Application of Relaxation Scheme to Degenerate Variational Inequalities

In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.     

On the cauchy problem for a class of degenerate differential equations with Lipschitz right-hand side

This note deals with an application of the fixed point theorem for multivalued contraction mappings to the study of degenerate differential equations with Lipschitz right-hand side and with degeneration determined by a closed surjective linear operator.     

STUDIES OF MELNIKOV METHOD AND TRANSVERSAL HOMOCLINIC ORBITS IN THE CIRCULAR PLANAR RESTRICTED THREE－BODY PROBLEM

ＳＴＵＤＩＥＳ　ＯＦ　ＭＥＬＮＩＫＯＶ　ＭＥＴＨＯＤ　ＡＮＤ　ＴＲＡＮＳＶＥＲＳＡＬ　ＨＯＭＯＣＬＩＮＩＣ　ＯＲＢＩＴＳ　ＩＮ　ＴＨＥ　ＣＩＲＣＵＬＡＲ　ＰＬＡＮＡＲ　ＲＥＳＴＲＩＣＴＥＤ　ＴＨＲＥＥ－ＢＯＤＹ　ＰＲＯＢＬＥＭＺｈｕＲｕｚｅｎｇ（朱如...     

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