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https://www.zbmath.org/authors/?q=ai%3Abers.lipman	zbMATH — the first resource for mathematics Bers, Lipman Compute Distance To: Author ID: bers.lipman Published as: Bers, Lipman; Bers, L. External Links: IdRef · MGP · Math-Net.Ru · Wikidata · GND · MacTutor Documents Indexed: 122 Publications since 1939, including 18 Books Biographic References: 15 Publications all top 5 Co-Authors 102 single-authored 4 John, Fritz 4 Schechter, Martin 3 Ahlfors, Lars Valerian 3 Gelbart, Abe Markham 2 Kra, Irwin 2 Nirenberg, Louis 1 Agmon, Shmuel 1 Behnke, Heinrich 1 Bochner, Salomon 1 Ehrenpreis, Leon 1 Farkas, Hershel M. 1 Gårding, Lars 1 Grauert, Hans 1 Greenberg, Leon 1 Gunning, Robert Clifford 1 Heins, Maurice Haskell 1 Jenkins, James Allister 1 Karal, Frank 1 Kodaira, Kunihiko 1 Maskit, Bernard 1 Nevanlinna, Rolf Herman 1 Rauch, Harry Ernest 1 Royden, H. L. 1 Spencer, Donald Clayton all top 5 Serials 9 Communications on Pure and Applied Mathematics 8 Bulletin of the American Mathematical Society 7 American Journal of Mathematics 5 Journal d’Analyse Mathématique 5 Acta Mathematica 4 Annals of Mathematics. Second Series 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 4 Annals of Mathematics Studies 3 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 3 Transactions of the American Mathematical Society 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Advances in Mathematics 2 Quarterly of Applied Mathematics 2 Proceedings of the National Academy of Sciences of the United States of America 2 Princeton Mathematical Series 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Journal of Research of the National Bureau of Standards 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Bulletin of the London Mathematical Society 1 Commentarii Mathematici Helvetici 1 The Journal of the Indian Mathematical Society. New Series 1 Journal of Mathematics of Kyoto University 1 Mathematica Scandinavica 1 Proceedings of the American Mathematical Society 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 1 Lecture Notes in Mathematics 1 Journal of Rational Mechanics and Analysis all top 5 Fields 45 Functions of a complex variable (30-XX) 27 Several complex variables and analytic spaces (32-XX) 8 History and biography (01-XX) 7 Algebraic geometry (14-XX) 5 General and overarching topics; collections (00-XX) 3 Group theory and generalizations (20-XX) 3 Partial differential equations (35-XX) 2 Differential geometry (53-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations contained in zbMATH Open 94 Publications have been cited 2,293 times in 1,679 Documents Cited by Year Mathematical aspects of subsonic and transonic gas dynamics. Zbl 0083.20501 Bers, Lipman 1958 Riemann’s mapping theorem for variable metrics. Zbl 0104.29902 Ahlfors, Lars V.; Bers, Lipman 1960 Partial differential equations. Proceeding of the Summer Seminar, Boulder, Colorado, 1957. Zbl 0126.00207 Bers, Lipman (ed.); John, Fritz (ed.); Schechter, Martin (ed.) 1964 On boundaries of Teichmüller spaces and on Kleinian groups. I. Zbl 0197.06001 Bers, Lipman 1970 Uniformization, moduli, and Kleinian groups. Zbl 0257.32012 Bers, Lipman 1972 Existence and uniqueness of a subsonic flow past a given profile. Zbl 0058.40601 Bers, Lipman 1954 Simultaneous uniformization. Zbl 0090.05101 Bers, Lipman 1960 Theory of pseudo-analytic functions. Zbl 0051.31603 Bers, Lipman 1953 Fiber spaces over Teichmüller spaces. Zbl 0249.32014 Bers, Lipman 1973 Local behavior of solutions of general linear elliptic equations. Zbl 0066.08101 Bers, Lipman 1955 Holomorphic families of injections. Zbl 0619.30027 Bers, Lipman; Royden, H. L. 1986 Quasiconformal mappings and Teichmüller’s theorem. Zbl 0100.28904 Bers, Lipman 1960 An extremal problem for quasiconformal mappings and a theorem by Thurston. Zbl 0389.30018 Bers, Lipman 1978 Finite dimensional Teichmueller spaces and generalizations. Zbl 0485.30002 Bers, Lipman 1981 Isolated singularities of minimal surfaces. Zbl 0043.15901 Bers, Lipman 1951 An outline of the theory of pseudoanalytic functions. Zbl 0072.07703 Bers, Lipman 1956 A non-standard integral equation with applications to quasi-conformal mappings. Zbl 0145.09502 Bers, Lipman 1966 Spaces of degenerating Riemann surfaces. Zbl 0294.32016 Bers, Lipman 1974 Automorphic forms for Schottky groups. Zbl 0327.32011 Bers, Lipman 1975 Uniformization by Beltrami equations. Zbl 0138.06101 Bers, Lipman 1961 Inequalities for finitely generated Kleinian groups. Zbl 0146.31601 Bers, Lipman 1967 An approximation theorem. Zbl 0134.05304 Bers, Lipman 1965 Spaces of Kleinian groups. Zbl 0211.10602 Bers, Lipman 1970 Automorphic forms and Poincaré series for infinitely generated Fuchsian groups. Zbl 0141.27502 Bers, Lipman 1965 On mildly nonlinear partial difference equations of elliptic type. Zbl 0053.40202 Bers, Lipman 1953 Holomorphic differentials as functions of moduli. Zbl 0102.06702 Bers, Lipman 1961 Partial differential equations. With supplements by Lars Garding and A. N. Milgram. With a preface by A. S. Householder. Repr. of the 1964 orig. publ. by John Wiley-Interscience. Zbl 0514.35001 Bers, Lipman; John, Fritz; Schechter, Martin 1979 Partial differential equations. (Уравнения с частными производными. Translation by Yu. V. Egorov. Edited by O. A. Oleĭnik.) Zbl 0143.32403 Bers, Lipman; John, Fritz; Schechter, Martin; Gårding, Lars 1966 On a theorem of Mori and the definition of quasiconformality. Zbl 0077.08001 Bers, Lipman 1957 An inequality for Riemann surfaces. Zbl 0575.30039 Bers, Lipman 1985 Quasiconformal mappings, with applications to differential equations, function theory and topology. Zbl 0419.30016 Bers, Lipman 1977 On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. Zbl 0067.32503 Bers, Lipman; Nirenberg, Louis 1955 On spaces of Riemann surfaces with nodes. Zbl 0294.32017 Bers, Lipman 1974 On rings of analytic functions. Zbl 0032.20302 Bers, Lipman 1948 Nielsen extensions of Riemann surfaces. Zbl 0352.30014 Bers, Lipman 1976 Holomorphic convexity of Teichmüller spaces. Zbl 0136.07004 Bers, Lipman; Ehrenpreis, Leon 1964 Abelian minimal surfaces. Zbl 0045.42501 Bers, Lipman 1951 On a class of differential equations in mechanics of continua. Zbl 0063.00340 Bers, Lipman; Gelbart, Abe 1943 Function-theoretical properties of solutions of partial differential equations of elliptic type. Zbl 0057.08602 Bers, Lipman 1954 Elliptic equations. Zbl 0128.09404 Bers, Lipman; Schechter, Martin 1964 The expansion theorem for sigma-monogenic functions. Zbl 0039.08701 Bers, Lipman 1950 On linear and non-linear elliptic boundary value problems in the plane. Zbl 0067.32504 Bers, Lipman; Nirenberg, Louis 1955 Deformations and moduli of Riemann surfaces with nodes and signatures. Zbl 0301.32019 Bers, Lipman 1975 On moduli of Kleinian groups. Zbl 0304.30013 Bers, Lipman 1974 Isomorphisms between Teichmüller spaces. Zbl 0224.32013 Bers, Lipman; Greenberg, Leon 1971 Partial differential equations and pseudoanalytic functions on Riemann surfaces. Zbl 0053.05201 Bers, Lipman 1953 Non-linear elliptic equations without non-linear entire solutions. Zbl 0056.32101 Bers, Lipman 1954 Formal powers and power series. Zbl 0072.29802 Bers, Lipman 1956 Remark on an application of pseudoanalytic functions. Zbl 0074.30004 Bers, Lipman 1956 Spaces of Riemann surfaces as bounded domains. Zbl 0106.28501 Bers, Lipman 1960 A remark on Mumford’s compactness theorem. Zbl 0249.30019 Bers, Lipman 1972 Spaces of Riemann surfaces. Zbl 0116.28803 Bers, Lipman 1960 Contributions to the theory of partial differential equations. Zbl 0056.31602 Bers, Lipman (ed.); Bochner, Salomon (ed.); John, Fritz (ed.) 1954 A crash course on Kleinian groups. Lectures given at a special session at the January 1974 meeting of the American Mathematical Society at San Francisco. Zbl 0279.00010 Bers, Lipman (ed.); Kra, Irwin (ed.) 1974 Mathematical aspects of subsonic and transonic gas dynamics. Reprint of the 1958 original. Zbl 1348.82003 Bers, Lipman 2016 The expansion theorem for pseudo-analytic functions. Zbl 0047.32101 Agmon, Shmuel; Bers, Lipman 1952 Univalent solutions of linear elliptic systems. Zbl 0051.31701 Bers, Lipman 1953 On moduli of Kleinian groups. Zbl 0301.30017 Bers, Lipman 1974 On Ahlfors’ finiteness theorem. Zbl 0167.07003 Bers, Lipman 1967 On a class of functions defined by partial differential equations. Zbl 0061.15905 Bers, Lipman; Gelbart, Abe 1944 Local theory of pseudoanalytic functions. Zbl 0068.06501 Bers, Lipman 1955 A new proof of a fundamental inequality for quasiconformal mappings. Zbl 0436.30016 Bers, Lipman 1979 Holomorphic families of isomorphisms of Möbius groups. Zbl 0598.30063 Bers, Lipman 1986 Results and conjectures in the mathematical theory of subsonic and transonic gas flows. Zbl 0058.41301 Bers, Lipman 1954 Survey of local properties of solutions of elliptic partial differential equations. Zbl 0074.08001 Bers, Lipman 1956 On Hilbert’s 22nd problem. Zbl 0348.30013 Bers, Lipman 1976 On Sullivan’s proof of the finiteness theorem and the eventual periodicity theorem. Zbl 0632.30025 Bers, Lipman 1987 Fricke spaces. Zbl 0634.32020 Bers, Lipman 1986 Automorphic forms and general Teichmüller spaces. Zbl 0141.27501 Bers, Lipman 1965 Eichler integrals with singularities. Zbl 0235.30024 Bers, Lipman 1971 Boundary value problems for minimal surfaces with singularities at infinity. Zbl 0043.15902 Bers, Lipman 1951 Finite dimensional Teichmüller spaces and generalizations. Zbl 0559.32003 Bers, Lipman 1983 Poincaré series for Kleinian groups. Zbl 0277.30016 Bers, Lipman 1973 Uniformization, moduli, and Kleinian groups. Zbl 0281.32016 Bers, Lipman 1973 Universal Teichmüller space. Zbl 0213.35701 Bers, Lipman 1970 Extremal quasiconformal mappings. Zbl 0231.30028 Bers, Lipman 1971 Partial differential equations and generalized analytic functions. Zbl 0036.05301 Bers, Lipman 1950 Partial differential equations and generalized analytic functions. II. Zbl 0042.08803 Bers, Lipman 1951 On bounded analytic functions of two complex variables in certain domains with distinguished boundary surface. Zbl 0060.24401 Bers, Lipman 1942 The action of the modular group on the complex boundary. Zbl 0476.32026 Bers, Lipman 1981 On iterates of hyperbolic transformations of Teichmueller space. Zbl 0525.30036 Bers, Lipman 1983 On a method of constructing two-dimensional subsonic compressible flows around closed profiles. Zbl 0063.00341 Bers, Lipman 1945 Analytic functions. Zbl 0100.28702 Nevanlinna, Rolf; Behnke, Heinrich; Grauert, Hans; Ahlfors, Lars V.; Spencer, D. C.; Bers, Lipman; Kodaira, Kunihiko; Heins, Maurice; Jenkins, James A. 1960 Uniformizzazione e moduli. (Unifomization and moduli). Zbl 0108.07603 Bers, Lipman 1960 The equivalence of two definitions of quasiconformal mappings. Zbl 0108.07702 Bers, Lipman 1962 L$$_1$$ approximation of analytic functions. Zbl 0251.30037 Bers, Lipman 1971 Completeness theorems for Poincaré series in one variable. Zbl 0131.08201 Bers, Lipman 1961 On avoiding the mean value theorem. Zbl 0154.05602 Bers, Lipman 1967 On a class of Kleinian groups. Zbl 0168.06203 1966 On generalized Laplace transformations. Zbl 0029.40003 Bers, Lipman; Gelbart, Abe 1947 An existence theorem in two-dimensional gas dynamics. Zbl 0037.11602 Bers, Lipman 1949 On the circulatory subsonic flow of a compressible fluid past a circular cylinder. Zbl 0063.00342 Bers, Lipman 1945 Finitely generated Kleinian groups. An introduction. Zbl 0672.30034 Bers, Lipman 1989 On Teichmüller’s proof of Teichmüller’s theorem. Zbl 0606.30024 Bers, Lipman 1986 Mathematical aspects of subsonic and transonic gas dynamics. Reprint of the 1958 original. Zbl 1348.82003 Bers, Lipman 2016 Finitely generated Kleinian groups. An introduction. Zbl 0672.30034 Bers, Lipman 1989 On Sullivan’s proof of the finiteness theorem and the eventual periodicity theorem. Zbl 0632.30025 Bers, Lipman 1987 Holomorphic families of injections. Zbl 0619.30027 Bers, Lipman; Royden, H. L. 1986 Holomorphic families of isomorphisms of Möbius groups. Zbl 0598.30063 Bers, Lipman 1986 Fricke spaces. Zbl 0634.32020 Bers, Lipman 1986 On Teichmüller’s proof of Teichmüller’s theorem. Zbl 0606.30024 Bers, Lipman 1986 An inequality for Riemann surfaces. Zbl 0575.30039 Bers, Lipman 1985 Finite dimensional Teichmüller spaces and generalizations. Zbl 0559.32003 Bers, Lipman 1983 On iterates of hyperbolic transformations of Teichmueller space. Zbl 0525.30036 Bers, Lipman 1983 Finite dimensional Teichmueller spaces and generalizations. Zbl 0485.30002 Bers, Lipman 1981 The action of the modular group on the complex boundary. Zbl 0476.32026 Bers, Lipman 1981 Partial differential equations. With supplements by Lars Garding and A. N. Milgram. With a preface by A. S. Householder. Repr. of the 1964 orig. publ. by John Wiley-Interscience. Zbl 0514.35001 Bers, Lipman; John, Fritz; Schechter, Martin 1979 A new proof of a fundamental inequality for quasiconformal mappings. Zbl 0436.30016 Bers, Lipman 1979 An extremal problem for quasiconformal mappings and a theorem by Thurston. Zbl 0389.30018 Bers, Lipman 1978 Quasiconformal mappings, with applications to differential equations, function theory and topology. Zbl 0419.30016 Bers, Lipman 1977 Nielsen extensions of Riemann surfaces. Zbl 0352.30014 Bers, Lipman 1976 On Hilbert’s 22nd problem. Zbl 0348.30013 Bers, Lipman 1976 Automorphic forms for Schottky groups. Zbl 0327.32011 Bers, Lipman 1975 Deformations and moduli of Riemann surfaces with nodes and signatures. Zbl 0301.32019 Bers, Lipman 1975 Spaces of degenerating Riemann surfaces. Zbl 0294.32016 Bers, Lipman 1974 On spaces of Riemann surfaces with nodes. Zbl 0294.32017 Bers, Lipman 1974 On moduli of Kleinian groups. Zbl 0304.30013 Bers, Lipman 1974 A crash course on Kleinian groups. Lectures given at a special session at the January 1974 meeting of the American Mathematical Society at San Francisco. Zbl 0279.00010 Bers, Lipman; Kra, Irwin 1974 On moduli of Kleinian groups. Zbl 0301.30017 Bers, Lipman 1974 Fiber spaces over Teichmüller spaces. Zbl 0249.32014 Bers, Lipman 1973 Poincaré series for Kleinian groups. Zbl 0277.30016 Bers, Lipman 1973 Uniformization, moduli, and Kleinian groups. Zbl 0281.32016 Bers, Lipman 1973 Uniformization, moduli, and Kleinian groups. Zbl 0257.32012 Bers, Lipman 1972 A remark on Mumford’s compactness theorem. Zbl 0249.30019 Bers, Lipman 1972 Isomorphisms between Teichmüller spaces. Zbl 0224.32013 Bers, Lipman; Greenberg, Leon 1971 Eichler integrals with singularities. Zbl 0235.30024 Bers, Lipman 1971 Extremal quasiconformal mappings. Zbl 0231.30028 Bers, Lipman 1971 L$$_1$$ approximation of analytic functions. Zbl 0251.30037 Bers, Lipman 1971 On boundaries of Teichmüller spaces and on Kleinian groups. I. Zbl 0197.06001 Bers, Lipman 1970 Spaces of Kleinian groups. Zbl 0211.10602 Bers, Lipman 1970 Universal Teichmüller space. Zbl 0213.35701 Bers, Lipman 1970 Inequalities for finitely generated Kleinian groups. Zbl 0146.31601 Bers, Lipman 1967 On Ahlfors’ finiteness theorem. Zbl 0167.07003 Bers, Lipman 1967 On avoiding the mean value theorem. Zbl 0154.05602 Bers, Lipman 1967 A non-standard integral equation with applications to quasi-conformal mappings. Zbl 0145.09502 Bers, Lipman 1966 Partial differential equations. (Уравнения с частными производными. Translation by Yu. V. Egorov. Edited by O. A. Oleĭnik.) Zbl 0143.32403 Bers, Lipman; John, Fritz; Schechter, Martin; Gårding, Lars 1966 On a class of Kleinian groups. Zbl 0168.06203 1966 An approximation theorem. Zbl 0134.05304 Bers, Lipman 1965 Automorphic forms and Poincaré series for infinitely generated Fuchsian groups. Zbl 0141.27502 Bers, Lipman 1965 Automorphic forms and general Teichmüller spaces. Zbl 0141.27501 Bers, Lipman 1965 Partial differential equations. Proceeding of the Summer Seminar, Boulder, Colorado, 1957. Zbl 0126.00207 Bers, Lipman; John, Fritz; Schechter, Martin 1964 Holomorphic convexity of Teichmüller spaces. Zbl 0136.07004 Bers, Lipman; Ehrenpreis, Leon 1964 Elliptic equations. Zbl 0128.09404 Bers, Lipman; Schechter, Martin 1964 The equivalence of two definitions of quasiconformal mappings. Zbl 0108.07702 Bers, Lipman 1962 Uniformization by Beltrami equations. Zbl 0138.06101 Bers, Lipman 1961 Holomorphic differentials as functions of moduli. Zbl 0102.06702 Bers, Lipman 1961 Completeness theorems for Poincaré series in one variable. Zbl 0131.08201 Bers, Lipman 1961 Riemann’s mapping theorem for variable metrics. Zbl 0104.29902 Ahlfors, Lars V.; Bers, Lipman 1960 Simultaneous uniformization. Zbl 0090.05101 Bers, Lipman 1960 Quasiconformal mappings and Teichmüller’s theorem. Zbl 0100.28904 Bers, Lipman 1960 Spaces of Riemann surfaces as bounded domains. Zbl 0106.28501 Bers, Lipman 1960 Spaces of Riemann surfaces. Zbl 0116.28803 Bers, Lipman 1960 Analytic functions. Zbl 0100.28702 Nevanlinna, Rolf; Behnke, Heinrich; Grauert, Hans; Ahlfors, Lars V.; Spencer, D. C.; Bers, Lipman; Kodaira, Kunihiko; Heins, Maurice; Jenkins, James A. 1960 Uniformizzazione e moduli. (Unifomization and moduli). Zbl 0108.07603 Bers, Lipman 1960 Mathematical aspects of subsonic and transonic gas dynamics. Zbl 0083.20501 Bers, Lipman 1958 On a theorem of Mori and the definition of quasiconformality. Zbl 0077.08001 Bers, Lipman 1957 An outline of the theory of pseudoanalytic functions. Zbl 0072.07703 Bers, Lipman 1956 Formal powers and power series. Zbl 0072.29802 Bers, Lipman 1956 Remark on an application of pseudoanalytic functions. Zbl 0074.30004 Bers, Lipman 1956 Survey of local properties of solutions of elliptic partial differential equations. Zbl 0074.08001 Bers, Lipman 1956 Local behavior of solutions of general linear elliptic equations. Zbl 0066.08101 Bers, Lipman 1955 On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. Zbl 0067.32503 Bers, Lipman; Nirenberg, Louis 1955 On linear and non-linear elliptic boundary value problems in the plane. Zbl 0067.32504 Bers, Lipman; Nirenberg, Louis 1955 Local theory of pseudoanalytic functions. Zbl 0068.06501 Bers, Lipman 1955 Existence and uniqueness of a subsonic flow past a given profile. Zbl 0058.40601 Bers, Lipman 1954 Function-theoretical properties of solutions of partial differential equations of elliptic type. Zbl 0057.08602 Bers, Lipman 1954 Non-linear elliptic equations without non-linear entire solutions. Zbl 0056.32101 Bers, Lipman 1954 Contributions to the theory of partial differential equations. Zbl 0056.31602 Bers, Lipman; Bochner, Salomon; John, Fritz 1954 Results and conjectures in the mathematical theory of subsonic and transonic gas flows. Zbl 0058.41301 Bers, Lipman 1954 Theory of pseudo-analytic functions. Zbl 0051.31603 Bers, Lipman 1953 On mildly nonlinear partial difference equations of elliptic type. Zbl 0053.40202 Bers, Lipman 1953 Partial differential equations and pseudoanalytic functions on Riemann surfaces. Zbl 0053.05201 Bers, Lipman 1953 Univalent solutions of linear elliptic systems. Zbl 0051.31701 Bers, Lipman 1953 The expansion theorem for pseudo-analytic functions. Zbl 0047.32101 Agmon, Shmuel; Bers, Lipman 1952 Isolated singularities of minimal surfaces. Zbl 0043.15901 Bers, Lipman 1951 Abelian minimal surfaces. Zbl 0045.42501 Bers, Lipman 1951 Boundary value problems for minimal surfaces with singularities at infinity. Zbl 0043.15902 Bers, Lipman 1951 Partial differential equations and generalized analytic functions. II. Zbl 0042.08803 Bers, Lipman 1951 The expansion theorem for sigma-monogenic functions. Zbl 0039.08701 Bers, Lipman 1950 Partial differential equations and generalized analytic functions. Zbl 0036.05301 Bers, Lipman 1950 An existence theorem in two-dimensional gas dynamics. Zbl 0037.11602 Bers, Lipman 1949 On rings of analytic functions. Zbl 0032.20302 Bers, Lipman 1948 On generalized Laplace transformations. Zbl 0029.40003 Bers, Lipman; Gelbart, Abe 1947 On a method of constructing two-dimensional subsonic compressible flows around closed profiles. Zbl 0063.00341 Bers, Lipman 1945 On the circulatory subsonic flow of a compressible fluid past a circular cylinder. Zbl 0063.00342 Bers, Lipman 1945 On a class of functions defined by partial differential equations. Zbl 0061.15905 Bers, Lipman; Gelbart, Abe 1944 On a class of differential equations in mechanics of continua. Zbl 0063.00340 Bers, Lipman; Gelbart, Abe 1943 On bounded analytic functions of two complex variables in certain domains with distinguished boundary surface. Zbl 0060.24401 Bers, Lipman 1942 all top 5 all top 5 Cited in 275 Serials 96 Transactions of the American Mathematical Society 58 Proceedings of the American Mathematical Society 53 Journal d’Analyse Mathématique 46 Journal of Differential Equations 44 Archive for Rational Mechanics and Analysis 43 Inventiones Mathematicae 42 Acta Mathematica 39 Siberian Mathematical Journal 38 Journal of Mathematical Sciences (New York) 36 Duke Mathematical Journal 34 Mathematische Annalen 33 Communications in Mathematical Physics 32 Mathematische Zeitschrift 30 Tohoku Mathematical Journal. Second Series 29 Journal of Mathematical Analysis and Applications 29 Bulletin of the American Mathematical Society 27 Geometry & Topology 25 Advances in Mathematics 24 Bulletin of the American Mathematical Society. New Series 22 Communications in Partial Differential Equations 20 Israel Journal of Mathematics 19 Conformal Geometry and Dynamics 17 Geometriae Dedicata 17 Ergodic Theory and Dynamical Systems 16 Manuscripta Mathematica 15 Numerische Mathematik 15 Acta Mathematica Sinica. English Series 14 The Journal of Geometric Analysis 12 Communications on Pure and Applied Mathematics 12 Journal of Mathematical Physics 12 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 11 Mathematical Notes 11 Ukrainian Mathematical Journal 11 Annales de l’Institut Fourier 11 Nagoya Mathematical Journal 11 Journal of the American Mathematical Society 11 Geometric and Functional Analysis. GAFA 11 Complex Variables and Elliptic Equations 10 Journal of Geometry and Physics 10 Kodai Mathematical Journal 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Arkiv för Matematik 9 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 9 Mathematische Nachrichten 9 SIAM Journal on Mathematical Analysis 8 Mathematical Methods in the Applied Sciences 8 Chinese Annals of Mathematics. Series B 8 Advances in Applied Clifford Algebras 8 Complex Analysis and Operator Theory 7 Applicable Analysis 7 Mathematics of Computation 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Functional Analysis and its Applications 7 Journal of Functional Analysis 7 Journal of Soviet Mathematics 7 Monatshefte für Mathematik 7 Rendiconti del Circolo Matemàtico di Palermo. Serie II 7 Calculus of Variations and Partial Differential Equations 7 Annales Academiae Scientiarum Fennicae. Mathematica 7 Doklady Mathematics 7 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 Archiv der Mathematik 6 Compositio Mathematica 6 Osaka Journal of Mathematics 6 Zeitschrift für Analysis und ihre Anwendungen 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 6 Journal of the European Mathematical Society (JEMS) 6 Differential Equations 6 Algebraic & Geometric Topology 6 Science China. Mathematics 5 Bulletin of the Australian Mathematical Society 5 Rocky Mountain Journal of Mathematics 5 Publications of the Research Institute for Mathematical Sciences, Kyoto University 5 Topology and its Applications 5 Revista Matemática Iberoamericana 5 Journal of High Energy Physics 5 Computational Methods and Function Theory 5 Kodai Mathematical Seminar Reports 4 Fluid Dynamics 4 International Journal of Theoretical Physics 4 Journal of the Franklin Institute 4 Prikladnaya Matematika i Mekhanika 4 Michigan Mathematical Journal 4 Tokyo Journal of Mathematics 4 Applied Mathematics Letters 4 Science in China. Series A 4 Computational Mathematics and Mathematical Physics 4 Journal of Elasticity 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Acta Mathematica Sinica. New Series 4 Russian Mathematics 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Annals of Mathematics. Second Series 4 Communications in Contemporary Mathematics 4 Lobachevskii Journal of Mathematics 4 Groups, Geometry, and Dynamics 4 Analysis and Mathematical Physics 4 Nonlinear Analysis. Theory, Methods & Applications ...and 175 more Serials all top 5 Cited in 53 Fields 711 Functions of a complex variable (30-XX) 493 Partial differential equations (35-XX) 329 Several complex variables and analytic spaces (32-XX) 163 Fluid mechanics (76-XX) 157 Differential geometry (53-XX) 149 Manifolds and cell complexes (57-XX) 143 Dynamical systems and ergodic theory (37-XX) 99 Global analysis, analysis on manifolds (58-XX) 81 Algebraic geometry (14-XX) 71 Group theory and generalizations (20-XX) 48 Quantum theory (81-XX) 44 Numerical analysis (65-XX) 41 Potential theory (31-XX) 41 Calculus of variations and optimal control; optimization (49-XX) 31 Number theory (11-XX) 30 Functional analysis (46-XX) 23 Ordinary differential equations (34-XX) 22 Operator theory (47-XX) 22 Mechanics of deformable solids (74-XX) 20 Topological groups, Lie groups (22-XX) 20 Measure and integration (28-XX) 20 Relativity and gravitational theory (83-XX) 12 Special functions (33-XX) 12 Probability theory and stochastic processes (60-XX) 11 Integral equations (45-XX) 11 Geometry (51-XX) 10 General topology (54-XX) 10 Optics, electromagnetic theory (78-XX) 9 Real functions (26-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 History and biography (01-XX) 8 Statistical mechanics, structure of matter (82-XX) 5 General and overarching topics; collections (00-XX) 5 Approximations and expansions (41-XX) 5 Abstract harmonic analysis (43-XX) 5 Convex and discrete geometry (52-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Integral transforms, operational calculus (44-XX) 4 Algebraic topology (55-XX) 3 Combinatorics (05-XX) 3 Nonassociative rings and algebras (17-XX) 3 Geophysics (86-XX) 2 Associative rings and algebras (16-XX) 2 Difference and functional equations (39-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Statistics (62-XX) 1 Astronomy and astrophysics (85-XX) 1 Biology and other natural sciences (92-XX) Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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http://dergipark.gov.tr/jocrest/issue/40461/506191	Yıl 2018, Cilt 4, Sayı 2, Sayfalar 135 - 142 2018-12-31 \| \| \| \| ## trenA Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway AirportA Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport #### Ramazan Kürşat ÇEÇEN [1] ##### 6 36 Airports play an important role for air transportation industry. Using airport facilities effectively such as runways provide opportunities to decrease delays and increase the runway capacities. Otherwise, delays cause more congestion and reduce the capacities. To handle this problem, we present two mixed integer linear models to minimize total delay for combined arrival and departure operations in a single runway. The first model does not allow to change aircraft runway sequence whereas the second model allows to change aircraft runway sequence within the delay limits. The separation time between aircraft pair changes according to wake-vortex effects and operation types. When we compare the first and second model, the results demonstrate that total delay decreases in the second model. Airports play an important role for air transportation industry. Using airport facilities effectively such as runways provide opportunities to decrease delays and increase the runway capacities. Otherwise, delays cause more congestion and reduce the capacities. To handle this problem, we present two mixed integer linear models to minimize total delay for combined arrival and departure operations in a single runway. The first model does not allow to change aircraft runway sequence whereas the second model allows to change aircraft runway sequence within the delay limits. The separation time between aircraft pair changes according to wake-vortex effects and operation types. When we compare the first and second model, the results demonstrate that total delay decreases in the second model. • Airbus Global Market Forecast (2018), Blagnac Cedex, France • Bennell, J.A., Mesgarpour, M., Potts, C.N., (2011), “Airport runway scheduling”, OR: Quarterly Journal of Operations Research Vol. 9, No. 2, pp. 115-138. • Bayen AM., Tomlin CJ., Ye Y, Zhang J. 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Proceedings of 12th national conference of the Australian society for operations research, 1993 Adelaide, Australia, • Ernst AT, Krishnamoorthy M, Storer RH (1999), “Heuristic and exact algorithms for scheduling aircraft landings”. Networks International Journal Vol. 34, No. 3, pp 229–241 • Beasley JE, Sonander J, Havelock P (2001), “Scheduling aircraft landing at London Heathrow using a population heuristic” Journal of Operational Research Society Vol. 52, No. 5, pp 483–493 • Bianco L and Bielli M (1993), “System aspects and optimization models in ATC planning”. Large scale computation and information processing in ATC. Springer, Berlin, pp 47–100 • Hansen JV (2004), “Genetic search methods in air traffic control” Computer Operation Research Vol. 31, No.3 pp 445–459 • Capri S, Ignaccolo M (2004), “Genetic algorithms for solving the aircraft-sequencing problem: the introduction of departures into the dynamic model”, Journal of Air Transport Management Vol. 10, No.5, pp 345–351 • Hu X-B and Chen W-H (2005), “Receding horizon control for aircraft arrival sequencing and scheduling”. IEEE Transactions Intelligent Transport System Vol. 6, No. 2, pp. 189–197 • SHERALI, Hanif D., et al. (1992), “An integrated simulation and dynamic programming approach for determining optimal runway exit locations”. Management science, Vol. 38, No.7, pp 1049-1062. Birincil Dil tr Mühendislik Makaleler Yazar: Ramazan Kürşat ÇEÇEN (Sorumlu Yazar) Bibtex @araştırma makalesi { jocrest506191, journal = {Journal of Current Researches on Engineering, Science and Technology}, issn = {}, eissn = {2651-2521}, address = {Huriye UÇAR}, year = {2018}, volume = {4}, pages = {135 - 142}, doi = {}, title = {A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport}, key = {cite}, author = {ÇEÇEN, Ramazan Kürşat} } APA ÇEÇEN, R . (2018). A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport. Journal of Current Researches on Engineering, Science and Technology, 4 (2), 135-142. Retrieved from http://dergipark.gov.tr/jocrest/issue/40461/506191 MLA ÇEÇEN, R . "A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport". Journal of Current Researches on Engineering, Science and Technology 4 (2018): 135-142 Chicago ÇEÇEN, R . "A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport". Journal of Current Researches on Engineering, Science and Technology 4 (2018): 135-142 RIS TY - JOUR T1 - A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport AU - Ramazan Kürşat ÇEÇEN Y1 - 2018 PY - 2018 N1 - DO - T2 - Journal of Current Researches on Engineering, Science and Technology JF - Journal JO - JOR SP - 135 EP - 142 VL - 4 IS - 2 SN - -2651-2521 M3 - UR - Y2 - 2019 ER - EndNote %0 Journal of Current Researches on Engineering, Science and Technology A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport %A Ramazan Kürşat ÇEÇEN %T A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport %D 2018 %J Journal of Current Researches on Engineering, Science and Technology %P -2651-2521 %V 4 %N 2 %R %U ISNAD ÇEÇEN, Ramazan Kürşat . "A Mixed Integer Linear Program Model to Minimize both Arrival and Departure Delays for Single Runway Airport". Journal of Current Researches on Engineering, Science and Technology 4 / 2 (Aralık 2019): 135-142.	2019-03-20T09:33:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.293022483587265, "perplexity": 7026.231501091211}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202324.5/warc/CC-MAIN-20190320085116-20190320111116-00028.warc.gz"}
http://mathonline.wikidot.com/converting-binary-numbers-to-decimal-numbers	Converting Binary Numbers to Decimal Numbers Table of Contents # Converting Binary Numbers to Decimal Numbers We have already seen a little bit in terms of converting binary numbers into decimal number from The Decimal and Binary Number Systems. We will now formalize this process. Let $(x)_2 = a_na_{n-1}...a_1a_0a_{-1}...a_{-m+1}a_{-m}$ be a binary number. Then the digits of $x$ are either $0$ or $1$, that is, $a_j \in \{ 0, 1 \}$ for $-m ≤ j ≤ n$. We can easily convert $(x)_{2}$ into a decimal number with the following formula: (1) \begin{align} \quad \quad (x)_2 = \left [ \left ( a_n \cdot 2^n \right ) + \left (a_{n-1} \cdot 2^{n-1} \right) + .... + \left (a_1 \cdot 2^1 \right ) + \left (a_0 \cdot 2^0 \right ) + \left (a_{-1} \cdot 2^{-1} \right ) + ... + \left ( a_{-m+1} \cdot 2^{-m+1} \right ) + \left (a_{-m} \cdot 2^{-m} \right ) \right ]_{10} \end{align} For example, consider the binary number $(110101.1001)_2$. Applying the formula above and we get that the decimal representation of the binary number $(110101.1001)_2$ is: (2) \begin{align} \quad \quad (110101.1001)_2 = \left ( 1 \cdot 2^5 \right ) + \left (1 \cdot 2^4 \right ) + \left (0 \cdot 2^3 \right ) + \left (1 \cdot 2^2 \right ) + \left ( 0 \cdot 2^1 \right ) + \left (1 \cdot 2^0 \right) + \left (1 \cdot 2 ^{-1} \right) + \left ( 0 \cdot 2^{-2} \right) + \left (0 \cdot 2^{-3} \right) + \left (1 \cdot 2^{-4} \right) \\ \quad \quad (110101.1001)_2 = \left (32 + 16 + 0 + 4 + 0 + 1 + \frac{1}{2} + 0 + 0 + \frac{1}{16} \right)_{10} \\ \quad \quad (110101.1001)_2 = (53.5625)_{10} \end{align} ## Example 1 Convert the binary number $(1101101)_{2}$ into a decimal number. We have that: (3) \begin{align} \quad (1101101)_{2} = \left ( 1 \cdot 2^6 \right ) + \left ( 1 \cdot 2^5 \right ) + \left ( 0 \cdot 2^4 \right ) + \left ( 1 \cdot 2^3 \right ) + \left ( 1 \cdot 2^2 \right ) + \left ( 0 \cdot 2^1 \right ) + \left ( 1 \cdot 2^0 \right ) \\ \quad (1101101)_{2} = \left ( 64 + 32 + 0 + 8 + 4 + 0 + 1 \right)_{10} = (109)_{2} \end{align} ## Example 2 Convert the binary numbers $(11)_{2}$, $(111)_{2}$, $(1111)_{2}$, …, $(\underbrace{111...1}_{\mathrm{n-times}})_{2}$ into decimal numbers. Note that $(11)_{2} = 2 + 1 = (3)_{2} = 2^{2} - 1$, $(111)_{2} = 4 + 2 + 1 = (7)_{2} = 2^3 - 1$, $(1111)_{2} = 8 + 4 + 2 + 1 = (15)_{2} = 2^4 - 1$. In general, we see that: (4) \begin{align} (\underbrace{111...1}_{\mathrm{n-times}})_{2} = 2^n - 1 \end{align} Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License	2017-01-24T15:09:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 311.3487402249627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560284429.99/warc/CC-MAIN-20170116095124-00168-ip-10-171-10-70.ec2.internal.warc.gz"}
https://www.pakp.gov.pk/2013/assembly-business/	## Assembly Business Session No Summoned By Period From Period To No of Sittings 1 Governor 29th May 2013 25th May 2013 3 2 Governor 17th Jun 2013 3rd Jul 2013 13 3 Governor 29th Jul 2013 6th Aug 2013 1 4 Governor 10th Sep 2013 19th Sep 2013 7 5 Speaker 30th Sep 2013 1st Oct 2013 2 6 Governor 7th Oct 2013 11th Oct 2013 4 7 Governor 23rd Oct 2013 31st Oct 2013 5 8 Governor 4th Nov 2013 4th Nov 2013 1 9 Governor 6th Jan 2014 22nd Jan 2014 10 10 Speaker 18th Feb 2014 6th Mar 2014 10 11 Governor 11th Mar 2014 21st Mar 2014 7 12 Speaker 16th Apr 2014 13th May 2014 8 13 Speaker 30th May 2014 6th Jun 2014 3 14 Governor 14th Jun 2014 26th Jun 2014 9 15 Governor 23rd Oct 2014 11th Jan 2016 80 16 Governor 11th Mar 2016 1st Apr 2016 8 17 Governor 29th Apr 2016 6th May 2016 4 18 Governor 17th May 2016 27th May 2016 5 19 Governor 14th Jun 2016 24th Jun 2016 8 20 Governor 3rd Aug 2016 15th Aug 2016 6 21 Governor 19th Sep 2016 20th Dec 2016 21 22 Governor 24th Jan 2017 6th Feb 2017 4 23 Speaker 20th Feb 2017 2nd Mar 2017 3 24 Governor 11th Apr 2017 23rd May 2017 14 25 Governor 7th Jun 2017 16th Jun 2017 8 26 Governor 19th Sep 2017 27th Oct 2017 12 27 Governor 4th Dec 2017 2nd Mar 2018 19 28 Governor 13th Apr 2018 16th Apr 2018 2 29 Governor 27th May 2018 28th May 2018 2	2020-11-29T11:03:52	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8562789559364319, "perplexity": 9373.295566827455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141197593.33/warc/CC-MAIN-20201129093434-20201129123434-00516.warc.gz"}
http://legisquebec.gouv.qc.ca/en/showversion/cr/Q-2,%20r.%204.1?code=se:199&pointInTime=20191104	### Q-2, r. 4.1 - Clean Air Regulation 199. For the purposes of this Regulation, an emission limit or other emission standard established for a source of contamination is complied with if (1) the arithmetic average of 3 results of measures taken during the same sampling run carried out is less than or equal to the limit or standard; (2) at least 2 of the results are less than the limit or standard; and (3) none of the 3 results exceeds the limit or standard by not more than 20%. This section does not apply to emission limits and other emission standards for which a provision of this Regulation prescribes a contaminant sampling taken by a continuous measuring and recording system, or to the limits prescribed by section 137 for fluorides. It also does not apply to the limits prescribed by Title IV. O.C. 501-2011, s. 199.	2020-07-03T11:51:58	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8121504783630371, "perplexity": 1754.8936047086656}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655881984.34/warc/CC-MAIN-20200703091148-20200703121148-00148.warc.gz"}
https://xmm-tools.cosmos.esa.int/external/sas/current/doc/evigweight/node7.html	XMM-Newton Science Analysis System evigweight (evigweight-1.8) [xmmsas_20211130_0941-20.0.0] ## Spectral analysis One can then define (via evselect called with withzcolumn=Y withzerrorcolumn=N) a corrected' spectrum within region (usually in sky coordinates) and its associated error : (3) (4) where is the exposure time for the CCD/node where the event was detected and the width of bin . If the region extends over a single CCD, the exposure time may be taken out of the sums. is an estimate of the spectrum one would get if the detector was flat. In terms of the usual uncorrected' spectrum: (5) (6) where the denote the average over the photons in bin . The corresponding source spectrum is also obtained by summing over the region, and the model spectrum (to be compared to the data) by multiplying with the central effective area and applying the response matrix. (7) (8) Of course the response matrix should be taken (via rmfgen) in the true detector region (not at the center) associated with the sky region . The central effective area may be obtained by calling arfgen with special settings: arfgen arfset=your_arf spectrumset=your_spectrum withbadpixcorr=N modelee=N \ withdetbounds=Y filterdss=N detmaptype=flat detxbins=1 detybins=1 \ withsourcepos=Y sourcecoords=tel sourcex=0 sourcey=0 Model fitting may be performed via XSPEC, entering as RATE, and as STAT_ERR, with and in the Ancillary Response File and Redistribution Matrix File, respectively. Note that the weighting procedure is incompatible with using the Poisson model (C-statistic) in XSPEC (the formula must be used). This means that care must be taken to have enough counts per spectral bin. XMM-Newton SOC -- 2021-11-30	2022-05-17T21:11:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9179449677467346, "perplexity": 3232.0628830979144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662520817.27/warc/CC-MAIN-20220517194243-20220517224243-00120.warc.gz"}
https://par.nsf.gov/biblio/10082739-dark-energy-survey-year-results-methodology-projections-joint-analysis-galaxy-clustering-galaxy-lensing-cmb-lensing-two-point-functions	Dark Energy Survey Year 1 results: Methodology and projections for joint analysis of galaxy clustering, galaxy lensing, and CMB lensing two-point functions Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Publication Date: NSF-PAR ID: 10082739 Journal Name: Physical Review D Volume: 99 Issue: 2 ISSN: 2470-0010; PRVDAQ Publisher: American Physical Society 1. ABSTRACT We compare predictions for galaxy–galaxy lensing profiles and clustering from the Henriques et al. public version of the Munich semi-analytical model (SAM) of galaxy formation and the IllustrisTNG suite, primarily TNG300, with observations from KiDS + GAMA and SDSS-DR7 using four different selection functions for the lenses (stellar mass, stellar mass and group membership, stellar mass and isolation criteria, and stellar mass and colour). We find that this version of the SAM does not agree well with the current data for stellar mass-only lenses with $M_\ast \gt 10^{11}\, \mathrm{ M}_\odot$. By decreasing the merger time for satellite galaxies as well as reducing the radio-mode active galactic nucleus accretion efficiency in the SAM, we obtain better agreement, both for the lensing and the clustering, at the high-mass end. We show that the new model is consistent with the signals for central galaxies presented in Velliscig et al. Turning to the hydrodynamical simulation, TNG300 produces good lensing predictions, both for stellar mass-only (χ2 = 1.81 compared to χ2 = 7.79 for the SAM) and locally brightest galaxy samples (χ2 = 3.80 compared to χ2 = 5.01). With added dust corrections to the colours it matches the SDSS clustering signal well for red low-mass galaxies. We find that both themore » 2. ABSTRACT Galaxy–galaxy lensing is a powerful probe of the connection between galaxies and their host dark matter haloes, which is important both for galaxy evolution and cosmology. We extend the measurement and modelling of the galaxy–galaxy lensing signal in the recent Dark Energy Survey Year 3 cosmology analysis to the highly non-linear scales (∼100 kpc). This extension enables us to study the galaxy–halo connection via a Halo Occupation Distribution (HOD) framework for the two lens samples used in the cosmology analysis: a luminous red galaxy sample (redmagic) and a magnitude-limited galaxy sample (maglim). We find that redmagic (maglim) galaxies typically live in dark matter haloes of mass log10(Mh/M⊙) ≈ 13.7 which is roughly constant over redshift (13.3−13.5 depending on redshift). We constrain these masses to ${\sim}15{{\ \rm per\ cent}}$, approximately 1.5 times improvement over the previous work. We also constrain the linear galaxy bias more than five times better than what is inferred by the cosmological scales only. We find the satellite fraction for redmagic (maglim) to be ∼0.1−0.2 (0.1−0.3) with no clear trend in redshift. Our constraints on these halo properties are broadly consistent with other available estimates from previous work, large-scale constraints, and simulations. The framework built in this paper willmore » 3. ABSTRACT The DMASS sample is a photometric sample from the DES Year 1 data set designed to replicate the properties of the CMASS sample from BOSS, in support of a joint analysis of DES and BOSS beyond the small overlapping area. In this paper, we present the measurement of galaxy–galaxy lensing using the DMASS sample as gravitational lenses in the DES Y1 imaging data. We test a number of potential systematics that can bias the galaxy–galaxy lensing signal, including those from shear estimation, photometric redshifts, and observing conditions. After careful systematic tests, we obtain a highly significant detection of the galaxy–galaxy lensing signal, with total S/N = 25.7. With the measured signal, we assess the feasibility of using DMASS as gravitational lenses equivalent to CMASS, by estimating the galaxy-matter cross-correlation coefficient rcc. By jointly fitting the galaxy–galaxy lensing measurement with the galaxy clustering measurement from CMASS, we obtain $r_{\rm cc}=1.09^{+0.12}_{-0.11}$ for the scale cut of $4 \, h^{-1}{\rm \,\,Mpc}$ and $r_{\rm cc}=1.06^{+0.13}_{-0.12}$ for $12 \, h^{-1}{\rm \,\,Mpc}$ in fixed cosmology. By adding the angular galaxy clustering of DMASS, we obtain rcc = 1.06 ± 0.10 for the scale cut of $4 \, h^{-1}{\rm \,\,Mpc}$ and rcc = 1.03 ± 0.11 for $12 \, h^{-1}{\rm \,\,Mpc}$. The resultingmore »	2022-10-02T22:28:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5284239649772644, "perplexity": 3314.855628583728}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337360.41/warc/CC-MAIN-20221002212623-20221003002623-00556.warc.gz"}
https://pos.sissa.it/334/216/	Volume 334 - The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) - Standard Model Parameters and Renormalization Towards non-perturbative matching of three/four-flavor Wilson coefficients with aposition-space procedure M. Tomii Full text: pdf Published on: 2019 May 29 Abstract We propose a strategy to non-perturbatively match the Wilson coefficients in the three- and four-flavor theories, which uses two-point Green's functions of the corresponding four-quark operators at long distances. The idea is refined by combining with the spherical averaging technique, which enables us to convert two-point functions calculated on the lattice into continuous functions of the distance $\|x-y\|$ between two operators. We also show the result for an exploratory calculation of two-point functions of the $\Delta S=1$ operators $Q_7$ and $Q_8$ that are in the $(8_L,8_R)$ representation of ${\rm SU(3)}_L\times{\rm SU(3)}_R$ and mix with each other. DOI: https://doi.org/10.22323/1.334.0216 Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2020-06-01T13:58:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3223826587200165, "perplexity": 951.8042201744769}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347417746.33/warc/CC-MAIN-20200601113849-20200601143849-00002.warc.gz"}
https://pos.sissa.it/363/177/	Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session Sp(2N) Yang-Mills towards large N. J. Holligan*, E. Bennett, D.K. Hong, J.W. Lee, C.J.D. Lin, B. Lucini, M. Piai and D. Vadacchino Full text: pdf Pre-published on: January 04, 2020 Published on: August 27, 2020 Abstract Non-perturbative aspects of the physics of $Sp(2N)$ gauge theories are interesting for phenomenological and theoretical reasons, and little studied so far, particularly in the approach to the large-$N$ limit. We examine the spectrum of glueballs and the string tension of Yang-Mills theories based upon these groups. Glueball masses are calculated numerically with a variational method from Monte-Carlo generated lattice gauge configurations. After taking continuum limits for $N$ = 1, 2, 3 and 4, we extrapolate the results towards large $N$. We compare the resulting spectrum with that of $SU(N)$ gauge theories, both at finite $N$ and as $N$ approaches infinity. DOI: https://doi.org/10.22323/1.363.0177 How to cite Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete. Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2023-02-02T18:25:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4533563554286957, "perplexity": 1529.8909339441498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500035.14/warc/CC-MAIN-20230202165041-20230202195041-00532.warc.gz"}
https://par.nsf.gov/biblio/10008966-measurement-ratio-differential-cross-sections-ppz+bjet-ppz+jet-pp-collisions	Measurement of the ratio of differential cross sections $σ(pp¯→Z+b jet)/σ(pp¯→Z+jet)$ in $pp¯$ collisions at $s=1.96 TeV$ Publication Date: NSF-PAR ID: 10008966 Journal Name: Physical Review D Volume: 87 Issue: 9 ISSN: 1550-7998 Publisher: American Physical Society	2022-08-13T12:40:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 23, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8961262702941895, "perplexity": 10800.810544296062}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571950.76/warc/CC-MAIN-20220813111851-20220813141851-00631.warc.gz"}
https://pos.sissa.it/396/420/	Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation On the behaviour of the interquark potential in the vicinity of the deconfinement transition M. Caselle*, F. Caristo, N. Magnoli, A. Nada, M. Panero and A. Smecca Full text: pdf Pre-published on: May 16, 2022 Published on: Abstract In the vicinity of the deconfinement transition the behaviour of the interquark potential can be precisely predicted using the Effective String Theory (EST). If the transition is continuous we can combine EST results with a conformal perturbation analysis and reach the degree of precision needed to detect the corrections beyond the Nambu-Goto approximation in the EST. We discuss in detail this issue in the case of the deconfinement transition of the $SU(2)$ gauge theory in $(2+1)$ dimensions (which belongs to the same universality class of the 2d Ising model) by means of an extensive set of high precision simulations. We show that the Polyakov loops correlator of the $SU(2)$ model is precisely described by the spin-spin correlator of the 2d Ising model not only at the critical point, but also down to temperatures of the order of $0.8 T_c$. Thanks to the exact integrability of the Ising model we can extend the comparison in the whole range of Polyakov loop separations, even beyond the conformal perturbation regime. We use these results to quantify the first EST correction beyond Nambu-Goto and show that it is compatible with the bounds imposed by a bootstrap analysis of EST. This correction encodes important physical information and may shed light on the nature of the flux tube and of its EST description. DOI: https://doi.org/10.22323/1.396.0420 How to cite Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete. Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2022-06-28T06:48:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6631938219070435, "perplexity": 729.5832673538637}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103355949.26/warc/CC-MAIN-20220628050721-20220628080721-00051.warc.gz"}
https://par.nsf.gov/biblio/10351318-carnegie-supernova-project-ii-near-infrared-spectroscopy-stripped-envelope-core-collapse-supernovae	This content will become publicly available on February 1, 2023 Carnegie Supernova Project-II: Near-infrared Spectroscopy of Stripped-envelope Core-collapse Supernovae* Abstract We present 75 near-infrared (NIR; 0.8−2.5 μ m) spectra of 34 stripped-envelope core-collapse supernovae (SESNe) obtained by the Carnegie Supernova Project-II (CSP-II), encompassing optical spectroscopic Types IIb, Ib, Ic, and Ic-BL. The spectra range in phase from pre-maximum to 80 days past maximum. This unique data set constitutes the largest NIR spectroscopic sample of SESNe to date. NIR spectroscopy provides observables with additional information that is not available in the optical. Specifically, the NIR contains the strong lines of He i and allows a more detailed look at whether Type Ic supernovae are completely stripped of their outer He layer. The NIR spectra of SESNe have broad similarities, but closer examination through statistical means reveals a strong dichotomy between NIR “He-rich” and “He-poor” SNe. These NIR subgroups correspond almost perfectly to the optical IIb/Ib and Ic/Ic-BL types, respectively. The largest difference between the two groups is observed in the 2 μ m region, near the He i λ 2.0581 μ m line. The division between the two groups is not an arbitrary one along a continuous sequence. Early spectra of He-rich SESNe show much stronger He i λ 2.0581 μ m absorption compared to the He-poor group, but with more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10351318 Journal Name: The Astrophysical Journal Volume: 925 Issue: 2 Page Range or eLocation-ID: 175 ISSN: 0004-637X National Science Foundation ##### More Like this 1. ABSTRACT ASASSN-18am/SN 2018gk is a newly discovered member of the rare group of luminous, hydrogen-rich supernovae (SNe) with a peak absolute magnitude of MV ≈ −20 mag that is in between normal core-collapse SNe and superluminous SNe. These SNe show no prominent spectroscopic signatures of ejecta interacting with circumstellar material (CSM), and their powering mechanism is debated. ASASSN-18am declines extremely rapidly for a Type II SN, with a photospheric-phase decline rate of ∼6.0 mag (100 d)−1. Owing to the weakening of H i and the appearance of He i in its later phases, ASASSN-18am is spectroscopically a Type IIb SN with a partially stripped envelope. However, its photometric and spectroscopic evolution shows significant differences from typical SNe IIb. Using a radiative diffusion model, we find that the light curve requires a high synthesized 56Ni mass $M_{\rm Ni} \sim 0.4\, \rm {M_{\odot }}$ and ejecta with high kinetic energy Ekin = (7–10) × 1051 erg. Introducing a magnetar central engine still requires $M_{\rm Ni} \sim 0.3\, \rm {M_{\odot }}$ and Ekin = 3 × 1051 erg. The high 56Ni mass is consistent with strong iron-group nebular lines in its spectra, which are also similar to several SNe Ic-BL with high 56Ni yields. The earliest spectrum shows ‘flash ionization’ features, from which we estimatemore » 2. ABSTRACT The ultraviolet (UV) and near-infrared (NIR) photometric and optical spectroscopic observations of SN 2020acat covering ∼250 d after explosion are presented here. Using the fast rising photometric observations, spanning from the UV to NIR wavelengths, a pseudo-bolometric light curve was constructed and compared to several other well-observed Type IIb supernovae (SNe IIb). SN 2020acat displayed a very short rise time reaching a peak luminosity of $\mathrm{{\rm Log}_{10}}(L) = 42.49 \pm 0.17 \, \mathrm{erg \, s^{-1}}$ in only ∼14.6 ± 0.3 d. From modelling of the pseudo-bolometric light curve, we estimated a total mass of 56Ni synthesized by SN 2020acat of MNi = 0.13 ± 0.03 M⊙, with an ejecta mass of Mej = 2.3 ± 0.4 M⊙ and a kinetic energy of Ek = 1.2 ± 0.3 × 1051 erg. The optical spectra of SN 2020acat display hydrogen signatures well into the transitional period (≳ 100 d), between the photospheric and the nebular phases. The spectra also display a strong feature around 4900 Å that cannot be solely accounted for by the presence of the Fe ii 5018 line. We suggest that the Fe ii feature was augmented by He i 5016 and possibly by the presence of N ii 5005. From both photometric and spectroscopic analysis, we inferred that the progenitor of SN 2020acat was an intermediate-mass compact star with an MZAMS of 15–20 M⊙. 3. ABSTRACT We present BVRI and unfiltered (Clear) light curves of 70 stripped-envelope supernovae (SESNe), observed between 2003 and 2020, from the Lick Observatory Supernova Search follow-up program. Our SESN sample consists of 19 spectroscopically normal SNe Ib, 2 peculiar SNe Ib, six SNe Ibn, 14 normal SNe Ic, 1 peculiar SN Ic, 10 SNe Ic-BL, 15 SNe IIb, 1 ambiguous SN IIb/Ib/c, and 2 superluminous SNe. Our follow-up photometry has (on a per-SN basis) a mean coverage of 81 photometric points (median of 58 points) and a mean cadence of 3.6 d (median of 1.2 d). From our full sample, a subset of 38 SNe have pre-maximum coverage in at least one passband, allowing for the peak brightness of each SN in this subset to be quantitatively determined. We describe our data collection and processing techniques, with emphasis toward our automated photometry pipeline, from which we derive publicly available data products to enable and encourage further study by the community. Using these data products, we derive host-galaxy extinction values through the empirical colour evolution relationship and, for the first time, produce accurate rise-time measurements for a large sample of SESNe in both optical and infrared passbands. By modelling multiband light curves, we find that SNe Ic tend to have lower ejectamore » 4. Abstract Few published ultraviolet (UV) spectra exist for stripped-envelope supernovae and none to date for broad-lined Type Ic supernovae (SNe Ic-bl). These objects have extremely high ejecta velocities and are the only supernova type directly linked to gamma-ray bursts (GRBs). Here we present two epochs of HST/STIS spectra of the SN Ic-bl 2014ad, the first UV spectra for this class. We supplement this with 26 new epochs of ground-based optical spectra, augmenting a rich spectral time series. The UV spectra do not show strong features and are consistent with broadened versions of other SN Ic spectra observed in the UV. We measure Feii5169 Å velocities and show that SN 2014ad has even higher ejecta velocities than most SNe Ic both with and without observed GRBs. We construct models of the SN 2014ad UV+optical spectra usingtardis, a 1D Monte Carlo radiative-transfer spectral synthesis code. The models fit the data well at multiple epochs in the optical but underestimate the flux in the UV, likely due to simplifying assumptions. We find that high densities at high velocities are needed to reproduce the spectra, with ∼3Mof material atv> 22,000 km s−1, assuming spherical symmetry. Our nebular line fits suggest a steep density profilemore » 5. Abstract We present a multiwavelength photometric and spectroscopic analysis of 13 super-Chandrasekhar-mass/2003fg-like Type Ia supernovae (SNe Ia). Nine of these objects were observed by the Carnegie Supernova Project. The 2003fg-like SNe have slowly declining light curves (Δ m 15 ( B ) < 1.3 mag), and peak absolute B -band magnitudes of −19 < M B < −21 mag. Many of the 2003fg-like SNe are located in the same part of the luminosity–width relation as normal SNe Ia. In the optical B and V bands, the 2003fg-like SNe look like normal SNe Ia, but at redder wavelengths they diverge. Unlike other luminous SNe Ia, the 2003fg-like SNe generally have only one i -band maximum, which peaks after the epoch of the B -band maximum, while their near-IR (NIR) light-curve rise times can be ≳40 days longer than those of normal SNe Ia. They are also at least 1 mag brighter in the NIR bands than normal SNe Ia, peaking above M H = −19 mag, and generally have negative Hubble residuals, which may be the cause of some systematics in dark-energy experiments. Spectroscopically, the 2003fg-like SNe exhibit peculiarities such as unburnt carbon well past maximum light, a large spread (8000–12,000more »	2022-12-04T15:50:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5782650113105774, "perplexity": 5182.05467905331}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710974.36/warc/CC-MAIN-20221204140455-20221204170455-00455.warc.gz"}
https://mooseframework.inl.gov/modules/tensor_mechanics/VolumetricLocking.html	# Volumetric Locking Correction Volumetric locking is the over stiffening of elements when the material is close to being incompressible (Poisson's ratio nearing 0.5). This stiffening happens when a fully integrated element (such as Hex8 elements with 8 quadrature points or Quad4 elements with 4 quadrature points) is used. This is a numerical artifact introduced because shape functions used in finite element analysis cannot properly approximate the incompressibility condition throughout the element. To avoid this locking of elements, B-bar correction Hughes (1987) is implemented in MOOSE. ## Theory In this method, both the strain () and the virtual strain () in an element are separated into volumetric and deviatoric components. The volumetric component is then replaced with an element averaged volumetric strain. This ensures that the volumetric strain remains constant throughout the element. For example, in the case of small strain linear elasticity, the equation of motion is: (1) The element averaged volumetric strain (assuming small strain formulation) is: (2) where is the volume of the element and tr(.) is the trace of the matrix. The strain in each element is replaced by the approximation: (3) where is the identity matrix. Similarly, the virtual strain is also approximated by: (4) The modified equation of motion is: (5) More details about this method can be found in Section 8.6 of Bower (2009). When finite strain formulation is used, the volumetric component of the strain is separated using the determinant of the deformation matrix. ## Usage Volumetric locking correction is set to false by default in tensor mechanics. When dealing with problems involving plasticity or incompressible materials, it can be turned on by setting volumetric_locking_correction=true in both the stress divergence kernel and the strain calculator or in the Tensor Mechanics master action. When volumetric locking correction is turned on, using a SMP preconditioner with coupled displacement variables may help with convergence. For a 3-D problem with only displacement as unknown variables, the following pre-conditioner block may be used: [Preconditioning] [./SMP] type = SMP full = true [../] [] (modules/tensor_mechanics/test/tests/finite_strain_elastic/elastic_rotation_test.i) ## Verification of locking correction on Cook's membrane A 2D trapezoidal membrane Figure 1 with Poisson's ratio of 0.4999 is fixed at the left edge and sheared at the right edge. Locking behavior of the membrane is observed with the use of first order (Quad4) elements with no volumetric locking correction. This locking results in much lower vertical displacement at Point A than that observed in other scenarios Figure 2. Locking can be avoided with the use of Quad4 elements along with volumetric locking correction or with the use of second order elements (Quad8) with or without volumetric locking correction. These results match with that presented in Fig. 6 of Nakshatrala et al. (2008). Figure 1: 2D problem to demonstrate volumetric locking. Figure 2: Vertical displacement at Point A for different element types and mesh density. Locking behavior is observed when Quad4 elements with no volumetric locking correction are used. Note that at least 20 nodes per edge are required to converge to the correct solution even when volumetric locking correction is used for this problem. Also, second order elements do not display locking behavior, so volumetric locking correction is not required for second order elements. Using volumetric locking correction with second order elements causes a different convergence pattern for the displacements Figure 2 and it is also shown to result in noisy zigzag pattern in stress or strain profiles. ## References 1. A. F. Bower. Applied Mechanics of Solids. CRC press, 2009.[BibTeX] 2. T. J. R Hughes. The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. New Jersey:Prentice-Hall, 1987.[BibTeX] 3. K. B. Nakshatrala, A. Masud, and K. D. Hjelmstad. On finite element formulations for nearly incompressible linear elasticity. Computational Mechanics, 41:547–561, 2008.[BibTeX]	2019-03-18T13:55:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48288241028785706, "perplexity": 1471.7020463186798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201329.40/warc/CC-MAIN-20190318132220-20190318154220-00203.warc.gz"}
http://www-cdf.fnal.gov/physics/new/bottom/040408.blessed-bsphiphi/blessed-bsphiphi/blessed-bsphiphi.html	Next: Introduction # Observation of decay Text for the blessed web page - CDF note 6937 The CDF Collaboration 28 May 2004 ### Abstract: We study the yield of various decays in the displaced track trigger of CDF II. In particular we search for evidence of the QCD penguin dominated decay of meson to two , that has never been observed before, using of data collected up to August 2003. Additionally we study the decay to be used as a normalization signal for the extraction of the Branching Ratio of . We have performed a blind analysis and the procedure to fix the cuts and estimate the expected background are reported here. We have found a significant excess of events in the signal region and measure the Branching Ratio where the last error is due to the uncertainty in the Branching Ratio. Marco Rescigno 2004-05-28	2014-11-28T08:17:06	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8357424736022949, "perplexity": 961.0858405241122}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931009900.4/warc/CC-MAIN-20141125155649-00008-ip-10-235-23-156.ec2.internal.warc.gz"}
https://par.nsf.gov/biblio/10303270-quantum-codes-from-neural-networks	Quantum codes from neural networks Abstract We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we initiate the study of neural network states in quantum information-processing tasks. We demonstrate that neural network states are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction, supplying further evidence for the usefulness of neural network states to describe multipartite entanglement. In particular, we show the following main results: (a) neural network states yield quantum codes with a high coherent information for two important quantum channels, the generalized amplitude damping channel and the dephrasure channel. These codes outperform all other known codes for these channels, and cannot be found using a direct parametrization of the quantum state. (b) For the depolarizing channel, the neural network state ansatz reliably finds the best known codes given by repetition codes. (c) more » Authors: ; Publication Date: NSF-PAR ID: 10303270 Journal Name: New Journal of Physics Volume: 22 Issue: 2 Page Range or eLocation-ID: Article No. 023005 ISSN: 1367-2630 Publisher: IOP Publishing A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/Mwith the numberMof sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like$1/M$. However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision withMis less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values ofM. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios. 3. Abstract The possibility of achieving and controlling scalable classically entangled, i.e., inseparable, multipartite states, would fundamentally challenge the advantages of quantum systems in harnessing the power of complexity in information science. Here, we investigate experimentally the extent of classical entanglement in a $$16$$ 16 acoustic qubit-analogue platform. The acoustic qubit-analogue, a.k.a., logical phi-bit, results from the spectral partitioning of the nonlinear acoustic field of externally driven coupled waveguides. Each logical phi-bit is a two-level subsystem characterized by two independently measurable phases. The phi-bits are co-located within the same physical space enabling distance independent interactions. We chose a vector state representation of the $$16$$ 16 -phi-bit system which lies in a $${2}^{16}$$ 2 16 -dimensional Hilbert space. The calculation of the entropy of entanglement demonstrates the possibility of achieving inseparability of the vector state and of navigating the corresponding Hilbert space. This work suggests a new direction in harnessing the complexity of classical inseparability in information science.	2022-12-02T22:34:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7196153402328491, "perplexity": 947.80257036994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710916.70/warc/CC-MAIN-20221202215443-20221203005443-00693.warc.gz"}
https://www.pnnl.gov/explainer-articles?explainer-articles%5B0%5D=research-topic%3A74&explainer-articles%5B1%5D=research-topic%3A268	2 results found Filtered by Wind Energy and Quantum Information Sciences SEPTEMBER 27, 2022 ### Renewable Integration Renewable integration is the process of plugging renewable sources of energy into the electric grid. FEBRUARY 15, 2022	2022-12-10T04:35:03	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8145495057106018, "perplexity": 4992.612859754558}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711712.26/warc/CC-MAIN-20221210042021-20221210072021-00249.warc.gz"}
https://par.nsf.gov/biblio/10363242-dynamical-mass-exoplanet-host-star-hr	Dynamical Mass of the Exoplanet Host Star HR 8799 Abstract HR 8799 is a young A5/F0 star hosting four directly imaged giant planets at wide separations (∼16–78 au), which are undergoing orbital motion and have been continuously monitored with adaptive optics imaging since their discovery over a decade ago. We present a dynamical mass of HR 8799 using 130 epochs of relative astrometry of its planets, which include both published measurements and new medium-band 3.1μm observations that we acquired with NIRC2 at Keck Observatory. For the purpose of measuring the host-star mass, each orbiting planet is treated as a massless particle and is fit with a Keplerian orbit using Markov chain Monte Carlo. We then use a Bayesian framework to combine each independent total mass measurement into a cumulative dynamical mass using all four planets. The dynamical mass of HR 8799 is$1.47−0.17+0.12$Massuming a uniform stellar mass prior, or$1.46−0.15+0.11$Mwith a weakly informative prior based on spectroscopy. There is a strong covariance between the planets’ eccentricities and the total system mass; when the constraint is limited to low-eccentricity solutions ofe< 0.1, which are motivated by dynamical stability, our mass measurement improves to$1.43−0.07+0.06$M. Our dynamical mass and other fundamental measured parameters of HR more » Authors: ; Publication Date: NSF-PAR ID: 10363242 Journal Name: The Astronomical Journal Volume: 163 Issue: 2 Page Range or eLocation-ID: Article No. 52 ISSN: 0004-6256 Publisher: DOI PREFIX: 10.3847 National Science Foundation ##### More Like this 1. Abstract Populating the exoplanet mass–radius diagram in order to identify the underlying relationship that governs planet composition is driving an interdisciplinary effort within the exoplanet community. The discovery of hot super-Earths—a high-temperature, short-period subset of the super-Earth planet population—has presented many unresolved questions concerning the formation, evolution, and composition of rocky planets. We report the discovery of a transiting, ultra-short-period hot super-Earth orbitingTOI-1075(TIC351601843), a nearby (d= 61.4 pc) late-K/early-M-dwarf star, using data from the Transiting Exoplanet Survey Satellite. The newly discovered planet has a radius of 1.791$−0.081+0.116$Rand an orbital period of 0.605 day (14.5 hr). We precisely measure the planet mass to be 9.95$−1.30+1.36$Musing radial velocity measurements obtained with the Planet Finder Spectrograph mounted on the Magellan II telescope. Our radial velocity data also show a long-term trend, suggesting an additional planet in the system. While TOI-1075 b is expected to have a substantial H/He atmosphere given its size relative to the radius gap, its high density ($9.32−1.85+2.05$g cm−3) is likely inconsistent with this possibility. We explore TOI-1075 b’s location relative to the M-dwarf radius valley, evaluate the planet’s prospects for atmospheric characterization, andmore » 2. Abstract Benchmark brown dwarf companions with well-determined ages and model-independent masses are powerful tools to test substellar evolutionary models and probe the formation of giant planets and brown dwarfs. Here, we report the independent discovery of HIP 21152 B, the first imaged brown dwarf companion in the Hyades, and conduct a comprehensive orbital and atmospheric characterization of the system. HIP 21152 was targeted in an ongoing high-contrast imaging campaign of stars exhibiting proper-motion changes between Hipparcos and Gaia, and was also recently identified by Bonavita et al. (2022) and Kuzuhara et al. (2022). Our Keck/NIRC2 and SCExAO/CHARIS imaging of HIP 21152 revealed a comoving companion at a separation of 0.″37 (16 au). We perform a joint orbit fit of all available relative astrometry and radial velocities together with the Hipparcos-Gaia proper motions, yielding a dynamical mass of$24−4+6MJup$, which is 1–2σlower than evolutionary model predictions. Hybrid grids that include the evolution of cloud properties best reproduce the dynamical mass. We also identify a comoving wide-separation (1837″ or 7.9 × 104au) early-L dwarf with an inferred mass near the hydrogen-burning limit. Finally, we analyze the spectra and photometry of HIP 21152 B using the Saumon & Marley (2008)more » 3. Abstract We present the stellar population properties of 69 short gamma-ray burst (GRB) host galaxies, representing the largest uniformly modeled sample to date. Using theProspectorstellar population inference code, we jointly fit photometry and/or spectroscopy of each host galaxy. We find a population median redshift of$z=0.64−0.32+0.83$(68% confidence), including nine photometric redshifts atz≳ 1. We further find a median mass-weighted age oftm=$0.8−0.53+2.71$Gyr, stellar mass of log(M/M) =$9.69−0.65+0.75$, star formation rate of SFR =$1.44−1.35+9.37$Myr−1, stellar metallicity of log(Z/Z) =$−0.38−0.42+0.44$, and dust attenuation of$AV=0.43−0.36+0.85$mag (68% confidence). Overall, the majority of short GRB hosts are star-forming (≈84%), with small fractions that are either transitioning (≈6%) or quiescent (≈10%); however, we observe a much larger fraction (≈40%) of quiescent and transitioning hosts atz≲ 0.25, commensurate with galaxy evolution. We find that short GRB hosts populate the star-forming main sequence of normal field galaxies, but do not include as many high-mass galaxies as the general galaxy population, implying that their binary neutron star (BNS) merger progenitors are dependent on a combination of host star formation and stellar mass. The distribution of ages and redshifts implies a broad delay-time distribution,more » 4. Abstract We present the direct imaging discovery of a low-mass companion to the nearby accelerating F star, HIP 5319, using SCExAO coupled with the CHARIS, VAMPIRES, and MEC instruments in addition to Keck/NIRC2 imaging. CHARISJHK(1.1–2.4μm) spectroscopic data combined with VAMPIRES 750 nm, MECY, and NIRC2Lpphotometry is best matched by an M3–M7 object with an effective temperature ofT= 3200 K and surface gravity log(g) = 5.5. Using the relative astrometry for HIP 5319 B from CHARIS and NIRC2, and absolute astrometry for the primary from Gaia and Hipparcos, and adopting a log-normal prior assumption for the companion mass, we measure a dynamical mass for HIP 5319 B of$31−11+35MJ$, a semimajor axis of$18.6−4.1+10$au, an inclination of$69.4−15+5.6$degrees, and an eccentricity of$0.42−0.29+0.39$. However, using an alternate prior for our dynamical model yields a much higher mass of$128−88+127MJ$. Using data taken with the LCOGT NRES instrument we also show that the primary HIP 5319 A is a single star in contrast to previous characterizations of the system as a spectroscopic binary. This work underscores the importance of assumed priors in dynamical models for companions detected with imaging andmore » 5. Abstract We report the discovery of MAGAZ3NE J095924+022537, a spectroscopically confirmed protocluster at$z=3.3665−0.0012+0.0009$around a spectroscopically confirmedUVJ-quiescent ultramassive galaxy (UMG;$M⋆=2.34−0.34+0.23×1011M⊙$) in the COSMOS UltraVISTA field. We present a total of 38 protocluster members (14 spectroscopic and 24 photometric), including the UMG. Notably, and in marked contrast to protoclusters previously reported at this epoch that have been found to contain predominantly star-forming members, we measure an elevated fraction of quiescent galaxies relative to the coeval field ($73.3−16.9+26.7%$versus$11.6−4.9+7.1%$for galaxies with stellar massM≥ 1011M). This high quenched fraction provides a striking and important counterexample to the seeming ubiquitousness of star-forming galaxies in protoclusters atz> 2 and suggests, rather, that protoclusters exist in a diversity of evolutionary states in the early universe. We discuss the possibility that we might be observing either “early mass quenching” or nonclassical “environmental quenching.” We also present the discovery of MAGAZ3NE J100028+023349, a second spectroscopically confirmed protocluster, at a very similar redshift of$z=3.3801−0.0281+0.0213$. We present a total of 20 protocluster members, 12 of which are photometric and eight spectroscopic including a poststarburst UMG ($M⋆=2.95−0.20+0.21×1011M⊙$). Protoclusters MAGAZ3NE J0959more »	2023-03-25T08:27:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 25, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5864059329032898, "perplexity": 6011.405900704484}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945317.85/warc/CC-MAIN-20230325064253-20230325094253-00238.warc.gz"}
