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## Deferred Corrections Software and Its Application to Seismic Ray Tracing

### Defect Correction Methods (1984-01-01) 5: 211-226 , January 01, 1984

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.

## Estimates for the Levy-Prokhorov distance in terms of characteristic functions and some of their applications

### Journal of Soviet Mathematics (1984-12-01) 27: 3070-3083 , December 01, 1984

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.

## On numerical computation of singular integrals

### BIT Numerical Mathematics (1984-03-01) 24: 113-116 , March 01, 1984

## Algèbres Symétriques et Singularités

### Annali dell’Università di Ferrara (1984-12-01) 30: 1-10 , December 01, 1984

### Riassunto

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.

## On the uniqueness of solutions of a certain characteristic Cauchy problem

### Annals of Global Analysis and Geometry (1984-06-01) 2: 153-162 , June 01, 1984

The question of uniqueness of solutions of the global Cauchy problem (1)–(2) below is discussed. We assume that there exists a complex constant c such that the modified equation $$\frac{{\partial ^2 u}}{{\partial t^2 }} = c_{\left| \alpha \right| \leqq 2} \sum a_\alpha (x) D_x^\alpha u$$ becomes hyperbolic. Under this and some other additional conditions (See Condition A in §2) we prove the uniqueness of solutions of the Cauchy problem within the class of functions u(t, x) such that $$|u(t,x)| \leqq C exp(a|x|^2 ) ,$$ C and a being positive constants

## Connection between the law of large numbers for squares and the law of the iterated logarithm

### Journal of Soviet Mathematics (1984-12-01) 27: 3054-3058 , December 01, 1984

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.

## The enzymatic neuron as a reaction-diffusion network of cyclic nucleotides

### Bulletin of Mathematical Biology (1984-09-01) 46: 765-783 , September 01, 1984

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.

## Integrabilidade das distribuições dadas por subalgebras de lie de codimensão finita no gh(n,C)

### Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society (1984-03-01) 15: 97-100 , March 01, 1984

## Uncertainty in the solution of linear operator equations

### BIT Numerical Mathematics (1984-03-01) 24: 92-101 , March 01, 1984

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.

## Bayesian Sequential Analysis of Multivariate Point Processes

### Premium Calculation in Insurance (1984-01-01) 121: 475-487 , January 01, 1984

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.