Therefore Polydectes, unknowingly, sealed Perseus's fate to achieve a place in the Hall of Heroes.

Therefore Samlesbury Hall reflects the building styles and religious beliefs from the 14th century to the present day.

Therefore, Hammer was first invited to perform the song " U Can't Touch This ", prior to its release, on The Arsenio Hall Show in 1989.

Therefore Radio 3 moved out to Adrian Boult Hall in the centre of the city, with the newly developed BBC Resources, turning Studio 1 into a full-time TV studio.

Therefore, from its completion in 1928 until 1964, the City Hall was the tallest building in Los Angeles, and shared the skyline with only a few structures having decorative towers, including the Richfield Tower and the Eastern Columbia Building.

Therefore, Jin Sun Hall was extended in October 1972 for construction of 3, 100 pyeong of Seorabol Hall, and 2, 400 pyeong devoted to the construction of Natural Hall as part of the College of Medicine in 1974.

Therefore, Hall and Ball decided to quit professional climbing and form a high-altitude guiding business.

Therefore in 2005 it was decided to switch to Moore Hall, which Marlatt has a better, more " accepting ," relationship with.

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, it works as a neutron reflector and neutron moderator, effectively slowing the neutrons to the thermal energy range of below 0. 03 eV, where the total cross section is at least an order of magnitude lower – exact value strongly depends on the purity and size of the crystallites in the material.

Therefore, the distillate will not be pure – its composition will be identical to the composition of the vapors at the given temperature and pressure, and can be computed from Raoult's law.

Therefore it is advised to change terrain occasionally – such as trail, beach, or grass running.

Therefore, to properly understand the theory of evolution via natural selection, one must understand the genotype – phenotype distinction.

Therefore the EGP is now turning its attention to Eastern Europe – all these countries have Green parties, but in materially poor Eastern Europe the success of Green Parties is very patchy, except for Hungary, where the local Green party, Politics Can Be Different ( LMP ), has succeeded in getting into the parliament and many city councils.

Therefore, other members of the survivor ’ s family – in particular the spouse and children – are also offered treatment and counselling.

Therefore, the radius of an atom is more than 10, 000 times the radius of its nucleus ( 1 – 10 fm ), and less than 1 / 1000 of the wavelength of visible light ( 400 – 700 nm ).

Therefore it is also sometimes called the DJP algorithm, the Jarník algorithm, or the Prim – Jarník algorithm.

Therefore RDF swaps object for subject that would be used in the classical notation of an Entity – attribute – value model within Object oriented design ; object ( sky ), attribute ( color ) and value ( blue ).

Therefore the two other – very close – definitions: 1200 / 7227 inch and 350 / 83 mm are both unofficial.

Therefore Gaiseric freed Licinia Eudoxia ( thus fulfilling Daniel's prophesy ) and her daughter Placidia ( Olybrius ' wife ), but did not stop his raids on Italian's coasts, in order to press for the election of his candidate on the Western throne, but his project failed, because Ricimer, who had become the Magister militum of the West, chose Libius Severus as new Emperor ( 461 – 465 ).

Therefore, this approach to treatment of Tay – Sachs disease has also been ineffective so far.

Therefore, Luns decided to study law at Amsterdam University during the period 1932 – 1937.

Therefore, 36 – 48 m < sup > 2 </ sup > of solar-exposed thermal mass is required.

* United States of America – Our Lady of the Immaculate Conception unofficial due to the Establishment Clause of the First Amendment to the Constitution of the United States which states, " Congress ( Therefore the U. S. Government ) shall make no law respecting an establishment of religion ,..."

Therefore the only online exchange that meets the railway line is Pescara – Rome station Avezzano.

Therefore, the only rail interchange is characterized by the Adriatic railway line Bologna – Bari, Abruzzo is Martinsicuro rail-Broad-S.

Therefore large variety of euphemisms were used instead, including comparisons, human names and other anthropomorphic terms – e. g. snakes were likened to ropes or called brides, while wolf was named Juris or Ansis or referred to as man ( also brother or friend ) of the forest.

Therefore we see that any two spins can be lined with a ferromagnetic or an antiferromagnetic bond and the distribution of these is given exactly as in the case of Edwards – Anderson model.

Therefore, winning 4 – 1 on aggregate.

Therefore, the Janko piano retains the colouring of traditional keyboards ( white naturals, black sharps and flats ) without the usual necessity to learn all other key patterns as an alteration of a C major scale.

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, each node knows the exact network topology, i. e. it has a graph representation of the network.

Therefore, by trying this replacement for all edges incident to some chosen vertex of G, the Hamiltonian cycle problem can be solved by at most n Hamiltonian path computations, where n is the number of vertices in the graph.

Therefore, much of the theory about the clique problem is devoted to identifying special types of graph that admit more efficient algorithms, or to establishing the computational difficulty of the general problem in various models of computation.

Therefore, the graph of the function ƒ ( x − h ) = ( x − h )< sup > 2 </ sup > is a parabola shifted to the right by h whose vertex is at ( h, 0 ), as shown in the top figure.

Therefore, the planar graphs have a forbidden minor characterization, which in this case is given by Wagner's theorem: the set H of minor-minimal nonplanar graphs contains exactly two graphs, the complete graph K < sub > 5 </ sub > and the complete bipartite graph K < sub > 3, 3 </ sub >, and the planar graphs are exactly the graphs that do not have a minor in the set

Therefore the graph is mixed: it has eight vertices, eight arrows, and four edges.

The corresponding set K of vertices in G ( the vertices whose expanded cliques in G * intersect K *) is a clique in G with the property that it intersects every maximum independent set in G. Therefore, the graph formed from G by removing K has clique cover number at most one less than the clique number of G, and independence number at least one less than the independence number of G, and the result follows by induction on this number.

Therefore, by Beineke's characterization, this example cannot be a line graph.

Therefore, the achromatic number of the Clebsch graph is 8.

Therefore, if a minimally imperfect graph has a 2-join, it must equal one of its blocks, from which it follows that it must be an odd cycle and not Berge.

Therefore, by the De Bruijn – Erdős theorem, P itself also has a w-colorable incomparability graph, and thus has the desired partition into chains.

Therefore, the complement of any comparability graph is perfect ; this is essentially just Dilworth's theorem itself, restated in graph-theoretic terms.

Therefore, by the Robertson – Seymour theorem, the linklessly embeddable graphs have a forbidden graph characterization as the graphs that do not contain any of a finite set of minors.

Therefore, every cubic graph other than K < sub > 4 </ sub > has an independent set of at least n / 3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.

Therefore, finding the Euclidean minimum spanning tree as a spanning tree of the complete graph or as a spanning tree of the Delaunay triangulation both take O ( dn < sup > 2 </ sup >) time.

Therefore, the expression on the right-hand side is just the equation for the tangent line to the graph of f at ( a, f ( a )).

Therefore the Heawood graph is a symmetric graph.

Therefore, the Euclidean shortest path problem may be decomposed into two simpler subproblems: constructing the visibility graph, and applying a shortest path algorithm such as Dijkstra's algorithm to the graph.