http://www.hmrc.gov.uk/manuals/ahmanual/ah2101.htm	# AH2101 - SA Appeals: Assessments, Amendments and Enquiries: Closure notices: referral to Appeals Unit Once a closure notice has been issued we are unable to make any more enquiries into a return so it is important that a closure notice is not issued prematurely. (Issuing a closure does not preclude further enquires to advance the appeal. But you cannot then use SA powers.) If a case is potentially contentious refer it to the AU before you issue the closure notice, and thus lose the opportunity to use SA powers to advance the enquiry. The AU will ensure that there is sufficient evidence to be able to draw soundly based conclusions that can be defended before the Commissioners.	2013-05-23T11:42:19	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8017283082008362, "perplexity": 3265.2962735035712}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703298047/warc/CC-MAIN-20130516112138-00053-ip-10-60-113-184.ec2.internal.warc.gz"}
https://pos.sissa.it/333/011/	Volume 333 - Theoretical Advanced Study Institute Summer School 2018 "Theory in an Era of Data" (TASI2018) - Theoretical Advanced Study Institute Summer School 2018 "Theory in an Era of Data" As Scales Become Separated: Lectures on Effective Field Theory T. Cohen Full text: pdf Published on: 2019 July 22 Abstract These lectures aim to provide a pedagogical introduction to the philosophical underpinnings and technical features of Effective Field Theory (EFT). Improving control of $S$-matrix elements in the presence of a large hierarchy of physical scales $m \ll M$ is emphasized. Utilizing $\lambda \sim m/M$ as a power counting expansion parameter, we show how matching an ultraviolet (UV) model onto an EFT makes manifest the notion of separating scales. Renormalization Group (RG) techniques are used to run the EFT couplings from the UV to the infrared (IR), thereby summing large logarithms that would otherwise reduce the efficacy of perturbation theory. A variety of scalar field theory based toy examples are worked out in detail. An approach to consistently evolving a coupling across a heavy particle mass threshold is demonstrated. Applying the same method to the scalar mass term forces us to confront the hierarchy problem. The summation of a logarithm that lacks explicit dependence on an RG scale is performed. After reviewing the physics of IR divergences, we build a scalar toy version of Soft Collinear Effective Theory (SCET), highlighting many subtle aspects of these constructions. We show how SCET can be used to sum the soft and collinear IR Sudakov double logarithms that often appear for processes involving external interacting light-like particles. We conclude with the generalization of SCET to theories of gauge bosons coupled to charged fermions. These lectures were presented at TASI 2018. DOI: https://doi.org/10.22323/1.333.0011 Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2020-05-30T12:53:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3895556628704071, "perplexity": 1605.4200980018668}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347409171.27/warc/CC-MAIN-20200530102741-20200530132741-00114.warc.gz"}
https://pdglive.lbl.gov/Particle.action?node=S064&init=0	GAUGE AND HIGGS BOSONS #### Charged Higgs Bosons (${{\mathit H}^{\pm}}$ and ${{\mathit H}^{\pm\pm}}$ ), Searches for ${{\mathit H}^{\pm}}$ (charged Higgs) mass limits for m$_{{{\mathit H}^{+}} }<$ m(top) $> 80$ GeV CL=95.0% ${{\mathit H}^{\pm}}$ (charged Higgs) mass limits for m$_{{{\mathit H}^{+}} }>$ m(top) $>1.103 \times 10^{3}$ GeV CL=95.0% ${{\mathit H}^{\pm\pm}}$ (doubly-charged Higgs boson) mass limits Limits for ${{\mathit H}^{\pm\pm}}$ with $\mathit T_{3}$ = $\pm{}$1 Limits for ${{\mathit H}^{\pm\pm}}$ with $\mathit T_{3}$ = 0 FOOTNOTES	2022-12-07T20:44:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9016131162643433, "perplexity": 6383.966648240696}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711218.21/warc/CC-MAIN-20221207185519-20221207215519-00412.warc.gz"}
https://www.usgs.gov/faqs/why-do-usgs-earthquake-magnitudes-differ-those-published-other-agencies?qt-news_science_products=0	# Why do USGS earthquake magnitudes differ from those published by other agencies? Magnitude estimates for a given earthquake can vary between reporting agencies due to differences in methodology, data availability, and inherent uncertainties in seismic data. Individual agencies use magnitude estimation procedures designed to meet the agency's specific needs and monitoring capabilities. Even for well-recorded events, differences in magnitude of 0.2 or 0.3 units are common and representative of the inherent uncertainty of the magnitude estimation process. Obtaining an accurate measure of an earthquake's size is difficult. Earthquakes are complex processes that occur below the Earth’s surface away from direct observation and measurement. Determining a single number to represent an earthquake’s size has inherent uncertainties due to our assumptions about the material in which they occur and our inability to fully reconstruct the hidden process. Multiple methods are used to estimate magnitude. Fundamentally different calculation methods are specified by magnitude type. The USGS National Earthquake Information Center (NEIC) routinely calculates as many as a dozen different magnitude types. Multiple magnitude types are necessary because no single method is capable of accurately estimating the size of all earthquakes. Some magnitude types are calculated to provide a consistent comparison to past earthquakes, for which modern techniques cannot be applied. Attempts have been made to calibrate these magnitudes to the original Richter Scale, but since different techniques often measure different physical processes there can be large discrepancies between different magnitude types calculated for the same earthquake. These differences can be as large as 0.5 even in magnitude ranges where both techniques are considered valid. Some magnitudes types are fast to calculate and can be completely automated, while others require manual processing by a trained seismologist. Changes in the preferred USGS magnitude in the minutes and hours following significant earthquakes are often a result of a change in magnitude type as well as the inclusion of more data. This iterative procedure addresses the desire for rapid information and allows for timely improvement to derived USGS products such as ShakeMap and PAGER. Even for a given magnitude type, there can be differences in magnitude estimates from different agencies. These differences generally arise due to the use of different Earth models, data availability and data processing. The USGS National Earthquake Information Center reports on earthquakes worldwide. We strive for global consistency in the methods used for calculating earthquake parameters. This approach requires a systematic process as well as a more generic model of Earth's physical properties. A seismic network that is focused on a specific region will often tune their underlying models to their area of interest and monitoring history. To obtain the most consistent and meaningful information from magnitude estimates, researchers and policy makers should consider and specify both the magnitude type and source of that information. For example, local networks are generally the best source for consistent quality information in that region whereas global monitoring agencies such as the USGS National Earthquake Information Center can provide valuable information when comparing earthquakes across the globe. ## Related Content Filter Total Items: 12 ### What is UTC, and why don’t you report earthquakes in the local time where the earthquake occurred? UTC stands for Coordinated Universal Time, and for this purpose is the same as GMT ( Greenwich Mean Time). Since the USGS and other seismic network agencies record earthquakes around the globe in all the various time zones, using a single standard time reference is best for record-keeping and exchange of data. Also, we tried converting Coordinated... ### Why do so many earthquakes occur at a depth of 10km? Ten kilometers is a "fixed depth". Sometimes data are too poor to compute a reliable depth for an earthquake. In such cases, the depth is assigned to be 10 km. Why that number? In many areas around the world, reliable depths tend to average 10 km or close to it. For example, if we made a histogram of the reliable depths in such an area, we'd... ### How fast does the earthquake information get posted to the website, get sent out via the Earthquake Notification Service (ENS), ATOM feeds, etc? USGS earthquake information mechanisms are all triggered by the same system, so they all receive the information at the same time. The time it takes for the system to receive the information primarily depends on the size and location of the earthquake: An earthquake in California is processed and posted to the system in 2.5 minutes (on average)... ### Where can I see current or past seismograms? The USGS Earthquake Hazards Program has helicorders (seismogram displays) available for several areas in the United States and the World. Our research partner IRIS (Incorporated Research Institutions for Seismology) has two applications, the Station Monitor and the Global Seismogram Viewer , for viewing seismograms. IRIS also supplies software... ### When are tsunami information and links included on the Earthquake Event pages? Tsunami information is added to individual USGS event pages for earthquakes under two conditions: If we get information (alerts) from any of NOAA's Tsunami Warning Centers, or For any earthquake of magnitude 5.0 or greater that occurs in the Pacific Ocean, Indonesia, Papua New Guinea, the Caribbean Sea, or Hawaii For More Information, See NOAA's... ### Why/When does the USGS update the magnitude of an earthquake? The USGS often updates an earthquake's magnitude in the hours and sometimes days following the event. Updates occur as more data become available for analysis and more time-intensive analysis is performed. Additional updates are possible as part of the standard procedure of assembling a final earthquake catalog. There are physical and operational... ### Why do some earthquakes disappear from the map/list? The USGS and networks contributing to the Advance National Seismic System (ANSS) take great effort to provide accurate and timely earthquake information. Occasionally our systems produce erroneous information that is released to the public via our web pages or Earthquake Notification System . These mistakes are generally promptly identified by... ### Why isn't the fault on which the earthquake occurred or the distance to the nearest fault provided? Seismologists evaluate the hypocenter location and the focal mechanism of an earthquake to decide if the earthquake occurs on a named fault. Research shows that many earthquakes occur on small, un-named faults located near well-known faults. For example, most of the aftershocks of the 1989 M6.9 Loma Prieta earthquake occurred on small, subsidiary... ### Did I feel an earthquake? Can I report feeling an earthquake? Report an earthquake experience or related observation through the Did You Feel It? citizen science webpage. The best way to do this is to click on the earthquake that you think you felt on one of the lists on the Earthquakes webpage, and then select the "Tell Us!" link. If you don't see the earthquake you think you felt, use the green "Report an... ### Why is the earthquake that was reported/recorded by network X, or that I felt, not on the map/list? The maps and lists show events which have been located by the USGS and contributing agencies within the last 30 days. They should not be considered to be complete lists of all events in the US and adjacent areas and especially should not be considered to be complete lists of all events M4.5+ in the world. In most cases, we locate and report on... ### Where can I find current earthquake lists and maps for the world or for a specific area? The Earthquake Hazards Program Latest Earthquakes Map displays earthquakes in near-realtime and up to the past 30 days of earthquakes. The interface includes three panels: a list of earthquakes, a map, and a settings/options panel. You can pan and zoom the map to view specific areas. Click on an event on the list or map for additional information... Filter Total Items: 4 Date published: May 25, 2017 ### Updated USGS Earthquake Monitoring Strategy Released The USGS Earthquake Hazards Program recently released a new strategic plan for earthquake monitoring entitled the “Advanced National Seismic System – Current Status, Development Opportunities, Priorities, 2017-2027.” Date published: January 23, 2012 ### A 100-year-long History of Earthquakes and Seismic Monitoring in Hawaii The Hawaiian Volcano Observatory’s 1912–2012 Centennial—100 Years of Tracking Eruptions and Earthquakes HAWAI‘I ISLAND, Hawaii —The history of earthquakes and seismic monitoring in Hawai‘i during the past century will be the topic of a presentation at the University of Hawai‘i at Hilo on Thursday, January 26, at 7:00 p.m. Date published: May 3, 2010 More than $7 million in cooperative agreements will be awarded for earthquake monitoring by the U.S Geological Survey in 2010. This funding will contribute to the development and operation of the USGS Advanced National Seismic System (ANSS). Date published: September 24, 2009 ### Recovery Act Funds Will Upgrade Earthquake Monitoring USGS will Grant Universities$5 Million to Beef Up Public Safety Grants totaling \$5 million under the American Recovery and Reinvestment Act are being awarded to 13 universities nationwide to upgrade critical earthquake monitoring networks and increase public safety. Filter Total Items: 6 December 31, 2017 ### Earthquake Catalog Map Results Example Example of results returned when searching the USGS Earthquake Catalog. The ANSS Comprehensive Earthquake Catalog (ComCat) contains earthquake source parameters (e.g. hypocenters, magnitudes, phase picks and amplitudes) and other products (e.g. moment tensor solutions, macroseismic information, tectonic summaries, maps) produced by contributing seismic ... February 24, 2017 ### Earthquakes Greater Than or Equal to Magnitude 2.7 Since 1980 USGS charts showing the number of earthquakes greater than or equal to magnitude 2.7 since 1980 in the five focus areas identified as having especially high ground-shaking hazard in the central and eastern U.S. in 2017. November 21, 2016 ### Magnitude 6.9 Earthquake off Japan on November 21, 2016 USGS map of the magnitude 6.9 earthquake off the coast of Japan on November 21, 2016. August 31, 2016 October 17, 1989 ### Seismographs at the U.S. Geological Survey Seismographs at the U.S. Geological Survey record (1) north-south horizontal, (2) east-west horizontal, and (3) vertical components of the earthquake. ### Cumulative number of earthquakes with a magnitude of 3.0 or larger in the central and eastern United States, 1973-2014 Cumulative number of earthquakes with a magnitude of 3.0 or larger in the central and eastern United States, 1973-2014. The rate of earthquakes began to increase starting around 2009 and accelerated in 2013-2014.	2019-10-20T20:42:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.253807008266449, "perplexity": 2656.7437269000634}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986718918.77/warc/CC-MAIN-20191020183709-20191020211209-00365.warc.gz"}
https://indico.fnal.gov/event/53004/contributions/246567/	# NuFact 2022: The 23rd International Workshop on Neutrinos from Accelerators July 30, 2022 to August 6, 2022 Cliff Lodge US/Mountain timezone ## Preparing for MUonE experiment --- what can we learn from lattice and dispersive data? Aug 4, 2022, 11:20 AM 30m Magpie A ### Speaker The hadronic vacuum polarization (HVP) is one of the main contributors to the total uncertainty in the theoretical prediction of the muon $g - 2$. The HVP term is historically obtained from a data-driven calculation based on a dispersive approach from time-like processes. To improve the theoretical prediction of HVP, in parallel to the lattice communities' effort to obtain HVP by space-like simulations, an alternative space-like data-driven approach is proposed, known as the MUonE experiment. In this talk, we first review the advantage of exploiting the space-like over the time-like processes. We present an overview of lattice calculations of the HVP term and discuss how the choice of fit functions affects the systematic error in lattice calculations and potentially the MUonE experiment. In particular, we explore Pad\'e-based fits and investigate their effects when employed on the space-like data with the precision expected from the MUonE experiment.	2023-01-28T19:48:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5557832717895508, "perplexity": 2137.529527851104}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499654.54/warc/CC-MAIN-20230128184907-20230128214907-00239.warc.gz"}
https://gea.esac.esa.int/archive/documentation/GDR2/Data_processing/chap_cu5pho/sec_cu5pho_intro/ssec_cu5pho_intro_refsyst.html	# 5.1.4 Reference System Author(s): Dafydd W. Evans An essential aspect of the photometric data processing is the split between internal and external calibrations. The internal calibrations bring all observations onto the same reference system, while the external calibrations provide the transformation between this internal system and an absolute one that can be interpreted physically. This general principle is applied to both the flux photometry and the BP/RP spectra. The models used for the internal calibration are described in Section 5.3.5. The external calibration model is described in Section 5.3.6. For the internal calibration of the fluxes ($G$-band, integrated BP/RP and extracted SSC fluxes, Section 5.1.3), the reference system needs to be set up. No external data is used in the generation of these reference fluxes. The reason for only using data from the satellite is that if ground-based data is used, seasonal and hemispheric systematic effects can be introduced into the system. Also, Gaia has the potential to provide data that has better uncertainties and sky coverage than any current survey. The internal calibration is carried out in a bootstrap manner illustrated in Figure 5.4. Initially, the reference fluxes are generated for each source by accumulating all the raw (uncalibrated) fluxes and generating weighted mean values. Using these as an initial reference, calibrations are carried out. There then follows an iterative loop where the calibrations are used in accumulating calibrated fluxes to generate a better set of reference fluxes and the calibrations repeated. This method converges since the observations for the sources have different calibrations applied to them and provided that each calibration is carried out with different sources. Given that there is good mixing between the calibrations and sources, i.e., more than half of the sources are observed in two or more configurations (CCD, Gate, FoV, …), this process should converge quickly. Conversely, if there is no mixing between sources and calibrations, multiple photometric systems could form, e.g., two sets of sources observed in different configurations, each needing their own set of calibrations, would result in two independent photometric systems. In general, this is not the case with Gaia, but there are cases in which there is poor mixing, where additional calibrations are needed to speed up the convergence. These calibrations are referred to as link calibrations since they link the photometric systems between different configurations. The two identified link calibrations are: • Time Link Calibration. During the early stages of the mission, Gaia observed in a configuration known as Ecliptic Pole Scanning Law (see Section 1.1.4). This was also the period when the contamination of the mirrors was at the highest level and with large dependency in time, thus creating a systematic effect in the data orders of magnitude larger than any expectations (Section 1.3.3). Including these data in the calibrations caused the early attempts at defining the reference system to show a linear trend with time in the residuals. The initial accumulation of the raw fluxes had imprinted the contamination signal into the reference system. The Time Link Calibration uses differential measurements to largely remove this signal from the raw data without the need for a large number of iterations. • Gate/Window Class Link Calibration. The determination of the gate and window class used for an observation is made on-board using an instantaneous magnitude determination. If this is accurate and the source is constant, there will be very poor mixing since a source will almost always be observed with the same gate and window class configuration and thus be associated with the same set of calibrations. Although, the accuracy is poor (0.3–0.5 mag) at the bright end ($G$ $<12$), it is sufficiently good at fainter magnitudes to cause problems for setting up the photometric reference system. The Gate/Window Class Link Calibration uses only the sources that have been observed in several calibration units. Further details on these link calibrations can be found in Section 5.3.3 and Section 5.3.4. A similar scheme is applied for the instrument calibration of the BP/RP spectra in that there is an iterative loop between the instrument calibration and the source update process which creates the reference spectra. For more details on the photometric reference system, see Carrasco et al. (2016).	2019-03-24T15:29:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 3, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.669876754283905, "perplexity": 1013.4746470758367}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203462.50/warc/CC-MAIN-20190324145706-20190324171706-00227.warc.gz"}
http://www.legisquebec.gouv.qc.ca/en/version/cr/R-15.1,%20r.%206?code=se:5_1&history=20211014	### R-15.1, r. 6 - Regulation respecting supplemental pension plans 5.1. (Replaced). O.C. 1073-2009, s. 2; O.C. 1183-2017, s. 4. 5.1. Where the provision for adverse deviation is calculated on the basis of estimates authorized by section 60.5, the report must contain the following information: (1) the amount; (2) a certification of the actuary certifying that a complete actuarial valuation of the plan carried out at the valuation date would have established an amount for the provision for adverse deviation equal to or less than the amount indicated in paragraph 1; (3) the maximum amount of surplus assets that may be appropriated to the payment of employer contributions; (4) the maximum amount of the reduction to which the pension committee may agree under section 15.0.0.5; (5) the maximum amount of the reduction to which the pension committee may agree under the first paragraph of section 15.0.0.6, specifying that the amount is established on the assumption that the surplus assets of the plan will be in no way appropriated to the payment of employer contributions; (6) a certification of the actuary certifying that, should complete actuarial valuation be carried out, the resulting amounts would be at least equal to those indicated in paragraphs 3 to 5. O.C. 1073-2009, s. 2.	2022-01-27T12:51:09	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.872735321521759, "perplexity": 2858.6932521595722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305260.61/warc/CC-MAIN-20220127103059-20220127133059-00360.warc.gz"}
https://par.nsf.gov/biblio/10200741-new-connection-between-node-edge-depth-robust-graphs	A New Connection Between Node and Edge Depth Robust Graphs Given a directed acyclic graph (DAG) G=(V,E), we say that G is (e,d)-depth-robust (resp. (e,d)-edge-depth-robust) if for any set S⊆V (resp. S⊆E) of at most \|S\|≤e nodes (resp. edges) the graph G−S contains a directed path of length d. While edge-depth-robust graphs are potentially easier to construct, many applications in cryptography require node depth-robust graphs with small indegree. We create a graph reduction that transforms an (e,d)-edge-depth-robust graph with m edges into a (e/2,d)-depth-robust graph with O(m) nodes and constant indegree. One immediate consequence of this result is the first construction of a provably (nloglognlogn,nlogn(logn)loglogn)-depth-robust graph with constant indegree. Our reduction crucially relies on ST-robust graphs, a new graph property we introduce which may be of independent interest. We say that a directed, acyclic graph with n inputs and n outputs is (k1,k2)-ST-robust if we can remove any k1 nodes and there exists a subgraph containing at least k2 inputs and k2 outputs such that each of the k2 inputs is connected to all of the k2 outputs. If the graph if (k1,n−k1)-ST-robust for all k1≤n we say that the graph is maximally ST-robust. We show how to construct maximally ST-robust graphs with constant indegree and O(n) nodes. Given a more » Authors: ; Award ID(s): Publication Date: NSF-PAR ID: 10200741 Journal Name: ITCS 2021 3. Memory-hard functions (MHFs) are a key cryptographic primitive underlying the design of moderately expensive password hashing algorithms and egalitarian proofs of work. Over the past few years several increasingly stringent goals for an MHF have been proposed including the requirement that the MHF have high sequential space-time (ST) complexity, parallel space-time complexity, amortized area-time (aAT) complexity and sustained space complexity. Data-Independent Memory Hard Functions (iMHFs) are of special interest in the context of password hashing as they naturally resist side-channel attacks. iMHFs can be specified using a directed acyclic graph (DAG) $G$ with $N=2^n$ nodes and low indegree and themore »	2022-07-03T11:02:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3764929473400116, "perplexity": 1832.9705315648234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104240553.67/warc/CC-MAIN-20220703104037-20220703134037-00298.warc.gz"}
http://pdglive.lbl.gov/ParticleGroup.action;jsessionid=EF7001A4EA8910D978621488AF03EF33?node=MXXX025&init=0	# ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit c}}}$ MESONS Reviews: The Charmonium System Branching Ratio of ${{\mathit \psi}{(2S)}}$ and ${{\mathit \chi}_{{c0}}}_{,1,2}$ (rev.) ${{\mathit \eta}_{{c}}{(1S)}}$ ${{\mathit J / \psi}{(1S)}}$ ${{\mathit \chi}_{{c0}}{(1P)}}$ ${{\mathit \chi}_{{c1}}{(1P)}}$ ${{\mathit h}_{{c}}{(1P)}}$ ${{\mathit \chi}_{{c2}}{(1P)}}$ ${{\mathit \eta}_{{c}}{(2S)}}$ ${{\mathit \psi}{(2S)}}$ ${{\mathit \psi}{(3770)}}$ ${{\mathit \psi}{(3823)}}~$was ${{\mathit X}{(3823)}}$ ${{\mathit X}{(3872)}}$ ${{\mathit X}{(3900)}}$ ${{\mathit X}{(3915)}}~$was ${{\mathit \chi}_{{c0}}{(3915)}}$ ${{\mathit \chi}_{{c2}}{(2P)}}$ ${{\mathit X}{(3940)}}$ ${{\mathit X}{(4020)}}$ ${{\mathit \psi}{(4040)}}$ ${{\mathit X}{(4050)}^{\pm}}$ ${{\mathit X}{(4055)}^{\pm}}$ ${{\mathit X}{(4140)}}$ ${{\mathit \psi}{(4160)}}$ ${{\mathit X}{(4160)}}$ ${{\mathit X}{(4200)}^{\pm}}$ ${{\mathit X}{(4230)}}$ ${{\mathit X}{(4240)}^{\pm}}$ ${{\mathit X}{(4250)}^{\pm}}$ ${{\mathit X}{(4260)}}$ ${{\mathit X}{(4274)}}$ ${{\mathit X}{(4350)}}$ ${{\mathit X}{(4360)}}$ ${{\mathit \psi}{(4415)}}$ ${{\mathit X}{(4430)}^{\pm}}$ ${{\mathit X}{(4500)}}$ ${{\mathit X}{(4660)}}$ ${{\mathit X}{(4700)}}$	2018-04-24T12:19:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9609349966049194, "perplexity": 70.03359115232477}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946688.88/warc/CC-MAIN-20180424115900-20180424135900-00292.warc.gz"}
https://par.nsf.gov/biblio/10387094-detection-anisotropic-satellite-quenching-galaxy-clusters-up	Detection of anisotropic satellite quenching in galaxy clusters up to z ∼ 1 ABSTRACT Satellite galaxies in the cluster environment are more likely to be quenched than galaxies in the general field. Recently, it has been reported that satellite galaxy quenching depends on the orientation relative to their central galaxies: satellites along the major axis of centrals are more likely to be quenched than those along the minor axis. In this paper, we report a detection of such anisotropic quenching up to z ∼ 1 based on a large optically selected cluster catalogue constructed from the Hyper Suprime-Cam Subaru Strategic Program. We calculate the quiescent satellite galaxy fraction as a function of orientation angle measured from the major axis of central galaxies and find that the quiescent fractions at 0.25 < z < 1 are reasonably fitted by sinusoidal functions with amplitudes of a few per cent. Anisotropy is clearer in inner regions (<r200m) of clusters and not significant in cluster outskirts (>r200m). We also confirm that the observed anisotropy cannot be explained by differences in local galaxy density or stellar mass distribution along the two axes. Quiescent fraction excesses between the two axes suggest that the quenching efficiency contributing to the anisotropy is almost independent of stellar mass, at least down to our stellar more » Authors: ; ; Publication Date: NSF-PAR ID: 10387094 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 519 Issue: 1 Page Range or eLocation-ID: p. 13-25 ISSN: 0035-8711 Publisher: Oxford University Press 1. ABSTRACT We study the alignments of satellite galaxies, and their anisotropic distribution, with respect to location and orientation of their host central galaxy in MassiveBlack-II (MB-II) and IllustrisTNG simulations. We find that: the shape of the satellite system in haloes of mass ($\gt 10^{13}\, h^{-1}\, \mathrm{M}_{\odot }$) is well aligned with the shape of the central galaxy at z = 0.06 with the mean alignment between the major axes being ∼Δθ = 12° when compared to a uniform random distribution; that satellite galaxies tend to be anisotropically distributed along the major axis of the central galaxy with a stronger alignment in haloes of higher mass or luminosity; and that the satellite distribution is more anisotropic for central galaxies with lower star formation rate, which are spheroidal, and for red central galaxies. Radially, we find that satellites tend to be distributed along the major axis of the shape of the stellar component of central galaxies at smaller scales and the dark matter component on larger scales. We find that the dependence of satellite anisotropy on central galaxy properties and the radial distance is similar in both the simulations with a larger amplitude in MB-II. The orientation of satellite galaxies tends tomore » The star formation and gas content of satellite galaxies around the Milky Way (MW) and Andromeda (M31) are depleted relative to more isolated galaxies in the Local Group (LG) at fixed stellar mass. We explore the environmental regulation of gas content and quenching of star formation in z = 0 galaxies at $M_{}=10^{5\!-\!10}\, \rm {M}_{\odot }$ around 14 MW-mass hosts from the Feedback In Realistic Environments 2 (FIRE-2) simulations. Lower mass satellites ($M_{}\lesssim 10^7\, \rm {M}_{\odot }$) are mostly quiescent and higher mass satellites ($M_{}\gtrsim 10^8\, \rm {M}_{\odot }$) are mostly star forming, with intermediate-mass satellites ($M_{}\approx 10^{7\!-\!8}\, \rm {M}_{\odot }$) split roughly equally between quiescent and star forming. Hosts with more gas in their circumgalactic medium have a higher quiescent fraction of massive satellites ($M_{*}=10^{8\!-\!9}\, \rm {M}_{\odot }$). We find no significant dependence on isolated versus paired (LG-like) host environments, and the quiescent fractions of satellites around MW-mass and Large Magellanic Cloud (LMC)-mass hosts from the FIRE-2 simulations are remarkably similar. Environmental effects that lead to quenching can also occur as pre-processing in low-mass groups prior to MW infall. Lower mass satellites typically quenched before MW infall as central galaxies or rapidly during infall into a low-mass group ormore » 4. ABSTRACT We measure the rate of environmentally driven star formation quenching in galaxies at z ∼ 1, using eleven massive ($M\approx 2\times 10^{14}\, \mathrm{M}_\odot$) galaxy clusters spanning a redshift range 1.0 < z < 1.4 from the GOGREEN sample. We identify three different types of transition galaxies: ‘green valley’ (GV) galaxies identified from their rest-frame (NUV − V) and (V − J) colours; ‘blue quiescent’ (BQ) galaxies, found at the blue end of the quiescent sequence in (U − V) and (V − J) colour; and spectroscopic post-starburst (PSB) galaxies. We measure the abundance of these galaxies as a function of stellar mass and environment. For high-stellar mass galaxies (log M/M⊙ > 10.5) we do not find any significant excess of transition galaxies in clusters, relative to a comparison field sample at the same redshift. It is likely that such galaxies were quenched prior to their accretion in the cluster, in group, filament, or protocluster environments. For lower stellar mass galaxies (9.5 < log M/M⊙ < 10.5) there is a small but significant excess of transition galaxies in clusters, accounting for an additional ∼5–10 per cent of the population compared with the field. We show that our data are consistent with a scenario inmore »	2023-03-24T10:42:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5709572434425354, "perplexity": 1991.1010997217682}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945279.63/warc/CC-MAIN-20230324082226-20230324112226-00269.warc.gz"}
https://beconnected.esafety.gov.au/topic-library/identifying-and-avoiding-scams/remote-access-scams/how-to-identify-a-remote-access-scam	## How to identify a remote access scam Close lesson You have completed 0% # How to identify a remote access scam ## What's coming up? In this activity, you’ll learn how a remote access scam works, step by step via a scenario. You’ll meet Costa, who receives a call from what he thinks is Microsoft, but is actually a scammer. You’ll see how the scammer uses Costa’s limited technical knowledge to convince him to purchase unnecessary software. Start activity ## Costa receives a call from a scammer One day at home, Costa gets a mobile phone call from someone claiming to be from the Microsoft Windows technical department. The scammer tells Costa that Microsoft has detected some serious problems with his computer. ## The scammer asks Costa to check his computer The scammer guides Costa thought some simple steps to bring up a screen on his Windows computer, which shows a list of errors and warnings. In fact, this screen is a normal part of his computer’s operation, and is just a log of the computer’s internal workings. The errors are real but also normal and the computer has already fixed these itself. Due to Costa’s limited technical understanding, this log causes confusion. ## eSafety tip Using a normal Windows screen to show errors is just one of the tricks that remote access scammers can use. If you are unable or refuse to open this screen, the scammer will move on to a different technique. For example, they may claim a new virus has just come out which no antivirus software (except theirs) can detect and remove. ## Costa sees his computer get worse Costa is concerned by the apparent errors, so he is keen to follow the scammer’s instructions to fix his computer. This gives the scammer even more access, and to Costa’s horror, even more things seem to go wrong as he watches! The scammer pretends to be very concerned about the state of Costa’s computer. ## Well done! This is the end of the How to identify a remote access scam activity. You’ve learned what a remote access scam can look like, by following along with Costa’s unfortunate experience. Up next, find out how to avoid being tricked by these scams in the Protecting yourself from remote access scams activity.	2023-02-07T20:32:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1933048665523529, "perplexity": 3415.5946816953215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500641.25/warc/CC-MAIN-20230207201702-20230207231702-00845.warc.gz"}
https://par.nsf.gov/biblio/10355941-mhd-turbulent-power-anisotropy-inner-heliosphere	This content will become publicly available on July 1, 2023 MHD Turbulent Power Anisotropy in the Inner Heliosphere Abstract We study anisotropic magnetohydrodynamic (MHD) turbulence in the slow solar wind measured by Parker Solar Probe (PSP) and Solar Orbiter (SolO) during its first orbit from the perspective of variance anisotropy and correlation anisotropy. We use the Belcher & Davis approach (M1) and a new method (M2) that decomposes a fluctuating vector into parallel and perpendicular fluctuating vectors. M1 and M2 calculate the transverse and parallel turbulence components relative to the mean magnetic field direction. The parallel turbulence component is regarded as compressible turbulence, and the transverse turbulence component as incompressible turbulence, which can be either Alfvénic or 2D. The transverse turbulence energy is calculated from M1 and M2, and the transverse correlation length from M2. We obtain the 2D and slab turbulence energy and the corresponding correlation lengths from those transverse turbulence components that satisfy an angle between the mean solar wind flow speed and mean magnetic field θ UB of either (i) 65° < θ UB < 115° or (ii) 0° < θ UB < 25° (155° < θ UB < 180°), respectively. We find that the 2D turbulence component is not typically observed by PSP near perihelion, but the 2D component dominates turbulence in the inner more » Authors: ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10355941 Journal Name: The Astrophysical Journal Volume: 933 Issue: 1 Page Range or eLocation-ID: 56 ISSN: 0004-637X National Science Foundation ##### More Like this 1. Abstract We present a theoretical and observational study of 2D and slab turbulence cascade (or heating) rates of transverse total turbulence energies, transverse cross helicity, transverse outward and inward Elsässer energy, transverse fluctuating magnetic energy density, and transverse fluctuating kinetic energy from the perihelion of the first Parker Solar Probe (PSP) orbit at ∼36.6 R ⊙ to Solar Orbiter (SolO) at ∼177 R ⊙ . We use the Adhikari et al. (2021a) approach to calculate the observed transverse turbulence heating rate, and the nearly incompressible magnetohydrodynamic (NI MHD) turbulence transport theory to calculate the theoretical turbulence cascade rate. We find from the 1 day long PSP measurements at 66.5 R ⊙ , and the SolO measurements at 176.3 R ⊙ that various transverse turbulent cascade rates increase with increasing angle, from 10° to 98°, between the mean solar wind speed and mean magnetic field ( θ UB ), indicating that the 2D heating rate is largest in the inner heliosphere. Similarly, we find from the theoretical and observed results that the 2D heating rate is larger than the slab heating rate as a function of heliocentric distance. We present a comparison between the theoretical and observed 2D and slab turbulencemore » 2. Aims. Solar Orbiter (SolO) was launched on February 9, 2020, allowing us to study the nature of turbulence in the inner heliopshere. We investigate the evolution of anisotropic turbulence in the fast and slow solar wind in the inner heliosphere using the nearly incompressible magnetohydrodynamic (NI MHD) turbulence model and SolO measurements. Methods. We calculated the two dimensional (2D) and the slab variances of the energy in forward and backward propagating modes, the fluctuating magnetic energy, the fluctuating kinetic energy, the normalized residual energy, and the normalized cross-helicity as a function of the angle between the mean solar wind speed and the mean magnetic field ( θ UB ), and as a function of the heliocentric distance using SolO measurements. We compared the observed results and the theoretical results of the NI MHD turbulence model as a function of the heliocentric distance. Results. The results show that the ratio of 2D energy and slab energy of forward and backward propagating modes, magnetic field fluctuations, and kinetic energy fluctuations increases as the angle between the mean solar wind flow and the mean magnetic field increases from θ UB = 0° to approximately θ UB = 90° and then decreases as θ UB → 180°.more » 3. Abstract The Parker Solar Probe (PSP) entered a region of sub-Alfvénic solar wind during encounter 8, and we present the first detailed analysis of low-frequency turbulence properties in this novel region. The magnetic field and flow velocity vectors were highly aligned during this interval. By constructing spectrograms of the normalized magnetic helicity, cross-helicity, and residual energy, we find that PSP observed primarily Alfvénic fluctuations, a consequence of the highly field-aligned flow that renders quasi-2D fluctuations unobservable to PSP. We extend Taylor’s hypothesis to sub- and super-Alfvénic flows. Spectra for the fluctuating forward and backward Elsässer variables (z±, respectively) are presented, showing thatz+modes dominatezby an order of magnitude or more, and thez+spectrum is a power law in frequency (parallel wavenumber)f−3/2($k∥−3/2$) compared to the convexzspectrum withf−3/2($k∥−3/2$) at low frequencies, flattening around a transition frequency (at which the nonlinear and Alfvén timescales are balanced) tof−1.25at higher frequencies. The observed spectra are well fitted using a spectral theory for nearly incompressible magnetohydrodynamics assuming a wavenumber anisotropy$k⊥∼k∥3/4$, that thez+fluctuations experience primarily nonlinear interactions, and that the minorityzfluctuations experience both nonlinear and Alfvénic interactions withz+fluctuations. The density spectrum is a powermore » 4. Abstract During its 10th orbit around the Sun, the Parker Solar Probe sampled two intervals where the local Alfvén speed exceeded the solar wind speed, lasting more than 10 hours in total. In this paper, we analyze the turbulence and wave properties during these periods. The turbulence is observed to be Alfvénic and unbalanced, dominated by outward-propagating modes. The power spectrum of the outward-propagating Elsässer z + mode steepens at high frequencies while that of the inward-propagating z − mode flattens. The observed Elsässer spectra can be explained by the nearly incompressible (NI) MHD turbulence model with both 2D and Alfvénic components. The modeling results show that the z + spectra are dominated by the NI/slab component, and the 2D component mainly affects the z − spectra at low frequencies. An MHD wave decomposition based on an isothermal closure suggests that outward-propagating Alfvén and fast magnetosonic wave modes are prevalent in the two sub-Alfvénic intervals, while the slow magnetosonic modes dominate the super-Alfvénic interval in between. The slow modes occur where the wavevector is nearly perpendicular to the local mean magnetic field, corresponding to nonpropagating pressure-balanced structures. The alternating forward and backward slow modes may also be features of magneticmore » 5. Context. The Parker Solar Probe (PSP) measures solar wind protons and electrons near the Sun. To study the thermodynamic properties of electrons and protons, we include electron effects, such as distributed turbulent heating between protons and electrons, Coulomb collisions between protons and electrons, and heat conduction of electrons. Aims. We develop a general theoretical model of nearly incompressible magnetohydrodynamic (NI MHD) turbulence coupled with a solar wind model that includes electron pressure and heat flux. Methods. It is important to note that 60% of the turbulence energy is assigned to proton heating and 40% to electron heating. We use an empirical expression for the electron heat flux. We derived a nonlinear dissipation term for the residual energy that includes both the Alfvén effect and the turbulent small-scale dynamo effect. Similarly, we obtained the NI/slab time-scale in an NI MHD phenomenology to use in the derivation of the nonlinear term that incorporates the Alfvén effect. Results. A detailed comparison between the theoretical model solutions and the fast solar wind measured by PSP and Helios 2 shows that they are consistent. The results show that the nearly incompressible NI/slab turbulence component describes observations of the fast solar wind periods when the solarmore »	2023-01-27T11:22:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6684952974319458, "perplexity": 1805.410092930748}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494976.72/warc/CC-MAIN-20230127101040-20230127131040-00820.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Arabinowitz.philip	# zbMATH — the first resource for mathematics ## Rabinowitz, Philip Compute Distance To: Author ID: rabinowitz.philip Published as: Rabinowitz, Philip; Rabinowitz, P.; Rabinowitz, Ph. External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 90 Publications since 1954, including 10 Books Biographic References: 1 Publication all top 5 #### Co-Authors 46 single-authored 12 Davis, Philip J. 5 Richter, Nira 4 Lubinsky, Doron S. 3 Smith, William E. 3 Vértesi, Péter 2 Elhay, Sylvan 2 Kautsky, Jaroslav 2 Ralston, Anthony 1 Abramowitz, Milton 1 Butcher, John C. 1 Caliò, Franca 1 Cools, Ronald 1 Curtis, A. Robert 1 Dagnino, Catterina 1 Demichelis, Vittoria 1 Freilich, J. H. 1 Fröberg, Carl-Erik 1 Mantel, Francis 1 Marchetti, Elena 1 Nowiński, Jerzy L. 1 Santi, Elisabetta 1 Sloan, Ian Hugh 1 Weiss, George-Herbert 1 Zeilberger, Doron all top 5 #### Serials 19 Mathematics of Computation 7 Journal of Computational and Applied Mathematics 6 BIT 5 Communications of the ACM 4 Journal of Approximation Theory 3 SIAM Journal on Numerical Analysis 3 International Journal of Computer Mathematics 3 Mathematical Tables and other Aids to Computation 2 Journal of Research of the National Bureau of Standards 1 Computers & Mathematics with Applications 1 Israel Journal of Mathematics 1 Journal of the Australian Mathematical Society, Series B 1 Journal of Mathematical Analysis and Applications 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Calcolo 1 Canadian Journal of Mathematics 1 Journal of the American Statistical Association 1 Journal of the Association for Computing Machinery 1 Rendiconti del Seminario Matematico 1 Applied Numerical Mathematics 1 Numerical Algorithms 1 SIAM Review 1 Computers and Mathematics with Applications. Part B 1 Annals of Numerical Mathematics 1 Physical Review, II. Series 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Advances in Computers 1 Journal of the Society for Industrial and Applied Mathematics. Series B, Numerical Analysis all top 5 #### Fields 55 Numerical analysis (65-XX) 50 Approximations and expansions (41-XX) 13 Functions of a complex variable (30-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) #### Citations contained in zbMATH Open 81 Publications have been cited 1,824 times in 1,534 Documents Cited by Year Methods of numerical integration. 2nd ed. Zbl 0537.65020 Davis, Philip J.; Rabinowitz, Philip 1984 Numerical integration. Zbl 0154.17802 Davis, P. J.; Rabinowitz, P. 1967 Methods of numerical integration. Zbl 0304.65016 Davis, Philip J.; Rabinowitz, Philip 1975 A first course in numerical analysis. 2nd ed. Zbl 0408.65001 Ralston, Anthony; Rabinowitz, Philip 1978 Methods of numerical integration. Corrected reprint of the 1984 2nd ed. Zbl 1139.65016 Davis, Philip J.; Rabinowitz, Philip 2007 Monomial cubature rules since “Stroud”: A compilation. Zbl 0799.65027 Cools, Ronald; Rabinowitz, Philip 1993 A first course in numerical analysis. Reprint of 1978 2nd ed. Zbl 0976.65001 Ralston, Anthony; Rabinowitz, Philip 2001 Rates of convergence of Gaussian quadrature for singular integrands. Zbl 0574.41028 Lubinsky, D. S.; Rabinowitz, P. 1984 Gaussian integration in the presence of a singularity. Zbl 0183.18102 Rabinowitz, P. 1967 Product integration in the presence of a singularity. Zbl 0547.65011 Rabinowitz, Philip; Sloan, Ian H. 1984 Numerical integration based on approximating splines. Zbl 0716.65018 Rabinowitz, Philip 1990 Applications of linear programming to numerical analysis. Zbl 0236.65001 Rabinowitz, Philip 1968 On the estimation of quadrature errors for analytic functions. Zbl 0056.29103 Davis, P.; Rabinowitz, P. 1954 Ignoring the singularity in approximate integration. Zbl 0141.13901 Davis, P. J.; Rabinowitz, P. 1965 Perfectly symmetric two-dimensional integration formulas with minimal numbers of points. Zbl 0208.18702 Rabinowitz, P.; Richter, N. 1969 Product integration of singular integrands using quasi-interpolatory splines. Zbl 0866.41008 Dagnino, C.; Rabinowitz, P. 1997 Numerical integration in the presence of an interior singularity. Zbl 0627.41022 Rabinowitz, Philip 1987 Application of approximating splines for the solution of Cauchy singular integral equations. Zbl 0812.65134 Rabinowitz, Philip 1994 Abscissas and weights for Gaussian quadratures of high order. Zbl 0074.33004 Davis, P.; Rabinowitz, P. 1956 The application of integer programming to the computation of fully symmetric integration formulas in two and three dimensions. Zbl 0361.90079 Mantel, Francis; Rabinowitz, Philip 1977 Gauss-Kronrod integration rules for Cauchy principal value integrals. Zbl 0545.65012 Rabinowitz, Philip 1983 Advances in orthonormalizing computation. Zbl 0136.13405 Davis, P. J.; Rabinowitz, P. 1961 New error coefficients for estimating quadrature errors for analytic functions. Zbl 0217.52402 Rabinowitz, P.; Richter, N. 1970 Gaussian integration of functions with branch point singularities. Zbl 0222.65028 Rabinowitz, Philip 1970 Some geometrical theorems for abscissas and weights of Gauss type. Zbl 0168.14704 Davis, P. J.; Rabinowitz, P. 1961 The exact degree of precision of generalized Gauss-Kronrod integration rules. Zbl 0461.65019 Rabinowitz, Philip 1980 On the convergence of closed interpolatory integration rules based on the zeros of Gegenbauer polynomials. Zbl 0625.41020 Rabinowitz, Philip 1987 Rates of convergence of Gauss, Lobatto, and Radau integration rules for singular integrands. Zbl 0619.41022 Rabinowitz, Philip 1986 Tables of abscissas and weights for numerical evaluation of integrals of the form $$\int_0^\infty e^{-x} x^n f(x) dx$$. Zbl 0094.11809 Rabinowitz, Philip; Weiss, George 1959 Hermite and Hermite-Fejér interpolation and associated product integration rules on the real line: The $$L_ 1$$ theory. Zbl 0758.41006 Lubinsky, D. S.; Rabinowitz, P. 1992 On the Gaussian integration of Chebyshev polynomials. Zbl 0261.65019 Curtis, A. R.; Rabinowitz, P. 1972 Numerical experiments in conformal mapping by the method of orthonormal polynomials. Zbl 0139.11002 Rabinowitz, P. 1966 Convergence results for piecewise linear quadratures for Cauchy principal value integrals. Zbl 0699.65017 Rabinowitz, Philip 1988 Uniform convergence results for Cauchy principal value integrals. Zbl 0725.65024 Rabinowitz, Philip 1991 On the error in the numerical integration of Chebyshev polynomials. Zbl 0222.65029 Nicholson, D.; Rabinowitz, P.; Richter, N.; Zeilberger, D. 1971 Additional abscissas and weights for Gaussian quadratures of high order: Values for $$n$$=64, 80, and 96. Zbl 0092.33101 Davis, Philip; Rabinowitz, Philip 1958 Abscissas and weights for Lobatto quadrature of high order. Zbl 0096.10203 Rabinowitz, Philip 1960 On the uniform convergence of Cauchy principal values of quasi-interpolating splines. Zbl 0859.65015 Rabinowitz, Philip; Santi, Elisabetta 1995 On the numerical solution of the generalized Prandtl equation using variation-di/-minishing splines. Zbl 0838.65134 Caliò, F.; Marchetti, E.; Rabinowitz, P. 1995 The convergence of interpolatory product integration rules. Zbl 0629.41002 Rabinowitz, Philip 1986 Some Monte Carlo experiments in computing multiple integrals. Zbl 0072.14403 Davis, P.; Rabinowitz, P. 1956 Rough and ready error estimates in Gaussian integration of analytic functions. Zbl 0174.47203 Rabinowitz, P. 1969 Error bounds in Gaussian integration of functions of low-order continuity. Zbl 0181.17802 Rabinowitz, Philip 1968 On an interpolatory product rule for evaluating Cauchy principal value integrals. Zbl 0688.65019 Rabinowitz, Philip 1989 On the convergence of interpolatory product integration rules based on Gauss, Radau and Lobatto points. Zbl 0619.41023 Rabinowitz, Philip 1986 Interpolatory product integration for Riemann-integrable functions. Zbl 0636.41021 Rabinowitz, Philip; Smith, William E. 1987 Noninterpolatory integration rules for Cauchy principal value integrals. Zbl 0682.41037 Rabinowitz, P.; Lubinsky, D. S. 1989 Asymptotic properties of minimal integration rules. Zbl 0222.65024 Rabinowitz, Philip; Richter, Nira 1971 Chebyshev-type integration rules of minimum norm. Zbl 0222.65025 Rabinowitz, Philip; Richter, Nira 1971 Numerical methods for nonlinear algebraic equations. Zbl 0244.00003 Rabinowitz, Philip (ed.) 1970 Extrapolation methods in numerical integration. Zbl 0790.65016 Rabinowitz, Philip 1992 Finite-part integrals and modified splines. Zbl 1074.65028 Demichelis, V.; Rabinowitz, P. 2004 Ignoring the singularity in numerical integration. Zbl 0435.65018 Rabinowitz, Philip 1977 On the definiteness of Gauss-Kronrod integration rules. Zbl 0619.41024 Rabinowitz, Philip 1986 On sequences of imbedded integration rules. Zbl 0635.41024 Rabinowitz, Philip; Kautsky, Jaroslav; Elhay, Sylvan; Butcher, John C. 1987 The convergence of noninterpolatory product integration rules. Zbl 0646.65017 Rabinowitz, Philip 1987 Some practical aspects in the numerical evaluation of Cauchy principal value integrals. Zbl 0654.65019 Rabinowitz, Philip 1986 A stable Gauss-Kronrod algorithm for Cauchy principal-value integrals. Zbl 0625.65011 Rabinowitz, P. 1986 Evaluations of Coulomb wave functions along the transition line. Zbl 0055.42406 Abramowitz, Milton; Rabinowitz, Philip 1954 Product integration of singular integrands using optimal nodal splines. Zbl 0840.41024 Rabinowitz, P. 1993 On avoiding the singularity in the numerical integration of proper integrals. Zbl 0413.65015 Rabinowitz, Philip 1979 Product integration based on Hermite-Fejér interpolation. Zbl 0686.65010 Rabinowitz, Philip 1989 Generalized composite integration rules in the presence of a singularity. Zbl 0543.41031 Rabinowitz, P. 1983 Empirical mathematics: The first Patterson extension of Gauss-Kronrod rules. Zbl 0707.65010 Rabinowitz, Philip; Elhay, Sylvan; Kautsky, Jaroslav 1990 Numerical evaluation of Cauchy principal value integrals with singular integrands. Zbl 0708.65023 Rabinowitz, Philip 1990 A short bibliography on solution of systems of nonlinear algebraic equations. Zbl 0245.65025 Rabinowitz, P. 1970 Generalized noninterpolatory rules for Cauchy principal value integrals. Zbl 0686.65011 Rabinowitz, Philip 1990 Interpolatory product integration in the presence of singularities: $$L_ 2$$ theory. Zbl 0751.41027 Rabinowitz, Philip; Smith, William E. 1992 Interpolatory product integration in the presence of singularities: $$L_ p$$ theory. Zbl 0747.41029 Rabinowitz, Philip; Smith, William E. 1992 Multiple-precision division. Zbl 0098.10106 Rabinowitz, Philip 1961 The method of the kernel function in the theory of elastic plates. Zbl 0113.18403 Nowiński, Jerzy; Rabinowitz, P. 1962 Practical error coefficients for estimating quadrature errors for analytic functions. Zbl 0165.17802 Rabinowitz, P. 1968 Uniform convergence of Cauchy principal value integrals of interpolating splines. Zbl 0820.41011 Rabinowitz, Philip 1991 Hermite-Fejér-related interpolation and product integration. Zbl 0822.41003 Rabinowitz, Philip; Vértesi, Péter 1994 Optimal quasi-interpolatory splines for numerical integration. Zbl 0823.41028 Rabinowitz, Philip 1995 On an osculatory quadrature formula. Zbl 0525.41029 Rabinowitz, Philip 1983 Hermite-Fejér interpolation with boundary conditions for $$\rho$$-normal sets. Zbl 0734.41001 Rabinowitz, Philip; Vértesi, Péter 1990 Practical error coefficeints in the integration of periodic analytic functions by the trapezoidal rule. Zbl 0191.45001 Rabinowitz, P. 1968 Mathematical programming and approximation. Zbl 0219.41001 Rabinowitz, P. 1970 On the nonexistence of simplex integration rules for infinite integrals. Zbl 0263.65028 Davis, P. J.; Rabinowitz, P. 1972 Asymptotic approximation by polynomials in the L$$_1$$ norm. Zbl 0265.41002 Freilich, J. H.; Rabinowitz, P. 1973 Methods of numerical integration. Corrected reprint of the 1984 2nd ed. Zbl 1139.65016 Davis, Philip J.; Rabinowitz, Philip 2007 Finite-part integrals and modified splines. Zbl 1074.65028 Demichelis, V.; Rabinowitz, P. 2004 A first course in numerical analysis. Reprint of 1978 2nd ed. Zbl 0976.65001 Ralston, Anthony; Rabinowitz, Philip 2001 Product integration of singular integrands using quasi-interpolatory splines. Zbl 0866.41008 Dagnino, C.; Rabinowitz, P. 1997 On the uniform convergence of Cauchy principal values of quasi-interpolating splines. Zbl 0859.65015 Rabinowitz, Philip; Santi, Elisabetta 1995 On the numerical solution of the generalized Prandtl equation using variation-di/-minishing splines. Zbl 0838.65134 Caliò, F.; Marchetti, E.; Rabinowitz, P. 1995 Optimal quasi-interpolatory splines for numerical integration. Zbl 0823.41028 Rabinowitz, Philip 1995 Application of approximating splines for the solution of Cauchy singular integral equations. Zbl 0812.65134 Rabinowitz, Philip 1994 Hermite-Fejér-related interpolation and product integration. Zbl 0822.41003 Rabinowitz, Philip; Vértesi, Péter 1994 Monomial cubature rules since “Stroud”: A compilation. Zbl 0799.65027 Cools, Ronald; Rabinowitz, Philip 1993 Product integration of singular integrands using optimal nodal splines. Zbl 0840.41024 Rabinowitz, P. 1993 Hermite and Hermite-Fejér interpolation and associated product integration rules on the real line: The $$L_ 1$$ theory. Zbl 0758.41006 Lubinsky, D. S.; Rabinowitz, P. 1992 Extrapolation methods in numerical integration. Zbl 0790.65016 Rabinowitz, Philip 1992 Interpolatory product integration in the presence of singularities: $$L_ 2$$ theory. Zbl 0751.41027 Rabinowitz, Philip; Smith, William E. 1992 Interpolatory product integration in the presence of singularities: $$L_ p$$ theory. Zbl 0747.41029 Rabinowitz, Philip; Smith, William E. 1992 Uniform convergence results for Cauchy principal value integrals. Zbl 0725.65024 Rabinowitz, Philip 1991 Uniform convergence of Cauchy principal value integrals of interpolating splines. Zbl 0820.41011 Rabinowitz, Philip 1991 Numerical integration based on approximating splines. Zbl 0716.65018 Rabinowitz, Philip 1990 Empirical mathematics: The first Patterson extension of Gauss-Kronrod rules. Zbl 0707.65010 Rabinowitz, Philip; Elhay, Sylvan; Kautsky, Jaroslav 1990 Numerical evaluation of Cauchy principal value integrals with singular integrands. Zbl 0708.65023 Rabinowitz, Philip 1990 Generalized noninterpolatory rules for Cauchy principal value integrals. Zbl 0686.65011 Rabinowitz, Philip 1990 Hermite-Fejér interpolation with boundary conditions for $$\rho$$-normal sets. Zbl 0734.41001 Rabinowitz, Philip; Vértesi, Péter 1990 On an interpolatory product rule for evaluating Cauchy principal value integrals. Zbl 0688.65019 Rabinowitz, Philip 1989 Noninterpolatory integration rules for Cauchy principal value integrals. Zbl 0682.41037 Rabinowitz, P.; Lubinsky, D. S. 1989 Product integration based on Hermite-Fejér interpolation. Zbl 0686.65010 Rabinowitz, Philip 1989 Convergence results for piecewise linear quadratures for Cauchy principal value integrals. Zbl 0699.65017 Rabinowitz, Philip 1988 Numerical integration in the presence of an interior singularity. Zbl 0627.41022 Rabinowitz, Philip 1987 On the convergence of closed interpolatory integration rules based on the zeros of Gegenbauer polynomials. Zbl 0625.41020 Rabinowitz, Philip 1987 Interpolatory product integration for Riemann-integrable functions. Zbl 0636.41021 Rabinowitz, Philip; Smith, William E. 1987 On sequences of imbedded integration rules. Zbl 0635.41024 Rabinowitz, Philip; Kautsky, Jaroslav; Elhay, Sylvan; Butcher, John C. 1987 The convergence of noninterpolatory product integration rules. Zbl 0646.65017 Rabinowitz, Philip 1987 Rates of convergence of Gauss, Lobatto, and Radau integration rules for singular integrands. Zbl 0619.41022 Rabinowitz, Philip 1986 The convergence of interpolatory product integration rules. Zbl 0629.41002 Rabinowitz, Philip 1986 On the convergence of interpolatory product integration rules based on Gauss, Radau and Lobatto points. Zbl 0619.41023 Rabinowitz, Philip 1986 On the definiteness of Gauss-Kronrod integration rules. Zbl 0619.41024 Rabinowitz, Philip 1986 Some practical aspects in the numerical evaluation of Cauchy principal value integrals. Zbl 0654.65019 Rabinowitz, Philip 1986 A stable Gauss-Kronrod algorithm for Cauchy principal-value integrals. Zbl 0625.65011 Rabinowitz, P. 1986 Methods of numerical integration. 2nd ed. Zbl 0537.65020 Davis, Philip J.; Rabinowitz, Philip 1984 Rates of convergence of Gaussian quadrature for singular integrands. Zbl 0574.41028 Lubinsky, D. S.; Rabinowitz, P. 1984 Product integration in the presence of a singularity. Zbl 0547.65011 Rabinowitz, Philip; Sloan, Ian H. 1984 Gauss-Kronrod integration rules for Cauchy principal value integrals. Zbl 0545.65012 Rabinowitz, Philip 1983 Generalized composite integration rules in the presence of a singularity. Zbl 0543.41031 Rabinowitz, P. 1983 On an osculatory quadrature formula. Zbl 0525.41029 Rabinowitz, Philip 1983 The exact degree of precision of generalized Gauss-Kronrod integration rules. Zbl 0461.65019 Rabinowitz, Philip 1980 On avoiding the singularity in the numerical integration of proper integrals. Zbl 0413.65015 Rabinowitz, Philip 1979 A first course in numerical analysis. 