Non-Commutative Martingale Inequalities

We prove the analogue of the classical Burkholder-Gundy inequalites for non-commutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an L ^p -martingale via its integrand, and then extend the Ito-Clifford integral theory in L ², developed by Barnett, Streater and Wilde, to L ^p for all 1<p<∞. We include an appendix on the non-commutative analogue of the classical Fefferman duality between $H ¹ and BMO. Received: 20 March 1997 / Accepted: 21 March 1997     

Embedding of C q and R q into noncommutative L p -spaces, 1≤p<q≤2

We prove that a quotient of a subspace of C_p⊕_pR_p (1≤p<2) embeds completely isomorphically into a noncommutative L_p -space, where C_p and R_p are respectively the p-column and p-row Hilbertian operator spaces. We also represent C_q and R_q (p<q≤2) as quotients of subspaces of C_p⊕_pR_p. Consequently, C_q and R_q embed completely isomorphically into a noncommutative L_p (M). We further show that the underlying von Neumann algebra M cannot be semifinite.     

Harmonic Analysis on Quantum Tori

This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded L _p Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman’s H₁-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory.     

高温气体热化学反应的DSMC微观模型分析

热化学耦合的非平衡现象一直是高温气体热化学问题研究的难点, 制约了诸如爆轰波胞格结构、低温点火速率等现象的分析. 本文以高温氮气离解和氢氧燃烧中的链式置换反应为例, 从微观反应概率、振动态指定的反应速率、热力学非平衡态的宏观反应速率、碰撞后的能量再分配等角度, 分析了直接蒙特卡罗模拟中的典型化学反应模型(TCE, VFD, QK模型)的微观动力学性质. 研究发现, 无论是高活化能的高温离解反应还是低活化能的链式置换反应, 实际参与反应的分子的振动能概率分布都偏离了平衡态的Boltzmann分布, 包含较强振动能额外影响的VFD模型可以很好地模拟高温离解反应, 而TCE (VFD的一个特例)和QK模型对活化能较低的链式置换反应的预测效果相对更好. 此外, 化学反应碰撞后的能量再分配应遵循微观细致平衡原理, 细微的偏差都可能造成平动能和振动能难以达到最终的平衡状态. 直接蒙特卡罗模拟的应用评估结果表明, 化学反应的振动倾向对热化学耦合过程产生了明显的影响, 特别是由于高振动能分子更多地参与了化学反应, 气体平均振动能的下降将影响后续化学反应的进行.      

放电等离子体技术在固态生物质聚合中的应用

本文介绍了高电压放电等离子体技术在生物质高分子聚合中的应用及机理,提出了把等离子体聚合技术应用于固体高分子生物质中,拓宽了等离子体聚合的应用范围及聚合产物的形态,讨论了在实现生物质等离子体聚合中,固体高分子原料聚合需要解决的问题,并就等离子体聚合在这方面的应用进展状况进行了扼要介绍,同时对其发展前景进行了展望。     

The strongp-variation of martingales and orthogonal series

Let 1p< and letx=(x _n)n0 be a sequence of scalars. The strongp-variation ofx, denoted byW _p (x), is defined as

Fuzzy压缩原理

本文给出以Ｆｕｚｚｙ数作为Ｌｉｐｓｃｈｉｔｚ常数的压缩映射的新概念，并成功证明了Ｆｕｚｚｙ数值函数的不动点定理。     

Effects of mesh resolution on hypersonic heating prediction

Aeroheating prediction is a challenging and critical problem for the design and optimization of hypersonic vehicles. One challenge is that the solution of the Navier-Stokes equations strongly depends on the computational mesh. In this letter, the effect of mesh resolution on heat flux prediction is studied. It is found that mesh-independent solutions can be obtained using fine mesh, whose accuracy is confirmed by results from kinetic particle simulation. It is analyzed that mesh-induced numerical error comes mainly from the flux calculation in the boundary layer whereas the temperature gradient on the surface can be evaluated using a wall function. Numerical schemes having strong capability of boundary layer capture are therefore recommended for hypersonic heating prediction.     

Representation of certain homogeneous Hilbertian operator spaces and applications

Following Grothendieck’s characterization of Hilbert spaces we consider operator spaces F such that both F and F ^* completely embed into the dual of a C*-algebra. Due to Haagerup/Musat’s improved version of Pisier/Shlyakhtenko’s Grothendieck inequality for operator spaces, these spaces are quotients of subspaces of the direct sum C ⊕ R of the column and row spaces (the corresponding class being denoted by QS(C ⊕ R)). We first prove a representation theorem for homogeneous F∈QS(C ⊕ R) starting from the fundamental sequences $\Phi _{c}(n)=\Bigg\|\sum_{k=1}^ne_{k1}\otimes e_k\Bigg\|_{C\otimes _{\min}F}^2\quad\mbox{and}\quad \Phi _{r}(n)=\Bigg\|\sum_{k=1}^ne_{1k}\otimes e_k\Bigg\|_{R\otimes _{\min}F}^2$ given by an orthonormal basis (e _k ) of F. Under a mild regularity assumption on these sequences we show that they completely determine the operator space structure of F and find a canonical representation of this important class of homogeneous Hilbertian operator spaces in terms of weighted row and column spaces. This canonical representation allows us to get an explicit formula for the exactness constant of an n-dimensional subspace F _n of F: $\mathit{ex}(F_n)\sim\biggl[\frac{n}{ \Phi _{c}(n)}\Phi _{r}\bigg(\frac{ \Phi _{c}(n)}{\Phi _{r}(n)}\bigg)+\frac{n}{ \Phi _{r}(n)}\Phi _{c}\bigg(\frac{ \Phi _{r}(n)}{\Phi _{c}(n)}\bigg)\biggr]^{1/2}.$ In the same way, the projection (=injectivity) constant of F _n is explicitly expressed in terms of Φ _c and Φ _r too. Orlicz space techniques play a crucial role in our arguments. They also permit us to determine the completely 1-summing maps in Effros and Ruan’s sense between two homogeneous spaces E and F in QS(C ⊕ R). The resulting space Π ₁ ^o (E,?F) isomorphically coincides with a Schatten-Orlicz class S _φ . Moreover, the underlying Orlicz function φ is uniquely determined by the fundamental sequences of E and F. In particular, applying these results to the column subspace C _p of the Schatten p-class, we find the projection and exactness constants of C _p ⁿ , and determine the completely 1-summing maps from C _p to C _q for any 1≤p,?q≤∞.