It turns out that a more suitable quantity for updating is the sum of squares of differences from the ( current ) mean,, here denoted:

It is also known from Livy that the mines and the forests were leased for a fixed sum under Philip V, and it appears that the same happened under the Argaead dynasty: from here possibly comes the leasing system that was used in Ptolemaic Egypt.

Note that commutativity is crucial here ; it ensures that the sum of two group homomorphisms is again a homomorphism.

He wrote " If you wanted to sum up the relative position of Britain and America in this century – the ebbing away of the pink areas of the map, the fading of national self-confidence as Uncle Sam proceeded to colonise the globe with fizzy drinks and Hollywood – you could do it like this: they had Star Trek, we had Blake's 7 ... No ' boldly going ' here: instead, we got the boot stamping on a human face which George Orwell offered as a vision of humanity's future in Nineteen Eighty-Four.

Built-in generator 10 produces a sum of sinusoids, here only one.

where is a vector of real-valued weights, is the dot product ( which here computes a weighted sum ), and is the ' bias ', a constant term that does not depend on any input value.

:* John Lennon was once asked to sum up the 60s in one phrase-his reply, " Be here now ", was used by Gallagher for Oasis ' 1997 album, and for the album's title track.

is true for every integer n ≥ 1 with strict inequality if n > 1 ; here σ ( n ) denotes the sum of the divisors of n.

with the connection form and d the exterior derivative, or via the same expression in which is a gauge form for the gauge group of V. The scalar t is used here only as an indeterminate to generate the sum from the determinant, and I denotes the n × n identity matrix.

It is important to note here Brahmagupta found the result in terms of the sum of the first n integers, rather than in terms of n as is the modern practice.

In his concession speech O ' Donoghue remarked " I hope that the irony will not be lost upon you that I stand here, on my evening of defeat, in a hall – this magnificent sports complex – which I helped to build .” He will receive a lump sum of € 237, 000 and an annual pension of € 128, 000.

Note that because of the second condition, power series are used here only to allow infinitely many terms of a fixed degree, rather than to sum terms of all possible degrees.

That sum will be performed in parallel with the fused add / decode described here.

where here stands for the Legendre symbol ( a / p ), and the sum is taken over residue classes modulo p. More generally, given a Dirichlet character χ mod n, the Gauss sum mod n associated with χ is

* For every index set I, the addition map M < sup >( I )</ sup > → M can be extended to a module homomorphism M < sup > I </ sup > → M ( here M < sup >( I )</ sup > denotes the direct sum of copies of M, one for each element of I ; M < sup > I </ sup > denotes the product of copies of M, one for each element of I ).

A special case of the above is the wedge sum or one-point union ; here we take X and Y to be pointed spaces and Z the one-point space.

* Elizalde Emilio ; ' Zeta regularization techniques with applications ' ISBN 978-981-02-1441-8981-02-1441-3, here the author explain in what sense the problem of HIlbert-Polya is related with the problem of Gutzwiller Trace formula and what would be the value of the sum taken over the imaginary parts of the zeros.

< td valign =" top "> The image shows the sum of all 50, 000 single images but here with the center of gravity ( centroid ) of each image shifted to the same reference position.

The dot product is defined here as the sum of the products of corresponding components, i. e.,

The notation ~ here means that the sum represents the function in some sense.

The term was first used by Davis in 1949, " We here propose the name phenome for the sum total of extragenic, non-autoreproductive portions of the cell, whether cytoplasmic or nuclear.

It is here she is introduced to powerful politician, Bhagwat Choudhary, who pays a hefty sum and asks Manilal to bring Ganga to Calcutta where he intends to keep her as his and Jeeva Sahay's mistress.

Note that a process may be of finite quadratic variation in the sense of the definition given here and its paths be nonetheless a. s. of infinite quadratic variation for every t > 0 in the classical sense of taking the supremum of the sum over all partitions ; this is in particular the case for Brownian Motion.

where the sum extends over all positive divisors d of n.

where the sum extends over all paths with the property that and.

where the sum extends over all possible values of q.

The sum extends over all non-zero ideals a of O < sub > K </ sub >.

where the sum extends over all positive divisors d of n, or equivalently over all pairs ( a, b ) of positive integers whose product is n.

where n is the total number of players and the sum extends over all subsets S of N not containing player i. The formula can be interpreted as follows.

* Interior angle sum of polygons: a general formula, Provides an interactive Java activity that extends the interior angle sum formula for simple closed polygons to include crossed ( complex ) polygons

The concept of defect extends to higher dimensions as the amount by which the sum of the dihedral angles of the cells at a peak falls short of a full circle.

More generally, the PBW theorem as formulated above extends to cases such as where ( 1 ) L is a flat K-module, ( 2 ) L is torsion-free as an abelian group, ( 3 ) L is a direct sum of cyclic modules ( or all its localizations at prime ideals of K have this property ), or ( 4 ) K is a Dedekind domain.

where the sum extends over all permutations σ of

where the sum extends over the c-th roots of unity other than 1, i. e. over all such that and.

where this sum extends over all partitions of into parts ; that is, the sum extends over all such that

She had quarreled with Lucien, she had resisted his demands for money -- and if she died, by the provisions of her marriage contract, Lucien would inherit legally not only the immediate sum of gold under the floorboards in the office, but later, when the war was over, her father's entire estate.

where the first sum is over positive energy states and the second over those of negative energy.

He soon transferred his services to Teos's cousin and rival Nectanebo II, who, in return for his help, gave him a sum of over 200 talents.

For private suits the minimum jury size was 201 ( increased to 401 if a sum of over 1000 drachmas was at issue ), for public suits 501.

and mean that the sum or product is over all prime numbers:

Similarly, and mean that the sum or product is over all prime powers with strictly positive exponent ( so 1 is not counted ):

and mean that the sum or product is over all positive divisors of n, including 1 and n.

The notations can be combined: and mean that the sum or product is over all prime divisors of n.

and similarly and mean that the sum or product is over all prime powers dividing n.

If more than one wavelength is present ( as is usually the case ), one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity.

Corporatism refers to a form of collectivism that views the whole as being greater than the sum of its individual parts, and gives priority to group rights over individual rights.

The path integral formulation replaces the classical notion of a single, unique trajectory for a system, with a sum over all possible trajectories.

In sum, given an equivalence relation ~ over A, there exists a transformation group G over A whose orbits are the equivalence classes of A under ~.

Some ecological principles, however, do exhibit collective properties where the sum of the components explain the properties of the whole, such as birth rates of a population being equal to the sum of individual births over a designated time frame.

If we allow to incorporate the algebraic sign, this becomes a sum and implies that there is a function of state which is conserved over a complete cycle.

In such case the total decay rate is the sum over all rates:

The amplitude for scattering is the sum of each possible interaction history over all possible intermediate particle states.

The Dyson series can be alternately rewritten as a sum over Feynman diagrams, where at each interaction vertex both the energy and momentum are conserved, but where the length of the energy momentum four vector is not equal to the mass.

:, where is the sum over any n-sequence of length N.

: where is the sum over any k-sequence of length N.

In her prime, she made over $ 50, 000 a year, then a vast sum, far more than her husband's $ 20, 000 per year.

where the sum is taken over all particles and their corresponding potentials ; the result is that the Hamiltonian of the system is the sum of the separate Hamiltonians for each particle.