2nd ed. Zbl 0408.65001 Ralston, Anthony; Rabinowitz, Philip 1978 The application of integer programming to the computation of fully symmetric integration formulas in two and three dimensions. Zbl 0361.90079 Mantel, Francis; Rabinowitz, Philip 1977 Ignoring the singularity in numerical integration. Zbl 0435.65018 Rabinowitz, Philip 1977 Methods of numerical integration. Zbl 0304.65016 Davis, Philip J.; Rabinowitz, Philip 1975 Asymptotic approximation by polynomials in the L$$_1$$ norm. Zbl 0265.41002 Freilich, J. H.; Rabinowitz, P. 1973 On the Gaussian integration of Chebyshev polynomials. Zbl 0261.65019 Curtis, A. R.; Rabinowitz, P. 1972 On the nonexistence of simplex integration rules for infinite integrals. Zbl 0263.65028 Davis, P. J.; Rabinowitz, P. 1972 On the error in the numerical integration of Chebyshev polynomials. Zbl 0222.65029 Nicholson, D.; Rabinowitz, P.; Richter, N.; Zeilberger, D. 1971 Asymptotic properties of minimal integration rules. Zbl 0222.65024 Rabinowitz, Philip; Richter, Nira 1971 Chebyshev-type integration rules of minimum norm. Zbl 0222.65025 Rabinowitz, Philip; Richter, Nira 1971 New error coefficients for estimating quadrature errors for analytic functions. Zbl 0217.52402 Rabinowitz, P.; Richter, N. 1970 Gaussian integration of functions with branch point singularities. Zbl 0222.65028 Rabinowitz, Philip 1970 Numerical methods for nonlinear algebraic equations. Zbl 0244.00003 Rabinowitz, Philip 1970 A short bibliography on solution of systems of nonlinear algebraic equations. Zbl 0245.65025 Rabinowitz, P. 1970 Mathematical programming and approximation. Zbl 0219.41001 Rabinowitz, P. 1970 Perfectly symmetric two-dimensional integration formulas with minimal numbers of points. Zbl 0208.18702 Rabinowitz, P.; Richter, N. 1969 Rough and ready error estimates in Gaussian integration of analytic functions. Zbl 0174.47203 Rabinowitz, P. 1969 Applications of linear programming to numerical analysis. Zbl 0236.65001 Rabinowitz, Philip 1968 Error bounds in Gaussian integration of functions of low-order continuity. Zbl 0181.17802 Rabinowitz, Philip 1968 Practical error coefficients for estimating quadrature errors for analytic functions. Zbl 0165.17802 Rabinowitz, P. 1968 Practical error coefficeints in the integration of periodic analytic functions by the trapezoidal rule. Zbl 0191.45001 Rabinowitz, P. 1968 Numerical integration. Zbl 0154.17802 Davis, P. J.; Rabinowitz, P. 1967 Gaussian integration in the presence of a singularity. Zbl 0183.18102 Rabinowitz, P. 1967 Numerical experiments in conformal mapping by the method of orthonormal polynomials. Zbl 0139.11002 Rabinowitz, P. 1966 Ignoring the singularity in approximate integration. Zbl 0141.13901 Davis, P. J.; Rabinowitz, P. 1965 The method of the kernel function in the theory of elastic plates. Zbl 0113.18403 Nowiński, Jerzy; Rabinowitz, P. 1962 Advances in orthonormalizing computation. Zbl 0136.13405 Davis, P. J.; Rabinowitz, P. 1961 Some geometrical theorems for abscissas and weights of Gauss type. Zbl 0168.14704 Davis, P. J.; Rabinowitz, P. 1961 Multiple-precision division. Zbl 0098.10106 Rabinowitz, Philip 1961 Abscissas and weights for Lobatto quadrature of high order. Zbl 0096.10203 Rabinowitz, Philip 1960 Tables of abscissas and weights for numerical evaluation of integrals of the form $$\int_0^\infty e^{-x} x^n f(x) dx$$. Zbl 0094.11809 Rabinowitz, Philip; Weiss, George 1959 Additional abscissas and weights for Gaussian quadratures of high order: Values for $$n$$=64, 80, and 96. Zbl 0092.33101 Davis, Philip; Rabinowitz, Philip 1958 Abscissas and weights for Gaussian quadratures of high order. Zbl 0074.33004 Davis, P.; Rabinowitz, P. 1956 Some Monte Carlo experiments in computing multiple integrals. Zbl 0072.14403 Davis, P.; Rabinowitz, P. 1956 On the estimation of quadrature errors for analytic functions. Zbl 0056.29103 Davis, P.; Rabinowitz, P. 1954 Evaluations of Coulomb wave functions along the transition line. Zbl 0055.42406 Abramowitz, Milton; Rabinowitz, Philip 1954 all top 5 #### Cited by 1,799 Authors 33 Rabinowitz, Philip 22 Sidi, Avram 17 Dagnino, Catterina 17 Xiang, Shuhuang 15 González-Vera, Pablo 14 Mastroianni, Giuseppe 13 Cools, Ronald 13 Hasegawa, Takemitsu 13 Notaris, Sotirios E. 12 Lubinsky, Doron S. 12 Santi, Elisabetta 11 Demichelis, Vittoria 11 Petras, Knut 10 Criscuolo, Giuliana 10 Eslahchi, Mohammad Reza 10 Gautschi, Walter 10 Haegemans, Ann 10 Ioakimidis, Nikolaos Ioakim 10 Lether, Frank G. 10 Piessens, Robert 9 Dehghan Takht Fooladi, Mehdi 9 Masjed-Jamei, Mohammad 9 Milovanović, Gradimir V. 9 Sugiura, Hiroshi 9 Wang, Haiyong 8 Cruz-Barroso, Ruymán 8 Diethelm, Kai 8 Huybrechs, Daan 8 Monegato, Giovanni 8 Quarteroni, Alfio M. 8 Sloan, Ian Hugh 8 Zhang, Zhimin 7 Anastasselou, Eleni G. 7 Bultheel, Adhemar François 7 Iserles, Arieh 7 Maday, Yvon 7 Pečarić, Josip 7 Sangawi, Ali W. K. 7 Santos-León, Juan-Carlos 7 Xu, Yuesheng 6 Alaylioglu, Ayse 6 Barnhill, Robert E. 6 Bernardi, Christine 6 Brunner, Hermann 6 Caliò, Franca 6 Chawla, Man M. 6 Evans, Gwynne A. 6 Favati, Paola 6 Genz, Alan C. 6 Huang, Jin 6 Li, Zi-Cai 6 Marchetti, Elena 6 Murid, Ali Hassan Mohamed 6 Romani, Francesco 6 Shizgal, Bernie D. 6 Zhong, Hongzhi 5 Branders, Maria 5 Daruis, Leyla 5 Elliott, David L. 5 Giraldo, Francis X. 5 Greengard, Leslie F. 5 Hashemiparast, S. M. 5 Kim, Kyung Joong 5 Kravchenko, Vladislav V. 5 Laurita, Concetta 5 Lotti, Grazia 5 Njåstad, Olav 5 Ramm, Alexander G. 5 Richter, Nira 5 Sacchi Landriani, Giovanni 5 Torba, Sergii M. 5 Wasilkowski, Grzegorz W. 5 Xu, Yuan 5 Zampieri, Elena 5 Zou, Qingsong 4 Chen, Chin-Yun 4 Elnagar, Gamal N. 4 Förster, Klaus-Jürgen 4 Funaro, Daniele 4 Georgiadis, H. G. 4 Gori, Laura 4 Hunter, David B. 4 Ixaru, Liviu Gr. 4 Jackiewicz, Zdzislaw 4 Jódar Sanchez, Lucas Antonio 4 Kazemi, Mohammad-Ali Afshar 4 Lamberti, Paola 4 Laurie, Dirk P. 4 Locher, Franz 4 Marzban, Hamid-Reza 4 Mori, Masatake 4 Nasser, Mohamed M. S. 4 Rafajłowicz, Ewaryst 4 Sbibih, Driss 4 Schmeisser, Gerhard 4 Schwab, Christoph 4 Shampine, Lawrence Fred 4 Van Keer, Roger 4 Verlinden, Pierre 4 Wang, Tongke ...and 1,699 more Authors all top 5 #### Cited in 248 Serials 207 Journal of Computational and Applied Mathematics 128 Mathematics of Computation 103 Numerische Mathematik 58 Applied Mathematics and Computation 54 BIT 51 Journal of Computational Physics 43 Numerical Algorithms 39 Computing 38 Computers & Mathematics with Applications 35 Applied Numerical Mathematics 33 Journal of Scientific Computing 28 International Journal of Computer Mathematics 27 Computer Methods in Applied Mechanics and Engineering 27 Calcolo 26 Journal of Approximation Theory 19 International Journal for Numerical Methods in Engineering 16 BIT. Nordisk Tidskrift for Informationsbehandling 14 Computer Physics Communications 14 Journal of Mathematical Analysis and Applications 13 Journal of Integral Equations and Applications 13 Computational Statistics and Data Analysis 12 Journal of Statistical Computation and Simulation 12 Advances in Computational Mathematics 11 Acta Mechanica 10 SIAM Journal on Scientific Computing 9 SIAM Journal on Numerical Analysis 9 Journal of Complexity 9 Mathematical and Computer Modelling 8 International Journal of Mathematical Education in Science and Technology 8 Annals of Operations Research 7 Mathematics and Computers in Simulation 7 Numerical Functional Analysis and Optimization 7 Applied Mathematics Letters 7 Applied Mathematical Modelling 7 Mathematical Problems in Engineering 6 Applicable Analysis 6 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 6 Journal of Econometrics 6 Constructive Approximation 6 Computational Mechanics 6 Communications in Statistics. Theory and Methods 6 Linear Algebra and its Applications 6 Engineering Analysis with Boundary Elements 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 The Annals of Statistics 5 RAIRO. Analyse Numérique 5 Numerical Methods for Partial Differential Equations 5 European Journal of Operational Research 4 International Journal of Engineering Science 4 International Journal for Numerical Methods in Fluids 4 Journal of Engineering Mathematics 4 Mathematical Biosciences 4 Wave Motion 4 Aplikace Matematiky 4 International Journal of Mathematics and Mathematical Sciences 4 Journal of Statistical Planning and Inference 4 RAIRO. Modélisation Mathématique et Analyse Numérique 4 Communications in Numerical Methods in Engineering 4 Communications in Nonlinear Science and Numerical Simulation 4 Foundations of Computational Mathematics 3 Communications on Pure and Applied Mathematics 3 International Journal of Control 3 International Journal of Systems Science 3 Journal of Fluid Mechanics 3 Journal of Mathematical Physics 3 Physics Letters. A 3 Transport Theory and Statistical Physics 3 Automatica 3 Journal of Multivariate Analysis 3 Mathematische Zeitschrift 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Results in Mathematics 3 Statistics & Probability Letters 3 Acta Mathematica Hungarica 3 Communications in Applied Numerical Methods 3 COMPEL 3 Computational Statistics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal of Nonparametric Statistics 3 Journal of Mathematical Chemistry 3 Abstract and Applied Analysis 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 International Journal of Theoretical and Applied Finance 3 Computational Methods in Applied Mathematics 3 Mediterranean Journal of Mathematics 2 Astrophysics and Space Science 2 Bulletin of the Australian Mathematical Society 2 The Canadian Journal of Statistics 2 Computers and Fluids 2 Journal of the Franklin Institute 2 Journal of the Mechanics and Physics of Solids 2 Mathematical Methods in the Applied Sciences 2 Physica A 2 Psychometrika 2 Rocky Mountain Journal of Mathematics 2 Theoretical and Computational Fluid Dynamics 2 Biometrical Journal 2 Journal of Applied Probability 2 Mathematical Programming 2 Proceedings of the American Mathematical Society ...and 148 more Serials all top 5 #### Cited in 50 Fields 1,089 Numerical analysis (65-XX) 529 Approximations and expansions (41-XX) 147 Partial differential equations (35-XX) 110 Integral equations (45-XX) 105 Functions of a complex variable (30-XX) 99 Statistics (62-XX) 84 Harmonic analysis on Euclidean spaces (42-XX) 83 Mechanics of deformable solids (74-XX) 68 Special functions (33-XX) 62 Ordinary differential equations (34-XX) 62 Fluid mechanics (76-XX) 51 Operations research, mathematical programming (90-XX) 43 Probability theory and stochastic processes (60-XX) 39 Computer science (68-XX) 31 Integral transforms, operational calculus (44-XX) 28 Real functions (26-XX) 27 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 25 Biology and other natural sciences (92-XX) 23 Systems theory; control (93-XX) 20 Optics, electromagnetic theory (78-XX) 16 Quantum theory (81-XX) 15 Number theory (11-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 15 Dynamical systems and ergodic theory (37-XX) 11 Sequences, series, summability (40-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Information and communication theory, circuits (94-XX) 9 Potential theory (31-XX) 8 Classical thermodynamics, heat transfer (80-XX) 8 Geophysics (86-XX) 7 Operator theory (47-XX) 6 Combinatorics (05-XX) 6 Functional analysis (46-XX) 5 Mechanics of particles and systems (70-XX) 5 Astronomy and astrophysics (85-XX) 4 Field theory and polynomials (12-XX) 3 History and biography (01-XX) 3 Measure and integration (28-XX) 3 Convex and discrete geometry (52-XX) 3 Differential geometry (53-XX) 2 General and overarching topics; collections (00-XX) 2 Commutative algebra (13-XX) 2 Difference and functional equations (39-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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https://zbmath.org/authors/?q=ai%3Ahumphreys.james-e	# zbMATH — the first resource for mathematics ## Humphreys, James E. Compute Distance To: Author ID: humphreys.james-e Published as: Humphreys, J. E.; Humphreys, James E. Homepage: http://people.math.umass.edu/~jeh/ External Links: MGP · Wikidata · MathOverflow · dblp · GND Documents Indexed: 59 Publications since 1967, including 16 Books #### Co-Authors 57 single-authored 1 Jantzen, Jens Carsten 1 Verma, Daya-Nand all top 5 #### Serials 9 Journal of Algebra 5 Graduate Texts in Mathematics 3 Communications in Algebra 2 American Mathematical Monthly 2 Bulletin of the American Mathematical Society. New Series 2 Bulletin of the American Mathematical Society 2 Cambridge Studies in Advanced Mathematics 2 Lecture Notes in Mathematics 1 Communications on Pure and Applied Mathematics 1 Advances in Mathematics 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Experimental Mathematics 1 Graduate Studies in Mathematics 1 London Mathematical Society Lecture Note Series 1 Mathematical Surveys and Monographs 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae all top 5 #### Fields 48 Group theory and generalizations (20-XX) 22 Nonassociative rings and algebras (17-XX) 10 Algebraic geometry (14-XX) 9 Topological groups, Lie groups (22-XX) 2 Number theory (11-XX) 2 Associative rings and algebras (16-XX) 2 Category theory; homological algebra (18-XX) 2 Geometry (51-XX) #### Citations contained in zbMATH Open 54 Publications have been cited 4,113 times in 3,708 Documents Cited by Year Introduction to Lie algebras and representation theory. Zbl 0254.17004 Humphreys, J. E. 1972 Reflection groups and Coxeter groups. Zbl 0725.20028 Humphreys, James E. 1990 Linear algebraic groups. Zbl 0325.20039 Humphreys, James E. 1975 Introduction to Lie algebras and representation theory. 2nd printing, rev. Zbl 0447.17001 Humphreys, James E. 1978 Linear algebraic groups. (Linejnye algebraicheskie gruppy). Transl. from the English by A. E. Zalesskij. Zbl 0507.20017 Humphreys, J. E. 1980 Representations of semisimple Lie algebras in the BGG category $$\mathcal O$$. Zbl 1177.17001 Humphreys, James E. 2008 Conjugacy classes in semisimple algebraic groups. Zbl 0834.20048 Humphreys, James E. 1995 Reflection groups and Coxeter groups. Zbl 0768.20016 Humphreys, James E. 1992 Linear algebraic groups. Corr. 2nd printing. Zbl 0471.20029 Humphreys, James E. 1981 Introduction to Lie algebras and representation theory. 3rd printing, rev. Zbl 0447.17002 Humphreys, James E. 1980 Modular representations of finite groups of Lie type. Zbl 1113.20016 Humphreys, James E. 2006 Modular representations of classical Lie algebras and semi-simple groups. Zbl 0219.17003 Humphreys, J. E. 1971 Ordinary and modular representations of Chevalley groups. Zbl 0341.20037 Humphreys, James E. 1976 Comparing modular representations of semisimple groups and their Lie algebras. Zbl 0919.17013 Humphreys, J. E. 1997 Algebraic groups and modular Lie algebras. Zbl 0173.03001 Humphreys, J. E. 1967 Finite and infinite dimensional modules for semisimple Lie algebras. Zbl 0392.17006 Humphreys, J. E. 1978 Defect groups for finite groups of Lie type. Zbl 0198.04502 Humphreys, J. E. 1971 On the authomorphisms of infinite Chevalley groups. Zbl 0181.03803 Humphreys, J. E. 1969 Projective modules for SL(2,q). Zbl 0258.20010 Humphreys, J. E. 1973 Symmetry for finite dimensional Hopf algebras. Zbl 0349.16001 Humphreys, J. E. 1978 The Steinberg representation. Zbl 0627.20024 Humphreys, J. E. 1987 Modular representations of simple Lie algebras. Zbl 0962.17013 Humphreys, J. E. 1998 Modular representations of finite groups of Lie type. Zbl 0472.20015 Humphreys, J. E. 1980 Arithmetic groups. Zbl 0426.20029 Humphreys, James E. 1980 Blocks and indecomposable modules for semisimple algebraic groups. Zbl 0398.20047 Humphreys, J. E.; Jantzen, J. C. 1978 Remarks on ”A theorem on special linear groups”. Zbl 0237.20045 Humphreys, J. E. 1972 Ordinary and modular characters of $$\mathrm{SL}(3,p)$$. Zbl 0474.20021 Humphreys, J. E. 1981 Projective modules for finite Chevalley groups. Zbl 0258.20007 Humphreys, J. E.; Verma, D. N. 1973 On the hyperalgebra of a semi-simple algebraic group. Zbl 0367.20043 Humphreys, J. E. 1977 Existence of Levi factors in certain algebraic groups. Zbl 0157.36701 Humphreys, J. E. 1967 Deligne-Lusztig characters and principal indecomposable modules. Zbl 0427.20033 Humphreys, J. E. 1980 Cohomology of G/B in characteristic p. Zbl 0612.20023 Humphreys, J. E. 1986 Modular representations of classical Lie algebras. Zbl 0199.35103 Humphreys, J. E. 1970 On the structure of Weyl modules. Zbl 0546.20036 Humphreys, J. E. 1984 Hilbert’s fourteenth problem. Zbl 0391.14002 Humphreys, J. E. 1978 Representations of SL(2,p). Zbl 0296.20020 Humphreys, J. E. 1975 Cartan invariants. Zbl 0555.20009 Humphreys, J. E. 1985 Some computations of Cartan invariants for finite groups of Lie type. Zbl 0358.20013 Humphreys, J. E. 1973 Restricted Lie algebras (and beyond). Zbl 0501.17007 Humphreys, J. E. 1982 Non-zero $$Ext^ 1$$ for Chevalley groups (via algebraic groups). Zbl 0567.20029 Humphreys, J. E. 1985 Generic Cartan invariants for Frobenius kernels and Chevalley groups. Zbl 0674.20023 Humphreys, J. E. 1989 Cohomology of line bundles on G/B for the exceptional group $$G_ 2$$. Zbl 0615.20023 Humphreys, J. E. 1987 Projective modules for Sp(4,p) in characteristic p. Zbl 0618.20027 Humphreys, J. E. 1986 A construction of projective modules in the category O of Bernstein- Gel’fand-Gel’fand. Zbl 0367.17005 Humphreys, J. E. 1977 Extremal composition factors for groups of Lie type. Zbl 0840.20035 Humphreys, J. E. 1994 Weyl modules and Bott’s theorem in characteristic p. Zbl 0395.20023 Humphreys, J. E. 1978 Arithmetic groups. Zbl 0248.20060 Humphreys, J. E. 1971 Induced modules for semisimple groups and Lie algebras. Zbl 0582.17004 Humphreys, J. E. 1986 Weyl groups, deformations of linkage classes, and character degrees for Chevalley groups. Zbl 0286.20055 Humphreys, J. E. 1974 Cartan invariants and decomposition numbers of Chevalley groups. Zbl 0451.20038 Humphreys, J. E. 1980 Ordinary and modular characters of $$\mathrm{SU}(3,p)$$. Zbl 0699.20032 Humphreys, J. E. 1990 Representations of reduced enveloping algebras and cells in the affine Weyl group. Zbl 1155.17301 Humphreys, J. E. 2006 Another look at Dickson’s invariants for finite linear groups. Zbl 0835.20055 Humphreys, J. E. 1994 Analogues of Weyl’s formula for reduced enveloping algebras. Zbl 1162.17302 Humphreys, J. E. 2002 Representations of semisimple Lie algebras in the BGG category $$\mathcal O$$. Zbl 1177.17001 Humphreys, James E. 2008 Modular representations of finite groups of Lie type. Zbl 1113.20016 Humphreys, James E. 2006 Representations of reduced enveloping algebras and cells in the affine Weyl group. Zbl 1155.17301 Humphreys, J. E. 2006 Analogues of Weyl’s formula for reduced enveloping algebras. Zbl 1162.17302 Humphreys, J. E. 2002 Modular representations of simple Lie algebras. Zbl 0962.17013 Humphreys, J. E. 1998 Comparing modular representations of semisimple groups and their Lie algebras. Zbl 0919.17013 Humphreys, J. E. 1997 Conjugacy classes in semisimple algebraic groups. Zbl 0834.20048 Humphreys, James E. 1995 Extremal composition factors for groups of Lie type. Zbl 0840.20035 Humphreys, J. E. 1994 Another look at Dickson’s invariants for finite linear groups. Zbl 0835.20055 Humphreys, J. E. 1994 Reflection groups and Coxeter groups. Zbl 0768.20016 Humphreys, James E. 1992 Reflection groups and Coxeter groups. Zbl 0725.20028 Humphreys, James E. 1990 Ordinary and modular characters of $$\mathrm{SU}(3,p)$$. Zbl 0699.20032 Humphreys, J. E. 1990 Generic Cartan invariants for Frobenius kernels and Chevalley groups. Zbl 0674.20023 Humphreys, J. E. 1989 The Steinberg representation. Zbl 0627.20024 Humphreys, J. E. 1987 Cohomology of line bundles on G/B for the exceptional group $$G_ 2$$. Zbl 0615.20023 Humphreys, J. E. 1987 Cohomology of G/B in characteristic p. Zbl 0612.20023 Humphreys, J. E. 1986 Projective modules for Sp(4,p) in characteristic p. Zbl 0618.20027 Humphreys, J. E. 1986 Induced modules for semisimple groups and Lie algebras. Zbl 0582.17004 Humphreys, J. E. 1986 Cartan invariants. Zbl 0555.20009 Humphreys, J. E. 1985 Non-zero $$Ext^ 1$$ for Chevalley groups (via algebraic groups). Zbl 0567.20029 Humphreys, J. E. 1985 On the structure of Weyl modules. Zbl 0546.20036 Humphreys, J. E. 1984 Restricted Lie algebras (and beyond). Zbl 0501.17007 Humphreys, J. E. 1982 Linear algebraic groups. Corr. 2nd printing. Zbl 0471.20029 Humphreys, James E. 1981 Ordinary and modular characters of $$\mathrm{SL}(3,p)$$. Zbl 0474.20021 Humphreys, J. E. 1981 Linear algebraic groups. (Linejnye algebraicheskie gruppy). Transl. from the English by A. E. Zalesskij. Zbl 0507.20017 Humphreys, J. E. 1980 Introduction to Lie algebras and representation theory. 3rd printing, rev. Zbl 0447.17002 Humphreys, James E. 1980 Modular representations of finite groups of Lie type. Zbl 0472.20015 Humphreys, J. E. 1980 Arithmetic groups. Zbl 0426.20029 Humphreys, James E. 1980 Deligne-Lusztig characters and principal indecomposable modules. Zbl 0427.20033 Humphreys, J. E. 1980 Cartan invariants and decomposition numbers of Chevalley groups. Zbl 0451.20038 Humphreys, J. E. 1980 Introduction to Lie algebras and representation theory. 2nd printing, rev. Zbl 0447.17001 Humphreys, James E. 1978 Finite and infinite dimensional modules for semisimple Lie algebras. Zbl 0392.17006 Humphreys, J. E. 1978 Symmetry for finite dimensional Hopf algebras. Zbl 0349.16001 Humphreys, J. E. 1978 Blocks and indecomposable modules for semisimple algebraic groups. Zbl 0398.20047 Humphreys, J. E.; Jantzen, J. C. 1978 Hilbert’s fourteenth problem. Zbl 0391.14002 Humphreys, J. E. 1978 Weyl modules and Bott’s theorem in characteristic p. Zbl 0395.20023 Humphreys, J. E. 1978 On the hyperalgebra of a semi-simple algebraic group. Zbl 0367.20043 Humphreys, J. E. 1977 A construction of projective modules in the category O of Bernstein- Gel’fand-Gel’fand. Zbl 0367.17005 Humphreys, J. E. 1977 Ordinary and modular representations of Chevalley groups. Zbl 0341.20037 Humphreys, James E. 1976 Linear algebraic groups. Zbl 0325.20039 Humphreys, James E. 1975 Representations of SL(2,p). Zbl 0296.20020 Humphreys, J. E. 1975 Weyl groups, deformations of linkage classes, and character degrees for Chevalley groups. Zbl 0286.20055 Humphreys, J. E. 1974 Projective modules for SL(2,q). Zbl 0258.20010 Humphreys, J. E. 1973 Projective modules for finite Chevalley groups. Zbl 0258.20007 Humphreys, J. E.; Verma, D. N. 1973 Some computations of Cartan invariants for finite groups of Lie type. Zbl 0358.20013 Humphreys, J. E. 1973 Introduction to Lie algebras and representation theory. Zbl 0254.17004 Humphreys, J. E. 1972 Remarks on ”A theorem on special linear groups”. Zbl 0237.20045 Humphreys, J. E. 1972 Modular representations of classical Lie algebras and semi-simple groups. Zbl 0219.17003 Humphreys, J. E. 1971 Defect groups for finite groups of Lie type. Zbl 0198.04502 Humphreys, J. E. 1971 Arithmetic groups. Zbl 0248.20060 Humphreys, J. E. 1971 Modular representations of classical Lie algebras. Zbl 0199.35103 Humphreys, J. E. 1970 On the authomorphisms of infinite Chevalley groups. Zbl 0181.03803 Humphreys, J. E. 1969 Algebraic groups and modular Lie algebras. Zbl 0173.03001 Humphreys, J. E. 1967 Existence of Levi factors in certain algebraic groups. Zbl 0157.36701 Humphreys, J. E. 1967 all top 5 #### Cited by 3,500 Authors 30 Brenti, Francesco 24 Nakano, Daniel K. 24 Putcha, Mohan S. 19 Biswas, Indranil 18 Donkin, Stephen 16 Green, Richard M. 16 Humphreys, James E. 16 Kannan, Subramaniam Senthamarai 16 Mazorchuk, Volodymyr 15 Farnsteiner, Rolf 14 Andersen, Henning Haahr 14 Borovik, Alexandre V. 14 de Graaf, Willem Adriaan 13 Bunina, E. I. 13 Coulembier, Kevin 13 Marberg, Eric 13 Reiner, Victor 13 Roichman, Yuval 13 Stroppel, Catharina H. 12 Billey, Sara C. 12 Guralnick, Robert Michael 12 Hohlweg, Christophe 12 Marietti, Mario 12 Renner, Lex E. 11 Chari, Vyjayanthi 11 Hultman, Axel 11 Malle, Gunter 11 Papi, Paolo 11 Pillen, Cornelius 11 Premet, Alexander A. 11 Shi, Jianyi 11 Singer, Michael F. 11 Testerman, Donna M. 11 Zhao, Kaiming 10 Azam, Saeid 10 Bendel, Christopher P. 10 Dyer, Matthew J. 10 Shu, Bin 10 Stembridge, John R. 10 Tiep Pham Huu 10 Vavilov, Nikolaĭ Aleksandrovich 10 Wang, Dengyin 10 Zalesski, Alexandre Efimovich 9 Adin, Ron M. 9 Benkart, Georgia M. 9 Caselli, Fabrizio 9 Chen, Zhengxin 9 Hare, Kathryn E. 9 Helminck, Aloysius G. 9 Hosaka, Tetsuya 9 Huang, Wenxue 9 Khare, Apoorva 9 Lin, Zongzhu 9 McNinch, George J. 9 Parshall, Brian J. 9 Proctor, Robert A. 9 Reading, Nathan 9 Sentinelli, Paolo 9 Snow, Dennis M. 9 Terwilliger, Paul M. 9 Williamson, Geordie 8 Carnovale, Giovanna 8 Chastkofsky, Leonard 8 Douglas, Andrew S. 8 Draper, Cristina 8 Elduque, Alberto 8 Jantzen, Jens Carsten 8 Larsen, Michael Jeffrey 8 Musson, Ian M. 8 Navarro, Gabriel 8 Navarro, Rosa María 8 Panyushev, Dmitri Ivanovich 8 Repka, Joe 8 Sobaje, Paul 7 Altınel, Tuna 7 Athanasiadis, Christos A. 7 Biagioli, Riccardo 7 Burness, Timothy C. 7 Cellini, Paola 7 Dechant, Pierre-Philippe 7 Deckhart, Robert W. 7 Donnelly, Robert G. 7 Doty, Stephen R. 7 Eswara Rao, Senapathi 7 Guillemin, Victor W. 7 Kaneda, Masaharu 7 Komori, Yasushi 7 Lam, Thomas F. 7 Li, Haisheng 7 Postnikov, Alexander 7 Simson, Daniel 7 Stump, Christian 7 Xu, Xiaoping 6 Andruskiewitsch, Nicolás 6 Benito, Pilar 6 Bergeron, Nantel 6 Boe, Brian Douglas 6 Bremner, Murray R. 6 Breuil, Christophe 6 Brown, Kenneth Alexander ...and 3,400 more Authors all top 5 #### Cited in 344 Serials 570 Journal of Algebra 193 Communications in Algebra 171 Transactions of the American Mathematical Society 157 Advances in Mathematics 133 Journal of Pure and Applied Algebra 94 Linear Algebra and its Applications 87 Proceedings of the American Mathematical Society 83 Mathematische Zeitschrift 65 Journal of Algebraic Combinatorics 63 Journal of Combinatorial Theory. 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Mathematics 8 Reports on Mathematical Physics 8 Mathematics of Computation 8 Journal für die Reine und Angewandte Mathematik 8 International Journal of Mathematics 8 Annals of Physics 8 Expositiones Mathematicae 8 The Electronic Journal of Combinatorics 8 Séminaire Lotharingien de Combinatoire 8 Central European Journal of Mathematics 7 Glasgow Mathematical Journal 7 Results in Mathematics 7 Forum Mathematicum 7 Experimental Mathematics 7 Advances in Applied Clifford Algebras 7 The Ramanujan Journal 7 Communications in Contemporary Mathematics 7 Algebraic & Geometric Topology 7 Journal of the Institute of Mathematics of Jussieu 6 Journal of Mathematical Analysis and Applications 6 Physics Letters. A 6 Rocky Mountain Journal of Mathematics 6 Canadian Journal of Mathematics 6 Publications Mathématiques 6 Monatshefte für Mathematik 6 Nagoya Mathematical Journal 6 Rendiconti del Seminario Matematico della Università di Padova 6 Annals of Global Analysis and Geometry 6 Order ...and 244 more Serials all top 5 #### Cited in 60 Fields 1,555 Group theory and generalizations (20-XX) 1,193 Nonassociative rings and algebras (17-XX) 615 Algebraic geometry (14-XX) 517 Combinatorics (05-XX) 416 Topological groups, Lie groups (22-XX) 340 Associative rings and algebras (16-XX) 208 Number theory (11-XX) 195 Quantum theory (81-XX) 187 Differential geometry (53-XX) 157 Linear and multilinear algebra; matrix theory (15-XX) 130 Manifolds and cell complexes (57-XX) 123 Convex and discrete geometry (52-XX) 121 Dynamical systems and ergodic theory (37-XX) 114 Commutative algebra (13-XX) 107 Order, lattices, ordered algebraic structures (06-XX) 96 Several complex variables and analytic spaces (32-XX) 85 Special functions (33-XX) 84 Geometry (51-XX) 83 Category theory; homological algebra (18-XX) 71 Global analysis, analysis on manifolds (58-XX) 68 Algebraic topology (55-XX) 58 Abstract harmonic analysis (43-XX) 52 Computer science (68-XX) 51 Field theory and polynomials (12-XX) 48 Ordinary differential equations (34-XX) 38 Probability theory and stochastic processes (60-XX) 37 Functional analysis (46-XX) 35 Partial differential equations (35-XX) 33 Mathematical logic and foundations (03-XX) 32 Statistical mechanics, structure of matter (82-XX) 25 Mechanics of particles and systems (70-XX) 24 $$K$$-theory (19-XX) 22 Relativity and gravitational theory (83-XX) 21 Functions of a complex variable (30-XX) 19 Harmonic analysis on Euclidean spaces (42-XX) 17 Operator theory (47-XX) 17 Information and communication theory, circuits (94-XX) 16 Systems theory; control (93-XX) 15 Numerical analysis (65-XX) 15 Biology and other natural sciences (92-XX) 11 Measure and integration (28-XX) 10 Potential theory (31-XX) 9 General algebraic systems (08-XX) 9 Difference and functional equations (39-XX) 7 Integral transforms, operational calculus (44-XX) 6 Approximations and expansions (41-XX) 5 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Real functions (26-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 General topology (54-XX) 3 Mechanics of deformable solids (74-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-07-25T13:34:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27748751640319824, "perplexity": 3067.6262450753343}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151672.96/warc/CC-MAIN-20210725111913-20210725141913-00355.warc.gz"}
https://arrow.fandom.com/wiki/User_talk:Operep	6,423 Pages # Operep ## aka Zexal 0 Discussion posts My favorite wikis • I live in Japan; Tokyo • I was born on October 10 • I am Male ## Moving pages Hey, it's appreciated you tried to help with moving pages but that's not how it's done. Only admins can through the move function and that needs to be used so edit history is retained.TIMESHADE \|T - C\| 23:08, August 25, 2017 (UTC) ## Locking Pages Howdy, in regards to us locking pages, we lock high traffic pages when there's edit wars going on, so for now I'll unlock it, however just because "you editors" need to edit it, remember there are other articles that need to be edited too. Wraiyf You know, I'm getting real tired of people and their lazy writing 02:38, May 21, 2018 (UTC) • As well, please don't go spamming the administrators pages with the same post. Ask one, if that one doesn't respond within a reasonable time frame, then ask another. $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) 14:11, May 21, 2018 (UTC) ## OfCharacter I just wanted to let you know of a new template we have Template:OfCharacter for the Image of Character category pages that automatically adds it to the "images of characters" category. Check out the edit I made after you on Category:Images of Erika Morrison. $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) ## Show parameter Hey, please stop moving the "show" parameter on templates to the top. Our standard here at this wiki is that it goes at the bottom. It needs to be in a central location so that it can be easily found. Thanks, $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) • Look at your changes that you recently made to the page "Arsenal suit". On the infobox, you moved "\|show=Arrow" to the top of the parameter list. We keep the show parameter at the bottom. I have seen you move this several times before and at this wiki we keep it at the bottom. Please in the future try to keep it at the bottom and don't move it. Thanks, $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) ## Sections If you aren't going to add anything to a section, don't bother adding it. I didn't remove it by accident along with the "wrongful" part. Think twice before undoing an admins edit. We know what we're doing.TIMESHADE \|T - C\| 16:15, October 16, 2018 (UTC) ## Infobox It's part of the Elseworlds theme.TIMESHADE \|T - C\| 17:55, December 9, 2018 (UTC) ## "Sophie" page Hi, I saw that you created the character page named Sophie. Could you tell me what the timestamp was when it mentioned her name? Because I've looked through scripts and subtitles and none of them have the part where someone says her name. Thanks. ~ COƧMO THE CHOCOBO \| TALK? \| at 5:23, Dec 17, 2018 (UTC) Well if that's the case, then it's weird that the comment on your first edit was "(Created page with "{{Stub}} {{Image needed}} {{Character \|homeuniverse = Earth Thirty-Eight \|show = Supergirl \|species = \|status = Alive \|name = Sophie \|occupation = Student of [[National City U...")", and also the first edit made in the history. Well, it's okay. I was just verifying some info. Sorry if I mistook you for another user again. And thanks ~ COƧMO THE CHOCOBO \| TALK? \| at 14:22, Dec 17, 2018 (UTC) ## Changing Earth Designation Hey, like the announcement says, please don't edit while the bot is running through the pages. It will change all of these links and texts, you don't have to. So stop. $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) Please stop editing, we know those categories will need to be deleted. We're on it. No need to worry. $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) SERIOUSLY, STOP. $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) DUDE, STOP. How many warnings do you need? STOP EDITING. $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) ## Reshuffling infoboxes Hey, I'd ask that you please don't just resort infoboxes as you please, as you did in your edit here. We like to keep them consistent so it's easier to edit, and mixing them around just confuses matters. —MakeShift (talk page) 12:57, February 8, 2019 (UTC) Ahh, no worries, I think I see the issue here, it's not your fault. Visual editor is seriously broken, and staff clearly couldn't care less about it. I'd definitely recommend using source editor, it causes less problems with editing (like not adding extra quotation marks after episode names, as visual editor does), plus it's super easy to get your head around! —MakeShift (talk page) 15:40, February 8, 2019 (UTC) ## S template. Hey, please don't remove the S template off of pages. I found a few where you have done this. Please do not. It is like the Ep template in which it is equipped with a hovering feature. Please don't remove it. Thanks, $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) Hey, please do not spam admin talk pages (i.e. write the same message on all of their walls). Write a message on one, then wait. If no response for a while, then you can message another one. But do not go spamming the entire admin board. $\int$ IHH dt 15:17, Oct 14, 2019 (UTC) ## RE: Emiko No, the block expires on May 7th.--Kir the Wizard (talk) 16:51, May 1, 2019 (UTC) ## Spoiler Please note adding pictures of suits that haven't been aired in an episode is against our spoiler policy.TIMESHADE \|T - C\| 13:04, July 23, 2019 (UTC) ## Semi-colon Hi, it's okay that you use semi-colons for independent clauses with interconnected ideas, but please don't overdo it, as most grammar experts recommend that at most, two independent clauses is enough. Just a friendly reminder. ~ COƧMO THE CHOCOBO \| TALK? \| at 21:01, Oct 13, 2019 (UTC) In the Bruce Wayne page, you interconnected several sentences by a semi-colon into one single sentence, which is not incorrect, though you may limit the number of sentences to at most two when connecting them by semi-colons, if that makes sense. ~ COƧMO THE CHOCOBO \| TALK? \| at 15:17, Oct 14, 2019 (UTC) Community content is available under CC-BY-SA unless otherwise noted.	2019-10-19T03:36:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5098674297332764, "perplexity": 3475.38858161745}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986688674.52/warc/CC-MAIN-20191019013909-20191019041409-00426.warc.gz"}
https://finalfantasy.fandom.com/wiki/Flare_(ability)	## FANDOM 36,471 Pages Relm: I couldn't miss the chance to practice my drawing! Know pain. Flare (フレア, Furea?), also known as Nuke, is a recurring spell throughout the Final Fantasy series. Though its name implies fire-elemental properties, rarely is this the case as it is usually non-elemental Black Magic. Flare is considered an "Ultimate" spell, along with Ultima, Meteor, Holy, Burst, Freeze, and Tornado. Flare is often the Black Magic equivalent and opposite of the spell Holy when the spell Meteor is not. There are many versions of Flare. Bahamut's signature attack is Megaflare, with variations being Gigaflare and Teraflare. Flare Star is enemy-exclusive and Shadow Flare is a dark-elemental version of the spell. ## Appearances Edit ### Final Fantasy Edit Blasts all foes with light and heat. —Description Flare (NUKE on the NES) is a level 8 Black Magic spell which inflicts large non-elemental damage to all enemies. Offensively, it is the most powerful spell. Flare can be cast by Chronodia, Shinryu, Death Knight, Lich, and Chaos. The spell can be bought at Lufenia and can only be learned by the Black Wizard job class. In the Dawn of Souls and 20th Anniversary Edition releases it costs 50 MP to cast. ### Final Fantasy II Edit Sets off a fusion reaction to damage foes. —Description Flare is a Black Magic spell which inflicts a heavy amount of non-elemental damage to one or all enemies. Offensively, it is one of the most powerful spells, second to Ultima. As the spell's level grows, so too does its potency. Any character can learn Flare by having them use the Flare Tome (Flare Scroll in Origins). Flare Tome Effect Allows the target to learn Flare when used outside of battle. Casts Flare VIII on all enemies when used in battle. Find Mysidian Tower Drop Li'l Murderer, Tiamat, Thunder Gigas, Wizard, Yamatano Orochi Cost 40,000 gil (all releases) Flare X is used exclusively by Wizard, while Flare XVI is used by Beelzebub, Emperor in the final battle, Zombie Borghen, Light Emperor, and Ultima Weapon. According to the cutscene immediately prior to the Light Emperor battle, the Emperor utilized Flare XVI on Maria during their fight, in retaliation for her casting Holy Lv. 16 on him. ### Final Fantasy III Edit Flare is a level 8 Black Magic, which can only be cast by the Magus and Sage. It can be bought in Eureka, and it costs 60,000 gil to buy. Doga can cast Flare when he joins the party as a guest in the 3D version, and the player can also use Flare through the Chocobo's Wrath item. It has a base power of 200. The enemies Titan, Scylla, and Echidna can use Flare against the party. ### Final Fantasy IV Edit Causes damage by combustion. —Description Flare is the second strongest Black Magic spell after Meteor, but is cast faster and for half the MP. In the 2D versions it takes 50 MP cast, and in 3D versions it takes 55 MP. In the 3D versions it has a spell power of 160 and 400 in all other versions. In the Advance and Complete Collection versions Flare Sledgehammer randomly casts Flare when attacking with it, even if the weapon is actually Ice-elemental due to a bug. Flare can be cast by Zeromus EG, Dark Bahamut, Zeromus, and Deathmask. It was known as Nuke in the SNES version, with Flare as the Twincast spell. In the Game Boy Advance version onwards, the Black Magic spell is called Flare and the Twin spell was called Pyro. #### Final Fantasy IV -Interlude- Edit Flare is a Black Magic spell. it can be learned by imposter Rydia (level 55) and Palom (level 52). It deals massive non-elemental damage to one enemy at the cost of 50 MP. #### Final Fantasy IV: The After Years Edit Flare is a powerful Black Magic that can be cast by Rydia (Level 60), Fusoya (Initial skill), Golbez (Level 55), Palom (Level 50), and Leonora (Level 85). It costs 50 MP to cast and inflicts major non-elemental damage. It may only affect a single target. ### Final Fantasy V Edit Flare is a Level 6 Black Magic spell, and it is obtained in the magical part of the Fork Tower, where you must defeat Omniscient. The physical part contains Holy and the Minotaur must be defeated. If the party takes too long getting one after the other, the tower will explode and result in a Game Over. Damage calculation parameters are: $Attack = Spell Attack + (0..(Spell Attack/32))$[1] $M = (LevelMagic Power)/256 + 4$ $Defense = (Magic Defense/32)$ The formula for Flare is: $Damage = (Spell Attack + (0..(Spell Attack/32)) - (Magic Defense/32)) M$[1] Flare can be used by Barrier, Enuo, Exdeath in the final battle, Famed Mimic Gogo, Necrophobe, Neo Exdeath, Omniscient, and Archeodemon. The player can also utilize the Flare spell without having to obtain the spell by catching and then releasing either a Goblin, Flaremancer, Fury, or Claret Dragon. Flare is one of the spells that can be cast from the Wonder Wand for free. ### Final Fantasy VI Edit Blasts the target with concentrated thermal explosions. —Description Flare is an Attack spell that does non-elemental damage and ignores magic defense. It is taught by Bahamut at a rate of x2, though Celes can learn it naturally at level 81. Its Spell Power is 60, its Hit Rate is 150, and is vulnerable to Runic. It costs 45 MP to cast. Flare is an Added Ability to the Ragnarok weapon. Flare can be cast by Flame Eater, Guardian, Shambling Corpse, Level 90 Magic, Cherry, Magic, Necromancer, Red Dragon, Ultima Weapon, Kaiser Dragon, and Behemoth King (Living). ### Final Fantasy VII Edit Flare is found in the Contain Materia, as the level 4 spell that costs 100 MP to cast and requires 15,000 AP to learn. It does extreme fire damage, its spell power being equal to 7.1875x the base magic damage. Only the enemy Behemoth casts the spell against the party. The King Behemoth has access to the spell, but only when under Manipulate. #### Crisis Core -Final Fantasy VII- Edit Flare is usable by the Flare Materia. It lights up the screen with a bright red flash, all enemies taking damage when it dies down. Flare costs 77 MP to cast, and is one of the few spells that cannot be used with Dualcast. Flare can be obtained through missions 2-4-2, 3-4-4, 3-5-3, 5-4-3, 8-6-4, 9-3-6, 9-4-4, 9-4-5, 9-4-6, 9-5-1, 9-5-2, 9-6-1, 9-6-4 or Materia Fusion by fusing a mastered Electrocute Materia with any of the following: Libra, Dash, Tri-Fire, Tri-Thundaga, Goblin Punch, Iron Fist, or Magical Punch. It can also be made by fusing a mastered Tri-Fire with a mastered Libra. ### Final Fantasy VIII Edit Non-elemental magic damage/one enemy —Description Flare is a powerful spell that inflicts major non-elemental damage on one opponent. It can only be drawn from some of the most powerful random encounter enemies and a few bosses, and can only be created using rare items. Flare is also a powerful junctioning magic, having one of the largest effects when junctioned to Str-J and Elem-Def-J. Casting Flare in battle increases compatibility with Eden by 0.4 and with Brothers, Diablos, Leviathan and Bahamut by 0.2. Casting Flare doesn't lower compatibility with any GF. Flare Draw from Level 1-100: Bahamut, Mobile Type 8, Omega Weapon, Sorceress, Tiamat, Ultimecia Level 30-100: Abadon, Diablos, Tri-Face Level 40-100: Behemoth Level 45-100: Ruby Dragon Draw points Esthar City Dr. Odine's lab (hidden, never refills), Ultimecia Castle Entrance (hidden, never refills), Island Closest to Heaven, Island Closest to Hell Refine F Mag-RF: Flare Stone x1 = Flare x1, Inferno Fang x1 = Flare x20 HP-J Str-J Vit-J Mag-J Spr-J Spd-J Eva-J Hit-J Luk-J +32 +0.56 +0.26 +0.44 +0.26 +0.12 +0.03 +0.26 +0.12 Elem-Atk-J Elem-Def-J ST-Atk-J ST-Def-J No effect Fire, Thunder, Ice: +0.8% No effect No effect Flare is cast in battle by Adel, Behemoth, Griever, Ruby Dragon, Seifer (fourth battle), Sorceress B, and Ultimecia's final form. ### Final Fantasy IX Edit Causes Non-elemental damage. —Description Flare is a Black Magic spell for Vivi that deals non-elemental damage, but cannot be toggled to target more than one foe. Vivi can learn the spell for 95 AP by equipping the Black Robe, and costs 40 MP to cast. It can be reflected and works with Return Magic. Additionally, Kuja, Garland, Trance Kuja and Ozma can all cast Flare. Thorn can cast a lesser version called Light Flare after being charged by Zorn. The spell has a power of 119 and is the strongest single-target spell Vivi can cast. It can also be used in Steiner's Sword Magic. #### Tetra Master Edit Tetra Master #059 Location: Treno, Card Stadium ### Final Fantasy X Edit Flare deals non-elemental damage on one target. It can be reflected. It is the final ability on Lulu's standard Sphere Grid path, and is near the end of Rikku's expert Sphere Grid path. The spell can be cast by Abaddon, Behemoth King, Black Element, Catoblepas, Coeurlregina, Dark Flan, Earth Eater, Greater Sphere, Jumbo Flan, Sleep Sprout, Mindy, Seymour Flux, Seymour Natus. It costs 54 MP to cast and has a spell power is 60. #### Final Fantasy X-2 Edit Flare is a Black Magic spell used by equipping either the Conflagration or Megiddo Garment Grids and spherechanging through the colored gates. The spell will then appear in the Black Magic skillset. It inflicts major non-elemental damage and costs 54 MP to cast. A similar attack called Flare Whirl is used by Yuna's Floral Fallal dressphere, and hits three times against random enemies. Flare can also be used via Yuna's Festivalist dressphere ability Flare Sandals, which hits two enemies. Flare can be used by many enemies. Quick Flare allows a character to cast Flare with reduced recovery time. Captured creatures can learn the ability by equipping the Garment Grid Tricks of the Trade. ### Final Fantasy XI Edit Flare is a Fire-elemental Ancient Magic spell for the Black Mage at level 60. It deals fire damage to an enemy and lowers its resistance against water. It takes 12 seconds to cast and can be recast every 60 seconds. It costs 315 MP to cast. ### Final Fantasy XII Edit Flare is the Black Magick 7 License for 70 LP, and it inflicts heavy non-elemental damage on a single target for 48 MP. In the PlayStation 2 versions, Flare has the maximum Effect Capacity, which means no other spell or Technick can be performed simultaneously. Flare costs 11,200 gil at Balfonheim Port after the events in Pharos. In the Zodiac versions, Flare is found in Pharos - Third Ascent. It requires the Black Magick 12 License for 120 LP and can be used by the Black Mage job. The Zodiac Age versions no longer have the Effect Capacity limitation. The spell Ghis casts at the party in the Dreadnought Leviathan in a cut scene appears to be Flare. #### Final Fantasy XII: Revenant Wings Edit Flare is Kytes's ultimate ability at Level 42 and inflicts massive non-elemental damage to one enemy. The Esper Chaos can use Flare as its ultimate ability. ### Lightning Returns: Final Fantasy XIII Edit Deals fire-based magic damage to all enemies. The less HP Lightning has, the more powerful this attack becomes. —Description Flare is a magic ability. Flare deals fire damage to all foes in range. It deals more damage the less HP Lightning has. At level 1, it has an ATB cost of 100, Attack x10.00, and Stagger Power of A. Flare Lv. 1 can be found in a treasure sphere at the Altar of Salvation, one of the four Trials in God's Sanctum (there is a rare chance to obtain the ability with an increased Attack value of x11.00. The game's internal random number generator affecting this probability can be reset by reloading a game that was saved prior to opening the treasure sphere). Flare is a rare drop included in Caius's loot table (Hard-Mode). Flare Lv. 3 is a Locked-Ability on the Astral Lord Garb. ### Final Fantasy XIV Edit Flare appeared as an ability in the original version and it dealt massive fire-elemental damage to the target and nearby enemies. At the initial release, Flare was a Conjurer spell available for use at Rank 44 and it cost 4 action points to set. After the release of patch 1.20, Flare became a high level fire-elemental spell for Black Mages, learned by completing the International Relations quest. Flare appears in the relaunch, as a Black Mage spell obtained after completing their level 50 job quest. It has a cast time of 4 seconds and consumes all of the user's remaining MP with a minimum MP cost of 266. When the spell is cast, it grants the Astral Fire III effect for 10 seconds and removes Umbral Ice. Red Mages can also learn a variation of Flare called Verflare at Lv. 68, first requiring the Combo chain of Enchanted Riposte, Enchanted Zwerchhau and Enchanted Redoublement to be executed. From there, the spell can be cast for 600 MP without a cast time required and fills the Black Magic gauge by 21 and a 20% chance of Verfire being available to cast. ### Final Fantasy XV Edit Flare is the ultimate fire elemancy spell and is capable of breaking the damage limit. It inflicts massive fire damage on all enemies. Flare is created by adding a catalyst that grants Limit Break while making a Fire-type spell. ### Final Fantasy Tactics Edit Black magick that converts energy into heat, scorching the battlefield with searing temperatures. —Description Inscript the dark god into a rotting body! Flare! —Upon casting (PlayStation) Flare is learned by the Black Mage for 900/1000 (WotL) JP, and is their ultimate spell. It costs 60 MP to cast and has a speed of 15. The Lucavi Zalera can cast an upgraded form called Flareja, and some high-level enemies can cast Giga Flare. ### Final Fantasy Tactics Advance Edit Sudden temperature spike. Deals damage. —Description Flare is learned by Alchemists from the Lotus Mace, which costs 300 AP to learn and inflicts extreme non-elemental damage to one enemy. It costs 36 MP to cast, has a Magic Power of 65, is stealable through the ability Steal: Ability, and is also susceptible to Return Magic and Absorb MP. The spell cannot be reflected. Sages possess an area version, Giga Flare, also learned from the Lotus Mace for 300 AP. There is also a Blue Magic called LV? S-Flare which is learned from Vampire, and deals Dark-elemental damage to all enemies of the same level. #### Final Fantasy Tactics A2: Grimoire of the Rift Edit Flare is learned by Alchemists by equipping the Lotus Mace. It costs 400 AP to master and costs 16 MP to use. ### Final Fantasy Tactics S Edit This article or section is a stub about an ability in Final Fantasy Tactics S. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Mystic Quest Edit Flare is a Wizard spell, and the strongest spell. It does heavy Fire-elemental damage to one or more enemies. It can be repelled. Only Benjamin can cast the spell. It is found inside Pazuzu's Tower. ### Final Fantasy Adventure Edit The Nuke spell is the most destructive force. It can only travel in a straight line. It is obtained by defeating Lich in the Sealed Cave, and cost 3 MP to cast. This spell is needed to gain access to the Cave of Ruins due to a crystal in the desert blocking the entrance. Nuke is also an enemy ability used by Julius in his first and third forms, taking the form of a projectile that is shot in all eight directions. ### The Final Fantasy Legend Edit Flare is an ability that has 3 uses and has an attack power of 8 which damages all enemies, the damage formula is base on Mana. This ability is used by Lich, Athtalot, Ashura and the Creator. Flare appears as a Magic book with a book icon before its name. It cast Flare, and can be bought in Hidden Town for 50,000 GP. It only has 20 uses and an attack power of 10, the damage formula for Flare is base on Mana. Deals non-elemental damage to all enemies. ### Final Fantasy Legend II Edit Flare is a magical attack that has 5 uses, it also increases a Robot's HP by 9 (though it cannot be equipped to them). The damage formula for Flare is the user's Mana x10 while Apollo's Flare is Mana x8. The ability target's all enemies. This attack can be used by Athtalot, Haniwa, Lich, Titania, and Apollo. A Magic Book called Flare appears with a book icon before its name. It cast Flare, and can be bought in Final Town for 50000 GP or found in chests. It only has 10 uses, and also increases a Robot's HP by 144 when equipped on them. The damage formula for Flare is the user's Mana x13, deals non-elemental damage to all enemies. ### Final Fantasy Legend III Edit Flare, a Lost Magic spell, is the strongest magic spell. It costs 56 MP to use, and it can be made by combining two Fire elemental stones from Shar aboard the Talon. Because there are only four Fire elemental stones, it is only possible to have two copies of Flare, at the expense of several weaker Lost spells. Nuke is a separate spell entirely. While much weaker than Flare, it is the strongest Black Magic spell. It costs 36 MP to use, and it can be bought for 25000 GP in Dwelg Town (Underworld). ### Final Fantasy: The 4 Heroes of Light Edit The legendary Flare Tome is mentioned by a scientist at Guera Palace, but it does not appear as a usable spell or enemy ability. ### Bravely Default Edit Flare is an enemy ability that deals high magical fire damage to the entire party. It is used by Airy (second form). Zeta Flare is an enemy ability that deals very high magical fire damage to the party. It is used by Airy (third form). #### Bravely Second: End Layer Edit Flare is a level 7 Black Magic for the Black Mage. It deals major fire damage to all targets and can be group-cast. It costs 80 MP to use. It can be bought at Vampire Castle for 12800 pg. ### Final Fantasy Dimensions Edit Flare is a level 8 Black Magic learned by Level 1 Magus (Warriors of Darkness). ### Final Fantasy Dimensions II Edit This article or section is a stub about an ability in Final Fantasy Dimensions II. You can help the Final Fantasy Wiki by expanding it. ### Dissidia Final Fantasy Edit Scorch!... Detonate! —Onion Knight using Flare Onion Knight has Flare as an HP attack chained from Thunder. As a Mime, Bartz is able to use Onion Knight's version of Flare, but his version is chained from Holy. Their versions of Flare summon streams of fire to bombard enemies from three directions. Onion Knight's Flare costs 40 CP to equip and 300 AP to master, while Bartz's Flare costs 45 CP to equip and 180 AP to master. Terra can cast Flare as a part of Holy Combo. After landing a hit with Holy Combo, Terra shoots several fireballs at the opponent. This can chain further into Ultima. How's that? —Kuja using Remote Flare Kuja has a variation called Remote Flare, which summons several small explosive fireballs to surround opponents. It costs 30 CP to equip and 180 AP to master. Kuja also uses Flare in many of his Bravery attacks, and his Flare Star HP attack. Run amok! —Emperor using Flare The Emperor has two versions of Flare as HP attacks, one which fires a blue fireball that moves slowly and tracks enemies, and another which fires an orange fireball that stays in place. Both versions cost 40 CP to equip and 180 AP to master. Shantotto's Spirit Magic: Fire casts Flare when she has over 6000 Bravery, launching a barrage of smaller fireballs towards her opponent, culminating in a massive explosion. #### Dissidia 012 Final Fantasy Edit Unleash the fury! Crumble! —Garland using Flare Garland has Flare as an HP attack. He enchants his sword with fire and attacks the opponent with two overhead slam attacks. Shantotto's Spirit Magic: Fire now casts Flare when she has over 4000 Bravery. Onion Knight's Flare now costs 30 CP to equip and 160 AP to master. Terra's Flare now has Ranged Mid Damage Priority, causing it to stagger blocking opponents. Kuja's Remote Flare costs 100 AP to master now. Both versions of the Emperor's Flare now cost 30 CP to equip and 130 AP to master, and his aerial Flare inflicts downwards Wall Rush. Bartz's Flare is unchanged. #### Dissidia Final Fantasy NT Edit Several characters retain the use of Flare in their movesets, though they have been changed significantly. Garland's Flare launches a fireball from his sword. Emperor's Flares, renamed Blue Soul and Red Soul are Bravery attacks and both follow the target. Terra's Flare comes in two variations depending on whether or not she is in a charged state. Shantotto also gains the spell as a Bravery attack, though it turns into a rapid fire Fire spell in her enranged state This article or section is a stub about an ability in Dissidia Final Fantasy NT. You can help the Final Fantasy Wiki by expanding it. #### Dissidia Final Fantasy Opera Omnia Edit This article or section is a stub about an ability in Dissidia Final Fantasy Opera Omnia. You can help the Final Fantasy Wiki by expanding it. ### Pictlogica Final Fantasy Edit This article or section is a stub about a spell in Pictlogica Final Fantasy. You can help the Final Fantasy Wiki by expanding it. #### Pictlogica Final Fantasy ≒ Edit This article or section is a stub about an ability in Pictlogica Final Fantasy ≒. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Airborne Brigade Edit This article or section is a stub about a spell in Final Fantasy Airborne Brigade. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy All the Bravest Edit Flare Thundaga is the ability that is used by Magus during battle. It is also an enemy ability that is used by Exdeath and Lich during battle. ### Final Fantasy Record Keeper Edit Flare is a Black Magic ability with a Rarity of 5☆. It deals massive non-elemental magic damage to one target, it can initially be used two times and it can be honed to Rank 5. It can be created by using Major Black Orb x10, Major Non-Elemental Orb x6, Major Fire Orb x6, and 50000 gil. This article or section is a stub about an ability in Final Fantasy Record Keeper. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Explorers Edit Concentrate a spectrum of forces in front of you to trigger a massive blast. —Description This article or section is a stub about a spell in Final Fantasy Explorers. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Brave Exvius Edit Flare is a level 7 black magic spell that cost 35 MP to cast. It causes fire damage on a single foe and reduces the target's water resistance. This ability can be obtained by Kuja as his Trust Master Reward. Four other characters, including Emperor from Final Fantasy II and Terra from Final Fantasy VI, learn the ability on their own. ### World of Final Fantasy Edit Flare is an active magic ability that inflicts neutral magical damage on a single target for 9 AP. It can be used by Bahamut★ and Lich. It is also an enemy ability used by Brandelis, Exnine Bahamut (1st), and Enna Kros. ### Chocobo's Dungeon 2 Edit This article or section is a stub about a spell in Chocobo's Dungeon 2. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Fables: Chocobo's Dungeon Edit Flare is a Lv. 7 spell that cost 5 SP to cast and attacks all enemies in a 7x7 grid around Chocobo. ### Final Fantasy Trading Card Game Edit One of Lulu's cards has the Flare ability. Flare costs one Thunder CP, the discard of a Lulu card, and the player must Dull Lulu. Flare deals 8000 damage to a Forward of the player's choice. ## Non-Final Fantasy appearances Edit ### Chrono Trigger Edit Flare is the final tech that Lucca learns and is her most powerful attack. It deals severe Fire-elemental damage to all targets at a cost of 20 MP. ### Ehrgeiz: God Bless the Ring Edit Flare Materia. —Description Flare is a magic spell within the Forsaken Dungeon. The Basic Magic version surrounds the user with a ring of fire and consume one Magic Stone when used. The Ultra Magic version encases the user's body in fire and damages enemies upon contact with the user's body, it consumes three Magic Stones when used. ### Heavenstrike Rivals Edit Flare is Julius and Demon Form Julius's ability. At the start of the player turn, deal 2-6 damage split between random enemy units. ### Kingdom Hearts Edit In Kingdom Hearts III, Flare Force is a team attack where Donald and Sora launch fireworks at enemies. In a cutscene during the climax, Donald uses Zettaflare in an attempt to defeat Terra-Xehanort but falls unconscious afterward. ### Tekken 7Edit Noctis can use Flare as one of his attacks. Within the Move List option, this attack is called "Flare Drive". ## Gallery Edit This gallery is incomplete and requires Flare III cast on one enemy in Final Fantasy II (iOS), Flare III cast on all enemies in Final Fantasy II (iOS), Flare VI cast on one enemy in Final Fantasy II (iOS), Flare VI cast on all enemies in Final Fantasy II (iOS), Flare X cast on one enemy in Final Fantasy II (iOS), Flare X cast on all enemies in Final Fantasy II (iOS), Flare XVI cast on one enemy in Final Fantasy II (iOS), The Final Fantasy Legend and Final Fantasy: The 4 Heroes of Light added. You can help the Final Fantasy Wiki by uploading images. ## Etymology Edit A flare is a pyrotechnical phenomenon that produces intense amounts of heat and energy that does not result in an explosion (an immediate release of energy). In the case of Final Fantasy, while this may seem weaker than an explosion, a flare is a contained release of energy, which fully exposes the enemy to the source rather than blow them away from it after a while. ## References Edit Community content is available under CC-BY-SA unless otherwise noted.	2019-07-18T07:01:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21902859210968018, "perplexity": 11167.172071007326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525524.12/warc/CC-MAIN-20190718063305-20190718085305-00422.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=B037W1&home=sumtabB	#### PRODUCTION EXPERIMENTS VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT $\bf{ 50.5 \pm2.0}$ OUR AVERAGE $62$ $\pm10$ 2013 SPEC ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit \Lambda}{(1405)}}{{\mathit K}^{+}}$ $50$ $\pm2$ 1 1991 M-matrix fit • • We do not use the following data for averages, fits, limits, etc. • • $24$ ${}^{+4}_{-3}$ 2010 RVUE ${}^{4}\mathrm {He}$ ${{\mathit K}^{-}}$ $\rightarrow$ ${{\mathit \Sigma}^{\pm}}{{\mathit \pi}^{\mp}}{{\mathit X}}$ at rest $32$ $\pm1$ 700 1 1985 HBC ${{\mathit K}^{-}}{{\mathit p}}$ 4.2 ${\mathrm {GeV/}}\mathit c$ $45\text{ to }55$ 400 2 1973 HBC ${{\mathit \pi}^{-}}{{\mathit p}}$ 1.69 ${\mathrm {GeV/}}\mathit c$ $35$ 120 1968 B DBC ${{\mathit K}^{-}}{{\mathit d}}$ 2.1$-$2.7 ${\mathrm {GeV/}}\mathit c$ $50$ $\pm10$ 67 1966 HBC ${{\mathit K}^{-}}{{\mathit p}}$ 3.5 ${\mathrm {GeV/}}\mathit c$ $89$ $\pm20$ 1965 HDBC $60$ $\pm20$ 1965 HBC $35$ $\pm5$ 1962 HBC $50$ 1962 HBC $20$ 1961 B HBC 1 DALITZ 1991 fits the HEMINGWAY 1985 data. 2 THOMAS 1973 data is fit by CHAO 1973 (see next section). References: HASSANVAND 2013 PR C87 055202 Theoretical Analysis of ${{\mathit \Lambda}{(1405)}}$ $\rightarrow$ (${{\mathit \Sigma}}{{\mathit \pi}}$ )${}^{0}$ Mass Spectra Produced in ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit \Lambda}{(1405)}}{{\mathit K}^{+}}$ Reactions Also PR C88 019905 (errat.) Addendum to HASSANVAND 2013 : Theoretical Analysis of ${{\mathit \Lambda}{(1405)}}$ $\rightarrow$ ( ${{\mathit \Sigma}}{{\mathit \pi}}$ ) ${}^{0}$ Mass Spectra Produced in ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}$ ${{\mathit \Lambda}{(1405)}}$ ${{\mathit K}^{+}}$ Reactions ESMAILI 2010 PL B686 23 Experimental Confirmation of the ${{\mathit \Lambda}{(1405)}}$ Ansatz from Resonant Formation of a ${{\mathit K}^{-}}{{\mathit p}}$ Quasi-Bound State in ${{\mathit K}^{-}}$ Absorption by ${}^{3}\mathrm {He}$ and ${}^{4}\mathrm {He}$ DALITZ 1991 JP G17 289 The Shape and Parameters of the ${{\mathit \Lambda}{(1405)}}$ Resonance HEMINGWAY 1985 NP B253 742 Production of ${{\mathit \Lambda}{(1405)}}$ in ${{\mathit K}^{-}}$ ${{\mathit p}}$ Reactions at 4.2 ${\mathrm {GeV/}}\mathit c$ THOMAS 1973 NP B56 15 Strange Particle Production from ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ Interactions at 1.69 ${\mathrm {GeV/}}\mathit c$ BARBARO-GALTIERI 1968B PRL 21 573 Search for $\mathit I = 2$ Hyperons and Study of Resonances in ${{\mathit K}^{-}}{{\mathit d}}$ Interactions BIRMINGHAM 1966 PR 152 1148 Reactions ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ Hyperon Meson at 3.5 ${\mathrm {GeV/}}\mathit c$ ENGLER 1965 PRL 15 224 Spin of the ${{\mathit Y}_{{0}}^{*}{(1405)}}$ MUSGRAVE 1965 NC 35 735 Study of ${{\mathit Y}}$ ${{\overline{\mathit Y}}}$ Production in Two, Three, and Four Body Final States by 3.0, 3.6 and 4.0 ${\mathrm {GeV/}}\mathit c$ Antiprotons in Hydrogen ALEXANDER 1962 PRL 8 447 Production of Strange Particle Resonant States by 2.1 ${\mathrm {GeV/}}\mathit c$ ${{\mathit \pi}^{-}}$ Mesons ALSTON 1962 CERN Conf. 311 Study of Resonances in the ${{\mathit \Sigma}}$ ${{\mathit \pi}}$ System ALSTON 1961B PRL 6 698 Study of Resonances in the ${{\mathit \Sigma}}$ ${{\mathit \pi}}$ System	2023-04-01T02:03:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6376610994338989, "perplexity": 6814.455675265464}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00191.warc.gz"}
http://www.p2psp.org/en/p2psp-protocol?cap=indexsu11.html	## P2PSP (Peer-to-Peer “Straightforward” Protocol) #### 4.11 The Content Integrity Set of rules The CIS (Content Integrity Set of rules) is responsible for ﬁghting against a DoS (Denial of Service) attacks by stream spoiling (also known as pollution attacks). This action could be carried out by possible custom implementations of peers that might to poison A poisoned chunk is a chunk that seems to be OK, but which the sender has changed in such a way that when played, introduces no information (for example, a chunk ﬁlled with zeroes) or even wrong information. (by altering willfully) the content of the stream. This set of rules could be also useful in those situations where the transmission links are error-prone and the error detection mechanism of the underlaying transport protocol has been disabled. In the CIS is proposed use a hash of the content of Chunks to discover a attacker peer. The rules are: 1. One or more peers of the team are selected as trusted peers so that only the splitter knows of its existence through of endpoint of each them. It’s possible that all peers in the team are trusted-peers except the attacker. 2. The trusted peers create a hash (ﬁngerprint) for a number of received chunks (included the chunk number) plus an other hash of the endpoint from where each chunk has been received. Depending on the computational power available in the trusted peer host, all or a subset (can be random) of chunks are processed. 3. The hashes (both chunks and endpoints) are sent to the splitter, which checks if the received chunks have been altered (calculate the hash is necessary). 4. The splitter knows what chunk has been sent to each peer. Therefore if the splitter receives a hash that does not match the one he has calculated can deduce that one of the chunks was altered and depending on the number of corresponding chunk is able to determine to which peer was sent the altered chunk (note that all chunks follow the following process: the chunk ﬁrst travels from the splitter to a peer which sends it to all other peers of the team). 5. When the number of altered/peer exceeds a treshold, the peer is rejected of the team. This is achieved not sending more chunks to the attacker(s) peer(s). Moreover the splitter sends a reject message that contain the endpoint of the attacker to all peers of the team, this ensures that the attacker is removed from the peers list of all peers of the team as soon as possible. ##### 4.11.1 A model of the impact of an attack This mathematical model estimates the averages of poisoned chunks $X$ into a team depending of number of trusted peers $T$, the numer of attackers peers $A$ concurrently in a team and the $P$ number of total peers (attackers or not) in the team. In addition, the model estimates the number of poisoned chunks that arrives to any peer, always in average values. As noted in the begin of this section, the identity of the trusted peers is unknow for all except for the splitter. Moreover, the behavior of the attackers will be poison the maximun number of chunks. Note, however, that any intermediate selective situation with the chunks poisoned can be consider similar to this one (are poisoned all possible chunks) where the attackers number is lower. Suppose initially that $T=1$ (only exist one trusted peer in the team). In the more favorable situation (and unlikely) for an attacker, this could reach up to $P-1$ chunks if in the retransmission cycle the last chunk is sent to the only one trusted peer. Moreover, It may also happen that the ﬁrst poisoned chunk sent by an attacker arrives to an only one trusted peer. In this case, only one chunk is poisoned. As the position of the peers is random, the average number of poisoned chunks when $A=1$ and $T=1$ is $X=\frac{P-1+1}{2}=\frac{P}{2}$ (10) Suppose that exist more of one trusted peer ($T>1$ and $A=1$). As now the probability of deliver a poisoned chunk to a trusted peer increment proportionality with $T$, the average number of poisoned chunks would be $T$ times lower, i.e., the average number of poisoned chunks would be $X=\frac{P}{2T}$ (11) Finally, if there is more of one attacker ($T>1$ and $A>1$), that amount would be multiplied by $A$ (suppose that the $A$ attackers poisons the chunks in parallel), getting $X=\frac{AP}{2T}$ (12) From this expression can be derived two hypotheses. The ﬁrst one, that the impact of an attack depends of the ratio between number of attackers and trusted peers ( expected behavior ). And second, that when $A$ and $T$ are of the same order the average poisoned chunks tend to be $P∕2$ In the case of exist also normal peers, clearly $X$ will increase. For example, if there is a friendly peer too, $X$ will increase in a poisoned chunk per each concurrently attacker in the team. Therefore, it’s determined that $X=\frac{AP}{2T}+\left(P-A-T\right)$ (13) As seen, the latter term does not signiﬁcantly aﬀect the average number of poisoned chunks, unless the team is very large, in which case, the attack is diluted because never the number of received chunks for each peer in the same retransmission cycle can be bigger than $A$. P2PSP (Peer-to-Peer Straightforward Protocol) by Cristobal Medina-López, J. A. M. Naranjo, L. G. Casado and Vicente González-Ruiz is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.	2017-06-22T20:43:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 26, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4411378800868988, "perplexity": 1609.0248137465326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128319902.52/warc/CC-MAIN-20170622201826-20170622221826-00165.warc.gz"}
https://par.nsf.gov/biblio/10338781-portrait-higgs-boson-cms-experiment-ten-years-after-discovery	This content will become publicly available on July 7, 2023 A portrait of the Higgs boson by the CMS experiment ten years after the discovery Abstract In July 2012, the ATLAS and CMS collaborations at the CERN Large Hadron Collider announced the observation of a Higgs boson at a mass of around 125 gigaelectronvolts. Ten years later, and with the data corresponding to the production of a 30-times larger number of Higgs bosons, we have learnt much more about the properties of the Higgs boson. The CMS experiment has observed the Higgs boson in numerous fermionic and bosonic decay channels, established its spin–parity quantum numbers, determined its mass and measured its production cross-sections in various modes. Here the CMS Collaboration reports the most up-to-date combination of results on the properties of the Higgs boson, including the most stringent limit on the cross-section for the production of a pair of Higgs bosons, on the basis of data from proton–proton collisions at a centre-of-mass energy of 13 teraelectronvolts. Within the uncertainties, all these observations are compatible with the predictions of the standard model of elementary particle physics. Much evidence points to the fact that the standard model is a low-energy approximation of a more comprehensive theory. Several of the standard model issues originate in the sector of Higgs boson physics. An order of magnitude larger number of Higgs bosons, expected more » Authors: Award ID(s): Publication Date: NSF-PAR ID: 10338781 Journal Name: Nature Volume: 607 Issue: 7917 Page Range or eLocation-ID: 60 to 68 ISSN: 0028-0836 1. A bstract A search for nonresonant production of Higgs boson pairs via gluon-gluon and vector boson fusion processes in final states with two bottom quarks and two photons is presented. The search uses data from proton-proton collisions at a center-of-mass energy of $$\sqrt{s}$$ s = 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb − 1 . No significant deviation from the background-only hypothesis is observed. An upper limit at 95% confidence level is set on the product of the Higgs boson pair production cross section and branching fraction into $$\gamma \gamma \mathrm{b}\overline{\mathrm{b}}$$ γγ b b ¯ . The observed (expected) upper limit is determined to be 0.67 (0 . 45) fb, which corresponds to 7.7 (5.2) times the standard model prediction. This search has the highest sensitivity to Higgs boson pair production to date. Assuming all other Higgs boson couplings are equal to their values in the standard model, the observed coupling modifiers of the trilinear Higgs boson self-coupling κ λ and the coupling between a pair of Higgs bosons and a pair of vector bosons c 2V are constrained within the ranges − 3 .more » 2. Abstract The rate for Higgs ( $${\mathrm{H}}$$ H ) bosons production in association with either one ( $${\mathrm{t}} {\mathrm{H}}$$ t H ) or two ( $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}}$$ t t ¯ H ) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of $$13\,\text {TeV}$$ 13 TeV by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137 $$\,\text {fb}^{-1}$$ fb - 1 . The analysis is aimed at events that contain $${\mathrm{H}} \rightarrow {\mathrm{W}} {\mathrm{W}}$$ H → W W , $${\mathrm{H}} \rightarrow {\uptau } {\uptau }$$ H → τ τ , or $${\mathrm{H}} \rightarrow {\mathrm{Z}} {\mathrm{Z}}$$ H → Z Z decays and each of the top quark(s) decays either to lepton+jets or all-jet channels. Sensitivity to signal is maximized by including ten signatures in the analysis, depending on the lepton multiplicity. The separation among $${\mathrm{t}} {\mathrm{H}}$$ t H , $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}}$$ t t ¯ H , and the backgrounds is enhanced through machine-learning techniques and matrix-element methods. The measured production rates for the $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}}$$more » 3. A bstract A search for standard model Higgs bosons (H) produced with transverse momentum ( p T ) greater than 450 GeV and decaying to bottom quark-antiquark pairs ( $$\mathrm{b}\overline{\mathrm{b}}$$ b b ¯ ) is performed using proton-proton collision data collected by the CMS experiment at the LHC at $$\sqrt{s}$$ s = 13 TeV. The data sample corresponds to an integrated luminosity of 137 fb − 1 . The search is inclusive in the Higgs boson production mode. Highly Lorentz-boosted Higgs bosons decaying to $$\mathrm{b}\overline{\mathrm{b}}$$ b b ¯ are reconstructed as single large-radius jets, and are identified using jet substructure and a dedicated b tagging technique based on a deep neural network. The method is validated with Z → $$\mathrm{b}\overline{\mathrm{b}}$$ b b ¯ decays. For a Higgs boson mass of 125 GeV, an excess of events above the background assuming no Higgs boson production is observed with a local significance of 2.5 standard deviations ( σ ), while the expectation is 0.7. The corresponding signal strength and local significance with respect to the standard model expectation are μ H = 3 . 7 ± 1 . 2(stat) $${}_{-0.7}^{+0.8}$$ − 0.7more » 5. A bstract A search for a light pseudoscalar Higgs boson (a) decaying from the 125 GeV (or a heavier) scalar Higgs boson (H) is performed using the 2016 LHC proton-proton collision data at $$\sqrt{s}$$ s = 13 TeV, corresponding to an integrated luminosity of 35 . 9 fb − 1 , collected by the CMS experiment. The analysis considers gluon fusion and vector boson fusion production of the H, followed by the decay H → aa → μμττ , and considers pseudoscalar masses in the range 3 . 6 < m a < 21 GeV. Because of the large mass difference between the H and the a bosons and the small masses of the a boson decay products, both the μμ and the ττ pairs have high Lorentz boost and are collimated. The ττ reconstruction efficiency is increased by modifying the standard technique for hadronic τ lepton decay reconstruction to account for a nearby muon. No significant signal is observed. Model-independent limits are set at 95% confidence level, as a function of m a , on the branching fraction (ℬ) for H → aa → μμττ , down to 1 . 5 (2 . 0) × 10 −more »	2022-10-03T04:43:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8368914127349854, "perplexity": 831.8724527978721}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337398.52/warc/CC-MAIN-20221003035124-20221003065124-00088.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S077A00	# Limits on $\vert {{\boldsymbol U}}_{ {{\boldsymbol e}} {{\boldsymbol x}} }\vert ^2$ INSPIRE search Quoted limits are either the best limit near the kinematic threshold of the experiment, or a characteristic value in the mass range of the experimental sensitivity VALUE CL% DOCUMENT ID TECN COMMENT $<2 \times 10^{-5}$ 95 1 2019 F ATLS ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $15 - 40$ GeV $<1 \times 10^{-9}$ 90 2 2019 B T2K Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres. $<1 \times 10^{-4}$ 90 3 2019 AL BES3 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.3 - 0.7$ GeV $<1 \times 10^{-8}$ 90 4 2018 A PIEN ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $60 - 120$ MeV $<3 \times 10^{-7}$ 90 5 2018 NA62 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $200 - 400$ MeV $<3 \times 10^{-5}$ 95 6 1997 I DLPH ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $6 - 50$ GeV $<2 \times 10^{-5}$ 95 7 1997 I DLPH Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 3.5 GeV $<1 \times 10^{-5}$ 90 8 1993 Near ${\mathit m}_{{{\mathit \pi}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres. $<2 \times 10^{-7}$ 90 8 1993 Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres. $<1 \times 10^{-7}$ 9, 10 1988 CNTR Near ${\mathit m}_{{{\mathit \pi}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres. $<2 \times 10^{-9}$ 11, 10 1988 CNTR Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres. $<1 \times 10^{-7}$ 90 12 1986 CHRM Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres. $<1 \times 10^{-7}$ 90 13 1985 BEBC Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres. • • • We do not use the following data for averages, fits, limits, etc. • • • 14 2016 BELL ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.2 - 1.4$ GeV 1 Limit from prompt lepton number violating trilepton search. 2 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}_{ {{\mathit e}} {{\mathit x}} }$. ABE 2019B also considers bounds on $\vert {{\mathit U}}_{ {{\mathit \ell}} {{\mathit x}} }{{\mathit U}}_{ {{\mathit \ell}^{\,'}} {{\mathit x}} }\vert$ for combinations of lepton flavors in the ${{\mathit \nu}_{{x}}}$ decay final state. 3 Searches for a Majorana Heavy Neutral Lepton producing a ${{\mathit \pi}^{-}}{{\mathit e}^{+}}$ resonance in the same sign dilepton decay ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{+}}$ . 4 Search for ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ . 5 Search for ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ . 6 Search for prompt ${{\mathit \nu}_{{x}}}$ decay signatures. 7 Search for displaced ${{\mathit \nu}_{{x}}}$ decay signatures. 8 Searches for ${{\mathit K}}$ or ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \nu}_{{e}}}$ using a beam dump experiment at the 70 GeV Serpukhov proton synchrotron. BARANOV 1993 also considers limits for $\vert {{\mathit U}}_{ {{\mathit e}} {{\mathit x}} }{{\mathit U}}_{ {{\mathit \mu}} {{\mathit x}} }\vert$ from ${{\mathit K}}$ or ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \nu}_{{e}}}$ . 9 ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}_{ {{\mathit e}} {{\mathit x}} }$. 10 BERNARDI 1988 also considers bounds on $\vert {{\mathit U}}_{ {{\mathit e}} {{\mathit x}} }{{\mathit U}}_{ {{\mathit \mu}} {{\mathit x}} }\vert$. 11 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}_{ {{\mathit e}} {{\mathit x}} }$. 12 ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ . 13 ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ or ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit \pi}^{+}}$ . 14 PARK 2016 quotes an approximate limit B( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ ) $<$ $3 \times 10^{-6}$ in the mass range ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.2 - 1.4$ GeV. References: JHEP 1910 265 Search for heavy neutral leptons in decays of $W$ bosons produced in 13 TeV $pp$ collisions using prompt and displaced signatures with the ATLAS detector ABE 2019B PR D100 052006 Search for heavy neutrinos with the T2K near detector ND280 ABLIKIM 2019AL PR D99 112002 Search for heavy Majorana neutrino in lepton number violating decays of $D\to K \pi e^+ e^+$ AGUILAR-AREVALO 2018A PR D97 072012 Improved search for heavy neutrinos in the decay $\pi\rightarrow e\nu$ CORTINA-GIL 2018 PL B778 137 Search for heavy neutral lepton production in $K^+$ decays PARK 2016 PR D94 012003 Search for a Massive Invisible Particle ${{\mathit X}^{0}}$ in ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ and ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit X}^{0}}$ Decays ABREU 1997I ZPHY C74 57 Search for Neutral Heavy Leptons Produced in ${{\mathit Z}}$ Decays BARANOV 1993 PL B302 336 Search for Heavy Neutrinos at the IHEP-JINR Neutrino Detector BERNARDI 1988 PL B203 332 Further Limit on Heavy Neutrino Coupling DORENBOSCH 1986 PL 166B 473 A Search for Decays of Heavy Neutrinos in the Mass Range of 0.5 $−$ 2.8 GeV COOPER-SARKAR 1985 PL 160B 207 Search for Heavy Neutrino Decays in the BEBC Beam Dump Experiment	2021-04-17T12:12:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9355011582374573, "perplexity": 4858.473365300308}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038119532.50/warc/CC-MAIN-20210417102129-20210417132129-00207.warc.gz"}
