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21.
《中国化学快报》1999,(8)
Previouspublications'fromourlaboratoryhadreportedtheringenlargementreactionofquatemaryarnrnoniumsaltSofN-methyl-tetTahydroisoquinolinefollowedbyreductivedecyanationwiththenetresuItoftheinserti0nofanextraCH2group,assh0wninSckemeI.ThemethodologyfailedwithsomenatUrallyoccurringalkaloidssuchascephalotaxineandatropine'.Onereasonisthatsomeofthequaternaryammoniumsaltsaredifficulttoprepare,theotheroneisthatsome0fthequaternaryafnmoniumsaItsunderwentHofinarineliminationorSofnmeletrearrangement'.But… 相似文献
22.
We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, an approximate extragradient-type step is performed using information obtained from an approximate solution of a proximal point subproblem. The algorithm is of a hybrid type, as it combines steps of the extragradient and proximal methods. Furthermore, the algorithm uses elements in the enlargement (proposed by Burachik, Iusem and Svaiter) of the operator defining the problem. One of the important features of our approach is that it allows significant relaxation of tolerance requirements imposed on the solution of proximal point subproblems. This yields a more practical proximal-algorithm-based framework. Weak global convergence and local linear rate of convergence are established under suitable assumptions. It is further demonstrated that the modified forward-backward splitting algorithm of Tseng falls within the presented general framework. 相似文献
23.
Karl-Georg Schlesinger 《Acta Appl Math》1997,49(1):35-54
It is known that it is not possible to introduce C0 -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rn. Classically these amount to considering the space of all systems on a given subset of Rn as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there. 相似文献
24.
Ron Buckmire 《Numerical Methods for Partial Differential Equations》2004,20(3):327-337
The boundary value problem Δu + λeu = 0 where u = 0 on the boundary is often referred to as “the Bratu problem.” The Bratu problem with cylindrical radial operators, also known as the cylindrical Bratu‐Gelfand problem, is considered here. It is a nonlinear eigenvalue problem with two known bifurcated solutions for λ < λc, no solutions for λ > λc and a unique solution when λ = λc. Numerical solutions to the Bratu‐Gelfand problem at the critical value of λc = 2 are computed using nonstandard finite‐difference schemes known as Mickens finite differences. Comparison of numerical results obtained by solving the Bratu‐Gelfand problem using a Mickens discretization with results obtained using standard finite differences for λ < 2 are given, which illustrate the superiority of the nonstandard scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 327–337, 2004 相似文献
25.
Ronald E. Mickens P. M. Jordan 《Numerical Methods for Partial Differential Equations》2004,20(5):639-649
A positivity‐preserving nonstandard finite difference scheme is constructed to solve an initial‐boundary value problem involving heat transfer described by the Maxwell‐Cattaneo thermal conduction law, i.e., a modified form of the classical Fourier flux relation. The resulting heat transport equation is the damped wave equation, a PDE of hyperbolic type. In addition, exact analytical solutions are given, special cases are mentioned, and it is noted that the positivity condition is equivalent to the usual linear stability criteria. Finally, solution profiles are plotted and possible extensions to a delayed diffusion equation and nonlinear reaction‐diffusion systems are discussed. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. 相似文献
26.
We design and analyze an unconditionally convergent nonstandard finite-difference method to study transmission dynamics of a mathematical model of HIV-TB co-infection. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves positivity of the solution which is one of the essential requirements when modelling epidemic diseases. Furthermore, we show that the numerical method is unconditionally stable. Competitive numerical results confirming theoretical investigations are provided. Comparisons are also made with other conventional approaches that are routinely used to solve these types of problems. 相似文献
27.
In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. To allow for mutual dependence between the financial and the insurance markets, we use the progressive enlargement of filtration approach. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor that also influences the mortality rate of the policyholder. We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk–Kunita–Watanabe decomposition of the insurance claim with respect to the minimal martingale measure and the available information flow. We provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure. Finally, we discuss applications in a Markovian setting via filtering. 相似文献
28.
Zhen ZhangMin Shi 《Tetrahedron letters》2011,52(49):6541-6544
Titanium(IV) chloride-mediated intramolecular ring enlargement of methylenecyclopropanes with propargylic esters has been described in this context, affording the corresponding chlorinated bicyclo[4.2.0]oct-5-ene derivatives in moderate to good yields under mild conditions. The E- and Z-methylenecyclopropanes could all be converted to the corresponding bicyclo[4.2.0]oct-5-enes with moderate to high diastereoselectivities. 相似文献
29.
For a given filtered probability space (Ω,F,P), an F-adapted continuous increasing process Λ and a positive P-F local martingale N such that Λ0=0 and Nte−Λt≤1, we construct a probability measure QZ and a random time τ such that Q|F∞=P|F∞ and Q[τ>t|Ft]=Zt. The probability QZ is linked with the well-known Cox model by an explicit density function. Various properties exist, which characterize QZ from others. Let G=(Gt)t≥0 with Gt=Ft∨σ({τ≤s}:s≤t). We establish the (H′)-property between the filtrations F and G, and we provide the enlargement of filtration formula. 相似文献
30.
Liping Liu Dominic P. Clemence Ronald E. Mickens 《Numerical Methods for Partial Differential Equations》2011,27(4):767-785
This study focuses on a contaminant transport model with Langmuir sorption under nonequilibrium conditions. The numerical instabilities of the standard finite difference schemes including the upwind method are investigated. By using the nonstandard finite difference method, a better finite difference model is constructed. The numerical simulation on a specific system configuration proves the advantages of the new finite difference model. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 767–785, 2011 相似文献