Exploring the intermediates of photochemical CO2 reduction: reaction of Re(dmb)(CO)3 COOH with CO2

We have investigated the reaction of Re(dmb)(CO)(3)COOH with CO(2) using density functional theory, and propose a mechanism for the production of CO. This mechanism supports the role of Re(dmb)(CO)(3)COOH as a key intermediate in the formation of CO. Our new experimental work supports the proposed scheme.     

Disconnected Colors in Generalized Gallai‐Colorings

Gallai‐colorings of complete graphs—edge colorings such that no triangle is colored with three distinct colors—occur in various contexts such as the theory of partially ordered sets (in Gallai's original paper), information theory and the theory of perfect graphs. A basic property of Gallai‐colorings with at least three colors is that at least one of the color classes must span a disconnected graph. We are interested here in whether this or a similar property remains true if we consider colorings that do not contain a rainbow copy of a fixed graph F. We show that such graphs F are very close to bipartite graphs, namely, they can be made bipartite by the removal of at most one edge. We also extend Gallai's property for two infinite families and show that it also holds when F is a path with at most six vertices.     

Asymptotic Solutions of Viscous Hamilton–Jacobi Equations with Ornstein–Uhlenbeck Operator

We study the long time behavior of solutions of the Cauchy problem for semilinear parabolic equations with the Ornstein–Uhlenbeck operator in ? ^N . The long time behavior in the main results is stated with help of the corresponding to ergodic problem, which complements, in the case of unbounded domains, the recent developments on long time behaviors of solutions of (viscous) Hamilton–Jacobi equations due to Namah (1996 Namah , G. ( 1996 ). Asymptotic solution of a Hamilton–Jacobi equation . Asymptotic Anal. 12 ( 4 ): 355 – 370 . [CSA] [Web of Science ®] , [Google Scholar]), Namah and Roquejoffre (1999 Namah , G. , Roquejoffre , J.-M . ( 1999 ). Remarks on the long-time behavior of the solutions of Hamilton–Jacobi equations . Comm. PDE 24 ( 5–6 ): 883 – 893 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Roquejoffre (1998 Roquejoffre , J.-M . ( 1998 ). Comportement asymptotique des solutions d’équations de Hamilton–Jacobi monodimensionnelles . C. R. Acad. Sci. Paris Sér. I Math. 326 ( 2 ): 185 – 189 . [CSA] [Crossref] , [Google Scholar]), Fathi (1998 Fathi , A. ( 1998 ). Sur la convergence du semi-groupe de Lax–Oleinik semigroup . C. R. Acad. Sci. Paris Sér. I Math. 327 ( 3 ): 267 – 270 . [CSA] [Crossref] , [Google Scholar]), Barles and Souganidis (2000 Barles , G. , Souganidis , P. E. ( 2000 ). On the large time behavior of solutions of Hamilton–Jacobi equaitons . SIAM J. Math. Anal. 31 ( 4 ): 925 – 939 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar] 2001 Barles , G. , Souganidis , P. E. ( 2001 ). Space-time periodic solutions and long-time behavior of solutions to quasi-periodic parabolic equations . SIAM J. Math. Anal. 32 ( 6 ): 1311 – 1323 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). We also establish existence and uniqueness results for solutions of the Cauchy problem and ergodic problem for semilinear parabolic equations with the Ornstein–Uhlenbeck operator.     

Derived Equivalences for Triangular Matrix Rings

We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev.     

On Derived Equivalences for Selfinjective Algebras

We show that if A is a representation-finite selfinjective Artin algebra, then every P ^? ? K ^b(𝒫 _A ) with Hom _K(Mod?A)(P ^?,P ^?[i]) = 0 for i ≠ 0 and add(P ^?) = add(νP ^?) is a direct summand of a tilting complex, and that if A, B are derived equivalent representation-finite selfinjective Artin algebras, then there exists a sequence of selfinjective Artin algebras A = B ₀, B ₁,…, B _m  = B such that, for any 0 ≤ i < m, B _i+1 is the endomorphism algebra of a tilting complex for B _i of length ≤ 1.     

Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds.     

Contractible elements in k‐connected graphs not containing some specified graphs

In 15 , Thomassen proved that any triangle‐free k‐connected graph has a contractible edge. Starting with this result, there are several results concerning the existence of contractible elements in k‐connected graphs which do not contain specified subgraphs. These results extend Thomassen's result, cf., 2 , 3 , 9 - 13 . In particular, Kawarabayashi 12 proved that any k‐connected graph without K subgraphs contains either a contractible edge or a contractible triangle. In this article, we further extend these results, and prove the following result. Let k be an integer with k ≥ 6. If G is a k‐connected graph such that G does not contain as a subgraph and G does not contain as an induced subgraph, then G has either a contractible edge which is not contained in any triangle or a contractible triangle. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:97–109, 2008     

Effect of triaxial stress constraint on the deformation and fracture of polymers

One purpose of this paper is to give a brief overview on the research status of deformation, fracture and toughening mechanisms of polymers, including experimental, theoretical and numerical studies. Emphasis is on the more recent progresses of micromechanics of rubber particle cavitation and crazing, and the development of fracture criteria for ductile polymers. The other purpose is to study the effect of triaxial stress constraint on the deformation and fracture behavior of polymers. Polycarbonate (PC), acrylonitrile-butadienestyrene (ABS) and PC/ABS alloy are considered in this investigation. A series of circumferentially blunt-notched bars are used to experimentally generate different triaxial stress fields. The fracture surfaces of specimens with different notch radius are examined by scanning electron microscope (SEM) to study the fracture and toughening mechanisms of polymer alloy. It is shown that the triaxial stress constraint has a significant effect on the deformation, fracture and toughening of PC, ABS and PC/ABS alloy. We will also discuss the extent to which a micromechanics criterion proposed by the first author can serve as a fracture criterion for ductile polymers. A new ductile fracture parameter is emphasized, which can be employed to evaluate the fracture ductility of polymers. Stress state independence of the parameter for the PC, ABS and PC/ABS alloy has been experimentally verified. The project supported by the National Natural Science Foundation of China (10125212), the Trans-Century Training Program Foundation and the Key Research Fund of the Education Ministry of China (01159)