http://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Spectrum_of_a_ring	# Spectrum of a ring In algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by ${\displaystyle \operatorname {Spec} (R)}$, is the set of all prime ideals of R. It is commonly augmented with the Zariski topology and with a structure sheaf, turning it into a locally ringed space. A locally ringed space of this form is called an affine scheme. ## Zariski topology For any ideal I of R, define ${\displaystyle V_{I}}$ to be the set of prime ideals containing I. We can put a topology on ${\displaystyle \operatorname {Spec} (R)}$ by defining the collection of closed sets to be ${\displaystyle \{V_{I}\colon I{\text{ is an ideal of }}R\}.}$ This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For fR, define Df to be the set of prime ideals of R not containing f. Then each Df is an open subset of ${\displaystyle \operatorname {Spec} (R)}$, and ${\displaystyle \{D_{f}:f\in R\}}$ is a basis for the Zariski topology. ${\displaystyle \operatorname {Spec} (R)}$ is a compact space, but almost never Hausdorff: in fact, the maximal ideals in R are precisely the closed points in this topology. By the same reasoning, it is not, in general, a T1 space.[1] However, ${\displaystyle \operatorname {Spec} (R)}$ is always a Kolmogorov space (satisfies the T0 axiom); it is also a spectral space. ## Sheaves and schemes Given the space ${\displaystyle X=\operatorname {Spec} (R)}$ with the Zariski topology, the structure sheaf OX is defined on the distinguished open subsets Df by setting Γ(Df, OX) = Rf, the localization of R by the powers of f. It can be shown that this defines a B-sheaf and therefore that it defines a sheaf. In more detail, the distinguished open subsets are a basis of the Zariski topology, so for an arbitrary open set U, written as the union of {Dfi}iI, we set Γ(U,OX) = limiI Rfi. One may check that this presheaf is a sheaf, so ${\displaystyle \operatorname {Spec} (R)}$ is a ringed space. Any ringed space isomorphic to one of this form is called an affine scheme. General schemes are obtained by gluing affine schemes together. Similarly, for a module M over the ring R, we may define a sheaf ${\displaystyle {\tilde {M}}}$ on ${\displaystyle \operatorname {Spec} (R)}$. On the distinguished open subsets set Γ(Df, ${\displaystyle {\tilde {M}}}$) = Mf, using the localization of a module. As above, this construction extends to a presheaf on all open subsets of ${\displaystyle \operatorname {Spec} (R)}$ and satisfies gluing axioms. A sheaf of this form is called a quasicoherent sheaf. If P is a point in ${\displaystyle \operatorname {Spec} (R)}$, that is, a prime ideal, then the stalk of the structure sheaf at P equals the localization of R at the ideal P, and this is a local ring. Consequently, ${\displaystyle \operatorname {Spec} (R)}$ is a locally ringed space. If R is an integral domain, with field of fractions K, then we can describe the ring Γ(U,OX) more concretely as follows. We say that an element f in K is regular at a point P in X if it can be represented as a fraction f = a/b with b not in P. Note that this agrees with the notion of a regular function in algebraic geometry. Using this definition, we can describe Γ(U,OX) as precisely the set of elements of K which are regular at every point P in U. ## Functorial perspective It is useful to use the language of category theory and observe that ${\displaystyle \operatorname {Spec} }$ is a functor. Every ring homomorphism ${\displaystyle f:R\to S}$ induces a continuous map ${\displaystyle \operatorname {Spec} (f):\operatorname {Spec} (S)\to \operatorname {Spec} (R)}$ (since the preimage of any prime ideal in ${\displaystyle S}$ is a prime ideal in ${\displaystyle R}$). In this way, ${\displaystyle \operatorname {Spec} }$ can be seen as a contravariant functor from the category of commutative rings to the category of topological spaces. Moreover, for every prime ${\displaystyle {\mathfrak {p}}}$ the homomorphism ${\displaystyle f}$ descends to homomorphisms ${\displaystyle {\mathcal {O}}_{f^{-1}({\mathfrak {p}})}\to {\mathcal {O}}_{\mathfrak {p}}}$ of local rings. Thus ${\displaystyle \operatorname {Spec} }$ even defines a contravariant functor from the category of commutative rings to the category of locally ringed spaces. In fact it is the universal such functor hence can be used to define the functor ${\displaystyle \operatorname {Spec} }$ up to natural isomorphism. The functor ${\displaystyle \operatorname {Spec} }$ yields a contravariant equivalence between the category of commutative rings and the category of affine schemes; each of these categories is often thought of as the opposite category of the other. ## Motivation from algebraic geometry Following on from the example, in algebraic geometry one studies algebraic sets, i.e. subsets of Kn (where K is an algebraically closed field) that are defined as the common zeros of a set of polynomials in n variables. If A is such an algebraic set, one considers the commutative ring R of all polynomial functions AK. The maximal ideals of R correspond to the points of A (because K is algebraically closed), and the prime ideals of R correspond to the subvarieties of A (an algebraic set is called irreducible or a variety if it cannot be written as the union of two proper algebraic subsets). The spectrum of R therefore consists of the points of A together with elements for all subvarieties of A. The points of A are closed in the spectrum, while the elements corresponding to subvarieties have a closure consisting of all their points and subvarieties. If one only considers the points of A, i.e. the maximal ideals in R, then the Zariski topology defined above coincides with the Zariski topology defined on algebraic sets (which has precisely the algebraic subsets as closed sets). Specifically, the maximal ideals in R, i.e. ${\displaystyle \operatorname {MaxSpec} (R)}$, together with the Zariski topology, is homeomorphic to A also with the Zariski topology. One can thus view the topological space ${\displaystyle \operatorname {Spec} (R)}$ as an "enrichment" of the topological space A (with Zariski topology): for every subvariety of A, one additional non-closed point has been introduced, and this point "keeps track" of the corresponding subvariety. One thinks of this point as the generic point for the subvariety. Furthermore, the sheaf on ${\displaystyle \operatorname {Spec} (R)}$ and the sheaf of polynomial functions on A are essentially identical. By studying spectra of polynomial rings instead of algebraic sets with Zariski topology, one can generalize the concepts of algebraic geometry to non-algebraically closed fields and beyond, eventually arriving at the language of schemes. ## Examples • The affine scheme ${\displaystyle \operatorname {Spec} (\mathbb {Z} )}$ is the final object in the category of affine schemes since ${\displaystyle \mathbb {Z} }$ is the initial object in the category of commutative rings. • The affine scheme ${\displaystyle \mathbb {A} _{\mathbb {C} }^{n}=\operatorname {Spec} (\mathbb {C} [x_{1},\ldots ,x_{n}])}$ is scheme theoretic analogue of ${\displaystyle \mathbb {C} ^{n}}$. From the functor of points perspective, a point ${\displaystyle (\alpha _{1},\ldots ,\alpha _{n})\in \mathbb {C} ^{n}}$ can be identified with the evaluation morphism ${\displaystyle \mathbb {C} [x_{1},\ldots ,x_{n}]{\xrightarrow {ev_{(\alpha _{1},\ldots ,\alpha _{n})}}}\mathbb {C} }$. This fundamental observation allows us to give meaning to other affine schemes. • ${\displaystyle \operatorname {Spec} (\mathbb {C} [x,y]/(xy))}$ looks topologically like the transverse intersection of two complex planes at a point, although typically this is depicted as a ${\displaystyle +}$ since the only well defined morphisms to ${\displaystyle \mathbb {C} }$ are the evaluation morphisms associated from the points ${\displaystyle \{(\alpha _{1},0),(0,\alpha _{2}):\alpha _{1},\alpha _{2}\in \mathbb {C} \}}$. ## Non-affine Examples Here are some examples of schemes that are not affine schemes. They are constructed from gluing affine schemes together. • The Projective ${\displaystyle n}$-Space ${\displaystyle \mathbb {P} _{k}^{n}=\operatorname {Proj} k[x_{0},\ldots ,x_{n}]}$ over a field ${\displaystyle k}$ . This can be easily generalized to any base ring, see Proj construction (in fact, we can define Projective Space for any base scheme). The Projective ${\displaystyle n}$-Space for ${\displaystyle n\geq 1}$ is not affine as the global section of ${\displaystyle \mathbb {P} _{k}^{n}}$ is ${\displaystyle k}$. • Affine plane minus the origin.[2] Inside ${\displaystyle \mathbb {A} _{k}^{2}=\operatorname {Spec} \,k[x,y]}$ are distinguished open affine subschemes ${\displaystyle D_{x},D_{y}}$. Their union ${\displaystyle D_{x}\cup D_{y}=U}$ is the affine plane with the origin taken out. The global sections of ${\displaystyle U}$ are pairs of polynomials on ${\displaystyle D_{x},D_{y}}$ that restrict to the same polynomial on ${\displaystyle D_{xy}}$, which can be shown to be ${\displaystyle k[x,y]}$, the global section of ${\displaystyle \mathbb {A} _{k}^{2}}$. ${\displaystyle U}$ is not affine as ${\displaystyle V_{(x)}\cap V_{(y)}=\varnothing }$ in ${\displaystyle U}$. ## Global or relative Spec There is a relative version of the functor ${\displaystyle \operatorname {Spec} }$ called global ${\displaystyle \operatorname {Spec} }$, or relative ${\displaystyle \operatorname {Spec} }$. If ${\displaystyle S}$ is a scheme, then relative ${\displaystyle \operatorname {Spec} }$ is denoted by ${\displaystyle {\underline {\operatorname {Spec} }}_{S}}$ or ${\displaystyle \mathbf {Spec} _{S}}$. If ${\displaystyle S}$ is clear from the context, then relative Spec may be denoted by ${\displaystyle {\underline {\operatorname {Spec} }}}$ or ${\displaystyle \mathbf {Spec} }$. For a scheme ${\displaystyle S}$ and a quasi-coherent sheaf of ${\displaystyle {\mathcal {O}}_{S}}$-algebras ${\displaystyle {\mathcal {A}}}$, there is a scheme ${\displaystyle {\underline {\operatorname {Spec} }}_{S}({\mathcal {A}})}$ and a morphism ${\displaystyle f:{\underline {\operatorname {Spec} }}_{S}({\mathcal {A}})\to S}$ such that for every open affine ${\displaystyle U\subseteq S}$, there is an isomorphism ${\displaystyle f^{-1}(U)\cong \operatorname {Spec} ({\mathcal {A}}(U))}$, and such that for open affines ${\displaystyle V\subseteq U}$, the inclusion ${\displaystyle f^{-1}(V)\to f^{-1}(U)}$ is induced by the restriction map ${\displaystyle {\mathcal {A}}(U)\to {\mathcal {A}}(V)}$. That is, as ring homomorphisms induce opposite maps of spectra, the restriction maps of a sheaf of algebras induce the inclusion maps of the spectra that make up the Spec of the sheaf. Global Spec has a universal property similar to the universal property for ordinary Spec. More precisely, just as Spec and the global section functor are contravariant right adjoints between the category of commutative rings and schemes, global Spec and the direct image functor for the structure map are contravariant right adjoints between the category of commutative ${\displaystyle {\mathcal {O}}_{S}}$-algebras and schemes over ${\displaystyle S}$. In formulas, ${\displaystyle \operatorname {Hom} _{{\mathcal {O}}_{S}{\text{-alg}}}({\mathcal {A}},\pi _{}{\mathcal {O}}_{X})\cong \operatorname {Hom} _{{\text{Sch}}/S}(X,\mathbf {Spec} ({\mathcal {A}})),}$ where ${\displaystyle \pi \colon X\to S}$ is a morphism of schemes. ### Example of a relative Spec The relative spec is the correct tool for parameterizing the family of lines through the origin of ${\displaystyle \mathbb {A} _{\mathbb {C} }^{2}}$ over ${\displaystyle X=\mathbb {P} _{a,b}^{1}.}$ Consider the sheaf of algebras ${\displaystyle {\mathcal {A}}={\mathcal {O}}_{X}[x,y],}$ and let ${\displaystyle {\mathcal {I}}=(ay-bx)}$ be a sheaf of ideals of ${\displaystyle {\mathcal {A}}.}$ Then the relative spec ${\displaystyle {\underline {\operatorname {Spec} }}_{X}({\mathcal {A}}/{\mathcal {I}})\to \mathbb {P} _{a,b}^{1}}$ parameterizes the desired family. In fact, the fiber over ${\displaystyle [\alpha :\beta ]}$ is the line through the origin of ${\displaystyle \mathbb {A} ^{2}}$ containing the point ${\displaystyle (\alpha ,\beta ).}$ Assuming ${\displaystyle \alpha \neq 0,}$ the fiber can be computed by looking at the composition of pullback diagrams ${\displaystyle {\begin{matrix}\operatorname {Spec} \left({\frac {\mathbb {C} [x,y]}{\left(y-{\frac {\beta }{\alpha }}x\right)}}\right)&\to &\operatorname {Spec} \left({\frac {\mathbb {C} \left[{\frac {b}{a}}\right][x,y]}{\left(y-{\frac {b}{a}}x\right)}}\right)&\to &{\underline {\operatorname {Spec} }}_{X}\left({\frac {{\mathcal {O}}_{X}[x,y]}{\left(ay-bx\right)}}\right)\\\downarrow &&\downarrow &&\downarrow \\\operatorname {Spec} (\mathbb {C} )&\to &\operatorname {Spec} \left(\mathbb {C} \left[{\frac {b}{a}}\right]\right)=U_{a}&\to &\mathbb {P} _{a,b}^{1}\end{matrix}}}$ where the composition of the bottom arrows ${\displaystyle \operatorname {Spec} (\mathbb {C} ){\xrightarrow {[\alpha :\beta ]}}\mathbb {P} _{a,b}^{1}}$ gives the line containing the point ${\displaystyle (\alpha ,\beta )}$ and the origin. This example can be generalized to parameterize the family of lines through the origin of ${\displaystyle \mathbb {A} _{\mathbb {C} }^{n+1}}$ over ${\displaystyle X=\mathbb {P} _{a_{0},...,a_{n}}^{n}}$ by letting ${\displaystyle {\mathcal {A}}={\mathcal {O}}_{X}[x_{0},...,x_{n}]}$ and ${\displaystyle {\mathcal {I}}=\left(2\times 2{\text{ minors of }}{\begin{pmatrix}a_{0}&\cdots &a_{n}\\x_{0}&\cdots &x_{n}\end{pmatrix}}\right).}$ ## Representation theory perspective From the perspective of representation theory, a prime ideal I corresponds to a module R/I, and the spectrum of a ring corresponds to irreducible cyclic representations of R, while more general subvarieties correspond to possibly reducible representations that need not be cyclic. Recall that abstractly, the representation theory of a group is the study of modules over its group algebra. The connection to representation theory is clearer if one considers the polynomial ring ${\displaystyle R=K[x_{1},\dots ,x_{n}]}$ or, without a basis, ${\displaystyle R=K[V].}$ As the latter formulation makes clear, a polynomial ring is the group algebra over a vector space, and writing in terms of ${\displaystyle x_{i}}$ corresponds to choosing a basis for the vector space. Then an ideal I, or equivalently a module ${\displaystyle R/I,}$ is a cyclic representation of R (cyclic meaning generated by 1 element as an R-module; this generalizes 1-dimensional representations). In the case that the field is algebraically closed (say, the complex numbers), every maximal ideal corresponds to a point in n-space, by the nullstellensatz (the maximal ideal generated by ${\displaystyle (x_{1}-a_{1}),(x_{2}-a_{2}),\ldots ,(x_{n}-a_{n})}$ corresponds to the point ${\displaystyle (a_{1},\ldots ,a_{n})}$). These representations of ${\displaystyle K[V]}$ are then parametrized by the dual space ${\displaystyle V^{},}$ the covector being given by sending each ${\displaystyle x_{i}}$ to the corresponding ${\displaystyle a_{i}}$. Thus a representation of ${\displaystyle K^{n}}$ (K-linear maps ${\displaystyle K^{n}\to K}$) is given by a set of n numbers, or equivalently a covector ${\displaystyle K^{n}\to K.}$ Thus, points in n-space, thought of as the max spec of ${\displaystyle R=K[x_{1},\dots ,x_{n}],}$ correspond precisely to 1-dimensional representations of R, while finite sets of points correspond to finite-dimensional representations (which are reducible, corresponding geometrically to being a union, and algebraically to not being a prime ideal). The non-maximal ideals then correspond to infinite-dimensional representations. ## Functional analysis perspective The term "spectrum" comes from the use in operator theory. Given a linear operator T on a finite-dimensional vector space V, one can consider the vector space with operator as a module over the polynomial ring in one variable R=K[T], as in the structure theorem for finitely generated modules over a principal ideal domain. Then the spectrum of K[T] (as a ring) equals the spectrum of T (as an operator). Further, the geometric structure of the spectrum of the ring (equivalently, the algebraic structure of the module) captures the behavior of the spectrum of the operator, such as algebraic multiplicity and geometric multiplicity. For instance, for the 2×2 identity matrix has corresponding module: ${\displaystyle K[T]/(T-1)\oplus K[T]/(T-1)}$ the 2×2 zero matrix has module ${\displaystyle K[T]/(T-0)\oplus K[T]/(T-0),}$ showing geometric multiplicity 2 for the zero eigenvalue, while a non-trivial 2×2 nilpotent matrix has module ${\displaystyle K[T]/T^{2},}$ showing algebraic multiplicity 2 but geometric multiplicity 1. In more detail: • the eigenvalues (with geometric multiplicity) of the operator correspond to the (reduced) points of the variety, with multiplicity; • the primary decomposition of the module corresponds to the unreduced points of the variety; • a diagonalizable (semisimple) operator corresponds to a reduced variety; • a cyclic module (one generator) corresponds to the operator having a cyclic vector (a vector whose orbit under T spans the space); • the last invariant factor of the module equals the minimal polynomial of the operator, and the product of the invariant factors equals the characteristic polynomial. ## Generalizations The spectrum can be generalized from rings to C-algebras in operator theory, yielding the notion of the spectrum of a C-algebra. Notably, for a Hausdorff space, the algebra of scalars (the bounded continuous functions on the space, being analogous to regular functions) are a commutative C-algebra, with the space being recovered as a topological space from ${\displaystyle \operatorname {MaxSpec} }$ of the algebra of scalars, indeed functorially so; this is the content of the Banach–Stone theorem. Indeed, any commutative C-algebra can be realized as the algebra of scalars of a Hausdorff space in this way, yielding the same correspondence as between a ring and its spectrum. Generalizing to non-commutative C*-algebras yields noncommutative topology. ## References 1. A.V. Arkhangel'skii, L.S. Pontryagin (Eds.) General Topology I (1990) Springer-Verlag ISBN 3-540-18178-4 (See example 21, section 2.6.) 2. R.Vakil, Foundations of Algebraic Geometry (see Chapter 4, example 4.4.1) This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. 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https://read.dukeupress.edu/demography/article/58/1/247/167586/Motherhood-Penalties-and-Fatherhood-Premiums	## Abstract Despite much interest in how parenthood contributes to the gender pay gap, prior research has rarely explored firms' roles in shaping the parenthood pay penalty or premium. The handful of studies that investigated parenthood's effects within and across firms generally compared parents and their childless peers at a given time and failed to account for unobserved heterogeneity between the two groups. Such comparisons also cannot inform how having children may alter individuals' earnings trajectories within and across firms. Using 26 rounds of the National Longitudinal Survey of Youth 1979 and fixed-effects models, we examine how being a mother or father is linked to earnings growth within and across firms. We find that women's pay decreases as they become mothers and that the across-employer motherhood penalty is larger than the within-employer penalty. By contrast, fatherhood is associated with a pay premium, and the within-employer fatherhood premium is considerably greater than the across-employer one. We argue that these results are consistent with the discrimination explanation of the motherhood penalty and fatherhood premium. Because employers are likely to trust women who become mothers while working for them more than new recruits who are mothers, their negative bias against mothers would be more salient when evaluating the latter, which could result in a larger between-organizational motherhood penalty. Conversely, employers' likely greater trust in existing workers who become fathers than fathers they hire from elsewhere may amplify their positive bias favoring fathers in assessing the former, which could explain the greater within-firm fatherhood premium. ## Introduction Research on gender and family has long shown that parenthood has divergent effects on women's and men's earnings. Whereas women typically undergo a wage decrease with the arrival of each child (Budig and England 2001; Gangl and Ziefle 2009; Gough and Noonan 2013; Yu and Kuo 2017), men's earnings tend to increase with their transition to fatherhood (Glauber 2008; Hodges and Budig 2010; Killewald 2013). As a result of the wage penalty associated with motherhood and the wage premium tied to fatherhood, the gender pay gap widens as men and women move through the life course. Parenthood is therefore a key contributor to gender inequality (Angelov et al. 2016; England 2005). Corresponding to the important role of parenthood in shaping earnings inequality, much research has been devoted to explaining the motherhood pay penalty (Budig and England 2001; Correll et al. 2007; Gough and Noonan 2013; Staff and Mortimer 2012) and exploring factors that mitigate or amplify this penalty (Anderson et al. 2002; England et al. 2016; Gangl and Ziefle 2009; Glauber 2012; Yu and Kuo 2017). Because employing organizations are potential driving forces for wage disparities (Baron and Bielby 1980; Petersen and Morgan 1995), recent studies called attention to the organizations in which mothers work (Fuller 2018; Fuller and Hirsh 2019; Petersen et al. 2010). Using linked employer-employee data from Norway and Canada, respectively, two studies showed that mothers' lower earnings largely resulted from their greater concentration in firms that pay less. Wage differences between mothers and nonmothers within firms accounted for a relatively small portion of the motherhood pay penalty in these countries (Fuller 2018; Petersen et al. 2010). Despite existing evidence on the within- and across-firm motherhood penalties, it remains unclear how women's earnings change with motherhood and firm settings. Because the relevant research has generally relied on cross-sectional observations (Fuller 2018; Petersen et al. 2010),1 we do not know whether the wage differences between mothers' and nonmothers' firms indicate that the firms for which women work before and after childbearing pay differently or that women in lower-paying organizations more likely become mothers. It is possible that women prioritizing family over careers choose a particular type of employer to begin with and that such women tend to become mothers soon after entering their firms. Similarly, with cross-sectional comparisons between mothers and their childless peers within firms, prior research cannot tell whether the transition into motherhood indeed hampers a woman's earnings growth within her firm or, instead, certain unobserved personal traits, such as relative commitment to work, lead those who chose to become mothers to receive lower wages than their coworkers who chose otherwise. Precisely because of the difficulty of ruling out alternative explanations with cross-sectional comparisons, most research on the motherhood penalty has used longitudinal data and conceptualized this penalty as the pay decrease a woman experiences after childbearing rather than as the wage gap between mothers and their childless counterparts (Anderson et al. 2002; Budig and England 2001; Budig and Hodges 2010; England et al. 2016; Gangl and Ziefle 2009; Yu and Kuo 2017). To be consistent with this conceptualization, researchers interested in motherhood's effects within and across firms should ask how much post-birth shifts in women's earnings within organizations, compared with pay differences between women's organizations before and after childbearing, contribute to the overall earnings disadvantage of mothers. This study specifically addresses this question using 36 years of data from the National Longitudinal Survey of Youth 1979 (NLSY79). In the paper, we refer to a post-birth decrease in earnings within a firm as the within-firm motherhood penalty; we refer to a pay reduction between a woman's pre- and post-birth employers as the across-firm motherhood penalty. Unlike previous studies focusing only on mothers (Fuller 2018; Petersen et al. 2010), we also ask how fatherhood shapes men's earnings growth within and across employing organizations, and we compare their experiences with women's. Prior research has rarely examined the within- and across-firm fatherhood premiums, with just one Canadian study showing how the differing employers between fathers and childless men explain the former's higher wages (Cooke and Fuller 2018). Because that study relied on cross-sectional data, however, the question of how fatherhood alters earnings growth within and across firms remains unanswered. Besides showing the within- and across-employer parenthood penalties or premiums, this study helps disentangle the various mechanisms proposed to explain how having children alters women's and men's earnings. For example, one explanation of why becoming a parent increases men's and decreases women's pay is that it enhances men's motivation to provide for the family but reduces women's available time and energy for their jobs (Budig and England 2001; Gough and Noonan 2013; Killewald 2013). The corresponding changes in effort and productivity lead mothers to earn less and lead fathers to earn more. If this is the case, then parenthood should hamper women's earnings growth while amplifying men's both within and across firms because men and women would modify their effort regardless of their organizational settings. Conversely, because discrimination based on the assumption that motherhood reduces women's work effort is likely weaker when an employer is already familiar with the woman's job performance (Fuller 2018), a discrimination-based explanation would lead us to expect the impact of parenthood to be weaker when women remain with the same employers than when they move across firms. Our analysis of within- and across-firm pay penalties and premiums thus has theoretical implications for explanations of gendered relationships between parenthood and earnings. ## Parenthood and Pay Within and Across Firms Researchers have studied parenthood's effects on earnings extensively. Using data from various cohorts and across industrial countries, several studies have shown that having a child leads to a wage penalty for women, even after many observable and unobservable personal traits were taken into account (Anderson et al. 2002; Budig and England 2001; Fuller 2018; Gangl and Ziefle 2009; Gough and Noonan 2013; Petersen et al. 2010; Staff and Mortimer 2012; Yu and Kuo 2017). Conversely, fatherhood is associated with a 3% to 10% pay premium (Glauber 2008; Hodges and Budig 2010; Killewald 2013; Lundberg and Rose 2000, 2002). The findings from the studies in Canada and Norway suggest that for women and at least some men, parenthood's effect on earnings may be greater across than within firms. Nearly all these studies, however, compared parents and nonparents who were otherwise similar (Cooke and Fuller 2018; Fuller 2018; Fuller and Cooke 2018), making it possible that the results were confounded by unmeasured personal traits that both distinguish parents from nonparents and explain the two groups' different earnings (e.g., values placed on jobs vis-à-vis family). More important, cross-sectional comparisons cannot inform whether having a child actually alters an individual's earnings within and across firms. Some evidence suggests that the within-firm earnings shifts following childbirth may contribute to a relatively small part of the overall motherhood penalty. Two studies, for example, found that mothers with more employer changes since childbirth receive lower wages (Gangl and Ziefle 2009; Glass 2004). Cooke and Fuller (2018) also showed that Canadian men who moved to their jobs recently experienced smaller fatherhood premiums, implying that fathers gain more by remaining with the same employer over time. None of these studies, however, offered direct estimates on the parenthood penalty or premium attributable to post-birth changes in earnings within firms vis-à-vis that resulting from the pay discrepancies between individuals' organizations before and after having a child. ## Rationales for Within- and Cross-Firm Parenthood Effects Answering the question of how parenthood affects pay differently within and across firms requires an understanding of why mothers face a pay penalty while fathers receive a pay premium in the first place. Prior research has proposed three major explanations, which have distinctive implications for whether having children may affect earnings growth more within or across firms. We discuss these explanations and their corresponding hypotheses regarding the within- and across-firm parenthood effects. ### Work Effort and Productivity One main reason why parenthood may alter women's and men's earnings is that it strengthens traditional gender roles, making men feel a greater responsibility to provide for the family and compelling women to spend more time on domestic work (Sanchez and Thomson 1997; Sayer 2005). These changes are thought to lead fathers to allocate more effort to their jobs and mothers to allocate less (Becker 1985). Because fathers' increased work effort enhances productivity, fatherhood may augment men's earnings even if they spend the same amount of time at work as they did before having a child (Killewald 2013). Conversely, because lower effort reduces productivity, women experience a wage decrease with each additional child (Gough and Noonan 2013). If parenthood does amplify men's work effort and productivity and if, as the productivity-based explanation assumes, men are able to bargain for higher wages or move to organizations that properly compensate their increased productivity, then we should find that a man's earnings increase equally whether he remains in the same firm or moves to a different firm. We should therefore find comparable fatherhood pay premiums within and across employing organizations. Likewise, a mother with reduced work effort would experience decreases in productivity and pay after having a child regardless of whether she was in the same or a different organization, as long as her reduced effort is entirely due to motherhood. Thus, the within- and between-firm motherhood penalties should also be similar in magnitude. We summarize these expectations and present them as the effort and productivity hypothesis in Table 1. Because the effort and productivity perspective assumes that mothers' diminished work effort is rooted in their increased care obligations at home and fathers' enhanced effort reflects the extra financial burden an additional child brings, this perspective has another implication: as mothers' care responsibilities and fathers' financial burden both grow with the number of children, the changes in their work effort should correspond to rises in their family size. Therefore, we can further expect women's earnings to decrease and men's to increase proportionally, both within and across firms, with increases in the number of children. ### Compensating Differentials and Selection Into Workplaces An alternative explanation for the motherhood pay penalty is rooted in the compensating differentials theory, which focuses on workers' selection into jobs and workplaces. This theory maintains that worker compensations encompass both wages and nonpecuniary amenities, such as paid leaves and schedule flexibility, and that individuals may trade part of their wages for preferred amenities in choosing jobs (Glauber 2012; Heywood et al. 2007). Having a child is thought to affect workers' preferences and, therefore, their decisions about the trade between pay and job amenities. Because motherhood intensifies women's preferences for jobs compatible with their family obligations, mothers may more likely choose family-friendly workplaces at the expense of earnings (Fuller 2018; Petersen et al. 2010). Conversely, because parenthood amplifies men's responsibility to provide financially for their family, fathers may be more willing to sacrifice nonpecuniary amenities, such as a short commute, for jobs that pay more. A few prior studies have cast doubt on the argument that mothers' work settings are more family-friendly than nonmothers' (e.g., Glass and Camarigg 1992; Glauber 2012). However, because such studies did not account for all differences between workplaces, it remains possible that parenthood leads people to select workplaces with unmeasured amenities or disamenities, resulting in decreased or increased pay. Although we cannot tell whether people actually trade wages for job amenities or vice versa when changing employers, we should find a sizable fatherhood premium across firms if the compensating differentials argument is valid. Compared with childless men, fathers may more actively seek to move to high-paying workplaces and bargain harder for wages (instead of other amenities) when they move. Men therefore are likely to earn more at the firms they shift to after becoming fathers. At the same time, if mothers indeed prioritize family-friendly working conditions over pay in choosing workplaces, women can be expected to be compensated less at the firms they enter after childbirth, resulting in a negative association between motherhood and earnings across firms. According to this framework, parenthood should not significantly affect earnings growth within firms because people who change parenthood status while with the same employer likely made decisions about trade-offs between pay and nonpecuniary job amenities before the change. Because most nonpecuniary benefits and family-responsive policies are workplace-specific (Fuller 2018; Heywood et al. 2007), workers are typically unable to trade job amenities for pay (or vice versa) upon entering parenthood without changing employers.2 Of course, the decision to stay with a given employer upon having a child may not be random. It is possible that women in relatively family-friendly workplaces, which may have a lower potential for long-term wage growth (Glass 2004; Heywood et al. 2007), are more likely to make the choice to have a child without leaving their employer. Similarly, men may elect to have a child when they work for employers that offer better wage prospects over the long run. Nevertheless, neither selection would lead a given worker to have different earnings trajectories before and after parenthood within the same firm, as long as the employer does not discriminate based on parenthood status. Because our analysis focuses on within-person, within-firm earnings changes by parenthood status, workers' decisions to stay with an employer would not alter the compensating differentials-based hypothesis, which suggests that motherhood will decrease earnings and fatherhood will increase earnings across firms but not within firms. We also list this hypothesis in Table 1. ### Discrimination on the Basis of Parenthood Status Another perspective commonly proposed to explain the motherhood wage penalty and fatherhood wage premium centers on employer biases, which tend to work against mothers but favor fathers (Budig and England 2001; Fuller 2018; Hodges and Budig 2010; Killewald 2013).3 This perspective contends that employers' ability to measure workers' productivity is limited, which prompts them to use parenthood status as a proxy for workers' productivity levels. Being a mother, as a status characteristic, signals to employers that the woman must divide her devotion between family and work, making her the opposite of the “ideal worker” that employers have in mind (Ridgeway and Correll 2004; Williams 2001). Upon being convinced that mothers are suboptimal workers, employers may hold mothers to a higher standard, devaluate their job performance, and reward them less financially (Correll et al. 2007). By contrast, the status of fathers is associated with a greater financial responsibility and a higher level of motivation to earn. Employers are therefore likely to view fathers as more devoted to their jobs than childless men. In turn, employers may apply a more lenient standard to fathers and overpay fathers for a given level of productivity. Consistent with this argument, experiments have shown that fathers have an advantage in obtaining a job over equivalently qualified men who are not fathers (Correll et al. 2007). Fuller and Cooke (2018) also found that the fatherhood wage premium is greater in firms that lack formalized procedures to evaluate job performance, supporting the argument about employers' tendency to overestimate fathers' productivity. Although discrimination or favoritism based on parenthood status could affect parents' earnings growth both within and across firms, the magnitudes of the parenthood effects may not be the same. Differences in magnitude likely arise from employers' differential trust in their existing employees vis-à-vis new recruits, who are virtually strangers to them. Research has shown that individuals' trust in others depends on their social distance from the people they are judging and whether they consider those people in-group members (Brewer 1999; Buchan et al. 2002; Foddy et al. 2009; Platow et al. 2012). People are likely to trust acquaintances more than strangers, especially if the acquaintances share certain identities with them or belong to the same loosely defined group (e.g., same workplaces) as they do. Employers are generally more familiar with their existing employees than with new job applicants, and they are more likely to see the former as in-group members. Because individuals tend to judge those they trust less harshly than others (Taylor and Koivumaki 1976), employers' greater trust in existing employees compared with unfamiliar new recruits should lead them to apply a more lenient standard to the former. This leniency may strengthen employers' belief that fatherhood enhances productivity when they evaluate those who became fathers within their organizations, and this combination would lead to a larger fatherhood bonus for these fathers than for fathers hired from elsewhere. Conversely, employers may discount the productivity of mothers who are job seekers more than that of women who became mothers while working for them because employers are more lenient toward the latter. Being a mother may therefore be more detrimental to earnings when women move across firms than when they stay with the same employers. This argument—differential discrimination by trust—thus leads to the hypothesis that the within-firm motherhood penalty will be smaller than the across-firm one, whereas the within-firm fatherhood premium will be larger than the across-firm one (see Table 1). There is an alternative reason why employer discrimination or favoritism may lead the wage effects of parenthood to differ within and across organizations. Based on the discrimination account, employers use stereotypes associated with mothers and fathers to estimate their worth partly because an accurate measure of productivity is rarely available. Although psychological research has yielded mixed results regarding whether familiarity reduces the use of stereotypes in judging people (Funder and Colvin 1988; Garcia-Marques et al. 2016; Smith et al. 2006), it is possible that having more direct information enables employers to gauge workers' performance more objectively. Because employers typically know more about their existing employees than about new recruits, they may let the former's parenthood status affect their assessment less than they do new recruits. Thus, fathers and mothers alike would encounter a greater parenthood-based bias when changing employers than when staying with the same employers. This argument leads to the differential discrimination by information availability hypothesis, which contends that both the motherhood penalty and the fatherhood premium will be smaller within than across firms (as shown in Table 1).4 ## Data and Methods The data for the study come from 26 rounds of the NLSY79, conducted from 1979 to 2014. The survey has followed a nationally representative cohort of individuals who were 14–22 years old in 1979, collecting information annually through 1994 and biannually thereafter. At the last round included in our sample, fielded in 2014–2015, virtually all respondents were in their 50s. Because childbirth over age 50 is rare even among men, the 26 rounds of the NLSY79 have essentially captured the respondents' complete fertility histories. In addition to including comprehensive fertility histories, the NLSY79 data have the advantage of containing long and detailed work histories. At each round, the survey asks respondents to report jobs they have held each week since the last interview and to identify the employer for each job. Over the 36 years covered by the 26 rounds of the NLSY79, nearly all respondents have worked for multiple employers, and many of their employer spells are long. Such data make it possible to examine how individuals' earnings growth within and across firms corresponds to changes in their parenthood status. Although the NLSY79 does not contain employer-employee linked data, which are typically used to assess within- and across-firm wage inequality (Fuller 2018; Petersen and Morgan 1995; Petersen et al. 2010), it has the advantage of having repeated observations of a national sample. To our knowledge, no large-scale, longitudinal employer-employee linked data are available in the United States. Without a random sample of workers from each firm, the NSLY79 data cannot tell us whether firms in which parents concentrate pay differently from other firms. We can nevertheless address the extent to which pay differences between one's firms before and after childbearing contribute to the overall penalty or premium one experiences with parenthood, which is a central question in studies comparing the effects of parenthood within and across firms (Cooke and Fuller 2018; Fuller 2018). The longitudinal nature of the NLSY79 also enables us to estimate how much parenthood alters earnings growth within organizations. Because the vast majority of research measures the motherhood penalty and fatherhood premium as an individual's gain or loss in earnings with the transition to parenthood (Budig and England 2001; Gangl and Ziefle 2009; Glauber 2008; Killewald 2013; Yu and Kuo 2017), rather than as pay differences between parents and their childless peers, our estimates of how having a child changes people's earnings within and across organizations are more consistent with previous research than those based on pay gaps between different groups within and across firms. To conduct the statistical analysis, we pool all rounds of the NLSY79 to create a person-month sample. Although the NLSY79 is widely used, researchers rarely take advantage of its weekly job records, which can better capture employer changes and variations within each employer spell than annual or biannual records. The typical approach, which uses respondents' jobs held at the interview time to generate a person-year sample (e.g., Budig and England 2001; England et al. 2016; Killewald 2013), would exclude employer spells that respondents experienced between rounds. As a result, firms with high turnover rates would likely be underrepresented. Moreover, when using the person-year approach, researchers can observe earnings changes within employer spells only if respondents reported the same employers at two or more interview times, making the observed within-employer earnings growth selective.5 Using person-month data provides more accurate information on earnings changes over time. We convert respondents' weekly reports of jobs and employment status (i.e., having a job, unemployed, or voluntarily away from the labor force) to monthly observations. When a respondent held multiple jobs or statuses within the same month, we use the job or employment status with the longest duration to represent the month's status. In our person-month sample, we fill in respondents' time-varying marital and parenthood status using the NLSY79’s reports of the years and months during which respondents' marital status changed and their children were born, respectively. For variables that are recorded on only a yearly basis, such as respondents' geographic location, we assume that respondents' information did not change between interviews if they reported the same conditions for two adjacent rounds. When there was a change between interviews, we assume that the change occurred in the month in the middle of the two adjacent rounds.6 Because the NLSY79 provides limited job information for those on active military duty, we exclude such person-month observations from the sample. Given our focus on earnings and firms, we also limit the sample to months during which respondents reported having a job and provided valid information about their employers and pay. Because parents' obligations considerably decline when all their children reach adulthood, we further eliminate person-months when respondents' youngest child was age 20 or older. When we used different ages of the youngest child to restrict the sample (e.g., 18 or 25 years old) or imposed no such restriction at all, the main results were similar. To show how variation in parenthood status corresponds to changes in respondents' earnings between and within their employing organizations, we also eliminate cases where no changes are possible. Specifically, we exclude 6.4% of NLSY79 respondents for having reported only one employer or only employer spells that lasted one month or less throughout the observation period. Finally, we restrict the sample to those whose job information was provided within three years from the time the job was held because information such as earnings provided many years later—as a result of respondents missing certain rounds—may suffer from recall errors. After all these selections and elimination of cases missing information on key variables, our analytic sample contains 1,176,234 monthly observations from 5,933 men and 1,039,476 monthly observations from 5,749 women. ## Models and Measurement The outcome of interest for our study is the reported hourly pay of respondents' jobs (in cents). Because of the skewedness of earnings distribution, we take the natural log of the hourly earnings. Like most studies of the motherhood pay penalty and fatherhood pay premium, we use fixed-effects models to predict log hourly earnings (Budig and England 2001; Gangl and Ziefle 2009; Glauber 2008; Killewald 2013; Yu and Kuo 2017). Because the selection into parenthood is unlikely to be random, regression models that compare earnings between parents and their otherwise similar peers face the problem that other unobserved factors that contribute to the two groups' childbearing decisions, such as devotion to employment careers, may also account for differences in pay. Fixed-effects models, by contrast, enable us to take into account all unmeasured characteristics that do not vary across observations for a given subject, be it a person, an occupation, or an employing organization (Allison 2009). Such models can better address the problem of unobserved heterogeneity. We begin with a model of the following form: $ln(payit)=γ0+γ1parentit+ΣajXjit+μi+yeark+εit,$ (1) where the outcome is the log hourly pay of person i (i = 1, 2, 3, . . . , n) at month t; γ0 is the intercept; γ1 is the coefficient for being a parent; Xjit denotes j time-varying variables that may also affect earnings (e.g., education, work experience); μi and yeark are fixed effects for i individuals and k calendar years in the data set, respectively; and εit is the error term. Equivalent to a dummy variable for each person, μi captures all time-constant characteristics for the individuals, even when the characteristics are unobservable. With yeark, the equivalent of a dummy variable for each calendar year, the model further takes into account any year-to-year shifts that influence workers' pay (e.g., economic downturns).7 Because occupational characteristics are important to earnings (Kilbourne et al. 1994), especially mothers' earnings (Yu and Kuo 2017), we also fit the following model: $ln(payit)=γ0+γ¨1parentit+ΣajXjit+μi+yeark+occpo+εit,$ (2) where occpo represents fixed effects for the o occupations. Adding occupation fixed effects enables us to account for all stable occupational differences that may shape earnings, such as occupational training and qualifications, occupational status, and the gender dominance of the occupation. The difference between γ1, the estimated parenthood effect from Eq. (1), and $γ¨1$, the estimated effect from Eq. (2), thus indicates the extent to which occupational shifts before and since entering parenthood explain the associations between parenthood and earnings. We fit models with broad and fine occupation fixed effects, respectively. The NLSY79 used the three-digit 1970 census occupational codes through 2000 and switched to the 2000 census codes thereafter. We follow Meyer and Osborne's (2005) guidelines to create standard three-digit occupational codes across all the years, resulting in 372 fine occupations in the analytic sample. We then group various fine occupations under the same general occupational category to create 22 broad occupational categories (e.g., executive and managerial occupations, technician and related support occupations, mechanics and repairers, and machine operators and assemblers). We use broad occupational categories as an alternative measure to assess how occupational differences account for parenthood's association with pay. Next, we investigate how beyond occupations, employing organizations may further contribute to the parenthood premium or penalty. The specific model can be expressed as follows: $ln(payit)=γ0+γ1˜parentit+ΣajXjit+μi+yeark+occpo+employerf+εit,$ (3) where employerf denotes fixed effects for f employers. The NLSY79 provides a unique identification number for each employer a respondent has had throughout his or her career. The availability of multiple monthly observations with each employer enables us to estimate models with employer fixed effects. Because all employer identification numbers in the survey are respondent-specific, our measure of employers is fully nested in the observations of the same individuals: each individual's months in the sample can be divided into various employer spells. Thus, the employer fixed effects included here are, in fact, person-employer fixed effects, which capture all stable between-firm differences for given individuals. Because the person-employer fixed effects would capture any time-constant between-individual differences, the results would be identical regardless of whether we include individual fixed effects in Eq. (3). With employerf taking into account differences between employer spells, Eq. (3) ultimately estimates how alterations in individual attributes correlate with changes in earnings within employer spells. Thus, $γ1˜$ represents how becoming a parent affects an individual's earnings while the individual works for the same firm—that is, the within-employer parenthood premium or penalty. Following Fuller (2018), we estimate the between-employer parenthood penalty or premium by comparing the models before and after adding employer fixed effects (i.e., Eqs. (2) and (3)). Specifically, because Eq. (3) further accounts for average pay differences between employers, the change in the parenthood coefficient from Eqs. (2) to (3) can be interpreted as the extent to which the parenthood penalty or premium is attributable to pay differences across employing organizations. Fuller (2018:1450–1451) referred to this change as the “between-firm parenthood penalty” (or premium). We similarly consider as the between-employer contribution to the parenthood effect on earnings. We test the statistical significance of this contribution following Clogg and colleagues' (1995) procedures to compare coefficients for the same variable from two nested models. To provide more details about employer spells in the analytic sample, Table 2 shows the number of employers and durations with reported employers by gender. Both men and women experienced more than seven employers during the months observed. Altogether, these experiences amount to 43,505 person-employer spells for men and 38,744 person-employer spells for women (i.e., the average number of employers multiplied by the total number of respondents). Because the average number of employers is somewhat large, virtually all the respondents who have ever had a child changed employers after they became parents.8 Hence, our estimate of how much pay differences between respondents' pre- and post-birth firms contribute to the overall parenthood penalty or premium is not just based on the experiences of a small, selective group of parents. On average, men and women both spent more than 3 years with any given employer, and the mean of the longest duration with an employer is nearly 10 years for men and nearly 9 years for women. The considerable length of time most respondents spent with a firm enables us to observe ample earnings variation within their employer spells. We measure the main predictor of interest, parenthood, as a binary variable based on the presence of any biological children. We focus on biological children because research has shown that the fatherhood wage premium applies to only fathers with biological children (Killewald 2013) and because the NLSY79 lacks information on nonbiological children's birth months or the exact month when they entered respondents' lives. For an additional analysis examining how men's and women's earnings vary by their number of children, we also construct time-varying dummy variables indicating whether respondents have (1) no child, (2) one child, (3) two children, or (4) three or more children during a given month. All the fixed-effects models also control for a series of time-varying individual characteristics that may affect earnings. First, we introduce a set of human capital indicators, including the level of education completed (less than high school, high school, some college, and university or more), work experience, and job tenure. We create a monthly measure of work experience based on the NLSY79’s weekly records of the total amount of time respondents have held jobs. Job tenure is measured as the number of months respondents have worked for the same employer.9 We also include the square terms of work experience and job tenure to capture potentially nonlinear relationships. To account for the possibility that mothers' frequent job turnover and career interruptions obstruct their earnings growth (Gangl and Ziefle 2009), we introduce the number of employer changes and major employment breaks into the models. We define an employer change as a transition from one employer to another with no more than six months without a job between the two spells. By contrast, an employment break is a job separation followed by a jobless period of six months or longer.10 Because the NLSY79 has limited information on work histories before respondents entered the survey, which was as late as age 22 for some, we count only the number of employer changes and employment breaks from age 22 onward. Our other reason for doing so is that workers are unlikely penalized for high job turnover rates at a very young age, when job instability is common and expected. Starting counting employer changes and employment breaks at age 22 also requires us to include a dummy variable to capture the person-months before that age in the sample. Our exploratory analysis nonetheless indicates that measuring employer changes and employment breaks from the time respondents entered the survey or not including the dummy variable for age under 22 years would not cause meaningful changes in the results. In addition to human capital variables, we introduce a binary variable indicating the job's full-time status (more than 35 weekly working hours) because part-time jobs may impose an additional pay penalty. We also take into account marital status, which is thought to be relevant to fathers' pay premiums and mothers' pay penalties (Killewald 2013; Petersen et al. 2010). Because a spouse's working hours may affect the amount of time and effort individuals can put into their jobs, we create a series of mutually exclusive dummy variables containing information about respondents' marital status and spousal working hours: (1) never-married, not cohabiting; (2) never-married, cohabiting; (3) married with the spouse working fewer than 20 hours per week; (3) married with the spouse working 20–34 hours per week; (4) married with the spouse working full-time; and (5) separated, divorced, or widowed.11 Finally, we control for region (Northeast, North Central, South, and West, according to the census definitions) and whether respondents lived in urban areas. Table A1 in the online appendix presents detailed information about the predictors in the models. We estimate all the statistical models separately by gender. To adjust for the NLSY79’s oversampling of certain minority groups and for attrition over time, we apply the survey's longitudinal weights to all models. Along with the use of weights, we also estimate robust standard errors throughout the analysis. ## Results Table 3 presents a series of fixed-effects models predicting log hourly earnings for men and women. Model 1, featuring no controls except individual and calendar-year fixed effects, shows that becoming a father is associated with a 13% increase in earnings (exp(.124) – 1 = .132). The equivalent model for women (Model 5), by contrast, indicates a 9% gross motherhood penalty (exp(–.092) – 1 = –.088). Adding human capital indicators, marital status, and geographical locations reduces men's earnings premium by 60% ([.124 – .049] / .124 = .60), according to Model 2. Nevertheless, being a father is still associated with a 5% pay increase (exp(.049) – 1 = .050). Human capital differences also explain a large part of the motherhood penalty, reducing the penalty to 5% of the hourly pay in Model 6 (exp(–.050) – 1 = –.049). Models 3 and 4 further take into account potential differences in occupations before and after men's entry into fatherhood. The inclusion of broad-occupation fixed effects, which controls for fathers' and nonfathers' distributions across broad occupational categories, changes the coefficient of being a parent very little. Accounting for the pay differences across fine occupational categories explains a slightly larger share of the fatherhood pay premium, but men's hourly earnings still rise by slightly more than 4% as they become fathers. Similar to the results for men, including fixed effects of broad occupational categories, hardly alters the extent of mothers' pay disadvantage. Women continue to receive about 5% less pay as they become mothers (Model 6). Adding fine occupational fixed effects, however, reduces the motherhood earnings penalty considerably, by 47%. This change indicates that how women are distributed across fine occupations before and after they become mothers explains a large part of the motherhood penalty. This finding is important because most research on the motherhood penalty has taken into account just a handful of occupational characteristics (e.g., occupational female concentration, occupational training and skill requirements) and found them to be of little relevance (Budig and England 2001; Budig and Hodges 2010). We show that when using a fixed-effects approach, which accounts for all stable differences across detailed occupational categories, occupational differences do contribute to the motherhood penalty substantially. The control variables in the models in Table 3 are generally consistent with what would typically be expected, boosting our confidence in the results. For example, increases in education, work experience, and job tenure all raise hourly earnings, whereas a higher number of employment breaks is associated with lower pay. Moreover, marriage, especially to spouses who work relatively few hours, tends to be associated with higher earnings for men. To examine earnings changes within firms, we further add employer fixed effects to the models. Table 4 contrasts the parenthood effects between the models without employer fixed effects (identical to Models 4 and 8 in Table 3) and the models with such effects. Model 2 indicates that even after we control for differences across employers, fatherhood is linked to a near 4% increase in pay. Entering fatherhood clearly boosts men's pay growth within employer spells. Conversely, once we account for employer differences, being a mother is hardly associated with any decrease in women's hourly earnings (Model 4). Thus, women are rarely penalized for becoming a parent while they work for the same firms. Although the results presented so far suggest that mothers' and fathers' productivity levels cannot fully account for their respective earnings penalties and premiums, it is possible that changes in work effort resulting from parenthood contribute to some of the motherhood penalty and fatherhood premium. Because such changes should be sensitive to the number of children added to the household, we fit additional fixed-effects models in which we distinguish parents according to their number of children at the time of observation. Using the same methods as in Table 4 and regression models with and without employer fixed effects (the models also include individual, year, and occupation fixed effects, along with sociodemographic controls), we calculate the within- and across-employer contributions to the earnings premiums or penalties of having one, two, or three or more children. Figure 1 illustrates the results. The figure shows that compared with being childless, having any number of children enhances men's earnings. Nevertheless, each additional child does not proportionally increase the fatherhood premium. Overall, men experience the largest gain when transitioning from having no children to having one child—that is, when they begin to be subjected to positive stereotypes associated with fathers. The additional gain from having a second or third child is comparatively small. This pattern further suggests that increases in men's work effort with their increasing financial obligations is not sufficient to explain the fatherhood premium. More important, distinguishing fathers according to their number of children does not alter the fact that the within-employer fatherhood premium is greater than the across-employer premium. As Figure 1 indicates, the differences between employers hardly contribute to the fatherhood premium: none of the across-employer effects are statistically significant. Conversely, the within-employer pay premiums are significant and sizable for men with one, two, or three or more children. Once again, the uneven fatherhood premiums within and across employers is congruent with the hypothesis that employers especially favor the men who become fathers while working for them. The fact that the within-employer fatherhood bonus increases slightly with the number of children (p < .05 for the differences in the effects) while the across-employer bonus does not also suggests that employer favoritism, rather than work effort, more likely explains the fatherhood premium. Specifically, the pattern that men's earnings rise only with the number of children within employer spells could reflect employers' uneven knowledge; employers are likely to know when their existing employees have an additional child but are perhaps unaware of such information about their new recruits. Figure 1 shows that mothers with any number of children experience reductions in earnings. The size of the motherhood penalty generally corresponds to the number of children both within and across employing organizations, suggesting that mothers' greater caring responsibilities and hampered work effort at least partly contribute to their earnings disadvantage. The within-employer motherhood penalty, however, remains smaller than the between-employer penalty when women have just one or two children, which is consistent with the argument emphasizing employers' discrimination and greater trust in workers they know more. When women have three or more children, the relative magnitudes of the within- and across-employer motherhood penalties nevertheless change. Compared with having no children, having three or more children is associated with a considerable earnings reduction within firms (about 6%) but a smaller pay reduction across firms (about 2%). The especially large increase in the within-employer motherhood penalty when women transition from having two to more children suggests a potential limit to employers' trust in the mothers who have been working for them. Although trust could reduce employers' bias against women in their organizations who are having their first or second child, employers might draw a line for female employees they perceive as having too many children. Employers may view women having three or more children as having greater-than-average devotion to their family and may no longer be willing to give them the benefit of doubt as they do for women with fewer children. Perhaps because employers have the chance to learn about each childbirth of their existing workers but typically could not differentiate new recruits based on their number of children, we find that women's earnings are disproportionately reduced when they transition from having two to three children within the same firms but not between firms. In this sense, the finding that the within-employer motherhood penalty is greater than the across-employer penalty for mothers with three or more children is still consistent with the argument about employer bias. The perspectives about mothers' lower work effort or selection into lower-paying firms, by contrast, cannot explain the greater within-firm pay penalty for women with three or more children. So far we have argued that our results suggest that employer discrimination explains a substantial part, if not all, of mothers' earnings disadvantage and fathers' earnings advantage. There is, however, an alternative explanation for our findings that the motherhood penalty is larger across than within firms but the fatherhood premium is larger within than across firms: mothers and fathers may stay longer in firms where they experience smaller penalties and larger premiums. If so, our estimates of within-firm fatherhood premium and motherhood penalty would be disproportionately based on experiences from firms that treat parents especially well, explaining the relatively large fatherhood premium and relatively small motherhood penalty within firms. To test whether the extent of parenthood penalty or premium is indeed related to how long one stays in a firm, we fit additional models dividing employer spells based on whether they ended soon after respondents entered parenthood or had a childbirth. We argue that only upon parenthood are workers likely to know how much their organizations penalize or reward