summation

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summation

1. the act or process of determining a sum; addition
2. the result of such an act or process
3. US law the concluding statements made by opposing counsel in a case before a court

Summation

 

in physiology, the cumulative effect of several stimuli following one another in rapid succession (temporal summation) or occurring simultaneously (spatial summation) and arising in such excitable structures as receptors, neurons, and muscles.

Summation was first described in 1868 by I. M. Sechenov, who observed that under certain conditions of rhythmic stimulation there was a delay in the appearance and subsequent intensification of reflexes. Temporal summation occurs in the intervals between stimuli. These intervals are limited by the period of subthreshold or trace shifts in membrane potential toward depolarization, with development of excitation, or toward hyper-polarization, with development of inhibition. Temporal summation ensures that the duration of the reaction will be sufficient and that it can be maintained by the circular relationship between the neurons.

Spatial summation changes continuously and is manifested by the simultaneous excitation or inhibition of many neurons in different parts of the brain as well as of numerous synapses in a single neuron. Summation helps to intensify individual reactions and to coordinate the body’s reactions. In muscles, spatial summation intensifies contractions by increasing the number of excited motor units, that is, groups of fibers innervated by a single neuron. Temporal summation in muscles induces tetanus by uniting successive individual contractions.

A. N. KABANOV

References in periodicals archive ?
The closed form expressions for the infinite summation over odd integers for sin(nz) divided odd powers of n and also for cos(nz) divided even powers of n are:
Jain, "Midpoint summation: A method for accurate and efficient summation of series appearing in electromagnetics," IEEE Antennas and Wireless Propagation Letters, Vol.
Song, "Numerical acceleration of spectral domain approach for shielded microstrip lines by approximating summation with corrected integral," IEEE Electrical Performance of Electronic Packaging and Systems, Oct.
These investigations were exclusively devoted to the derivation of summation formulae (which quite surprisingly even exist in the noncommutative case), aiming to build up a theory of explicit identities analogous to the rich theory of identities for hypergeometric and basic hypergeometric series in the classical, commutative case (cf.
In this paper, we define noncommutative bilateral basic hypergeometric series of type I and type II (over an abstract unital Banach algebra R) and prove, using functional equations, noncommutative extensions of Ramanujan's [sup.1][[psi].sub.1] summation. These generalize the noncommutative Q-binomial theorem of [14, Th.
Unfortunately, Ramanujan (who very rarely gave any proofs) did not provide a proof of the above bilateral summation. The first proof of (2.4) was given by Hahn [7, [kappa] = 0 in Eq.
The presentation of a summation must be consistent with the rest of the trial, and it must meet the expectations of the jury.
Any summation longer than 30 to 45 minutes risks losing its audience.
It would be interesting, he adds, to give summation tests to chimps with no language training.
Summation may be a primitive link inthe developmental chain of counting skills, says Rumbaugh.
If we sum an expression such as 2[X.sub.i], where 2 is a constant and [X.sub.i] is a variable, written [summation]2[X.sub.i], then we may factor the constant outside of the summation and write it as 2[summation][X.sub.i].
The summation sign distributes over an expression in parentheses.