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where C is an arbitrary path connecting the point with zero potential to r. When the curl is zero, the line integral above does not depend on the specific path C chosen but only on its endpoints.
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where and C
Compound comparisons typically compare two sets of groups means where one set has two or more groups ( e. g., compare average group means of group A, B and C with group D ).
Doubleday assumed administrative duties in the defenses of Washington, D. C., where he was in charge of courts martial, which gave him legal experience that he used after the war.
where C is the " overhead " added by the program GenerateParadoxicalString.
For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.
where n < sub > d </ sub >, n < sub > F </ sub > and n < sub > C </ sub > are the refractive indices of the material at the wavelengths of the Fraunhofer d -, F-and C-spectral lines ( 587. 6 nm, 486. 1 nm and 656. 3 nm respectively ).
where F ' and C ' are the blue and red cadmium lines at 480. 0 nm and 643. 8 nm, respectively.
Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.
The Volta Laboratory and the Volta Bureau were earlier located at Bell's father's house at 1527 35th Street in Washington, D. C., where its carriage house became their headquarters in 1889.
The simplest type of carbohydrate is a monosaccharide, which among other properties contains carbon, hydrogen, and oxygen, mostly in a ratio of 1: 2: 1 ( generalized formula C < sub > n </ sub > H < sub > 2n </ sub > O < sub > n </ sub >, where n is at least 3 ).
Watterson was born in Washington, D. C., where his father, James G. Watterson ( born 1932 ), worked as a patent examiner while going to George Washington University Law School before becoming a patent attorney in 1960.
In the early 1990s, she worked as an associate at the Washington, D. C .- based law firm of Wilmer Cutler & Pickering where she did civil litigation for several years before becoming an Assistant U. S. Attorney.
Instead, it is put in parallel with chapter 4 ( C ) where divine judgements are pronounced against the Babylonian kings.
where is the Gelfand representation of x defined as follows: is the continuous function from Δ ( A ) to C given by The spectrum of in the formula above, is the spectrum as element of the algebra C ( Δ ( A )) of complex continuous functions on the compact space Δ ( A ).
where C < sub > α </ sub > denotes I < sub > α </ sub > or e < sup > απi </ sup > K < sub > α </ sub >.
where A < sub > α </ sub > and B < sub > α </ sub > are any two solutions of Bessel's equation, and C < sub > α </ sub > is a constant independent of x ( which depends on α and on the particular Bessel functions considered ).
After moving from his home in Chicago to Washington, D. C., he set up one of the first home recording studios where he not only recorded the album Bo Diddley Is a Gunslinger but he recorded his valet, Marvin Gaye.
The temperature range from 41 ° F to 135 ° F ( 5 ° C to 57 ° C ) is the " Danger zone " where bacteria is likely to proliferate, food therefore should not be stored in this temperature range.
Peeling vegetables can also substantially reduce the vitamin C content, especially in the case of potatoes where most vitamin C is in the skin.
Already a couple of weeks later, an Antonov cargo plane crossed the border from Sudan and landed at Tiringoulou airport in C. A. R., where it unloaded weapons and about 50 armed men who spread out in the area.
where and is
But California is where we're goin ''.
He thought of the jungles below him, and of the wild, strange, untracked beauty there and he promised himself that someday he would return, on foot perhaps, to hunt in this last corner of the world where man is sometimes himself the hunted, and animals the lords.
Now I wish to enter the American market, where the competition is very strong.
from downstream, where the water level is much lower, it is a high, elaborately facaded pavilion.
The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.
Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.
Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.
A dominant motive is the poet's longing for his homeland and its boyhood associations: `` Not men-folk, but the fields where I would stray, The stones where as a child I used to play ''.
In a society where everything is for sale, Marlowe is the only man who cannot be bought.
This is done for simplicity of commands and to bring the hidden redundancy up to where misunderstanding has almost zero possibility.
As to benefits to employees, it is notorious for its callous disregard except where it depends on them for services.
`` The Moral Creed '' and `` The Will To Risk '' live happily together, if we do not examine where the line is to be drawn.
Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.
Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.
She was exposing herself to temptation which it is best to avoid where it can consistently be done.