parents. Those who feel that their employers overpenalize mothers or undercompensate fathers likely leave their workplaces soon after they find out. Following this logic, parenthood would be associated with a greater penalty for women and a smaller premium for men in the organizations that individuals leave shortly after having a child than in other organizations. Table 5 presents models in which we introduce an interaction between being a parent and a binary indicator for employer spells that ended less than three years after individuals' entry into parenthood or after any childbirth, along with all other variables included in the most comprehensive models in Tables 3 and 4. Because the models include employer fixed effects, the main effects for the employer-spell characteristics are dropped from the models, given that they do not vary within an employer spell. Models 1 and 2 for men indicate that employer spells that ended early in parenthood or shortly after a childbirth indeed reward fathers less; there is virtually no fatherhood premium within such spells. For mothers, however, the results contradict the argument that women experiencing greater within-firm motherhood penalties are likely to leave their employers soon after childbearing. Women actually encounter a pay increase with motherhood during employer spells that end early in parenthood or soon after a childbirth (p < .05 for the parenthood plus interaction effects). Although men's results in Table 5 are consistent with the alternative explanation that they tend to remain in firms that compensate fatherhood more, it is noteworthy that men receive a very small fatherhood premium across firms (0.6%, as shown in Table 4). If men indeed leave their employers because their fatherhood status is not rewarded, they are likely to move to firms that pay a sizable premium for the status, which should lead the across-firm fatherhood premium to be somewhat comparable with the within-firm premium. Given the minimal between-organizational fatherhood premium and the lack of consistent results for women, we suggest that the argument that emphasizes the selection to stay based on the extent of the motherhood penalty and fatherhood premium is unlikely to explain our findings. ## Conclusions Despite much scholarly interest in pay premiums and penalties for parents, research on how parenthood alters individuals' earnings trajectories within and across employing organizations has been limited. To our knowledge, this study is the first to compare within- and between-firm fatherhood premiums and motherhood penalties in the United States. With fixed-effects models, we show that the fatherhood premium primarily results from the additional pay raises fathers receive within firms; being a father brings a rather small bonus when men move to another employer. Conversely, women experience a greater across-employer than within-employer motherhood penalty except when they have a comparatively large number of children. Until women have three or more children, they tend to encounter a smaller pay reduction with their childbearing transition if they stick with the same firm rather than moving to a different firm. Earlier in this paper, we described the three major explanations for the motherhood pay penalty and fatherhood pay premium: workers' effort and productivity, workers' trade-offs between monetary and nonpecuniary compensations, and employer discrimination. We proposed that these explanations predict differences in the relative magnitude of within- and across-firm parenthood premiums or penalties. Results from our analysis are most consistent with the theory that employers favor fathers but discriminate against mothers and that the extent of their favoritism and discrimination corresponds to how well they know and trust their workers. Employers appear to offer a larger fatherhood bonus to men who become fathers while working for them than to fathers they hire from elsewhere, contributing to a greater within- than across-firm fatherhood premium. Even though we do not have direct evidence on employers' intentions, their likely greater trust in women who become mothers while working for them compared with women who are mothers at the point of hire could also explain the smaller within-firm motherhood penalty. Although our findings are consistent with the account emphasizing employer favoritism and discrimination, they do not entirely rule out the possibility that heightened work-family conflict obstructs mothers' work effort, leading to their earnings disadvantage. We show that the motherhood penalty is amplified with the number of children, both within and across organizations. This result suggests that the increased family burden with each additional child may hamper mothers' job performance somewhat, even though the effort-based account cannot fully explain why the motherhood penalty is generally greater across organizations than within them. Compared with the findings on women, the evidence for fathers' enhanced work effort with the addition of each child is weaker. Men experience only a modest pay increase with their second or third child, and the pattern of earnings growth with each additional child only appears within, not across, employer spells. This lack of symmetrical gains across firms suggests that employers' beliefs about what adding a child does to men's productivity, rather than men's actual changes in work effort, more likely account for men's within-firm pay raises with each additional child. Our results provide little support for the account concerning mothers' and fathers' selection into jobs that involve different trade-offs between nonpecuniary amenities and pay. For men, the between-firm fatherhood premium is relatively small, indicating that being a father does not lead men to move to workplaces that offer higher wages at the expense of other amenities. That the fatherhood premium mostly results from fathers' greater earnings growth within firms also shows that fathers do not have to choose different trade-offs between job amenities and pay to gain financially. As for women, although we show that they receive lower pay in the firms they shift to after childbearing, this pattern does not necessarily support the argument that having a child leads women to choose firms that are more family-friendly but pay less. Instead, the finding could reflect a heightened penalty that employers apply to prospective employees who are mothers. Because our data do not include multiple workers for each employer, we unfortunately cannot determine whether the firms women move to after entering motherhood pay all workers less or just the women less. It is, however, noteworthy that women encounter a considerable within-firm motherhood penalty—more than the between-firm one—when they have three or more children. This evidence directly contradicts the claim that selection into family-friendly workplaces is the root of mothers' pay disadvantage. Taken all together, our results suggest that the compensating differentials account is unlikely to be valid. Beyond offering evidence for the different perspectives, this study contributes to the gender and work literature by examining parenthood and earnings growth within firms. As far as we know, no prior research has systematically examined how parenthood shapes the extent to which individuals' earnings grow within their workplaces over time. Our study demonstrates that having a child is linked with a steeper earnings growth for men within firms, but it hampers women's earnings growth within firms when they have more than one child. Thus, even if women can avoid the extra pay penalty for job seekers who are mothers by remaining with the same employer for a long period, they still face an increasing gender pay gap as they and their male colleagues have additional children. Despite prior research noting that mothers' frequent job turnover rates diminish their earnings prospects (e.g., Gangl and Ziefle 2009; Glass 2004), our study shows that a thorough understanding of gender inequality at work also requires attention to how fathers' earnings advantage extends with their tenure within a firm. More generally, our study illustrates an innovative way to examine how workplaces contribute to pay disparities in the absence of employer-employee linked data. As discussed earlier, our approach of using unique employer identification information from individual-level data means that we lack data from multiple employees in each firm, making it impossible to tell how firms pay other workers. Despite this limitation, this approach has the important advantage of enabling longitudinal models that account for unobserved heterogeneity. Because long-term longitudinal data are more readily available than employer-employee linked data, researchers can easily use our approach to shed light on how other time-varying conditions, such as individuals' marital status, health, and receipt of special training or certificates, may affect earnings differently within and across employing organizations. Finally, this study has a general theoretical implication. Our results demonstrate the important roles of employing organizations in shaping gender inequality. We find, for example, that women's shifts across employers contribute to nearly as much of the motherhood pay penalty as do their shifts across detailed occupations. This finding suggests that firms are just as important as occupations in determining women's earnings trajectories throughout the life course, even though much more research focuses on the influences of occupational characteristics on wages (e.g., Glauber 2012; Kilbourne et al. 1994; Levanon et al. 2009; Yu and Kuo 2017). Our results about the uneven effects of parenthood within and across firms further suggest that much of the earnings disadvantage or advantage parents face occurs at the firm level. This study thus echoes sociologists' long-standing call to regard employing organizations as the driving force for social stratification (Baron and Bielby 1980; Stolzenberg 1978). More research on firm settings would help enrich our understanding of earnings inequality between women and men. ## Acknowledgments A part of the study was supported by the Eunice Kennedy Shriver National Center for Child Health and Human Development grant (P2C-HD041041) awarded to Maryland Population Research Center. An earlier version of this article was presented at the 2018 Population Association of America's annual meeting in Austin, Texas, where the authors received valuable comments. ## Notes 1 Although Petersen and colleagues’ (2010) study included a subanalysis using repeated observations of the same women, their main findings—related to the magnitudes of within- and across-organizational motherhood wage penalties—were based on the comparison of different women within and across organizations. 2 In less common cases, an employee may be able to switch to a position with different amenities or a part-time schedule within the same firm upon entering parenthood, but controlling for changes in detailed occupations and work schedules should largely account for these scenarios. 3 Although we generally use “employers” to refer to the ones who evaluate workers’ performance and determine the latter’s pay, sometimes it is actually the workers’ supervisors, managers, or even the people hiring the workers for contract work who are responsible for pay discrimination. For simplicity, however, we use “employers” to represent all agents who may evaluate workers and determine workers’ earnings. 4 The lack of information on prospective employees may also lead employers to be uncertain about the former’s parenthood status, hence penalizing or rewarding them less for being a parent. If this is the case, both the motherhood penalty and fatherhood premium will be greater within than across firms. We do not formally propose this hypothesis, however, because research has shown that employers often pick up non–job-related information of prospective employees from subtle cues in resumes or interviews (Rivera 2012; Rivera and Tilcsik 2016). Employers may even actively seek information that is illegal to use in recruitment (Rivera 2017). In addition, employers may obtain ideas about prospective employees’ parenthood status when checking the latter’s references. 5 Our exploratory analysis showed that using a person-year, instead of person-month, sample would reduce the number of employers included in the analysis by more than one-half. 6 When respondents missed a round, we use the information provided by the next available interview to code the 12 months before the interview for the years through 1994 (when the survey conducted annual interviews) and to code the 24 months before the interview for years after 1994 (when biennial interviews were conducted). 7 We use reghdfe, a user-written program for Stata to estimate models with multiple fixed effects (Correia 2016). The program uses an algorithm to achieve the equivalent of including dummy variables for every fixed-effects category, given that the latter is computationally difficult. 8 Less than 4% of the respondents never had a new employer since they became parents. 9 Had everyone moved strictly from one firm to the next and never returned to a previous employer, the increases in job tenure and work experience with time would be identical within each employer spell. Nevertheless, a number of respondents reported working for the same employer for separate periods of time, and when they returned to an employer, they generally experienced a greater gain in work experience than tenure with the employer. It is therefore possible to include both job tenure and work experience even in models focusing on within-employer pay variation (i.e., those with employer fixed effects). 10 We do not consider a jobless spell of six months or longer as an employment break if respondents returned to the employer they were working for immediately before the jobless period: such breaks may represent parental or other family leaves obtained from the employer. 11 Our exploratory analysis indicated that differentiating those who cohabited based on their partner’s working hours would not affect the main results. Similarly, delineating those who were separated from those who were divorced or widowed, or using somewhat different cutoff points for the spousal working hours, made no meaningful difference to the results. ## References Allison, P. D. ( 2009 ). Fixed effects regression models (Series/No. 07-160). Thousand Oaks, CA : SAGE . Anderson, D. J., Binder, J. M., & Krause, K. ( 2002 ). 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This is an open access article distributed under the terms of a Creative Commons license (CC BY-NC-ND 4.0).	2022-05-21T22:23:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30628126859664917, "perplexity": 5444.439984153058}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00229.warc.gz"}
http://dlmf.nist.gov/28.26	# §28.26 Asymptotic Approximations for Large $q$ ## §28.26(i) Goldstein’s Expansions Denote 28.26.1 $\displaystyle\mathop{{\mathrm{Mc}^{(3)}_{m}}\/}\nolimits\!\left(z,h\right)$ $\displaystyle=\dfrac{e^{\mathrm{i}\phi}}{(\pi h\mathop{\cosh\/}\nolimits z)^{% \ifrac{1}{2}}}\\left(\mathop{\mathrm{Fc}_{m}\/}\nolimits\!\left(z,h\right)-% \mathrm{i}\mathop{\mathrm{Gc}_{m}\/}\nolimits\!\left(z,h\right)\right),$ 28.26.2 $\displaystyle\mathrm{i}\mathop{{\mathrm{Ms}^{(3)}_{m+1}}\/}\nolimits\!\left(z,% h\right)$ $\displaystyle=\dfrac{e^{\mathrm{i}\phi}}{(\pi h\mathop{\cosh\/}\nolimits z)^{% \ifrac{1}{2}}}\{\left(\mathop{\mathrm{Fs}_{m}\/}\nolimits\!\left(z,h\right)-% \mathrm{i}\mathop{\mathrm{Gs}_{m}\/}\nolimits\!\left(z,h\right)\right)},$ where 28.26.3 $\phi=2h\mathop{\sinh\/}\nolimits z-\left(m+\tfrac{1}{2}\right)\mathop{\mathrm{% arctan}\/}\nolimits\!\left(\mathop{\sinh\/}\nolimits z\right).$ Symbols: $\mathop{\sinh\/}\nolimits\NVar{z}$: hyperbolic sine function, $\mathop{\mathrm{arctan}\/}\nolimits\NVar{z}$: arctangent function, $m$: integer, $h$: parameter, $z$: complex variable and $\phi$ A&S Ref: 20.9.8 (in slightly different notation) Permalink: http://dlmf.nist.gov/28.26.E3 Encodings: TeX, pMML, png See also: Annotations for 28.26(i) Then as $h\to+\infty$ with fixed $z$ in $\Re{z}>0$ and fixed $s=2m+1$, 28.26.4 $\mathop{\mathrm{Fc}_{m}\/}\nolimits\!\left(z,h\right)\sim 1+\dfrac{s}{8h{% \mathop{\cosh\/}\nolimits^{2}}z}+\dfrac{1}{2^{11}h^{2}}\left(\dfrac{s^{4}+86s^% {2}+105}{{\mathop{\cosh\/}\nolimits^{4}}z}-\dfrac{s^{4}+22s^{2}+57}{{\mathop{% \cosh\/}\nolimits^{2}}z}\right)+\dfrac{1}{2^{14}h^{3}}\left(-\dfrac{s^{5}+14s^% {3}+33s}{{\mathop{\cosh\/}\nolimits^{2}}z}-\dfrac{2s^{5}+124s^{3}+1122s}{{% \mathop{\cosh\/}\nolimits^{4}}z}+\dfrac{3s^{5}+290s^{3}+1627s}{{\mathop{\cosh% \/}\nolimits^{6}}z}\right)+\cdots,$ Symbols: $\sim$: Poincaré asymptotic expansion, $\mathop{\cosh\/}\nolimits\NVar{z}$: hyperbolic cosine function, $m$: integer, $h$: parameter and $z$: complex variable A&S Ref: 20.9.9 (in slightly different notation) Referenced by: §28.26(i) Permalink: http://dlmf.nist.gov/28.26.E4 Encodings: TeX, pMML, png See also: Annotations for 28.26(i) 28.26.5 $\mathop{\mathrm{Gc}_{m}\/}\nolimits\!\left(z,h\right)\sim\dfrac{\mathop{\sinh% \/}\nolimits z}{{\mathop{\cosh\/}\nolimits^{2}}z}\left(\dfrac{s^{2}+3}{2^{5}h}% +\dfrac{1}{2^{9}h^{2}}\left(s^{3}+3s+\dfrac{4s^{3}+44s}{{\mathop{\cosh\/}% \nolimits^{2}}z}\right)+\dfrac{1}{2^{14}h^{3}}\left(5s^{4}+34s^{2}+9-\dfrac{s^% {6}-47s^{4}+667s^{2}+2835}{12{\mathop{\cosh\/}\nolimits^{2}}z}+\dfrac{s^{6}+50% 5s^{4}+12139s^{2}+10395}{12{\mathop{\cosh\/}\nolimits^{4}}z}\right)\right)+\cdots.$ Symbols: $\sim$: Poincaré asymptotic expansion, $\mathop{\cosh\/}\nolimits\NVar{z}$: hyperbolic cosine function, $\mathop{\sinh\/}\nolimits\NVar{z}$: hyperbolic sine function, $m$: integer, $h$: parameter and $z$: complex variable A&S Ref: 20.9.10 (in slightly different notation) Referenced by: §28.26(i) Permalink: http://dlmf.nist.gov/28.26.E5 Encodings: TeX, pMML, png See also: Annotations for 28.26(i) The asymptotic expansions of $\mathop{\mathrm{Fs}_{m}\/}\nolimits\!\left(z,h\right)$ and $\mathop{\mathrm{Gs}_{m}\/}\nolimits\!\left(z,h\right)$ in the same circumstances are also given by the right-hand sides of (28.26.4) and (28.26.5), respectively. For additional terms see Goldstein (1927). ## §28.26(ii) Uniform Approximations See §28.8(iv). For asymptotic approximations for $\mathop{{\mathrm{M}^{(3,4)}_{\nu}}\/}\nolimits\!\left(z,h\right)$ see also Naylor (1984, 1987, 1989).	2017-05-27T00:43:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 50, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9763716459274292, "perplexity": 14077.169111486392}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608726.4/warc/CC-MAIN-20170527001952-20170527021952-00245.warc.gz"}
https://pdglive.lbl.gov/Particle.action?init=0&node=M176&home=MXXX025	${\boldsymbol {\boldsymbol c}}$ ${\boldsymbol {\overline{\boldsymbol c}}}$ MESONS(including possibly non- ${\boldsymbol {\boldsymbol q}}$ ${\boldsymbol {\overline{\boldsymbol q}}}$ states) INSPIRE search # ${{\boldsymbol \chi}_{{c1}}{(3872)}}$ $I^G(J^{PC})$ = $0^+(1^{+ +})$ also known as ${{\mathit X}{(3872)}}$ This state shows properties different from a conventional ${{\mathit q}}{{\overline{\mathit q}}}$ state. A candidate for an exotic structure. See the review on non- ${{\mathit q}}{{\overline{\mathit q}}}$ states. First observed by CHOI 2003 in ${{\mathit B}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}{(1S)}}$ decays as a narrow peak in the invariant mass distribution of the ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}{(1S)}}$ final state. Isovector hypothesis excluded by AUBERT 2005B and CHOI 2011 . AAIJ 2013Q perform a full five-dimensional amplitude analysis of the angular correlations between the decay products in ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \chi}_{{c1}}{(3872)}}{{\mathit K}^{+}}$ decays, where ${{\mathit \chi}_{{c1}}{(3872)}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , which unambiguously gives the $\mathit J{}^{PC} = 1{}^{++}$ assignment under the assumption that the ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit J / \psi}}$ are in an ${\mathit S}{\mathrm -wave}$. AAIJ 2015AO extend this analysis with more data to limit ${\mathit D}{\mathrm -wave}$ contributions to $<$ 4$\%$ at 95$\%$ CL. See the review on Spectroscopy of Mesons Containing Two Heavy Quarks.'' ${{\mathit \chi}_{{c1}}{(3872)}}$ MASS FROM ${{\mathit J / \psi}}{{\mathit X}}$ MODE $3871.69 \pm0.17$ MeV ${{\mathit \chi}_{{c1}}{(3872)}}$ MASS FROM ${{\overline{\mathit D}}^{0}}{{\mathit D}^{0}}$ MODE ${\boldsymbol m}_{{{\boldsymbol \chi}_{{c1}}{(3872)}}}–{\boldsymbol m}_{{{\boldsymbol J / \psi}}}$ ${\mathit m}_{{{\mathit \chi}_{{c1}}{(3872)}}}–{\mathit m}_{{{\mathit J / \psi}}}$ $775 \pm4$ MeV ${\mathit m}_{{{\mathit \chi}_{{c1}}{(3872)}}}–{\mathit m}_{{{\mathit \psi}{(2S)}}}$ ${{\mathit \chi}_{{c1}}{(3872)}}$ WIDTH $<1.2$ MeV CL=90.0% ${{\mathit \chi}_{{c1}}{(3872)}}$ WIDTH FROM ${{\overline{\mathit D}}^{0}}{{\mathit D}^{0}}$ MODE	2020-11-29T16:26:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8938686847686768, "perplexity": 1221.8320435510377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141201836.36/warc/CC-MAIN-20201129153900-20201129183900-00332.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=M062W&home=sumtabM	${{\boldsymbol D}^{}{(2010)}^{\pm}}$ WIDTH INSPIRE search VALUE (keV) CL% EVTS DOCUMENT ID TECN COMMENT $\bf{ 83.4 \pm1.8}$ OUR AVERAGE $83.3$ $\pm1.2$ $\pm1.4$ 312.8k 1 2013 X BABR ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{\pm}}$ $\rightarrow$ ( ${{\mathit K}}{{\mathit \pi}}$ , ${{\mathit K}}$3 ${{\mathit \pi}}$ )${{\mathit \pi}^{\pm}}$ $96$ $\pm4$ $\pm22$ 1 2002 CLE2 ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{\pm}}$ $\rightarrow$ ( ${{\mathit K}}{{\mathit \pi}}$ ) ${{\mathit \pi}^{\pm}}$ • • • We do not use the following data for averages, fits, limits, etc. • • • $83.4$ $\pm1.7$ $\pm1.5$ 138.5k 1 2013 X BABR ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{\pm}}$ $\rightarrow$ ( ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ )${{\mathit \pi}^{\pm}}$ $83.2$ $\pm1.5$ $\pm2.6$ 174.3k 1 2013 X BABR ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{\pm}}$ $\rightarrow$ ( ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ )${{\mathit \pi}^{\pm}}$ $<131$ 90 110 1992 B ACCM ${{\mathit \pi}^{-}}$ 230 GeV 1 Ignoring the electromagnetic contribution from ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{\pm}}{{\mathit \gamma}}$ . References: LEES 2013X PRL 111 111801 Measurement of the ${{\mathit D}^{}{(2010)}^{+}}$ Meson Width and the ${{\mathit D}^{}{(2010)}^{+}}−{{\mathit D}^{0}}$ Mass Difference ANASTASSOV 2002 PR D65 032003 First Measurement of $\Gamma ({{\mathit D}^{+}}$) and Precision Measurement of ${\mathit m}_{{{\mathit D}^{+}}}–{\mathit m}_{{{\mathit D}^{0}}}$ BARLAG 1992B PL B278 480 Measurement of the Mass and Width of the Charmed Meson ${{\mathit D}^{*}{(2010)}^{+}}$	2020-12-02T12:31:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7042259573936462, "perplexity": 5145.403332101736}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141708017.73/warc/CC-MAIN-20201202113815-20201202143815-00040.warc.gz"}
http://dlmf.nist.gov/18.18	# §18.18 Sums ## §18.18(i) Series Expansions of Arbitrary Functions ### ¶ Jacobi Let be analytic within an ellipse with foci , and Then when lies in the interior of . Moreover, the series (18.18.2) converges uniformly on any compact domain within . Alternatively, assume is real and continuous and is piecewise continuous on . Assume also the integrals and converge. Then (18.18.2), with replaced by , applies when ; moreover, the convergence is uniform on any compact interval within . ### ¶ Chebyshev See §3.11(ii), or set in the above results for Jacobi and refer to (18.7.3)–(18.7.6). ### ¶ Laguerre The convergence of the series (18.18.4) is uniform on any compact interval in . ### ¶ Hermite Assume is real and continuous and is piecewise continuous on . Assume also converges. Then where The convergence of the series (18.18.6) is uniform on any compact interval in . ## §18.18(ii) Addition Theorems ### ¶ Legendre For (18.18.8), (18.18.9), and the corresponding formula for Jacobi polynomials see Koornwinder (1975b). See also (14.30.9). ## §18.18(iv) Connection Formulas ### ¶ Jacobi and a similar pair of equations by symmetry; compare the second row in Table 18.6.1. ## §18.18(v) Linearization Formulas ### ¶ Hermite The coefficients in the expansions (18.18.22) and (18.18.23) are positive, provided that in the former case . ## §18.18(vii) Poisson Kernels ### ¶ Hermite These Poisson kernels are positive, provided that are real, , and in the case of (18.18.27) . ## §18.18(viii) Other Sums In this subsection the variables and are not confined to the closures of the intervals of orthogonality; compare §18.2(i). ## §18.18(ix) Compendia For further sums see Hansen (1975, pp. 292-330), Gradshteyn and Ryzhik (2000, pp. 978–993), and Prudnikov et al. (1986b, pp. 637-644 and 700-718).	2013-05-22T05:35:42	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8886294364929199, "perplexity": 4408.697994150228}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368701370254/warc/CC-MAIN-20130516104930-00091-ip-10-60-113-184.ec2.internal.warc.gz"}
https://mooseframework.inl.gov/source/meshgenerators/ImageMeshGenerator.html	ImageMeshGenerator Description The ImageMeshGenerator object is a convenience tool for setting up a mesh to match the pixel structure of a two or three dimensional image. It is generally used in union with the ImageFunction object to perform simulations that rely on image data, such as setting up an initial condition of a grain structure. By default the generated mesh is sized to the dimensions of the images and creates one element per pixel. Input Parameters • file_suffixSuffix of the file to open, e.g. 'png' C++ Type:std::string Options: Description:Suffix of the file to open, e.g. 'png' • scale_to_oneTrueWhether or not to scale the image so its max dimension is 1 Default:True C++ Type:bool Options: Description:Whether or not to scale the image so its max dimension is 1 • zmax1Upper Z Coordinate of the generated mesh Default:1 C++ Type:double Options: Description:Upper Z Coordinate of the generated mesh • ymax1Upper Y Coordinate of the generated mesh Default:1 C++ Type:double Options: Description:Upper Y Coordinate of the generated mesh • cells_per_pixel1The number of mesh cells per pixel, must be <=1 Default:1 C++ Type:double Options: Description:The number of mesh cells per pixel, must be <=1 Default:False C++ Type:bool Options: • zmin0Lower Z Coordinate of the generated mesh Default:0 C++ Type:double Options: Description:Lower Z Coordinate of the generated mesh • file_baseImage file base to open, use this option when a stack of images must be read (ignored if 'file' is given) C++ Type:FileNameNoExtension Options: Description:Image file base to open, use this option when a stack of images must be read (ignored if 'file' is given) • nz1Number of elements in the Z direction Default:1 C++ Type:unsigned int Options: Description:Number of elements in the Z direction • bias_y1The amount by which to grow (or shrink) the cells in the y-direction. Default:1 C++ Type:double Options: Description:The amount by which to grow (or shrink) the cells in the y-direction. • nx1Number of elements in the X direction Default:1 C++ Type:unsigned int Options: Description:Number of elements in the X direction • ny1Number of elements in the Y direction Default:1 C++ Type:unsigned int Options: Description:Number of elements in the Y direction • bias_z1The amount by which to grow (or shrink) the cells in the z-direction. Default:1 C++ Type:double Options: Description:The amount by which to grow (or shrink) the cells in the z-direction. • fileName of single image file to extract mesh parameters from. If provided, a 2D mesh is created. C++ Type:FileName Options: Description:Name of single image file to extract mesh parameters from. If provided, a 2D mesh is created. • xmin0Lower X Coordinate of the generated mesh Default:0 C++ Type:double Options: Description:Lower X Coordinate of the generated mesh • file_rangeRange of images to analyze, used with 'file_base' (ignored if 'file' is given) C++ Type:std::vector Options: Description:Range of images to analyze, used with 'file_base' (ignored if 'file' is given) • ymin0Lower Y Coordinate of the generated mesh Default:0 C++ Type:double Options: Description:Lower Y Coordinate of the generated mesh • xmax1Upper X Coordinate of the generated mesh Default:1 C++ Type:double Options: Description:Upper X Coordinate of the generated mesh • bias_x1The amount by which to grow (or shrink) the cells in the x-direction. Default:1 C++ Type:double Options: Description:The amount by which to grow (or shrink) the cells in the x-direction. • elem_typeThe type of element from libMesh to generate (default: linear element for requested dimension) C++ Type:MooseEnum Description:The type of element from libMesh to generate (default: linear element for requested dimension) Optional Parameters • control_tagsAdds user-defined labels for accessing object parameters via control logic. C++ Type:std::vector Options: Description:Adds user-defined labels for accessing object parameters via control logic. • enableTrueSet the enabled status of the MooseObject. Default:True C++ Type:bool Options: Description:Set the enabled status of the MooseObject.	2019-04-25T04:28:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2332301288843155, "perplexity": 5481.516589400146}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578681624.79/warc/CC-MAIN-20190425034241-20190425060241-00505.warc.gz"}
https://conferences.lbl.gov/event/212/contributions/6083/	# Nuclear Structure 2022 13-17 June 2022 Berkeley, CA US/Pacific timezone ## Recent results on nobelium isotopes spectroscopy @ SHELS 13 Jun 2022, 11:00 30m Berkeley, CA #### Berkeley, CA Lawrence Berkeley National Laboratory Invited Abstract Oral Presentations ### Speaker Olivier Dorvaux (Universite de Strasbourg, CNRS/IPHC) ### Description The very/super-heavy nuclei area is a unique laboratory in the nuclear chart for the fundamental study of the atomic nucleus since excitation and decay modes are governed by the competition between the short-range strong nuclear interaction, long-range Coulomb repulsion, surface effects and the properties of individual quasiparticle states. For such studies, a wide scientific program has been launched at the FLNR Dubna laboratory with the emergence of new experimental setups such as the SHELS separator [1] and its focal plane detection system, GABRIELA [2] . Thanks to the high α, γ and ICE efficiency detection, some really new results on nobelium isotopes will be presented. Namely, the first γ and ICE spectroscopy of the $^{256}$No nucleus [3] and the revisiting of the $^{254}$No level scheme with an indication of a possible shape coexistence/superdeformed state. [1] Popeko, A. G. et al. Separator for Heavy ELement Spectroscopy - velocity filter SHELS. Nucl. Instrum. Methods Phys. Res. B 376, 140-143, doi:10.1016/j.nimb.2016.03.045 (2016). [2] Hauschild, K. et al. GABRIELA: A new detector array for gamma-ray and conversion electron spectroscopy of transfermium elements. Nucl. Instrum. Methods 560, 388-394 (2006). [3] Kessaci, K. et al. Evidence of high-$K$ isomerism in $_{102}^{256}$No$_{154}$. Phys. Rev. C 104, 044609, doi:10.1103/PhysRevC.104.044609 (2021). ### Primary authors Olivier Dorvaux (Universite de Strasbourg, CNRS/IPHC) M. Forge (Universite de Strasbourg, CNRS/IPHC) A. Lopez-Martens (IJCLab, IN2P3-CNRS, Universite Paris Saclay) ### Presentation Materials There are no materials yet.	2022-08-14T06:41:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31637322902679443, "perplexity": 14299.459639231918}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571996.63/warc/CC-MAIN-20220814052950-20220814082950-00157.warc.gz"}
https://www.anl.gov/event/an-overview-of-recent-progress-in-nuclear-quantum-monte-carlo	# Argonne National Laboratory Seminar \| Physics Division # An Overview of Recent Progress in Nuclear Quantum Monte Carlo PHY Seminar Abstract: The last decades have witnessed the emergence of the basic model of theoretical nuclear physics. Effective field theories exploit the symmetries of quantum chromodynamics to systematically construct nuclear potentials and consistent electroweak currents. They are the main input to ab nitio” many-body methods, aimed at solving the Schrödinger equation. Among them, quantum Monte Carlo approaches are known for their accuracy and their capability of dealing with short-range nuclear dynamics. I will report on recent quantum Monte Carlo progress toward a comprehensive description of nucleon-nucleon scattering, the structure and electroweak interactions of light nuclei, and the nucleonic matter equation of state. The impact of these calculations on the long-baseline neutrino-oscillation experimental program will also be discussed.	2020-06-05T16:06:34	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.802183210849762, "perplexity": 1372.6090399411555}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348502097.77/warc/CC-MAIN-20200605143036-20200605173036-00178.warc.gz"}
https://evolkov.net/moodle/mod/forum/discuss.php?d=1629	### A belief in meritocracy is not only false: it’s bad for you by Евгений Волков - Number of replies: 0 Проблема не в -кратиях, а в принципах, правилах и выстраивании социоинженерии. Не «кого выбрать», а «как делать». # A belief in meritocracy is not only false: it’s bad for you Most people don't just think the world should be run meritocratically, they think it ismeritocratic. 'We are true to our creed when a little girl born into the bleakest poverty knows that she has the same chance to succeed as anybody else …'Barack Obama, inaugural address, 2013 'We must create a level playing field for American companies and workers.' Donald Trump, inaugural address, 2017 Meritocracy has become a leading social ideal. Politicians across the ideological spectrum continually return to the theme that the rewards of life – money, power, jobs, university admission – should be distributed according to skill and effort. The most common metaphor is the "even playing field" upon which players can rise to the position that fits their merit. Conceptually and morally, meritocracy is presented as the opposite of systems such as hereditary aristocracy, in which one's social position is determined by the lottery of birth. Under meritocracy, wealth and advantage are merit's rightful compensation, not the fortuitous windfall of external events. Most people don't just think the world should be run meritocratically, they think it is meritocratic. In the U.K., 84 percent of respondents to the 2009 British Social Attitudes survey stated that hard work is either 'essential' or 'very important' when it comes to getting ahead, and in 2016 the Brookings Institute found that 69 percent of Americans believe that people are rewarded for intelligence and skill. Respondents in both countries believe that external factors, such as luck and coming from a wealthy family, are much less important. While these ideas are most pronounced in these two countries, they are popular across the globe. Although widely held, the belief that merit rather than luck determines success or failure in the world is demonstrably false. This is not least because merit itself is, in large part, the result of luck. Talent and the capacity for determined effort, sometimes called 'grit', depend a great deal on one's genetic endowments and upbringing. This is to say nothing of the fortuitous circumstances that figure into every success story. In his book Success and Luck (2016), the US economist Robert Frank recounts the long-shots and coincidences that led to Bill Gates's stellar rise as Microsoft's founder, as well as to Frank's own success as an academic. Luck intervenes by granting people merit, and again by furnishing circumstances in which merit can translate into success. This is not to deny the industry and talent of successful people. However, it does demonstrate that the link between merit and outcome is tenuous and indirect at best. According to Frank, this is especially true where the success in question is great, and where the context in which it is achieved is competitive. There are certainly programmers nearly as skillful as Gates who nonetheless failed to become the richest person on Earth. In competitive contexts, many have merit, but few succeed. What separates the two is luck. In addition to being false, a growing body of research in psychology and neuroscience suggests that believing in meritocracy makes people more selfish, less self-critical and even more prone to acting in discriminatory ways. Meritocracy is not only wrong; it's bad. The 'ultimatum game' is an experiment, common in psychological labs, in which one player (the proposer) is given a sum of money and told to propose a division between him and another player (the responder), who may accept the offer or reject it. If the responder rejects the offer, neither player gets anything. The experiment has been replicated thousands of times, and usually the proposer offers a relatively even split. If the amount to be shared is $100, most offers fall between$40–\$50. One variation on this game shows that believing one is more skilled leads to more selfish behaviour. In research at Beijing Normal University, participants played a fake game of skill before making offers in the ultimatum game. Players who were (falsely) led to believe they had 'won' claimed more for themselves than those who did not play the skill game. Other studies confirm this finding. The economists Aldo Rustichini at the University of Minnesota and Alexander Vostroknutov at Maastricht University in the Netherlands found that subjects who first engaged in a game of skill were much less likely to support the redistribution of prizes than those who engaged in games of chance. Just having the idea of skill in mind makes people more tolerant of unequal outcomes. While this was found to be true of all participants, the effect was much more pronounced among the 'winners'. By contrast, research on gratitude indicates that remembering the role of luck increases generosity. Frank cites a study in which simply asking subjects to recall the external factors (luck, help from others) that had contributed to their successes in life made them much more likely to give to charity than those who were asked to remember the internal factors (effort, skill). Perhaps more disturbing, simply holding meritocracy as a value seems to promote discriminatory behaviour. The management scholar Emilio Castilla at the Massachusetts Institute of Technology and the sociologist Stephen Benard at Indiana University studied attempts to implement meritocratic practices, such as performance-based compensation in private companies. They found that, in companies that explicitly held meritocracy as a core value, managers assigned greater rewards to male employees over female employees with identical performance evaluations. This preference disappeared where meritocracy was not explicitly adopted as a value. This is surprising because impartiality is the core of meritocracy's moral appeal. The 'even playing field' is intended to avoid unfair inequalities based on gender, race and the like. Yet Castilla and Benard found that, ironically, attempts to implement meritocracy leads to just the kinds of inequalities that it aims to eliminate. They suggest that this 'paradox of meritocracy' occurs because explicitly adopting meritocracy as a value convinces subjects of their own moral bona fides. Satisfied that they are just, they become less inclined to examine their own behaviour for signs of prejudice. Meritocracy is a false and not very salutary belief. As with any ideology, part of its draw is that it justifies the status quo, explaining why people belong where they happen to be in the social order. It is a well-established psychological principle that people prefer to believe that the world is just. However, in addition to legitimation, meritocracy also offers flattery. Where success is determined by merit, each win can be viewed as a reflection of one's own virtue and worth. Meritocracy is the most self-congratulatory of distribution principles. Its ideological alchemy transmutes property into praise, material inequality into personal superiority. It licenses the rich and powerful to view themselves as productive geniuses. While this effect is most spectacular among the elite, nearly any accomplishment can be viewed through meritocratic eyes. Graduating from high school, artistic success or simply having money can all be seen as evidence of talent and effort. By the same token, worldly failures becomes signs of personal defects, providing a reason why those at the bottom of the social hierarchy deserve to remain there. This is why debates over the extent to which particular individuals are 'self-made' and over the effects of various forms of 'privilege' can get so hot-tempered. These arguments are not just about who gets to have what; it's about how much 'credit' people can take for what they have, about what their successes allow them to believe about their inner qualities. That is why, under the assumption of meritocracy, the very notion that personal success is the result of 'luck' can be insulting. To acknowledge the influence of external factors seems to downplay or deny the existence of individual merit. Despite the moral assurance and personal flattery that meritocracy offers to the successful, it ought to be abandoned both as a belief about how the world works and as a general social ideal. It's false, and believing in it encourages selfishness, discrimination and indifference to the plight of the unfortunate. Clifton Mark This article was originally published at Aeon and has been republished under Creative Commons. 1384 words Tags:	2023-01-31T16:22:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21017053723335266, "perplexity": 3400.4626330062597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499888.62/warc/CC-MAIN-20230131154832-20230131184832-00600.warc.gz"}
https://www.usgs.gov/media/images/horizontal-displacement-vectors-mount-st-helens-2008-2014	# Horizontal displacement vectors at Mount St. Helens (2008-2014) 1905 (approx.) ### Detailed Description Map of horizontal displacement vectors for Global Positioning System (GPS) stations in and around Mount St. Helens. Blue arrows show the direction and magnitude of horizontal movement, as measured at the GPS station from 2008-2014. The total horizontal displacement is indicated in millimeters (mm) and inches (in). Light blue circles at the end of the arrows are measurement uncertainty. Public Domain. M. Lisowski	2023-01-28T14:37:27	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.829206109046936, "perplexity": 2640.32992553306}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499634.11/warc/CC-MAIN-20230128121809-20230128151809-00118.warc.gz"}
https://lammps.sandia.gov/doc/compute_cna_atom.html	# compute cna/atom command ## Syntax compute ID group-ID cna/atom cutoff • ID, group-ID are documented in compute command • cna/atom = style name of this compute command • cutoff = cutoff distance for nearest neighbors (distance units) ## Examples compute 1 all cna/atom 3.08 ## Description Define a computation that calculates the CNA (Common Neighbor Analysis) pattern for each atom in the group. In solid-state systems the CNA pattern is a useful measure of the local crystal structure around an atom. The CNA methodology is described in (Faken) and (Tsuzuki). Currently, there are five kinds of CNA patterns LAMMPS recognizes: • fcc = 1 • hcp = 2 • bcc = 3 • icosahedral = 4 • unknown = 5 The value of the CNA pattern will be 0 for atoms not in the specified compute group. Note that normally a CNA calculation should only be performed on mono-component systems. The CNA calculation can be sensitive to the specified cutoff value. You should insure the appropriate nearest neighbors of an atom are found within the cutoff distance for the presumed crystal structure. E.g. 12 nearest neighbor for perfect FCC and HCP crystals, 14 nearest neighbors for perfect BCC crystals. These formulas can be used to obtain a good cutoff distance: $\begin{split}r_{c}^{fcc} = & \frac{1}{2} \left(\frac{\sqrt{2}}{2} + 1\right) \mathrm{a} \simeq 0.8536 \:\mathrm{a} \\ r_{c}^{bcc} = & \frac{1}{2}(\sqrt{2} + 1) \mathrm{a} \simeq 1.207 \:\mathrm{a} \\ r_{c}^{hcp} = & \frac{1}{2}\left(1+\sqrt{\frac{4+2x^{2}}{3}}\right) \mathrm{a}\end{split}$ where a is the lattice constant for the crystal structure concerned and in the HCP case, x = (c/a) / 1.633, where 1.633 is the ideal c/a for HCP crystals. Also note that since the CNA calculation in LAMMPS uses the neighbors of an owned atom to find the nearest neighbors of a ghost atom, the following relation should also be satisfied: $r_c + r_s > 2*{\rm cutoff}$ where $$r_c$$ is the cutoff distance of the potential, $$r_s$$ is the skin distance as specified by the neighbor command, and cutoff is the argument used with the compute cna/atom command. LAMMPS will issue a warning if this is not the case. The neighbor list needed to compute this quantity is constructed each time the calculation is performed (e.g. each time a snapshot of atoms is dumped). Thus it can be inefficient to compute/dump this quantity too frequently or to have multiple compute/dump commands, each with a cna/atom style. Output info: This compute calculates a per-atom vector, which can be accessed by any command that uses per-atom values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options. The per-atom vector values will be a number from 0 to 5, as explained above. none	2020-08-10T12:18:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7196753621101379, "perplexity": 2762.637679173726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738674.42/warc/CC-MAIN-20200810102345-20200810132345-00547.warc.gz"}
https://lammps.sandia.gov/doc/pair_mgpt.html	# pair_style mgpt command ## Syntax pair_style mgpt ## Examples pair_style mgpt pair_coeff * * Ta6.8x.mgpt.parmin Ta6.8x.mgpt.potin Omega cp ~/lammps/potentials/Ta6.8x.mgpt.parmin parmin cp ~/lammps/potentials/Ta6.8x.mgpt.potin potin pair_coeff * * parmin potin Omega volpress yes nbody 1234 precision double pair_coeff * * parmin potin Omega volpress yes nbody 12 ## Description Within DFT quantum mechanics, generalized pseudopotential theory (GPT) (Moriarty1) provides a first-principles approach to multi-ion interatomic potentials in d-band transition metals, with a volume-dependent, real-space total-energy functional for the N-ion elemental bulk material in the form where the prime on each summation sign indicates the exclusion of all self-interaction terms from the summation. The leading volume term E_vol as well as the two-ion central-force pair potential v_2 and the three- and four-ion angular-force potentials, v_3 and v_4, depend explicitly on the atomic volume Omega, but are structure independent and transferable to all bulk ion configurations, either ordered or disordered, and with of without the presence of point and line defects. The simplified model GPT or MGPT (Moriarty2, Moriarty3), which retains the form of E_tot and permits more efficient large-scale atomistic simulations, derives from the GPT through a series of systematic approximations applied to E_vol and the potentials v_n that are valid for mid-period transition metals with nearly half-filled d bands. Both analytic (Moriarty2) and matrix (Moriarty3) representations of MGPT have been developed. In the more general matrix representation, which can also be applied to f-band actinide metals and permits both canonical and non-canonical d/f bands, the multi-ion potentials are evaluated on the fly during a simulation through d- or f-state matrix multiplication, and the forces that move the ions are determined analytically. Fast matrix-MGPT algorithms have been developed independently by Glosli (Glosli, Moriarty3) and by Oppelstrup (Oppelstrup) The mgpt pair style calculates forces, energies, and the total energy per atom, E_tot/N, using the Oppelstrup matrix-MGPT algorithm. Input potential and control data are entered through the pair_coeff command. Each material treated requires input parmin and potin potential files, as shown in the above examples, as well as specification by the user of the initial atomic volume Omega through pair_coeff. At the beginning of a time step in any simulation, the total volume of the simulation cell V should always be equal to Omega*N, where N is the number of metal ions present, taking into account the presence of any vacancies and/or interstitials in the case of a solid. In a constant-volume simulation, which is the normal mode of operation for the mgpt pair style, Omega, V and N all remain constant throughout the simulation and thus are equal to their initial values. In a constant-stress simulation, the cell volume V will change (slowly) as the simulation proceeds. After each time step, the atomic volume should be updated by the code as Omega = V/N. In addition, the volume term E_vol and the potentials v_2, v_3 and v_4 have to be removed at the end of the time step, and then respecified at the new value of Omega. In all simulations, Omega must remain within the defined volume range for E_vol and the potentials for the given material. The default option volpress yes in the pair_coeff command includes all volume derivatives of E_tot required to calculate the stress tensor and pressure correctly. The option volpress no disregards the pressure contribution resulting from the volume term E_vol, and can be used for testing and analysis purposes. The additional optional variable nbody controls the specific terms in E_tot that are calculated. The default option and the normal option for mid-period transition and actinide metals is nbody 1234 for which all four terms in E_tot are retained. The option nbody 12, for example, retains only the volume term and the two-ion pair potential term and can be used for GPT series-end transition metals that can be well described without v_3 and v_4. The nbody option can also be used to test or analyze the contribution of any of the four terms in E_tot to a given calculated property. The mgpt pair style makes extensive use of matrix algebra and includes optimized kernels for the BlueGene/Q architecture and the Intel/AMD (x86) architectures. When compiled with the appropriate compiler and compiler switches (-msse3 on x86, and using the IBM XL compiler on BG/Q), these optimized routines are used automatically. For BG/Q machines, building with the default Makefile for that architecture (e.g., “make bgq”) should enable the optimized algebra routines. For x-86 machines, there is a provided Makefile.mgptfast which enables the fast algebra routines, i.e. build LAMMPS with “make mgptfast”. The user will be informed in the output files of the matrix kernels in use. To further improve speed, on x86 the option precision single can be added to the pair_coeff command line, which improves speed (up to a factor of two) at the cost of doing matrix calculations with 7 digit precision instead of the default 16. For consistency the default option can be specified explicitly by the option precision double. All remaining potential and control data are contained with the parmin and potin files, including cutoffs, atomic mass, and other basic MGPT variables. Specific MGPT potential data for the transition metals tantalum (Ta4 and Ta6.8x potentials), molybdenum (Mo5.2 potentials), and vanadium (V6.1 potentials) are contained in the LAMMPS potentials directory. The stored files are, respectively, Ta4.mgpt.parmin, Ta4.mgpt.potin, Ta6.8x.mgpt.parmin, Ta6.8x.mgpt.potin, Mo5.2.mgpt.parmin, Mo5.2.mgpt.potin, V6.1.mgpt.parmin, and V6.1.mgpt.potin . Useful corresponding informational “README” files on the Ta4, Ta6.8x, Mo5.2 and V6.1 potentials are also included in the potentials directory. These latter files indicate the volume mesh and range for each potential and give appropriate references for the potentials. It is expected that MGPT potentials for additional materials will be added over time. Useful example MGPT scripts are given in the examples/USER/mgpt directory. These scripts show the necessary steps to perform constant-volume calculations and simulations. It is strongly recommended that the user work through and understand these examples before proceeding to more complex simulations. Note For good performance, LAMMPS should be built with the compiler flags “-O3 -msse3 -funroll-loops” when including this pair style. The src/MAKE/OPTIONS/Makefile.mgptfast is an example machine Makefile with these options included as part of a standard MPI build. Note that it as provided, it will build with whatever low-level compiler (g++, icc, etc) is the default for your MPI installation. Mixing, shift, table tail correction, restart: This pair style does not support the pair_modify mix, shift, table, and tail options. This pair style does not write its information to binary restart files, since it is stored in potential files. Thus, you needs to re-specify the pair_style and pair_coeff commands in an input script that reads a restart file. This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords. ## Restrictions This pair style is part of the USER-MGPT package and is only enabled if LAMMPS is built with that package. See the Making LAMMPS section for more info. The MGPT potentials require the newtion setting to be “on” for pair style interactions. The stored parmin and potin potential files provided with LAMMPS in the “potentials” directory are written in Rydberg atomic units, with energies in Rydbergs and distances in Bohr radii. The mgpt pair style converts Rydbergs to Hartrees to make the potential files compatible with LAMMPS electron units. The form of E_tot used in the mgpt pair style is only appropriate for elemental bulk solids and liquids. This includes solids with point and extended defects such as vacancies, interstitials, grain boundaries and dislocations. Alloys and free surfaces, however, require significant modifications, which are not included in the mgpt pair style. Likewise, the hybrid pair style is not allowed, where MGPT would be used for some atoms but not for others. Electron-thermal effects are not included in the standard MGPT potentials provided in the “potentials” directory, where the potentials have been constructed at zero electron temperature. Physically, electron-thermal effects may be important in 3d (e.g., V) and 4d (e.g., Mo) transition metals at high temperatures near melt and above. It is expected that temperature-dependent MGPT potentials for such cases will be added over time. ## Default The options defaults for the pair_coeff command are volpress yes, nbody 1234, and precision double. (Moriarty1) Moriarty, Physical Review B, 38, 3199 (1988). (Moriarty2) Moriarty, Physical Review B, 42, 1609 (1990). Moriarty, Physical Review B 49, 12431 (1994). (Moriarty3) Moriarty, Benedict, Glosli, Hood, Orlikowski, Patel, Soderlind, Streitz, Tang, and Yang, Journal of Materials Research, 21, 563 (2006). (Glosli) Glosli, unpublished, 2005. Streitz, Glosli, Patel, Chan, Yates, de Supinski, Sexton and Gunnels, Journal of Physics: Conference Series, 46, 254 (2006). (Oppelstrup) Oppelstrup, unpublished, 2015. Oppelstrup and Moriarty, to be published.	2018-07-19T15:28:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5988808870315552, "perplexity": 5181.928904398799}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591140.45/warc/CC-MAIN-20180719144851-20180719164851-00442.warc.gz"}
https://par.nsf.gov/biblio/10363360	Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering Abstract Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a hierarchical Vecchia approximation, whose conditional-independence assumptions imply sparsity in the Cholesky factors of both the precision and the covariance matrix. This remarkable property is crucial for applications to high-dimensional spatiotemporal filtering. We present a fast and simple algorithm to compute our hierarchical Vecchia approximation, and we provide extensions to nonlinear data assimilation with non-Gaussian data based on the Laplace approximation. In several numerical comparisons, including a filtering analysis of satellite data, our methods strongly outperformed alternative approaches. Authors: ; Award ID(s): Publication Date: NSF-PAR ID: 10363360 Journal Name: Statistics and Computing Volume: 32 Issue: 1 ISSN: 0960-3174 Publisher: 1. Abstract Modifications of the matter power spectrum due to baryonic physics are one of the major theoretical uncertainties in cosmological weak lensing measurements. Developing robust mitigation schemes for this source of systematic uncertainty increases the robustness of cosmological constraints, and may increase their precision if they enable the use of information from smaller scales. Here we explore the performance of two mitigation schemes for baryonic effects in weak lensing cosmic shear: the principal component analysis (PCA) method and the halo-model approach in hmcode. We construct mock tomographic shear power spectra from four hydrodynamical simulations, and run simulated likelihood analyses with cosmolike assuming LSST-like survey statistics. With an angular scale cut of ℓmax < 2000, both methods successfully remove the biases in cosmological parameters due to the various baryonic physics scenarios, with the PCA method causing less degradation in the parameter constraints than hmcode. For a more aggressive ℓmax = 5000, the PCA method performs well for all but one baryonic physics scenario, requiring additional training simulations to account for the extreme baryonic physics scenario of Illustris; hmcode exhibits tensions in the 2D posterior distributions of cosmological parameters due to lack of freedom in describing the power spectrum for $k \gt 10\more » 2. Abstract The ensemble Kalman filter (EnKF) is a popular technique for data assimilation in high-dimensional nonlinear state-space models. The EnKF represents distributions of interest by an ensemble, which is a form of dimension reduction that enables straightforward forecasting even for complicated and expensive evolution operators. However, the EnKF update step involves estimation of the forecast covariance matrix based on the (often small) ensemble, which requires regularization. Many existing regularization techniques rely on spatial localization, which may ignore long-range dependence. Instead, our proposed approach assumes a sparse Cholesky factor of the inverse covariance matrix, and the nonzero Cholesky entries are further regularized. The resulting method is highly flexible and computationally scalable. In our numerical experiments, our approach was more accurate and less sensitive to misspecification of tuning parameters than tapering-based localization. 3. We present an ensemble filtering method based on a linear model for the precision matrix (the inverse of the covariance) with the parameters determined by Score Matching Estimation. The method provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. The parameters are found by solving a system of linear equations. The analysis step uses the inverse formulation of the Kalman update. Several filter versions, differing in the construction of the analysis ensemble, are proposed, as well as a Score matching version of the Extended Kalman Filter. 4. Summary This paper is concerned with empirical likelihood inference on the population mean when the dimension$p$and the sample size$n$satisfy$p/n\rightarrow c\in [1,\infty)$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when$p/n>1/2$because the convex hull of the$n$observations in$\mathbb{R}^p$becomes too small to cover the true mean value. Moreover, when$p> n\$, the sample covariance matrix becomes singular, and this results in the breakdown of the first sandwich approximation for the log empirical likelihood ratio. To deal with these two challenges, we propose a new strategy of adding two artificial data points to the observed data. We establish the asymptotic normality of the proposed empirical likelihood ratio test. The proposed test statistic does not involve the inverse of the sample covariance matrix. Furthermore, its form is explicit, so the test can easily be carried out with low computational cost. Our numerical comparison shows that the proposed test outperforms some existing tests for high-dimensional mean vectors in terms of power. We also illustrate the proposed procedure with an empirical analysis of stock data.	2023-02-03T05:04:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5417230129241943, "perplexity": 937.2572648399096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500042.8/warc/CC-MAIN-20230203024018-20230203054018-00041.warc.gz"}
https://www.usgs.gov/centers/umesc/science/monarch-conservation-science-partnership?qt-science_center_objects=0	# Monarch Conservation Science Partnership ## Science Center Objects The Monarch Conservation Science Partnership is a USGS led group of scientists, managers, and conservation organizations who perform science related to the conservation of monarch butterflies. We come from federal agencies, non profits, and academia and from the three countries where monarchs range (Mexico, Canada, and the United States). To date meetings of the MCSP have been hosted by the USGS John Wesley Powell Center for Analysis and Synthesis in Ft. Collins, CO. PIs include Darius Semmens and Jay Diffendorfer (GECSC) and Wayne Thogmartin (UMESC). Are we witnessing the end of the migration of monarchs in the eastern U.S.? What is the issue? The Eastern, migratory population of monarch butterflies has declined by ~80% over the last decade, despite efforts in Mexico to end illegal logging in the fir forests used by overwintering monarchs. These declines are coincident with the rapid adoption of glyphosate-resistant crops on agricultural lands of the north central U.S. What are the challenges? The monarch’s multi-generational migration between overwintering grounds in central Mexico and summer breeding grounds in northern U.S. and southern Canada creates shared management responsibilities across North America. No national-level monitoring and insufficient basic ecological research (e.g., few habitat-specific estimates of milkweed density) lead to key gaps in our understanding of monarch life history and ecology. Threats are numerous, including herbicide and pesticide application, loss of natural and conserved areas, and disruption from climate change and consequences of extreme weather, leading to ‘death by a thousand cuts’. Strategies for mitigating threats are weakly defined. The Partnership is engaged in considerable research to address information gaps associated with the ecology and conservation of monarch butterflies. Among these efforts include analyses of extinction risk, continental-scale full-annual-cycle demography, threats assessment, overwinter density estimation, milkweed target estimation, and storylines for conservation recovery. Strategies for sampling monarchs and the milkweed that sustains them are being developed. In addition, geospatial tools, both desktop and online, for aiding in conservation planning have been completed. Decline in the eastern migratory monarch butterfly population as surveyed by the World Wildlife Fund-Mexico.Populations in the high-elevation Oyamel fir forests where eastern monarchs overwinter are indexed by the area over which they occur.Semmens et al. (2016) provided an adjusted measurement of population size which corrects for observation error.(Public domain.) Quasi-extinction risk and population targets for the Eastern, migratory population of monarch butterflies (Danaus plexippus) http://www.nature.com/articles/srep23265 The Eastern, migratory population of monarch butterflies (Danaus plexippus), an iconic North American insect, has declined by ~80% over the last decade. The monarch’s multi-generational migration between overwintering grounds in central Mexico and the summer breeding grounds in the northern U.S. and southern Canada is celebrated in all three countries and creates shared management responsibilities across North America. Here we present a novel Bayesian multivariate auto-regressive state-space model to assess quasi-extinction risk and aid in the establishment of a target population size for monarch conservation planning. We find that, given a range of plausible quasi-extinction thresholds, the population has a substantial probability of quasi-extinction, from 11–57% over 20 years, although uncertainty in these estimates is large. Exceptionally high population stochasticity, declining numbers, and a small current population size act in concert to drive this risk. An approximately 5-fold increase of the monarch population size (relative to the winter of 2014–15) is necessary to halve the current risk of quasi-extinction across all thresholds considered. Conserving the monarch migration thus requires active management to reverse population declines, and the establishment of an ambitious target population size goal to buffer against future environmentally driven variability. Density estimates of monarch butterflies overwintering in central Mexico https://peerj.com/articles/3221/ Given the rapid population decline and recent petition for listing of the monarch butterfly (Danaus plexippus L.) under the Endangered Species Act, an accurate estimate of the Eastern, migratory population size is needed. Because of difficulty in counting individual monarchs, the number of hectares occupied by monarchs in the overwintering area is commonly used as a proxy for population size, which is then multiplied by the density of individuals per hectare to estimate population size. There is, however, considerable variation in published estimates of overwintering density, ranging from 6.9–60.9 million ha−1. We develop a probability distribution for overwinter density of monarch butterflies from six published density estimates. The mean density among the mixture of the six published estimates was ∼27.9 million butterflies ha−1 (95% CI [2.4–80.7] million ha−1); the mixture distribution is approximately log-normal, and as such is better represented by the median (21.1 million butterflies ha−1). Based upon assumptions regarding the number of milkweed needed to support monarchs, the amount of milkweed (Asclepias spp.) lost (0.86 billion stems) in the northern US plus the amount of milkweed remaining (1.34 billion stems), we estimate >1.8 billion stems is needed to return monarchs to an average population size of 6 ha. Considerable uncertainty exists in this required amount of milkweed because of the considerable uncertainty occurring in overwinter density estimates. Nevertheless, the estimate is on the same order as other published estimates. The studies included in our synthesis differ substantially by year, location, method, and measures of precision. A better understanding of the factors influencing overwintering density across space and time would be valuable for increasing the precision of conservation recommendations. National Valuation of Monarch Butterflies Indicates an Untapped Potential for Incentive-Based Conservation http://onlinelibrary.wiley.com/doi/10.1111/conl.12065/abstract The annual migration of monarch butterflies (Danaus plexippus) has high cultural value and recent surveys indicate monarch populations are declining. Protecting migratory species is complex because they cross international borders and depend on multiple regions. Understanding how much, and where, humans place value on migratory species can facilitate market-based conservation approaches. We performed a contingent valuation study of monarchs to understand the potential for such approaches to fund monarch conservation. The survey asked U.S. respondents about the money they would spend, or have spent, growing monarch-friendly plants, and the amount they would donate to monarch conservation organizations. Combining planting payments and donations, the survey indicated U.S. households valued monarchs as a total one-time payment of $4.78–$6.64 billion, levels similar to many endangered vertebrate species. The financial contribution of even a small percentage of households through purchases or donations could generate new funding for monarch conservation through market-based approaches. A trans-national monarch butterfly population model and implications for regional conservation priorities http://onlinelibrary.wiley.com/doi/10.1111/een.12351/full The monarch has undergone considerable population declines over the past decade, and the governments of Mexico, Canada, and the United States have agreed to work together to conserve the species. Given limited resources, understanding where to focus conservation action is key for widespread species like monarchs. To support planning for continental-scale monarch habitat restoration, the authors addressed the question of where restoration efforts are likely to have the largest impacts on monarch butterfly population growth rates. They did so by developing a spatially explicit trans-national model of the monarch butterfly's multi-generational life cycle. The authors reported that improving monarch habitat in the north central or southern parts of the monarch range yields a slightly greater increase in the population growth rate than restoration in other regions. However, combining restoration efforts across multiple regions yields population growth rates above replacement with smaller simulated improvements in habitat per region than single-region strategies. These findings suggest that conservation investment in projects across the full monarch range will be more effective than focusing on one or a few regions, and will require international cooperation across many land use categories. (Public domain.) Monarch Conservation Science Partnership Map Viewer and Tools County Ranking Tool The County Ranking Tool gives users the ability to prioritize counties within the conterminous United States according to multiple input field criteria important for monarch butterfly conservation. A spatial data layer representing U.S. counties was assembled and attributed with the information for each input criteria. Some of these criteria represent positive attributes for monarch butterfly conservation while others quantify potential threats. (Public domain.) Milkweed Calculator Tools Two separate milkweed calculator tools were developed to allow users the ability to model the anticipated number of milkweeds on the landscape. The tools use a county summary shapefile (attribute table) as a base layer for analysis. A seamless milkweed habitat raster was used as the source for the summary information contained within this shapefile. (Public domain.) Monarch Conservation Science Partnership Map Viewer and Tools A separate tool was developed to allow users the ability to make hypothetical adjustments to the area (in hectares or acres) of milkweed habitat classes for a user-defined set of counties. The results of these hypothetical changes can then be used as input in the milkweed calculator tools and can help to inform the user on the impact of specific conservation development activities. (Public domain.) Thogmartin, W. E., L. López-Hoffman, J. Rohweder, J. Diffendorfer, R. Drum, D. Semmens, S. Black, I. Caldwell, D. Cotter, P. Drobney, L. L. Jackson, M. Gale, D. Helmers, S. Hilburger, E. Howard, K. Oberhauser, J. Pleasants, B. Semmens, O. Taylor, P. Ward, J. Weltzin, and R. Wiederholt. 2017. Restoring monarch butterfly habitat in the Midwestern U.S.: “All Hands on Deck”. Environmental Research Letters 12:074005. DOI: 10.1088/1748-9326/aa7637 The eastern migratory population of monarch butterflies (Danaus plexippus plexippus) has declined by >80% within the last two decades. One possible cause of this decline is the loss of ≥1.3 billion stems of milkweed (Asclepias spp.), which monarchs require for reproduction. In an effort to restore monarchs to a population goal established by the US Fish and Wildlife Service and adopted by Mexico, Canada, and the US, we developed scenarios for amending the Midwestern US landscape with milkweed. Scenarios for milkweed restoration were developed for protected area grasslands, Conservation Reserve Program land, powerline, rail and roadside rights of way, urban/suburban lands, and land in agricultural production. Agricultural land was further divided into productive and marginal cropland. We elicited expert opinion as to the biological potential (in stems per acre) for lands in these individual sectors to support milkweed restoration and the likely adoption (probability) of management practices necessary for affecting restoration. Sixteen of 218 scenarios we developed for restoring milkweed to the Midwestern US were at levels (>1.3 billion new stems) necessary to reach the monarch population goal. One of these scenarios would convert all marginal agriculture to conserved status. The other 15 scenarios converted half of marginal agriculture (730 million stems), with remaining stems contributed by other societal sectors. Scenarios without substantive agricultural participation were insufficient for attaining the population goal. Agricultural lands are essential to reaching restoration targets because they occupy 77% of all potential monarch habitat. Barring fundamental changes to policy, innovative application of economic tools such as habitat exchanges may provide sufficient resources to tip the balance of the agro-ecological landscape toward a setting conducive to both robust agricultural production and reduced imperilment of the migratory monarch butterfly. Thogmartin, W. E., R. Wiederholt, K. Oberhauser, R. G. Drum, J. E. Diffendorfer, S. Altizer, O. R. Taylor, J. Pleasants, D. Semmens, B. X. Semmens, R. Erickson, K. Libby, and L. López-Hoffman. 2017. Monarch butterfly population decline in North America: identifying the threatening processes. Royal Society Open Science 4:170760. DOI: 10.1098/rsos.170760 The monarch butterfly (Danaus plexippus) population in North America has sharply declined over the last two decades. Despite rising concern over the monarch butterfly’s status, no comprehensive study of the factors driving this decline has been conducted. Using partial least-squares regressions and time-series analysis, we investigated climatic and habitatrelated factors influencing monarch population size from 1993 to 2014. Potential threats included climatic factors, habitat loss (milkweed and overwinter forest), disease and agricultural insecticide use (neonicotinoids). While climatic factors, principally breeding season temperature, were important determinants of annual variation in abundance, our results indicated strong negative relationships between population size and habitat loss variables, principally glyphosate use, but also weaker negative effects from the loss of overwinter forest and breeding season use of neonicotinoids. Further declines in population size because of glyphosate application are not expected. Thus, if remaining threats to habitat are mitigated we expect climate-induced stochastic variation of the eastern migratory population of monarch butterfly around a relatively stationary population size. Pleasants, J. M., M. P. Zalucki, K. S. Oberhauser, L. P. Brower, O. R. Taylor, and W. E. Thogmartin. 2017. Interpreting surveys to estimate the size of the monarch butterfly population: pitfalls and prospects. PLoS ONE 12(7): e0181245. DOI: 10.1371/journal.pone.0181245 To assess the change in the size of the eastern North American monarch butterfly summer population, studies have used long-term data sets of counts of adult butterflies or eggs per milkweed stem. Despite the observed decline in the monarch population as measured at overwintering sites in Mexico, these studies found no decline in summer counts in the Midwest, the core of the summer breeding range, leading to a suggestion that the cause of the monarch population decline is not the loss of Midwest agricultural milkweeds but increased mortality during the fall migration. Using these counts to estimate population size, however, does not account for the shift of monarch activity from agricultural fields to non-agricultural sites over the past 20 years, as a result of the loss of agricultural milkweeds due to the near ubiquitous use of glyphosate herbicides. We present the counter-hypotheses that the proportion of the monarch population present in non-agricultural habitats, where counts are made, has increased and that counts reflect both population size and the proportion of the population observed. We use data on the historical change in the proportion of milkweeds, and thus monarch activity, in agricultural fields and non-agricultural habitats to show why using counts can produce misleading conclusions about population size. We then separate out the shifting proportion effect from the counts to estimate the population size and show that these corrected summer monarch counts show a decline over time and are correlated with the size of the overwintering population. In addition, we present evidence against the hypothesis of increased mortality during migration. The milkweed limitation hypothesis for monarch decline remains supported and conservation efforts focusing on adding milkweeds to the landscape in the summer breeding region have a sound scientific basis. Saunders, S. P., L. Ries, K. S. Oberhauser, W. E. Thogmartin, and E. F. Zipkin. 2018. Local and cross-seasonal effects of climate and land-use on breeding abundances of a migratory species. Ecography DOI: 10.1111/ecog.02719 Quantifying how climate and land use factors drive population dynamics at regional scales is complex because it depends on the extent of spatial and temporal synchrony among local populations, and the integration of population processes throughout a species’ annual cycle. We modeled weekly, site-specific summer abundance (1994–2013) of monarch butterflies Danaus plexippus at sites across Illinois, USA to assess relative associations of monarch abundance with climate and land use variables during the winter, spring, and summer stages of their annual cycle. We developed negative binomial regression models to estimate monarch abundance during recruitment in Illinois as a function of local climate, site-specific crop cover, and county-level herbicide (glyphosate) application. We also incorporated cross-seasonal covariates, including annual abundance of wintering monarchs in Mexico and climate conditions during spring migration and breeding in Texas, USA. We provide the first empirical evidence of a negative association between county-level glyphosate application and local abundance of adult monarchs, particularly in areas of concentrated agriculture. However, this association was only evident during the initial years of the adoption of herbicide-resistant crops (1994–2003). We also found that wetter and, to a lesser degree, cooler springs in Texas were associated with higher summer abundances in Illinois, as were relatively cool local summer temperatures in Illinois. Site-specific abundance of monarchs averaged approximately one fewer per site from 2004–2013 than during the previous decade, suggesting a recent decline in local abundance of monarch butterflies on their summer breeding grounds in Illinois. Our results demonstrate that seasonal climate and land use are associated with trends in adult monarch abundance, and our approach highlights the value of considering fine-resolution temporal fluctuations in population-level responses to environmental conditions when inferring the dynamics of migratory species. Semmens, D. J., J. E. Diffendorfer, K. J. Bagstad, R. Wiederholt, K. Oberhauser, L. Ries, B. X. Semmens, J. Goldstein, J. Loomis, W. E. Thogmartin, B. J. Mattsson, L. López-Hoffman. 2018. Quantifying ecosystem service flows at multiple scales across the range of a long-distance migratory species. Ecosystem Services DOI: 10.1016/j.ecoser.2017.12.002 Migratory species provide ecosystem goods and services throughout their annual cycles, often over long distances. Designing effective conservation solutions for migratory species requires knowledge of both species ecology and the socioeconomic context of their migrations. We present a framework built around the concept that migratory species act as carriers, delivering benefit flows to people throughout their annual cycle that are supported by the network of ecosystems upon which the species depend. We apply this framework to the monarch butterfly (Danaus plexippus) migration of eastern North America by calculating their spatial subsidies. Spatial subsidies are the net ecosystem service flows throughout a species’ range and a quantitative measure of the spatial mismatch between the locations where people receive most benefits and the locations of habitats that most support the species. Results indicate cultural benefits provided by monarchs in the U.S. and Canada are subsidized by migration and overwintering habitat in Mexico. At a finer scale, throughout the monarch range, habitat in rural landscapes subsidizes urban residents. Understanding the spatial distribution of benefits derived from and ecological support provided to monarchs and other migratory species offers a promising means of understanding the costs and benefits associated with conservation across jurisdictional borders.	2019-07-23T06:46:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3442641794681549, "perplexity": 8942.35934670837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195529007.88/warc/CC-MAIN-20190723064353-20190723090353-00309.warc.gz"}
