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summation and its
And I select this sentence as its pertinent summation: `` in essence the drama of his ( Eisenhower's ) Presidency can be described as the ordeal of a nation turned conservative and struggling -- thus far with but limited and precarious success -- to give effective voice and force to that conservatism ''.
The topology has the particularly pleasant property that an infinite summation converges if and only if the sequence of its terms converges to 0, which just means that any fixed power of X occurs in only finitely many terms.
This topology, which is also the I-adic topology, where I = ( X, Y ) is the ideal generated by X and Y, still enjoys the property that a summation converges if and only if its terms tend to 0.
With this topology it would not be the case that a summation converges if and only if its terms tend to 0.
Likewise, at the uniquely configured intersections of many streets, one is met with a new perspective as suddenly several sections of the district become visible .” ( source: Michigan State Historic Preservation Office ) Another significant aspect of the district is its pioneering developer, Louise Lathrup Kelley: “ As a woman acting as developer starting in the 1920s, she was essentially alone, however her dogged persistence and insistence on quality resulted in a unique community that was the summation of her career .” ( source: Michigan State Historic Preservation Office )
Darrow ’ s summation in their trial is noted for its influential criticism of capital punishment and retributive, as opposed to rehabilitative, penal systems.
A situation similar to an empty summation can arise for other operations than addition ; notably, its counterpart for multiplication is an empty product, a product of no factors at all.
Since an empty sum by definition has no terms, it seems contradictory to talk about its terms ; however in practice there almost always is an expression that describes the terms of a summation, even if the range of summation happens to be empty.
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 an object plane transparency is imagined as a summation over small sources ( as in the Whittaker-Shannon interpolation formula, Scott ), each of which has its spectrum truncated in this fashion, then every point of the entire object plane transparency suffers the same effects of this low pass filtering.
* Axon-The axon gets its signal from the summation behavior which occurs inside the soma.
A careful analysis of the errors in compensated summation is needed to appreciate its accuracy characteristics.
For any summation method L, its abelian theorem is the result that if c = ( c < sub > n </ sub >) is a convergent sequence, with limit C, then L ( c ) = C. An example is given by the Cesàro method, in which L is defined as the limit of the arithmetic means of the first N terms of c, as N tends to infinity.
Les troyens is Berlioz's most ambitious work, the summation of his entire artistic career, but he did not live to see it performed in its entirety.
Invariance refers to the fact that elasticity is an independent physical property which is only recovered through the determinant of stress / strain tensors – ( summation over all indices ), irrespective whether in cylindrical or rectangular coordinates and the transform and its adjoint commute.
" This formula, remarquable by its simplicity, can be proven easily with the help Cauchy's theorem, so important for the summation of series " wrote Jensen ( 1895 ).
The aphorism is all the more beguiling because it appears near the end of the poem, for its apparently climactic position has generally led to the assumption that it is the abstract summation of the poem ...
With another definition, and the transform property becomes a periodic summation ( with period P ) and its equivalent Fourier series:
Many symbols have traditional uses, such as lower case epsilon ( ε ) for an arbitrarily small positive number, lower case pi ( π ) for the ratio of the circumference of a circle to its diameter, capital sigma ( Σ ) for summation, and lower case sigma ( σ ) for standard deviation.
In addition to its three-register operational stack, consisting of X, Y, and Z registers, the SR-50 also included one memory ( M ) register to which the value in the X ( display ) register could be directly added using the " summation " key.

summation and opening
Threshold is when the summation of MEPPs reaches a certain potential and induces the opening of the ligand gated ion channels.

summation and statements
The reason why there is a difference between calculation and presentation linkbases, is that the total element that stands for the summation of all others usually appears at the bottom in the financial statements whereas in the calculation linkbase it must be placed as the top concept.

summation and your
Hill's powerful summation of this lesson is this: " You have the power to control your thoughts and direct them to do your bidding.

