曲边区域上的多边形网格间断有限元离散及其多重网格算法

本文利用多边形网格上的间断有限元方法离散二阶椭圆方程,在曲边区域上,采用多条直短边逼近曲边的以直代曲的策略,实现了高阶元在能量范数下的最优收敛.本文还将这一方法用于带曲边界面问题的求解,同样得到高阶元的最优收敛.此外我们还设计并分析了这一方法的\linebreakW-cycle和Variable V-cycle多重网格预条件方法,证明当光滑次数足够多时,多重网格预条件算法一致收敛.最后给出了数值算例,证实该算法的可行性并验证了理论分析的结果.     

静脉血流动力学模型基本波的相互作用北大核心CSCD

静脉系统是心血管系统的重要组成部分.脉搏波在血液流动中有着突出的重要性.本文主要研究静脉血流动力学模型基本波的相互作用.血流动力学模型是2×2严格双曲型方程组,其基本波包括疏散波和激波,属于血液流动中的脉搏波.基本波相互作用后血管截面面积和血流速度发生相应的变化.     

Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes,II

Acta Mathematica Sinica, English Series - This paper is a continuation of our recent paper (Electron. J. Probab., 24(141), (2019)) and is devoted to the asymptotic behavior of a class of...     

A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy

Methodology and Computing in Applied Probability - Risk measures for tail risk have an important application in the dynamic portfolio insurance strategies. We propose a new risk measure called...     

On the relative Wall-Witt groups

LetR* be a simplicial involutive ring. According to certain involutions onK(R*) and _ε L R _∗, there are 1/2-local splittings and . It is known [2] that _ε L _\ga ^α R _∗, the Wall-Witt group. SupposeI→R S is a split extension of discrete involutive rings withI ²=0, andI is a freeS-bimodule. Then we have and . The trace map Tr: Prim _n ∧*M(I ⊗ ℚ)→ ₀ ρ _n ;I ⊗ ℚ) is an isomorphism. We prove in Lemma 1 that the trace map Tr is ℤ/2-equivariant. In Theorem 2 we show that under a certain assumption the rational relative Wall-Witt group vanishes. Theorem 2 can be extended to a more general case (Theorem 3) by employing Goodwillie’s reduction technique [3]. This work was partially supported by KOSEF under Grant 923-0100-010-1.     

Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

Summary We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n–1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1pn, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n–p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.