https://zbmath.org/authors/?q=ai%3Apillai.k-c-sreedharan	# zbMATH — the first resource for mathematics ## Pillai, K. C. Sreedharan Compute Distance To: Author ID: pillai.k-c-sreedharan Published as: Pillai, K. C. S.; Pillai, K. C. Sreedharan; Pillai, K. C.; Sreedharan Pillai, K. C.; Pillai, K. C. Sridharan External Links: MGP · Wikidata · GND · MacTutor Documents Indexed: 80 Publications since 1943, including 4 Books Biographic References: 1 Publication all top 5 #### Co-Authors 24 single-authored 8 Nagarsenker, Brahmanand N. 4 Jouris, Gary M. 4 Young, Dennis L. 3 Gupta, Arjun Kumar 3 Hsu, Yu-Sheng 3 Li, Hung C. 3 Saweris, Nashat B. 2 Chang, Tseng-Chung 2 Chu, S. Sylvia 2 Gupta, Shanti Swarup 2 Singh, Anita Kumari 2 Sudjana 1 Bantegui, Celia G. 1 Buenaventura, Angeles R. 1 Dotson, C. O. 1 Flury, Bernhard N. 1 Mathai, Arakaparampli Mathai 1 Mijares, Tito A. 1 Ramachandran, K. V. 1 Sabri Al-Ani 1 Samson, Pablo jun. 1 Shen, S. Sylvia 1 Sreedharan, K. C. 1 Steck, George P. 1 Tienzo, Benjamin P. all top 5 #### Serials 18 Annals of Mathematical Statistics 15 Biometrika 13 Annals of the Institute of Statistical Mathematics 4 Journal of Multivariate Analysis 4 Sankhyā. Series B. Methodological 3 The Annals of Statistics 3 Communications in Statistics 3 Sankhyā 2 The Canadian Journal of Statistics 2 Journal of Statistical Planning and Inference 2 Communications in Statistics. Theory and Methods 1 Journal of the American Statistical Association 1 Revista Técnica de la Facultad de Ingenieria 1 Proceedings of the Indian Academy of Sciences #### Fields 45 Statistics (62-XX) 3 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) #### Citations contained in zbMATH Open 69 Publications have been cited 433 times in 235 Documents Cited by Year Some new test criteria in multivariate analysis. Zbl 0064.13801 Pillai, K. C. S. 1955 On the exact distribution of Wilks’s criterion. Zbl 0181.46202 Pillai, K. C.; Gupta, A. K. 1969 The distribution of the sphericity test criterion. Zbl 0258.62035 Nagarsenker, B. N.; Pillai, K. C. S. 1973 On linear functions of ordered correlated normal random variables. Zbl 0166.15202 Gupta, Shanti S.; Pillai, K. C. Sridharan 1965 On the non-central distributions of two test criteria in multivariate analysis of variance. Zbl 0155.27102 Khatri, C. G.; Pillai, K. C. S. 1968 On the distributions of the ratios of the roots of a covariance matrix and Wilk’s criterion for tests of three hypotheses. Zbl 0193.16102 Pillai, K. C. S.; Al-Ani, S.; Jouris, G. M. 1969 On the distribution of the largest or the smallest root of a matrix in multivariate analysis. Zbl 0070.37602 Pillai, K. C. S. 1956 Asymptotic expansions for the distributions of characteristic roots when the parameter matrix has several multiple roots. Zbl 0363.62042 Chattopadhyay, A. K.; Pillai, K. C. S. 1973 On the distribution of the sphericity test criterion in classical and complex normal populations having unknown covariance matrices. Zbl 0218.62051 Pillai, K. C. S.; Nagarsenker, B. N. 1971 Some results useful in multivariate analysis. Zbl 0073.13701 Pillai, K. C. S. 1956 Upper percentage points of the largest root of a matrix in multivariate analysis. Zbl 0149.15803 Pillai, K. C. S. 1967 On the distribution of the largest characteristic root of a matrix in multivariate analysis. Zbl 0203.21203 Pillai, K. C. S. 1965 Some distribution problems in the multivariate complex Gaussian case. Zbl 0218.62050 Pillai, K. C. S.; Jouris, G. M. 1971 Asymptotic expansions for distributions of the roots of two matrices from classical and complex Gaussian populations. Zbl 0211.51001 Li, H. C.; Pillai, K. C. S.; Chang, Tseng C. 1970 On the moments of elementary symmetric functions of the roots of two matrices. Zbl 0223.62063 Pillai, K. C. Sreedharan; Jouris, Gary M. 1969 On the distribution of the ratio of the $$i$$-th observation in an ordered sample from a normal population to an independent estimate of the standard deviation. Zbl 0056.37701 Pillai, K. C. S.; Ramachandran, K. V. 1954 Further results on the trace of a noncentral Wishart matrix. Zbl 0521.62042 Mathai, A. M.; Pillai, K. C. S. 1982 Exact robustness studies of tests of two multivariate hypotheses based on four criteria and their distribution problems under violations. Zbl 0342.62032 Pillai, K. C. S.; Sudjana 1975 Distributions of characteristic roots in multivariate analysis. part II. Non-null distributions. Zbl 0378.62056 Pillai, K. C. S. 1977 Distribution of the likelihood ratio criterion for testing a hypothesis specifying a covariance matrix. Zbl 0261.62039 Nagarsenker, B. N.; Pillai, K. C. S. 1973 Some results on the non-central multivariate beta distribution and moments of traces of two matrices. Zbl 0133.42503 Khatri, C. G.; Pillai, K. C. S. 1965 Power comparisons of two-sided tests of equality of two covariance matrices based on six criteria. Zbl 0447.62054 Chu, S. Sylvia; Pillai, K. C. S. 1979 Distributions of characteristic roots in multivariate analysis. Part 1: Null distributions. Zbl 0378.62055 Pillai, K. C. S. 1976 On the distribution of the largest root of a matrix in multivariate analysis. Zbl 0171.17201 Pillai, K. C. S. 1967 Maximization of an integral of a matrix function and asymptotic expansions of distributions of latent roots of two matrices. Zbl 0345.62039 Chattopadhyay, A. K.; Pillai, K. C. S.; Li, Hung C. 1976 On the moments of elementary symmetric functions of the roots of two matrices. Zbl 0129.11605 Pillai, K. C. S. 1964 Power comparisons of tests of equality two covariance matrices based on individual characteristic roots. Zbl 0195.19905 Sreedharan Pillai, K. C.; Sabri Al-Ani 1970 On the exact distribution of Hotelling’s generalized $$T_ 0^ 2$$. Zbl 0218.62052 Pillai, K. C. S.; Young, D. L. 1971 On the moment generating function of Pillai’s $$V^{(s)}$$ criterion. Zbl 0244.62041 Pillai, K. C. Sreedharan 1968 Asymptotic formulae for the distributions of some criteria for tests of equality of covariance matrices. Zbl 0255.62046 Chattopadhyay, A. K.; Pillai, K. C. S. 1971 On the distribution of Hotelling’s trace and power comparisons. Zbl 0281.62051 Pillai, K. C. S.; Sudjana 1974 The distribution of the characteristic roots of $$S_1S^{-1}_2$$ under violations. Zbl 0312.62040 Pillai, K. C. S. 1975 The distribution of the characteristic roots of $$S_ 1 S_ 2^{-1}$$ under violations in the complex case and power comparisons of four tests. Zbl 0463.62046 Pillai, K. C. S.; Hsu, Yu-Sheng 1979 On the moments of elementary symmetric functions of the roots of two matrices and approximations to a distribution. Zbl 0165.21303 Khatri, C. G.; Pillai, K. C. S. 1968 On the distributions of a class of statistics in multivariate analysis. Zbl 0231.62068 Pillai, K. C. S.; Nagarsenker, B. N. 1972 Concise tables for statisticians. Zbl 0077.33404 Pillai, K. C. Sreedharan 1957 On elementary symmetric functions of the roots of two matrices in multivariate analysis. Zbl 0139.37507 Pillai, K. C. S. 1965 Exact robustness studies of the test of independence based on four multivariate criteria and their distribution problems under violations. Zbl 0453.62031 Pillai, K. C. S.; Hsu, Yu-Sheng 1979 An approximation to the C. D. F. of the largest root of a covariance matrix. Zbl 0379.62039 Pillai, K. C. S.; Chang, T. C. 1970 On the distribution of the largest of seven roots of a matrix in multivariate analysis. Zbl 0129.11604 Pillai, K. C. 1964 Percentage points of the largest characteristic root of the multivariate beta matrix. Zbl 0559.62040 Pillai, K. C. S.; Flury, Bernhard N. 1984 Power comparisons of tests of two multivariate hypotheses based on individual characteristic roots. Zbl 0179.23903 Pillai, K. C.; Sreedharan, K. C.; Dotson, C. O. 1969 On the moments of the trace of a matrix and approximations to its distribution. Zbl 0225.62070 Pillai, K. C. S.; Mijares, Tito A. 1959 Distribution of the likelihood ratio criterion for testing $$\Sigma=\Sigma_0$$, $$\mu =\mu_0$$. Zbl 0297.62032 Nagarsenker, B. N.; Pillai, K. C. S. 1974 Confidence interval for the correlation coefficient. Zbl 0063.06225 Pillai, K. C. S. 1946 On the distribution of the largest of six roots of a matrix in multivariate analysis. Zbl 0085.13717 Pillai, K. C. Sreedharan; Bantegui, Celia G. 1959 On Hotelling’s generalization of $$T^2$$. Zbl 0096.12404 Pillai, K. C. Sreedharan; Samson, Pablo jun. 1959 On the moments of traces of two matrices in multivariate analysis. Zbl 0161.38201 Khatri, C. G.; Pillai, K. C. S. 1967 Some complex variable transformations and exact power comparisons of two- sided tests of equality of two Hermitian covariance matrices. Zbl 0458.62046 Chu, S. Sylvia; Pillai, K. C. S. 1980 Asymptotic distribution of Hotelling’s trace for two unequal covariance matrices and robustness study of test of equality of mean vectors. Zbl 0367.62062 Pillai, K. C. S.; Saweris, Nashat B. 1977 The max trace-ratio test of the hypothesis $$H_0: \Sigma_1=\dots \Sigma_k$$ =$$\lambda \Sigma_0$$. Zbl 0252.62033 Pillai, K. C. S.; Young, Dennis L. 1973 An approximation to the distribution of the largest root of a complex Wishart matrix. Zbl 0262.62025 Pillai, K. C. S.; Young, D. L. 1971 On the non-central distribution of the second elementary symmetric function of the roots of a matrix. Zbl 0164.49602 Pillai, K. C. S.; Gupta, A. K. 1968 On the exact non-null distribution of Wilks’ L(VC) criterion and power studies. Zbl 0519.62043 Pillai, K. C. S.; Singh, Anita 1981 An approximation to the distribution of the largest root of a matrix in the complex Gaussian case. Zbl 0379.62040 Pillai, K. C. S.; Jouris, G. M. 1972 Asymptotic formulae for the percentiles and C.D.F. of Hotelling’s trace under violations. Zbl 0435.62020 Pillai, K. C.; Saweris, N. B. 1979 Asymptotic formulae for the c.d.f. of Hotelling’s trace and robustness studies for three tests of hypotheses under violations. Zbl 0591.62047 Hsu, Yu-Sheng; Pillai, K. C. S. 1985 On the distribution of linear functions and ratios of linear functions of ordered correlated normal random variables with emphasis on range. Zbl 0192.26103 Gupta, S. S.; Sreedharan Pillai, K. C.; Steck, G. P. 1964 Non-central distributions of the largest latent roots of three matrices in multivariate analysis. Zbl 0214.46702 Pillai, K. C. S.; Sugiyama, T. 1969 Monotonicity of the power functions of some tests of hypotheses concerning multivariate complex normal distributions. Zbl 0223.62065 Pillai, K. C. S.; Li, Hung C. 1970 On the non-central distributions of the largest roots of two matrices in multivariate analysis. Zbl 0225.62142 Pillai, K. C. Sreedharan 1970 Distribution of the likelihood ratio criterion for testing $$\Sigma = \Sigma_0 , \mu = \mu_0$$. Zbl 0257.62037 Nagarsenker, B. N.; Pillai, K. C. S. 1973 Noncentral multivariate beta distribution and the moments of traces of some matrices. Zbl 0259.62049 Pillai, K. C. Sreedharan 1966 On the max U-ratio and likelihood ratio tests of equality of several covariance matrices. Zbl 0274.62035 Pillai, K. C. S.; Young, Dennis L. 1974 Formulae for the asymptotic distribution of Hotelling’s trace under violations. Zbl 0303.62046 Pillai, K. C. S.; Saweris, Nashat B. 1975 On the distributions of midrange and semi-range in samples from a normal population. Zbl 0036.09302 Pillai, K. C. S. 1950 Upper percentage points of the extreme studentized deviate from the sample mean. Zbl 0101.12703 Pillai, K. C. S. 1959 On the moments of the trace of a matrix and approximations to its non- central distribution. Zbl 0149.15804 Khatri, C. G.; Pillai, K. C. S. 1966 On the distribution of the second elementary symmetric function of the roots of a matrix. Zbl 0152.36304 Pillai, K. C.; Gupta, A. K. 1967 Asymptotic formulae for the c.d.f. of Hotelling’s trace and robustness studies for three tests of hypotheses under violations. Zbl 0591.62047 Hsu, Yu-Sheng; Pillai, K. C. S. 1985 Percentage points of the largest characteristic root of the multivariate beta matrix. Zbl 0559.62040 Pillai, K. C. S.; Flury, Bernhard N. 1984 Further results on the trace of a noncentral Wishart matrix. Zbl 0521.62042 Mathai, A. M.; Pillai, K. C. S. 1982 On the exact non-null distribution of Wilks’ L(VC) criterion and power studies. Zbl 0519.62043 Pillai, K. C. S.; Singh, Anita 1981 Some complex variable transformations and exact power comparisons of two- sided tests of equality of two Hermitian covariance matrices. Zbl 0458.62046 Chu, S. Sylvia; Pillai, K. C. S. 1980 Power comparisons of two-sided tests of equality of two covariance matrices based on six criteria. Zbl 0447.62054 Chu, S. Sylvia; Pillai, K. C. S. 1979 The distribution of the characteristic roots of $$S_ 1 S_ 2^{-1}$$ under violations in the complex case and power comparisons of four tests. Zbl 0463.62046 Pillai, K. C. S.; Hsu, Yu-Sheng 1979 Exact robustness studies of the test of independence based on four multivariate criteria and their distribution problems under violations. Zbl 0453.62031 Pillai, K. C. S.; Hsu, Yu-Sheng 1979 Asymptotic formulae for the percentiles and C.D.F. of Hotelling’s trace under violations. Zbl 0435.62020 Pillai, K. C.; Saweris, N. B. 1979 Distributions of characteristic roots in multivariate analysis. part II. Non-null distributions. Zbl 0378.62056 Pillai, K. C. S. 1977 Asymptotic distribution of Hotelling’s trace for two unequal covariance matrices and robustness study of test of equality of mean vectors. Zbl 0367.62062 Pillai, K. C. S.; Saweris, Nashat B. 1977 Distributions of characteristic roots in multivariate analysis. Part 1: Null distributions. Zbl 0378.62055 Pillai, K. C. S. 1976 Maximization of an integral of a matrix function and asymptotic expansions of distributions of latent roots of two matrices. Zbl 0345.62039 Chattopadhyay, A. K.; Pillai, K. C. S.; Li, Hung C. 1976 Exact robustness studies of tests of two multivariate hypotheses based on four criteria and their distribution problems under violations. Zbl 0342.62032 Pillai, K. C. S.; Sudjana 1975 The distribution of the characteristic roots of $$S_1S^{-1}_2$$ under violations. Zbl 0312.62040 Pillai, K. C. S. 1975 Formulae for the asymptotic distribution of Hotelling’s trace under violations. Zbl 0303.62046 Pillai, K. C. S.; Saweris, Nashat B. 1975 On the distribution of Hotelling’s trace and power comparisons. Zbl 0281.62051 Pillai, K. C. S.; Sudjana 1974 Distribution of the likelihood ratio criterion for testing $$\Sigma=\Sigma_0$$, $$\mu =\mu_0$$. Zbl 0297.62032 Nagarsenker, B. N.; Pillai, K. C. S. 1974 On the max U-ratio and likelihood ratio tests of equality of several covariance matrices. Zbl 0274.62035 Pillai, K. C. S.; Young, Dennis L. 1974 The distribution of the sphericity test criterion. Zbl 0258.62035 Nagarsenker, B. N.; Pillai, K. C. S. 1973 Asymptotic expansions for the distributions of characteristic roots when the parameter matrix has several multiple roots. Zbl 0363.62042 Chattopadhyay, A. K.; Pillai, K. C. S. 1973 Distribution of the likelihood ratio criterion for testing a hypothesis specifying a covariance matrix. Zbl 0261.62039 Nagarsenker, B. N.; Pillai, K. C. S. 1973 The max trace-ratio test of the hypothesis $$H_0: \Sigma_1=\dots \Sigma_k$$ =$$\lambda \Sigma_0$$. Zbl 0252.62033 Pillai, K. C. S.; Young, Dennis L. 1973 Distribution of the likelihood ratio criterion for testing $$\Sigma = \Sigma_0 , \mu = \mu_0$$. Zbl 0257.62037 Nagarsenker, B. N.; Pillai, K. C. S. 1973 On the distributions of a class of statistics in multivariate analysis. Zbl 0231.62068 Pillai, K. C. S.; Nagarsenker, B. N. 1972 An approximation to the distribution of the largest root of a matrix in the complex Gaussian case. Zbl 0379.62040 Pillai, K. C. S.; Jouris, G. M. 1972 On the distribution of the sphericity test criterion in classical and complex normal populations having unknown covariance matrices. Zbl 0218.62051 Pillai, K. C. S.; Nagarsenker, B. N. 1971 Some distribution problems in the multivariate complex Gaussian case. Zbl 0218.62050 Pillai, K. C. S.; Jouris, G. M. 1971 On the exact distribution of Hotelling’s generalized $$T_ 0^ 2$$. Zbl 0218.62052 Pillai, K. C. S.; Young, D. L. 1971 Asymptotic formulae for the distributions of some criteria for tests of equality of covariance matrices. Zbl 0255.62046 Chattopadhyay, A. K.; Pillai, K. C. S. 1971 An approximation to the distribution of the largest root of a complex Wishart matrix. Zbl 0262.62025 Pillai, K. C. S.; Young, D. L. 1971 Asymptotic expansions for distributions of the roots of two matrices from classical and complex Gaussian populations. Zbl 0211.51001 Li, H. C.; Pillai, K. C. S.; Chang, Tseng C. 1970 Power comparisons of tests of equality two covariance matrices based on individual characteristic roots. Zbl 0195.19905 Sreedharan Pillai, K. C.; Sabri Al-Ani 1970 An approximation to the C. D. F. of the largest root of a covariance matrix. Zbl 0379.62039 Pillai, K. C. S.; Chang, T. C. 1970 Monotonicity of the power functions of some tests of hypotheses concerning multivariate complex normal distributions. Zbl 0223.62065 Pillai, K. C. S.; Li, Hung C. 1970 On the non-central distributions of the largest roots of two matrices in multivariate analysis. Zbl 0225.62142 Pillai, K. C. Sreedharan 1970 On the exact distribution of Wilks’s criterion. Zbl 0181.46202 Pillai, K. C.; Gupta, A. K. 1969 On the distributions of the ratios of the roots of a covariance matrix and Wilk’s criterion for tests of three hypotheses. Zbl 0193.16102 Pillai, K. C. S.; Al-Ani, S.; Jouris, G. M. 1969 On the moments of elementary symmetric functions of the roots of two matrices. Zbl 0223.62063 Pillai, K. C. Sreedharan; Jouris, Gary M. 1969 Power comparisons of tests of two multivariate hypotheses based on individual characteristic roots. Zbl 0179.23903 Pillai, K. C.; Sreedharan, K. C.; Dotson, C. O. 1969 Non-central distributions of the largest latent roots of three matrices in multivariate analysis. Zbl 0214.46702 Pillai, K. C. S.; Sugiyama, T. 1969 On the non-central distributions of two test criteria in multivariate analysis of variance. Zbl 0155.27102 Khatri, C. G.; Pillai, K. C. S. 1968 On the moment generating function of Pillai’s $$V^{(s)}$$ criterion. Zbl 0244.62041 Pillai, K. C. Sreedharan 1968 On the moments of elementary symmetric functions of the roots of two matrices and approximations to a distribution. Zbl 0165.21303 Khatri, C. G.; Pillai, K. C. S. 1968 On the non-central distribution of the second elementary symmetric function of the roots of a matrix. Zbl 0164.49602 Pillai, K. C. S.; Gupta, A. K. 1968 Upper percentage points of the largest root of a matrix in multivariate analysis. Zbl 0149.15803 Pillai, K. C. S. 1967 On the distribution of the largest root of a matrix in multivariate analysis. Zbl 0171.17201 Pillai, K. C. S. 1967 On the moments of traces of two matrices in multivariate analysis. Zbl 0161.38201 Khatri, C. G.; Pillai, K. C. S. 1967 On the distribution of the second elementary symmetric function of the roots of a matrix. Zbl 0152.36304 Pillai, K. C.; Gupta, A. K. 1967 Noncentral multivariate beta distribution and the moments of traces of some matrices. Zbl 0259.62049 Pillai, K. C. Sreedharan 1966 On the moments of the trace of a matrix and approximations to its non- central distribution. Zbl 0149.15804 Khatri, C. G.; Pillai, K. C. S. 1966 On linear functions of ordered correlated normal random variables. Zbl 0166.15202 Gupta, Shanti S.; Pillai, K. C. Sridharan 1965 On the distribution of the largest characteristic root of a matrix in multivariate analysis. Zbl 0203.21203 Pillai, K. C. S. 1965 Some results on the non-central multivariate beta distribution and moments of traces of two matrices. Zbl 0133.42503 Khatri, C. G.; Pillai, K. C. S. 1965 On elementary symmetric functions of the roots of two matrices in multivariate analysis. Zbl 0139.37507 Pillai, K. C. S. 1965 On the moments of elementary symmetric functions of the roots of two matrices. Zbl 0129.11605 Pillai, K. C. S. 1964 On the distribution of the largest of seven roots of a matrix in multivariate analysis. Zbl 0129.11604 Pillai, K. C. 1964 On the distribution of linear functions and ratios of linear functions of ordered correlated normal random variables with emphasis on range. Zbl 0192.26103 Gupta, S. S.; Sreedharan Pillai, K. C.; Steck, G. P. 1964 On the moments of the trace of a matrix and approximations to its distribution. Zbl 0225.62070 Pillai, K. C. S.; Mijares, Tito A. 1959 On the distribution of the largest of six roots of a matrix in multivariate analysis. Zbl 0085.13717 Pillai, K. C. Sreedharan; Bantegui, Celia G. 1959 On Hotelling’s generalization of $$T^2$$. Zbl 0096.12404 Pillai, K. C. Sreedharan; Samson, Pablo jun. 1959 Upper percentage points of the extreme studentized deviate from the sample mean. Zbl 0101.12703 Pillai, K. C. S. 1959 Concise tables for statisticians. Zbl 0077.33404 Pillai, K. C. Sreedharan 1957 On the distribution of the largest or the smallest root of a matrix in multivariate analysis. Zbl 0070.37602 Pillai, K. C. S. 1956 Some results useful in multivariate analysis. Zbl 0073.13701 Pillai, K. C. S. 1956 Some new test criteria in multivariate analysis. Zbl 0064.13801 Pillai, K. C. S. 1955 On the distribution of the ratio of the $$i$$-th observation in an ordered sample from a normal population to an independent estimate of the standard deviation. Zbl 0056.37701 Pillai, K. C. S.; Ramachandran, K. V. 1954 On the distributions of midrange and semi-range in samples from a normal population. Zbl 0036.09302 Pillai, K. C. S. 1950 Confidence interval for the correlation coefficient. Zbl 0063.06225 Pillai, K. C. S. 1946 all top 5 #### Cited by 248 Authors 18 Pillai, K. C. Sreedharan 12 Jamalizadeh, Ahad 11 Gupta, Arjun Kumar 10 Balakrishnan, Narayanaswamy 7 Krishnaiah, Paruchuri Rama 7 Muirhead, Robb J. 7 Nagarsenker, Brahmanand N. 6 Chikuse, Yasuko 6 Davis, Arthur W. 6 Schott, James R. 5 Fujikoshi, Yasunori 5 Mathai, Arakaparampli Mathai 5 Provost, Serge B. 5 Saweris, Nashat B. 4 Kropf, Siegfried 4 Pham-Gia, Thu 3 Harrar, Solomon W. 3 Kshirsagar, Anant M. 3 Mahmoodian, Hamed 3 Nagar, Daya K. 3 Singh, Anita Kumari 3 Siotani, Minoru 3 Turkkan, Noyan 3 Waikar, Vasant B. 3 Zheng, Shurong 2 Adolf, Daniela 2 Arellano-Valle, Reinaldo Boris 2 Boente, Graciela 2 Butler, Ronald W. 2 Chu, S. Sylvia 2 Coelho, Carlos Agra 2 Constantine, A. G. 2 Fang, Biqi 2 Genç, Ali İ. 2 Ha, Hyungtae 2 Hirakawa, Fumiko 2 Hsu, Yu-Sheng 2 Javier, Walfredo R. 2 Kulp, Richard W. 2 Liu, Baisen 2 Loperfido, Nicola M. R. 2 Mardia, Kanti V. 2 Marques, Filipe J. 2 Muller, Keith E. 2 Nadarajah, Saralees 2 Nagao, Hisao 2 Nagel, Jan 2 Oja, Hannu 2 Orellana, Liliana 2 Phillips, Peter Charles Bonest 2 Richards, Donald St. P. 2 Solomon, Herbert 2 Sugiura, Nariaki 2 Taskinen, Sara 1 Al-Mouel, Abdul-Hussein Saber 1 Amiri, Mehdi 1 Anderson, Theodore Wilbur jun. 1 Arbia, Giuseppe 1 Arnold, Barry Charles 1 Baecke, Sebastian 1 Bai, Zhi-Dong 1 Bansal, Naveen K. 1 Bao, Shaokun 1 Baringhaus, Ludwig 1 Basser, Peter J. 1 Bathke, Arne C. 1 Berger, Martijn P. F. 1 Bernarding, Johannes 1 Bhandary, Madhusudan 1 Bhargava, Anil K. 1 Bhargava, R. P. 1 Bingham, Christopher 1 Bock, Mary Ellen 1 Boik, Robert J. 1 Bolivar-Cime, Addy 1 Bretz, Frank 1 Bristol, David R. 1 Canale, Antonio 1 Carter, Edward M. 1 Chang, Tseng-Chung 1 Chiani, Marco 1 Chmielewski, M. A. 1 Cho, Jin Seo 1 Chou, Charissa 1 Chou, Rouh-Jane 1 Choudhury, Kingshuk Roy 1 Critchley, Frank 1 de Leon, Alexander R. 1 de Waal, Daan J. 1 Dette, Holger 1 Deutsch, Stuart Jay 1 Di Nardo, Elvira 1 Díaz-García, José Antonio 1 Ding, Guo-Chun 1 Dinh Ngoc Thanh 1 Dotson, C. O. 1 Duong Thanh Phong 1 Ferré, Louis 1 Fine, Jason Peter 1 Flury, Bernard D. ...and 148 more Authors all top 5 #### Cited in 46 Serials 49 Journal of Multivariate Analysis 42 Annals of the Institute of Statistical Mathematics 23 Communications in Statistics. Theory and Methods 14 Journal of Statistical Planning and Inference 13 Communications in Statistics. Simulation and Computation 13 Computational Statistics and Data Analysis 8 Journal of Statistical Computation and Simulation 7 Statistics & Probability Letters 7 American Journal of Mathematical and Management Sciences 4 Statistics 3 Metrika 3 Linear Algebra and its Applications 3 Test 3 Statistical Methodology 2 The Canadian Journal of Statistics 2 The Annals of Statistics 2 Biometrical Journal 2 Journal of Econometrics 2 Metron 2 Journal of Information & Optimization Sciences 2 Statistical Methods and Applications 2 The Annals of Applied Statistics 1 Psychometrika 1 Scandinavian Journal of Statistics 1 Theory of Probability and its Applications 1 Aplikace Matematiky 1 Archiv der Mathematik 1 Kybernetika 1 Journal of Time Series Analysis 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Applied Mathematics. Series B (English Edition) 1 Statistical Papers 1 Monte Carlo Methods and Applications 1 Revista Matemática Complutense 1 Brazilian Journal of Probability and Statistics 1 Unternehmensforschung 1 Journal of Statistical Theory and Practice 1 Electronic Journal of Statistics 1 SIAM Journal on Imaging Sciences 1 Journal of the Italian Statistical Society 1 Chilean Journal of Statistics 1 Statistics and Computing 1 Dependence Modeling all top 5 #### Cited in 17 Fields 221 Statistics (62-XX) 22 Probability theory and stochastic processes (60-XX) 21 Special functions (33-XX) 20 Numerical analysis (65-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 5 Approximations and expansions (41-XX) 4 Combinatorics (05-XX) 3 Integral transforms, operational calculus (44-XX) 3 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-08-05T14:26:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6793873906135559, "perplexity": 4329.616189395923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155925.8/warc/CC-MAIN-20210805130514-20210805160514-00506.warc.gz"}
https://pavpanchekha.com/blog/crossbot-stan.html	## By Pavel Panchekha ### 28 October 2018 Share under CC-BY-SA. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. # Crossword Science with Stan One of the biggest Slack channels at UW is called #minicrossword: it is a channel for fans of the NYT Minicrossword to post their times. Times are recorded by a Slack bot that Max wrote, so that we can crown a daily winner, improve over time, or try to beat our nemeses. But one scary truth is that some people solve crosswords better than others; so some people win almost every day while others are nearly always at the bottom of the standings. I wanted to fix this, and thought it would be neat to do that by predicting people's times for each crossword, and then congratulating people who do much better than predicted. If the predictions are good, your innate skill at crossword won't affect your place in the rankings much. ## Modeling the Crossword data I started by downloading all of the times anyone had ever posted in the channel; in total, there were about eight thousand submissions, covering almost 500 crosswords. Since each submission was defined by a player and a date, I figured that the simplest model would have a per-crossword difficulty and a per-player skill, and the two of those would predict the time. Since I've been reading Andrew Gelman's blog for years, I figured this was a good opportunity to learn Stan, and in fact, Stan made it pretty easy to set up this model. I created three array's worth of data: one for the submitted times, one for the user that did the submitting, and one for the date they were submitting for. In Stan, you can write that like this: data { int<lower=0> Ss; // number of submissions int<lower=0> Us; // number of users int<lower=0> Ds; // number of dates real secs[Ss]; int<lower=1,upper=Us> uids[Ss]; int<lower=1,upper=Ds> dates[Ss]; } Note that the users and the dates are integers from 1 up to some bound. This is because Stan's only data types are integers and reals, and arrays of both.11 It also has matrices and vectors, but I don't know how they differ from arrays of reals. I make the users and dates count from 1 because I want them to be array indices, and in Stan arrays start at 1. Now, the great thing about Stan is that you can just freely define your model. Here, I wanted to have a per-user skill parameter and a per-date difficulty parameter: parameters { vector[Us] skill_effect; vector[Ds] difficulty_effect; ... } However, I also need a few other parameters to make this work. I wanted skills and difficulties to be normalized to 0, so to do that I'd need to subtract out the average time. And skills and difficulties would have to be drawn from some distribution—normal seemed like a good assumption—so I'd need to define parameters for that distribution: parameters { ... real<lower=0> mu; // average time real<lower=0> sigma; // size of errors in prediction real<lower=0> skill_dev; // st. dev. of skills real<lower=0> difficulty_dev; // st. dev. of difficulties } I already knew (from plotting the data) that crossword times are log-normal,22 The fastest time in the dataset is six seconds, and the slowest about nine minutes. so I combined all these parameters in a log-normal distribution: model { skill_effect ~ normal(0, skill_dev); difficulty_effect ~ normal(0, difficulty_dev); secs ~ lognormal(mu + skill_effect[uids] + difficulty_effect[dates], sigma); } Here, I've defined skills and effects to be normally distributed around 0, effectively normalizing them.33 Actually… it's complicated. If I hadn't included the mu parameter, something weird would have happened, and skill and difficulty would not have been normalized. The times are defined to be log-normally distributed, and the skill and difficulty apply additively to log-seconds. The secs line can be tricky to read, but that's because of Stan's vector syntax. If the thing on the left of the twiddle is a vector (or an array, or whatever), then everything on right that shares an index space can have its indices left off. It makes for pretty code. Given this model, Stan can learn the difficulty and skill parameters in a couple of minutes. I used PyStan as the driver: sm = pystan.StanModel(file="crossbot.stan") fm = sm.sampling(data=munge_data(*data), iter=1000, chains=4) Note by the way that I know little about statistics, so the 1000 iterations and the 4 chains were chosen pretty randomly. But the $$\^r$$ values all came out to 1.0, so I think that means everything is fine.44 Is it? This initial version of the model successfully made reasonable choices both for easiest and hardest days55 25 May 2018 was the easiest day and 12 September 2017 was the hardest. I looked them up and they in fact were crosswords I remembered as particularly easy and hard. and strongest and weakest players. One refinement I quickly added was to special-case Saturdays. Saturday mini-crosswords are larger than on other days (7×7 instead of 5×5) and so take longer. To do so, I computed the day of the week for each date, and added it as a new piece of data: data { int<lower=1,upper=7> dows[Ss]; } I then create an array of booleans for whether or not it is Saturday: transformed data { int<lower=0,upper=1> is_sat[Ss]; for (j in 1:Ss) is_sat[j] = (dows[j] == 7 ? 1 : 0); } Then there's an additional parameter which defines how much harder Saturday is than other days. Actually, at first I created an array of seven effects, one for each day of the weak, in case mini-crosswords get progressively harder throughout the week, but I found that the effects for every day but Saturday were indistinguishable, so I stripped that out. parameters { real sat_effect; } model { secs ~ lognormal(... + sat_effect to_vector(is_sat), sigma); } Here, the to_vector call converts the array of booleans into a vector that can be multiplied by the scalar sat_effect and added to the other vectors. Note, by the way, that since we're adding sat_effect to the parameter of a log-normal distribution, what we're really saying is that log-seconds increase by sat_effect; in other words, Saturdays have a multiplicative effect on times. I checked a few users with a lot of times and the Saturday multiplier seemed pretty close for them, so I went with this model. Saturdays, it turns out, take roughly twice as long as other days. ## Results It turns out that it's pretty easy to model large, relatively clean datasets like the crossword times data in Stan, and the results yield a pretty nice ranking of every crossword submitter, by skill: I know you can't see the user names there, but it accords quite well with my own estimates of how good various users are. I've also done a bit of validation, where I take a pair of users and compute how many times one has been faster than the other, out of all the times they've done the same crossword. You can compare that number to the difference in their skills, and the results are quite close most of the time. I'm excited to start using the model to congratulate people on doing well: I've been doing it manually for a few days now, and once a port to Django is complete I'll add it into the Slack bot source code. So far, it really does seem to call out users who do well. In the future, I also hope to improve the model. In particular, this model assumes skill is static and unchanging. I want to see how to add improvement over time. 1 It also has matrices and vectors, but I don't know how they differ from arrays of reals. 2 The fastest time in the dataset is six seconds, and the slowest about nine minutes. 3 Actually… it's complicated. If I hadn't included the mu parameter, something weird would have happened, and skill and difficulty would not have been normalized. 4 Is it? 5 25 May 2018 was the easiest day and 12 September 2017 was the hardest. I looked them up and they in fact were crosswords I remembered as particularly easy and hard.	2018-12-11T13:13:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6285426020622253, "perplexity": 1336.4236355382602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823621.10/warc/CC-MAIN-20181211125831-20181211151331-00450.warc.gz"}
https://aferro.dynu.net/research_engineering/face_segmentation/	# Robust Face Segmentation ###### PUBLISHED ON NOV 28, 2020 — CATEGORIES: utilities Please note that the system described in this post is a fusion of 2 preexisting Deep Learning systems. For several reasons this post does not provide the actual code, but the given descriptions, references and discussion should provide enough information to get started. ## Motivation Whenever collecting a dataset with human faces, chances are that these need to be blurred out. This can be e.g. for the sake of anonymization, or to analyze the information that facial expressions provide. Either case, face segmentation (i.e. detecting the pixels that belong to a face) can be an extremely time-consuming task, if manually done. Luckily, nowadays this issue is almost entirely removed thanks to Deep Learning. In fact, looking at existing open-source solutions (October 2020), It seems that the field has advanced to more complex scenarios like face parsing (i.e. segmentation of the different facial regions). Furthermore, models are not only able to discriminate but also to generate photorealistic faces, the most notable example being StyleGANs (see https://thispersondoesnotexist.com/). ## Setup Among the few open-source solutions tested, the following one proved to be the most reliable and robust: Deep Face Segmentation in Extremely Hard Conditions (many thanks to the authors Yuval Nirkin et al). The corresponding paper, On Face Segmentation, Face Swapping and Face Perception can be found online, and also hosted here. Here is a small teaser from the paper (Figure 1): can you recognize who is that? Given a close-up, well iluminated image of a face, the system performed quite well against many forms of occlusion.The image at the beginning of this post (from the COCO dataset) is an example of such an ideal output. But there were still 2 technicalities to address: • Detection of the faces in a broad and potentially complex context • Segmentation of the faces at different (smaller) scales The first one can be addressed robustly if we first look for human keypoints, and then filter the ones related to the head. Note that, if the model is able to detect any noses, eyes and/or ears, the chances of missing a face (even sideways or slightly from the back) are pretty low. Luckily, I had been doing quite some work on Human Keypoint Estimation (see e.g. here) and had already a state-of-the-art HigherHRnet up and running: The second issue is a little trickier. In our setup, the distance between the person and the camera was fixed, so fixing the size of the bounding boxes ended up providing quite robust results. For variable scales, a naive implementation discussed below is to infer the size of the head by the distances between keypoints, as follows: 1. Perform keypoint estimation and grouping 2. For each person, keep all nose, eye and ear keypoints above a confidence threshold $t$. 3. Center the bounding box on the average of all head keypoints 4. Assuming a square bounding box, measure the maximal pixel distance $d$ between any 2 head keypoints. Multiply this by a factor to obtain the side length of the box. As you may see, this is not robust against occlusions: If we only detect a single keypoint (e.g. the nose), the length of the box cannot be determined, and more refined approaches (like e.g. head detectors) are needed. This is a problem inherent to using keypoint estimation. ## Brief Experiment To illustrate the performance, the system is run below on the COCO 2017 validation dataset, presenting different kinds of scales, occlusions, contexts and faces. After running the keypoint estimation, segmentations were extracted using a bounding-box radius of 3 times the max distance between the found head keypoints (or alternatively at least 20 pixels radius). The images in the bounding boxes were resized to (400, 400) pixels and centered around the following RGB value: (104.00698793,116.66876762,122.67891434) before passing them to the face segmentation network. The value was picked from the original code and left unchanged. ## Qualitative Discussion As already mentioned, due to the particularities of the face segmentation model, the system is very sensitive to the bounding box size. The following images illustrate various out-of-scale segmentations: Also, segmentation seems to be sensitive to challenging lighting conditions and small resolutions (pixelized input). E.g. changing the normalization RGB vector impacted the performance notably. This may also be improved with better preprocessing. It remains to be quantified to what extent this could entail biases agains people of different genders, ages and skin colors: In general, there is potential for improvement if both the bounding-box size and preprocessing steps are refined. In our simple and well-lit scene, it turned out to work very well. In case you are considering doing something similar, the following images (also from COCO) provide an idea of the system’s performance on various scenes: Last but not least, we went for the best quality that can fit on a single 8GB GPU, regardless of runtime. The resulting performance is far from real-time (expect between 1 and 5 fps on an RTX2… series), but still much faster than manual. This was in any case good enough for our purpose of curating/preprocessing a mid-sized dataset. Deployment Bonus: Docker Image You may have noted that the face segmentation system runs on Caffe, and the human keypoint estimation system on PyTorch. Not a problem :) But if you ever tried to get PyCaffe running on your system, chances are that it wasn’t a smooth ride, mainly due to dependency and version compatibility issues. As for November 2020 (Ubuntu 20.04), the challenge was to triangulate the compilation of Caffe and the face recognition system together with OpenCV4 and the miniconda environment, while keeping compatibility with relatively recent CUDA and CUDNN versions. These kinds of problems can be greatly reduced by containerizing the application. For that sake, I’ve prepared a CUDA-compatible Docker image with the following facilities: • Ubuntu 18 • CUDA 11.1 • CUDNN 8 • OpenCV 4 • TensorFlow 2 • PyTorch 1.6 The corresponding container is rather big (around 20GB in memory), but likely worth it. Feel free to pull/build it or simply take a look at the Dockerfile at my Dockerhub profile! (Note that the container does not have the face segmentation system installed) Another problem that came up to mind is if both systems would fit on the same GPU. The HigherHRNet is quite large (takes around 7GB of the GPU). Luckily, the Caffe model did fit in the remainder space and the Python code was remarkably stable (no hiccups whatsoever). The images presented here are derivations from the COCO dataset, released under a Creative Commons license. I do not own the copyrights. Please see here for more details.	2022-09-25T00:53:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3883478343486786, "perplexity": 1796.3421282709123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334332.96/warc/CC-MAIN-20220925004536-20220925034536-00630.warc.gz"}
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2019.07.003	• • ### 中国短期资本外流规模再估算及其影响因素分析 • 出版日期:2019-07-25 发布日期:2019-07-29 ### Re-estimation of China’s Short term Capital Outflow Scale and Analysis of Influencing Factors Li Xin & Tan Ying • Online:2019-07-25 Published:2019-07-29 Abstract: By comparing the accounting calibers related to capital outflow, this paper chooses the indirect method combined with interest gap adjustment method to estimate the scale of China’s capital outflow from 1982 to 2016. The result shows that since the financial crisis, China’s capital outflow has increased year by year, and has shown a faster expanding trend in recent years. By using a non-restrictive VAR model and analysis framework including structural and cyclical “push” factors and “pull” factors that reflect capital outflows, this article finds that from the financial crisis to 2013 before the Fed monetary cyclical reversion, the main driving factors are domestic “push” factors such as the expectation of RMB depreciation and the cyclical adjustment of the domestic economy. Since 2014, China’s capital outflow has further intensified mainly due to domestic and international “pull” or “push” factors such as the acceleration of the US economic recovery and the adjustment of the domestic real estate market. Among them, the “pull” factor is the main cause. In the context of accelerated capital outflows, China needs to be more prudential in financial liberalization.	2023-01-29T13:07:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1750394105911255, "perplexity": 5265.194365516104}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499713.50/warc/CC-MAIN-20230129112153-20230129142153-00376.warc.gz"}
https://par.nsf.gov/biblio/10369918-chip-spin-orbit-locking-quantum-emitters-materials-chiral-emission	On-chip spin-orbit locking of quantum emitters in 2D materials for chiral emission Light carries both spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used as potential degrees of freedom for quantum information processing. Quantum emitters are ideal candidates towards on-chip control and manipulation of the full SAM–OAM state space. Here, we show coupling of a spin-polarized quantum emitter in a monolayer$WSe2$with the whispering gallery mode of a$Si3N4$ring resonator. The cavity mode carries a transverse SAM of$σ<#comment/>=±<#comment/>1$in the evanescent regions, with the sign depending on the orbital power flow direction of the light. By tailoring the cavity–emitter interaction, we couple the intrinsic spin state of the quantum emitter to the SAM and propagation direction of the cavity mode, which leads to spin–orbit locking and subsequent chiral single-photon emission. Furthermore, by engineering how light is scattered from the WGM, we create a high-order Bessel beam which opens up the possibility to generate optical vortex carrying OAM states. Authors: ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10369918 Journal Name: Optica Volume: 9 Issue: 8 Page Range or eLocation-ID: Article No. 953 ISSN: 2334-2536 Publisher: Optical Society of America 1. We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intra-group power coupling among linearly polarized (LP) modes in a graded-index few-mode fiber (GI FMF). Generally, in this fiber, the coupling between degenerate modes inside a modal group tends to be stronger than between modes belonging to different groups. In our approach, the coupling inside the$LP11$group can be represented by a combination of orbital-angular-momentum (OAM) modes, such that reducing power coupling in OAM set tends to indicate the capability to reduce the coupling inside the$LP11$group. We employ two output OAM modes$l=+1$and$l=−<#comment/>1$as resultant linear combinations of degenerate$LP11a$and$LP11b$modes inside the$LP11$group of a$∼<#comment/>0.6-km$GI FMF. The power coupling is mitigated by shaping the amplitude and phase of the distorted OAM modes. Each OAM mode carries an independent 20-, 40-, or 100-Gbit/s quadrature-phase-shift-keying data stream. We measure the transmission matrix (TM) in the OAM basis within$LP11$group, which is a subset of the full LP TMmore » 2. We experimentally demonstrate simultaneous turbulence mitigation and channel demultiplexing in a 200 Gbit/s orbital-angular-momentum (OAM) multiplexed link by adaptive wavefront shaping and diffusing (WSD) the light beams. Different realizations of two emulated turbulence strengths (the Fried parameter$r0=0.4,1.0mm$) are mitigated. The experimental results show the following. (1) Crosstalk between OAM$l=+1$and$l=−<#comment/>1$modes can be reduced by$><#comment/>10.0$and$><#comment/>5.8dB$, respectively, under the weaker turbulence ($r0=1.0mm$); crosstalk is further improved by$><#comment/>17.7$and$><#comment/>19.4dB$, respectively, under most realizations in the stronger turbulence ($r0=0.4mm$). (2) The optical signal-to-noise ratio penalties for the bit error rate performance are measured to be$∼<#comment/>0.7$and$∼<#comment/>1.6dB$under weaker turbulence, while measured to be$∼<#comment/>3.2$and$∼<#comment/>1.8dB$under stronger turbulence for OAM$l=+1$and$l=−<#comment/>1$mode, respectively. 3. We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the$k$th input carrying a phase delay of$(k−<#comment/>1)Δ<#comment/>φ<#comment/>$. The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay$Δ<#comment/>φ<#comment/>$; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., $l={−<#comment/>1},{−<#comment/>1,+1},{−<#comment/>1,0,+1}$, or${−<#comment/>2,−<#comment/>1,+1,+2}$); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own$Δ<#comment/>φ<#comment/>$value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% formore »), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for$l={−<#comment/>1}$to 122 nm for$l={−<#comment/>2,−<#comment/>1,+1,+2}$), and (c) increased crosstalk within the C-band (from$−<#comment/>23.7$to$−<#comment/>13.2dB$when the tunable range increases from 2 to 4). 4. Electro-optic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the near-infrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electro-optic sampling was shown to reach quantum-level sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an on-chip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the near-infrared and a confinement of the terahertz wave to a volume of$VTHz∼<#comment/>10−<#comment/>9(λ<#comment/>THz/2)3$in combination with ultraperformant organic molecules ($r33=170pm/V$) and accomplish a record-high single-photon electro-optic coupling rate of, 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The single-photon cooperativity is$C0=1.6×<#comment/>10−<#comment/>8$, and the multiphoton cooperativity is$C=0.002$at room temperature. We show$><#comment/>70dB$dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and near-infrared quantum bits. 5. In this Letter, the electron-blocking-layer (EBL)-free AlGaN ultraviolet (UV) light-emitting diodes (LEDs) using a strip-in-a-barrier structure have been proposed. The quantum barrier (QB) structures are systematically engineered by integrating a 1 nm intrinsic$AlxGa(1−<#comment/>x)N$strip into the middle of QBs. The resulted structures exhibit significantly reduced electron leakage and improved hole injection into the active region, thus generating higher carrier radiative recombination. Our study shows that the proposed structure improves radiative recombination by$∼<#comment/>220%<#comment/>$, reduces electron leakage by$∼<#comment/>11$times, and enhances optical power by$∼<#comment/>225%<#comment/>$at 60 mA current injection compared to a conventional AlGaN EBL LED structure. Moreover, the EBL-free strip-in-a-barrier UV LED records the maximum internal quantum efficiency (IQE) of$∼<#comment/>61.5%<#comment/>$which is$∼<#comment/>72%<#comment/>$higher, and IQE droop is$∼<#comment/>12.4%<#comment/>$, which is$∼<#comment/>333%<#comment/>$less compared to the conventional AlGaN EBL LED structure at$∼<#comment/>284.5nm$wavelength. Hence, the proposed EBL-free AlGaN LED is the potential solution to enhance the optical power and produce highly efficient UV emitters.	2023-02-05T20:16:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 57, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6030210256576538, "perplexity": 3610.264134137228}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500288.69/warc/CC-MAIN-20230205193202-20230205223202-00622.warc.gz"}
https://dlmf.nist.gov/10.7	# §10.7 Limiting Forms ## §10.7(i) $z\to 0$ When $\nu$ is fixed and $z\to 0$, 10.7.1 $\displaystyle J_{0}\left(z\right)$ $\displaystyle\to 1,$ $\displaystyle Y_{0}\left(z\right)$ $\displaystyle\sim(2/\pi)\ln z,$ 10.7.2 ${H^{(1)}_{0}}\left(z\right)\sim-{H^{(2)}_{0}}\left(z\right)\sim(2i/\pi)\ln z,$ 10.7.3 $J_{\nu}\left(z\right)\sim(\tfrac{1}{2}z)^{\nu}/\Gamma\left(\nu+1\right),$ $\nu\neq-1,-2,-3,\dots$, ⓘ Symbols: $J_{\NVar{\nu}}\left(\NVar{z}\right)$: Bessel function of the first kind, $\Gamma\left(\NVar{z}\right)$: gamma function, $\sim$: asymptotic equality, $z$: complex variable and $\nu$: complex parameter A&S Ref: 9.1.7 Referenced by: §10.7(i), §10.7(i) Permalink: http://dlmf.nist.gov/10.7.E3 Encodings: TeX, pMML, png See also: Annotations for 10.7(i), 10.7 and 10 10.7.4 $\displaystyle Y_{\nu}\left(z\right)$ $\displaystyle\sim-(1/\pi)\Gamma\left(\nu\right)(\tfrac{1}{2}z)^{-\nu},$ $\Re\nu>0$ or $\nu=-\tfrac{1}{2},-\tfrac{3}{2},-\tfrac{5}{2},\ldots$, 10.7.5 $\displaystyle Y_{-\nu}\left(z\right)$ $\displaystyle\sim-(1/\pi)\cos\left(\nu\pi\right)\Gamma\left(\nu\right)(\tfrac{% 1}{2}z)^{-\nu},$ $\Re\nu>0$, $\nu\neq\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},\ldots$, 10.7.6 $Y_{i\nu}\left(z\right)=\frac{i\operatorname{csch}\left(\nu\pi\right)}{\Gamma% \left(1-i\nu\right)}(\tfrac{1}{2}z)^{-i\nu}-\frac{i\coth\left(\nu\pi\right)}{% \Gamma\left(1+i\nu\right)}(\tfrac{1}{2}z)^{i\nu}+e^{\|\nu\operatorname{ph}z\|}o% \left(1\right),$ $\nu\in\mathbb{R}$ and $\nu\neq 0$. See also §10.24 when $z=x$ $(>0)$. 10.7.7 ${H^{(1)}_{\nu}}\left(z\right)\sim-{H^{(2)}_{\nu}}\left(z\right)\sim-(i/\pi)% \Gamma\left(\nu\right)(\tfrac{1}{2}z)^{-\nu},$ $\Re\nu>0$. For ${H^{(1)}_{-\nu}}\left(z\right)$ and ${H^{(2)}_{-\nu}}\left(z\right)$ when $\Re\nu>0$ combine (10.4.6) and (10.7.7). For ${H^{(1)}_{i\nu}}\left(z\right)$ and ${H^{(2)}_{i\nu}}\left(z\right)$ when $\nu\in\mathbb{R}$ and $\nu\neq 0$ combine (10.4.3), (10.7.3), and (10.7.6). ## §10.7(ii) $z\to\infty$ When $\nu$ is fixed and $z\to\infty$, 10.7.8 $\displaystyle J_{\nu}\left(z\right)$ $\displaystyle=\sqrt{2/(\pi z)}\left(\cos\left(z-\tfrac{1}{2}\nu\pi-\tfrac{1}{4% }\pi\right)+e^{\|\Im z\|}o\left(1\right)\right),$ $\displaystyle Y_{\nu}\left(z\right)$ $\displaystyle=\sqrt{2/(\pi z)}\left(\sin\left(z-\tfrac{1}{2}\nu\pi-\tfrac{1}{4% }\pi\right)+e^{\|\Im z\|}o\left(1\right)\right),$ $\|\operatorname{ph}z\|\leq\pi-\delta(<\pi)$. For the corresponding results for ${H^{(1)}_{\nu}}\left(z\right)$ and ${H^{(2)}_{\nu}}\left(z\right)$ see (10.2.5) and (10.2.6).	2018-05-25T01:32:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 109, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9495890736579895, "perplexity": 3362.689060949249}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866917.70/warc/CC-MAIN-20180525004413-20180525024413-00286.warc.gz"}
