Homogeneous factorisations of Johnson graphs

For a graph Γ, subgroups , and an edge partition of Γ, the pair is a (G, M)-homogeneous factorisation if M is vertex-transitive on Γ and fixes setwise each part of , while G permutes the parts of transitively. A classification is given of all homogeneous factorisations of finite Johnson graphs. There are three infinite families and nine sporadic examples. This paper forms part of an ARC Discovery grant of the last two authors. The second author holds an Australian Research Council Australian Research Fellowship.     

Gonality of complete graphs with a small number of omitted edges

Let be the complete metric graph on d vertices. We compute the gonality of graphs obtained from by omitting edges forming a , or general configurations of at most edges. We also investigate if these graphs can be lifted to curves with the same gonality. We lift the former graphs and the ones obtained by removing up to edges not forming a K ₃ using models of plane curves with certain singularities. We also study the gonality when removing edges not forming a K ₃. We use harmonic morphism to lift these graphs to curves with the same gonality because in this case plane singular models can no longer be used due to a result of Coppens and Kato.     

Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes

This a first step to develop a theory of smooth, étale, and unramified morphisms between Noetherian formal schemes. Our main tool is the complete module of differentials, which is, a coherent sheaf whenever the map of formal schemes is of pseudofinite type. Among our results, we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitable closed subsets. We characterize unramifiedness by the vanishing of the module of differentials. Also we see that a smooth morphism of Noetherian formal schemes is flat and its module of differentials is locally free. The article closes with a version of Zariski's Jacobian criterion.     

Existence of Gradings on Associative Algebras

In this article, we study the existence of gradings on finite dimensional associative algebras. We prove that a connected algebra A does not have a nontrivial grading if and only if A is basic, its quiver has one vertex, and its group of outer automorphisms is unipotent. We apply this result to prove that up to graded Morita equivalence there do not exist nontrivial gradings on the blocks of group algebras with quaternion defect groups and one isomorphism class of simple modules.     

Hochschild cohomology of partial relation extensions

We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra.     

Intersection Matrices Revisited

Several intersection matrices of s‐subsets versus k‐subsets of a v‐set are introduced in the literature. We study these matrices systematically through counting arguments and generating function techniques. A number of new or known identities appear as natural consequences of this viewpoint; especially, use of the derivative operator and some related operators reveals some connections between intersection matrices and the “combinatorics of creation‐annihilation.” As application, the eigenvalues of several intersection matrices including some generalizations of the adjacency matrices of the Johnson scheme are derived; two new bases for the Bose–Mesner algebra of the Johnson scheme are introduced and the associated intersection numbers are obtained as well. Finally, we determine the rank of some intersection matrices. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 383–397, 2012     

RiskMetrics模型评估与扩展

RiskMetrics是当今最为流行的风险度量模型,然而其基础假设-标准化收益服从正态分布,却备受置疑.放宽此假设,以更灵活的t分布,广义误差分布,混合正态分布,Johnson Su-正态,Pearson IV分布代替,建立了五种扩展的RiskMetrics模型.我们用沪深股市日收益数据进行实证比较分析,回测结果表明,扩展模型明显优于标准模型,而基于非对称分布假设的模型优于基于对称分布的模型.     

Degrees of irreducible morphisms in generalized standard coherent almost cyclic components

We study the degrees of irreducible morphisms between indecomposable modules lying in generalized standard coherent almost cyclic components of Auslander-Reiten quivers of artin algebras.     

Generation of all carbon quaternary stereocenters at the C-3 carbon of piperidinones and pyrrolidinones and its application in natural product total synthesis

Methodologies regarding the construction of an all carbon quaternary stereocenters at C-3 of lactams have posed significant challenges in the total synthesis of natural products. This review summarizes the advancements for the construction of an all carbon quaternary stereocenters at C-3 of piperidinones and pyrrolidinones and its application in the total synthesis of biologically active and architecturally complex alkaloids.     

Categorical Aspects in Projective Geometry

After introducing morphisms between projective geometries, some categorical questions are examined. It is shown that there are three kinds of embeddings and two kinds of quotients. Furthermore the morphisms decompose in a canonical way into four factors.