Classes of 2-step nilpotent lie algebras

We give a characterization of the Lie algebras of H-type independent of the inner product used in the definition. We classify the real 2-step nilpotent Lie algebras with 2-dimensional center. Using these results we give examples of regular Lie algebras that are not H-type.     

Mechanistic discussion of cationic crosslinking copolymerizations of 1,2‐epoxycyclohexane with diepoxide crosslinkers accompanied by intramolecular and intermolecular chain transfer reactions

Our previous mechanistic discussion of the free‐radical crosslinking monoallyl/diallyl copolymerizations was extended to the cationic crosslinking monoepoxide/diepoxide copolymerizations, typically including 1,2‐epoxycyclohexane (ECH) as a monoepoxide and bis[3,4‐epoxycyclohexylmethyl] adipate (BECHMA) as a diepoxide crosslinker. In the cationic polymerization, oligomer is usually obtained because of the occurrence of characteristic chain‐forming reactions. Therefore, cationic crosslinking monoepoxide/diepoxide copolymerizations could be in the category of the network formation through free‐radical crosslinking monoallyl/diallyl copolymerizations. Thus, the gelation behavior was discussed by comparing the actual gel points with the theoretical ones; the greatly delayed gelation from theory was observed. Then, the resulting network polymer precursors (NPPs) were characterized by SEC‐MALLS‐viscometry to clarify the cationic crosslinking ECH/BECHMA copolymerization mechanism. Notably, the correlation lines of molecular weight versus elution volume were specific for the NPPs obtained at a high conversion close to the gel point as compared with those obtained by the free‐radical crosslinking monoallyl/diallyl copolymerization. This may be ascribed to the occurrence of intramolecular and intermolecular chain transfer reactions characteristic of cationic polymerization; the chain transfer reactions involve the intramolecular and intermolecular nucleophilic attack of ether oxygen or terminal hydroxyl oxygen in the NPPs to a terminal growing cation that leads to the formation of not only the loop‐ but also the crosslink‐structures containing NPPs, providing fragile ultrahigh‐molecular‐weight NPP in the SEC columns. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Cycle embedding in star graphs with more conditional faulty edges

The star graph is one of the most attractive interconnection networks. The cycle embedding problem is widely discussed in many networks, and edge fault tolerance is an important issue for networks since edge failures may occur when a network is put into use. In this paper, we investigate the cycle embedding problem in star graphs with conditional faulty edges. We show that there exist fault-free cycles of all even lengths from 6 to n! in any n-dimensional star graph S_n (n ? 4) with ?3n − 10 faulty edges in which each node is incident with at least two fault-free edges. Our result not only improves the previously best known result where the number of tolerable faulty edges is up to 2n − 7, but also extends the result that there exists a fault-free Hamiltonian cycle under the same condition.     

Synthesis and Characterization of Polyurethane/Poly (Urethane Modified Bismaleimide-Bismaleimide) IPNs

Themethodofblendingbyinterpenetratingpolymernetworks(IPNs)isoftenusedtoobtainelastomerswithpropertiesinexcessofthoseexhibitedbytraditionalblendingways'.Inthispaper,aseriesofnovelpolyurethane/poly(urethanemodifiedbismaleimide-bismaleimide)(PU/P(UBMI-BMI))IPNsweresynthesizedandcharacterizedby'HNMR,FTIR,TEM,andTGAanaIysis.BMIwassynthesizedasfollowsfUBMlwasintroducedtomodifythecompatibilityofthetwonetworks,whichwassynthesizedasfollows:Where(l)ishydroxyl-terminatedpoly(diethyleneadipa…     

The homotopy limit problem for Hermitian K-theory, equivariant motivic homotopy theory and motivic Real cobordism

The homotopy limit problem for Karoubi?s Hermitian K-theory (Karoubi, 1980) [26] was posed by Thomason (1983) [44]. There is a canonical map from algebraic Hermitian K-theory to the Z/2-homotopy fixed points of algebraic K-theory. The problem asks, roughly, how close this map is to being an isomorphism, specifically after completion at 2. In this paper, we solve this problem completely for fields of characteristic 0 (Theorems 16, 20). We show that the 2-completed map is an isomorphism for fields F of characteristic 0 which satisfy cd₂(F[i])<∞, but not in general.     

Tripod molecules build molecular networks and open-dimer capsules by weak interactions

Three tripod molecules, tris(2-methoxy-5-nitrobenzyl)phosphine oxide (1), tris(2-butoxy-3-methyl-5-nitrobenzyl)phosphine oxide (2), and tris(3-nitrobenzyl)amine (TNBA), were synthesized and crystallized. The structures of 1, 2, and their comparison (TNBA) were determined by X-ray crystallography. It is noteworthy that compound 1 interacted with adjacent molecules via π-π stacking and C-H···π interactions to yield an open supramolecular network with the porosity P in 8.9%, whereas compound 2 gathered closely...