Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Strong edge-coloring for planar graphs with large girth

A strong edge-coloring of a graph $G=(V,E)$ is a partition of its edge set $E$ into induced matchings. Let $G$ be a connected planar graph with girth $k\ge 26$ and maximum degree $\Delta$. We show that either $G$ is isomorphic to a subgraph of a very special $\Delta$-regular graph with girth $k$, or $G$ has a strong edge-coloring using at most $2\Delta +\lceil \frac{12(\Delta -2)}{k}\rceil$ colors.     

Beyond Stereoselectivity,Switchable Catalysis: Some of the Last Frontier Challenges in Ring‐Opening Polymerization of Cyclic Esters

Metal‐based catalysts and initiators have played a pivotal role in the ring‐opening polymerization (ROP) of cyclic esters, thanks to their high activity and remarkable ability to control precisely the architectures of the resulting polyesters in terms of molar mass, dispersity, microstructure, or tacticity. Today, after two decades of extensive research, the field is slowly reaching maturity. However, several challenges remain, while original concepts have emerged around new types or new applications of catalysis. This Review is not intended to comprehensively cover all of these aspects. Rather, it provides a personal overview of the very recent progress achieved in some selected, important aspects of ROP catalysis—stereocontrol and switchable catalysis. Hence, the first part addresses the development of new metal‐based catalysts for the isoselective ROP of racemic lactide towards stereoblock copolymers, and the use of syndioselective ROP metal catalysts to control the monomer sequence in copolymers. A second part covers the development of ROP catalysts—primarily metal‐based catalysts, but also organocatalysts—that can be externally regulated by the use of chemical or photo stimuli to switch them between two states with different catalytic abilities. Current challenges and opportunities are highlighted.     

一类特殊根及其刻划

研究了任一个超幂零根为零的亚直不可约环所确定的环类 ,证明了由这样的环类所确定的上根都是特殊根 ,并且给出了这类根的一些刻划     

与半群的完全不可逆生成集相关的几个性质

讨论了半群环的两个性质以及关于半群的a.c.c.p.（主理想升链条件）的一个结论。     

关于Herstein定理的逆问题研究

设R是一个环,如果存在n>1使f:x→xn为R的一个环同态,则映射f:R→R称为一个幂自同态。本文将完全刻划出无零因子环的所有幂自同态。     

Some necessary and sufficient conditions for Hypercyclicity Criterion

We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion. This paper is a part of the second author’s Doctoral thesis, written at Shiraz University under the direction of the first author.     

Ultrasonic spectroscopic evaluation of the ring‐opening metathesis polymerization of dicyclopentadiene

An in situ ultrasonic spectroscopy technique was used to study the ring‐opening metathesis polymerization of dicyclopentadiene catalyzed by bis(tricyclohexylphosphine)benzylidene ruthenium dichloride. A reaction cell employing a flexible poly(ethylene terephthalate) window for pulse echo ultrasonic spectroscopy was used to monitor the polymerization. The changes in the density, wave speed, acoustic modulus, and attenuation were all simultaneously monitored. In comparison with Fourier transform infrared (FTIR) spectroscopy data, the changes in the density, velocity, and modulus only accurately measured the rate constant for the metathesis of the cyclopentyl unsaturation. The ultrasonic values were within 6% of the values determined by FTIR. The activation energy for metathesis of the cyclopentyl unsaturation was 84 kJ mol^?1, following first‐order kinetics. Rate constants for the polymerization of the norbornyl unsaturation could not be determined by ultrasound. The gel point, vitrification, and qualitative information about the reaction rate could be determined from the change in the attenuation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1323–1333, 2003     

Rhythmic growth of ring‐banded spherulites in blends of liquid crystalline methoxy‐poly(aryl ether ketone) and poly(aryl ether ether ketone)

Rhythmic growth of ring‐banded spherulites in blends of liquid crystalline methoxy‐poly(aryl ether ketone) (M‐PAEK) and poly(aryl ether ether ketone) (PEEK) has been investigated by means of differential scanning calorimetry (DSC), polarized light microscopy (PLM), and scanning electron microscopy (SEM) techniques. The measurements reveal that the formation of the rhythmically grown ring‐banded spherulites in the M‐PAEK/PEEK blends is strongly dependent on the blend composition. In the M‐PAEK‐rich blends, upon cooling, an unusual ring‐banded spherulite is formed, which is ascribed to structural discontinuity caused by a rhythmic radial growth. For the 50:50 M‐PAEK/PEEK blend, ring‐banded spherulites and individual PEEK spherulites coexist in the system. In the blends with PEEK as the predominant component, M‐PAEK is rejected into the boundary of PEEK spherulites. The cooling rate and crystallization temperature have great effect on the phase behavior, especially the ring‐banded spherulite formation in the blends. In addition, the effects of M‐PAEK phase transition rate and phase separation rate on banded spherulite formation is discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3011–3024, 2007