单词 | isomorphism |
例句 | A professor of physics at Dartmouth College and a lifelong student of jazz, Dr. Alexander has taken on “the challenge to find an isomorphism between jazz and cosmology.” Review: As Goes Music, So Goes the Universe 2016-05-03T04:00:00Z These proof assistants have a mechanism that mimics the common mathematical practice of transferring information about one thing to another thing that is understood to be the same via an explicit isomorphism or homotopy equivalence. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z “Institutional isomorphism,” explained Mason President Ángel Cabrera, a former business school dean. Four tough things universities should do to rein in costs 2015-11-25T05:00:00Z Babai’s new proof introduces an algorithm that runs much faster than the previous best attempt, although not quite fast enough to group graph isomorphism with the problems in P. Graph-theory breakthrough tantalizes mathematicians 2015-11-18T05:00:00Z In the "graph isomorphism problem," the challenge is to determine whether two graphs are really the same or not. Mathematician claims breakthrough in complexity theory 2015-11-10T05:00:00Z So many schools today – traditional public, charter, and even private – suffer from a kind of institutional isomorphism: Each one looks like the next. Tiny Schools, Big Impact 2015-10-20T04:00:00Z This term refers to the notion of isomorphism in the more exotic homotopy category of spaces. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z It’s all based on a somewhat wonky theory known as organizational isomorphism — companies’ tendency to mimic each other to gain social legitimacy, and to remain competitive in the war for talent, customers, and profit. Work-Life Balance Is Having a Moment—But for the Wrong Reasons 2014-10-11T04:00:00Z But there was good reason to suspect that graph isomorphism was easier than this. Graph-theory breakthrough tantalizes mathematicians 2015-11-18T05:00:00Z An isomorphism of the Isomorphism of a group with itself. group with itself, established in this way, is called an inner isomorphism. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z The modified generalization of Gay-Lussac—"Equal volumes of elementary gases contain equal numbers of atoms;" the laws of "isomorphism" and of "atomic heat;" and the two empirical rules stated on p. Heroes of Science Chemists 2011-12-09T03:00:21.047Z In technical terms, these groups are connected by an “isomorphism,” a term whose etymology—from the Greek isos, meaning “equal,” and morphe, meaning “form”—indicates its meaning. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z Together, the two concepts of isomerism and isomorphism seemed to cover all the known exceptions from the simplest assumption as to specificity and chemical composition. History of Phosphorus The graph isomorphism problem simply asks whether two graphs are the same, regardless of how they are drawn or how their nodes are named. Graph-theory breakthrough tantalizes mathematicians 2015-11-18T05:00:00Z If from among the set of operations S, T, U, ... which constitute a group Subgroups, conjugate operations, isomorphism, &c. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z Identity, or approximate identity, of crystal form is not in itself sufficient to establish true isomorphism. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1 "Châtelet" to "Chicago" We can define the notion of isomorphism in any category, which allows us to transport this concept between mathematical contexts. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z The phenomena of isomorphism showed a relation between the units and crystalline forms; certain units are thus able to replace others in a crystalline body without altering its form, and others are not. The Advance of Science in the Last Half-Century In the same year Mitscherlich's law was propounded,—the law of isomorphism, according to which atoms of elements of the same class may replace each other in a compound without altering its crystalline structure. Outline of Universal History The groups are then said to be isomorphic, and the correspondence between their operations is spoken of as an isomorphism between the groups. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z The following table shows where isomorphism may be generally expected. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1 "Châtelet" to "Chicago" In the category of topological spaces, the categorical notion of isomorphism is represented by an inverse pair of continuous functions. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z It is clear that there may be two distinct cases of such isomorphism. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z In the first case the isomorphism is spoken of as simple, in the second as multiple. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z The isomorphism is multiple, since to a single operation of the second set there correspond the two operations of the first for which a, b, c, d and −a, −b, −c, −d are parameters. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z Every set of conjugate operations of a group is necessarily transformed into itself by an inner isomorphism, but two or more sets may be interchanged by an outer isomorphism. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z A subgroup of a group G, which is transformed into itself by every isomorphism of G, is called a characteristic subgroup. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z Moreover, the isomorphism is simple unless for one or more operations, other than identity, the sets all remain unaltered. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z This can only be the case for S, when every operation conjugate to S belongs to H. In this case H would contain a self-conjugate subgroup, and the isomorphism is multiple. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z |
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