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## On a table of the product-sum partition functionp(n, m)

### BIT Numerical Mathematics (1976-12-01) 16: 374-377 , December 01, 1976

A recurrence relation for the restricted partition function*p*(*n,m*) which denotes the number of partitions of a positive integer*n* such that the product of all the summands in each partition is*m* is given. The function*p*(*n,m*) is tabulated for*n* and*m* in the range 1,2,..., 100.

## Convergence of linear multistep methods for differential equations with discontinuities

### Numerische Mathematik (1976-03-01) 27: 1-10 , March 01, 1976

### Summary

A new stability functional is introduced for analyzing the stability and consistency of linear multistep methods. Using it and the general theory of [1] we prove that a linear multistep method of design order*q*≧*p*≧1 which satisfies the weak stability root condition, applied to the differential equation*y′ (t)*=*f (t, y (t))* where*f* is Lipschitz continuous in its second argument, will exhibit actual convergence of order*o*(*h*^{p−1}) if*y* has a (*p*−1)th derivative*y*^{(p−1)} that is a Riemann integral and order*o(h*^{p}) if*y*^{(p−1)} is the integral of a function of bounded variation. This result applies for a function*y* taking on values in any real vector space, finite or infinite dimensional.

## Cohomology of groups

### Algebraic K-Theory (1976-01-01) 551: 249-259 , January 01, 1976

## Generalized diffusion processes

### Proceedings of the Third Japan — USSR Symposium on Probability Theory (1976-01-01) 550: 500-523 , January 01, 1976

## Finding the nearest point in A polytope

### Mathematical Programming (1976-12-01) 11: 128-149 , December 01, 1976

A terminating algorithm is developed for the problem of finding the point of smallest Euclidean norm in the convex hull of a given finite point set in Euclidean*n*-space, or equivalently for finding an “optimal” hyperplane separating a given point from a given finite point set. Its efficiency and accuracy are investigated, and its extension to the separation of two sets and other convex programming problems described.

## Information Transmission by Model Neurones

### Models of the Stochastic Activity of Neurones (1976-01-01) 12: 334-363 , January 01, 1976

In the models discussed in sections 1 – 12, the idea has been that the experimentally recorded electrical activity of neurones, whether fluctuations in membrane potential, spike discharges or some measure of the activity of neural aggregates, is stochastic, and the problem has been to obtain models which generate a stochastic process with properties similar to the observed samples of activity. These models may be abstract, or may contain parameters and variables which correspond to biophysically measurable quantities, and so the models might give insights into possible mechanisms generating the stochastic activity. In this chapter I will consider a different kind of problem: does the stochastic nature of neural activity have any functional implications?