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By Pereyra, V.

5 Citations

We give first a historical account of the various stages of development of iterated deferred corrections software, mainly for ordinary two-point boundary value problems, but mentioning also some work on partial differential equations. Then we describe the latest code on the PASVA series (No. 4), which extends the earlier one to problems with discontinuous data and mixed systems of differential and algebraic conditions. Finally, an example of application of this code to two-point ray tracing on piece-wise continuous media is given.

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By Zaitsev, A. Yu.

3 Citations

One gives estimates of the Levy-Prokhorov distance between distributions in R^{k} in terms of integrals of the differences of the characteristic functions and of their derivatives, similar to Esseen's inequality.

By Bohman, Jan; Fröberg, Carl-Erik

1 Citations

By Escamilla-Castillo, Juan

Scopo di questo articolo è descrivere i generatori per la catena di ideali di Micali associati ad un ideale in un anello commutativo con elemento unità. Applichiamo i nostri risultati allo studio di singolarità di ipersuperfici algebriche.

By Egorov, V. A.

Let {X_{i}} be a sequence of independent random variable with E X_{i}=o, i=1, 2, ..., and let be a sequence of real numbers. Under certain conditions one proves that if a.s.), then a.s.), where.

By Kirby, Kevin G.; Conrad, Michael

23 Citations

Recent evidence suggests that the cyclic nucleotides play a central role in the intracellular processing of neural signals. The dynamics of this system may be seen as a realization of the enzymatic neuron model. Enzymatic neurons are formal neurons which map binary afferent signals into patterns of excitation across an abstract membrane. The distribution of enzyme-like elements called excitases enables a set of local threshold functions to determine the firing activity of the neuron. This paper analyzes the basic properties of enzymatic neurons in a simple continuous-time framework, and shows how they may be presented as reaction-diffusion networks which model the cyclic nucleotide system. We present the results of computer simulations of this neuron and discuss its implications for selectional learning and its relation to conventional two-factor systems. One fundamental property of the reaction-diffusion neuron is its so-called “double-dynamics” property; examination of this property and its contribution to the computing power of the neuron provides some insight into the obscure relation between microscopic and macroscopic models of computation.

By Salvitti, Reinaldo

By Linz, Peter

10 Citations

In this paper we introduce and explore the concept of uncertainty of an approximate solution of a linear operator equation. This uncertainty is a measure of the difference between a computed solution and other plausible answers. When the operator equation is wellposed, the uncertainty is closely related to the more traditional notion of the accuracy of an approximate solution. However, for illposed equations, the uncertainty concept gives a new way of looking at such problems and helps in assessing the meaning of the computed results.

By Rhiel, Raimund

Modern martingale theory is applied to treat the topic of multivariate point processes, e.g. risk processes, multivariate counting processes. The general decision theoretic model of sequential and nonsequential procedures is used to estimate the structural parameters. Likelihood ratios and posterior distributions can always be represented by means of compensators and intensities. It is indicated, how compensators and intensities with respect to the unconditional (collective) probability law can be derived from the compensators and intensities with respect to the conditional (individual) probability laws. Some special loss functions and intensities depending multilinearly on the structural parameters are discussed in detail as examples.

By Banaszczyk, Maria; Banaszczyk, Wojciech

6 Citations

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