Two mathematical structures are said to be isomorphic if there is an isomorphism between them.

Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.

Two systematic treatises on mathematical subjects were completed by Boole during his lifetime.

* Two solutions, called VSOP82 and VSOP87 are versions one mathematical theory for the orbits and positions of the major planets, which seeks to provide accurate positions over an extended period of time.

Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R < sup > 3 </ sup > upon itself ( known as an ambient isotopy ); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.

Two long papers published in 1840 — one on attractions and Clairaut's theorem, and the other on the variation of gravity at the surface of the earth — also demand notice, as do his mathematical memoirs on the critical values of sums of periodic series ( 1847 ) and on the numerical calculation of a class of definite integrals and infinite series ( 1850 ) and his discussion of a differential equation relating to the breaking of railway bridges ( 1849 ), research related to his evidence given to the Royal Commission on the Use of Iron in Railway structures after the Dee bridge disaster of 1847.

In addition to the above fonts, mathematical fonts for Lucida Bright, Lucida Sans, Lucida Sans Mono were also developed, as well as Lucida Math One, Lucida Math Two, Lucida Math Three, which contain only mathematical symbols.

Two popular filter metrics for classification problems are correlation and mutual information, although neither are true metrics or ' distance measures ' in the mathematical sense, since they fail to obey the triangle inequality and thus do not compute any actual ' distance ' – they should rather be regarded as ' scores '.

Two cross-country comparisons have found great variation in the gender differences regarding the degree of variance in mathematical ability.

Two quite different mathematical objects are called a pseudotensor in different contexts.

Two important strands of fictionalism are modal fictionalism developed by Gideon Rosen, which states that possible worlds, regardless of whether they exist or not, may be a part of a useful discourse, and mathematical fictionalism advocated by Hartry Field, which states that talk of numbers and other mathematical objects is nothing more than a convenience for doing science.

Two approaches can be used ( often in combination ) to elucidate how a particular lake works: field measurements and mathematical modeling.

Two works by Mauss in particular proved to have enduring relevance: Essay on the Gift, a seminal analysis of exchange and reciprocity, and his Huxley lecture on the notion of the person, the first comparative study of notions of person and selfhood cross-culturally.

Two other uncommon sources were promoted by Alexander: Anselm of Canterbury, whose writings had been ignored for almost a century gained an important advocate in Alexander and he used Anselm's works extensively in his teaching on Christology and soteriology ; and, Pseudo-Dionysius the Areopagite, whom Alexander used in his examination of the theology of Orders and ecclesiastical structures.

Two significant recent works written for solo bass include, Mario Davidovsky's Synchronisms No. 11 for double bass and electronic sounds and Elliott Carter's Figment III, for solo double bass.

Two other works by him were De Pulsus Variatione ( 1685 ), and Ars explorandi medicas facultates plantarum ex solo sapore ( 1688 ); His Opuscula were collected in 1687.

Two authors whose works are vital to an understanding of feminist theology are Mary Daly and Rosemary Radford Ruether.

Two notable Western composers for the kora are Brother Dominique Catta and Jacques Burtin ( France ), who wrote most of these scores, though composers like Carole Ouellet ( Canada ), Brother Grégoire Philippe ( Monastère de Keur Moussa ) and Sister Claire Marie Ledoux ( France ) contributed with original works.

Two of his works, the first edition of the Species Plantarum ( 1753 ) for plants and the tenth edition of the Systema Naturae ( 1758 ), are accepted as among the starting points of nomenclature ; his binomials ( names for species ) and his generic names take priority over those of others.

Two Creative Commons licences, Attribution and Attribution-ShareAlike, are libre licences ( they are marked as ‘ approved for free cultural works ’).

Two of its four sections may be performed separately as concert works: Hadewijch, De Stijl

Two of his best-known works, the Pietà and David, were sculpted before he turned thirty.

Two of his works from this period are the Senji Shō ( 撰時抄: " The Selection of the Time ") and the Hōon Shō ( 報恩抄: " On Repaying Debts of Gratitude "), which, along with his Risshō Ankoku Ron ( 立正安国論: " On Establishing the Correct Teaching for the Peace of the Land "), Kaimoku Shō (" The Opening of the Eyes "), and Kanjin no Honzon Shō (" The Object of Devotion for Observing the Mind "), constitute his Five Major Writings.

