On the Hochschild cohomology ring of tensor products of algebras

We prove that, as Gerstenhaber algebras, the Hochschild cohomology ring of the tensor product of two algebras is isomorphic to the tensor product of the respective Hochschild cohomology rings of these two algebras, when at least one of them is finite dimensional. In case of finite dimensional symmetric algebras, this isomorphism is an isomorphism of Batalin–Vilkovisky algebras. As an application, we explain by examples how to compute the Batalin–Vilkovisky structure, in particular, the Gerstenhaber Lie bracket, over the Hochschild cohomology ring of the group algebra of a finite abelian group.     

Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks

In this paper, we investigate an optimal reinsurance and investment problem for an insurer whose surplus process is approximated by a drifted Brownian motion. Proportional reinsurance is to hedge the risk of insurance. Interest rate risk and inflation risk are considered. We suppose that the instantaneous nominal interest rate follows an Ornstein–Uhlenbeck process, and the inflation index is given by a generalized Fisher equation. To make the market complete, zero-coupon bonds and Treasury Inflation Protected Securities (TIPS) are included in the market. The financial market consists of cash, zero-coupon bond, TIPS and stock. We employ the stochastic dynamic programming to derive the closed-forms of the optimal reinsurance and investment strategies as well as the optimal utility function under the constant relative risk aversion (CRRA) utility maximization. Sensitivity analysis is given to show the economic behavior of the optimal strategies and optimal utility.     

Optimal investment and risk control policies for an insurer: Expected utility maximization

Motivated by the AIG bailout case in the financial crisis of 2007–2008, we consider an insurer who wants to maximize his/her expected utility of terminal wealth by selecting optimal investment and risk control strategies. The insurer’s risk process is modeled by a jump-diffusion process and is negatively correlated with the capital gains in the financial market. We obtain explicit solutions of optimal strategies for various utility functions.     

GSOR方法最优迭代参数的简化推导

对于增广线性系统,Bai等研究了广义SOR方法（Bai Z Z,Parlett B,Wang Z Q.On generaliged successive overrelaxation methods for augmented linear systems.Numerische Mathematik,2005,102（1）：1-38）,并得到其最优迭代参数.给出了另外一种推导最优迭代参数的简化方法,这种方法对于求解其他参数加速定常迭代方法的最优迭代参数非常有意义.     

Hierarchically penalized additive hazards model with diverging number of parameters

In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.     

Synthesis and photoresponsive behavior of azobenzene‐containing side‐chain liquid crystalline diblock polymers with polypeptide block

Well‐defined azobenzene‐containing side‐chain liquid crystalline diblock copolymers composed of poly[6‐(4‐methoxy‐azobenzene‐4′‐oxy) hexyl methacrylate] (PMMAZO) and poly(γ‐benzyl‐L ‐glutamate) (PBLG) were synthesized by click reaction from alkyne‐ and azide‐functionalized homopolymers. The alkyne‐terminated PMMAZO homopolymers were synthesized by copper‐mediated atom transfer radical polymerization with a bromine‐containing alkyne bifunctional initiator, and the azido‐terminated PBLG homopolymers were synthesized by ring‐opening polymerization of γ‐benzyl‐L ‐glutamate‐N‐carboxyanhydride in DMF at room temperature using an amine‐containing azide initiator. The thermotropic phase behavior of PMMAZO‐b‐PBLG diblock copolymers in bulk were investigated using differential scanning calorimetry and polarized light microscopy. The PMMAZO‐b‐PBLG diblock copolymers exhibited a smectic phase and a nematic phase when the weight fraction of PMMAZO block was more than 50%. Photoisomerization behavior of PMMAZO‐b‐PBLG diblock copolymers and the corresponding PMMAZO homopolymers in solid film and in solution were investigated using UV–vis. In solution, trans–cis isomerization of diblock copolymers was slower than that of the corresponding PMMAZO homopolymers. These results may provide guidelines for the design of effective photoresponsive anisotropic materials. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

How a Zigzag Carbon Nanotube Grows

Owing to the unique structure of zigzag (ZZ) carbon nanotubes (CNTs), their ring‐by‐ring growth behavior is different from that of chiral or armchair (AC) CNTs, on the rims of which kinks serve as active sites for carbon attachment. Through first‐principle calculations, we found that, because of the high energy barrier of initiating a new carbon ring at the rim of a ZZ CNT, the growth rate of a ZZ CNT is proportional to its diameter and significantly (10–1000 times) slower than that of other CNTs. This study successfully explained the broad experimental observation of the lacking of ZZ CNTs in CNT samples and completed the theory of CNT growth.     

High Catalytic Activity of Nitrogen and Sulfur Co‐Doped Nanoporous Graphene in the Hydrogen Evolution Reaction

Chemical doping has been demonstrated to be an effective way to realize new functions of graphene as metal‐free catalyst in energy‐related electrochemical reactions. Although efficient catalysis for the oxygen reduction reaction (ORR) has been achieved with doped graphene, its performance in the hydrogen evolution reaction (HER) is rather poor. In this study we report that nitrogen and sulfur co‐doping leads to high catalytic activity of nanoporous graphene in HER at low operating potential, comparable to the best Pt‐free HER catalyst, 2D MoS₂. The interplay between the chemical dopants and geometric lattice defects of the nanoporous graphene plays the fundamental role in the superior HER catalysis.