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We will denote the Clifford algebra on C < sup > n </ sup > with the standard quadratic form by Cℓ < sub > n </ sub >( C ).
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We and will
We, in our country, think of war as an external threat which, if it occurs, will not be primarily of our own doing.
We will recall that the still confident liberals of the Truman administration gathered with other Western utopians in San Francisco to set up the legal framework, finally and at last, to rationalize war -- to rationalize want and fear -- out of the world: the United Nations.
We therefore leave the writer to the enjoyment of the unenvied reputation which the personal abuse he has heaped on us will entitle him to from the low and vulgar herd to which he belongs ''.
We may further grant to those of her ( Poetry's ) defenders who are lovers of poetry and yet not poets, the permission to speak in prose on her behalf: let them show not only that she is pleasant but also useful to States and to human life, and we will listen in a kindly spirit ; ;
We veterans acknowledge the fact that as time passes the demand for medical care at VA hospitals will grow proportionately as age fosters illness.
We feel that The Detroit News is to be complimented upon arranging for articles on these subjects and we hope that it will continue to provide material along wholesome lines.
We now have to think not only of our national security but also of the future generations who will suffer from any tests we might undertake.
We welcome this able brief for the negative as part of a many-sided discussion of the Atlantic Common Market which JNR will be continuing in our pages.
We all seek the same thing through different ways -- an end to this long night of two thousand years of darkness and unspeakable abuses which will continue to plague us until the Star of David flies over Zion ''.
We must ask ourselves which of the two alternatives will help the commuter -- the two-way B. & O. - C. & O. merger, or the three-way New York Central - B. & O. - C. & O. merger.
We should hope that peace corps projects will be truly international and that our citizens will find themselves working alongside citizens of the host country and also volunteers from other lands.
We are initiating research on the use of solid state materials for infrared detection using a method which will not require cooling of materials to attain high sensitivity.
We believe that these improved facilities will contribute income and effect savings which will fully justify the investment.
`` 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 and denote
We will use the notation to denote the multiplicative inverse of, it is defined exactly when and are coprime ; the following construction explains why the coprimality condition is needed.
We write hom ( a, b ) ( or hom < sub > C </ sub >( a, b ) when there may be confusion about to which category hom ( a, b ) refers ) to denote the hom-class of all morphisms from a to b. ( Some authors write Mor ( a, b ) or simply C ( a, b ) instead.
We can see this from the Bayesian update rule: letting U denote the unlikely outcome of the random process and M the proposition that the process has occurred many times before, we have
We are now left with the word tawdry to denote, essentially, the inferior garb worn by the poor and not a general put-down for St Ives itself, which remains a charming and attractive small river town.
We know from Plutarch that Xenocrates, if he did not explain the Platonic construction of the world-soul as Crantor after him did, nevertheless drew heavily on the Timaeus ; and further that he was at the head of those who, regarding the universe as unoriginated and imperishable, looked upon the chronological succession in the Platonic theory as a form in which to denote the relations of conceptual succession.
Suppose X is a normed vector space over R or C. We denote by its continuous dual, i. e. the space of all continuous linear maps from X to the base field.
We denote the canonical probability distributions for the Hamiltonian and the trial Hamiltonian by and, respectively.
We denote the diagonal components of the density matrices for the canonical distributions for and in this basis as:
We denote the unitary operators we get by U ( a, A ), and these give us a continuous, unitary and true representation in that the collection of U ( a, A ) obey the group law of the inhomogeneous SL ( 2, C ).
" is reporting the sentence " We shall all sin from time to time " ( assuming the archbishop is including himself in the proposition ), where shall is used to denote simple futurity.
Precisely, let T be a triangulation of an n-manifold M. Let S be a simplex of T. We denote the dual cell ( to be defined precisely ) corresponding to S by DS.
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