Novel bismaleimide containing cyclic phosphine oxide and an epoxy unit: Synthesis, characterization, thermal and flame properties

A new type of bismaleimide resin (EPBMI), containing epoxy unit and phosphorus in the main chain, was synthesized. The structure of the new resin was confirmed by infrared spectroscopy (IR), ¹H NMR and ¹³C NMR spectroscopies. In addition, the compositions of the new synthesized bismaleimide with two reactants, 4,4′-diaminodiphenylsulfone (DDS) and 4,4′-diaminodiphenylether (DDE), was used to compare its reactivity and thermal properties with conventional bismaleimide (EBMI). Reactivity was measured by differential scanning calorimetry. Thermogravimetric analysis revealed that the polymers, obtained through the reactions between bismaleimides and diamine agents, also demonstrated excellent thermal properties and high char yield.     

Sphere-preserving maps in inversive geometry

We give an extensive discussion of sphere-preserving maps defined on subdomains of Euclidean -space, and their relationship to Möbius maps and to the preservation of cross-ratios. In the case (the complex plane) we also relate these ideas to the solutions of certain functional equations.

     

A Schwarz lemma for multivalued functions and distortion theorems for Bloch functions with branch points

We give a version of the Schwarz lemma for multivalued mappings between hyperbolic plane regions. As in the original work of Nehari on this subject, the derivative must remain bounded near the branch points. Our version of the distance-decreasing principle represents a considerable strengthening of previous results. We apply it to the study of Bloch functions with branch points of specified order. We obtain upper and lower estimates for , an upper estimate for , and a lower estimate for the radius of the largest schlicht disk in the image of centered at . We also obtain some results requiring estimates of second order derivatives of .

     

The effect of phase transfer catalysts on the Reimer-Tiemann reaction

Quaternary ammonium salts were found inactive as phase transfer catalysts in the Reimer-Tiemann reaction. Tertiary amines, on the other hand, proved to have significant effect on the process.     

论新疆干旱区水资源利用对生态环境影响的规律与良化途径

新疆水资源的转化与时空分布规律和水资源在此特殊干旱区的重要地位及自然、人文因子共同影响下,本地区水资源利用表现出宏观与微观上的明显“向水”趋势,并在各种用水方式的作用中形成若干新的人工水体生态系统,因此产生了一系列生态环境问题。本文在总结以往经验的基础上,就目前新疆水资源利用存在的主要问题,进行环境综合评价,进而寻求规律,扬长避短,提出合理开发利用新疆水资源的战略对策。     

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations.     

Distortion theorems for locally univalent Bloch functions

A holomorphic functionf defined on the unit disk d is called a Bloch function provided {fx73-02} For α ∃ (0,1] letB∞(α)denote the class of locally univalent Bloch functionsf normalized by ∥f∥_B ≤1f(0) = 0 andf’(0) = α. A type of subordination theorem is established for B∞(α). This subordination theorem is used to derive sharp growth, distortion, curvature and covering theorems for B∞(α). Supported as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation. Research supported in part by a National Science Foundation grant.     

Discrete Morse Theory for Computing Cellular Sheaf Cohomology

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse theoretic techniques. As a consequence, we derive efficient techniques for distributed computation of (ordinary) cohomology of a cell complex.