具线性退化特征场对角型方程组Goursat问题的奇性形成机制

For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.     

N+2原子受简并双光子作用时的纠缠动力学

研究了N+2（其中N个原子与光场非共振作用,2个原子与光场共振作用）原子受简并双光子作用的纠缠动力学,得到2个共振原子的纠缠度的解析表达式。结果表明：在简并双光子作用下,纠缠度的时间演化出现有规则的崩塌回复现象,并且崩塌回复周期比单光子作用下时要短。此外,N+2原子与光场间的相对耦合系数对简并双光子情形下的纠缠度有更灵敏的影响。     

On the Properties of the Solution of a Strongly Degenerate Parabolic Equation

ＯｎｔｈｅＰｒｏｐｅｒｔｉｅｓｏｆｔｈｅＳｏｌｕｔｉｏｎｏｆａＳｔｒｏｎｇｌｙＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎＣｈｅｎｇＦｕｘｉａ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔ...     

SOURCE－TYPE SOLUTIONS OF A QUASILINEAR DEGENERATE PARABOLIC EQUATION WITH ABSORPTION

ＳＯＵＲＣＥ－ＴＹＰＥ ＳＯＬＵＴＩＯＮＳ ＯＦ Ａ ＱＵＡＳＩＬＩＮＥＡＲ ＤＥＧＥＮＥＲＡＴＥ ＰＡＲＡＢＯＬＩＣ ＥＱＵＡＴＩＯＮ ＷＩＴＨ ＡＢＳＯＲＰＴＩＯＮ￥ＺＨＡＯＪＵＮＮＩＮＧＡｂｓｔｒａｃｔ：Ｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｎｏｎｅｘ...     

Stability in the presence of degeneracy and error estimation

Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998     

Organometallic mediated radical polymerization of vinyl acetate with Fe(acac)2

The radical polymerization of vinyl acetate (VAc) is moderated by iron(II) acetylacetonate (Fe(acac)₂) by the organometallic route (OMRP), as well as by degenerative transfer polymerization (DTP) when in the presence of excess radicals, through the formation of thermally labile organometallic Fe^III dormant species. The poly(vinyl acetate) (PVAc)‐Fe^III(acac)₂ dormant species has been isolated in the form of an oligomer and characterized by ¹H NMR, EPR, and IR methods, and then used as a single‐component initiator for the OMRP of VAc. The degree of polymerization of this isolated oligomeric species demonstrates the limited ability of Fe(acac)₂, relative to the Co(acac)₂ congener, to rapidly trap the growing PVAc radical chain. Control under OMRP conditions is improved by the presence of Lewis bases, especially PMe₂Ph. On the other hand, iron(II) phthalocyanine inhibits the radical polymerization of VAc completely. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 3494–3504     

Comparison theorems for diffusion processes

We prove comparison theorems for diffusion processes onR ^d. From these theorems we derive lower and upper bounds for the transition probabilities of a diffusion process. In contrast to the known estimates for fundamental solutions of parabolic equations our bounds do not depend on the moduli of continuity of the coefficients of the differential operator.     

Continuous dependence estimates for viscosity solutions of integro-PDEs

We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. Moreover, these explicit estimates are used to prove regularity results and rates of convergence for some singular perturbation problems. Finally, we illustrate our results on some integro-PDEs arising when attempting to price European/American options in an incomplete stock market driven by a geometric Lévy process. Many of the results obtained herein are new even in the convex case where stochastic control theory provides an alternative to our pure PDE methods.     

Λ型原子与单模光场的非共振作用制备四光子相干态

根据简并Λ型三能级原子与单模光场的改进型有效哈密顿量 ,通过矩阵形式法推导出原子光场系统的波函数 ,提出利用简并Λ型三能级原子与单模光场的远离共振相互作用制备四光子相干态的有效方案。并且证明按照同样的方法不能制备出四成分以上的相干叠加态 ,即当在腔中注入的第三个原子的速度与第二个原子的速度相等时 ,腔场将保持这种四光子相干叠加态不变