The Equilibrium Measure for a Nonlocal Dislocation Energy

In this paper we characterize the equilibrium measure for a nonlocal and anisotropic weighted energy describing the interaction of positive dislocations in the plane. We prove that the minimum value of the energy is attained by a measure supported on the vertical axis and distributed according to the semicircle law, a well-known measure that also arises as the minimizer of purely logarithmic interactions in one dimension. In this way we give a positive answer to the conjecture that positive dislocations tend to form vertical walls. This result is one of the few examples where the minimizer of a nonlocal energy is explicitly computed and the only one in the case of anisotropic kernels. © 2018 Wiley Periodicals, Inc.     

Elucidating heteroatom influence on homonuclear 4J(H,H) coupling constants by DFT/NMR approach

We report the structural dependency of long range scalar J-coupling constant across four bonds as function of the dihedral angles Φ1 and Φ3. The calculated homonuclear coupling constants ⁴J(_H,H), obtained at a density functional theory level, were measured between C(1)─X(2) and X(2)─C(3) bonds in three-term models, where C, N, O, and S were systematically used as the second atom of the alkyl structures ( 1 - 4 ). The ⁴J_(H,H) calculated values, tabulated for variation of 30° for both Φ1 and Φ3, have disclosed an unexpected detectable coupling constant (⁴J(_H,H) ≥ 1 Hz) across heteroatoms, useful to provide valuable structural information. A 2-methyl-1,3-dithiane sulfide ( 5 ) was used as a case study to prove the applicability and reliability of the calculated values to real issues. The ⁴J(_H,H) values obtained at density functional theory for the system 4 have reproduced with good accuracy an unexpected experimental ⁴J(_H2ax-H4ax) = 1.01 Hz of sulfide molecule ( 5 ), suggesting these calculated coupling constant values as a new powerful tool for the organic synthesis and stereochemical analysis.     

Derivation of a rod theory for multiphase materials

A rigorous derivation is given of a rod theory for a multiphase material, starting from three-dimensional nonlinear elasticity. The stored energy density is supposed to be nonnegative and to vanish exactly on a set consisting of two copies of the group of rotations SO(3). The two potential wells correspond to the two crystalline configurations preferred by the material. We find the optimal scaling of the energy in terms of the diameter of the rod and we identify the limit, as the diameter goes to zero, in the sense of Γ-convergence.     

Wave features for consistent-order-extended thermodynamics

Linear and nonlinear waves propagating in a heat conductive gas described by Consistent-Order-Extended Thermodynamics of third order are studied. Firstly, the propagation of plane harmonic waves are analyzed and the frequency dependence of the phase velocity and of the attenuation is shown. Furthermore, our results are compared with the ones obtained in the context of Extended Thermodynamics at thirteen moments and with the experimental data. Finally, the propagation of acceleration waves is studied. The amplitude equation of the fastest mode is derived and the critical time is evaluated.     

Tricyclic heterocyclic systems: Pyrazolo[5′,4′:4,5]-and pyrazolo-[3′,4′:4,5]pyrano[2,3-b]pyridine derivatives

By reacting 2-chloronicotinoyl chloride with acetyl or benzoyl acetate, ethyl 2-methyl- or 2-phenyl-4-oxopyrano[2,3-b]pyridine-3-carboxylates were prepared. The nucleophilic rearrangement of the latter with hydrazines gave rise to the title compounds.     

Directed frames

Predicate extensions of the intermediate logic of the weak excluded middle and of the modal logic S4.2 are introduced and investigated. In particular it is shown that some of them are characterized by subclasses of the class of directed frames with either constant or nested domains.This paper is dedicated to Professor Grigorij E. Mints who has incouraged us to persue this research     

Crystal and molecular structure of (+)-6,7∶8,9∶10,11-tri-O-isopropylidene-2,3-dideoxy-d-arabino-l-allo-undec-2-enono-1,4-lactone,C20H30O9

The crystal structure of the title lactone, C₂₀H₃₀O₉, a potential precursor of uncommon 11-carbon sugar derivatives, has been determined by single-crystal diffraction methods. The compound crystallizes in the orthorhombic space groupP2₁2₁2₁ witha=15.581(3),b=14.047(2),c=9.888(2) Å, andZ=4. The structure was solved by direct methods and refined by full-matrix least-squares toR=0.054. The absolute configuration of the seven stereogenic carbon atoms was deduced as 4R, 5R, 6R, 7R, 8S, 9R, 10R, being (R)-(+)-glyceraldehyde its progenitor. An intramolecular O-HO hydrogen bond is present. Weak interaction C-HO links the molecules in sheets parallel to the (100) plane.     

Crystal and molecular structure of (−)-1,2-O-isopropylidene-3-O-methyl-7,8-dideoxy-β-l-glycero-d-gluco-non-7-enofuranurono-9,6-lactone,C13H18O7

The crystal structure of the title lactone, C₁₃H₁₈O₇, has been determined by single crystal diffraction methods. The compound crystallizes in the monoclinic space groupP2₁ witha=13.231(2),b=10.248(2),c=5.348(1) Å,=96.66(2)°, andZ=2. A total of 1055 reflection intensities were recorded on a Siemens AED single-crystal diffractometer (CuK radiation) at room temperature. The structure was solved by direct methods and electron density calculations. Full-matrix least-squares refinement gaveR=0.055 for 946 unique reflections above 2(I). The absolute configuration of the six chiral carbon atoms was deduced as 4S, 5R, 6R, 7S, 9R, 10R (crystallographic numbering corresponds to C-6, 5, 4, 3, 2, 1 in the title compound). An intermolecular O-HO hydrogen bond joins the molecules in chains which run along the twofold screw axis.     

Unexpected one-step synthesis of 3-benzoyl-2-phenylbenzofurans under Wittig conditions

The reaction of 2-hydroxybenzyltriphenylphosphonium bromide with substituted benzoyl chlorides under Wittig conditions, led to 2-phenylbenzofuran derivatives 4a–p and the unexpected formation of 3-benzoyl-2-phenylbenzofuran derivatives 5a–p. Benzoyl chlorides possessing electron-withdrawing groups afforded 3-benzoyl-2-phenylbenzofuran derivatives in higher yields than those with electron-donating groups. This reaction represents a simple and regioselective, one-pot route towards the preparation of deactivated 3-benzoyl-2-phenylbenzofuran compounds which are difficult to obtain by the direct acylation of 2-phenylbenzofurans.     

Light Electrospun Polyvinylpyrrolidone Blanket for Low Frequencies Sound Absorption

Light polymeric soundproofing materials(density = 63 kg/m~3) of interest for the transportation industry were fabricated through electrospinning. Blankets of electrospun polyvinylpyrrolidone(average fiber diameter =(1.6 ± 0.5) or(2.8 ± 0.5) μm) were obtained by stacking disks of electrospun mats. The sound absorption coefficients were measured using the impedance tube instrument based on ASTM E1050 and ISO 10534-2. For a given set of disks(from a minimum of 6) the sound absorption coefficient changed with the frequency(in the range 200–1600 Hz) following a bell shape curve with a maximum(where the coefficient is greater than 0.9) that shifts to lower frequencies at higher piled disks number and greater fiber diameter. This work showed that electrospinning produced sound absorbers with reduced thickness(2–3 cm) and excellent sound-absorption properties in the low and medium frequency range.