Heinz‐type inequality and bi‐Lipschitz continuity for quasiconformal mappings satisfying inhomogeneous biharmonic equations

Let be the class of all sense‐preserving homeomorphic self‐mappings of . The aim of this paper is twofold. First, we obtain Heinz‐type inequality for (K,K′)‐quasiconformal mappings satisfying inhomogeneous biharmonic equation Δ(Δω) = g in unit disk with associated boundary value conditions and . Second, we establish biLipschitz continuity for (K,K′)‐quasiconformal mappings satisfying aforementioned inhomogeneous biharmonic equation when and are small enough.     

Post modification of zinc based coordination polymer to prepare Zn‐Mo‐ICP nanoparticles as efficient self‐supported catalyst for olefin epoxidation

Preparation, characterization, and catalytic properties of bimetallic coordination polymer constructed from 2‐aminoterephthalic acid as linker, zinc cations as node, and cis‐dioxo molybdenum units as catalytic active sites are reported via two pathways. Molybdenum centers were placed in N,O positions created by condensation reaction of 2‐aminoterephthalic acid with salicylaldehyde while zinc cations coordinated via carboxylic acid groups of linker to achieve infinite chains of metalo‐ligand. The obtained coordination polymer was fully characterized and its catalytic properties in the epoxidation of olefins with tert‐butyl hydroperoxide (TBHP) described. In comparison with previously reported heterogenized molybdenum catalysts, this new coordination polymer exhibited good conversion as well as high selectivity in the epoxidation of olefins. The catalyst is stable under ambient conditions and could be reused as active catalyst for at least five times.     

Synthesis,Reactions, Characterization and Biological Evaluation of 2,3′‐Bipyridine Derivatives (III)

1‐Pyridin‐3‐yl‐3‐(2‐thienyl of 2‐furyl)prop‐2‐en‐1‐ones 1a , 1b reacted with 2‐cyanoethanethioamide 2 to afford the corresponding 4‐(thiophen‐2‐yl or furan‐2‐yl)‐6‐sulfanyl‐2,3′‐bipyridine‐5‐carbonitriles 3a , 3b . The synthetic potentiality of compounds 3a , 3b were investigated in the present study via their reactions with several active halogen containing compounds 4a , 4b , 4c , 4d , 4e , 4f , 4g , 4h , 5 , 5a , 5b . Our aim here is the synthesis of 4‐(2‐thienyl or 2‐furyl)‐6‐pyridin‐3‐ylthieno[2,3‐b]pyridin‐3‐amines 6a , 6b , 6c , 6d , 6e , 6g , 6h , 6i , 6j , 6k , 6l , 6m , 6n ,via 6‐(alkyl‐thio)‐4‐(2‐thienyl or 2‐furyl)‐2,3′‐bipyridine‐5‐carbonitriles 5a , 5b , 5c , 5d , 5e , 5i , 5j , 5k , 5l , 5m . The structures of all newly synthesized heterocyclic compounds were elucidated by considering the data of IR, ¹H‐NMR, mass spectra, as well as that of elemental analyses. Anti‐cancer, anti‐Alzheimer, and anti‐COX‐2 activities were investigated for all the newly synthesized heterocyclic compounds.     

Wavelet bi‐frames with uniform symmetry

Wavelet bi‐frames with uniform symmetry are discussed in this paper. Every refinable function in the bi‐frame system is symmetric, which is very useful in the image processing and curve and surface multiresolution processing. By the aid of the lifting scheme, bi‐frame multiresolution algorithms can be divided into several iterative steps, and each step can be shown by a symmetric template. The template‐based procedure is established for constructing bi‐frames with uniform symmetry and N > 2 generators. In particular, we take the bi‐frame with three generators as an example to provide a clearer picture of the template‐based procedure for constructing bi‐frames. Three types of bi‐frames with three generators are studied, and some examples with certain smoothness are constructed. These examples include some bi‐frames with interpolating property. Copyright © 2016 John Wiley & Sons, Ltd.     

Synthesis of 2,2′‐Bi‐2H‐3,3′‐diaryl‐1,4‐benzothiazines from α,α‐Dibromoacetophenones and o‐Aminothiophenol

Some 2,2′‐bi‐2H‐3,3′‐diaryl‐1,4‐benzothiazines (5a–f) were synthesized from α,α‐dibromoacetophenones and o‐aminothiophenol.     

酚酞型聚芳醚砜——Ⅱ.侧基结构对Cardo双酚聚合反应性的影响

基于在“一步法”聚合反应过程中发现的酚酞对反应有特殊的“自催化”作用,本文合成了几种具有与酚酞类似结构的Cardo双酚,并通过对其聚合反应规律的研究,进一步探讨“自催化”作用的本质。实验结果表明,这类Cardo双酚也较普通结构双酚更易于进行异相成盐反应,表现为其聚合反应速度的明显加快。     

A Zariski Topology for Bicomodules and Corings

In this paper we introduce and investigate top (bi)comodules of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative) rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitable conditions) and study the interplay between the coalgebraic properties of such (bi)comodules and the introduced Zariski topology. In particular, we apply our results to introduce a Zariski topology on the fully coprime spectrum of a given non-zero coring considered canonically as duo object in its category of bicomodules. Supported by King Fahd University of Petroleum & Minerals, Research Project # INT/296.     

具有弹性夹层的文克勒地基上双层叠合梁的解

将双层叠合梁之间的接触状况拟合为一符合 Goodman假设的弹性夹层 ,导出了Winkler弹性地基上双层叠合梁的微分方程组及其解析解。通过引入“广义夹层反应模量”计入了夹层水平和竖向反力引起的梁截面的剪切和拉压形变效应 ,它有效地提高了计算精度 ,尤其是在双层梁结构有间断的场合。     

一个双目标单机调度问题及其几个多项式可解情形

研究了一个双目标单机调度问题及其几个多项式可解的情形。问题的主目标是延误工件数最小,在此条件下,最小化各工件加权提前期的总和,由于该问题是NP一难的,故研究求解它的一个启发式算法及问题的几个多项式可解的特殊情形。     

Existence of solutions for some non‐Fredholm integro‐differential equations with the bi‐Laplacian

We prove the existence of solutions for some semilinear elliptic equations in the appropriate H⁴ spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the previous results.