https://zbmath.org/authors/?q=rv%3A2321	## Heath-Brown, Roger Compute Distance To: Author ID: heath-brown.roger Published as: Heath-Brown, D. R.; Heath-Brown, Roger; Heath-Brown, David Rodney; Heath-Brown, D. Roger; Heath-Brown, D. more...less Homepage: https://www.maths.ox.ac.uk/people/roger.heath-brown External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef Documents Indexed: 185 Publications since 1974 5 Contributions as Editor · 8 Further Contributions Reviewing Activity: 724 Reviews Biographic References: 1 Publication Co-Authors: 48 Co-Authors with 60 Joint Publications 1,601 Co-Co-Authors all top 5 ### Co-Authors 128 single-authored 17 Browning, Timothy Daniel 6 Moroz, Boris Zelikovich Baruch ben Zelik 4 Pierce, Lillian B. 3 Iwaniec, Henryk 2 Banks, William David 2 Bui, Hung Manh 2 Conrey, John Brian 2 Dietmann, Rainer 2 Goldston, Daniel Alan 2 Jia, Chaohua 2 Konyagin, Sergeĭ Vladimirovich 2 Li, Xiannan 2 Manin, Yuriĭ Ivanovich 2 Shparlinski, Igor E. 1 Adleman, Leonard Max 1 Balasubramanian, Ramachandran 1 Colliot-Thélène, Jean-Louis 1 Davenport, Harold 1 Demeter, Ciprian 1 Dieulefait, Luis Victor 1 Evelyn, Cecil John Alvin 1 Faltings, Gerd 1 Ford, Kevin B. 1 Freeman, D. Eric 1 Friedlander, John Benjamin 1 Gallardo, Luis Henri 1 Garaev, Moubariz Z. 1 Ghosh, Amit 1 Gonek, Steven M. 1 Guth, Lawrence David 1 Halberstam, Heini 1 Hardy, Godfrey Harold 1 Huxley, Martin N. 1 Kaczorowski, Jerzy 1 Lioen, Walter M. 1 Macintyre, Angus John 1 Matiyasevich, Yuriĭ Vladimirovich 1 Michel, Philippe Gabriel 1 Micheli, Giacomo 1 Monsky, Paul 1 Patterson, Samuel James 1 Praeger, Cheryl Elisabeth 1 Richert, Hans-Egon 1 Salberger, Per 1 Schlage-Puchta, Jan-Christoph 1 Shalev, Aner 1 Silverman, Joseph Hillel 1 Skorobogatov, Alexei Nikolaïevitch 1 Starr, Jason Michael 1 te Riele, Herman 1 Testa, Damiano 1 Titchmarsh, Edward Charles 1 Tolev, Doychin I. 1 Tsang, Kai-Man 1 Vaughan, Robert C. 1 Wang, Hong 1 Wiles, Andrew John 1 Wilson, Pelham Mark Hedley 1 Wintenberger, Jean-Pierre 1 Wright, Edward Maitland all top 5 ### Serials 14 Acta Arithmetica 12 Journal of the London Mathematical Society. Second Series 12 Proceedings of the London Mathematical Society. Third Series 11 Journal für die Reine und Angewandte Mathematik 8 Inventiones Mathematicae 8 Mathematika 7 Bulletin of the London Mathematical Society 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 The Quarterly Journal of Mathematics. Oxford Second Series 5 Journal of Number Theory 4 Duke Mathematical Journal 3 Mathematische Annalen 3 Mathematische Zeitschrift 2 Israel Journal of Mathematics 2 Mathematics of Computation 2 Acta Mathematica 2 Canadian Journal of Mathematics 2 Compositio Mathematica 2 Functiones et Approximatio. Commentarii Mathematici 2 The Journal of the Indian Mathematical Society. New Series 2 Revista Matemática Iberoamericana 2 Forum Mathematicum 2 IMRN. International Mathematics Research Notices 2 Geometric and Functional Analysis. GAFA 2 Journal of Mathematical Sciences (New York) 2 The Quarterly Journal of Mathematics 2 Journal of the Institute of Mathematics of Jussieu 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Glasgow Mathematical Journal 1 Hardy-Ramanujan Journal 1 Analysis 1 Science in China. Series A 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Finite Fields and their Applications 1 The Asian Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 International Journal of Number Theory 1 Bonner Mathematische Schriften 1 Lecture Notes in Mathematics 1 London Mathematical Society Lecture Note Series 1 Proceedings of the Steklov Institute of Mathematics 1 Science China. Mathematics 1 Discrete Analysis 1 Cambridge Mathematical Library all top 5 ### Fields 191 Number theory (11-XX) 29 Algebraic geometry (14-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 2 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) ### Citations contained in zbMATH Open 166 Publications have been cited 2,312 times in 1,728 Documents Cited by Year The theory of the Riemann zeta-function. 2nd ed., rev. by D. R. Heath-Brown. Zbl 0601.10026 Titchmarsh, E. C. 1986 An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001 Hardy, G. H.; Wright, E. M. 2008 The Pjateckii-Sapiro prime number theorem. Zbl 0513.10042 Heath-Brown, D. R. 1983 The fourth power moment of the Riemann zeta function. Zbl 0403.10018 Heath-Brown, D. R. 1979 Artin’s conjecture for primitive roots. Zbl 0586.10025 Heath-Brown, D. R. 1986 The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044 Heath-Brown, D. R. 2002 Prime numbers in short intervals and a generalized Vaughan identity. Zbl 0478.10024 Heath-Brown, D. R. 1982 Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0739.11033 Heath-Brown, D. R. 1992 New bounds for Gauss sums derived from $$k$$th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052 Heath-Brown, D. R.; Konyagin, S. 2000 A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049 Heath-Brown, D. R. 1996 The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032 Heath-Brown, D. R. 1994 The twelfth power moment of the Riemann-function. Zbl 0394.10020 Heath-Brown, D. R. 1978 A mean value estimate for real character sums. Zbl 0828.11040 Heath-Brown, D. R. 1995 Lattice points in the sphere. Zbl 0929.11040 Heath-Brown, D. R. 1999 Integer sets containing no arithmetic progressions. Zbl 0589.10062 Heath-Brown, D. R. 1987 The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045 Heath-Brown, D. R. 1992 Fractional moments of the Riemann zeta-function. Zbl 0431.10024 Heath-Brown, D. R. 1981 The square sieve and consecutive square-free numbers. Zbl 0514.10038 Heath-Brown, D. R. 1984 Cubic forms in 10 variables. Zbl 0494.10012 Heath-Brown, D. R. 1983 Analytic methods for Diophantine equations and Diophantine inequalities. Edited and prepared by T. D. Browning. With a preface by R. C. Vaughan, D. R. Heath-Brown and D. E. Freeman. 2nd ed. Zbl 1125.11018 Davenport, Harold 2005 Hybrid bounds for Dirichlet L-functions. Zbl 0362.10035 Heath-Brown, D. R. 1978 Integers represented as a sum of primes and powers of two. Zbl 1097.11050 Heath-Brown, D. R.; Puchta, J.-C. 2002 The distribution of Kummer sums at prime arguments. Zbl 0412.10028 Heath-Brown, D. R.; Patterson, S. J. 1979 Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. Zbl 0549.10030 Balasubramanian, R.; Conrey, J. B.; Heath-Brown, D. R. 1985 The divisor function $$d_ 3(n)$$ in arithmetic progressions. Zbl 0549.10034 Heath-Brown, D. R. 1986 Hybrid bounds for Dirichlet L-functions. II. Zbl 0396.10030 Heath-Brown, D. R. 1980 Diophantine approximation with square-free numbers. Zbl 0539.10026 Heath-Brown, D. R. 1984 The number of primes in a short interval. Zbl 0646.10032 Heath-Brown, D. R. 1988 The size of Selmer groups for the congruent number problem. Zbl 0808.11041 Heath-Brown, D. R. 1993 Pair correlation for fractional parts of $$\alpha n^2$$. Zbl 1239.11081 Heath-Brown, D. R. 2010 Almost-primes in arithmetic progressions and short intervals. Zbl 0375.10027 Heath-Brown, D. R. 1978 Simple zeros of the Riemann zeta-function on the critical line. Zbl 0409.10027 Heath-Brown, D. R. 1979 On the difference between consecutive primes. Zbl 0424.10028 Heath-Brown, D. R.; Iwaniec, H. 1979 Cubic forms in 14 variables. Zbl 1135.11031 Heath-Brown, D. R. 2007 Primes represented by $$x^3+ 2y^3$$. Zbl 1007.11055 Heath-Brown, D. R. 2001 The average analytic rank of elliptic curves. Zbl 1063.11013 Heath-Brown, D. R. 2004 Counting rational points on algebraic varieties. Zbl 1098.14013 Browning, T. D.; Heath-Brown, D. R.; Salberger, P. 2006 The density of rational points on cubic surfaces. Zbl 0863.11021 Heath-Brown, D. R. 1997 The growth rate of the Dedekind zeta-function on the critical line. Zbl 0583.12011 Heath-Brown, D. R. 1988 Prime twins and Siegel zeros. Zbl 0517.10044 Heath-Brown, D. R. 1983 Gaps between primes, and the pair correlation of zeros of the zeta-function. Zbl 0414.10044 Heath-Brown, D. R. 1982 Weyl’s inequality, Hua’s inequality and Waring’s problem. Zbl 0619.10046 Heath-Brown, D. R. 1988 The divisor function at consecutive integers. Zbl 0529.10040 Heath-Brown, D. R. 1984 A new $$k$$th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110 Heath-Brown, D. R. 2017 Sign changes of $$E(T)$$, $$\Delta(x)$$, and $$P(x)$$. Zbl 0810.11046 Heath-Brown, D. R.; Tsang, K.-M. 1994 Counting rational points on hypersurfaces. Zbl 1079.11033 Browning, T. D.; Heath-Brown, D. R. 2005 An estimate for Heilbronn’s exponential sum. Zbl 0857.11041 Heath-Brown, D. R. 1996 The distribution of $$\alpha p$$ modulo one. Zbl 1023.11034 Heath-Brown, D. R.; Jia, Chaohua 2002 The fourth power mean of Dirichlet’s L-functions. Zbl 0479.10027 Heath-Brown, D. R. 1981 Forms in many variables and differing degrees. Zbl 1383.11039 Browning, Tim; Heath-Brown, Roger 2017 Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006 Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E. 2008 Counting rational points on algebraic varieties. Zbl 1152.11027 Heath-Brown, D. R. 2006 Rational solutions of certain equations involving norms. Zbl 1023.11033 Heath-Brown, Roger; Skorobogatov, Alexei 2002 Small solutions of quadratic congruences. Zbl 0581.10008 Heath-Brown, D. R. 1985 Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050 Heath-Brown, D. R.; Tolev, D. I. 2003 An asymptotic series for the mean value of Dirichlet $$L$$-functions. Zbl 0457.10020 Heath-Brown, D. R. 1981 The least square-free number in an arithmetic progression. Zbl 0493.10045 Heath-Brown, D. R. 1982 On the density of the zeros of the Dedekind zeta-function. Zbl 0325.12003 Heath-Brown, D. R. 1977 On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050 Heath-Brown, D. R.; Moroz, B. Z. 2004 Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042 Heath-Brown, D. R. 2000 Odd perfect numbers. Zbl 0805.11005 Heath-Brown, D. R. 1994 On the distribution of gaps between zeros of the zeta-function. Zbl 0557.10028 Conrey, J. B.; Ghosh, A.; Goldston, D.; Gonek, S. M.; Heath-Brown, D. R. 1985 The first case of Fermat’s last theorem. Zbl 0557.10034 Adleman, L. M.; Heath-Brown, D. R. 1985 On simple zeros of the Riemann zeta-function. Zbl 1291.11118 Bui, H. M.; Heath-Brown, D. R. 2013 Almost-prime $$k$$-tuples. Zbl 0886.11052 Heath-Brown, D. R. 1997 Burgess’s bounds for character sums. Zbl 1328.11088 Heath-Brown, D. R. 2013 Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031 Heath-Brown, D. R. 1993 Primes represented by binary cubic forms. Zbl 1030.11046 Heath-Brown, D. R.; Moroz, B. Z. 2002 The largest prime factor of $$X^3+2$$. Zbl 1023.11048 Heath-Brown, D. R. 2001 On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055 Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E. 2005 Siegel zeros and the least prime in an arithmetic progression. Zbl 0715.11049 Heath-Brown, D. R. 1990 Three primes and an almost-prime in arithmetic progression. Zbl 0425.10051 Heath-Brown, D. R. 1981 Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150 Heath-Brown, D. R. 2008 The mean value theorem for the Riemann zeta-function. Zbl 0387.10023 Heath-Brown, D. R. 1979 The differences between consecutive primes. Zbl 0387.10025 Heath-Brown, D. R. 1978 Zero density estimates for the Riemann zeta-function and Dirichlet L-functions. Zbl 0393.10043 Heath-Brown, D. R. 1979 Rational points on quartic hypersurfaces. Zbl 1169.11027 Browning, T. D.; Heath-Brown, D. R. 2009 Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233 Heath-Brown, David Rodney; Micheli, Giacomo 2019 The circle method and diagonal cubic forms. Zbl 0899.11051 Heath-Brown, D. R. 1998 The density of rational points on Cayley’s cubic surface. Zbl 1060.11038 Heath-Brown, D. R. 2003 A note on the differences between consecutive primes. Zbl 0514.10031 Heath-Brown, D. R.; Goldston, D. A. 1984 Zeros of $$p$$-adic forms. Zbl 1233.11039 Heath-Brown, D. R. 2010 Zeros of systems of $$\mathfrak p$$-adic quadratic forms. Zbl 1194.11047 Heath-Brown, D. R. 2010 Square-free values of $$n^2+1$$. Zbl 1312.11077 Heath-Brown, D. R. 2012 Burgess bounds for short mixed character sums. Zbl 1317.11083 Heath-Brown, D. R.; Pierce, L. B. 2015 The differences between consecutive primes. II. Zbl 0394.10021 Heath-Brown, D. R. 1979 The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015 Browning, T. D.; Heath-Brown, D. R.; Starr, J. M. 2006 The density of zeros of forms for which weak approximation fails. Zbl 0778.11017 Heath-Brown, D. R. 1992 The density of rational points on non-singular hypersurfaces. Zbl 0808.11042 Heath-Brown, D. R. 1994 Almost-primes in short intervals. Zbl 0461.10041 Halberstam, H.; Heath-Brown, D. R.; Richert, H.-E. 1981 Arithmetic applications of Kloosterman sums. Zbl 1173.11339 Heath-Brown, D. R. 2000 Quadratic polynomials represented by norm forms. Zbl 1264.14032 Browning, T. D.; Heath-Brown, D. R. 2012 Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121 Heath-Brown, D. R.; Pierce, L. B. 2017 Prime values of $$a^2 + p^4$$. Zbl 1405.11124 Heath-Brown, D. R.; Li, Xiannan 2017 The ternary Goldbach problem. Zbl 0599.10041 Heath-Brown, D. R. 1985 The differences between consecutive primes. III. Zbl 0407.10032 Heath-Brown, D. R. 1979 Rational points on intersections of cubic and quadric hypersurfaces. Zbl 1327.11043 Browning, T. D.; Dietmann, R.; Heath-Brown, D. R. 2015 Power-free values of polynomials. Zbl 1287.11114 Heath-Brown, D. R. 2013 A note on the Chevalley-Warning theorems. Zbl 1247.11089 Heath-Brown, D. R. 2011 Integral points on cubic hypersurfaces. Zbl 1244.11066 Browning, T. D.; Heath-Brown, D. R. 2009 The geometric sieve for quadrics. Zbl 1481.11035 Browning, Tim D.; Heath-Brown, Roger 2021 Small cap decouplings. With an appendix by D. R. Heath-Brown. Zbl 1454.42008 Demeter, Ciprian; Guth, Larry; Wang, Hong 2020 Density of rational points on a quadric bundle in $$\mathbb{P}^3 \times \mathbb{P}^3$$. Zbl 1477.11058 Browning, T. D.; Heath-Brown, D. R. 2020 Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233 Heath-Brown, David Rodney; Micheli, Giacomo 2019 Counting rational points on quadric surfaces. Zbl 1444.11142 Browning, T. D.; Heath-Brown, D. R. 2018 The differences between consecutive smooth numbers. Zbl 1446.11173 Heath-Brown, D. R. 2018 A new $$k$$th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110 Heath-Brown, D. R. 2017 Forms in many variables and differing degrees. Zbl 1383.11039 Browning, Tim; Heath-Brown, Roger 2017 Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121 Heath-Brown, D. R.; Pierce, L. B. 2017 Prime values of $$a^2 + p^4$$. Zbl 1405.11124 Heath-Brown, D. R.; Li, Xiannan 2017 Averages and moments associated to class numbers of imaginary quadratic fields. Zbl 1391.11151 Heath-Brown, D. R.; Pierce, L. B. 2017 Iteration of quadratic polynomials over finite fields. Zbl 1428.11204 Heath-Brown, D. R. 2017 Small solutions of quadratic congruences, and character sums with binary quadratic forms. Zbl 1375.11036 Heath-Brown, D. R. 2016 Almost prime triples and Chen’s theorem. Zbl 1390.11109 Heath-Brown, Roger; Li, Xiannan 2016 Burgess bounds for short mixed character sums. Zbl 1317.11083 Heath-Brown, D. R.; Pierce, L. B. 2015 Rational points on intersections of cubic and quadric hypersurfaces. Zbl 1327.11043 Browning, T. D.; Dietmann, R.; Heath-Brown, D. R. 2015 Large gaps between consecutive prime numbers containing perfect powers. Zbl 1391.11125 Ford, Kevin; Heath-Brown, D. R.; Konyagin, Sergei 2015 On simple zeros of the Riemann zeta-function. Zbl 1291.11118 Bui, H. M.; Heath-Brown, D. R. 2013 Burgess’s bounds for character sums. Zbl 1328.11088 Heath-Brown, D. R. 2013 Power-free values of polynomials. Zbl 1287.11114 Heath-Brown, D. R. 2013 $$p$$-adic zeros of systems of quadratic forms. Zbl 1333.11036 Heath-Brown, D. R. 2013 Square-free values of $$n^2+1$$. Zbl 1312.11077 Heath-Brown, D. R. 2012 Quadratic polynomials represented by norm forms. Zbl 1264.14032 Browning, T. D.; Heath-Brown, D. R. 2012 Counting rational points on smooth cyclic covers. Zbl 1248.14027 Heath-Brown, D. R.; Pierce, Lillian B. 2012 A note on the Chevalley-Warning theorems. Zbl 1247.11089 Heath-Brown, D. R. 2011 Pair correlation for fractional parts of $$\alpha n^2$$. Zbl 1239.11081 Heath-Brown, D. R. 2010 Zeros of $$p$$-adic forms. Zbl 1233.11039 Heath-Brown, D. R. 2010 Zeros of systems of $$\mathfrak p$$-adic quadratic forms. Zbl 1194.11047 Heath-Brown, D. R. 2010 A note on the fourth moment of Dirichlet $$L$$-functions. Zbl 1203.11056 Bui, H. M.; Heath-Brown, D. R. 2010 Fractional moments of Dirichlet $$L$$-functions. Zbl 1248.11059 Heath-Brown, D. R. 2010 Bounds for the cubic Weyl sum. Zbl 1282.11102 Heath-Brown, D. R. 2010 Counting rational points on cubic curves. Zbl 1229.11052 Heath-Brown, Roger; Testa, Damiano 2010 Rational points on quartic hypersurfaces. Zbl 1169.11027 Browning, T. D.; Heath-Brown, D. R. 2009 Integral points on cubic hypersurfaces. Zbl 1244.11066 Browning, T. D.; Heath-Brown, D. R. 2009 Convexity bounds for $$L$$-functions. Zbl 1169.11038 Heath-Brown, D. R. 2009 Sums and differences of three $$k$$th powers. Zbl 1182.11017 Heath-Brown, D. R. 2009 An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001 Hardy, G. H.; Wright, E. M. 2008 Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006 Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E. 2008 Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150 Heath-Brown, D. R. 2008 Cubic forms in 14 variables. Zbl 1135.11031 Heath-Brown, D. R. 2007 Quadratic class numbers divisible by 3. Zbl 1140.11050 Heath-Brown, D. Roger 2007 Every sum of cubes in $$\mathbb F_2[t]$$ is a strict sum of 6 cubes. Zbl 1172.11045 Gallardo, Luis H.; Heath-Brown, D. R. 2007 Carmichael numbers with three prime factors. Zbl 1151.11047 Heath-Brown, D. R. 2007 Analytic methods for the distribution of rational points of algebraic varieties. Zbl 1181.11042 Heath-Brown, D. R. 2007 Counting rational points on algebraic varieties. Zbl 1098.14013 Browning, T. D.; Heath-Brown, D. R.; Salberger, P. 2006 Counting rational points on algebraic varieties. Zbl 1152.11027 Heath-Brown, D. R. 2006 The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015 Browning, T. D.; Heath-Brown, D. R.; Starr, J. M. 2006 The density of rational points on non-singular hypersurfaces. I. Zbl 1174.11051 Browning, T. D.; Heath-Brown, D. R. 2006 Analytic methods for Diophantine equations and Diophantine inequalities. Edited and prepared by T. D. Browning. With a preface by R. C. Vaughan, D. R. Heath-Brown and D. E. Freeman. 2nd ed. Zbl 1125.11018 Davenport, Harold 2005 Counting rational points on hypersurfaces. Zbl 1079.11033 Browning, T. D.; Heath-Brown, D. R. 2005 On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055 Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E. 2005 Plane curves in boxes and equal sums of two powers. Zbl 1174.11380 Browning, T. D.; Heath-Brown, D. R. 2005 Permutation groups, simple groups, and sieve methods. Zbl 1091.11035 Heath-Brown, D. R.; Praeger, Cheryl E.; Shalev, Aner 2005 Prime number theory and the Riemann zeta-function. Zbl 1204.11144 Heath-Brown, D. R. 2005 The average analytic rank of elliptic curves. Zbl 1063.11013 Heath-Brown, D. R. 2004 On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050 Heath-Brown, D. R.; Moroz, B. Z. 2004 Equal sums of three powers. Zbl 1135.11052 Browning, T. D.; Heath-Brown, D. R. 2004 Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050 Heath-Brown, D. R.; Tolev, D. I. 2003 The density of rational points on Cayley’s cubic surface. Zbl 1060.11038 Heath-Brown, D. R. 2003 Linear relations amongst sums of two squares. Zbl 1161.11387 Heath-Brown, D. R. 2003 Proceedings of the session in analytic number theory and Diophantine equations held in Bonn, Germany, January–June, 2002. Zbl 1050.11003 2003 Lectures on sieves. Zbl 1070.11045 Heath-Brown, D. R. 2003 The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044 Heath-Brown, D. R. 2002 Integers represented as a sum of primes and powers of two. Zbl 1097.11050 Heath-Brown, D. R.; Puchta, J.-C. 2002 The distribution of $$\alpha p$$ modulo one. Zbl 1023.11034 Heath-Brown, D. R.; Jia, Chaohua 2002 Rational solutions of certain equations involving norms. Zbl 1023.11033 Heath-Brown, Roger; Skorobogatov, Alexei 2002 Primes represented by binary cubic forms. Zbl 1030.11046 Heath-Brown, D. R.; Moroz, B. Z. 2002 Heilbronn’s exponential sum and transcendence theory. Zbl 1177.11072 Heath-Brown, D. R. 2002 Primes represented by $$x^3+ 2y^3$$. Zbl 1007.11055 Heath-Brown, D. R. 2001 The largest prime factor of $$X^3+2$$. Zbl 1023.11048 Heath-Brown, D. R. 2001 New bounds for Gauss sums derived from $$k$$th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052 Heath-Brown, D. R.; Konyagin, S. 2000 Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042 Heath-Brown, D. R. 2000 Arithmetic applications of Kloosterman sums. Zbl 1173.11339 Heath-Brown, D. R. 2000 Exponential decay in the frequency of analytic ranks of automorphic $$L$$-functions. Zbl 1166.11326 Heath-Brown, D. R.; Michel, P. 2000 Lattice points in the sphere. Zbl 0929.11040 Heath-Brown, D. R. 1999 The density of rational points on the cubic surface $$X_0^3=X_1X_2X_3$$. Zbl 0938.11016 Heath-Brown, D. R.; Moroz, B. Z. 1999 The solubility of diagonal cubic Diophantine equations. Zbl 1029.11010 Heath-Brown, D. R. 1999 A note on the paper ‘consecutive almost-primes’. Zbl 1141.11318 Heath-Brown, D. R. 1999 The circle method and diagonal cubic forms. Zbl 0899.11051 Heath-Brown, D. R. 1998 The largest prime factor of the integers in an interval. II. Zbl 1066.11506 Heath-Brown, D. R.; Jia, Chaohua 1998 Counting rational points on cubic surfaces. Zbl 0926.11046 Heath-Brown, Roger 1998 The density of rational points on cubic surfaces. Zbl 0863.11021 Heath-Brown, D. R. 1997 Almost-prime $$k$$-tuples. Zbl 0886.11052 Heath-Brown, D. R. 1997 A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049 Heath-Brown, D. R. 1996 An estimate for Heilbronn’s exponential sum. Zbl 0857.11041 Heath-Brown, D. R. 1996 The largest prime factor of the integers in an interval. Zbl 0867.11064 Heath-Brown, D. R. 1996 A mean value estimate for real character sums. Zbl 0828.11040 Heath-Brown, D. R. 1995 The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032 Heath-Brown, D. R. 1994 Sign changes of $$E(T)$$, $$\Delta(x)$$, and $$P(x)$$. Zbl 0810.11046 Heath-Brown, D. R.; Tsang, K.-M. 1994 Odd perfect numbers. Zbl 0805.11005 Heath-Brown, D. R. 1994 The density of rational points on non-singular hypersurfaces. Zbl 0808.11042 Heath-Brown, D. R. 1994 The size of Selmer groups for the congruent number problem. Zbl 0808.11041 Heath-Brown, D. R. 1993 Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031 Heath-Brown, D. R. 1993 On solving the diophantine equation $$x^ 3+y^ 3+z^ 3=k$$ on a vector computer. Zbl 0783.11046 Heath-Brown, D. R.; Lioen, W. M.; te Riele, Herman J. J. 1993 The Dirichlet divisor problem. Zbl 0791.11048 Heath-Brown, D. R. 1993 Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0739.11033 Heath-Brown, D. R. 1992 The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045 Heath-Brown, D. R. 1992 The density of zeros of forms for which weak approximation fails. Zbl 0778.11017 Heath-Brown, D. R. 1992 Calabi-Yau threefolds with $$\rho > 13$$. Zbl 0759.14030 Heath-Brown, D. R.; Wilson, P. M. H. 1992 Zero-free regions of $$\zeta (s)$$ and $$L(s,\chi)$$. Zbl 0791.11042 Heath-Brown, D. R. 1992 ...and 66 more Documents all top 5 ### Cited by 1,350 Authors 59 Shparlinski, Igor E. 38 Browning, Timothy Daniel 35 Heath-Brown, Roger 27 Zhai, Wenguang 21 Wooley, Trevor D. 20 Ivić, Aleksandar 20 Lu, Guangshi 18 Harman, Glyn 17 Iwaniec, Henryk 15 Baier, Stephan 15 Michel, Philippe Gabriel 15 Zaharescu, Alexandru 14 Blomer, Valentin 14 Fouvry, Etienne 14 Goldston, Daniel Alan 13 Baker, Roger C. 13 Brüdern, Jörg 13 Li, Jinjiang 12 Banks, William David 12 Bourgain, Jean 12 Cao, Xiaodong 12 de la Bretèche, Régis 12 Murty, Maruti Ram 12 Tsang, Kai-Man 12 Zhang, Min 11 Kowalski, Emmanuel 11 Laurinčikas, Antanas 11 Pintz, Janos 11 Soundararajan, Kannan 11 Tao, Terence 11 Zhao, Liangyi 10 Cai, Yingchun 10 Cochrane, Todd 10 Friedlander, John Benjamin 10 Hu, Liqun 10 Liu, Zhixin 10 Munshi, Ritabrata 10 Perelli, Alberto 10 Pierce, Lillian B. 10 Tanigawa, Yoshio 10 Young, Matthew P. 9 Bazzanella, Danilo 9 Conrey, John Brian 9 Dietmann, Rainer 9 Garaev, Moubariz Z. 9 Liu, Huafeng 9 Radziwiłł, Maksym 8 Brandes, Julia 8 Chamizo Lorente, Fernando 8 Chang, Mei-Chu 8 Fomenko, Oleg Mstislavovich 8 Gao, Peng 8 Konyagin, Sergeĭ Vladimirovich 8 Lau, Yuk-Kam 8 Pollack, Paul 8 Sankaranarayanan, Ayyadurai 8 Shkredov, Il’ya Dmitrievich 8 Steuding, Jörn 8 Vaughan, Robert C. 7 Derenthal, Ulrich 7 Dimitrov, Stoyan Ivanov 7 Ford, Kevin B. 7 Keating, Jonathan Peter 7 Korolëv, Maksim Aleksandrovich 7 Kumchev, Angel V. 7 Luca, Florian 7 Maynard, James 7 Nowak, Werner Georg 7 Robles, Nicolas 7 Salberger, Per 7 Sarnak, Peter Clive 7 Wu, Jie 7 Xiao, Stanley Yao 7 Yamagishi, Shuntaro 7 Zhao, Lilu 6 Aistleitner, Christoph 6 Gritsenko, Sergeĭ Aleksandrovich 6 Helfgott, Harald Andrés 6 Jutila, Matti Ilmari 6 Lamzouri, Youness 6 Milinovich, Micah B. 6 Motohashi, Yoichi 6 Munsch, Marc 6 Parsell, Scott T. 6 Rassias, Michael Th. 6 Rivat, Joël 6 Rubin, Karl Cooper 6 Rudnick, Zeév 6 Sawin, William F. 6 Schindler, Damaris 6 Sofos, Efthymios 6 Sono, Keiju 6 Sun, Haiwei 6 Tolev, Doychin I. 6 Xi, Ping 6 Zaman, Asif 6 Zhang, Deyu 5 Bettin, Sandro 5 Bui, Hung Manh 5 Chen, Yonggao ...and 1,250 more Authors all top 5 ### Cited in 222 Serials 198 Journal of Number Theory 71 Mathematika 60 International Journal of Number Theory 45 Acta Arithmetica 39 Journal de Théorie des Nombres de Bordeaux 37 Mathematics of Computation 37 Mathematische Zeitschrift 37 Monatshefte für Mathematik 37 Proceedings of the American Mathematical Society 37 Transactions of the American Mathematical Society 36 Duke Mathematical Journal 32 Mathematische Annalen 32 The Ramanujan Journal 31 Functiones et Approximatio. Commentarii Mathematici 28 Advances in Mathematics 26 Acta Mathematica Hungarica 24 Lithuanian Mathematical Journal 24 Mathematical Proceedings of the Cambridge Philosophical Society 24 Inventiones Mathematicae 23 Journal für die Reine und Angewandte Mathematik 23 Algebra & Number Theory 23 Research in Number Theory 21 Rocky Mountain Journal of Mathematics 19 Compositio Mathematica 18 Israel Journal of Mathematics 18 Annals of Mathematics. Second Series 17 Mathematical Notes 16 Bulletin of the Australian Mathematical Society 16 Archiv der Mathematik 16 Bulletin of the American Mathematical Society. New Series 15 Journal of Mathematical Analysis and Applications 14 Forum Mathematicum 14 Finite Fields and their Applications 13 Acta Mathematica Sinica. New Series 12 Michigan Mathematical Journal 12 Indagationes Mathematicae. New Series 12 Journal of Mathematical Sciences (New York) 12 Science China. Mathematics 11 Journal d’Analyse Mathématique 11 Geometric and Functional Analysis. GAFA 11 Journal of the European Mathematical Society (JEMS) 10 Proceedings of the London Mathematical Society. Third Series 10 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 10 Proceedings of the Steklov Institute of Mathematics 9 Discrete Mathematics 9 Proceedings of the Japan Academy. Series A 9 Journal of the American Mathematical Society 9 Chebyshevskiĭ Sbornik 9 Forum of Mathematics, Sigma 8 Annales de l’Institut Fourier 8 Bulletin of the London Mathematical Society 8 Glasgow Mathematical Journal 8 Manuscripta Mathematica 8 Integers 8 Central European Journal of Mathematics 7 Periodica Mathematica Hungarica 7 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 7 Journal of the London Mathematical Society. Second Series 7 Revista Matemática Iberoamericana 7 Journal of the Australian Mathematical Society 7 Frontiers of Mathematics in China 7 Discrete Analysis 6 Communications in Mathematical Physics 6 Experimental Mathematics 6 Acta Mathematica Sinica. English Series 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 The Mathematical Intelligencer 5 Acta Mathematica 5 Journal of Soviet Mathematics 5 Designs, Codes and Cryptography 5 Expositiones Mathematicae 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 5 Forum of Mathematics, Pi 4 American Mathematical Monthly 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Canadian Journal of Mathematics 4 Journal of Algebra 4 Journal of Combinatorial Theory. Series A 4 Journal of Functional Analysis 4 Theoretical Computer Science 4 Combinatorica 4 Chinese Annals of Mathematics. Series B 4 Journal of Complexity 4 Journal of the Ramanujan Mathematical Society 4 Science in China. Series A 4 Sbornik: Mathematics 4 Taiwanese Journal of Mathematics 4 Portugaliae Mathematica. Nova Série 4 Research in the Mathematical Sciences 3 Mathematische Semesterberichte 3 Arkiv för Matematik 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Applied Mathematics and Computation 3 Commentarii Mathematici Helvetici 3 Czechoslovak Mathematical Journal 3 Pacific Journal of Mathematics 3 Rendiconti del Seminario Matematico della Università di Padova 3 St. Petersburg Mathematical Journal 3 Selecta Mathematica. New Series 3 Journal of High Energy Physics ...and 122 more Serials all top 5 ### Cited in 47 Fields 1,623 Number theory (11-XX) 188 Algebraic geometry (14-XX) 50 Combinatorics (05-XX) 31 Dynamical systems and ergodic theory (37-XX) 28 Group theory and generalizations (20-XX) 25 Information and communication theory, circuits (94-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 24 Probability theory and stochastic processes (60-XX) 19 Partial differential equations (35-XX) 18 Convex and discrete geometry (52-XX) 17 Computer science (68-XX) 15 Field theory and polynomials (12-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Global analysis, analysis on manifolds (58-XX) 11 Topological groups, Lie groups (22-XX) 11 Quantum theory (81-XX) 10 History and biography (01-XX) 10 Functions of a complex variable (30-XX) 9 Several complex variables and analytic spaces (32-XX) 9 Numerical analysis (65-XX) 8 Special functions (33-XX) 7 Mathematical logic and foundations (03-XX) 7 Measure and integration (28-XX) 7 Approximations and expansions (41-XX) 6 Geometry (51-XX) 5 Commutative algebra (13-XX) 5 Associative rings and algebras (16-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 General and overarching topics; collections (00-XX) 4 Abstract harmonic analysis (43-XX) 4 Differential geometry (53-XX) 3 Real functions (26-XX) 3 Statistics (62-XX) 2 $$K$$-theory (19-XX) 2 Potential theory (31-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Fluid mechanics (76-XX) 2 Operations research, mathematical programming (90-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Nonassociative rings and algebras (17-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2023-01-31T10:23:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7100116014480591, "perplexity": 4761.506221503696}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499857.57/warc/CC-MAIN-20230131091122-20230131121122-00404.warc.gz"}
https://par.nsf.gov/biblio/10365706-radio-far-ir-emission-associated-massive-star-forming-galaxy-candidate-radio-loud-agn-reionization-era	Radio and far-IR emission associated with a massive star-forming galaxy candidate at z ≃ 6.8: a radio-loud AGN in the reionization era? ABSTRACT We report the identification of radio (0.144–3 GHz) and mid-, far-infrared, and sub-mm (24–850μm) emission at the position of one of 41 UV-bright ($\mathrm{M_{\mathrm{UV}}}^{ }\lesssim -21.25$) z ≃ 6.6–6.9 Lyman-break galaxy candidates in the 1.5 deg2 COSMOS field. This source, COS-87259, exhibits a sharp flux discontinuity (factor >3) between two narrow/intermediate bands at 9450 and 9700 Å and is undetected in all nine bands blueward of 9600 Å, as expected from a Lyman alpha break at z ≃ 6.8. The full multiwavelength (X-ray through radio) data of COS-87529 can be self-consistently explained by a very massive (M* = 1010.8 M⊙) and extremely red (rest-UV slope β = −0.59) z ≃ 6.8 galaxy with hyperluminous infrared emission (LIR = 1013.6 L⊙) powered by both an intense burst of highly obscured star formation (SFR ≈ 1800 M⊙ yr−1) and an obscured ($\tau _{_{\mathrm{9.7\mu m}}} = 7.7\pm 2.5$) radio-loud (L1.4 GHz ≈ 1025.4 W Hz−1) active galactic nucleus (AGN). The radio emission is compact (1.04 ± 0.12 arcsec) and exhibits an ultra-steep spectrum between 1.32 and 3 GHz ($\alpha =-1.57^{+0.22}_{-0.21}$) that flattens at lower frequencies ($\alpha = -0.86^{+0.22}_{-0.16}$ between 0.144 and 1.32 GHz), consistent with known z > 4 radio galaxies. We also demonstrate that COS-87259 may reside in a significant (11×) galaxy more » Authors: ; ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10365706 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 512 Issue: 3 Page Range or eLocation-ID: p. 4248-4261 ISSN: 0035-8711 Publisher: Oxford University Press National Science Foundation ##### More Like this 1. ABSTRACT We present band 6 ALMA observations of a heavily obscured radio-loud (L1.4 GHz = 1025.4 W Hz−1) active galactic nucleus (AGN) candidate at zphot = 6.83 ± 0.06 found in the 1.5 deg2 COSMOS field. The ALMA data reveal detections of exceptionally strong [C ii]158 $\mu$m (z[C ii] = 6.8532) and underlying dust continuum emission from this object (COS-87259), where the [C ii] line luminosity, line width, and 158 $\mu$m continuum luminosity are comparable to those seen from z ∼ 7 sub-mm galaxies and quasar hosts. The 158 $\mu$m continuum detection suggests a total infrared luminosity of $9\times 10^{12}\, \mathrm{ L}_\odot$ with corresponding very large obscured star formation rate (1300 M⊙ yr−1) and dust mass ($2\times 10^9\, \mathrm{ M}_\odot$). The strong break seen between the VIRCam and IRAC photometry perhaps suggests that COS-87259 is an extremely massive reionization-era galaxy with $M_\ast \approx 1.7\times 10^{11}\, \mathrm{ M}_\odot$. Moreover, the MIPS, PACS, and SPIRE detections imply that this object harbours an AGN that is heavily obscured ($\tau _{_{\mathrm{9.7\,\mu m}}}=2.3$) with a bolometric luminosity of approximately $5\times 10^{13}\, \mathrm{ L}_\odot$. Such a very high AGN luminosity suggests that this object is powered by an ≈1.6 × 10$^9\, \mathrm{ M}_\odot$ black hole if accreting near the Eddington limit, and is effectively a highly obscured version of an extremely ultravioletmore » 2. ABSTRACT Our understanding of reionization has advanced considerably over the past decade, with several results now demonstrating that the intergalactic medium transitioned from substantially neutral at z = 7 to largely reionized at z = 6. However, little remains known about the sizes of ionized bubbles at z ≳ 7 as well as the galaxy overdensities which drive their growth. Fortunately, rest-ultraviolet (UV) spectroscopic observations offer a pathway towards characterizing these ionized bubbles thanks to the resonant nature of Lyman-alpha photons. In a previous work, we presented Ly α detections from three closely separated Lyman-break galaxies at z ≃ 6.8, suggesting the presence of a large (R > 1 physical Mpc) ionized bubble in the 1.5 deg2 COSMOS field. Here, we present new deep Ly α spectra of 10 UV-bright ($\mathrm{\mathit{ M}}_{\mathrm{UV}}^{} \le -20.4$) z ≃ 6.6–6.9 galaxies in the surrounding area, enabling us to better characterize this potential ionized bubble. We confidently detect (S/N > 7) Ly α emission at z = 6.701–6.882 in nine of ten observed galaxies, revealing that the large-scale volume spanned by these sources (characteristic radius R = 3.2 physical Mpc) traces a strong galaxy overdensity (N/〈N〉 ≳ 3). Our data additionally confirm that the Lymore » 3. ABSTRACT We report the discovery of a double-peaked Lyman-α (Ly α) emitter (LAE) at z = 3.2177 ± 0.0001 in VLT/MUSE data. The galaxy is strongly lensed by the galaxy cluster RXC J0018.5+1626 recently observed in the RELICS survey, and the double-peaked Ly α emission is clearly detected in the two counter images in the MUSE field of view. We measure a relatively high Ly α rest-frame equivalent width (EW) of EWLy α, 0 = (63 ± 2) Å. Additional spectroscopy with Gemini/GNIRS in the near-infrared (NIR) allows us to measure the H β, [O iii] λ4959 Å, and [O iii] λ5007 Å emission lines, which show moderate rest-frame EWs of the order of a few ∼10–100 Å, an [O iii] λ5007 Å/H β ratio of 4.8 ± 0.7, and a lower limit on the [O iii]/[O ii] ratio of >9.3. The galaxy has very blue UV-continuum slopes of βFUV = −2.23 ± 0.06 and βNUV = −3.0 ± 0.2, and is magnified by factors μ ∼ 7–10 in each of the two images, thus enabling a view into a low-mass ($M_{\star }\simeq 10^{7.5}\, \mathrm{M}_{\odot }$) high-redshift galaxy analogue. Notably, the blue peak of the Ly α profile is significantly stronger than the red peak, which suggests an inflow of matter and possibly very low H i column densities in its circumgalactic gas. To the best of our knowledge, this is the first detection of suchmore » 4. Abstract We present the radio properties of 66 spectroscopically confirmed normal star-forming galaxies (SFGs) at 4.4 <z< 5.9 in the COSMOS field that were [Cii]-detected in the Atacama Large Millimeter/submillimeter Array Large Program to INvestigate [Cii] at Early times (ALPINE). We separate these galaxies (“Cii-detected-all”) into lower-redshift (“Cii-detected-lz”; 〈z〉 = 4.5) and higher-redshift (“Cii-detected-hz”; 〈z〉 = 5.6) subsamples, and stack multiwavelength imaging for each subsample from X-ray to radio bands. A radio signal is detected in the stacked 3 GHz images of the Cii-detected-all and lz samples at ≳3σ. We find that the infrared–radio correlation of our sample, quantified byqTIR, is lower than the local relation for normal SFGs at a ∼3σsignificance level, and is instead broadly consistent with that of bright submillimeter galaxies at 2 <z< 5. Neither of these samples show evidence of dominant active galactic nucleus activity in their stacked spectral energy distributions (SEDs), UV spectra, or stacked X-ray images. Although we cannot rule out the possible effects of the assumed spectral index and applied infrared SED templates in causing these differences, at least partially, the lower obscured fraction of star formation than at lower redshift can alleviate the tension between our stackedqTIRs and those of localmore » 5. ABSTRACT We present the spectroscopic confirmation of the brightest known gravitationally lensed Lyman-break galaxy in the Epoch of Reionization (EoR), A1703-zD1, through the detection of [C ii] 158 $\mu$m at a redshift of z = 6.8269 ± 0.0004. This source was selected behind the strong lensing cluster Abell 1703, with an intrinsic luminosity and a very blue Spitzer/Infrared Array Camera (IRAC) [3.6]–[4.5] colour, implying high equivalent width line emission of [O iii] + Hβ. [C ii] is reliably detected at 6.1σ cospatial with the rest-frame ultraviolet (UV) counterpart, showing similar spatial extent. Correcting for the lensing magnification, the [C ii] luminosity in A1703-zD1 is broadly consistent with the local $L_{\rm [C\, {\small II}]}$–star formation rate (SFR) relation. We find a clear velocity gradient of 103 ± 22 km $\rm s^{-1}$ across the source that possibly indicates rotation or an ongoing merger. We furthermore present spectral scans with no detected [C ii] above 4.6σ in two unlensed Lyman-break galaxies in the Extended Groth Strip (EGS)-Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) field at z ∼ 6.6–6.9. This is the first time that the Northern Extended Millimeter Array (NOEMA) has been successfully used to observe [C ii] in a ‘normal’ star-forming galaxy at z > 6, and our results demonstrate its capability to complement the Atacama Large Millimeter/submillimeter Array (ALMA) inmore »	2023-03-25T09:08:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6039937138557434, "perplexity": 4722.5302059078285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945317.85/warc/CC-MAIN-20230325064253-20230325094253-00343.warc.gz"}
https://asphalt.fandom.com/wiki/Gambler%27s_fallacy	## FANDOM 3,460 Pages SOURCE EDITOR ONLY!This page uses LaTeX markup to display mathematical formulas. Editing the page with the VisualEditor or Classic rich-text editor disrupts the layout.Do not even switch to one of these editors while editing the page!For help with mathematical symbols, see Mathematical symbols and expressions. The gambler's fallacy, also known as the Monte Carlo fallacy[1], the fallacy of the maturity of chances[2][3] or, more scientifically, the negative recency effect[4], is the mistaken belief that, for random events, runs of a particular outcome (e. g., heads on the toss of a coin) will be balanced by a tendency for the opposite outcome (e. g., tails).[5] Or, in short: “If you have been losing, you are more likely to win in future.” [6] In situations where the outcome being observed is truly random and consists of independent trials of a random process, this belief is false. The fallacy can arise in many situations, but is most strongly associated with gambling, where it is common among players.[7] ## Examples ### Coin toss The gambler's fallacy can be illustrated by considering the repeated toss of a fair coin. The outcomes in different tosses are statistically independent and the probability of getting heads on a single toss is $\tfrac12$ (one in two). The probability of getting two heads in two tosses is $\tfrac12 \cdot \tfrac12 = \tfrac14$ (one in four) and the probability of getting three heads in three tosses is $\tfrac12 \cdot \tfrac12 \cdot \tfrac12 = \tfrac18$ (one in eight). In general, the probability of getting $n$ heads in $n$ tosses is $\displaystyle \underbrace{\frac12 \cdot \frac12 \cdot \ldots \cdot \frac12}_{n\, \mathrm{times}} = \left(\frac12\right)^n = \frac1{2^n}$. Let's assume that a player has flipped a coin five times and got five heads in a row. The probability of five heads is $(\tfrac12)^5 = \tfrac1{32} = 3.125 %$. There are two main reasons why it is believed that the next toss will be more likely to show tails than heads: #### “Ex-ante” probabilities The probability of getting even six heads in a row is $\tfrac1{64} = 1.5625 %$, so the probability of getting heads in the next toss could be assumed to be only 1.5625 %. While the first part of the sentence is correct, the conclusion is false. The misunderstanding lies in not realizing that the probability is only correct before the first coin is tossed. After the first five tosses, the results are no longer unknown. The tosses are independent, and a coin has no memory, so a run of luck in the past cannot influence the odds in the future. The probability of heads in the next toss is $\tfrac12$. If ex-ante probabilities are calculated, they have to be considered for both possible outcomes: • The probability of 5 heads, then 1 tail is $\displaystyle \underbrace{\frac12 \cdot \frac12 \cdot \frac12 \cdot \frac12 \cdot \frac12}_{\mathrm{heads}} \cdot \underbrace{\frac12}_{\mathrm{tail}} = \frac1{64} = 1.5625 %$. • The probability of 5 heads, then 1 head is $\displaystyle \underbrace{\frac12 \cdot \frac12 \cdot \frac12 \cdot \frac12 \cdot \frac12}_{\mathrm{heads}} \cdot \underbrace{\frac12}_{\mathrm{head}} = \frac1{64} = 1.5625 %$. Actually, any possible sequence of heads and tails in six tosses has the same probability of 1.5625 %. There is no difference, because both heads and tails have the same probability of $\frac12$. #### Law of large numbers Another reason lies in the erroneous belief that the law of large numbers applies to small numbers as well, thus creating a “law of small numbers”.[8] In other words, if five tosses of a fair coin have produced a sequence of five heads, people expect that the coin “ought to” have a 50:50 ratio of heads and tails in the long run and, as a result, more tails are “needed” to correct the deviation from that ratio produced by the first five tosses.[6] While it is true that the law of large numbers guarantees a 50:50 ratio in the long run, the conclusion is false. The misunderstanding lies in the term “in the long run”: The law of large numbers only states that the the expected ratio will be reached as the number of trials approaches infinity. It makes no predictions about a small number of trials. ### Roulette The alternative term “Monte Carlo fallacy” originates from a famous anecdote about the phenomenon, which occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913,[9] when the ball fell in black 26 times in a row. “During that [...] run, most gamblers bet against black, since they felt that the red must be ‘due’. In other words, they assumed that the randomness of the roulette wheel would somehow correct the imbalance and cause the wheel to land on red. The casino ended up making millions of francs.” [10] The explanation of the phenomenon works like in the coin example, only with different probabilities. A roulette wheel has 37 numbers: 18 black, 18 red, and 1 green (the zero). • The probability for black is the same as for red: $\tfrac{18}{37}$. • The “ex-ante” probability that the ball will land on black 26 times in a row, is extremely small: $(\tfrac{18}{37})^{26}$ or around 1 in 136.8 million. • However, like in the coin example, the probability of getting 25 blacks and then one red is the the same as of getting 26 blacks: $(\tfrac{18}{37})^{25} \cdot \tfrac{18}{37} = (\tfrac{18}{37})^{26}$. The gamblers' chance of getting red or black was the same every time, no matter when they joined the table and what the previous outcomes were. The fact that today's casinos install an LED marquee at roulette tables showing which numbers have occurred recently is no contradiction to this. On the contrary, it is to the casino's advantage if people believe in the gambler's fallacy and keep playing even after a streak of losses or wins: The law of large numbers guarantees that any streak by a player will eventually be overcome by the parameters of the game—which are always in favour of the casino. ### Daily Kit Box The Tech card of the from Asphalt 8 can serve as another example. Every Daily Kit Box grants exactly one Tech card, and this card can only be Advanced Tech (AT) or Mid-Tech (MT). As there are only two possible outcomes, the experiment can be compared to a coin toss, but with two differences: • While the probabilites for a coin toss are known, there are no official drop rates for AT and MT in Daily Kit Boxes. Therefore, they have been inferred statistically from currently 254 boxes, showing an average ratio of 30 % AT and 70 % MT. • As the probabilities for AT and MT are not the same, the analogy would be an unfair coin with a probability of $\tfrac3{10}$ for heads and $\tfrac7{10}$ for tails. As AT cards are legendary and MT cards are rare (see rarity), players often regard the occurrence of an AT as success and that of an MT as failure. There has been a report of a 12 MT streak by a player looking for AT.[11] • The probability of getting MT from a Daily Kit Box is $\tfrac7{10}$, while the probability of AT is $\tfrac3{10}$. • The “ex-ante” probability of a streak of 12 MTs is $(\tfrac7{10})^{12} = 1.38 %$. • In this case, contrary to the coin example, the probability of getting 11 MTs and then one AT is not the same as of getting 12 MTs, but less: $(\tfrac7{10})^{11} \cdot \tfrac{3}{10} = 0.59 %$. Players disappointed of not getting AT from Daily Kit Boxes should be aware that AT is always less likely to occur than MT, and that a streak of MT is actually the most probable sequence given the underlying probabilities: $\frac7{10} \cdot \frac7{10} \cdot \ldots \cdot \frac7{10} \cdot \color{limegreen}\frac7{10}$ is always greater than $\frac7{10} \cdot \frac7{10} \cdot \ldots \cdot \frac7{10} \cdot \color{limegreen}\frac3{10}$. Another comparison: Players would not be astonished to get a V6 Engine from an . However, as of the Showdown Update, the probability of getting it is actually only 0.45 % which is even less than the 1.38 % probability of a 12 MT streak from Daily Kit Boxes. ## Psychological aspects The tendency of players to regard a streak of equal values as “atypical” or “non-random” has been the subject of various psychological studies. First, a random process is not actively self-correcting, but the absence of such a law seems to conflict with people's everyday experience: “Some familiar processes in nature obey such laws: a deviation from a stable equilibrium produces a force that restores the equilibrium. The laws of chance, in contrast, do not work that way: deviations are not canceled as sampling proceeds, they are merely diluted.” [8] Second, it has been found that the notion of randomness itself mostly does not correspond with reality: “People's notion of randomness is biased in that they see clumps or streaks in truly random series and expect more alternation, or shorter runs, than are there. Similarly, [when asked to produce a ‘random’ series] they produce series with higher than expected alternation rates.” [12] This even leads to casinos in Las Vegas changing roulette weels more frequently than warranted. As soon as a wheel exhibits an usual run of reds, the wheel is changed, even if it is still operating perfectly fine (“randomly”),[13] just to please the gamblers' expectation that streaks are unsual—and thus reinforcing and increasing their belief in the fallacy. Regarding the Asphalt games, the incorrect notion of randomness also leads to a variety of “myths” among players, such as the game allegedly granting more or less of a desired card if players have performed certain actions or behave in a certain way. In reality, this perception is caused by mere coincidence—and by the fact that players usually do not keep track of all results of a random process, but only consider a small period of interest, mostly during special events when they need certain cards. These cards are then perceived as occurring less frequently, although their frequency does not differ from their normal drop rates. ## References 1. Corsini, Raymond J. (2002). The Dictionary of Psychology. New York: Brunner-Routledge, p. 607. ISBN 978-1583913284. Retrieved on 2019-08-10. 2. Robert-Houdin, Jean Eugène (1863). Les tricheries des Grecs dévoilées: l'art de gagner à tous les jeux (French). Paris: Hetzel, p. 71. Retrieved on 2019-08-10. “[...] la maturité des chances” 3. Huff, Darrell (1959). How to Take a Chance. New York: Norton, p. 28. Retrieved on 2019-08-10. 4. Bar-Hillel, Maya; Wagenaar, Willem A. (December 1991). “The Perception of Randomness”. Advances in Applied Mathematics 12 (4): 437. ISSN 0196-8858. Retrieved on 2019-08-10. 5. Ayton, Peter; Fischer, Ilan (December 2004). “The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness?”. Memory & Cognition 32 (8): 1369. ISSN 0090-502X. Retrieved on 2019-08-10. 6. 6.0 6.1 Xu, Juemin; Harvey, Nigel (May 2014). “Carry on winning: The gamblers’ fallacy creates hot hand effects in online gambling”. Cognition 131 (2): 174. ISSN 0010-0277. Retrieved on 2019-08-10. 7. Croson, Rachel; Sundali, James (May 2005). “The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos”. The Journal of Risk and Uncertainty 30 (3): 197. ISSN 0895-5646. Retrieved on 2019-08-10. 8. 8.0 8.1 Tversky, Amos; Kahneman, Daniel (August 1971). “Belief in the Law of Small Numbers”. Psychological Bulletin 76 (2): 106. ISSN 0033-2909. Retrieved on 2019-08-11. 9. Stafford, Tom (2015-01-28). Why we gamble like monkeys. BBC. Retrieved on 2019-08-10. 10. Lehrer, Jonah (2009). How We Decide. Boston, New York: Houghton Mifflin Harcourt, p. 66. ISBN 978-0618620111. Retrieved on 2019-08-10. 11. Luis Alejandro 2 (2019-07-08). User comment. Asphalt Wiki. Retrieved on 2019-08-11. 12. Bar-Hillel; Wagenaar (1991:428). 13. Bar-Hillel; Wagenaar (1991:450). Community content is available under CC-BY-SA unless otherwise noted.	2019-09-19T21:42:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8635861277580261, "perplexity": 1326.08249687972}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573735.34/warc/CC-MAIN-20190919204548-20190919230548-00063.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S046ZNO	# ${{\widetilde{\boldsymbol \chi}}_{{2}}^{0}}$, ${{\widetilde{\boldsymbol \chi}}_{{3}}^{0}}$, ${{\widetilde{\boldsymbol \chi}}_{{4}}^{0}}$ (Neutralinos) mass limits INSPIRE search Neutralinos are unknown mixtures of photinos, z-inos, and neutral higgsinos (the supersymmetric partners of photons and of ${{\mathit Z}}$ and Higgs bosons). The limits here apply only to ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$, ${{\widetilde{\mathit \chi}}_{{3}}^{0}}$, and ${{\widetilde{\mathit \chi}}_{{4}}^{0}}$. ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$ is the lightest supersymmetric particle (LSP); see ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$ Mass Limits. It is not possible to quote rigorous mass limits because they are extremely model dependent; i.e. they depend on branching ratios of various ${{\widetilde{\mathit \chi}}^{0}}$ decay modes, on the masses of decay products (${{\widetilde{\mathit e}}}$, ${{\widetilde{\mathit \gamma}}}$, ${{\widetilde{\mathit q}}}$, ${{\widetilde{\mathit g}}}$), and on the ${{\widetilde{\mathit e}}}$ mass exchanged in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\widetilde{\mathit \chi}}_{{i}}^{0}}{{\widetilde{\mathit \chi}}_{{j}}^{0}}$ . Limits arise either from direct searches, or from the MSSM constraints set on the gaugino and higgsino mass parameters $\mathit M_{2}$ and $\mu$ through searches for lighter charginos and neutralinos. Often limits are given as contour plots in the ${\mathit m}_{{{\widetilde{\mathit \chi}}^{0}}}–{\mathit m}_{{{\widetilde{\mathit e}}}}$ plane vs other parameters. When specific assumptions are made, e.g, the neutralino is a pure photino (${{\widetilde{\mathit \gamma}}}$), pure z-ino (${{\widetilde{\mathit Z}}}$), or pure neutral higgsino (${{\widetilde{\mathit H}}^{0}}$), the neutralinos will be labelled as such. Limits obtained from ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at energies up to 136 GeV, as well as other limits from different techniques, are now superseded and have not been included in this compilation. They can be found in the 1998 Edition (The European Physical Journal C3 1 (1998)) of this Review. Some later papers are now obsolete and have been omitted. They were last listed in our PDG 2014 edition: K. Olive, $\mathit et~al.$ (Particle Data Group), Chinese Physics C38 070001 (2014) (http://pdg.lbl.gov). VALUE (GeV) CL% DOCUMENT ID TECN COMMENT $> 680$ 95 1 2019 AU ATL 0, 1, 2 or more ${{\mathit \ell}}$, ${{\mathit H}}$ ( $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit b}}{{\mathit b}}$ , ${{\mathit W}}{{\mathit W}^{}}$ , ${{\mathit Z}}{{\mathit Z}^{}}$ , ${{\mathit \tau}}{{\mathit \tau}}$ ) (various searches), Tchi1n2E, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$=0 GeV $>112$ 95 2 2019 BU CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\widetilde{\mathit \chi}}_{{1}}^{+}}{{\widetilde{\mathit \chi}}_{{2}}^{0}}$ + 2 jets, ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , heavy sleptons, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 1 GeV, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{+}}}$ $>215$ 95 2 2019 BU CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\widetilde{\mathit \chi}}_{{1}}^{+}}{{\widetilde{\mathit \chi}}_{{2}}^{0}}$ + 2 jets, ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , heavy sleptons, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 30 GeV, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{+}}}$ $> 760$ 95 3 2018 AY ATLS 2${{\mathit \tau}}+\not E_T$, Tchi1n2D and ${{\widetilde{\mathit \tau}}_{{L}}}$-only, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $> 1125$ 95 4 2018 BT ATLS 2,3${{\mathit \ell}}+\not E_T$, Tchi1n2C, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$=0 GeV $\bf{> 580}$ 95 5 2018 BT ATLS 2,3${{\mathit \ell}}+\not E_T$, Tchi1n2F, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$=0 GeV $\text{none 130 - 230, 290 - 880}$ 95 6 2018 CK ATLS 2${{\mathit H}}$ ( $\rightarrow$ ${{\mathit b}}{{\mathit b}}$ )+$\not E_T$,Tn1n1A, GMSB $\text{none 220 - 600}$ 95 7 2018 CO ATLS 2,3${{\mathit \ell}}$ + $\not E_T$, recursive jigsaw, Tchi1n2F, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $> 145$ 95 8 2018 R ATLS 2${{\mathit \ell}}$ (soft) + $\not E_T$, Tchi1n2G, higgsino, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 5 GeV $> 175$ 95 9 2018 R ATLS 2${{\mathit \ell}}$ (soft) + $\not E_T$, Tchi1n2F, wino, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 10 GeV $> 1060$ 95 10 2018 U ATLS 2 ${{\mathit \gamma}}$ + $\not E_T$, GGM,Tchi1chi1A, any NLSP mass $> 167$ 95 11 2018 AJ CMS 2${{\mathit \ell}}$ (soft) + $\not E_T$, Tchi1n2G, higgsino, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 15 GeV $> 710$ 95 12 2018 DP CMS 2${{\mathit \tau}}+\not E_T$, Tchi1n2D, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $\text{none 220 - 490}$ 95 13 2017 AW CMS 1${{\mathit \ell}}$+ 2 ${{\mathit b}}$-jets + $\not E_T$, Tchi1n2E, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $>600$ 95 14 2016 AA ATLS 3,4${{\mathit \ell}}$ + $\not E_T$, Tn2n3A, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$=0GeV $>670$ 95 14 2016 AA ATLS 3,4${{\mathit \ell}}+\not E_T$,Tn2n3B,${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}<$ 200GeV $>250$ 95 15 2015 BA ATLS ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{\pm}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $> 380$ 95 16 2014 H ATLS ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}$ ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit \tau}^{\pm}}{{\mathit \nu}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}{{\mathit \tau}^{\pm}}{{\mathit \tau}^{\mp}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , simplified model, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{\pm}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $> 700$ 95 16 2014 H ATLS ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}$ ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit \ell}^{\pm}}{{\mathit \nu}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}{{\mathit \ell}^{\pm}}{{\mathit \ell}^{\mp}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , simplified model, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{\pm}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $> 345$ 95 16 2014 H ATLS ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}$ ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}{{\mathit Z}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , simplified model, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{\pm}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $> 148$ 95 16 2014 H ATLS ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}$ ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}{{\mathit H}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , simplified model, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{\pm}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV $> 620$ 95 17 2014 X ATLS ${}\geq{}4{{\mathit \ell}^{\pm}}$, ${{\widetilde{\mathit \chi}}_{{2,3}}^{0}}$ $\rightarrow$ ${{\mathit \ell}^{\pm}}{{\mathit \ell}^{\mp}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV 18 2013 ATLS 3${{\mathit \ell}^{\pm}}$ + $\not E_T$, pMSSM, SMS 19 2012 BJ CMS ${}\geq{}$2 ${{\mathit \ell}}$, jets + $\not E_T$, ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}{{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\bf{> 62.4}$ 95 20 2000 W DLPH ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$, 1${}\leq{}$tan $\beta {}\leq{}$40, all $\Delta \mathit m$, all $\mathit m_{0}$ $\bf{> 99.9}$ 95 20 2000 W DLPH ${{\widetilde{\mathit \chi}}_{{3}}^{0}}$, 1${}\leq{}$tan $\beta {}\leq{}$40, all $\Delta \mathit m$, all $\mathit m_{0}$ $\bf{> 116.0}$ 95 20 2000 W DLPH ${{\widetilde{\mathit \chi}}_{{4}}^{0}}$, 1${}\leq{}$tan $\beta {}\leq{}$40, all $\Delta \mathit m$, all $\mathit m_{0}$ • • • We do not use the following data for averages, fits, limits, etc. • • • $\text{none 180 - 355}$ 95 21 2014 G ATLS ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}$ ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}{{\mathit Z}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ , simplified model, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{\pm}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$, ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 0 GeV 22 2014 I CMS ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ( ${{\mathit Z}}$ , ${{\mathit H}}$) ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$ ${{\widetilde{\mathit \ell}}}{{\mathit \ell}}$ , simplified model 23 2012 AS ATLS 3${{\mathit \ell}^{\pm}}$ + $\not E_T$, pMSSM 24 2012 T ATLS ${{\mathit \ell}^{\pm}}{{\mathit \ell}^{\pm}}$ + $\not E_T$, ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}{{\widetilde{\mathit \chi}}_{{2}}^{0}}$ 1 AABOUD 2019AU searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for direct electroweak production of charginos and next-to-lightest neutralinos decaying into lightest neutralinos and a ${{\mathit W}}$ and a Higgs boson, respectively. Fully hadronic, semileptonic, diphoton, and multilepton (electrons, muons) final states with missing transverse momentum are considered in this search. Observations are consistent with the Standard Model expectations, and 95$\%$ confidence-level limits of up to 680 GeV on the chargino/next-to-lightest neutralino masses are set (Tchi1n2E model). See their Figure 14 for an overlay of exclusion contours from all searches. 2 SIRUNYAN 2019BU searched for pair production of gauginos via vector boson fusion assuming the gaugino spectrum is compressed, in 35.9 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The final states explored included zero leptons plus two jets, one lepton plus two jets, and one hadronic tau plus two jets. A similar bound is obtained in the light slepton limit. 3 AABOUD 2018AY searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for direct electroweak production of charginos and neutralinos as in Tchi1n2D models, in events characterised by the presence of at least two hadronically decaying tau leptons and large missing transverse energy. No significant deviation from the expected SM background is observed. Assuming decays via intermediate ${{\widetilde{\mathit \tau}}_{{L}}}$ and ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{\pm}}}$ = ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$, the observed limits rule out ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ masses up to 760 GeV for a massless ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$. See their Fig.7 (right). Interpretations are also provided in Fig 8 (bottom) for different assumptions on the ratio between ${\mathit m}_{{{\widetilde{\mathit \tau}}}}$ and ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ + ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$. 4 AABOUD 2018BT searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for direct electroweak production of charginos, chargino and next-to-lightest neutralinos and sleptons in events with two or three leptons (electrons or muons), with or without jets, and large missing transverse energy. No significant excess above the Standard Model expectations is observed. Limits are set on the next-to-lightest neutralino mass up to 1100 GeV for massless ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$ in the Tchi1n2C simplified model exploiting the 3${{\mathit \ell}}$ signature, see their Figure 8(c). 5 AABOUD 2018BT searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for direct electroweak production of charginos, chargino and next-to-lightest neutralinos and sleptons in events with two or three leptons (electrons or muons), with or without jets, and large missing transverse energy. No significant excess above the Standard Model expectations is observed. Limits are set on the next-to-lightest neutralino mass up to 580 GeV for massless ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$ in the Tchi1n2F simplified model exploiting the 2${{\mathit \ell}}$+2 jets and 3${{\mathit \ell}}$ signatures, see their Figure 8(d). 6 AABOUD 2018CK searched for events with at least 3 ${{\mathit b}}$-jets and large missing transverse energy in two datasets of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV of 36.1 ${\mathrm {fb}}{}^{-1}$ and 24.3 ${\mathrm {fb}}{}^{-1}$ depending on the trigger requirements. The analyses aimed to reconstruct two Higgs bosons decaying to pairs of ${{\mathit b}}$-quarks. No significant excess above the Standard Model expectations is observed. Limits are set on the Higgsino mass in the T1n1n1A simplified model, see their Figure 15(a). Constraints are also presented as a function of the BR of Higgsino decaying into an higgs boson and a gravitino, see their Figure 15(b). 7 AABOUD 2018CO searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for direct electroweak production of mass-degenerate charginos and next-to-lightest neutralinos in events with two or three leptons (electrons or muons), with or without jets, and large missing transverse energy. The search channels are based on recursive jigsaw reconstruction. Limits are set on the next-to-lightest neutralinos mass up to 600 GeV for massless neutralinos in the Tchi1n2F simplified model exploiting the statistical combination of 2${{\mathit \ell}}$+2 jets and 3${{\mathit \ell}}$ channels. Next-to-lightest neutralinos masses below 220 GeV are not excluded due to an excess of events above the SM prediction in the dedicated regions. See their Figure 13(d). 8 AABOUD 2018R searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for electroweak production in scenarios with compressed mass spectra in final states with two low-momentum leptons and missing transverse momentum. The data are found to be consistent with the SM prediction. Results are interpreted in Tchi1n2G higgsino models, and ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ masses are excluded up to 145 GeV for ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 5 GeV. The exclusion limits extend down to mass splittings of 2.5 GeV, see their Fig. 10 (top). Results are also interpreted in terms of exclusion bounds on the production cross-sections for the NUHM2 scenario as a function of the universal gaugino mass ${\mathit m}_{\mathrm {1/2}}$ and ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$, see their Fig. 12. 9 AABOUD 2018R searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for electroweak production in scenarios with compressed mass spectra in final states with two low-momentum leptons and missing transverse momentum. The data are found to be consistent with the SM prediction. Results are interpreted in Tchi1n2F wino models, and ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ masses are excluded up to 175 GeV for ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$ = 10 GeV. The exclusion limits extend down to mass splittings of 2 GeV, see their Fig. 10 (bottom). Results are also interpreted in terms of exclusion bounds on the production cross-sections for the NUHM2 scenario as a function of the universal gaugino mass ${\mathit m}_{\mathrm {1/2}}$ and ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{2}}^{0}}}$ $−$ ${\mathit m}_{{{\widetilde{\mathit \chi}}_{{1}}^{0}}}$, see their Fig. 12. 10 AABOUD 2018U searched in 36.1 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV in events with at least one isolated photon, possibly jets and significant transverse momentum targeting generalised models of gauge-mediated SUSY breaking. No significant excess of events is observed above the SM prediction. Results of the diphoton channel are interpreted in terms of lower limits on the masses of gauginos Tchi1chi1A models, which reach as high as 1.3 TeV. Gaugino masses below 1060 GeV are excluded for any NLSP mass, see their Fig. 10. 11 SIRUNYAN 2018AJ searched in 35.9 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for events containing two low-momentum, oppositely charged leptons (electrons or muons) and $\not E_T$. No excess over the expected background is observed. Limits are derived on the wino mass in the Tchi1n2F simplified model, see their Figure 5. Limits are also set on the stop mass in the Tstop10 simplified model, see their Figure 6. Finally, limits are set on the Higgsino mass in the Tchi1n2G simplified model, see Figure 8 and in the pMSSM, see Figure 7. 12 SIRUNYAN 2018DP searched in 35.9 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for direct electroweak production of charginos and neutralinos or of chargino pairs in events with a tau lepton pair and significant missing transverse momentum. Both hadronic and leptonic decay modes are considered for the tau lepton. No significant excess above the Standard Model expectations is observed. Limits are set on the chargino mass in the Tchi1chi1D and Tchi1n2 simplified models, see their Figures 14 and 15. Also, excluded stau pair production cross sections are shown in Figures 11, 12, and 13. 13 SIRUNYAN 2017AW searched in 35.9 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV for events with a charged lepton (electron or muon), two jets identified as originating from a ${{\mathit b}}$-quark, and large $\not E_T$. No significant excess above the Standard Model expectations is observed. Limits are set on the mass of the chargino and the next-to-lightest neutralino in the Tchi1n2E simplified model, see their Figure 6. 14 AAD 2016AA summarized and extended ATLAS searches for electroweak supersymmetry in final states containing several charged leptons, $\not E_T$, with or without hadronic jets, in 20 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. The paper reports the results of new interpretations and statistical combinations of previously published analyses, as well as new analyses. Exclusion limits at 95$\%$ C.L. are set on mass-degenerate ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ and ${{\widetilde{\mathit \chi}}_{{3}}^{0}}$ masses in the Tn2n3A and Tn2n3B simplified models. See their Fig. 15. 15 AAD 2015BA searched in 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV for electroweak production of charginos and neutralinos decaying to a final state containing a ${{\mathit W}}$ boson and a 125 GeV Higgs boson, plus missing transverse momentum. No excess beyond the Standard Model expectation is observed. Exclusion limits are derived in simplified models of direct chargino and next-to-lightest neutralino production, with the decays ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}$ $\rightarrow$ ${{\mathit W}^{\pm}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ and ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit H}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ having 100$\%$ branching fraction, see Fig. 8. A combination of the multiple final states for the Higgs decay yields the best limits (Fig. 8d). 16 AAD 2014H searched in 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV for electroweak production of charginos and neutralinos decaying to a final sate with three leptons and missing transverse momentum. No excess beyond the Standard Model expectation is observed. Exclusion limits are derived in simplified models of direct chargino and next-to-lightest neutralino production, with decays to the lightest neutralino via either all three generations of leptons, staus only, gauge bosons, or Higgs bosons, see Fig. 7. An interpretation in the pMSSM is also given, see Fig. 8. 17 AAD 2014X searched in 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV for events with at least four leptons (electrons, muons, taus) in the final state. No significant excess above the Standard Model expectations is observed. Limits are set on the neutralino mass in an R-parity conserving simplified model where the decay ${{\widetilde{\mathit \chi}}_{{2,3}}^{0}}$ $\rightarrow$ ${{\mathit \ell}^{\pm}}{{\mathit \ell}^{\mp}}{{\widetilde{\mathit \chi}}_{{1}}^{0}}$ takes place with a branching ratio of 100$\%$, see Fig. 10. 18 AAD 2013 searched in 4.7 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV for charginos and neutralinos decaying to a final state with three leptons (${{\mathit e}}$ and ${{\mathit \mu}}$) and missing transverse energy. No excess beyond the Standard Model expectation is observed. Exclusion limits are derived in the phenomenological MSSM, see Fig. 2 and 3, and in simplified models, see Fig. 4. For the simplified models with intermediate slepton decays, degenerate ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}$ and ${{\widetilde{\mathit \chi}}_{{2}}^{0}}$ masses up to 500 GeV are excluded at 95$\%$ C.L. for very large mass differences with the ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$. Supersedes AAD 2012AS. 19 CHATRCHYAN 2012BJ searched in 4.98 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV for direct electroweak production of charginos and neutralinos in events with at least two leptons, jets and missing transverse momentum. No significant excesses over the expected SM backgrounds are observed and 95$\%$ C.L. limits on the production cross section of ${{\widetilde{\mathit \chi}}_{{1}}^{\pm}}{{\widetilde{\mathit \chi}}_{{2}}^{0}}$ pair production were set in a number of simplified models, see Figs. 7 to 12. Most limits are for exactly 3 jets. 20 ABREU 2000W combines data collected at $\sqrt {\mathit s }$=189 GeV with results from lower energies. The mass limit is obtained by constraining the MSSM parameter space with gaugino and sfermion mass universality at the GUT scale, using the results of negative direct searches for neutralinos (including cascade decays and ${{\widetilde{\mathit \tau}}}{{\mathit \tau}}$ final states) from ABREU 2001 , for charginos from ABREU 2000J and ABREU 2000T (for all $\Delta \mathit m_{+}$), and for charged sleptons from ABREU 2001B. The results hold for the full parameter space defined by all values of $\mathit M_{2}$ and $\vert \mu \vert {}\leq{}$2 TeV with the ${{\widetilde{\mathit \chi}}_{{1}}^{0}}$ as LSP. 21 AAD 2014G searched in 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV for electroweak production of chargino-neutralino pairs, decaying to a final sate with two leptons (${{\mathit e}}$ and ${{\mathit \mu}}$) and missing transverse momentum. No excess beyond the Standard Model expectation is observed. Exclusion limits are derived in simplified models of chargino and next-to-lightest neutralino production, with decays to the lightest neutralino via gauge bosons, see Fig. 7. An interpretation in the pMSSM is also given, see Fig. 10. 22 KHACHATRYAN 2014I searched in 19.5 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV for electroweak production of charginos and neutralinos decaying to a final state with three leptons (${{\mathit e}}$ or ${{\mathit \mu}}$) and missing transverse momentum, or with a ${{\mathit Z}}$-boson, dijets and missing transverse momentum. No excess beyond the Standard Model expectation is observed. Exclusion limits are derived in simplified models, see Figs. $12 - 16$. 23 AAD 2012AS searched in 2.06 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV for charginos and neutralinos decaying to a final state with three leptons (${{\mathit e}}$ and ${{\mathit \mu}}$) and missing transverse energy. No excess beyond the Standard Model expectation is observed. Exclusion limits are derived in the phenomenological MSSM, see Fig. 2 (top), and in simplified models, see Fig. 2 (bottom). 