The maximum size of short character sums

The Ramanujan Journal - In the present note, we prove new lower bounds on large values of character sums $$\varDelta (x,q):=\max _{\chi \ne \chi _0} \big \vert \sum _{n\le x} \chi (n)\big \vert $$...     

An ab initio SCF-LCAO-MO study of the nitrogen inversion barriers in methylenimine,diimide and carbodiimide

The calculated values of the barriers to nitrogen inversion in methylenimine, diimide and carbodiimide are found to be respectively: 27.9, 50.1, and 8.4 kcal/mole.Theoretical Conformational Analysis. Part II. (Part I see Ref. [1]).Laboratoire associé au C.N.R.S.     

Adsorption and separation of amino acids from aqueous solutions on zeolites

The adsorption of various amino acids on zeolites with different structures was studied with regard to dependence of the pH value of the solution and the aluminum content of the zeolite in order to design tailor-made adsorbents for amino acid separations.     

Comparative study of the photochemistry of the azidopyridine 1-oxides

The photochemistry of azidopyridine 1-oxides was studied using an array of glass and matrix isolation techniques. As with room temperature, the photochemistry of 4-azidopyridine 1-oxide is dominated by triplet nitrene chemistry. However, in the case of the 3-azide, matrix photolysis indicates the formation of diazabicyclo[4.1.0]hepta-2,4,6-triene N-oxide and diazacycloheptatetraene N-oxide intermediates as well as triplet nitrene.     

Reactivity and structure of the 5-dehydro-m-xylylene anion

The electronic structure of dehydro-m-xylylene anion (DMX-) has been investigated by using chemical reactivity studies and electronic structure calculations. DMX- has been generated in the gas phase via the sequential reaction of trimethyl-3,5-bis(trimethylsilylmethyl)phenylsilane with F- and two molecules of F2. Reactivity and thermochemical properties of the ion indicate a phenyl-like anion (1a), consistent with theoretical predictions. Density functional calculations predict a nonplanar triplet anion, with an allenic singlet anion slightly higher in energy. The driving force for the out-of-plane distortion is more efficient charge delocalization that is achieved at lower symmetry.     

Analyse conformationnelle théorique

Résumé Une étude théorique ab initio SCF-LCAO-MO de la méthylène imine et de l'anion vinyle a été effectuée. Les barrières d'énergie calculées pour l'inversion de l'azote et pour la rotation autour de la liaison C=N sont respectivement de 26–28 kcal/mole et de 57 kcal/mole.La barrière d'inversion du carbanion calculée pour l'anion vinyle est de 39 kcal/mole et l'isomérisation des imines se fait donc par inversion de l'azote. Les anions vinyliques ont une configuration stable.L'origine physique de ces barrières d'inversion est étudiée et caractérisée par les variations des termes énergétiques, de la composition de l'OM du doublet libre et des populations électroniques.La comparaison des processus d'inversion du carbanion, de l'azote et de l'oxonium dans la série CH₂=CH, CH₂=NH et CH₂=OH a permis de mettre en évidence l'évolution des termes énergétiques, de la hauteur de la barrière et des transferts de population.

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Theoretical conformational analysisIV. An ab initio SCF-LCAO-MO study of methylenimine and of vinyl anion

An ab initio SCF-LCAO-MO study of methylenimine and vinyl anion has been performed. The calculated barriers to nitrogen inversion and to rotation about the C=N bond are equal to 26–28 kcal/mole and 57 kcal/mole respectively.The calculated barrier to carbanion inversion in the vinyl anion amounts to 39 kcal/mole. Thus isomerization of imines occurs by a nitrogen inversion process and vinyl anions are configurationally stable.The physical origin of these inversion barriers is studied and characterized by the changes in the energy terms, in lone pair MO composition, and in electron populations.Comparison of the carbanion, nitrogen and oxonium inversion processes in the isoelectronic series CH₂=CH, CH₂=NH and CH₂=OH permits to delineate general trends in the energy terms, barrier height and population transfers.

