Simultaneous measurement of transient stress and flow birefringence in one-sided compression (biaxial extension) of a polymer melt

Summary Investigation of time dependent behaviour of a polystyrene melt is carried out with the aid of a new apparatus for biaxial extension. Use is made of the method of two impinging fluid streams guided by lubricated trumpet shaped metal walls. The flow birefringence is measured in the plane of symmetry and, at the same time, the force is measured which tends to separate the trumpets. The linear stress-optical relation turns out to be valid in this new flow geometry. An accurate value for the stress-optical coefficient can be determined from the relaxation experiments. The stress build-up as calculated from the optical measurements, is compared with the pertinent result of the theory of linear viscoelasticity. For the desired interconversion of dynamic moduli use is made of the approximation by Schwarzl and Struik. The steady state measurements are checked by the results of the non-linear model of Acierno et al.With 16 figures and 2 tables     

Strain hardening behavior of polymer blends with fibril morphology

We investigate the rheological behavior of the polymer blends with fibril morphology, with special focus on the effect of fibril morphology on the extensional properties under uniaxial extension. We add a small amount of the dispersed phase to the matrix, and control the blend morphology by changing the viscosity ratio. When the fibril morphology is maintained, the blend shows not only a significant increase of the extensional viscosity but the strain hardening behavior. The extensional viscosity increases depending on the aspect ratio of the fibers, while the strain hardening behavior originates from the restricted stretching of deformable fibers, which has been confirmed theoretically by introducing the concept of rigidity of the fiber. It suggests a way to induce the strain hardening behavior by introducing deformable fibrils into the matrix, that is, by the design of polymer blends with a small amount of dispersed phase such that the fibril structure is maintained.     

The structures of the isomorphous potassium and rubidium salts of 4‐nitrobenzoic acid and an overview of the metal complex stereochemistries of the alkali metal salt series with this ligand

4‐Nitrobenzoic acid (PNBA) has proved to be a useful ligand for the preparation of metal complexes but the known structures of the alkali metal salts of PNBA do not include the rubidium salt. The structures of the isomorphous potassium and rubidium polymeric coordination complexes with PNBA, namely poly[μ₂‐aqua‐aqua‐μ₃‐(4‐nitrobenzoato)‐potassium], [K(C₇H₄N₂O₂)(H₂O)₂]_n, (I), and poly[μ₃‐aqua‐aqua‐μ₅‐(4‐nitrobenzoato)‐rubidium], [Rb(C₇H₄N₂O₂)(H₂O)₂]_n, (II), have been determined. In (I), the very distorted KO₆ coordination sphere about the K⁺ centres in the repeat unit comprise two bridging nitro O‐atom donors, a single bridging carboxylate O‐atom donor and two water molecules, one of which is bridging. In Rb complex (II), the same basic MO₆ coordination is found in the repeat unit, but it is expanded to RbO₉ through a slight increase in the accepted Rb—O bond‐length range and includes an additional Rb—O_carboxylate bond, completing a bidentate O,O′‐chelate interaction, and additional bridging Rb—O_nitro and Rb—O_water bonds. The comparative K—O and Rb—O bond‐length ranges are 2.7352 (14)–3.0051 (14) and 2.884 (2)–3.182 (2) Å, respectively. The structure of (II) is also isomorphous, as well as isostructural, with the known structure of the nine‐coordinate caesium 4‐nitrobenzoate analogue, (III), in which the Cs—O bond‐length range is 3.047 (4)–3.338 (4) Å. In all three complexes, common basic polymeric extensions are found, including two different centrosymmetric bridging interactions through both water and nitro groups, as well as extensions along c through the para‐related carboxylate group, giving a two‐dimensional structure in (I). In (II) and (III), three‐dimensional structures are generated through additional bridges involving the nitro and water O atoms. In all three structures, the two water molecules are involved in similar intra‐polymer O—H...O hydrogen‐bonding interactions to both carboxylate and water O‐atom acceptors. A comparison of the varied coordination behaviour of the full set of Li–Cs salts with 4‐nitrobenzoic acid is also made.     

Primer Extension Reaction Assays for Incorporation of Deoxynucleotide Analogue into DNA

Incorporation of deoxynucleotide analogues into DNA is important for the expansion of DNA functions. Primer extension reactions are commonly used for the assay of such reaction events. However, current assay protocols generally rely on radiolabeling, fluorescence reporter labeling, or removal of specific deoxynucleotide triphosphate in the reaction mixture. Herein we report on the design of two novel assay protocols that utilize a dideoxynucleotide‐terminated template strand and a phosphorothiolate‐modified deoxynucleotide‐terminated template strand. We designed and synthesized a deoxyuridine triphosphate analogue (dU*TP) containing 2‐bromoisobutyryl group and demonstrated that it could be well recognized by ?29DNA polymerase, E. coli DNA polymerase I Klenow Fragment, Bst DNA polymerase Large Fragment, and E. coli DNA polymerase I Klenow Fragment (exo⁽), which translated to effective incorporation of dU*TP into DNA. dU*TP was also successfully incorporated into extremely long single‐stranded DNA at high‐density using ?29 DNA polymerase by rolling circle amplification.     

Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.     

Isometries and additive mapping on the unit spheres of normed spaces

In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.     

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.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.     

Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .