LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.     

内蕴平方函数交换子在加权弱Hardy空间上的端点估计

证明了由BMO函数与α阶内蕴面积函数S_α和内蕴g_(λ,α)*函数生成的交换子都是由加权弱Hardy空间WH_(b,ω)~1到加权弱L1空间WL_ω~1上的有界算子.     

Bounds on partial derivatives of NURBS surfaces

In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.     

Generalized harmonic number summation formulae via hypergeometric series and digamma functions

By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers.     

Different supramolecular architectures mediated by different weak interactions in the crystals of three N‐aryl‐2,5‐dimethoxybenzenesulfonamides

The synthesis and evaluation of the pharmacological activities of molecules containing the sulfonamide moiety have attracted interest as these compounds are important pharmacophores. The crystal structures of three closely related N‐aryl‐2,5‐dimethoxybenzenesulfonamides, namely N‐(2,3‐dichlorophenyl)‐2,5‐dimethoxybenzenesulfonamide, C₁₄H₁₃Cl₂NO₄S, (I), N‐(2,4‐dichlorophenyl)‐2,5‐dimethoxybenzenesulfonamide, C₁₄H₁₃Cl₂NO₄S, (II), and N‐(2,4‐dimethylphenyl)‐2,5‐dimethoxybenzenesulfonamide, C₁₆H₁₉NO₄S, (III), are described. The asymmetric unit of (I) consists of two symmetry‐independent molecules, while those of (II) and (III) contain one molecule each. The molecular conformations are stabilized by different intramolecular interactions, viz. C—H…O interactions in (I), N—H…Cl and C—H…O interactions in (II), and C—H…O interactions in (III). The crystals of the three compounds display different supramolecular architectures built by various weak intermolecular interactions of the types C—H…O, C—H…Cl, C—H…π(aryl), π(aryl)–π(aryl) and Cl…Cl. A detailed Hirshfeld surface analysis of these compounds has also been conducted in order to understand the relationship between the crystal structures. The d _norm and shape‐index surfaces of (I)–(III) support the presence of various intermolecular interactions in the three structures. Analysis of the fingerprint plots reveals that the greatest contribution to the Hirshfeld surfaces is from H…H contacts, followed by H…O/O…H contacts. In addition, comparisons are made with the structures of some related compounds. Putative N—H…O hydrogen bonds are observed in 29 of the 30 reported structures, wherein the N—H…O hydrogen bonds form either C (4) chain motifs or R ₂²(8) rings. Further comparison reveals that the characteristics of the N—H…O hydrogen‐bond motifs, the presence of other interactions and the resultant supramolecular architecture is largely decided by the position of the substituents on the benzenesulfonyl ring, with the nature and position of the substituents on the aniline ring exerting little effect. On the other hand, the crystal structures of (I)–(III) display several weak interactions other than the common N—H…O hydrogen bonds, resulting in supramolecular architectures varying from one‐ to three‐dimensional depending on the nature and position of the substituents on the aniline ring.     

The global weak solution for the shallow water wave model of moderate amplitude

In this paper, we firstly establish the existence theorem of the global weak solutions of the Cauchy problem for the shallow water wave model of moderate amplitude, then following the idea in Xin and Zhang’s work (see Xin and Zhang, 2002), we prove the uniqueness of global weak solutions using the localization analysis in the transport equation theory. Finally, several travelling wave solutions are derived.     

Fundamental solution of the time‐fractional telegraph Dirac operator

In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α∈]0,1] and β∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. Finally, using the FS, we study some Poisson and Cauchy problems.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.