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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.
Some Related Sentences
Since and all
Since it was issued in the spring of 1611, the King James Version has been most generally considered the most poetic and beautiful of all translations of the Bible.
Since the validity of all subsequent planning depends on the accuracy of the basic inventory information, great care is being taken that the inventory is as complete as possible.
Since broadcast frequencies are very limited in number, these objectives are to some extent inconsistent in that not all of them can be fully realized, and to the extent that each is realized, there is a corresponding reduction of the possibilities for fullest achievement of the others.
Since he can neither accept nor reject them all, he must be governed by the time and energy available for his prime professional obligations.
Since they are all either rented or borrowed, the requested dates for their use have to be far in advance.
Since American life is committed above all to productivity and a higher standard of economic life, the countervailing forces of residential and religious exclusiveness have fought a desperate, rearguard action against the expanding interdependence of the metropolis.
Since rococo music tends to be pretty and elegant above all, it can seem rather vacuous to twentieth-century ears that have grown accustomed to the stress and dissonances of composers from Beethoven to Boulez.
Since " all beings " includes the individual, love and compassion in Buddhism are outside the opposition between self and other.
Since a player cannot control another player's bids, and since all bids are non-refundable, the auction involves a considerable amount of strategizing and prioritization by players.
Since all anchors that embed themselves in the bottom require the strain to be along the seabed, anchors can be broken out of the bottom by shortening the rode until the vessel is directly above the anchor ( at this point the anchor chain is " up and down " in naval parlance ).
Since the 1970s, self-help books, psychology, and some modern expressions of Christianity have viewed this disparity in terms of grace being an innate quality within all people who must be inspired or strong enough to find it: something to achieve.
Since the implementation of the Statute of Westminster 1931 in each of the Commonwealth realms ( on successive dates from 1931 onwards ), the Act of Settlement cannot be altered in any realm except by that realm's own parliament and, by convention, only with the consent of all the other realms, as it touches on the succession to the shared throne.
Since John Wesley ordained and sent forth every Methodist preacher in his day, who preached and baptized and ordained, and since every Methodist preacher who has ever been ordained as a Methodist was ordained in this direct " succession " from Wesley, then the Methodist Church teaches that it has all the direct merits coming from apostolic succession, if any such there be.
Since the Plebeian Aediles were elected by the Plebeians ( commoners ), rather than by all of the People of Rome ( Plebeians as well as members of the Patrician aristocracy ), they were not technically magistrates.
Since the implementation of concordats between the ELCA and the Episcopal Church of the United States and the ELCIC and the Anglican Church of Canada, all bishops, including the Presiding Bishop ( ELCA ) or the National Bishop ( ELCIC ), have been consecrated using the historic succession, with at least one Anglican bishop serving as co-consecrator.
Since going into ecumenical communion with their respective Anglican body, bishops in the ELCA or the ELCIC not only approve the " rostering " of all ordained pastors, diaconal ministers, and associates in ministry, but they serve as the principal celebrant of all pastoral ordination and installation ceremonies, diaconal consecration ceremonies, as well as serving as the " chief pastor " of the local synod, upholding the teachings of Martin Luther as well as the documentations of the Ninety-Five Theses and the Augsburg Confession.
* Since Big Brother 2, the UK series always opens with a twist which have included the public being able to choose the final housemate out of three possibilities ( Big Brother 2 ), the public voting for a housemate to leave during the first week and then the housemates choosing between the two housemates with the least number of votes ( Big Brother 3 ), First Night Nominations ( Big Brother 4 ), Suitcase Nominations ( Big Brother 5 ), Unlucky Housemate 13 ( Big Brother 6 ), Big Brother Hood ( Big Brother 7 ), an all-female House and the first inclusion of twins as contestants ( Big Brother 8 ), the first couple to enter as housemates and set a secret task to hide their real relationship ( Big Brother 9 ), all " housemates " really being " non-housemates " who had to earn their housemate status ( Big Brother 10 ), a mole entering the House with an " Impossible Task " ( Big Brother 11 ), Jackie Stallone entering a house containing her son's ex-wife ( Celebrity Big Brother 3 ), the entrance of a non-celebrity in a celebrity edition ( Celebrity Big Brother 4 ) and Jade Goody's family announced to be visiting.
Since the gene is recessive, all offspring will be heterozygous, and the offspring from that mating will not be resistant to Bt and therefore no longer a threat.
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 the donation of the Abbey Moutier-Grandvalto and all its possessions to Bishop Adalbero II in 999 till the Reformation, Basel was ruled by prince-bishops ( see Bishop of Basel, whose memory is preserved in the crosier shown on the Basel coat-of-arms – see above ).
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 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 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.
* Since the conjugate of a maximal torus is a maximal torus, every element of G lies in some maximal torus.
) 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 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 paths
Since the overwhelming majority of light rays from a given light source do not make it directly into the viewer's eye, a " forward " simulation could potentially waste a tremendous amount of computation on light paths that are never recorded.
Since all of these paths are of different lengths-plus some of these effects will also slow the signal down-this results in the different versions of the signal arriving at the receiver at different times.
Since the 1960s, many of these schools have become defunct as a result of financial difficulties stemming from parents ' decreased interest in paying for such an education for their daughters, and changing societal norms making it easier for daughters to pursue academic and professional paths not open to previous generations.
Since these frequencies propagate by ground wave only, the precision of time signals is not affected by varying propagation paths between the transmitter, the ionosphere, and the receiver.
Since for all mother nature knows ( or could know ) it is possible that these insects will cross paths ( sometime, somewhere ) with insectivorous birds, they had better be designed with some avoidance machinery.
Since the unit interval is simply connected, the lifting property for paths is a special case of the lifting property for maps stated above.
Since service roads serve a dual purpose, they are an inexpensive way to create routes in cycling network, compared to cycletracks or stand-alone bike paths.
Since the lenses of their eyes modify reciprocally the paths of the incoming and outgoing light the effect is that the eyes act as a strong retroreflector, sometimes seen at night when walking in wildlands with a flashlight.
Since the conception of the welfare state was intensifying the demand for social equality and democratisation, middle schools were reorganised in 1958 to include two academic paths: a 3-year academically oriented real department and the 8th-10th forms.
Since then, we have traveled the globe, released many records, and played thousands of shows ; pedaling the righteous name of piebald to all whose paths we crossed.
Since light is deflected in a gravitational field, it is possible for the light of a distant object to reach an observer along two or more paths.
Since graze paths rarely pass over established observatories, amateur astronomers have become the primary recorders of graze data.
Since the two paths through a neutron interferometer can be as far as to apart, the effect is hardly microscopic.
Since the underlying random process is the same, for enough price paths, the value of a european option here should be the same as under Black Scholes.
As James stated, " Since then we have moved on and actually made a second album but decided that we both wanted to go down different paths in our lives and going on the road as BodyRockers again for another three years promoting another album wasn't what we wanted ".
Since STA is capable of verifying every path, it can detect other problems like glitches, slow paths and clock skew.