不含三角形图的正常染色路和正常染色圈

图G为边染色图,对G中的任一顶点v,定义v的色度dc（v）：G中与顶点v相关联的边中不同染色的数目.用δc（G）表示图G的最小色度,即δc（G）=min{dc（v）：v∈G}.若图G为不含三角形的边染色图,且δc（G）≥2,则G含长为4d-2的正常染色路或长至少为2d-2的正常染色圈.     

Ideal Structure of Leavitt Path Algebras with Coefficients in a Unital Commutative Ring

For a (countable) graph E and a unital commutative ring R, we analyze the ideal structure of the Leavitt path algebra L _R (E) introduced by Mark Tomforde. We first modify the definition of basic ideals and then develop the ideal characterization of Mark Tomforde. We also give necessary and sufficient conditions for the primeness and the primitivity of L _R (E), and we then determine prime graded basic ideals and left (or right) primitive graded ideals of L _R (E). In particular, when E satisfies Condition (K) and R is a field, they imply that the set of prime ideals and the set of primitive ideals of L _R (E) coincide.     

On the Simplicity of the Lie Algebra of a Leavitt Path Algebra

For a field F and a row-finite directed graph Γ, let L(Γ) be the associated Leavitt path algebra. We find necessary and sufficient conditions for the Lie algebra [L(Γ), L(Γ)] to be simple.     

ConvexLAR: An Extension of Least Angle Regression

The least angle regression (LAR) was proposed by Efron, Hastie, Johnstone and Tibshirani in the year 2004 for continuous model selection in linear regression. It is motivated by a geometric argument and tracks a path along which the predictors enter successively and the active predictors always maintain the same absolute correlation (angle) with the residual vector. Although it gains popularity quickly, its extensions seem rare compared to the penalty methods. In this expository article, we show that the powerful geometric idea of LAR can be generalized in a fruitful way. We propose a ConvexLAR algorithm that works for any convex loss function and naturally extends to group selection and data adaptive variable selection. After simple modification, it also yields new exact path algorithms for certain penalty methods such as a convex loss function with lasso or group lasso penalty. Variable selection in recurrent event and panel count data analysis, Ada-Boost, and Gaussian graphical model is reconsidered from the ConvexLAR angle. Supplementary materials for this article are available online.     

Connectivity and minimal distance spectral radius of graphs

In this article, we study how the distance spectral radius behaves when the graph is perturbed by grafting edges. As applications, we also determine the graph with k cut vertices (respectively, k cut edges) with the minimal distance spectral radius.     

倒向随机微分方程与巴黎期权的非线性定价

巴黎期权是一种复杂的奇异期权. 本文基于倒向随机微分方程, 定义了巴黎期权的非线性价格过程, 分析其性质, 并且给出巴黎期权非线性定价的偏微分方程表达式. 在金融市场收益率不确定的情形以及存贷利率不同的情形下分别对连续巴黎期权进行定价和具体的数值分析, 结论显示巴黎期权的非线性定价机制更具合理性.     

Correlation Inequalities and Applications to Vector-Valued Gaussian Random Variables and Fractional Brownian Motion

In this paper we extend certain correlation inequalities for vector-valued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a correlation assumption, we prove a Borel-Cantelli lemma, maximal inequalities and several laws of large numbers. This extends results of Be?ka and Ciesielski and of Hytönen and the author. In the second part of the paper we consider a certain class of vector-valued Gaussian processes which are α-Hölder continuous in p-th moment. For these processes we obtain Besov regularity of the paths of order α. We also obtain estimates for the moments in the Besov norm. In particular, the results are applied to vector-valued fractional Brownian motions. These results extend earlier work of Ciesielski, Kerkyacharian and Roynette and of Hytönen and the author.