summation and only
The convolution integral ( or summation ) above need only extend to the full duration of the impulse response T, or the order N in a discrete time filter.
To rigorously complete the proof there are still serious technicalities to overcome, due to the fact that the summation over zeta zeros in the explicit formula for does not converge absolutely but only conditionally and in a " principal value " sense.
where X is a formal variable, the summation index k is an integer ( not necessarily positive ) and only finitely many coefficients p < sub > k </ sub > are non-zero.
1, 2 ,..., f. For the case where e = 1, the summation is trivial ( involving only a single term ).
In the second formula, the inner summation in the right hand side is only extended over indices within bounds, 0 ≤ i ≤ m and 0 ≤ j ≤ n. Alternative expressions of addition and multiplication, without using explicit bounds in the sums, are as follows:
With compensated summation, the worst-case error bound is independent of n, so a large number of values can be summed with an error that only depends on the floating-point precision.
Although Kahan's algorithm achieves error growth for summing n numbers, only slightly worse growth can be achieved by pairwise summation: one recursively divides the set of numbers into two halves, sums each half, and then adds the two sums.
If the summation in the denominator converges, the posterior probabilities will still sum ( or integrate ) to 1 even if the prior values do not, and so the priors may only need to be specified in the correct proportion.
The summation only runs to because we have taken to be proportional to the identity operator, in which case the summand vanishes.
The satguru is a title given specifically only to an enlightened rishi / sant whose life's purpose is to guide initiated shishya along the spiritual path, the summation of which is the realization of the Self through realization of God, who is omnipresent.
If a statistical or quantum field has three real valued scalar fields, and the energy or action only depends on combinations which are symmetric under rotations of these components into each other, the contributions with the lowest dimension are ( summation convention ):
where the summation is over all partitions, of n except for the trivial partition consisting of only n.
Here partial converse means that if M sums the series Σ, and some side-condition holds, then Σ was convergent in the first place ; without any side condition such a result would say that M only summed convergent series ( making it useless as a summation method for divergent series ).
where the symbol indicates that the summation is over only even values of, i. e, if n is odd, sum over even values of i and if n is even, sum only over odd values of i.

summation and ;
Essentially, Euler-MacLaurin summation can be applied whenever Carlson's theorem holds ; the Euler-MacLaurin formula is essentially a result obtaining from the study of finite differences and Newton series.
Even the " exact " FFT algorithms have errors when finite-precision floating-point arithmetic is used, but these errors are typically quite small ; most FFT algorithms, e. g. Cooley – Tukey, have excellent numerical properties as a consequence of the pairwise summation structure of the algorithms.
The product operator for the product of a sequence is denoted by the capital Greek letter Pi < span style =" font-family: times, serif ; font-size: 150 %">∏</ span > ( in analogy to the use of the capital Sigma < span style =" font-family: times, serif ; font-size: 150 %">∑</ span > as summation symbol ).
A distribution being " smoothed out " by summation, showing original Probability density function | density of distribution and three subsequent summations ; see Illustration of the central limit theorem for further details.
Note: Call set-up time is the summation of: ( a ) call request time — the time from initiation of a calling signal to the delivery to the caller of a proceed-to-select signal ; ( b ) selection time — the time from the delivery of the proceed-to-select signal until all the selection signals have been transmitted ; and ( c ) post selection time — the time from the end of the transmission of the selection signals until the delivery of the call-connected signal to the originating terminal.
converges to the power series suggested, which can be written as ; however the summation
As a consequence, for convergence of a sequence of elements of it then suffices that the coefficient of each power of Y converges to a formal power series in X, a weaker condition that stabilizing entirely ; for instance in the second example given here the coefficient of Y converges to, so the whole summation converges to.
An abridgment differs from an epitome in that an abridgment is made of selected quotations of a larger work ; no new writing is composed, as opposed to the epitome, which is an original summation of a work, at least in part.
His original work dealt, among other things, with Wheatstone's sound-figures, the characteristic notes of the different vowels, a manometric flame apparatus, a vibration microscope, among others ; but perhaps the most important of his researches are those devoted to the phenomena produced by the interference of two tones, in which he disputed the views of Helmholtz as to the existence of summation and difference tones.
Of her works on magical subjects, the best remembered of her books are ; The Cosmic Doctrine, a summation of her basic teachings on mysticism, Psychic Self-Defense, a manual on how to protect oneself from psychic attacks and The Mystical Qabalah, an introduction to Hermetic Qabalah which was first published in England in 1935, and is regarded by many occultists as one of the best books on magic ever written.
when ; in such case the summation has value 0 ( or the zero element of the additive group in which the terms t < sub > i </ sub > live ).
However, the kind of values denoted by the summand is of importance for the value of the summation ; for instance, an empty summation of elements of a vector space has as value the zero vector in that space, rather than the number 0.
Even more important is the fact that the operation is summation ; by contrast, the empty product — a product of no factors at all — has as value of one.
There are two predominant viewpoints here: pantheism, deity is the summation of Existence ; and panentheism, deity is an emergent property of Existence.
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 ".
Where, i represents the index of summation ; x < sub > i </ sub > is an indexed variable representing each successive term in the series ; m is the lower bound of summation, and n is the upper bound of summation.

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