Diethyl 2-[cyano(toluene-4-sulfinyl)methylene]propanedioate and its Diels–Alder adduct with cyclopentadiene

The thermal Diels–Alder cyclo­additon reaction of diethyl 2-­[cyano­(toluene-4-sulfinyl)­methyl­ene]­propane­dioate, C₁₆H₁₇­NO₅S, with cyclo­penta­diene gave the pure racemates of two of the four possible diastereomers, with a complete π-facial selectivity and a high (80:20) endo/exo-sulfinyl selectivity. X-ray diffraction studies of diethyl 2-[cyano­(toluene-4-sulfinyl)­methyl­ene]­propane­dioate and the major isomer of the cyclo­addition product, namely diethyl 3-cyano-3-(toluene-4-sulfinyl)­bi­cyclo­[2.2.1]­hepta-5-ene-2,2-di­carboxyl­ate, C₂₁H₂₃­NO₅S, reveal that the conformation of the substituents on the acrylo­nitrile moiety produces both steric and electronic effects, which affect the stereoselectivity of the reaction.     

Some classes of operators with symbol on the Lipschitz space of a tree

In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum.     

Optimal rates of linear convergence of the averaged alternating modified reflections method for two subspaces

Numerical Algorithms - The main difficulty for solving semi-infinite programming (SIP) problem is precisely that it has infinitely many constraints. By using a maximum function, the SIP problem can...     

Abelian varieties with finite abelian group action

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group. An early version of this article was inadvertently published before all the revisions had been completed and then retracted [https://doi.org/10.1007/s00013-018-1244-3]. This article is the final peer reviewed version.

     

Products of Jacobians as Prym-Tyurin varieties

Let X ₁, ..., X _m denote smooth projective curves of genus g _i ≥ 2 over an algebraically closed field of characteristic 0 and let n denote any integer at least equal to . We show that the product JX ₁ × ... × JX _m of the corresponding Jacobian varieties admits the structure of a Prym-Tyurin variety of exponent n ^m-1. This exponent is considerably smaller than the exponent of the structure of a Prym-Tyurin variety known to exist for an arbitrary principally polarized abelian variety. Moreover it is given by explicit correspondences.      

Strengthened splitting methods for computing resolvents

Computational Optimization and Applications - In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each...     

Quantum modified Regge–Teitelboim cosmology

In this paper we study the late evolution of Relic Gravitational Waves in coupled dark energy models, where dark energy interacts with cold dark matter. Relic Gravitational Waves are second tensorial order perturbations of the Lemaitre–Friedman–Robertson–Walker metric and experiment an evolution ruled by the scale factor of the metric. We find that the amplitude of Relic Gravitational Waves is smaller in coupled dark energy models than in models with non interacting dark energy. We also find that the amplitude of the waves predicted by the models with coupling term proportional to the dark energy density is smaller than those of the models with coupling term proportional to dark matter density.     

Role of gemini surfactants (m‐s‐m type; m = 16, s = 4–6) on the reaction of [Zn(II)‐Gly‐Phe]+ with ninhydrin

In the present paper, reaction of zinc‐glycylphenylalanine ([Zn(II)‐Gly‐Phe]⁺) with ninhydrin has been investigated in gemini (m‐s‐m type; m = 16, s = 4–6) surfactants at temperature (70 °C) and pH (5.0). Monitoring the appearance of product at 400 nm was used to follow the kinetics, spectrophotometrically. The order of the reaction with respect to [Zn(II)‐Gly‐Phe]⁺ was unity while with respect to [ninhydrin] was fractional. The reaction constants involved in the mechanism were obtained. In addition to the rate constant (k_Ψ) increase and leveling‐off regions are observed with the geminis, just like as seen with conventional surfactant hexadecyltrimethylammonium bromide (CTAB), the former produced a third region of increasing k_Ψ at higher concentrations. A close agreement between observed and calculated rate constants was found under varying experimental conditions. A suitable mechanism consistent with the experimental findings has been proposed. Copyright © 2014 John Wiley & Sons, Ltd.