Non-existence of extremals for the Adimurthi–Druet inequality

The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a $L^2$-type perturbation, quantified by $\alpha \in [0,{\lambda }_1)$, where ${\lambda }_1$ is the first Dirichlet eigenvalue of Δ on a smooth bounded domain. It is known [3], [10], [14], [19] that this inequality admits extremal functions, when the perturbation parameter α is small. By contrast, we prove here that the Adimurthi–Druet inequality does not admit any extremal, when the perturbation parameter α approaches ${\lambda }_1$. Our result is based on sharp expansions of the Dirichlet energy for blowing sequences of solutions of the corresponding Euler–Lagrange equation, which take into account the fact that the problem becomes singular as $\alpha \to {\lambda }_1$.     

Biobased vinyl levulinate as styrene replacement for unsaturated polyester resins

Vinyl levulinate (VL) is used as a biobased reactive diluent in styrene (St)‐free unsaturated polyester resins (UPR). The reactivity ratios for the radical copolymerization of VL with diethyl fumarate (DEF) are determined by the Jaacks method (r_VL = 0.01 and r_DEF = 0.81 at 60 °C in DMSO‐d₆). The properties of UPRs having a stoichiometric ratio between unsaturated groups from the UPR and either St or VL are compared. Defect‐free, slightly yellow, transparent, and rigid thermosets are obtained after a mild curing cycle. Due to unfavorable reactivity ratios about 5.5 wt % of unpolymerized VL remains inside the network and acts as plasticizer. Consequently, compared with St‐based ones, VL‐based UPRs exhibit lower α relaxation (T_α = 180 and 100 °C, respectively), lower elastic moduli at the rubbery plateau (G′ = 10⁸ and 10⁷ Pa) and lower mechanical properties as measured by three points bending tests. Strain at break (ε_f = 1.8 ± 0.2%) and Charpy impact strength (～2.7 ± 0.3 kJ m^?2) are comparable independently of the RD chemical nature. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3356–3364     

Azulenesulfonium Salts: Accessible,Stable, and Versatile Reagents for Cross‐Coupling

Azulenesulfonium salts may be readily prepared from the corresponding azulenes by an S_EAr reaction. These azulene sulfonium salts are bench‐stable species that may be employed as pseudohalides for cross‐coupling. Specifically, their application in Suzuki–Miyaura reactions has been demonstrated with a diverse selection of coupling partners. These azulenesulfonium salts possess significant advantages in comparison with the corresponding azulenyl halides, which are known to be unstable and difficult to prepare in pure form.     

New eco-friendly animal bone meal catalysts for preparation of chalcones and aza-michael adducts

ABSTRACT: Two efficient reactions were successfully carried out using Animal Bone Meal (ABM) and potassium fluoride or sodium nitrate doped ABMs as new heterogeneous catalysts under very mild conditions. After preparation and characterization of the catalysts, we first report their use in a simple and convenient synthesis of various chalcones by Claisen-Schmidt condensation and then in an aza-Michael addition involving several synthesized chalcones with aromatic amines. All the reactions were carried out at room temperature in methanol; the chalcone synthesis was also achieved in water environment under microwave irradiation. Doping ABM enhances the rate and yield at each reaction. Catalytic activities are discussed and the ability to re-use the ABM is demonstrated. RESULTS: For Claisen-Schmidt the use of ABM alone, yields never exceeded 17%. In each entry, KF/ABM and NaNO3/ABM (79-97%) gave higher yields than using ABM alone under thermic condition. Also the reaction proceeded under microwave irradiation in good yields (72-94% for KF/ABM and 81-97% for NaNO3/ABM) and high purity. For aza-Michael addition the use of ABM doped with KF or NaNO3 increased the catalytic activity remarkably. The very high yields could be noted (84-95% for KF/ABM and 81-94% for NaNO3/ABM). CONCLUSION: The present method is an efficient and selective procedure for the synthesis of chalcones anaaza-Michael adducts. The ABM and doped ABMs are a new, inexpensive and attractive solid supports which can contribute to the development of catalytic processes and reduced environmental problems.     

The assay of pterostilbene in spiked matrices by liquid chromatography tandem mass spectrometry and isotope dilution method

Pterostilbene (trans‐3,5‐dimethoxy‐4‐hydroxystilbene) is an active component found in several plant species, exhibiting important pharmacological properties. A new and reliable method of assaying this phyto compound in various matrices is presented; the assay is based on (1) the selectivity of liquid chromatography (LC) hyphenated with electrospray ionisation (ESI), (2) the specificity of a two‐step mass spectrometric analysis (MS/MS) and (3) the accuracy of the isotope dilution method. The labelled analogue may be conveniently synthesised in a few steps. The sensitivity of the method is confirmed by the very low limit of detection (LOD) and limit of quantitation (LOQ) values achieved in the assay of pterostilbene in two distinct fortified matrices, and is further supported by the observed accuracy values. Copyright © 2010 John Wiley & Sons, Ltd.     

On data-guided optimal control simulation of human motion

This work investigates the combination of optical motion capturing data with optimal control simulations of human motion, which can be important in a wide range of applications in the professional as well as the private sector, ranging from health and ergonomics over human-machine-interaction to sports and games [1–3]. There are methodically very different approaches to include optical measurement data in the simulation of human motion, see e.g. [4–6]. Two different approaches to combine data and simulation are investigated in this work. Either we use a soft constraints approach, where the difference of simulated and measured marker positions is part of the objective function (1), or we formulate an hard constraints approach with nonlinear constraints that set an upper bound on this difference (2), while the objective function is purely physiologically motivated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

BASE-CATALYZED HYDROGEN-DEUTERIUM EXCHANGE IN BENZO DERIVATIVES OF FIVE-MEMBERED AROMATIC HETEROCYCLES. PART VII. PRIMARY HYDROGEN ISOTOPE EFFECTS IN SOME 5- AND 6-SUBSTITUTED BENZOTHIAZOLES

Abstract

The rates of the base-catalyzed hydrogen-deuterium exchange at position 2, and the reverse, in some 5-and 6-substituted benzothiazoles are reported. The plots of log k _sH, and log k _sD against the [sgrave]_m + [sgrave]_p values of the substituents, according to the Hammett-Jaffé equations, are slightly curved. The primary hydrogen isotope effect k _sH/k _sD varies between 0.7 and 2.3 and the plot of log k _sH/k _sD against the [sgrave]_m + [sgrave]_p values of the substituents is a more pronounced curve, showing a maximum near to the [sgrave]_m + [sgrave]_p value of ?0.3. By these investigations the simple utilization of the primary hydrogen isotope effect in the prediction of reaction mechanisms seems extremely hazardous.     

Synthesis,Photophysics and Nonlinear Optical Properties of Stilbenoid Pyrimidine‐Based Dyes Bearing Methylenepyran Donor Groups

The nonlinear properties and the photophysical behavior of two π‐conjugated chromophores that incorporate an electron‐deficient pyrimidine core (A) and γ‐methylenepyrans as terminal donor (D) groups have been thoroughly investigated. Both dipolar and quadrupolar branching strategies are explored and rationalized on the basis of the Frenkel exciton model. Even though a cooperative effect is clearly observed if the dimensionality is increased, the nonlinear optical (NLO) response of this series is moderate if one considers the nature of the D/A couple and the size of the chromophores (as measured by the number of π electrons). This effect was attributed to a disruption in the electronic conjugation within the dyes’ scaffold for which the geometry deviates from planarity owing to a noticeable twisting of the pyranylidene end‐groups. This latter structural parameter also has a strong influence on the excited‐state dynamics, which leads to a very efficient fluorescence quenching.