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Since and conjugate
Since temperature is thermodynamically conjugate to entropy, the isothermal process is conjugate to the adiabatic process for reversible transformations.
Since 1918 it has been known that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.
Since < ƒ, ƒ > ≥ 0, φ ( f * f ) ≥ 0 for all ƒ in L < sup > 2 </ sup >( m ), where ƒ * is pointwise conjugate of ƒ.
Since the complex roots of a real polynomial are in conjugate pairs, the irreducible polynomials over the field of real numbers are the linear polynomials and the quadratic polynomials with no real roots.
Since g is equal to its conjugate it is the complexification of a real form on TM.

Since and maximal
Let A be a unital commutative Banach algebra over C. Since A is then a commutative ring with unit, every non-invertible element of A belongs to some maximal ideal of A.
Since a maximal ideal in A is closed, is a Banach algebra that is a field, and it follows from the Gelfand-Mazur theorem that there is a bijection between the set of all maximal ideals of A and the set Δ ( A ) of all nonzero homomorphisms from A to C. The set Δ ( A ) is called the " structure space " or " character space " of A, and its members " characters.
Since all maximal paths have the same number of black nodes, by property 5, this shows that no path is more than twice as long as any other path.
Since a one sided maximal ideal A is not necessarily two-sided, the quotient R / A is not necessarily a ring, but it is a simple module over R. If R has a unique maximal right ideal, then R is known as a local ring, and the maximal right ideal is also the unique maximal left and unique maximal two-sided ideal of the ring, and is in fact the Jacobson radical J ( R ).
Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.
Since f ( X ) is irreducible, ( f ( X )) is a maximal ideal and hence is, in fact, a field.
Since as shown above, the classical definition is essentially the modern definition with only maximal ideals considered, this shows that the interpretation of the modern definition as " zero sets of functions " agrees with the classical definition where they both make sense.
Since it is a collection of trees, and trees are contractible, consider the space where the equivalence relation is generated by if they are contained in a common tree in the maximal forest F. The quotient map is a homotopy equivalence.
) This follows from the fact that R has a maximal left ideal M, and the fact that the quotient module R / M is a simple left R-module, and that its annihilator is a proper two-sided ideal in R. Since R is a simple ring, this annihilator is
Since the velocity is maximal when all the enzyme is bound as the enzyme-substrate complex,.
Since the compact operators is a ( in fact, the only ) maximal norm-closed ideal in B ( H ), the Calkin algebra is simple.
Since the number of edges in a maximal spanning forest of a graph is equal to the number of vertices minus the number of components, the formula above for the cyclomatic number follows.
Since power is equal to force times velocity, the muscle generates no power at either isometric force ( due to zero velocity ) or maximal velocity ( due to zero force ).
Since the technostructure is composed of an hierarchical system of influential employees inside the enterprise, its primary goal is not to maximize their profits but rather survival, continuous growth and maximal size.
Since the alcohol in wine is produced by fermentation of the sugar, the Oechsle scale is used to predict the maximal possible alcohol content of the finished wine.

Since and torus
Since a standard torus is an orbit of a two dimensional abelian subgroup of the Euclidean group, it follows that the cyclides are orbits of two dimensional abelian subgroups of the group of Möbius transformations, and this provides a second way to define them.
Since the disk is contractible, the solid torus has the homotopy type of.
Since this mapping identifies opposite sides of the parallelogram as being the same, the fundamental parallelogram has the topology of a torus.

Since and is
Since the Supreme Court's decision of that year this is more doubtful ; ;
( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.
Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.
Since attack serves to stimulate interest in broadcasts, I added to my opening statement a sentence in which I claimed that German youth seemed to lack the enthusiasm which is a necessary ingredient of anger, and might be classified as uninterested and bored rather than angry.
Since the air is a continuum, the network of communication remains intact regardless of the positions or motions of the points ( the people ) in the net.
Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.
Since the difficulty of drawing the net is great, we will merely discuss it.
Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.
Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.
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.
Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.
Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.
Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.
Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.
Since the work is done by hand, the only limitation, it is said, `` is that of human conception ''.
Since the apparatus is new, it requires experimentation and changes in technique.
Since the obvious is not always true, the Republican National Committee wisely analyzed its defeat of last autumn and finds that it occurred, as suspected, in the larger cities.
Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.
Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.
Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.

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