Such performance is a great tribute to American scientists and engineers, who in the past five years have had to telescope time and technology to develop these long-range ballistic missiles, where America had none before.
but it is perennially restructured in situations where anchors are dragged or lost.
`` History has this in common with every other science: that the historian is not allowed to claim any single piece of knowledge, except where he can justify his claim by exhibiting to himself in the first place, and secondly to any one else who is both able and willing to follow his demonstration, the grounds upon which it is based.
Finally we may note that the idea appears in educational theory where its influence is at present widespread.
where and arbitrary
Caracalla left for the frontier, where for the rest of his short reign he was known for his unpredictable and arbitrary operations launched by surprise after a pretext of peace negotiations.
A binary relation R is usually defined as an ordered triple ( X, Y, G ) where X and Y are arbitrary sets ( or classes ), and G is a subset of the Cartesian product X × Y.
where and may be taken as arbitrary complex numbers.
All the earliest English criminal trials involved wholly extraordinary and arbitrary courts without any settled law to apply, whereas the civil ( delictual ) law operated in a highly developed and consistent manner ( except where a King wanted to raise money by selling a new form of writ ).
where A is a 2 × 2 orthogonal matrix and b = ( b < sub > 1 </ sub >, b < sub > 2 </ sub >) is an arbitrary ordered pair of numbers ; that is,
If S is an arbitrary set, then the set S < sup > N </ sup > of all sequences in S becomes a complete metric space if we define the distance between the sequences ( x < sub > n </ sub >) and ( y < sub > n </ sub >) to be, where N is the smallest index for which x < sub > N </ sub > is distinct from y < sub > N </ sub >, or 0 if there is no such index.
where C is an arbitrary constant.
Clenshaw – Curtis quadrature is essentially a change of variables to cast an arbitrary integral in terms of integrals of periodic functions where the Euler – Maclaurin approach is very accurate ( in that particular case the Euler – Maclaurin formula takes the form of a discrete cosine transform ).
" Hello world " is also used by computer hackers as a proof of concept that arbitrary code can be executed through an exploit where the system designers did not intend code to be executed — for example, on Sony's PlayStation Portable.
An example of a projection is the function π < sub > xy </ sub > defined by, which projects an arbitrary point in 3D space to a point on the x – y-plane, where the third coordinate ( z ) is equal to 0.
If r represents an arbitrary element of R, f can be viewed as a right R-homomorphism so that, or f can also be viewed as a left R module homomorphism, where.
The ICAO code is based on the region and country of the airport — for example, Charles de Gaulle Airport has an ICAO code of LFPG, where L indicates Southern Europe, F, France, PG, Paris de Gaulle, while Orly Airport has the code LFPO ( the 3rd letter sometimes refers to the particular flight information region ( FIR ) or the last two may be arbitrary ).
While there have been many claims through the years of companies achieving " perfect compression " where an arbitrary number N of random bits can always be compressed to N − 1 bits, these kinds of claims can be safely discarded without even looking at any further details regarding the purported compression scheme.
Only in dimension d = 2 can one construct entities where is replaced by an arbitrary complex number with magnitude 1 ( -> anyons ).
where A and θ < sub > 0 </ sub > are arbitrary constants.
An example of such a domain is the Gaussian integers Z, that is, the set of complex numbers of the form a + bi where i denotes the imaginary unit and a and b are arbitrary integers.
Each capability to be available in all contexts where meaningful-to exploit it as widely as possible and to avoid “ arbitrary restrictions ”.
Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).
Hence, the question of which is the largest peninsula in Europe is a debatable one, depending on arbitrary human definitions of where the peninsulas begin — and on which century one chooses to consider: sometimes, Scandinavia as a peninsula has not existed.
where F and G are arbitrary functions.
Let φ ( ξ, η, ζ ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta-function: that is, let F be a weak limit of continuous functions whose integral is unity, but whose support ( the region where the function is non-zero ) shrinks to the origin.
Let u, v be arbitrary vectors in a vector space V over F with an inner product, where F is the field of real or complex numbers.
However, the general definition remains valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered.
* In telecommunications, an isochronous signal is one where the time interval separating any two corresponding transitions is equal to the unit interval or to a multiple of the unit interval ; but phase is arbitrary ( and in some systems may change slowly over time ).
0.661 seconds.