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By similar reasoning, the complete bipartite graph has no 2-basis: is four-dimensional, and each nontrivial vector in has nonzero coordinates for at least four edges, so any augmented basis would have at least 20 nonzeros, exceeding the 18 nonzeros that would be allowed if each of the nine edges were nonzero in at most two basis vectors.
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By and similar
By opening the stop wider, similar deviations arise for lateral points as have been already discussed for axial points ; but in this case they are much more complicated.
By finding how similar two protein sequences are, we acquire knowledge about their structure and therefore their function.
Confucius never stated whether man was born good or evil, noting that ' By nature men are similar ; by practice men are wide apart ' — implying that whether good or bad, Confucius must have perceived all men to be born with intrinsic similarities, but that man is conditioned and influenced by study and practise.
By adopting the name Chung-cheng (" central uprightness "), he was choosing a name very similar to the name of Sun Yat-sen, who was ( and still is ) known among Chinese as Zhongshan ( 中山 — meaning " central mountain "), thus establishing a link between the two.
By the end of the decade, similar calculators were priced less than $ 10 (£ 5 ).
By analogy, the phenomenon of small events causing similar events leading to eventual catastrophe is called the domino effect.
By the 1st century AD, cattle and horses were used in mills, driving machines similar to those powered by humans in earlier times.
By a similar token, a fear of experts can arise from fear of an intellectual elite's power.
By the 18th century, a similar use was applied to harnesses or equipment used with horses.
By 1882 German makers also produced hexagonal grained powders of a similar size for artillery.
By similar procedure, an original mandate may be declared invalid.
By the 19th century, there existed similar games of håndbold from Denmark, házená in the Czech Republic, hádzaná in Slovakia, gandbol in Ukraine, and torball in Germany.
By 1937, all Harley-Davidson's flathead engines were equipped with dry-sump oil recirculation systems similar to the one introduced in the " Knucklehead " OHV engine.
By this time up to thirty steamers and a similar number of barges were working the river in season.
By 1784, similar requirements were made of Methodists as a whole, laity and clergy alike.
By comparing the photographic plates of the Pleiades cluster taken in 1918 with images taken in 1943, van Maanen was able to identify those stars that had a proper motion similar to the mean motion of the cluster, and were therefore more likely to be members.
By the late 1990s, not only DEC but most of the New England computer industry which had been built around minicomputers similar to the PDP-11 collapsed in the face of microcomputer-based workstations and servers.
By 1954, as rock and roll was beginning to emerge, a number of similar acts began to cross over from the R & B charts to mainstream success, often with added honking brass and saxophone, with The Crows, The Penguins, The El Dorados and The Turbans all scoring major hits.
By the early 1960s, the music industry category previously known as rhythm and blues was being called soul music, and similar music by white artists was labeled blue eyed soul.
By the 24th century, females wear a style similar to males.
By analogy, a similar graph depicting the progress of a string as time passes by can be obtained ; the string ( a one-dimensional object — a small line — by itself ) will trace out a surface ( a two-dimensional manifold ), known as the worldsheet.
By 1950, similar policies and legislation had been adopted by other states and territories.
By the Magdalenian period ( c. 15000-9500 BC ), spear-throwers similar to the later atlatl were in use
By the mid-1930s however, superheterodynes were using higher intermediate frequencies, ( typically around 440 – 470 kHz ), with tuned coils similar in construction to the aerial and oscillator coils.
By witnessing currents flowing through point-contacts, similar to what Bardeen and Brattain had accomplished earlier in December 1947, Mataré by June 1948, was able to produce consistent results by using samples of germanium produced by Welker.
By and reasoning
By the 1930s, statisticians and models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.
By their reasoning, existing laws relating to privacy in general should be sufficient.
By this reasoning, adding an incompatible belief corrupts the original religion, rendering it no longer true.
By the same reasoning, this statement is evidence that ( 2 ) everything that is not black is not a raven.
By the above reasoning, the null space of A is the orthogonal complement to the row space.
By late medieval reasoning, the city of Orléans had escalated the conflict and forced the use of violence upon the English, so a conquering lord would be just in exacting vengeance upon its citizens.
By backward reasoning, one can recursively evaluate a non-final position as identical to that of the position that is one move away and best valued for the player whose move it is.
By reasoning using " induction " Bacon meant the ability to gradually generalize a finding based on accumulating data-he advised proceeding by this method ( building a case from the ground up ).
By a complex chain of reasoning one can deduce that Eanhere married Osthryth, daughter of Oswiu of Northumbria, and had sons by her named Osric, Oswald and Oshere.
By the same reasoning, importation or continuation of cultural mores or elements from former colonial powers may be regarded as a form of neo-colonialism.
By this law he sought to explain, not only the phenomena of memory, which others had similarly explained before him, but also the phenomena of emotion, of reasoning, and of voluntary and involuntary action ( see Association of Ideas ).
By the same reasoning, it should import commodities in which it had an absolute disadvantage.
By way of example of how to clarify conceptions, he addressed conceptions about truth and the real as questions of the presuppositions of reasoning in general.
By Jaynes ' reasoning, if the particles are experimentally indistinguishable for whatever reason, Gibbs paradox is resolved, and quantum mechanics only provides an assurance that in the quantum realm, this indistinguishability will be true as a matter of principle, rather than being due to an insufficiently refined experimental capability.
By contrast, everyday reasoning is mostly nonmonotonic because it involves risk: we jump to conclusions from deductively insufficient premises.
By exactly the same reasoning as in the translational case, equipartition implies that in thermal equilibrium the average rotational energy of each particle is ( 3 / 2 ) k < sub > B </ sub > T.
According to opinion of Richard Helli: " By such reasoning, the Ephthalites are thought to have originated at Hsi-mo-ta-lo ( southwest of Badakhshan and near the Hindu Kush ), which tantalizingly, stands for Himtala, " snow plain ", which may be the Sanskritized form of Hephthal.
By this time, most surviving humans are bestial, with very limited reasoning ability.
By this reasoning, a person holding contempt would not have the urge to openly confront the person with whom they are at odds, nor would they themselves try to remove the object of contempt ; rather, one who holds contempt would have the tendency to hold the view that others should remove the object of contempt, or hold the view that the object of contempt should remove itself.
By the same reasoning, the Minardi team issued an official request that Gené be allowed to start, which was subsequently granted by the Stewarts of the Meeting.
By contrast, common sense represents society's cumulative, consensual reasoning that recognizes the wisdom of mutual benefit.
By this reasoning, the creation of a high-level research institute was a waste of scarce resources.
By a similar process of reasoning, as used in the decimation by 1 case, we obtain
By the end of Alcibiades I, the youth is much persuaded by Socrates ' reasoning, and accepts him as his mentor.
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