Generalized Variational-Like Inequalities with Nonmonotone Set-Valued Mappings

In this paper, we introduce a new class of generalized variational-like inequalities involving a nonmonotone-type set-valued mapping which is more general than those in the known literature. By applying a KKM-type theorem established by the author, some existence theorems for the solutions to the class of generalized variational-like inequalities are proved in Hausdorff locally convex topological vector spaces.     

SU(3)下的美介子半轻子衰变

强相互作用中近似成立的SU(3)对称性被用来分析美介子半轻子三体和四体衰变,获得了衰变宽度之间的一些SU(3)联系.这些联系可以为了解美介子半轻子衰变中产生的各种动力学效应的性质提供一些信息.     

Remarks on the Balance Relations for the Two-Dimensional Navier–Stokes Equation with Random Forcing

We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ξ(t,x) of a stationary solution has a finite exponential moment, and that for any the expectation of the integral of over the level-set , up to a constant factor equals the expectation of the integral of over the same set.     

Dimer Coverings on the Sierpinski Gasket

We present the number of dimer coverings N _d (n) on the Sierpinski gasket SG _d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N _d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as , is calculated to be ln (2)/3 exactly for SG ₂. The numbers of dimers on the generalized Sierpinski gasket SG _d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln (6)/7, ln (28)/12, ln (200)/18, respectively. The number of dimer coverings for SG ₃ is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG _d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of with d=3,4,5 can be evaluated with more than a hundred significant figures accurate. This paper is written during the Lung-Chi Chen visit to PIMS, University of British Columbia. The author thanks the institute for the hospitality.     

Thermal properties and structure of electrospun blends of PVDF with a fluorinated copolymer

We report the structure and thermal properties of blends comprising poly(vinylidene fluoride) (PVDF) and a random fluorinated copolymer (FCP) of poly(methyl methacrylate)‐random‐1H,1H,2H,2H‐perfluorodecyl methacrylate, promising membrane materials for oil–water separation. The roles of processing method and copolymer content on structure and properties were studied for fibrous membranes and films with varying compositions. Bead‐free, nonwoven fibrous membranes were obtained by electrospinning. Fiber diameters ranged from 0.4 to 1.9 μm, and thinner fibers were obtained for PVDF content >80%. As copolymer content increased, degree of crystallinity and onset of degradation for each blend decreased. Processing conditions have a greater impact on the crystallographic phase of PVDF than copolymer content. Fibers have polar beta phase; solution‐cast films contain gamma and beta phase; and melt crystallized films form alpha phase. Kwei's model was used to model the glass transition temperatures of the blends. Addition of FCP increases hydrophobicity of the electrospun membranes. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 312–322     

Compressing a Non-Planar Aromatic Heterocyclic [7]Helicene to a Planar Hetero[8]Circulene

This work describes a synthetic approach where a non-planar aromatic heterocyclic [7]helicene is compressed to yield a hetero[8]circulene containing an inner antiaromatic cyclooctatetraene (COT) core. This [8]circulene consists of four benzene rings and four heterocyclic rings, and it is the first heterocyclic [8]circulene containing three different heteroatoms. The synthetic pathway proceeds via a the flattened dehydro-hetero[7]helicene, which is partially a helicene and partially a circulene: it is non-planar and helically chiral as helicenes, and contains a COT motif like [8]circulenes. The antiaromaticity of the COT core is confirmed by nucleus independent chemical shift (NICS) calculations. The planarization from a helically π-conjugated [7]helicene to a fully planar heterocyclic [8]circulene significantly alters the spectroscopic properties of the molecules. Post-functionalization of the [7]helicenes and the [8]circulenes by oxygenation of the thiophene rings to the corresponding thiophene-sulfones allows an almost complete fluorescence emission coverage of the visible region of the optical spectrum (400–700 nm).     

Effect of intramolecular crosslinker properties on the mechanochemical fragmentation of covalently folded polymers

The mechanochemical stability of polymers in solution is enhanced if the chains are covalently folded. Under shear forces, the additional bonds absorb mechanical energy and inhibit unfolding, and as a result, slow down fragmentation. However, not all crosslinkers are equal in terms of their properties (length, strength, etc.). In order to understand the role of these added bonds in the polymers' stability under mechanical stress, a thorough study compares the rate of mechanochemistry on single-chain polymer nanoparticles which have been folded with crosslinkers with different lengths, strengths, positioning, and valencies. The usage of bonds with different mechanical strengths in the crosslinkers was found to be the most powerful way to change the mechanochemical fragmentation rate. In addition, positioning and valency also play significant role in the mechanical stabilization mechanism. © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 , 58, 692–703     

Toward a universal quantum QSPR operator

This article presents a discussion about the formalism, which might be associated to a general Quantum quantitative structure–properties relations operator, appearing in a Boltzmann‐like exponential form, which is based in turn on the definition of the concept of thermal voltage, applied to thermally scaled electronic density functions. Three practical numerical examples are presented, corresponding to the calculation of the polarization angle in assorted chiral molecules, the estimation of fish toxicity for perchlorobenzene within the set of chlorobenzenes and a typical quantum QSAR study on the popular Cramer steroid set.     

The effect of methyl group on the mechanical properties of hydrophobic association hydrogel

Hydrophobic association hydrogels were fabricated via micellar copolymerization of acrylamide and hydrophobic monomers lauryl (meth)acrylate (LA or LMA) in an aqueous solution of sodium dodecyl sulfate. The effect of methyl groups of hydrophobic monomers on the crosslinking network structure and mechanical behavior of the gels was investigated on the basis of rubber elastic theory. It was found that the LMA-gel exhibited higher effective crosslink density and elastic modulus. The methyl groups of hydrophobic monomers limited the flexibility of the methacrylate backbone in the association domain, which resulted in the increment of chains constraints. With the increase of stretch rate, the dissipated energy of LMA-gel increased more highly than that of LA-gel. In addition, the methyl group hindered the movement of polymer chains, leading to the lower recovery efficiency of dissipated energy for LMA-gel. In contract, the LA-gel exhibited a rapid response to external force, and possessed better elasticity and self-recovery property. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1505–1512     

Structural transformation from shish‐kebab crystals to micro‐fibrils through hot stretching process of gel‐spun ultra‐high molecular weight polyethylene fibers with high concentration solution

Structural evolution of gel‐spun ultra‐high molecular weight polyethylene fibers with high concentration solution via hot stretching process was investigated by in situ small‐angle X‐ray scattering, in situ wide‐angle X‐ray diffraction measurements, scanning electron microscopy, and differential scanning calorimetry. With the increase of stretching strain, the long period continuously increases at relative lower stretching temperature, while it first increases and then decreases rapidly at relative higher stretching temperature. The kebab thickness almost keeps constant during the whole hot‐stretching process and the kebab diameter continually decreases for all stretching temperatures. Moreover, the length of shish decreases slightly and the shish quantity increases although there is almost no change in the diameter of shish crystals during the hot stretching process. The degree of crystal orientation at different temperatures is as high as above 0.9 during the whole stretching process. These results indicate that the shish‐kebab crystals in ultra‐high molecular weight polyethylene fibers can transform continuously into the micro‐fibril structure composed mostly of shish crystals through the hot stretching process. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 225–238