Two professors of linguistics have claimed that de Vere wrote not only the works of Shakespeare, but most of what is memorable in English literature during his lifetime, with such names as Edmund Spenser, Christopher Marlowe, Philip Sidney, John Lyly, George Peele, George Gascoigne, Raphael Holinshed, Robert Greene, Thomas Phaer, and Arthur Golding being among dozens of further pseudonyms of de Vere.

Two of her philosophical works, Pensées diverses and Considérations générales sur l ' état des sciences et des letteres aux différentes epoques de leur culture, were published, both posthumously.

Two polemical works thought to be his-A Reply to the Reverend Dean of St. Paul's Reflections on the Rector of Sutton, & c. ( 1681 ) and The Rector of Sutton Committed with the Dean of St. Paul's, or, A Defence of Dr. Stillingfleet's Irenicum ( 1680 )-have also been attributed to the Nottingham Presbyterian John Barret.

Two of his best known prose works, the utopian News from Nowhere and A Dream of John Ball were first printed here in serialized form.

* Two previously written Chinese pharmaceutical works, one by Shen Kuo and another by Su Shi, are combined into one written work.

Among the works exhibited were Le Fauconnier's vast composition Les Montagnards attaqués par des ours ( Mountaineers Attacked by Bears ) now at Rhode Island School of Design Museum, Joseph Csaky's Deux Femme, Two Women ( a sculpture now lost ), in addition to the highly abstract paintings by Kupka, Amorpha ( The National Gallery, Prague ), and Picabia, La Source, The Spring ( Museum of Modern Art, New York ).

The following works are of doubtful authenticity: De spectaculis (" On Public Games "); De bono pudicitiae (" The Virtue of Modesty "); De idolorum vanitate (" On the Vanity of Images ," written by Novatian ); De laude martyrii (" In Praise of Martyrs "); Adversus aleatores ; De duobus montibus Sina et Sion ( On the Two Mountains Sinai and Zion ); Adversus Judaeos ; and the Cena Cypriani (" Cyprian's Banquet ", which enjoyed wide circulation in the Middle Ages ).

Early works by Hals, such as Two Boys Playing and Singing and the aforementioned Banquet of the Officers of the St George Militia ( 1616 ), show him as a careful draughtsman capable of great finish, yet spirited withal.

Two of Kripke's earlier works, A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic, the former written while he was still a teenager, were on the subject of modal logic.

During these years Holst also became interested in Hindu mysticism and spirituality, and this interest led to the composition of several works set to translations of Sanskrit texts, including: Sita ( 1899 – 1906 ), a three-act opera based on an episode in the Ramayana ; Sāvitri ( 1908 ), a chamber opera based on a tale from the Mahabharata ; 4 groups of Hymns from the Rig Veda ( 1908 – 14 ); and two texts originally by Kalidasa: Two Eastern Pictures ( 1909 – 10 ) and The Cloud Messenger ( 1913 ).

* German — Beckmann, Max: Pierrot and Mask ( 1920 ), Before the Masked Ball ( 1922 ), Carnival ( 1943 ); Campendonk, Heinrich: Pierrot with Mask ( 1916 ), Pierrot ( with Serpent ) ( 1923 ), Pierrot with Sunflower ( 1925 ); Faure, Amandus: Standing Artist and Pierrot ( 1909 ); Heckel, Erich: Dead Pierrot ( 1914 ); Hofer, Karl: Circus Folk ( c. 1921 ); Leman, Ulrich: The Juggler ( 1913 ); Macke, August: Many works, including Ballets Russes ( 1912 ), Clown ( Pierrot ) ( 1913 ), Face of Pierrot ( 1913 ), Pierrot and Woman ( 1913 ); Mammen, Jeanne: The Death of Pierrot ( n. d .); Nolde, Emil: Pierrot and White Lilies ( c. 1911 ), Women and Pierrot ( 1917 ); Schlemmer, Oskar: Pierrot and Two Figures ( 1923 ); Werner, Theodor: Pierrot lunaire ( 1942 ).

