We then decompose the integral into its contributions along each of these three contour segments.

We find Elizabeth not in the verbal domain, the world of words, but the nonverbal domain ( the two, he said, amount to different orders of abstraction ).

We note that the other form for a prime p > 3 is 6k + 1 or, equivalently, p ≡ 1 ( mod 6 ), and that 3 |( 2p + 1 ) — thus excluding such p from the Sophie Germain prime domain.

We note that for an arbitrary domain one may define the Picard group Pic ( R ) as the group of invertible fractional ideals Inv ( R ) modulo the subgroup of principal fractional ideals.

We define headers as finite subsets of C. A relational database schema is defined as a tuple S = ( D, R, h ) where D is the domain of atomic values ( see relational model for more on the notions of domain and atomic value ), R is a finite set of relation names, and

* Bah Humbug – A vocal version of " Sleigh Ride " originally played over the closing credits ; it was replaced by an instrumental version of " We Wish You a Merry Christmas " ( which is in the public domain ).

We can also do deconvolution directly in the frequency domain and get similar results.

We can divide this by one diagonal, and take one half ( a triangle ) as fundamental domain.

" We have made these changes for a number of reasons ; first the emergence of our domain portfolio as an anticipated high growth area of our business, second, the importance of email as a key driver of future growth, third the increased size of our retail business as a result of recent acquisitions, and fourth the de-emphasis of our software libraries ," said Noss.

" We changed the way that registrars create value out of domain registration, by positioning ourselves to not only take advantage of revenue growth but also to create a long-term asset in the domain name portfolio ," says Noss.

We are promised that the function is either constant ( 0 on all inputs or 1 on all inputs ) or balanced ( returns 1 for half of the input domain and 0 for the other half ); the task then is to determine if is constant or balanced by using the oracle.

We might expect this to be simplest when D is simply connected, since then both homomorphisms above have trivial domain.

His best-known titles, which have remained in print for many years after entering the public domain, were " The Development of Seership: The Science of Knowing the Future ; Hindoo and Oriental Methods " ( 1915 ), " Genuine Mediumship, or Invisible Powers ", and " Can We Talk to Spirit Friends?

* The Way We Live Now – unabridged public domain audiobook on Librivox. org.

We, therefore, because of your qualities of prudence, justice and worthiness of government, take you under St. Peter ’ s and our own protection, and grant and confirm by apostolic authority to your excellent domain, the kingdom of Portugal, full honours of kingdom and the dignity which corresponds to kings, as well as all places which, with the help of the celestial grace, you have wrested from the hands of the Saracens, and on which your neighbouring Christian princes may not claim any rights.

We begin with some domain of discourse, whose elements are called individuals ( a synonym for mereology is " the calculus of individuals ").

We happily submit this into the public domain via wikipedia.

We have a two dimensional domain whose boundary is a boundary line, which in turn can be described by the following parametric equations

We are then in a position to characterize the notion of a frame as being either the base of the concept profile, or ( more generally ) the domain that the profile is a part of.

At a drunken revelry in Babylon, Alexander declares, " I am the son of God " ( Zeus ) and " the world is my domain .... We will march to the end of the world.

We consider all quantities in the frequency domain, and so assume a time-dependency that is suppressed throughout.

We may thus trace the notion of individual autonomy from its manifestation in religious practice and theological reflection through practical politics and political theory into literature and the arts.

We would all meet at ten o'clock at the Kehl bridge, five miles from Strasbourg, and march triumphantly across into Germany.

We cannot truthfully say of anyone who has succeeded in entering deep into his sixties that he was never old.

We should stand firmly and courageously for our right to free access into Berlin.

We are interested in further diversification into other fields of capital goods, or components for industrial products, and have recently intensified our efforts in that direction.

We have recently entered into an agreement with Compagnie Generale De Telegraphie Sans Fil ( CSF ) of France for the exclusive exchange of technical information on thermoelectric materials.

We have entered into an agreement for the sale of the present Cranston properties, effective as soon as we have completed removal to our new plant.

We quickly ran into the same trouble that plagued Bill Ruger in his first experiments: Three or four bullets would be placed well in a six-inch bull at 100 yards and then, unaccountably, one could stray far out of the group.

We divided the country into five regions plus Hawaii and Alaska and in each is included a general description of the area plus specific recommendations of places and events to cover.

`` We, the Subscribers, do agree, that as soon as a convenient Number of Persons have subscribed to this, or a similar Writing, We will present a petition to the Hon'ble General Court of the Commonwealth of Massachusetts, praying for an Act incorporating into a Body politic the subscribers to such Writing with Liberty to build such a Bridge, and a Right to demand a Toll equal to that received at Malden Bridge, and on like Terms, and if such an Act shall be obtained, then we severally agree each with the others, that we will hold in the said Bridge the several shares set against our respective Names, the whole into two hundred shares being divided, and that we will pay such sums of Money at such Times and in such Manners, as by the said proposed Corporation, shall be directed and required ''.

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.

We will deal first with the program in the Congo though this was put into operation later than the other.

We were forced, as they were, to work a good deal of tempera into background and dark areas.

We are acutely aware that yours is a society which, in spite of several wars and many privations, has developed itself into one of the foremost nations of the world.

`` We have checked her in different parts of Europe and Egypt and finally back into this country.

We met at Maxine's and decided we were set to stay as long as it took, into or even through the evening, to talk things out.

We simply find ourselves in the position of having no means for inquiring into the structure and meaning of this range of our experience.

We can all breathe more easily this morning -- more easily and joyously, too -- because Joshua Logan has turned the stage show, `` Fanny '', into a delightful and heart-warming film.

`` We could put up cribs on the second floor sleeping porch and turn the front bedroom into a playroom where it's nice and sunny, but of course it would entail quite a bit of running up and down stairs and Chris said you were to be careful about that ''.

`` We ran into a guy at the Pagan Room who guarantees we can beat the wheel.

`` We are going to bring the Somers into New York harbor safe and sound ''.