In fact, the collection of all left cosets ( or right cosets ) of C in G is equal to the collection of all components of G. Therefore, the quotient topology induced by the quotient map from G to G / C is totally disconnected.

Therefore if a collection of fibers can be arranged permanently in a preferred direction within a material, and if the fibers can be prevented from buckling in compression, then that material will become preferentially strong in that direction.

Therefore, in a collection of atoms, over time, decay into the dark state will inevitably result in the system being " trapped " coherently in that state, a phenomenon known as coherent population trapping.

Therefore, collectives are formed to facilitate the collection of fees.

Therefore, diffusion can be deduced with some certainty only when the similarities involve a relatively complex and partly arbitrary collection of items — such as a writing system, a complex myth, or a pantheon of several gods.

Therefore, the collection was first to be known as Sonnets from the Bosnian, until Robert suggested that she change their imaginary original language to Portuguese, probably after her admiration for Camões and his nickname for her: " my little Portuguese.

Therefore the collection of squeeze mappings forms a one-parameter group isomorphic to the multiplicative group of positive real numbers.

Therefore, the designer could highlight the entire collection and apply only one style that will automatically format the entire story without having to go through and apply separate character styles to each of the 10 reviews.

Hamvas ’ three shorter novels, Szilveszter ( 1957, New Year ’ s Eve ), Bizonyos tekintetben ( 1961, From a Certain Aspect ) and Ugyanis ( 1966 – 67, Therefore ) were published together in 1991, followed by his collection of essays, Patmosz ( 1959 – 1966 ; Patmos ) in 1992, whose title alludes to John the Apostle ’ s exile to the island of Patmos, and the second part of Scientia Sacra: az őskori emberiség szellemi hagyománya II.

Therefore, in 2004, the government of Alfredo Palacio confined by decree the administration of Emelec's actives for five years to Corporación para la Administración Temporal Eléctrica de Guayaquil ( CATEG ; literally Corporation for the Temporal Electric Administration of Guayaquil ), an entity administrated by Venezuelan power company Electricidad de Valencia ( Eleval ), whose main duty beside supplying energy is debt collection from EMELEC's private debtors.

Therefore, notification systems with opt-in data collection can validate data in realtime for all said errors and more.

Therefore, Crankshaft sold an extensive collection of movie posters to set up a fund so they could attend college after graduation.

Therefore, the collection chronologically begins with the paintings of the first generation of Modernists ( Nadežda Petrović, Milan Milovanović, Kosta Miličević ), and continues with the works of the most esteemed representatives of Serbian art between the two World Wars ( Sava Šumanović, Milan

Therefore, belt sanders employed in woodworking are usually equipped with some type of dust collection system.

Therefore, if the sections never simultaneously vanish, they determine a form: ...: s < sub > r </ sub > which gives a map from X to P < sup > r </ sup >, and the pullback of the dual of the tautological bundle under this map is L. In this way, projective space acquires a universal property.

Therefore the classifying space BC < sub > 2 </ sub > is of the homotopy type of RP < sup >∞</ sup >, the real projective space given by an infinite sequence of homogeneous coordinates.

Therefore lines in the projective plane are closed curve, i. e., they are cyclical rather than linear.

Therefore, to produce the image which the retina beholds, using projective geometry techniques, it may be convenient to substitute a spherical surface of projection for a plane of projection, i. e., use a " picture sphere " rather than a " picture plane " and place the eye, or " station point ," at the center of the picture sphere.

These are ten in number ; therefore the cubic curves form a projective space of dimension 9, over any given field K. Each point P imposes a single linear condition on F, if we ask that C pass through P. Therefore we can find some cubic curve through any nine given points, which may be degenerate, and may not be unique, but will be unique and non-degenerate if the points are in general position ; compare to two points determining a line and how five points determine a conic.

Therefore it follows from projective determinacy, which in turn follows from sufficient large cardinals, that every projective set ( in a Polish space ) has the property of Baire.

Therefore, while sequences do not encode sufficient information about functions between topological spaces, nets do because collections of open sets in topological spaces are much like directed sets in behaviour.

Therefore Saul sets David in charge of the army.

Therefore, depending on how we modify the axiom scheme of comprehension in order to avoid Russell's paradox, arguments such as the non-existence of a set of all sets may or may not remain valid.

