Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.     

Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

取向聚对苯二甲酸乙二酯纤维的非等温结晶动力学

取向聚对苯二甲酸乙二酯纤维的非等温结晶动力学张志英，赵家森（天津纺织工学院材料科学系天津３００１６０）关键词取向高聚物，聚对苯二甲酸乙二酯，非等温结晶，结晶动力学研究高聚物结晶动力学常用的等温方法有光透射法、密度法、显微镜法、Ｘ－射线衍射法、差示扫描...     

On Tutte polynomial expansion formulas in perspectives of matroids and oriented matroids

We introduce the active partition of the ground set of an oriented matroid perspective (or morphism, or quotient, or strong map) on a linearly ordered ground set. The reorientations obtained by arbitrarily reorienting parts of the active partition share the same active partition. This yields an equivalence relation for the set of reorientations of an oriented matroid perspective, whose classes are enumerated by coefficients of the Tutte polynomial, and a remarkable partition of the set of reorientations into Boolean lattices, from which we get a short direct proof of a 4-variable expansion formula for the Tutte polynomial in terms of orientation activities. This formula was given in the last unpublished preprint by Michel Las Vergnas; the above equivalence relation and notion of active partition generalize a former construction in oriented matroids by Michel Las Vergnas and the author; and the possibility of such a proof technique in perspectives was announced in the aforementioned preprint. We also briefly highlight how the 5-variable expansion of the Tutte polynomial in terms of subset activities in matroid perspectives comes in a similar way from the known partition of the power set of the ground set into Boolean lattices related to subset activities (and we complete the proof with a property which was missing in the literature). In particular, the paper applies to matroids and oriented matroids on a linearly ordered ground set, and applies to graph and directed graph homomorphisms on a linearly ordered edge-set.     

Oriented hypergraphs: Balanceability

An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance.     

Orientation-reversing involutions on handlebodies

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

     

Immobilization of antibody fragment for immunosensor application based on surface plasmon resonance

Biosurface fabrication using the Fab′ fragment of immunoglobulin (IgG) was carried out by self-assembly (SA) technique. The pepsin-digested monoclonal antibody (Mab) against bovine insulin containing the F(ab′)₂ fragment and residual proteins was separated using affinity chromatography and dialysis. To prevent the nonspecific binding of F(ab′)₂ onto gold (Au) substrate, the native disulfide bridge was reduced using dithiothreitol (DTT) to convert F(ab′)₂ into Fab′, which made the immobilization to be carried out via the native thiol (–SH) group. The fabricated biosurface using SA technique showed the formation of stable thin film through AFM topography. Through the concentration change of DTT and Fab′, the absorption characteristics against the Au surface were investigated using surface plasmon resonance (SPR) with the flow cell. The amount of immobilized antibody fragment and the antigen binding capacity were regulated with respect to the reduction state and concentration of F(ab′)₂. Based on the biosurface of the fabricated Fab′, the insulin-detection was carried out by the measurement of SPR. The proposed antibody surface could successfully detect the bovine insulin at the concentration from 100 ng/mL to 10 μg/mL.     

MORPHOLOGICAL STUDIES ON THERMOTROPIC LIQUID CRYSTALLINE POLYESTER——MORPHOLOGY OF SHEAR ORIENTED FILMS

The morphology of shear-oriented films of a thermotropic liquid crystalline polyester containing a triad ester mesogenic unit and a flexible spacer has been investigated in details. The formation conditions and process, the fine structures and the relaxation process of mat structure in the oriented films have been observed and discussed.     

类椭球氧化锌纳米结构的制备与表征

"用普通氧化锌晶须作为原材料, 采用高压釜腐蚀法和高温(600 ℃)裂解结合的方法合成纳米棒构成的氧化锌类椭球结构．XRD、SEM和TEM结果表明这种类椭球结构是单晶的,纳米棒取向一致,自组装生长而成．"     

可控液体输运制备取向聚合物薄膜:面向性能增强的发光二极管

提出了一种由锥形纤维阵列引导的定向液体输运的简单策略, 实现了对聚二芳基芴(PODPF)的有序 排列. 通过热退火处理(～240 ℃), PODPF由无定形相转变为β相态, 制备的PODPF薄膜具有一定的取向性 并且结晶尺寸更大. 在去浸润过程中, 锥形纤维阵列能够精确控制三相接触线的后退, 从而使得共轭高分子在产生的定向应力作用下定向排列. 基于此制备了聚合物发光二极管(PLEDs)器件, 与由旋涂膜制备的器件相比具有更高的电流效率(1.53 cd/A)和更稳定的电致发光. 表明利用锥形纤维阵列可以制备高性能的有机发光 二极管.