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101.
Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois. 相似文献
102.
通过几何过渡方法,结合重新标度连续概念,利用隐式曲面与参数曲面的各自等距曲面的交线,构成隐式曲面与参数曲面问的过渡面.用曲面的隐式与隐式、参数与参数形式,证明了所作的过渡面与给出的隐式曲面与参数曲面在连接线处是G^3连接的。 相似文献
103.
Thierry Coulhon 《Potential Analysis》1992,1(4):343-353
One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L
1–L
norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.
Cet article a pu être terminé pendant un séjour de l'auteur à l'université d'Edimbourg. 相似文献
104.
105.
CheeWhye Chin 《Advances in Mathematics》2003,180(1):64-86
Let X be a smooth curve over a finite field of characteristic p, let ?≠p be a prime number, and let be an irreducible lisse -sheaf on X whose determinant is of finite order. By a theorem of L. Lafforgue, for each prime number ?′≠p, there exists an irreducible lisse -sheaf on X which is compatible with , in the sense that at every closed point x of X, the characteristic polynomials of Frobenius at x for and are equal. We prove an “independence of ?” assertion on the fields of definition of these irreducible ?′-adic sheaves : namely, that there exists a number field F such that for any prime number ?′≠p, the -sheaf above is defined over the completion of F at one of its ?′-adic places. 相似文献
106.
We describe special asymptotic structures of solutions of the semilinear heat equation
107.
Tai-Peng Tsai 《Journal of Differential Equations》2003,192(1):225-282
We consider a nonlinear Schrödinger equation with a bounded localized potential in . The linear Hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions. Suppose that the initial data is localized and small of order n in H1, and that its ground state component is larger than n3−ε with ε>0 small. We prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity. 相似文献
108.
ICP-AES法分析水质的探讨 总被引:1,自引:0,他引:1
本文用ICP-AES(电感耦合等离子体-原子发射光谱法)测定水中Al、B、Ba、Be、Ca、Cd、Co、Cr、Cu、Fe、Mg、Mo、Mn、Ni、Pb、Sr、V、Zn等18种微量元素。方法简便、快速,只将样品简单酸化,即可测定。方法检出限为0.0005-0.5μg/mL。相对标准偏差<18% 相似文献
109.
We prove that if $f:X \to Y$ is a surjective,
cohomologically (k - 1)-connected and
proper map between locally compact spaces, then for the cohomological descent
spectral sequence one has $E^{pq}_{2} = 0$ provided $q < pk$. 相似文献
110.
In this paper, we show that the discrete GI/G/1 system can be easily analysed as a QBD process with infinite blocks by using the elapsed time approach in conjunction with the Matrix-geometric approach. The positive recurrence of the resulting Markov chain is more easily established when compared with the remaining time approach. The G-measure associated with this Markov chain has a special structure which is usefully exploited. Most importantly, we show that this approach can be extended to the analysis of the GI
X
/G/1 system. We also obtain the distributions of the queue length, busy period and waiting times under the FIFO rule. Exact results, based on computational approach, are obtained for the cases of input parameters with finite support – these situations are more commonly encountered in practical problems. 相似文献