Therefore, if there are more than two Fatou domains, each point of the Julia set must have points of more than two different open sets infinitely close, and this means that the Julia set cannot be a simple curve.

Therefore an engine for a modern twin jet airliner has twin sets of all ancillaries mounted in the engine, which gives the required reliability rating.

Therefore we see that U is defined by taking the union of the sets of linear functionals defining the W < sub > i </ sub >.

Therefore, numerous sets of statistics should be interpreted to get an idea of a trend.

Therefore, data virtualization as well as data federation depends upon accidental data commonality to support combining data and information from disparate data sets.

Therefore, there are about 28 sets of clothing the daughter can wear over the years.

Therefore, knowledge about one set in the class can be applied directly to other sets in the class.

Therefore, the sets of reachable NFA states play the same role in the NFA simulation as single DFA states play in the DFA simulation, and in fact the sets of NFA states appearing in this simulation may be re-interpreted as being states of a DFA.

Therefore, many fonts contain " hints " which aid the system's rasterizer in deciding where to render pixels for particularly troublesome areas in the glyphs, or sets of hand-tweaked bitmaps to be used at specific pixel sizes.

Therefore, the complexity of what is being developed sets the maximal theoretic development speed.

Therefore there are at most disjoint dominating sets.

Therefore algebras on Boole's account cannot be interpreted by sets under the operations of union, intersection and complement, as is the case with modern Boolean algebra.

Therefore, applications that rely on G5-specific instruction sets must be modified by their developers to work on Rosetta-supported Intel-based Macs.

Therefore it's a genuine pleasure to tell you about an entirely happy bodybuilder who has never had to train in secret has never heard one unkind word from his parents and never has been taunted by his schoolmates!!

Whereas, John Brown has cheerfully risked his life in endeavoring to deliver those who are denied all rights and is this day doomed to suffer death for his efforts in behalf of those who have no helper: Therefore,

Therefore as through one man sin entered into the world and through sin death, and thus death has passed unto all men because all have sinned.

Therefore, if a lower court has ruled in an improper manner, or against legal precedent, that judgment will stand if not appealed – even if it might have been overturned on appeal.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

The final chapter of Acts ends with Paul condemning non-Christian Jews and saying " Therefore I want you to know that God's salvation has been sent to the Gentiles, and they will listen!

Therefore, the field of bioinformatics has evolved such that the most pressing task now involves the analysis and interpretation of various types of data.

Therefore, in order to break a pair, one has to change energies of all other pairs.

Therefore there are now a huge variety of different styles and types of map-for example, one area which has evolved a specific and recognisable variation are those used by public transport organisations to guide passengers, namely urban rail and metro maps, many of which are loosely based on 45 degree angles as originally perfected by Harry Beck and George Dow.

Therefore, just as Christianity does not accept that Mosaic Law has any authority over Christians, Judaism does not accept that the New Testament has any religious authority over Jews.

Therefore, he was buried in the Delft Nieuwe Kerk ( New Church ), starting a tradition for the House of Orange that has continued to the present day.

Therefore the age range of 635 to 542 million years before the present is based on correlations to other countries where dating has been possible.

More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.

Therefore whenever ( G ) appears before another representative lowercase letter ( subject ), the statement would read, " It is always Going to be the case ..." and whenever ( F ) appears before another subject, the statement would read, " At sometime in the Future it will be the case ...." Whenever ( H ) appears before another subject, the statement would read, " It Has always been the case ..." and whenever ( P ) appears before another subject, the statement would read, " At sometime in the Past it has been the case ...."

" Therefore, scholars are no longer looking for the identity of a single writer but for numerous authors whose authorship has been absorbed into the gospel's development over a period of time and in several stages.

Therefore this has been recognized as a plausible strategy for gene therapy, by removing the viral DNA and using the virus as a vehicle to deliver the therapeutic DNA.

Therefore, evidence of when human skin darkened has been used to date the loss of human body hair, assuming that the dark skin was needed after the fur was gone.

Therefore, in order to define the quantity of a catalyst, the rate of conversion of a defined chemical reaction has to be specified, preferably of the first order, under strictly controlled conditions.

Therefore, in addition to its strictly communicative uses, language also has many social and cultural uses, such as signifying group identity, social stratification, as well as for social grooming and entertainment.

Therefore, if the determinant equals zero then the parallelogram has no area, and that will happen when two vectors are on the same line.

: Therefore, Carl has long ears.