane motion of the sulfur atom in the five-membered ring of ^thG, is separated by a sizeable energy barrier (≥0.4 eV) from the minimum of the spectroscopic state, which explains the large experimental fluorescence quantum yield.     

Resolution and isolation of enantiomers of (±)‐isoxsuprine using thin silica gel layers impregnated with l‐glutamic acid,comparison of separation of its diastereomers prepared with chiral derivatizing reagents having l‐amino acids as chiral auxiliaries

Thin silica gel layers impregnated with optically pure l ‐glutamic acid were used for direct resolution of enantiomers of (±)‐isoxsuprine in their native form. Three chiral derivatizing reagents, based on DFDNB moiety, were synthesized having l ‐alanine, l ‐valine and S‐benzyl‐l ‐cysteine as chiral auxiliaries. These were used to prepare diastereomers under microwave irradiation and conventional heating. The diastereomers were separated by reversed‐phase high‐performance liquid chromatography on a C₁₈ column with detection at 340 nm using gradient elution with mobile phase containing aqueous trifluoroacetic acid and acetonitrile in different compositions and by thin‐layer chromatography (TLC) on reversed phase (RP) C₁₈ plates. Diastereomers prepared with enantiomerically pure (+)‐isoxsuprine were used as standards for the determination of the elution order of diastereomers of (±)‐isoxsuprine. The elution order in the experimental study of RP‐TLC and RP‐HPLC supported the developed optimized structures of diastereomers based on density functional theory. The limit of detection was 0.1–0.09 µg/mL in TLC while it was in the range of 22–23 pg/mL in HPLC and 11–13 ng/mL in RP‐TLC for each enantiomer. The conditions of derivatization and chromatographic separation were optimized. The method was validated for accuracy, precision, limit of detection and limit of quantification. Copyright © 2014 John Wiley & Sons, Ltd.     

A novel approach for enantioseparation as applied to (RS)‐etodolac from pharmaceutical formulations: LC MS and density functional theory support for confirmation of diastereomers so separated

In the present studies formation of diastereomers of (RS)‐etodolac was confirmed using LC‐MS when [M + H]⁺ or [M]⁺ were recorded for the diastereomers. The lowest energy optimized structures of two diastereomers were drawn, which confirmed the three‐dimensional geometry of the diastereomers. This supports the optimized analytical separation conditions. In addition, separation of diastereomers was successful using a C₁₈ column and a binary mixture of methanol and triethyl ammonium phosphate buffer of pH 4.5 (80:20, v/v) as mobile phase at a flow rate of 1 mL min^?1 and UV detection at 223 nm. The separation method was validated as per International Conference on Harmonization guidelines. (RS)‐Etodolac was isolated from commercial tablets and purified and characterized to be used as racemic standard. Three pairs of diastereomers were synthesized using enantiomerically pure amines, namely, (R)‐(+)‐α‐methyl benzyl amine, (S)‐(?)‐α,4‐dimethylbenzylamine and (R)‐(?)‐1‐cyclohexylethylamine. Derivatization reactions were carried out under conditions of stirring at room temperature (30 °C for 2 h) as well as under microwave irradiation (MWI), and the two types of diastereomers were compared. Reaction conditions for derivatization were optimized with respect to mole ratio of chiral derivatizing agent and (RS)‐etodolac and MWI time. No racemization was observed throughout the study. Copyright © 2015 John Wiley & Sons, Ltd.