Crossword clues for summation
Longman Dictionary of Contemporary English
The Collaborative International Dictionary
Summation \Sum*ma"tion\, n. [Cf. F. sommation. See Sum, v. t.] The act of summing, or forming a sum, or total amount; also, an aggregate.
Of this series no summation is possible to a finite
intellect.
--De Quincey.
Douglas Harper's Etymology Dictionary
1760, "process of calculating a sum," from Modern Latin summationem (nominative summatio) "an adding up," noun of action from Late Latin summatus, past participle of summare "to sum up," from Latin summa (see sum (n.)). Meaning "a summing up" is from 1836.
Wiktionary
n. 1 A summarization. 2 (context mathematics English): An adding up of a series of items.
WordNet
n. a concluding summary (as in presenting a case before a law court) [syn: summing up, rundown]
(physiology) the process whereby multiple stimuli can produce a response (in a muscle or nerve or other part) that one stimulus alone does not produce
the final aggregate; "the sum of all our troubles did not equal the misery they suffered" [syn: sum, sum total]
the arithmetic operation of summing; calculating the sum of two or more numbers; "the summation of four and three gives seven"; "four plus three equals seven" [syn: addition, plus]
Wikipedia
In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid). For finite sequences of such elements, summation always produces a well-defined sum.
The summation of an infinite sequence of values is called a series. A value of such a series may often be defined by means of a limit (although sometimes the value may be infinite, and often no value results at all). Another notion involving limits of finite sums is integration. The term summation has a special meaning related to extrapolation in the context of divergent series.
The summation of the sequence [1, 2, 4, 2] is an expression whose value is the sum of each of the members of the sequence. In the example, = 9. Because addition is associative, the sum does not depend on how the additions are grouped, for instance and both have the value 9; therefore, parentheses are usually omitted in repeated additions. Addition is also commutative, so permuting the terms of a finite sequence does not change its sum (for infinite summations this property may fail; see Absolute convergence for conditions under which it still holds).
There is no special notation for the summation of such explicit sequences, as the corresponding repeated addition expression will do. There is only a slight difficulty if the sequence has fewer than two elements: the summation of a sequence of one term involves no plus sign (it is indistinguishable from the term itself) and the summation of the empty sequence cannot even be written down (but one can write its value "0" in its place). If, however, the terms of the sequence are given by a regular pattern, possibly of variable length, then a summation operator may be useful or even essential. For the summation of the sequence of consecutive integers from 1 to 100 one could use an addition expression involving an ellipsis to indicate the missing terms: . In this case the reader easily guesses the pattern; however, for more complicated patterns, one needs to be precise about the rule used to find successive terms, which can be achieved by using the summation operator " Σ". Using this sigma notation the above summation is written as:
$$\sum_{i \mathop =1}^{100}i.$$
The value of this summation is 5050. It can be found without performing 99 additions, since it can be shown (for instance by mathematical induction) that
$$\sum_{ i \mathop =1}^ni = \frac{n(n+1)}{2}$$
for all natural numbers n. More generally, formulae exist for many summations of terms following a regular pattern.
The term " indefinite summation" refers to the search for an inverse image of a given infinite sequence s of values for the forward difference operator, in other words for a sequence, called antidifference of s, whose finite differences are given by s. By contrast, summation as discussed in this article is called "definite summation".
When it is necessary to clarify that numbers are added with their signs, the term algebraic sum is used. For example, in electric circuit theory Kirchhoff's circuit laws consider the algebraic sum of currents in a network of conductors meeting at a point, assigning opposite signs to currents flowing in and out of the node.
Summation is a mathematical operation.
Summation may also refer to:
- Addition
- Summation (neurophysiology), a way of achieving action potential in a neuron
- In law, a closing argument
Summation, which includes both spatial and temporal summation, is the process that determines whether or not an action potential will be triggered by the combined effects of excitatory and inhibitory signals, both from multiple simultaneous inputs (spatial summation), and from repeated inputs (temporal summation). Depending on the sum total of many individual inputs, summation may or may not reach the threshold voltage to trigger an action potential.
Neurotransmitters released from the terminals of a presynaptic neuron fall under one of two categories, depending on the ion channels gated or modulated by the neurotransmitter receptor. Excitatory neurotransmitters produce depolarization of the postsynaptic cell, whereas the hyperpolarization produced by an inhibitory neurotransmitter will mitigate the effects of an excitatory neurotransmitter.
Neurons can only excite or inhibit other neurons (or bias the excitability of each other through modulatory transmitters). Given these two basic actions, a chain of neurons can produce only a limited response. A pathway can be facilitated by excitatory input; removal of such input constitutes disfacilitation. A pathway may also be inhibited by inhibitory input. Removal of such input constitutes disinhibition, which, if other sources of excitation are present in the inhibitory input, can augment excitation.
When a given target neuron receives inputs from multiple sources, those inputs can be spatially summated if the inputs arrive closely enough in time before the influence of each has decayed. If a target neuron receives input from a single axon terminal and that input occurs repeatedly at short intervals, the inputs will summate temporally.
Usage examples of "summation".
As for their view of pragmatists, a succinct summation was first uttered in frustration by Representative Dick Armey of Texas in the late eighties, when Republicans were the long-standing minority in Congress.
And in that clear world, the Synthesis was talk and the Summation a promised sugar dollop meant to quiet children, not a thing podia took seriously for long.
Behind them the burning fortress groaned in ancient agony, a hundred timbrous voices expressing in final summation the anguish Pengalen had known in its span.
Years ago a lecturer at an American College of Trial Lawyers seminar had told Vecchio to use stories to make his points during summation.
Ellen Datlow and Terri Windling contained forty stories, eight poems, and an essay by Elizabeth Hand, along with detailed end-of-the-year summations by the editors, Edward Bryant, Charles Vess, Joan D.
EXISTS only as an abstraction exerting influence in the real world, a force acting upon imagination, a psychosocial web of hidden WILLS, a summation of biological, genetic, electromagnetic, microbiotic, social, pedagogic, psychological, karmic, cosmic, mythic, internal and external FORCES, a living IDEA, a socially-engineered MOON-CHILD, lurking around corners, creeping out of shadows, spilling from dreams, a macro-cabal whose roster includes not only the obvious -- Richard Nixon, the Vatican, ITT -- but also others preferring to remain silent and unseen.
Only after this has been done can conceptual analysis and summation of the meaning of his experiences be therapeutically productive.
Linda Ziegler made her closing argument, Dale followed with a passionate plea for leniency in his summation and argument, thenas California law allowedZiegler got the final word, presenting a summation that reminded the jurors that Cletus Calhoun was dead, and regardless of everything else, someone had to answer for that crime.
They may include elements of a summation, but they are not to be lengthy recapitulations of the trial.
The events are the concretes and the particulars, of which the speeches are the abstract summations.
When he had finished a succinct summation of why his life would be worth less than nothing after he had gotten an heir on one of Roelstra's daughters, Andrade smiled her approval.
He leaned back again, pleased with his summation of the events leading up to recent developments: denying the Hivers a new base from which to continue their unique form of colonization.
The Mentat philosopher had chewed deep into everything they accepted and what he disgorged did not agree with Archival dependence upon "our inviolate summations.
This is the smallest summation possible with any selection of dominoes from an ordinary box of twenty-eight.
But the puzzle is to make a selection of eighteen dominoes and arrange them (in exactly the form shown) so that the summations shall be 18 in all the fourteen directions mentioned.