* Italian — Modigliani, Amedeo ( worked mainly in France ): Pierrot ( 1915 ); Severini, Gino: Many works, including The Two Pierrots ( 1922 ), Pierrot ( 1923 ), Pierrot the Musician ( 1924 ), The Music Lesson ( 1928 – 1929 ), The Carnival ( 1955 ).

Phase Two of the development, which will shortly commence construction, will extend further down along the river front, on the site of the former Irish Oil Cake works.

Two facets of this aspect of the literary process have special significance for our time.

Two things have happened in recent months to bring the Council into perspective: each provides a basis for renewed hope and joy.

Two data centers have been established for the collection, indexing, critical evaluation, and dissemination of bibliographies and critical values in the fields of transition probabilities and collision cross sections.

Two stories will illustrate what I have in mind.

Two days before he was taken sick, Cousin Elec was out worrying about what too much rain might do to his sweetpeas, and Cousin Elec had always preserved in the top drawer of his secretary a mother-of-pearl paper knife which Theresa had coveted as a child and which he had promised she could have when he died.

Two related strands of research on altruism have emerged from traditional evolutionary analyses and from game theory.

Two other groups have similar inflorescences but a superior ovary, and have at times been put into separate families: the Agapanthaceae and the Alliaceae.

Two small sanctuaries, with terracotta votive offerings of Graeco-Phoenician age, lie not far off, but the location of the great shrines of Adonis and Aphrodite have not been identified ( M. Ohnefalsch-Richter, Kypros, i. ch. 1 ).

Two points in this brief description have attracted much scholarly commentary.

Two of Ammonius's students-Origen the Pagan, and Longinus-seem to have held philosophical positions which were closer to Middle Platonism than Neoplatonism, which perhaps suggests that Ammonius's doctrines were also closer to those of Middle Platonism than the Neoplatonism developed by Plotinus ( see the Enneads ), but Plotinus does not seem to have thought that he was departing in any significant way from that of his master.

Two other genera, Echinosphaerium and Camptonema, have been described but appear to be synonyms.

Two, from the Venus tablet of Ammisaduqa ( compiled in Babylon around 1700 BCE ) are reported to have been made during the reign of king Sargon of Akkad ( 2334 – 2279 BCE ).

Two theories of the direct initiation of apoptotic mechanisms in mammals have been suggested: the TNF-induced ( tumour necrosis factor ) model and the Fas-Fas ligand-mediated model, both involving receptors of the TNF receptor ( TNFR ) family coupled to extrinsic signals.

Two spiritual adversaries endeavour to tempt and corrupt humanity: these are often described through their mythological embodiments, Lucifer and his counterpart Ahriman, which have both positive and negative aspects.

Two Aegean vases were found at Sidon in 1885, and many fragments of Aegean and especially Cypriot pottery have been found during recent excavations of sites in Philistia by the Palestine Fund.

How do you do ?," Capp sardonically congratulated Lennon and Ono on their Two Virgins nude album cover: " I think that everybody owes it to the world to prove they have pubic hair.

The characters have made cameo appearances ( either visually or only voices ) and have been referenced in numerous television shows, such as Friends, Two and a Half Men, Celebrity Deathmatch, Robot Chicken, Space Ghost Coast to Coast, and Saturday Night Live ( TV Funhouse ), in films such as Airheads, Clueless, Austin Powers: International Man of Mystery and Jackass 3D, and even parodied in children shows such as Tiny Toon Adventures, Regular Show and Arthur.

Two groups of invertebrates have notably complex brains: arthropods ( insects, crustaceans, arachnids, and others ), and cephalopods ( octopuses, squids, and similar molluscs ).< ref name = Butler > The brains of arthropods and cephalopods arise from twin parallel nerve cords that extend through the body of the animal.

Two sets A and B are defined to be equal when they have precisely the same elements, that is, if every element of A is an element of B and every element of B is an element of A.

Two investigations have been held by the British government.

Two centuries ago, mummies were still believed to have medicinal properties against bleeding, and were sold as pharmaceuticals in powdered form ( see human mummy confection and mummia ).