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where and product
This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.
In physics, the most common orbital descriptions are based on the solutions to the hydrogen atom, where orbitals are given by the product between a radial function and a pure spherical harmonic.
Alpha decay is by far the most common form of cluster decay where the parent atom ejects a defined daughter collection of nucleons, leaving another defined product behind ( in nuclear fission, a number of different pairs of daughters of approximately equal size are formed ).
where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product.
where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.
The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: where p < sub > 1 </ sub > < p < sub > 2 </ sub > < ... < p < sub > k </ sub > are primes and the a < sub > j </ sub > are positive integers.
It is often convenient to write this as an infinite product over all the primes, where all but a finite number have a zero exponent.
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 is the Cartesian product of and
Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where ( x, y, z ) belongs to the subset if and only if f ( x, y ) = z.
Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.
One possible origin is Chun Shui Tang teahouse in Taichung, where Ms. Lin Hsiu Hui ( product development manager ) poured sweetened tapioca balls into the tea during a meeting in 1988.
The case where X is F, and we have a bilinear form, is particularly useful ( see for example scalar product, inner product and quadratic form ).
* Measure algebra: A Banach algebra consisting of all Radon measures on some locally compact group, where the product of two measures is given by convolution.
Celebrity endorsements have proven very successful around the world where, due to increasing consumerism, an individual is considered a status symbol when they purchase a celebrity-endorsed product.
The following is a typical reaction scheme, where C represents the catalyst, X and Y are reactants, and Z is the product of the reaction of X and Y:
The " Circe effect ", coined by the enzymologist William P. Jencks, refers to a scenario where an enzyme lures its substrate towards it through electrostatic forces exhibited by the enzyme molecule before transforming it into product.
Roughly two-thirds of the entire world's cocoa is produced in West Africa, with 43 % sourced from Côte d ' Ivoire, where child labor is a common practice to obtain the product.
As seen earlier, exploitation of land and labour is essential for human social advance, but only on the assumption that the product is made available within the area where the exploitation takes place.
where denotes the vector cross product and square brackets denote evaluation in the rotating frame of reference.
Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with all possible pairs of real numbers ; that is with the Cartesian product, where is the set of all reals.

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 over
Now, the next morning, they were anchored at The Elbow and the boat was riding directly over the underwater ledge where the green water turned to deepest blue and the cliff dropped straight down 600 fathoms, with the weighted line beside it ; ;
The fact that he has cast over those materials the light of a skeptical mind does not make him any the less Southern, I rather think, for the South has been no more solid than other regions except in the political and related areas where patronage and force and intimidation and fear may produce a surface uniformity.
it took them over an hour to get back to the station where they should have changed, in order to take the line that went to the Place Redoute.
By making inroads in the name of law enforcement into the protection which Congress has afforded to the marriage relationship, the Court today continues in the path charted by the recent decision in Wyatt v. United States, 362 U.S. 525, where the Court held that, under the circumstances of that case, a wife could be compelled to testify against her husband over her objection.
The word marina was coined by NAEBM originally to describe a waterfront facility where recreational boats could find protection and basic needs to lay over in relative comfort.
She would try to see over the bulge of her cheeks and somewhat under her teeth to the place where she was biting.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let Af where the maximization is over all admissible policies Af.
Thus Af where the maximization is over all admissible policies Af, and Af is related to Af by ( 5 ).
There he'd take a compass reading, figure his air speed, and deduce that in a certain number of minutes he'd be over the broad meadows of the Merrimack Valley where it would be safe to let down through the overcast and see the ground before it hit him.
But if there was evidence at the Trial that aimed over Eichmann's head at his collaborators in the societies where he functioned, the press seems to have missed it.
I finally went downstairs to the bar off the main lobby where most of the cast were drowning their sorrows over the untimely passing of Ask Tony.
Even from where he stood he could see the neatly folded blanket that he had spread over Burton, the pillow, the sheet of paper on top of it.
Nick recalled stories that the two best fishing spots in Southern California were over the La Jolla Deep and the Redondo Deep, two spots where the ocean dropped off to fantastic depths almost from the shoreline.
Also the department of justice building is located where J. Edgar Hoover presides over the federal bureau of investigation.
Dick Carroll and his accordion ( which we now refer to as `` Freida '' ) held over at Bahia Cabana where `` Sir '' Judson Smith brings in his calypso capers Oct. 13.
Out of the church and into his big car, it tooling over the road with him driving and the headlights sweeping the pike ahead and after he hit college, his expansiveness, the quaint little pine board tourist courts, cabins really, with a cute naked light bulb in the ceiling ( unfrosted and naked as a streetlight, like the one on the corner where you used to play when you were a kid, where you watched the bats swooping in after the bugs, watching in between your bouts at hopscotch ), a room complete with moths pinging the light and the few casual cockroaches cruising the walls, an insect Highway Patrol with feelers waving.
The Greek alphabet, in its Euboean form, was carried over by Greek colonists to the Italian peninsula, where it gave rise to a variety of alphabets used to write the Italic languages.
The righteous will live in heaven for a thousand years ( the millennium ) where they will sit with God in judgment over the unredeemed and the fallen angels.
Image: Colonnadeparkguell. jpg | Colonnaded pathway where the road projects out from the hillside, with the vaulting forming a retaining wall which curves over to support the road, and transmits the load onto sloping columns.
where the first sum is over positive energy states and the second over those of negative energy.
" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.
In 1880 the school moved to the Hillside Chapel, a building next to the house, where he held conversations and, over the course of successive summers, as he entered his eighties, invited others to give lectures on themes in philosophy, religion and letters.

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