Help


[permalink] [id link]
+
Page "Commutator" ¶ 46
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Then and is
Then he would get to his feet, as though rising in honor of his own remarkable powers, and say almost invariably, `` Gentlemen, this is an amazing story!!
Then, Jesus indicated that God's forgiveness is unlimited.
Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.
Then it added: `` It is not possible to determine how extensive these ill effects will be -- nor how many people will be affected ''.
Then the words fell into a pattern: `` Mollie the Mutton is scratching her nose, Scratching her nose in the rain.
Then he thought of Aaron Blaustein standing in his rich house saying: `` God is tired of taking the blame.
Then it is marked on the inside where it comes in contact with the transom, frames, keelson and all the battens.
Then it is replaced and fastened.
Then the chines are rounded off and the bottom is rough-sanded in preparation.
Then, a group of eggs is deposited in a cavity in the beebread loaf and the egg compartment is closed.
Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.
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, too, the utmost clinical flexibility is necessary in judiciously combining carefully timed family-oriented home visits, single and group office interviews, and appropriate telephone follow-up calls, if the worker is to be genuinely accessible and if the predicted unhealthy outcome is to be actually averted in accordance with the principles of preventive intervention.
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 she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.
Then comes the time when the last wire is removed and Susie walks out a healthier and more attractive girl than when she first went to the orthodontist.
Then, with the new affluence, there is actually a sallying forth into the wide, wide world beyond the precincts of New York.
Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;

Then and linear
Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.
Then the first argument becomes conjugate linear, rather than the second.
Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.
Then any vector in R < sup > 3 </ sup > is a linear combination of e < sub > 1 </ sub >, e < sub > 2 </ sub > and e < sub > 3 </ sub >.
Then express the seed ( the initial conditions of the LRS ) as a linear combination of the eigenbasis vectors:
Then standard methods can be used to solve the linear difference equation in.
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 the resultant perturbation can be written as a linear sum of the individual types of perturbations,
Then it transfers to the anilox roll ( or meter roll ) whose texture holds a specific amount of ink since it is covered with thousands of small wells or cups that enable it to meter ink to the printing plate in a uniform thickness evenly and quickly ( the number of cells per linear inch can vary according to the type of print job and the quality required ).
Then they became entirely geometric or linear with raised dots.
Using the natural isomorphism between and the space of linear transformations from V to V ,< ref name =" natural iso "> Let L ( V, V ) be the space of linear transformations from V to V. Then the natural map
Then the zero vector of this space can be expressed as a linear combination of no elements, which again is an empty sum.
Then any linear functional can be written in these coordinates as a sum of the form:
Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.
Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.
Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of vector bundles on X.
Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of coherent sheaves on X.
Then a linear map is called a symplectic map if the pullback preserves the symplectic form, i. e., where the pullback form is defined by.
Then, L < sub > 0 </ sub > is a Lie algebra, L < sub > 1 </ sub > is a linear representation of L < sub > 0 </ sub >, and there exists a symmetric L < sub > 0 </ sub >- equivariant linear map such that for all x, y and z in L < sub > 1 </ sub >,
Let e < sub > i </ sub > denote the trivial path at vertex i. Then we can associate to the vertex i, the projective KΓ module KΓe < sub > i </ sub > consisting of linear combinations of paths which have starting vertex i. This corresponds to the representation of Γ obtained by putting a copy of K at each vertex which lies on a path starting at i and 0 on each other vertex.

Then and i
) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is
Then, removing the catalyst would also result in reaction, producing energy ; i. e. the addition and its reverse process, removal, would both produce energy.
Then X is compact if and only if X is a complete lattice ( i. e. all subsets have suprema and infima ).
Then, depending on whether a laptop or compact or extended keyboard type is used, the shortcut is ++ 5 or + 5 ( numeric keypad ) or ++ i ( laptop ).
Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).
Then, ~ 150, 000 years later ( i. e. around 50, 000 years ago ), sub-groups of this population began to expand our species ' range to regions outside of, and ( later ) within, this continent ( Tishkoff, 1996 ).
Then a general definition of isomorphism that covers the previous and many other cases is: an isomorphism is a morphism that has an inverse, i. e. there exists a morphism with and.
Then the pair (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) is called an inverse system of groups and morphisms over I, and the morphisms f < sub > ij </ sub > are called the transition morphisms of the system.
* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.
Then the data are passed through high-performance restartable dithering engine which is used regardless of monitor bit depth, i. e. also for 24 bits per pixel colour.
Then the probability of a measurement returning the value λ < sub > i </ sub > can be calculated by integrating the spectral measure

2.025 seconds.