Regularity of Weak Solutions and Their Attractors for a Parabolic Feedback Control Problem

We investigate additional regularity properties of all globally defined weak solutions, their global and trajectory attractors for a class of autonomous differential inclusion with upper semi-continuous interaction function, when initial data $u_{\tau}\in L^2(\Omega)$ . The main contributions of this paper are: (i) additional regularity and new topological properties of all weak solutions of parabolic feedback control problem with upper semi-continuous interaction function, (ii) a sufficient condition for regularity of global and trajectory attractors, and (iii) new a priory estimates for all weak solutions.     

Chemical dynamics of the CH(X2Π) + C2H4(X1A1g), CH(X2Π) + C2D4(X1A1g), and CD(X2Π) + C2H4(X1A1g) reactions studied under single collision conditions

The crossed beam reactions of the methylidyne radical with ethylene (CH(X(2)Π) + C(2)H(4)(X(1)A(1g))), methylidyne with D4-ethylene (CH(X(2)Π) + C(2)D(4)(X(1)A(1g))), and D1-methylidyne with ethylene (CD(X(2)Π) + C(2)H(4)(X(1)A(1g))) were conducted at nominal collision energies of 17-18 kJ mol(-1) to untangle the chemical dynamics involved in the formation of distinct C(3)H(4) isomers methylacetylene (CH(3)CCH), allene (H(2)CCCH(2)), and cyclopropene (c-C(3)H(4)) via C(3)H(5) intermediates. By tracing the atomic hydrogen and deuterium loss pathways, our experimental data suggest indirect scattering dynamics and an initial addition of the (D1)-methylidyne radical to the carbon-carbon double bond of the (D4)-ethylene reactant forming a cyclopropyl radical intermediate (c-C(3)H(5)/c-C(3)D(4)H/c-C(3)H(4)D). The latter was found to ring-open to the allyl radical (H(2)CCHCH(2)/D(2)CCHCD(2)/H(2)CCDCH(2)). This intermediate was found to be long lived with life times of at least five times its rotational period and decomposed via atomic hydrogen/deuterium loss from the central carbon atom (C2) to form allene via a rather loose exit transition state in an overall strongly exoergic reaction. Based on the experiments with partially deuterated reactants, no compelling evidence could be provided to support the formation of the cyclopropene and methylacetylene isomers under single collision conditions. Likewise, hydrogen/deuterium shifts in the allyl radical intermediates or an initial insertion of the (D1)-methylidyne radical into the carbon-hydrogen/deuterium bond of the (D4)-ethylene reactant were found to be-if at all-of minor importance. Our experiments propose that in hydrocarbon-rich atmospheres of planets and their moons such as Saturn's satellite Titan, the reaction of methylidyne radicals should lead predominantly to the hitherto elusive allene molecule in these reducing environments.     

Tomographic probability and entropic inequalities for special functions

We discussed some aspects of the tomographic-probability representation of quantum mechanics. Using known generic inequalities for Shannon and relative entropies, we obtain some new inequalities for special functions such as Laguerre, Legendre, and two-variable Hermite polynomials.     

Nickel-Catalyzed Chain-Walking Cross-Electrophile Coupling of Alkyl and Aryl Halides and Olefin Hydroarylation Enabled by Electrochemical Reduction

The first electrochemical approach for nickel-catalyzed cross-electrophile coupling was developed. This method provides a novel route to 1,1-diarylalkane derivatives from simple and readily available alkyl and aryl halides in good yields and excellent regioselectivity under mild conditions. The procedure shows good tolerance for a broad variety of functional groups and both primary and secondary alkyl halides can be used. Furthermore, the reaction was successfully scaled up to the multigram scale, thus indicating potential for industrial application. Mechanistic investigation suggested the formation of a nickel hydride in the electroreductive chain-walking arylation, which led to the development of a new nickel-catalyzed hydroarylation of styrenes to provide a series of 1,1-diaryl alkanes in good yields under mild reaction conditions.     

Direct Trifluoromethylthiolation of Alcohols under Mild Reaction Conditions: Conversion of ROH into RSCF3

A direct process for the trifluoromethylthiolation of allylic and benzylic alcohols under mild conditions has been developed. A wide range of free alcohols underwent nucleophilic substitution in the presence of stable CuSCF₃ and BF₃ ? Et₂O to give the corresponding products in good to excellent yields.     

Direct Catalytic Trifluoromethylthiolation of Boronic Acids and Alkynes Employing Electrophilic Shelf‐Stable N‐(trifluoromethylthio)phthalimide

A new and safe method for the synthesis of N‐(trifluoromethylthio)phthalimide, a convenient and shelf‐stable reagent for the direct trifluoromethylthiolation, has been developed. N‐(Trifluoromethylthio)phthalimide can be used as an electrophilic source of F₃CS⁺ and reacts readily with boronic acids and alkynes under copper catalysis. The utility of CF₃S‐containing molecules as biologically active agents, the mild reaction conditions employed, and the high tolerance of functional groups demonstrate the potential of this new methodology to be widely applied in organic synthesis as well as industrial pharmaceutical and agrochemical research and development.     

A Facile Synthesis of Functionalized 1,2,6,7-Tetrahydroimidazo[1,5-c]pyrimidine-3,5-diones

A Pd-mediated hydrogenation of ethyl 6-azidomethyl-1,2,3,4-tetrahydro-4-R-2-oxo-5-pyrimidinecarboxylates leads to the corresponding ethyl 6-aminomethyl1,2,3,4-tetrahydro-4-R-2-oxo-5-pyrimidinecarboxylates. The latter react with bis(trichloromethyl)carbonate, yielding the title ethyl 1,2,3,5,6,7-hexahydro-7-R-3,5-dioxoimidazo[1,5-c]pyrimidine-8-carboxylates.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

β-Chlorocinnamonitriles in a New Synthesis of 3-Functionally Substituted 6-amino-1,2-Dihydropyridin-2-ones

β-Chlorocinnamonitriles react with methylene-active compounds containing N-substituted carboxamide group in DMSO solution in the presence of potassium hydroxide, forming 3-functionally substituted 1,2-dihydropyridin-2-ones.     

On p-norm linear discrimination

We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an “economical” representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted.     

Luminescence properties of pHEMA-TiO2 gels based hybrids materials

Photoluminescence (PL) of photochromic pHEMA-TiO₂ gels-based hybrids was studied by means of time- and energy-resolved spectroscopy at temperatures between 300 K and 10 K. The PL band at 485 nm is assigned to S0←T1 transition of methoxyphenol (organic molecule added to the commercial monomer hydroxyethyl methacrylate, HEMA and used as an inhibitor of spontaneous polymerisation) in the polymer environment, while the PL band at 600 nm is assigned to the self-trapped exciton onto octahedral TiO₆ site of the inorganic component. The mechanisms of the excited states population are discussed. In particular it is shown that both singlet-triplet energy transfer in methoxyphenol and methoxyphenol–TiO₂ charge transfer are strongly affected by the material composition and temperature. The hypothesis about the photoexcited holes annihilation with the trapped electrons is confirmed to be one of main mechanisms limiting the Ti³⁺ centres concentration.