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Then and functions
Then the periodic Bernoulli functions P < sub > n </ sub > are defined as
Then all the terms in the asymptotic series can be expressed in terms of elementary functions.
Then there are computable functions and.
Then he defined it for more complicated functions as the least upper bound of all the integrals of simple functions smaller than the function in question.
Then given the Hamiltonian operator, the equation to satisfy for all functions ( with associated multiplication operator ) is
Then, in 1978 an effort was made to consolidate the several singular functions ; FEMA was created to house civil defense and disaster preparedness under one roof.
The other class of Dedekind rings which is arguably of equal importance comes from geometry: let C be a nonsingular geometrically integral affine algebraic curve over a field k. Then the coordinate ring k of regular functions on C is a Dedekind domain.
Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.
Then one faces the problem of expression sin ( θ ) and cos ( θ ) as functions of x.
Then the subspace of consisting of functions φ such that all functional derivatives of at φ are zero, that is:
Then, for all measurable real-or complex-valued functions f and g on S,
Then it fulfilled a number of functions: for example, Gödöllő's first pharmacy was opened in it in 1814.
Then the quotient sheaf consists of equivalence classes of functions which vanish on the diagonal modulo higher order terms.
Then for all Riemann mapping functions F ( z )
Let be the algebra of functions defined on the manifold M. Then
Then one checks that these two functions are in fact both ring homomorphisms.
Then, the design of the compact kitchen unit “ UNIREX ” was designed in which one single large appliance had more functions, from the conservation to the cooking phase.
Then the assemblies are dipped into a bath of molten salt ( typically NaCl, KCl and other compounds ) which functions both as heat transfer medium and flux.
Then each critical function and or / process must have its own contingency plan in the event that one of the functions / processes ceases or fails.
Then the theorem states that for analytic functions f, if
Then it is possible to have zero divisors in the ring of regular functions, and consequently the fraction field no longer exists.
Now let F ′ be a specified topological space, equipped with a continuous left action of G. Then the bundle associated to E with fibre F ′ is a bundle E ′ with a local trivialization subordinate to the cover U < sub > i </ sub > whose transition functions are given by
Then π < sub > ρ </ sub >: E → X is a fiber bundle with fiber F and structure group G. The transition functions are given by ρ ( t < sub > ij </ sub >) where t < sub > ij </ sub > are the transition functions of the principal bundle P.

Then and may
Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.
Then there are a pair of old biddies played by Grace Carney and Sibly Bowan who may be right off the shelf of stock Irish characters, but they put such a combination of good will and malevolence into their parts that they're quite entertaining.
Then we have informed a large number of our crew that when they reach the United States, they will be punished but that in the meanwhile, they may run loose and are expected to perform their jobs in good order.
After this, the senior priest ( or bishop ) pours pure olive oil and a small amount of wine into the shrine lamp, and says the " Prayer of the Oil ", which calls upon God to "... sanctify this Oil, that it may be effectual for those who shall be anointed therewith, unto healing, and unto relief from every passion, every malady of the flesh and of the spirit, and every ill ..." Then follow seven series of epistles, gospels, long prayers, Ektenias ( litanies ) and anointings.
Then a single server may cause a bottleneck or constraints problem.
Then most pure part of the condensate may be extracted as product.
Then, the definition of a square may be recast with that abstraction as its genus:
Then, the definition of a square may be recast with that abstraction as its genus:
Then I say, such an engine may be made large enough to do the work required in employing eight, ten, fifteen, or twenty horses to be constantly maintained and kept for doing such a work …" The idea was later used by James Watt to help market his improved steam engine.
Then, choice of law clauses may specify which laws the court or tribunal should apply to each aspect of the dispute.
Many Christians support a secular state, and may acknowledge that the conception has support in Biblical teachings, particularly the statement of Jesus in the Book of Luke: " Then give to Caesar what is Caesar's, and to God what is God's .".
Then I and I < sup > 2 </ sup > are real vector spaces, and T < sub > x </ sub > M may be defined as the dual space of the quotient space I / I < sup > 2 </ sup >.
Then both concepts of particle and wave may be attributed to an observation problem of the gear.
Then note that we may also multiply by aaa, so we can convert A to aa and convert AA to a.
' Then he said: ' Sirs, ye are my men, my companions and friends in this journey: I require you bring me so far forward, that I may strike one stroke with my sword.
Then, instead of sending an offer to all people that are likely to churn, it may only want to send offers to loyal customers.
* Acts 8: 37-38 Then Philip said, " If you believe with all your heart, you may.
Then the loan gradually falls through in a plausible way, and the victim may end up being defrauded of tens of thousands of dollars or pounds, thinking only that the deal simply failed.
Then we may consider two concepts: Empty and Full.
Let R be a Noetherian ring and let I be an ideal of R. Then I may be written as the intersection of finitely many primary ideals with distinct radicals ; that is:
Then it may be buttered and eaten as a toast ( its most common use as a breakfast dish ), or it may be filled or topped with either doces ( sweet ) or salgados ( savory ) ingredients, which define the kind of meal the tapioca is used for: breakfast, afternoon tea or dessert.
Then the priest may deliver a homily and everyone comes forward to venerate the epitaphios.
Then in the willow-meads of Tasarinan we may meet in the spring.

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