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Thus, each vertex i in the digraph has a unique " successor " in the cycle cover, and is a permutation on where n is the number of vertices in the digraph.
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Thus, the alignment of the `` dots '' and `` tips '', respectively, indicate individual variability of the 21 growth centers of each child with respect to the mean values for these boys and girls.
Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.
Thus, the efficiency **yt couplers is given by -- Af or approximately 50 percent each.
Thus some provinces contained tribes which detested each other, and to them independence meant an opportunity for war.
Thus arose the first monastic community, consisting of anchorites living each in his own little dwelling, united together under one superior.
Thus, each person of the Trinity is described as uncreated ( increatus ), limitless ( Immensus ), eternal ( æternus ), and omnipotent ( omnipotens ).
Thus, each Spruance-class destroyer originally carried a maximum total of 24 ASROC.
Thus, there are 35 possible basic contracts ( five at each of the seven levels ); 1 being the lowest, followed by 1 etc., up to 7NT, the highest possible bid.
Thus, the broadcast domain is the entire inter-connected layer two network, and the segments connected to each switch / bridge port are each a collision domain.
Thus an understanding of how these two levels relate to each other is needed.
Thus, on a real computer display, each pixel is actually composed of separate red, green, and blue subpixels.
Thus the dynamic characteristic of DHTML is the way it functions while a page is viewed, not in its ability to generate a unique page with each page load.
Thus, the change in slope between each successive point is small, reducing the apparent " jaggedness " of the approximation.
Thus, speakers of two adjacent Inuit dialects would usually be able to understand one another, but speakers from dialects distant from each other on the dialect continuum would have difficulty understanding one another.
Thus, ecosystem processes are driven by the number of species in an ecosystem, the exact nature of each individual species, and the relative abundance organisms within these species.
Thus, churches actually had money-changing tables at which each coin would be examined separately and a token of actual worth given to the layperson so that he or she could be seen by the other parishioners as putting money in the basket during that part of the service.
Thus, medical practitioners would select treatment options for specific cases based on the best research for each patient they treat.
Thus in each term ( endothermic & exothermic ) the prefix refers to where heat goes as the reaction occurs.
Thus, over time we would expect each traditional song to become aesthetically ever more appealing — it would be collectively composed to perfection, as it were, by the community.
Thus, online conversations often involve a variety of assumptions and motives unique to each individual user.
Thus, the eight items of the path are not to be understood as stages, in which each stage is completed before moving on to the next.
Thus, in a sense, there is a different completeness theorem for each deductive system.
Thus, in place of one unchallenged military commander, the province now had five officers, each with command of only a small fraction of the garrison.
Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not.
Thus and vertex
Thus, the vertex is at point
( Thus we consider something like the winding number of the orientation of the sides, where at every vertex the contribution is between − and winding.
In one direction, the Hamiltonian path problem for graph G is equivalent to the Hamiltonian cycle problem in a graph H obtained from G by adding a new vertex and connecting it to all vertices of G. Thus, finding a Hamiltonian path cannot be significantly slower ( in the worst case, as a function of the number of vertices ) than finding a Hamiltonian cycle.
Thus in a cyclic quadrilateral, the circumcenter, the " vertex centroid ", and the anticenter are collinear.
Thus the permanent of a 01-matrix is equal to the number of vertex cycle covers of an unweighted directed graph.
( Thus, this usage distinguishes between graphs with identifiable vertex or edge sets on the one hand, and isomorphism types or classes of graphs on the other.
Thus, the " learning " vertex would be a central " hub " that connects to these other modifying words.
where is the graph distance between vertices w and v. Thus, this sum is over the nearest neighbors of the vertex v. For a graph with a finite number of edges and vertices, this definition is identical to that of the Laplacian matrix.
Thus, finding a minimum feedback vertex set in a graph is equivalent to finding a maximum induced forest ( resp.
Thus, there are three kinds of bidirected edges: those where the arrows point outward, towards the vertices, at both ends ; those where both arrows point inward, away from the vertices ; and those in which one arrow points away from its vertex and towards the opposite end, while the other arrow points in the same direction as the first, away from the opposite end and towards its own vertex.
Thus and i
If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).
Thus, Octavian's victory at the Battle of Actium gave him sole and uncontested control of " Mare Nostrum " ( Our Sea i. e. the Roman Mediterannean ) and he became " Augustus Caesar " and the " first citizen " of Rome.
Thus, body forces are specified by vector fields which are assumed to be continuous over the entire volume of the body, i. e. acting on every point in it.
Thus the probability of two failures in a same RAID group in time proximity is much smaller ( approximately the probability squared, i. e., multiplied by itself ).
Thus it works as a separation sign and not as an indication for an alternative version of the i. Diacritics can be used for emphasis ( érg koud for very cold ) or for disambiguation between a number of words that are spelled the same when context doesn't indicate the correct meaning ( één appel
Thus the probability of two failures in a same RAID group in time proximity is much smaller ( approximately the probability squared, i. e., multiplied by itself ).
Thus it is meaningful to speak of a " presentation of an equivalence relation ," i. e., a presentation of the corresponding groupoid ;
Thus in Modern Greek, Eta is pronounced and represents the sound / i / ( a close front unrounded vowel ).
Thus, for example, Odysseus is represented in Hecuba ( lines 131-32 ) as " agile-minded, sweet-talking, demos-pleasing " i. e. a type of the war-time demagogues that were active in Athens during the Peloponnesian War.
Thus it was significant which quarters had preferential opportunities in providing chief wives to imperial princes, i. e. supplying future empresses.
Thus when God doth work, who shall let ( i. e. prevent ) it?
Thus, the intention is that approximately 95 % of the population scores within two SDs of the mean, i. e. has an IQ between 70 and 130.
Thus, " discrimination " against ( i. e., negative differential treatment of ) potential insureds in the risk evaluation and premium-setting process is a necessary by-product of the fundamentals of insurance underwriting.
Thus when we realize the nature of knowledge, Berkeley's argument is seen to be wrong in substance as well as in form, and his grounds for supposing that ' idea '- i. e. the objects apprehended-must be mental, are found to have no validity whatever.
Thus he does not scruple to declare that Socrates and Heraclitus were Christians ( Apol., i. 46, ii.
implies that the entire NC hierarchy " collapses " down to some level i. Thus, there are 2 possibilities:
Thus each polynomial is actually equal to the sum of the terms used in its formal expression, if such a term a < sub > i </ sub > X < sup > i </ sup > is interpreted as a polynomial that has zero coefficients at all powers of X other than X < sup > i </ sup >.
Thus Kant effects his “ Copernican ” revolution of knowledge by changing our perspective on knowledge from a question of “ what can truly be known ” ( i. e. how can we actually come to know universals ), to a question of “ how does the knowing mind operate .”
Thus evil, in one aspect, i. e. as counter-balancing the deordination of sin, has the nature of good.
Thus the secular power of the Bishop of Rome, i. e., the Pope, was reduced to one square mile, the smallest sovereign nation on earth ( as a result of the 1929 Lateran Treaty which established a Concordat between Vatican City and the nation of Italy ).
Thus, the urban development ( i. e., buildings ) is optimized to occupy less than 50 % of the total area, while the rest is reserved for open space, including the Vatican Gardens.
Thus, F (− q ) has the same magnitude as F ( q ) but they have the opposite phase, i. e., φ ( q ) = − φ ( q )
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