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Zusammenfassung Für Methylenimin und das Vinylanion wird eine ab initio SCF-LCAO-MO-Studie durchgeführt. Die berechneten Barrieren für die Stíckstoffinversion und die Rotation um die C=N-Bindung betragen 26–28 kcal/Mol bzw. 57 kcal/Mol.Die berechnete Barriere für die Inversion des Carbanions im Vinylanion beträgt 39 kcal/Mol. Daher wird die Isomerisation von Iminen durch einen Stickstoffinversionsprozeß hervorgerufen, und die Konfigurationen von Vinyl-Anionen sind stabil.Der physikalische Ursprung dieser Inversionsbarrieren wird studiert und durch Änderungen in den Energietermen, in der Zusammensetzung von Ione pair-MO's und in den Besetzungszahlen der Elektronen charakterisiert.Ein Vergleich der Inversionsprozesse des Carbanions, des Stickstoffs und des Oxonium-Ions in der isoelektronischen Reihe CH₂=CH^–, CH₂=NH and CH₂=OH⁺ ermöglicht es, allgemeine Züge in den Energietermen, in den Höhen der Barrieren und den Besetzungsübergängen abzuleiten.

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Précédent article de cette série: cf. Réf. [1].

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Laboratoire associé au C.N.R.S.     

Scarlet Flax Linum grandiflorum (L.) In Vitro Cultures as a New Source of Antioxidant and Anti-Inflammatory Lignans

In vitro cultures of scarlet flax (Linum grandiflorum L.), an important ornamental flax, have been established as a new possible valuable resource of lignans and neolignans for antioxidant and anti-inflammatory applications. The callogenic potential at different concentrations of α-naphthalene acetic acid (NAA) and thidiazuron (TDZ), alone or in combinations, was evaluated using both L. grandiflorum hypocotyl and cotyledon explants. A higher callus induction frequency was observed on NAA than TDZ, especially for hypocotyl explants, with a maximum frequency (i.e., 95.2%) on 1.0 mg/L of NAA. The presence of NAA (1.0 mg/L) in conjunction with TDZ tended to increase the frequency of callogenesis relative to TDZ alone, but never reached the values observed with NAA alone, thereby indicating the lack of synergy between these two plant growth regulators (PGRs). Similarly, in terms of biomass, NAA was more effective than TDZ, with a maximum accumulation of biomass registered for medium supplemented with 1.0 mg/L of NAA using hypocotyls as initial explants (DW: 13.1 g). However, for biomass, a synergy between the two PGRs was observed, particularly for cotyledon-derived explants and for the lowest concentrations of TDZ. The influence of these two PGRs on callogenesis and biomass is discussed. The HPLC analysis confirmed the presence of lignans (secoisolariciresinol (SECO) and lariciresinol (LARI) and neolignan (dehydrodiconiferyl alcohol [DCA]) naturally accumulated in their glycoside forms. Furthermore, the antioxidant activities performed for both hypocotyl- and cotyledon-derived cultures were also found maximal (DPPH: 89.5%, FRAP 866: µM TEAC, ABTS: 456 µM TEAC) in hypocotyl-derived callus cultures as compared with callus obtained from cotyledon explants. Moreover, the anti-inflammatory activities revealed high inhibition (COX-1: 47.4% and COX-2: 51.1%) for extract of hypocotyl-derived callus cultures at 2.5 mg/L TDZ. The anti-inflammatory action against COX-1 and COX-2 was supported by the IC₅₀ values. This report provides a viable approach for enhanced biomass accumulation and efficient production of (neo)lignans in L. grandiflorum callus cultures.     

Polynomial products modulo primes and applications

Monatshefte für Mathematik - For any polynomial $$P(x)\in {\mathbb {Z}}[x],$$ we study arithmetic dynamical systems generated by $$\displaystyle {F_P(n)=\mathop {\prod \nolimits _{k\le...     

Character sums over squarefree and squarefull numbers

We give upper bounds for character sums over squarefree and squarefull numbers sharper than the prior known in the literature. As an application, we study the distribution of squarefull numbers in arithmetic progressions and sharpen (without restriction on the modulus) the recent results obtained by Liu and Zhang.     

Linearly polarized, single-mode spontaneous emission in a photonic nanowire

We introduce dielectric elliptical photonic nanowires to funnel efficiently the spontaneous emission of an embedded emitter into a single optical mode. Inside a wire with a moderate lateral aspect ratio, the electromagnetic environment is largely dominated by a single guided mode, with a linear polarization oriented along the ellipse major axis. The resulting monomode spontaneous emission is maintained over a broad wavelength range, a key asset of this 1D photonic structure. Our theoretical analysis is completed by an experimental study of GaAs elliptical photonic wires with embedded InAs quantum dots. In particular, the fraction of collected photons with the desired linear polarization can exceed 95%.