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Then and m

Then the Cartesian product set D 1 D 2 can be made into a directed set by defining ( n 1 , n 2 ) ≤ ( m 1 , m 2 ) if and only if n 1 ≤ m 1 and n 2 ≤ m 2 .

Then one need only check the records in each bucket T against those in buckets T where k ranges between − m and m.

* Let the index set I of an inverse system ( X i , f ij ) have a greatest element m. Then the natural projection π m : X → X m is an isomorphism.

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

Then, in the 9th century BC, Dorians founded the main Hellenic city-on Mesa Vouno, 396 m above sea level.

Then, at 5: 13 a. m. April 18, 1906, the earthquake hits and then the fires erupt.

Then for arbitrary ε > 0 there is an embedding ( or immersion ) ƒ ε : M m → R n which is

Let Then is called not included in the fuzzy set if is called fully included if and is called a fuzzy member if < math > 0 < m ( x ) < 1 .</ math >

Then that researcher's Bradford multiplier b m is 2 ( i. e. 10 / 5 ).

The Japanese repelled them, but they attacked again around 5: 00 p. m. Then, according to Major-General Iinuma's war journal, " a free-for-all ensued.

Then, she tied the 100 m world record, but this was never recognised officially, as she competed against men when setting the record.

Then to the Reschen Pass the main chain is ill-defined, though on it rises the Corno di Campo ( 3, 305 m ), beyond which it runs slightly north-east past the sources of the Adda and the Fraele Pass, sinks to form the depression of the Ofen Pass, soon heads north and rises once more in the Piz Sesvenna ( 3, 204 m ).

Then a general invitation was given to all who desired to partake, which many did until the keg was emptied … In the evening they reassembled, burning Prof. Humiston in effigy about 10 p. m.

Then, to prove ( 2 ), assume that m and p are injective and l is surjective.

Then, the B m make up a neighbourhood basis of 0 in K.

Then a will be a root of the formal derivative P ’, with multiplicity m − 1.

* " Then I'll Be Tired Of You " w. E. Y. Harburg m. Arthur Schwartz

Then and b

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

Let a, b, and c be elements of G. Then:

Then b 0 is the value of p ( x 0 ).

Then the image set f ( I ) is also an interval, and either it contains f ( b ), or it contains f ( a ); that is,

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

Consider some set P and a binary relation ≤ on P. Then ≤ is a preorder, or quasiorder, if it is reflexive and transitive, i. e., for all a, b and c in P, we have that:

Then, the chance that the first letter typed is ' b ' is 1 / 50, and the chance that the second letter typed is a is also 1 / 50, and so on.

Since they are even, they can be written as x = 2a and y = 2b respectively for integers a and b. Then the sum.

Then there is an exact sequence relating the kernels and cokernels of a, b, and c:

Let vectors and let denote the matrix with elements of a and b. Then the area of the parallelogram generated by a and b is equal to.

Let vectors and let Then the area of the parallelogram generated by a and b is equal to.

Then the area of the parallelogram with vertices at a, b and c is equivalent to the absolute value of the determinant of a matrix built using a, b and c as rows with the last column padded using ones as follows:

Denote the orthocenter of triangle ABC as H, denote the sidelengths as a, b, and c, and denote the circumradius of the triangle as R. Then

Then, if a, a ′, b and b ′ are alternative settings for the detectors,

Suppose a vertex joins three units with spin numbers a, b, and c. Then, these requirements are stated as:

Then A is an algebra over K if the following identities hold for any three elements x, y, and z of A, and all elements (" scalars ") a and b of K:

Since they are even, they can be written as x = 2a and y = 2b respectively for integers a and b. Then the sum.

g 1 ( x ), a ≤ x ≤ b. Then

g 2 ( x ), a ≤ x ≤ b. Then

Then, for some positive integers m and n, a n and b m are in I.

Then the element c = ba is nilpotent ( if non-zero ) as c 2 = ( ba ) 2 = b ( ab ) a = 0.

Then and form

Then he began to speak about the tension in art between the mess and form.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

Then the mass balance equation takes the form

Then one can rewrite the field in the form

Then the quotient space X /~ can be naturally identified with a torus: take a square piece of paper, bend and glue together the upper and lower edge to form a cylinder, then bend the resulting cylinder so as to glue together its two open ends, resulting in a torus.

Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

Then Jibril announced that consultations were under way to form an interim government within one month, followed by elections for a constitutional assembly within eight months and parliamentary and presidential elections to be held within a year after that.

Then on 4 June 1990, ethnic tensions between Uzbeks and Kyrgyz surfaced in an area of the Osh Oblast where Uzbeks form a majority of the population.

Then dividing both side by would result in the “ Two-point form ” shown above, but leaving it here allows the equation to still be valid when.

* November 6 – Agatha Christie's mystery novel And Then There Were None is published in book form in the United States.

Then, if we let g lie in the z direction for simplicity, the ε tensor simplifies to the form:

Then, a major uprising led by two brothers-Asen and Peter of the Asen dynasty, restored the Bulgarian state to form the Second Bulgarian Empire.

# Then used resolution to attempt to obtain a proof by contradiction by adding the clausal form of the negation of the theorem to be proved.

Then in 1817, in turn, a portion of Seneca County was combined with a piece of the remainder of Cayuga County to form Tompkins County.

Then he took his design for a miniature transistor pocket radio and sought a backer for its production in kit form.

Then in 1817, in turn, a portion of Seneca County was combined with a piece of the remainder of Cayuga County to form Tompkins County.

Then is an open cover of S, but any finite subcollection of has the form of C discussed previously, and thus cannot be an open subcover of S. This contradicts the compactness of S. Hence, every accumulation point of S is in S, so S is closed.

Then the solutions to the homogeneous system given in parametric form with x 3 , x 5 , and x 6 as free variables are

Then the columns of V such that the corresponding form an orthonormal basis of the nullspace of A.

Then the trope became an autonomous piece organized in stanza form.

Then, detailed study was undertaken to determine the painting's original form, using scientific tests ( especially infrared reflectoscopy and microscopic core-samples ), and original cartoons preserved in the Royal Library at Windsor Castle.

Then he realised this is the difference between natural-form fruit trees and the process of change of tree form resulting from abandoning previously-pruned unnatural fruit trees.

Then by substituting for I using Beer's law in natural logarithm form:

2.251 seconds.