24 AAD 2012T looked in 1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV for the production of supersymmetric particles decaying into final states with missing transverse momentum and exactly two isolated leptons (${{\mathit e}}$ or ${{\mathit \mu}}$). Same-sign dilepton events were separately studied. Additionally, in opposite-sign events, a search was made for an excess of same-flavor over different-flavor lepton pairs. No excess over the expected background is observed and limits are placed on the effective production cross section of opposite-sign dilepton events with $\not E_T$ $>$ 250 GeV and on same-sign dilepton events with $\not E_T$ $>$ 100 GeV. The latter limit is interpreted in a simplified electroweak gaugino production model. References: AABOUD 2019AU PR D100 012006 Search for chargino and neutralino production in final states with a Higgs boson and missing transverse momentum at $\sqrt{s} = 13$ TeV with the ATLAS detector SIRUNYAN 2019BU JHEP 1908 150 Search for supersymmetry with a compressed mass spectrum in the vector boson fusion topology with 1-lepton and 0-lepton final states in proton-proton collisions at $\sqrt{s}=$ 13 TeV AABOUD 2018BT EPJ C78 995 Search for electroweak production of supersymmetric particles in final states with two or three leptons at $\sqrt{s}=13\,$TeV with the ATLAS detector AABOUD 2018AY EPJ C78 154 Search for the direct production of charginos and neutralinos in final states with tau leptons in $\sqrt{s} =$ 13 TeV $pp$ collisions with the ATLAS detector AABOUD 2018R PR D97 052010 Search for electroweak production of supersymmetric states in scenarios with compressed mass spectra at $\sqrt{s}=13$ TeV with the ATLAS detector AABOUD 2018U PR D97 092006 Search for photonic signatures of gauge-mediated supersymmetry in 13 TeV $pp$ collisions with the ATLAS detector AABOUD 2018CO PR D98 092012 Search for chargino-neutralino production using recursive jigsaw reconstruction in final states with two or three charged leptons in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector AABOUD 2018CK PR D98 092002 Search for pair production of higgsinos in final states with at least three $b$-tagged jets in $\sqrt{s} = 13$ TeV $pp$ collisions using the ATLAS detector SIRUNYAN 2018DP JHEP 1811 151 Search for supersymmetry in events with a $\tau$ lepton pair and missing transverse momentum in proton-proton collisions at $\sqrt{s} =$ 13 TeV SIRUNYAN 2018AJ PL B782 440 Search for new physics in events with two soft oppositely charged leptons and missing transverse momentum in proton-proton collisions at $\sqrt{s}=$ 13 TeV SIRUNYAN 2017AW JHEP 1711 029 Search for Electroweak Production of Charginos and Neutralinos in ${{\mathit W}}{{\mathit H}}$ Events in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV PR D93 052002 Search for the Electroweak Production of Supersymmetric Particles in $\sqrt {s }$ = 8 TeV ${{\mathit p}}{{\mathit p}}$ Collisions with the ATLAS Detector EPJ C75 208 Search for Direct Pair Production of a Chargino and a Neutralino Decaying to the 125 GeV Higgs Boson in $\sqrt {s }$ = 8 TeV ${{\mathit p}}{{\mathit p}}$ Collisions with the ATLAS Detector JHEP 1405 071 Search for Direct Production of charginos, neutralinos and sleptons in Final States with Two Leptons and Missing Transverse Momentum in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector JHEP 1404 169 Search for Direct Production of Charginos and Neutralinos in Events with Three Leptons and Missing Transverse Momentum in $\sqrt {s }$ = 8 TeV ${{\mathit p}}{{\mathit p}}$ Collisions with the ATLAS Detector PR D90 052001 Search for Supersymmetry in Events with Four or More Leptons in $\sqrt {s }$ = 8 TeV ${{\mathit p}}{{\mathit p}}$ Collisions with the ATLAS Detector EPJ C74 3036 Searches for Electroweak Production of charginos, neutralinos, and sleptons Decaying to Leptons and ${{\mathit W}}$, ${{\mathit Z}}$, and Higgs Bosons in ${{\mathit p}}{{\mathit p}}$ Collisions at 8 TeV PL B718 841 Search for Direct Production of Charginos and Neutralinos in Events with Three Leptons and Missing Transverse Momentum in $\sqrt {s }$ = 7 TeV ${{\mathit p}}{{\mathit p}}$ Collisions with the ATLAS Detector PL B709 137 Searches for Supersymmetry with the ATLAS Detector using Final States with Two Leptons and Missing Transverse Momentum in $\sqrt {s }$ = 7 TeV Proton$−$Proton Collisions PRL 108 261804 Search for Supersymmetry in Events with Three Leptons and Missing Transverse Momentum in $\sqrt {s }$ = 7 TeV ${{\mathit p}}{{\mathit p}}$ Collisions with the ATLAS Detector JHEP 1211 147 Search for Electroweak Production of Charginos and Neutralinos using Leptonic Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV PL B489 38 Limits on the Masses of Supersymmetric Particles at $\sqrt {s }$ = 189-GeV	2020-09-20T02:24:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9229479432106018, "perplexity": 2487.4927768119733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": 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https://ftp.mcs.anl.gov/pub/fathom/moab-docs/classMBMesquite_1_1OFEvaluator.html	MOAB: Mesh Oriented datABase (version 5.4.1) MBMesquite::OFEvaluator Class Reference Evaluate objective function. More... #include <OFEvaluator.hpp> Collaboration diagram for MBMesquite::OFEvaluator: ## Public Member Functions OFEvaluator (ObjectiveFunction of) Constructor. void initialize_queue (MeshDomainAssoc mesh_and_domain, const Settings settings, MsqError &err) bool initialize (MeshDomainAssoc mesh_and_domain, const Settings settings, PatchSet patches, MsqError &err) Initialize OFEvaluator. bool update (PatchData &pd, double &value, MsqError &err) Update accumulated values for changes to vertex positions in a patch. bool update (PatchData &pd, double &value, std::vector< Vector3D > &grad, MsqError &err) Update accumulated values for changes to vertex positions in a patch. bool update (PatchData &pd, double &value, std::vector< Vector3D > &grad, std::vector< SymMatrix3D > &Hessian_diag_blocks, MsqError &err) Update accumulated values for changes to vertex positions in a patch. bool update (PatchData &pd, double &value, std::vector< Vector3D > &grad, MsqHessian &Hessian, MsqError &err) Update accumulated values for changes to vertex positions in a patch. bool is_nash_game () const Check if doing Nash game algorithm. void do_nash_game () Do Nash game algorithm. bool is_block_coordinate_descent () const Check if doing block coordinate descent algorithm. void do_block_coordinate_descent () Do block coordinate descent algorithm. bool evaluate (PatchData &pd, double &value, MsqError &err) const Evaluate the objective function without changing any accumulated values. bool evaluate (PatchData &pd, double &value, std::vector< Vector3D > &grad, MsqError &err) const Evaluate the objective function without changing any accumulated values. bool evaluate (PatchData &pd, double &value, std::vector< Vector3D > &grad, std::vector< SymMatrix3D > &Hessian_diag_blocks, MsqError &err) const Evaluate the objective function without changing any accumulated values. bool evaluate (PatchData &pd, double &value, std::vector< Vector3D > &grad, MsqHessian &Hessian, MsqError &err) const Evaluate the objective function without changing any accumulated values. bool reset () Reset for next inner iteration. ObjectiveFunctionget_objective_function () const Get ObjectiveFunction pointer. bool have_objective_function () const Check if we have an objective function. ## Private Member Functions OFEvaluator (const OFEvaluator &) Disallow copying. OFEvaluatoroperator= (const OFEvaluator &) Disallow assignment. ## Private Attributes ObjectiveFunction const OF bool doBCD ObjectiveFunction::EvalType tempType ObjectiveFunction::EvalType firstType ObjectiveFunction::EvalType updateType ObjectiveFunction::EvalType currUpdateType ## Detailed Description Evaluate objective function. This class handles the details of the differences between Nash and block coordinate descent methods for evaluation of the objective function, such that solvers need only interact with this interface and need not be aware of the Nash vs. BCD details. Definition at line 58 of file OFEvaluator.hpp. ## Constructor & Destructor Documentation MBMesquite::OFEvaluator::OFEvaluator ( ObjectiveFunction of ) Constructor. Parameters: of The objective function (may be NULL for Laplacian-type solvers) Nash True for Nash-type solutions, false for block coordinate descent. Definition at line 39 of file OFEvaluator.cpp. : OF( of ), doBCD( false ) {} MBMesquite::OFEvaluator::OFEvaluator ( const OFEvaluator & ) [private] Disallow copying. ## Member Function Documentation void MBMesquite::OFEvaluator::do_block_coordinate_descent ( ) [inline] Do block coordinate descent algorithm. Definition at line 193 of file OFEvaluator.hpp. { doBCD = true; } void MBMesquite::OFEvaluator::do_nash_game ( ) [inline] Do Nash game algorithm. Definition at line 181 of file OFEvaluator.hpp. { doBCD = false; } bool MBMesquite::OFEvaluator::evaluate ( PatchData & pd, double & value, MsqError & err ) const Evaluate the objective function without changing any accumulated values. Evaluate the objective function for the specified patch (or for the change to the specified patch for BCD). This method does not change any internal state or accumulated values. It is provided for FeasibleNewton and other solvers that need to obtain an OF value for some intermediate or temporary set of vertex positions. Parameters: pd The mesh patch value Output, the value of the objective function. Definition at line 143 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } bool b = get_objective_function()->evaluate( tempType, pd, value, OF_FREE_EVALS_ONLY, err ); return !MSQ_CHKERR( err ) && b; } bool MBMesquite::OFEvaluator::evaluate ( PatchData & pd, double & value, std::vector< Vector3D > & grad, MsqError & err ) const Evaluate the objective function without changing any accumulated values. Evaluate the objective function for the specified patch (or for the change to the specified patch for BCD). This method does not change any internal state or accumulated values. It is provided for FeasibleNewton and other solvers that need to obtain an OF value for some intermediate or temporary set of vertex positions. Parameters: pd The mesh patch value Output, the value of the objective function. grad Output, the gradient of the objective function with respect to each FREE vertex in the patch. Definition at line 154 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } return !MSQ_CHKERR( err ) && b; } bool MBMesquite::OFEvaluator::evaluate ( PatchData & pd, double & value, std::vector< Vector3D > & grad, std::vector< SymMatrix3D > & Hessian_diag_blocks, MsqError & err ) const Evaluate the objective function without changing any accumulated values. Evaluate the objective function for the specified patch (or for the change to the specified patch for BCD). This method does not change any internal state or accumulated values. It is provided for FeasibleNewton and other solvers that need to obtain an OF value for some intermediate or temporary set of vertex positions. Parameters: pd The mesh patch value Output, the value of the objective function. grad Output, the gradient of the objective function with respect to each FREE vertex in the patch. Hessian_diag_blocks Output, 3x3 submatrices along diagonal of Hessian of objective function Definition at line 165 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } bool b = get_objective_function()->evaluate_with_Hessian_diagonal( tempType, pd, value, grad, hess_diag, err ); return !MSQ_CHKERR( err ) && b; } bool MBMesquite::OFEvaluator::evaluate ( PatchData & pd, double & value, std::vector< Vector3D > & grad, MsqHessian & Hessian, MsqError & err ) const Evaluate the objective function without changing any accumulated values. Evaluate the objective function for the specified patch (or for the change to the specified patch for BCD). This method does not change any internal state or accumulated values. It is provided for FeasibleNewton and other solvers that need to obtain an OF value for some intermediate or temporary set of vertex positions. Parameters: pd The mesh patch value Output, the value of the objective function. grad Output, the gradient of the objective function with respect to each FREE vertex in the patch. Hessian Output, the Hessian of the objective function. Definition at line 180 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } bool b = get_objective_function()->evaluate_with_Hessian( tempType, pd, value, grad, Hessian, err ); return !MSQ_CHKERR( err ) && b; } ObjectiveFunction* MBMesquite::OFEvaluator::get_objective_function ( ) const [inline] Get ObjectiveFunction pointer. Definition at line 286 of file OFEvaluator.hpp. { return this->OF; } bool MBMesquite::OFEvaluator::have_objective_function ( ) const [inline] Check if we have an objective function. Definition at line 292 of file OFEvaluator.hpp. Referenced by evaluate(), initialize(), MBMesquite::TerminationCriterion::reset_inner(), and update(). { return 0 != get_objective_function(); } bool MBMesquite::OFEvaluator::initialize ( MeshDomainAssoc * mesh_and_domain, const Settings * settings, PatchSet * patches, MsqError & err ) Initialize OFEvaluator. For a Nash-type algorithm, this method will initialize some member variables. For a block coordinate descent solution, this method will calculate an initial value of the objective function for the mesh. Parameters: mesh The active mesh Definition at line 41 of file OFEvaluator.cpp. Referenced by MBMesquite::VertexMover::loop_over_mesh(). { if( doBCD ) { tempType = ObjectiveFunction::TEMPORARY; firstType = ObjectiveFunction::SAVE; updateType = ObjectiveFunction::UPDATE; } else { tempType = firstType = updateType = ObjectiveFunction::CALCULATE; } reset(); if( !doBCD ) // Nash return true; if( !have_objective_function() ) { MSQ_SETERR( err ) ( "Cannot perform block coordinate descent algorithm" " without an ObjectiveFunction", MsqError::INVALID_STATE ); return false; } bool result = get_objective_function()->initialize_block_coordinate_descent( mesh_and_domain, settings, user_set, err ); return !MSQ_CHKERR( err ) && result; } void MBMesquite::OFEvaluator::initialize_queue ( MeshDomainAssoc * mesh_and_domain, const Settings * settings, MsqError & err ) Definition at line 75 of file OFEvaluator.cpp. Referenced by MBMesquite::VertexMover::initialize_queue(). { if( get_objective_function() ) get_objective_function()->initialize_queue( mesh_and_domain, settings, err );MSQ_ERRRTN( err ); } bool MBMesquite::OFEvaluator::is_block_coordinate_descent ( ) const [inline] Check if doing block coordinate descent algorithm. Definition at line 187 of file OFEvaluator.hpp. { return doBCD; } bool MBMesquite::OFEvaluator::is_nash_game ( ) const [inline] Check if doing Nash game algorithm. Definition at line 175 of file OFEvaluator.hpp. { return !doBCD; } OFEvaluator& MBMesquite::OFEvaluator::operator= ( const OFEvaluator & ) [private] Disallow assignment. bool MBMesquite::OFEvaluator::reset ( ) Reset for next inner iteration. The control code for the vertex mover is responsible for calling this method before the beginning of each inner solver iteration so the necessary internal state can be updated for the correct behavior of the first call to the update() method for block coordinate descent algorithms. Definition at line 80 of file OFEvaluator.cpp. References currUpdateType, and firstType. Referenced by initialize(), and MBMesquite::VertexMover::loop_over_mesh(). { currUpdateType = firstType; return true; } bool MBMesquite::OFEvaluator::update ( PatchData & pd, double & value, MsqError & err ) Update accumulated values for changes to vertex positions in a patch. For a block coordinate descent solution, this method calculates the updated global objective function value for any modifications to the passed patch, as made by the solver. The change to the current patch state is considered relative to that of the previous patch passed to any of the update methods, except when the reset() method has been called by the solver to indicate that a new inner iteration is starting. For a Nash-type solution, this method simply returns the evaluation of the objective funtion for the local patch. The behavior is identical to calling the evaluate() method. Parameters: pd The mesh patch value Output, the value of the objective function. Definition at line 86 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } bool b = get_objective_function()->evaluate( currUpdateType, pd, value, OF_FREE_EVALS_ONLY, err ); currUpdateType = updateType; return !MSQ_CHKERR( err ) && b; } bool MBMesquite::OFEvaluator::update ( PatchData & pd, double & value, std::vector< Vector3D > & grad, MsqError & err ) Update accumulated values for changes to vertex positions in a patch. For a block coordinate descent solution, this method calculates the updated global objective function value for any modifications to the passed patch, as made by the solver. The change to the current patch state is considered relative to that of the previous patch passed to any of the update methods, except when the reset() method has been called by the solver to indicate that a new inner iteration is starting. For a Nash-type solution, this method simply returns the evaluation of the objective funtion for the local patch. The behavior is identical to calling the evaluate() method. Parameters: pd The mesh patch value Output, the value of the objective function. grad Output, the gradient of the objective function with respect to each FREE vertex in the patch. Definition at line 98 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } currUpdateType = updateType; return !MSQ_CHKERR( err ) && b; } bool MBMesquite::OFEvaluator::update ( PatchData & pd, double & value, std::vector< Vector3D > & grad, std::vector< SymMatrix3D > & Hessian_diag_blocks, MsqError & err ) Update accumulated values for changes to vertex positions in a patch. For a block coordinate descent solution, this method calculates the updated global objective function value for any modifications to the passed patch, as made by the solver. The change to the current patch state is considered relative to that of the previous patch passed to any of the update methods, except when the reset() method has been called by the solver to indicate that a new inner iteration is starting. For a Nash-type solution, this method simply returns the evaluation of the objective funtion for the local patch. The behavior is identical to calling the evaluate() method. Parameters: pd The mesh patch value Output, the value of the objective function. grad Output, the gradient of the objective function with respect to each FREE vertex in the patch. Hessian_diag_blocks Output, 3x3 submatrices along diagonal of Hessian of objective function Definition at line 110 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } bool b = get_objective_function()->evaluate_with_Hessian_diagonal( currUpdateType, pd, value, grad, hess_diag, err ); currUpdateType = updateType; return !MSQ_CHKERR( err ) && b; } bool MBMesquite::OFEvaluator::update ( PatchData & pd, double & value, std::vector< Vector3D > & grad, MsqHessian & Hessian, MsqError & err ) Update accumulated values for changes to vertex positions in a patch. For a block coordinate descent solution, this method calculates the updated global objective function value for any modifications to the passed patch, as made by the solver. The change to the current patch state is considered relative to that of the previous patch passed to any of the update methods, except when the reset() method has been called by the solver to indicate that a new inner iteration is starting. For a Nash-type solution, this method simply returns the evaluation of the objective funtion for the local patch. The behavior is identical to calling the evaluate() method. Parameters: pd The mesh patch value Output, the value of the objective function. grad Output, the gradient of the objective function with respect to each FREE vertex in the patch. Hessian Output, the Hessian of the objective function. Definition at line 127 of file OFEvaluator.cpp. { if( !have_objective_function() ) { MSQ_SETERR( err )( "No ObjectiveFunction", MsqError::INVALID_STATE ); return false; } bool b = get_objective_function()->evaluate_with_Hessian( currUpdateType, pd, value, grad, Hessian, err ); currUpdateType = updateType; return !MSQ_CHKERR( err ) && b; } ## Member Data Documentation ObjectiveFunction::EvalType MBMesquite::OFEvaluator::currUpdateType [private] Definition at line 311 of file OFEvaluator.hpp. Referenced by reset(), and update(). bool MBMesquite::OFEvaluator::doBCD [private] Nash or BCD Definition at line 308 of file OFEvaluator.hpp. Referenced by initialize(). ObjectiveFunction::EvalType MBMesquite::OFEvaluator::firstType [private] Definition at line 311 of file OFEvaluator.hpp. Referenced by initialize(), and reset(). ObjectiveFunction* const MBMesquite::OFEvaluator::OF [private] The ObjectiveFunction to evaluate Definition at line 305 of file OFEvaluator.hpp. ObjectiveFunction::EvalType MBMesquite::OFEvaluator::tempType [private] Nash vs. BCD and state of BCD data Definition at line 311 of file OFEvaluator.hpp. Referenced by evaluate(), and initialize(). ObjectiveFunction::EvalType MBMesquite::OFEvaluator::updateType [private] Definition at line 311 of file OFEvaluator.hpp. Referenced by initialize(), and update(). List of all members. The documentation for this class was generated from the following files:	2022-12-06T16:50:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3568628430366516, "perplexity": 11614.577240079167}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00304.warc.gz"}
https://gssc.esa.int/navipedia/index.php/GNSS_Broadcast_Orbits	If you wish to contribute or participate in the discussions about articles you are invited to join Navipedia as a registered user Fundamentals Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain. Level Intermediate Year of Publication 2011 The user receiver computes the satellites coordinates from the information broadcast by the GNSS satellites in the navigation messages. Two different approaches are followed by GPS/Galileo and GLONASS satellites to account for satellite orbit perturbations. Those approaches define their messages contain. In the case of GPS or Galileo satellites, the orbits are seen as Keplerian in first approximation, and the perturbations are treated as temporal variations in the orbital elements. Indeed, an extended set of sixteen quasi-Kleperian parameters (see table (1) in GPS and Galileo Satellite Coordinates Computation) is broadcast to the user in the navigation message and regularly updated. This expanded set consists of the six orbital elements $\displaystyle(a(t),e(t),i(t),$ $\displaystyle \Omega (t),\omega (t), M(t))$ plus three rate parameters to account for the linear changes with time $(\stackrel{\bullet}{\Omega},\stackrel{\bullet}{i},\Delta n)$, three pairs of sinusoidal corrections $\displaystyle(C_c,C_s)$ (i.e., $\displaystyle C_c\cos(2\phi)$, $\displaystyle C_s\sin(2\phi)$), and the reference ephemeris epoch $t_e$ (see article GPS and Galileo Satellite Coordinates Computation). For GLONASS satellites, the navigation message broadcasts initial conditions of position and velocity $(\mathbb{\mathbf r}_0,\mathbb{\mathbf v}_0)$ and moon and solar gravitational acceleration perturbation vector components (see table (1) in GLONASS Satellite Coordinates Computation) to perform a numerical integration of the orbit. The integration is based on applying a 4$^{th}$-order Runge-Kutta method to the equation: $\mathbb{\mathbf {\ddot r}}=\nabla V+\mathbb{\mathbf k}_{sun\_moon} \qquad \mbox{(1)}$ where $V$ is the potential defined by $\begin{array}{ll} V= & \displaystyle \frac{\mu}{r}\left[ 1- \displaystyle \sum_{n=2}^{\infty}{\left(\frac{a_e}{r}\right)^n J_n\; P_n(\sin \phi)} \right .\\ & + \left. \displaystyle \sum_{n=2}^{\infty}{\displaystyle \sum_{m=1}^{\infty}{\left(\frac{a_e}{r}\right)^n \left[ C_{nm} \cos m\lambda + S_{nm} \sin m\lambda \right ] P_{nm}(\sin \phi)}}\right ] \end{array} \qquad \mbox{(2)}$ presented in Perturbed Motion and ($\mathbb{\mathbf k}_{sun\_moon}$) are the moon-solar accelerations expressed in an inertial coordinate system (see article GLONASS Satellite Coordinates Computation). Note: In the differential equations system from GLONASS Satellite Coordinates Computation: $\left\{ \begin{array}{l} \frac{dx_a}{dt}=v_{x_a}(t)\\ \frac{dy_a}{dt}=v_{y_a}(t)\\ \frac{dz_a}{dt}=v_{z_a}(t)\\ \frac{dv_{x_a}}{dt}=-\bar{\mu} \bar{x}_a +\frac{3}{2}C_{20}\bar{\mu} \bar{x}_a \rho^2(1-5 \bar{z}_a^2)+ Jx_am+Jx_as\\ \frac{dv_{y_a}}{dt}=-\bar{\mu} \bar{y}_a +\frac{3}{2}C_{20}\bar{\mu} \bar{y}_a \rho^2(1-5 \bar{z}_a^2)+ Jy_am+Jy_as\\ \frac{dv_{z_a}}{dt}=-\bar{\mu} \bar{z}_a +\frac{3}{2}C_{20}\bar{\mu} \bar{z}_a \rho^2(3-5 \bar{z}_a^2)+ Jz_am+Jz_as\\ \end{array} \qquad \mbox{(3)} \right .$ the term $C_{20}=-J_2=+\sqrt{5}\bar{C}_{20}$ is used instead of $J_2$ to keep the same expressions as in GLONASS-ICD. Comment: At any epoch the state of motion of the satellite is given by six parameters: The position and velocity vector components $\displaystyle (\mathbb{\mathbf r},\mathbb{\mathbf v})$, or the six Keplerian elements $\displaystyle (a,e,i,\Omega, \omega,V)$; therefore, a point-to-point transformation can be done between them. The orbit elements are the natural representation of the orbit, because (in absence of perturbations) the motion along the orbit is described by a single parameter $\displaystyle(V(t))$. In presence of perturbing forces, time-varying Keplerian elements defining an ellipse tangent to the orbit at any epoch can be considered, i.e, an osculating orbit [footnotes 1]. ## Notes 1. ^ From the Latin verb osculor (to kiss).	2019-02-23T15:51:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6971853971481323, "perplexity": 1575.248640606479}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249504746.91/warc/CC-MAIN-20190223142639-20190223164639-00097.warc.gz"}
https://gea.esac.esa.int/archive/documentation/GEDR3/Catalogue_consolidation/chap_cu9val/sec_cu9val_943/ssec_cu9val_943_proper_motion.html	7.3.3 Proper motion distributions $\mu_{l}$ and $\mu_{b}$, the projections of the proper motion along the Galactic coordinates, are computed in order to see systematics due to the Galactic rotation. The median of the proper motions is computed in each healpix bin and shown in Figure 7.13 ($\mu_{l}$) and Figure 7.14 ($\mu_{b}$). At bright magnitudes, the dispersion is high, due to the small number of stars, and differences are not significant. The model and data present approximately similar patterns in all magnitude ranges. However, there are systematics, as was already noted in the validation of Gaia DR2. It is most probable that these systematic differences are due to inaccuracy in modelling (e.g. the Galactic rotation). Figure 7.15 gives the proper motion averaged over the whole sky per magnitude bin, for Gaia EDR3, Gaia DR2, and GOG20. At bright magnitudes, the difference between Gaia EDR3 and GOG20 in $\mu_{l}$ is at the level of 0.05 mas/yr, and increases at fainter magnitudes (up to $\sim$0.4 mas/yr). The systematics are less than 0.05 mas/yr in $\mu_{b}$. Summary of the results: • Overall, it seems that the Gaia EDR3 data are as expected from our knowledge of the Galactic kinematics up to very faint magnitudes and it is probably the model which suffers from systematics, or does not account for asymmetries. Indeed we note that the change of kinematics from GOG18 to GOG20 globally allows for a better agreement with the data.	2021-02-28T09:35:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 17, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7652339935302734, "perplexity": 997.1424331399553}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178360745.35/warc/CC-MAIN-20210228084740-20210228114740-00258.warc.gz"}
https://par.nsf.gov/biblio/10091972-benchmarking-gaze-prediction-categorical-visual-search	Benchmarking Gaze Prediction for Categorical Visual Search The prediction of human shifts of attention is a widely-studied question in both behavioral and computer vision, especially in the context of a free viewing task. However, search behavior, where the fixation scanpaths are highly dependent on the viewer's goals, has received far less attention, even though visual search constitutes much of a person's everyday behavior. One reason for this is the absence of real-world image datasets on which search models can be trained. In this paper we present a carefully created dataset for two target categories, microwaves and clocks, curated from the COCO2014 dataset. A total of 2183 images were presented to multiple participants, who were tasked to search for one of the two categories. This yields a total of 16184 validated fixations used for training, making our microwave-clock dataset currently one of the largest datasets of eye fixations in categorical search. We also present a 40-image testing dataset, where images depict both a microwave and a clock target. Distinct fixation patterns emerged depending on whether participants searched for a microwave (n=30) or a clock (n=30) in the same images, meaning that models need to predict different search scanpaths from the same pixel inputs. We report the results of more » Authors: ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10091972 Journal Name: CVPR Workshop - Mutual Benefits of Cognitive and Computer Vision Attention control is a basic behavioral process that has been studied for decades. The currently best models of attention control are deep networks trained on free-viewing behavior to predict bottom-up attention control – saliency. We introduce COCO-Search18, the first dataset of laboratory-qualitygoal-directed behaviorlarge enough to train deep-network models. We collected eye-movement behavior from 10 people searching for each of 18 target-object categories in 6202 natural-scene images, yielding$$\sim$$$\sim$300,000 search fixations. We thoroughly characterize COCO-Search18, and benchmark it using three machine-learning methods: a ResNet50 object detector, a ResNet50 trained on fixation-density maps, and an inverse-reinforcement-learning model trained on behavioral search scanpaths. Models were also trained/tested on images transformed to approximate a foveated retina, a fundamental biological constraint. These models, each having a different reliance on behavioral training, collectively comprise the new state-of-the-art in predicting goal-directed search fixations. Our expectation is that future work using COCO-Search18 will far surpass these initial efforts, finding applications in domains ranging from human-computer interactive systems that can anticipate a person’s intent and render assistance to the potentially early identification of attention-related clinical disorders (ADHD, PTSD, phobia) based on deviation from neurotypical fixation behavior.	2022-11-27T13:19:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30541637539863586, "perplexity": 4728.9571272953435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710237.57/warc/CC-MAIN-20221127105736-20221127135736-00767.warc.gz"}
https://darktarget.gsfc.nasa.gov/content/modis-3-km-aerosol-product-algorithm-and-global-perspective	Sorry, you need to enable JavaScript to visit this website. # MODIS 3 km aerosol product: algorithm and global perspective Title MODIS 3 km aerosol product: algorithm and global perspective Publication Type Journal Article Year of Publication 2013 Authors Remer, LA, Mattoo, S, Levy, RC, Munchak, LA Journal Atmospheric Measurement Techniques Volume 6 Pagination 1829–1844 Abstract After more than a decade of producing a nominal 10 km aerosol product based on the dark target method, the MODerate resolution Imaging Spectroradiometer (MODIS) aerosol team will be releasing a nominal 3 km product as part of their Collection 6 release. The new product differs from the original 10 km product only in the manner in which reflectance pixels are ingested, organized and selected by the aerosol algorithm. Overall, the 3 km product closely mirrors the 10 km product. However, the finer resolution product is able to retrieve over the ocean closer to islands and coastlines, and is better able to resolve fine aerosol features such as smoke plumes over both ocean and land. In some situations, it provides retrievals over entire regions that the 10 km product barely samples. In situations traditionally difficult for the dark target algorithm such as over bright or urban surfaces, the 3 km product introduces isolated spikes of artificially high aerosol optical depth (AOD) that the 10 km algorithm avoids. Over land, globally, the 3 km product appears to be 0.01 to 0.02 higher than the 10 km product, while over ocean, the 3 km algorithm is retrieving a proportionally greater number of very low aerosol loading situations. Based on collocations with ground-based observations for only six months, expected errors associated with the 3 km land product are determined to be greater than that of the 10 km product: $\pm$ 0.05 $\pm$ 0.20 AOD. Over ocean, the suggestion is for expected errors to be the same as the 10 km product: $\pm$ 0.03 $\pm$ 0.05 AOD, but slightly less accurate in the coastal zone. The advantage of the product is on the local scale, which will require continued evaluation not addressed here. Nevertheless, the new 3 km product is expected to provide important information complementary to existing satellite-derived products and become an important tool for the aerosol community. URL http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2013AMT.....6.1829R&link_type=ABSTRACT DOI 10.5194/amt-6-1829-2013	2022-01-27T10:40:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4746437072753906, "perplexity": 2872.930134820582}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305260.61/warc/CC-MAIN-20220127103059-20220127133059-00204.warc.gz"}
http://algebra2014.wikidot.com/cody-buehler	Cody Buehler My name is Cody Buehler, and I grew up here in St. Joseph. I'm a Mathematics major, and plan to use my degree to become an actuarial scientist. This is my last semester here at MWSU, and it couldn't have come any sooner. I don't particularly have a "favorite" math theorem, but one I find quite useful is the Central Limit Theorem: Let $Y_1, Y_2,...,Y_n$ be independent and identically distributed random variables with $E(Y_i)=\mu$ and $V(Y_i)=\sigma ^2 < \infty$. Define (1) \begin{align} U_n= \frac{\sum_{i=i}^{n} Y_i - n\mu}{\sigma \sqrt{n}} = \frac{\bar{Y} - \mu}{\sigma \: / \sqrt{n}} \;\;\; \text{where} \; \bar{Y} = \frac{1}{n} \sum_{i=1}^{n} Y_i . \end{align} Then the distribution function of $U_n$ converges to the standard normal distribution function as $n \to \infty$. That is, (2) \begin{align} \lim_{n \to \infty} P(U_n \leq u) = \int_{- \infty}^u \frac{1}{\sqrt{2\pi}}e^{\frac{-t^2}{2}} \! \: dt \;\;\; \text{for all} \: u. \end{align} This is very useful since it allows you to take raw data and relate it to a distribution in order to calculate various probabilities. Lastly, here is a picture of me and my girlfriend enjoying a few drinks: Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License	2019-02-21T21:06:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8334863781929016, "perplexity": 1036.2691685665832}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247508363.74/warc/CC-MAIN-20190221193026-20190221215026-00272.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Aderksen.harm	# zbMATH — the first resource for mathematics ## Derksen, Harm Compute Distance To: Author ID: derksen.harm Published as: Derksen, H.; Derksen, H. G. J.; Derksen, Harm External Links: MGP · Wikidata · GND Documents Indexed: 66 Publications since 1993, including 3 Books Reviewing Activity: 13 Reviews all top 5 #### Co-Authors 20 single-authored 13 Weyman, Jerzy M. 8 Makam, Visu 4 Kemper, Gregor 3 Kutzschebauch, Frank 3 Masser, David William 3 van den Essen, Arno 2 Fink, Alex 2 Sidman, Jessica 2 Zelevinskiĭ, Andreĭ V. 1 Chindris, Calin 1 Eggermont, Christian E. J. 1 Eggermont, Rob H. 1 Fei, Jiarui 1 Finston, David Robert 1 Fossum, Robert M. 1 Hadas, Ofer 1 Huisgen-Zimmermann, Birge 1 Jeandel, Emmanuel 1 Koiran, Pascal 1 Kraft, Hanspeter 1 Ma, Yi 1 Makar-Limanov, Leonid G. 1 Maubach, Stefan 1 Owen, Theodore 1 Schofield, Aidan 1 Snowden, Andrew W. 1 Teitler, Zach 1 Winkelmann, Jörg 1 Yang, Allen Y. 1 Zhao, Wenhua all top 5 #### Serials 10 Advances in Mathematics 5 Journal of Algebra 5 Journal of Pure and Applied Algebra 4 Linear and Multilinear Algebra 2 American Mathematical Monthly 2 Communications in Algebra 2 Compositio Mathematica 2 Journal of Symbolic Computation 2 Journal of the American Mathematical Society 2 Algebra & Number Theory 1 IEEE Transactions on Information Theory 1 Israel Journal of Mathematics 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Colloquium Mathematicum 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Ergodic Theory and Dynamical Systems 1 Linear Algebra and its Applications 1 SIAM Review 1 Notices of the American Mathematical Society 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Combinatorics 1 The Electronic Journal of Combinatorics 1 Selecta Mathematica. New Series 1 Foundations of Computational Mathematics 1 Graduate Studies in Mathematics 1 SIAM Journal on Applied Algebra and Geometry all top 5 #### Fields 27 Commutative algebra (13-XX) 23 Algebraic geometry (14-XX) 18 Associative rings and algebras (16-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 9 Combinatorics (05-XX) 8 Group theory and generalizations (20-XX) 7 Computer science (68-XX) 5 Number theory (11-XX) 4 Convex and discrete geometry (52-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Field theory and polynomials (12-XX) 2 Nonassociative rings and algebras (17-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) #### Citations contained in zbMATH 58 Publications have been cited 1,030 times in 775 Documents Cited by Year Quivers with potentials and their representations. I: Mutations. Zbl 1204.16008 Derksen, Harm; Weyman, Jerzy; Zelevinsky, Andrei 2008 Computational invariant theory. Zbl 1011.13003 Derksen, Harm; Kemper, Gregor 2002 Quivers with potentials and their representations. II: Applications to cluster algebras. Zbl 1208.16017 Derksen, Harm; Weyman, Jerzy; Zelevinsky, Andrei 2010 Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients. Zbl 0993.16011 Derksen, Harm; Weyman, Jerzy 2000 The combinatorics of quiver representations. Zbl 1271.16016 Derksen, Harm; Weyman, Jerzy 2011 On the canonical decomposition of quiver representations. Zbl 1016.16007 Derksen, Harm; Weyman, Jerzy 2002 A sharp bound for the Castelnuovo-Mumford regularity of subspace arrangements. Zbl 1040.13009 Derksen, Harm; Sidman, Jessica 2002 Quiver representations. Zbl 1143.16300 Derksen, Harm; Weyman, Jerzy 2005 Estimation of subspace arrangements with applications in modeling and segmenting mixed data. Zbl 1147.52010 Ma, Yi; Yang, Allen Y.; Derksen, Harm; Fossum, Robert 2008 On the Littlewood-Richardson polynomials. Zbl 1018.16012 Derksen, Harm; Weyman, Jerzy 2002 Computation of invariants for reductive groups. Zbl 0927.13007 Derksen, Harm 1999 Computing invariants of algebraic groups in arbitrary characteristic. Zbl 1138.13003 Derksen, Harm; Kemper, Gregor 2008 Generalized quivers associated to reductive groups. Zbl 1025.16010 Derksen, Harm; Weyman, Jerzy 2002 Polynomial bounds for rings of invariants. Zbl 0969.13003 Derksen, Harm 2001 Polynomial degree bounds for matrix semi-invariants. Zbl 1361.15033 Derksen, Harm; Makam, Visu 2017 Computational invariant theory. With two appendices by Vladimir L. Popov and an addendum by Nobert A. Campo and Vladimir L. Popov. 2nd enlarged edition. Zbl 1332.13001 Derksen, Harm; Kemper, Gregor 2015 The kernel of a derivation. Zbl 0768.12004 Derksen, H. G. J. 1993 A Skolem-Mahler-Lech theorem in positive characteristic and finite automata. Zbl 1205.11030 Derksen, Harm 2007 Quantum automata and algebraic groups. Zbl 1124.81004 Derksen, Harm; Jeandel, Emmanuel; Koiran, Pascal 2005 On the nuclear norm and the singular value decomposition of tensors. Zbl 1343.15016 Derksen, Harm 2016 Nonlinearizable holomorphic group actions. Zbl 0911.32042 Derksen, Harm; Kutzschebauch, Frank 1998 General presentations of algebras. Zbl 1361.16006 Derksen, Harm; Fei, Jiarui 2015 Linear equations over multiplicative groups, recurrences, and mixing. I. Zbl 1269.11062 Derksen, Harm; Masser, David 2012 Symmetric and quasi-symmetric functions associated to polymatroids. Zbl 1231.05276 Derksen, Harm 2009 Hilbert series of subspace arrangements. Zbl 1106.13016 Derksen, Harm 2007 Valuative invariants for polymatroids. Zbl 1221.05031 Derksen, Harm; Fink, Alex 2010 New graphs of finite mutation type. Zbl 1180.05052 Derksen, Harm; Owen, Theodore 2008 Subvarieties of $$\mathbb{C}^n$$ with non-extendable automorphisms. Zbl 0915.32005 Derksen, Harm; Kutzschebach, Frank; Winkelmann, Jörg 1999 Topological noetherianity for cubic polynomials. Zbl 06818950 Derksen, Harm; Eggermont, Rob; Snowden, Andrew 2017 Multimagic squares. Zbl 1141.05024 Derksen, Harm; Eggermont, Christian; van den Essen, Arno 2007 Newton polytopes of invariants of additive group actions. Zbl 0986.13005 Derksen, Harm; Hadas, Ofer; Makar-Limanov, Leonid 2001 On the number of subrepresentations of a general quiver representation. Zbl 1146.16007 Derksen, Harm; Schofield, Aidan; Weyman, Jerzy 2007 Global holomorphic linearization of actions of compact Lie groups on $$\mathbb{C}^n$$. Zbl 0933.32032 Derksen, Harm; Kutzschebauch, Frank 1999 Constructive invariant theory. Zbl 0883.13003 Derksen, Harm; Kraft, Hanspeter 1995 An introduction to quiver representations. Zbl 1426.16001 Derksen, Harm; Weyman, Jerzy 2017 Linear equations over multiplicative groups, recurrences, and mixing. II. Zbl 1314.11070 Derksen, H.; Masser, D. 2015 Castelnuovo-Mumford regularity by approximation. Zbl 1062.13003 Derksen, Harm; Sidman, Jessica 2004 Degree bounds for syzygies of invariants. Zbl 1067.13002 Derksen, Harm 2004 Semi-invariants for quivers with relations. Zbl 1048.16005 Derksen, Harm; Weyman, Jerzy 2002 The Gaussian moments conjecture and the Jacobian conjecture. Zbl 1365.14082 Derksen, Harm; van den Essen, Arno; Zhao, Wenhua 2017 Lower bound for ranks of invariant forms. Zbl 1322.15013 Derksen, Harm; Teitler, Zach 2015 On non-commutative rank and tensor rank. Zbl 1392.15034 Derksen, Harm; Makam, Visu 2018 Generating invariant rings of quivers in arbitrary characteristic. Zbl 1393.16008 Derksen, Harm; Makam, Visu 2017 Counterexamples to Okounkov’s log-concavity conjecture. Zbl 1184.05136 Chindris, Calin; Derksen, Harm; Weyman, Jerzy 2007 Universal denominators of Hilbert series. Zbl 1117.13017 Derksen, Harm 2005 Kruskal’s uniqueness inequality is sharp. Zbl 1267.15022 Derksen, Harm 2013 Quotients of algebraic group actions. Zbl 0838.14039 Derksen, Harm 1995 Degree bounds for semi-invariant rings of quivers. Zbl 1410.16020 Derksen, Harm; Makam, Visu 2018 Top-stable degenerations of finite dimensional representations. II. Zbl 1303.16017 Derksen, H.; Huisgen-Zimmermann, B.; Weyman, J. 2014 On global degree bounds for invariants. Zbl 1072.14056 Derksen, Harm; Kemper, Gregor 2004 Inverse degrees and the Jacobian conjecture. Zbl 0815.13009 Derksen, Harm 1994 Linear equations over multiplicative groups, recurrences, and mixing. III. Zbl 1398.37005 Derksen, H.; Masser, D. 2018 Matrix completion and tensor rank. Zbl 1346.15026 Derksen, Harm 2016 The graph isomorphism problem and approximate categories. Zbl 1283.05183 Derksen, Harm 2013 Unipotent group actions on affine varieties. Zbl 1242.14055 Derksen, Harm; van den Essen, Arno; Finston, David R.; Maubach, Stefan 2011 Error-correcting codes and $$B_h$$-sequences. Zbl 1288.94117 Derksen, Harm 2004 Construction invariant theory. Zbl 1067.13001 Derksen, Harm 2004 The fundamental theorem of algebra and linear algebra. Zbl 1082.12002 Derksen, Harm 2003 On non-commutative rank and tensor rank. Zbl 1392.15034 Derksen, Harm; Makam, Visu 2018 Degree bounds for semi-invariant rings of quivers. Zbl 1410.16020 Derksen, Harm; Makam, Visu 2018 Linear equations over multiplicative groups, recurrences, and mixing. III. Zbl 1398.37005 Derksen, H.; Masser, D. 2018 Polynomial degree bounds for matrix semi-invariants. Zbl 1361.15033 Derksen, Harm; Makam, Visu 2017 Topological noetherianity for cubic polynomials. Zbl 06818950 Derksen, Harm; Eggermont, Rob; Snowden, Andrew 2017 An introduction to quiver representations. Zbl 1426.16001 Derksen, Harm; Weyman, Jerzy 2017 The Gaussian moments conjecture and the Jacobian conjecture. Zbl 1365.14082 Derksen, Harm; van den Essen, Arno; Zhao, Wenhua 2017 Generating invariant rings of quivers in arbitrary characteristic. Zbl 1393.16008 Derksen, Harm; Makam, Visu 2017 On the nuclear norm and the singular value decomposition of tensors. Zbl 1343.15016 Derksen, Harm 2016 Matrix completion and tensor rank. Zbl 1346.15026 Derksen, Harm 2016 Computational invariant theory. With two appendices by Vladimir L. Popov and an addendum by Nobert A. Campo and Vladimir L. Popov. 2nd enlarged edition. Zbl 1332.13001 Derksen, Harm; Kemper, Gregor 2015 General presentations of algebras. Zbl 1361.16006 Derksen, Harm; Fei, Jiarui 2015 Linear equations over multiplicative groups, recurrences, and mixing. II. Zbl 1314.11070 Derksen, H.; Masser, D. 2015 Lower bound for ranks of invariant forms. Zbl 1322.15013 Derksen, Harm; Teitler, Zach 2015 Top-stable degenerations of finite dimensional representations. II. Zbl 1303.16017 Derksen, H.; Huisgen-Zimmermann, B.; Weyman, J. 2014 Kruskal’s uniqueness inequality is sharp. Zbl 1267.15022 Derksen, Harm 2013 The graph isomorphism problem and approximate categories. Zbl 1283.05183 Derksen, Harm 2013 Linear equations over multiplicative groups, recurrences, and mixing. I. Zbl 1269.11062 Derksen, Harm; Masser, David 2012 The combinatorics of quiver representations. Zbl 1271.16016 Derksen, Harm; Weyman, Jerzy 2011 Unipotent group actions on affine varieties. Zbl 1242.14055 Derksen, Harm; van den Essen, Arno; Finston, David R.; Maubach, Stefan 2011 Quivers with potentials and their representations. II: Applications to cluster algebras. Zbl 1208.16017 Derksen, Harm; Weyman, Jerzy; Zelevinsky, Andrei 2010 Valuative invariants for polymatroids. Zbl 1221.05031 Derksen, Harm; Fink, Alex 2010 Symmetric and quasi-symmetric functions associated to polymatroids. Zbl 1231.05276 Derksen, Harm 2009 Quivers with potentials and their representations. I: Mutations. Zbl 1204.16008 Derksen, Harm; Weyman, Jerzy; Zelevinsky, Andrei 2008 Estimation of subspace arrangements with applications in modeling and segmenting mixed data. Zbl 1147.52010 Ma, Yi; Yang, Allen Y.; Derksen, Harm; Fossum, Robert 2008 Computing invariants of algebraic groups in arbitrary characteristic. Zbl 1138.13003 Derksen, Harm; Kemper, Gregor 2008 New graphs of finite mutation type. Zbl 1180.05052 Derksen, Harm; Owen, Theodore 2008 A Skolem-Mahler-Lech theorem in positive characteristic and finite automata. Zbl 1205.11030 Derksen, Harm 2007 Hilbert series of subspace arrangements. Zbl 1106.13016 Derksen, Harm 2007 Multimagic squares. Zbl 1141.05024 Derksen, Harm; Eggermont, Christian; van den Essen, Arno 2007 On the number of subrepresentations of a general quiver representation. Zbl 1146.16007 Derksen, Harm; Schofield, Aidan; Weyman, Jerzy 2007 Counterexamples to Okounkov’s log-concavity conjecture. Zbl 1184.05136 Chindris, Calin; Derksen, Harm; Weyman, Jerzy 2007 Quiver representations. Zbl 1143.16300 Derksen, Harm; Weyman, Jerzy 2005 Quantum automata and algebraic groups. Zbl 1124.81004 Derksen, Harm; Jeandel, Emmanuel; Koiran, Pascal 2005 Universal denominators of Hilbert series. Zbl 1117.13017 Derksen, Harm 2005 Castelnuovo-Mumford regularity by approximation. Zbl 1062.13003 Derksen, Harm; Sidman, Jessica 2004 Degree bounds for syzygies of invariants. Zbl 1067.13002 Derksen, Harm 2004 On global degree bounds for invariants. Zbl 1072.14056 Derksen, Harm; Kemper, Gregor 2004 Error-correcting codes and $$B_h$$-sequences. Zbl 1288.94117 Derksen, Harm 2004 Construction invariant theory. Zbl 1067.13001 Derksen, Harm 2004 The fundamental theorem of algebra and linear algebra. Zbl 1082.12002 Derksen, Harm 2003 Computational invariant theory. Zbl 1011.13003 Derksen, Harm; Kemper, Gregor 2002 On the canonical decomposition of quiver representations. Zbl 1016.16007 Derksen, Harm; Weyman, Jerzy 2002 A sharp bound for the Castelnuovo-Mumford regularity of subspace arrangements. Zbl 1040.13009 Derksen, Harm; Sidman, Jessica 2002 On the Littlewood-Richardson polynomials. Zbl 1018.16012 Derksen, Harm; Weyman, Jerzy 2002 Generalized quivers associated to reductive groups. Zbl 1025.16010 Derksen, Harm; Weyman, Jerzy 2002 Semi-invariants for quivers with relations. Zbl 1048.16005 Derksen, Harm; Weyman, Jerzy 2002 Polynomial bounds for rings of invariants. Zbl 0969.13003 Derksen, Harm 2001 Newton polytopes of invariants of additive group actions. Zbl 0986.13005 Derksen, Harm; Hadas, Ofer; Makar-Limanov, Leonid 2001 Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients. Zbl 0993.16011 Derksen, Harm; Weyman, Jerzy 2000 Computation of invariants for reductive groups. Zbl 0927.13007 Derksen, Harm 1999 Subvarieties of $$\mathbb{C}^n$$ with non-extendable automorphisms. Zbl 0915.32005 Derksen, Harm; Kutzschebach, Frank; Winkelmann, Jörg 1999 Global holomorphic linearization of actions of compact Lie groups on $$\mathbb{C}^n$$. Zbl 0933.32032 Derksen, Harm; Kutzschebauch, Frank 1999 Nonlinearizable holomorphic group actions. Zbl 0911.32042 Derksen, Harm; Kutzschebauch, Frank 1998 Constructive invariant theory. Zbl 0883.13003 Derksen, Harm; Kraft, Hanspeter 1995 Quotients of algebraic group actions. Zbl 0838.14039 Derksen, Harm 1995 Inverse degrees and the Jacobian conjecture. Zbl 0815.13009 Derksen, Harm 1994 The kernel of a derivation. Zbl 0768.12004 Derksen, H. G. J. 1993 all top 5 #### Cited by 857 Authors 27 Derksen, Harm 18 Schiffler, Ralf 14 Domokos, Mátyás 14 Sezer, Müfit 10 Igusa, Kiyoshi 10 Kutzschebauch, Frank 10 Weyman, Jerzy M. 9 Chindris, Calin 9 Fei, Jiarui 9 Labardini-Fragoso, Daniel 8 Cecotti, Sergio 8 Iyama, Osamu 8 Keller, Bernhard 8 Kohls, Martin 8 Makam, Visu 8 Shank, R. James 7 Dufresne, Emilie 7 Garver, Alexander 7 Herbig, Hans-Christian 7 Kemper, Gregor 7 Kuroda, Shigeru 7 Seaton, Christopher 7 Serhiyenko, Khrystyna 6 Cerulli Irelli, Giovanni 6 Chen, Yin 6 Draisma, Jan 6 Elmer, Jonathan 6 Geiss, Christof 6 Lopatin, Artem A. 5 Amiot, Claire 5 Assem, Ibrahim 5 Bocklandt, Raf 5 Chen, Kejun 5 Del Zotto, Michele 5 Drensky, Vesselin 5 Kaliman, Shulim I. 5 Lee, Kyungyong 5 Lerman, Gilad 5 Marsh, Robert James 5 McConville, Thomas 5 Mekareeya, Noppadol 5 Nowicki, Andrzej 5 Plamondon, Pierre-Guy 5 Ressayre, Nicolas 5 Schröer, Jan 5 Seven, Ahmet I. 5 Stella, Salvatore 5 Todorov, Gordana 5 Van den Bergh, Michel 5 Wehlau, David Louis 5 Weist, Thorsten 5 Young, Matthew B. 4 Aldroubi, Akram 4 Ballico, Edoardo 4 Baur, Karin 4 Bell, Jason P. 4 Campbell, H. E. A. Eddy 4 Elsenhans, Andreas-Stephan 4 Erdmann, Karin 4 Felikson, Anna Aleksandrovna 4 Fomin, Sergey Vladimirovich 4 Freudenburg, Gene 4 Gupta, Neena 4 Herden, Daniel 4 Ivanyos, Gábor 4 King, Alastair D. 4 Leclerc, Bernard 4 Mizuno, Yuya 4 Musiker, Gregg 4 Olive, Marc 4 Paquette, Charles 4 Qiao, Youming 4 Qin, Fan 4 Qiu, Yu 4 Sam, Steven V. 4 Sergeichuk, Vladimir Vasil’evich 4 Skowroński, Andrzej 4 Snowden, Andrew W. 4 Teitler, Zach 4 Thomas, Hugh Ross 4 Tumarkin, Pavel 4 Varbaro, Matteo 4 Zelevinskiĭ, Andreĭ V. 4 Zhang, Yong 4 Zubkov, Alexandr N. 3 Amrutiya, Sanjaykumar Hansraj 3 Belkale, Prakash 3 Bik, Arthur 3 Bobiński, Grzegorz 3 Brüstle, Thomas 3 Cao, Peigen 3 Chuai, Jianjun 3 Crachiola, Anthony J. 3 Cziszter, Kálmán 3 de Graaf, Willem Adriaan 3 Dupont, Grégoire 3 Erdemirci Erkuş, Deniz 3 Fındık, Şehmus 3 Gatermann, Karin 3 Hanany, Amihay ...and 757 more Authors all top 5 #### Cited in 169 Serials 97 Journal of Algebra 64 Advances in Mathematics 52 Journal of Pure and Applied Algebra 26 Proceedings of the American Mathematical Society 23 Communications in Algebra 22 Transactions of the American Mathematical Society 21 Algebras and Representation Theory 20 Linear Algebra and its Applications 18 Transformation Groups 17 Journal of Symbolic Computation 16 Journal of High Energy Physics 14 Compositio Mathematica 14 Journal of Algebraic Combinatorics 12 Journal of Combinatorial Theory. Series A 12 Journal of Algebra and its Applications 11 Mathematische Zeitschrift 10 Selecta Mathematica. New Series 9 Communications in Mathematical Physics 9 Foundations of Computational Mathematics 8 Journal of the American Mathematical Society 7 Inventiones Mathematicae 7 Indagationes Mathematicae. New Series 6 Nuclear Physics. B 6 Mathematics of Computation 6 Glasgow Mathematical Journal 6 Nagoya Mathematical Journal 5 Discrete Mathematics 5 Linear and Multilinear Algebra 5 Annales de l’Institut Fourier 5 Duke Mathematical Journal 5 Advances in Applied Mathematics 4 Memoirs of the American Mathematical Society 4 Proceedings of the London Mathematical Society. Third Series 4 Acta Applicandae Mathematicae 4 International Journal of Algebra and Computation 4 Bulletin of the American Mathematical Society. New Series 4 Annals of Mathematics. Second Series 4 Communications in Contemporary Mathematics 4 SIAM Journal on Applied Algebra and Geometry 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Journal of Number Theory 3 Manuscripta Mathematica 3 Mathematische Annalen 3 Michigan Mathematical Journal 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 SIAM Journal on Matrix Analysis and Applications 3 Computational Complexity 3 Journal of Mathematical Sciences (New York) 3 Documenta Mathematica 3 Séminaire Lotharingien de Combinatoire 3 Central European Journal of Mathematics 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Algebra & Number Theory 3 Algebraic Combinatorics 2 International Journal of Modern Physics A 2 Journal of Mathematical Physics 2 Theoretical and Mathematical Physics 2 Journal of Geometry and Physics 2 Beiträge zur Algebra und Geometrie 2 The Annals of Statistics 2 Bulletin of the London Mathematical Society 2 Collectanea Mathematica 2 Journal of the Mathematical Society of Japan 2 Journal für die Reine und Angewandte Mathematik 2 Le Matematiche 2 Pacific Journal of Mathematics 2 Theoretical Computer Science 2 Discrete & Computational Geometry 2 International Journal of Mathematics 2 International Journal of Foundations of Computer Science 2 Proceedings of the National Academy of Sciences of the United States of America 2 Applicable Algebra in Engineering, Communication and Computing 2 Computational Optimization and Applications 2 Journal of Algebraic Geometry 2 Applied and Computational Harmonic Analysis 2 International Journal of Computer Vision 2 The Electronic Journal of Combinatorics 2 Journal of Combinatorial Designs 2 Bulletin des Sciences Mathématiques 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Annals of Combinatorics 2 Annales Henri Poincaré 2 Journal of Commutative Algebra 2 Science China. Mathematics 1 Archive for Rational Mechanics and Analysis 1 International Journal of Theoretical Physics 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 The Mathematical Gazette 1 Mathematical Notes 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 Reports on Mathematical Physics 1 Arkiv för Matematik 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Automatica 1 Calcolo 1 Canadian Journal of Mathematics ...and 69 more Serials all top 5 #### Cited in 53 Fields 364 Commutative algebra (13-XX) 279 Associative rings and algebras (16-XX) 260 Algebraic geometry (14-XX) 116 Combinatorics (05-XX) 89 Group theory and generalizations (20-XX) 79 Linear and multilinear algebra; matrix theory (15-XX) 55 Category theory; homological algebra (18-XX) 54 Quantum theory (81-XX) 47 Computer science (68-XX) 46 Nonassociative rings and algebras (17-XX) 37 Number theory (11-XX) 27 Several complex variables and analytic spaces (32-XX) 26 Convex and discrete geometry (52-XX) 25 Differential geometry (53-XX) 22 Manifolds and cell complexes (57-XX) 19 Dynamical systems and ergodic theory (37-XX) 17 Field theory and polynomials (12-XX) 16 Topological groups, Lie groups (22-XX) 14 Statistics (62-XX) 12 Numerical analysis (65-XX) 11 Operator theory (47-XX) 10 Operations research, mathematical programming (90-XX) 10 Information and communication theory, circuits (94-XX) 9 Algebraic topology (55-XX) 8 Ordinary differential equations (34-XX) 7 Functional analysis (46-XX) 6 Mathematical logic and foundations (03-XX) 6 Functions of a complex variable (30-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 5 Geometry (51-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 $$K$$-theory (19-XX) 3 General algebraic systems (08-XX) 3 Partial differential equations (35-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of particles and systems (70-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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https://pdglive.lbl.gov/ConservationLaws.action?node=CNXX&init=0&name=B1	$\Delta \mathit B$ = 1 WEAK NEUTRAL CURRENT FORBIDDEN Allowed by higher-order electroweak interactions. $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{+}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} nonresonant)}$ $/$ $\Gamma\mathrm {(total)}$ $(4.37\pm{0.27})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{+}} {{\mathit \tau}^{+}} {{\mathit \tau}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.25\times 10^{-3}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit \phi}} {{\mathit K}^{+}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(7.9^{+2.1}_{-1.7})\times 10^{-8}$ $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{+}} {{\mathit \pi}^{+}} {{\mathit \pi}^{-}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(4.3\pm{0.4})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{}{(892)}^{+}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<4.0\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit \rho}^{+}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<3.0\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit \pi}^{+}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<4.9\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit \pi}^{+}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.4\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{}{(892)}^{+}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ [1] $(1.01\pm{0.11})\times 10^{-6}$ (S = 1.1) $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{+}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ [1] $(4.7\pm{0.5})\times 10^{-7}$ (S = 2.3) $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{+}} {{\overline{\mathit \nu}}} {{\mathit \nu}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.6\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{}{(892)}^{+}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(9.6\pm{1.0})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{}{(892)}^{+}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(1.55^{+0.40}_{-0.31})\times 10^{-6}$ $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit \pi}^{+}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(1.78\pm{0.23})\times 10^{-8}$ $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit \pi}^{+}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<8.0\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{+}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(5.6\pm{0.6})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}^{+}} \rightarrow {{\mathit K}^{+}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(4.53\pm{0.35})\times 10^{-7}$ (S = 1.8) $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \pi}^{+}} {{\mathit \pi}^{-}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(2.1\pm{0.5})\times 10^{-8}$ $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit S}} {{\mathit P}} , {{\mathit S}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} , {{\mathit P}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ [2] $<6.0\times 10^{-10}$ CL=95.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<6.9\times 10^{-10}$ CL=95.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \eta}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.12\times 10^{-7}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \eta}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.08\times 10^{-7}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \eta}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<6.4\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \phi}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.27\times 10^{-4}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \rho}^{0}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<4.0\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{0}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.6\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \pi}^{0}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<9\times 10^{-6}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} {{\mathit \gamma}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.0\times 10^{-9}$ CL=95.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit e}^{+}} {{\mathit e}^{-}} {{\mathit \gamma}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.2\times 10^{-7}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \pi}^{0}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<5.3\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \pi}^{0}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<6.9\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \pi}^{0}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<8.4\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \tau}^{+}} {{\mathit \tau}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.1\times 10^{-3}$ CL=95.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \nu}} {{\overline{\mathit \nu}}} {{\mathit \gamma}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.6\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow invisible)}$ $/$ $\Gamma\mathrm {(total)}$ $<2.4\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{}{(892)}^{0}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ [1] $(9.9^{+1.2}_{-1.1})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{0}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ [1] $(3.3\pm{0.6})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{}{(892)}^{0}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.8\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \gamma}} {{\mathit \gamma}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<3.2\times 10^{-7}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{}{(892)}^{0}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(1.03^{+0.19}_{-0.17})\times 10^{-6}$ $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{}{(892)}^{0}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(9.4\pm{0.5})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{0}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(2.5^{+1.1}_{-0.9})\times 10^{-7}$ (S = 1.3) $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit K}^{0}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(3.39\pm{0.35})\times 10^{-7}$ (S = 1.1) $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(7^{+13}_{-11})\times 10^{-11}$ (S = 1.8) $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.5\times 10^{-9}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit \rho}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.8\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit \pi}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<8\times 10^{-6}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit \pi}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<5.0\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit \pi}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.10\times 10^{-7}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<1.6\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}^{}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.7\times 10^{-5}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit \pi}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<5.9\times 10^{-8}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}^{}{(892)}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(1.05\pm{0.10})\times 10^{-6}$ $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(4.8\pm{0.4})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}^{}{(892)}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(1.06\pm{0.09})\times 10^{-6}$ $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(4.4\pm{0.4})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}^{}{(892)}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(1.19\pm{0.20})\times 10^{-6}$ (S = 1.2) $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit K}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(4.4\pm{0.6})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit s}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(4.3\pm{1.0})\times 10^{-6}$ $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit s}} {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(6.7\pm{1.7})\times 10^{-6}$ (S = 2.0) $\Gamma\mathrm {( {{\mathit B}} \rightarrow {{\mathit s}} {{\mathit \ell}^{+}} {{\mathit \ell}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ [1] $(5.8\pm{1.3})\times 10^{-6}$ (S = 1.8) $\Gamma\mathrm {( {{\overline{\mathit b}}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} anything)}$ $/$ $\Gamma\mathrm {(total)}$ $<3.2\times 10^{-4}$ CL=90.0% $\Gamma\mathrm {( {{\overline{\mathit b}}} \rightarrow {{\overline{\mathit s}}} {{\overline{\mathit \nu}}} {{\mathit \nu}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<6.4\times 10^{-4}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\overline{\mathit K}}^{*}{(892)}^{0}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(2.9\pm{1.1})\times 10^{-8}$ $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \tau}^{+}} {{\mathit \tau}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<6.8\times 10^{-3}$ CL=95.0% $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \pi}^{+}} {{\mathit \pi}^{-}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(8.4\pm{1.7})\times 10^{-8}$ $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit S}} {{\mathit P}} , {{\mathit S}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} , {{\mathit P}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ [2] $<2.2\times 10^{-9}$ CL=95.0% $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<2.5\times 10^{-9}$ CL=95.0% $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \phi}{(1020)}} {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(8.4\pm{0.4})\times 10^{-7}$ $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit e}^{+}} {{\mathit e}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<9.4\times 10^{-9}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \phi}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<5.4\times 10^{-3}$ CL=90.0% $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \phi}} {{\mathit \gamma}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(3.4\pm{0.4})\times 10^{-5}$ $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \mu}^{+}} {{\mathit \mu}^{-}} )}$ $/$ $\Gamma\mathrm {(total)}$ $(3.01\pm{0.35})\times 10^{-9}$ $\Gamma\mathrm {( {{\mathit B}_{{s}}^{0}} \rightarrow {{\mathit \gamma}} {{\mathit \gamma}} )}$ $/$ $\Gamma\mathrm {(total)}$ $<3.1\times 10^{-6}$ CL=90.0% [1] An ${{\mathit \ell}}$ indicates an ${{\mathit e}}$ or a ${{\mathit \mu}}$ mode, not a sum over these modes. [2] Here ${{\mathit S}}$ and ${{\mathit P}}$ are the hypothetical scalar and pseudoscalar particles with masses of 2.5 GeV/c${}^{2}$ and 214.3 MeV/c${}^{2}$, respectively.	2023-03-20T09:46:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9399193525314331, "perplexity": 495.1724785364376}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00767.warc.gz"}
https://nai.nasa.gov/annual-reports/2015/vpl-uw/charnay-nai-npp-postdoc-report/	## 2015 Annual Science Report ### Charnay NAI NPP PostDoc Report ##### Project Summary My project focuses on the modeling of clouds and photochemical haze in the atmospheres of the early Earth and exoplanets. I use a 3D model, developed to simulate any kind of atmosphere, to study the formation, dynamics, climatic impact and observational features of clouds/haze. My first object of interest is GJ1214b, a mini-Neptune whose observations by HST revealed a cloudy/hazy atmosphere. The formation of such high and thick clouds is not understood. My second object of interest is the Archean Earth for periods with a methane-rich atmosphere leading to the formation of organic haze. 4 Institutions 3 Teams 4 Publications 0 Field Sites Field Sites #### Project Progress This document reports on activities during the year 2015 as an NAI/NPP postdoctoral Fellow (started in August 2014) at the VPL. During this time, I finished my work on the clouds on the exoplanet GJ1214b. Using the Generic LMD GCM, I showed that the circulation is strong enough to transport micrometric KCl and ZnS cloud particles to the upper atmosphere (Charnay et al., 2015a), producing the flat spectrum observed by the Hubble Space Telescope (Charnay et al., 2015b; see Figure 1). Figure 1. Transit spectra of GJ1214b showing the deviation (in parts per million) of the transit depth as a function of wavelength and obtained with the outputs of the generic GCM for a hydrogen-dominated atmosphere (100 times the solar metallicity) with and without clouds (0.1, 0.5 and 1 $\mu$m particle radii). Black dots are observations from the Hubble space telescope. I also showed that future telescopes (in particular JWST) should be able to detect molecules and estimate the mean atmospheric composition by observing in the mid-infrared. This work constitutes the first 3D simulations of clouds on a warm exoplanet and is of prime interest for the preparation of future space telescopes. I published this work in two papers, the first one is focused on the atmospheric dynamics and vertical mixing (Charnay et al., 2015a), the second one is focused on cloud distribution and observational impact (Charnay et al., 2015b). I presented this work at the DPS meeting in November 2015 and at the Extreme Solar System meeting in December 2015. I am planning for next months to study the formation of photochemical haze (rather than the condensate clouds I studied in my two previous papers) in the atmosphere of GJ1214b and other warm mini-Neptunes. I participated in a study on the possibility of identifying Earth-like planets from direct imaging using colors (Krissansen-Totton et al., 2016). For this study, I provided spectra of mini-Neptunes, based on my work on GJ1214b. In parallel to this work on GJ1214b, I published a paper in Nature Geoscience on the formation of Titan’s dunes by methane storms (Charnay et al., 2015c). I did most of this work during my PhD but I finished it during my NPP postdoc. I proposed a new mechanism to the formation of Titan’s dunes by methane storms, solving the long standing mystery of the eastward propagation of dunes. The Cassini spacecraft has detected dust storms. I provided a mechanism to their formation thanks to methane storms. I am coauthor on a submitted paper that describes these observations. I am currently working on the climates of the early Earth during the Hadean using the Generic LMD GCM with potentially high amounts of CO2 (up to 1 bar). A paper describing the climate and the carbon cycle during the Hadean is in preparation. I also used the GCM to compute lightning on the early Earth. The results of my simulations have been used by VPL researchers at Caltech to study the production by lightning of NOx molecules, which are important for the development of life. I am second author on a paper describing these results and submitted to Astrobiology. For the next months, I planning to study the impact of atmospheric escape on the composition of mini-Neptunes and in particular the trapping of condensable species for planets experiencing a strong hydrodynamic escape. I will also collaborate on a study on the recently discovered super-Earth GJ1132b. I will produce 3D simulations of the atmosphere of this planet to predict the future observations by JWST. In addition, I am planning to study with the 3D GCM the formation and climatic impact of organic haze on the early Earth. • ##### PROJECT INVESTIGATORS: Benjamin Charnay Project Investigator • ##### PROJECT MEMBERS: David Catling Co-Investigator	2019-12-10T05:42:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.562714695930481, "perplexity": 2193.5425291699203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540525821.56/warc/CC-MAIN-20191210041836-20191210065836-00230.warc.gz"}
http://dergipark.gov.tr/ieja/issue/25192/266195	\| \| \| \| ## ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS #### Ashish Kumar Das [1] , Deiborlang Nongsiang [2] ##### 184 263 The commuting graph of a non-abelian group is a simple graph in which the vertices are the non-central elements of the group, and two distinct vertices are adjacent if and only if they commute. In this paper, we determine (up to isomorphism) all finite non-abelian groups whose commuting graphs are acyclic, planar or toroidal. We also derive explicit formulas for the genus of the commuting graphs of some well-known class of finite non-abelian groups, and show that, every collection of isomorphism classes of finite non-abelian groups whose commuting graphs have the same genus is finite. Commuting graph, finite group, AC-group, genus of the commuting graphs Konular JA57HS68AS Makaleler Yazar: Ashish Kumar Das Yazar: Deiborlang Nongsiang Bibtex @ { ieja266195, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2016}, volume = {19}, pages = {91 - 109}, doi = {10.24330/ieja.266195}, title = {ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS}, key = {cite}, author = {Nongsiang, Deiborlang and Das, Ashish Kumar} } APA Das, A , Nongsiang, D . (2016). ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS. International Electronic Journal of Algebra, 19 (19), 91-109. DOI: 10.24330/ieja.266195 MLA Das, A , Nongsiang, D . "ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS". International Electronic Journal of Algebra 19 (2016): 91-109 Chicago Das, A , Nongsiang, D . "ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS". International Electronic Journal of Algebra 19 (2016): 91-109 RIS TY - JOUR T1 - ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS AU - Ashish Kumar Das , Deiborlang Nongsiang Y1 - 2016 PY - 2016 N1 - doi: 10.24330/ieja.266195 DO - 10.24330/ieja.266195 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 91 EP - 109 VL - 19 IS - 19 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266195 UR - http://dx.doi.org/10.24330/ieja.266195 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS %A Ashish Kumar Das , Deiborlang Nongsiang %T ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS %D 2016 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 19 %N 19 %R doi: 10.24330/ieja.266195 %U 10.24330/ieja.266195 ISNAD Das, Ashish Kumar , Nongsiang, Deiborlang . "ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS". International Electronic Journal of Algebra 19 / 19 (Haziran 2016): 91-109. http://dx.doi.org/10.24330/ieja.266195	2019-02-21T04:38:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20246019959449768, "perplexity": 2961.575298656965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247499009.48/warc/CC-MAIN-20190221031117-20190221053117-00614.warc.gz"}
http://legisquebec.gouv.qc.ca/en/showversion/cr/T-0.1,%20r.%202?code=se:350_51r7_1&pointInTime=20201120	### T-0.1, r. 2 - Regulation respecting the Québec sales tax 350.51R7.1. The prescribed information for the purposes of the second paragraph of section 350.51 of the Act is the following where the operator is not a registrant: (1) the information required under paragraphs 1 to 4 of section 350.51R3; (2) a sufficiently detailed description of each property or service supplied; (3) where an admission or payment of another property or service entitles the recipient to one or more beverages, (a) a mention to the effect that the property or service includes the supply of a beverage; (b) a mention concerning the number of beverages included; and (c) a sufficiently detailed description of each beverage included; (4) the amount paid or payable by the recipient in respect of each property or service supplied or, if the property or service is provided free of charge, mention to that effect; and (5) the total amount paid or payable for the supply. O.C. 586-2015, s. 5.	2021-01-24T07:05:09	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8149187564849854, "perplexity": 3794.7131605170503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703547333.68/warc/CC-MAIN-20210124044618-20210124074618-00452.warc.gz"}
https://par.nsf.gov/biblio/10156667	Turaev-Viro invariants, colored Jones polynomial and volume. We obtain a formula for the Turaev-Viro invariants of a link complement in terms of values of the colored Jones polynomial of the link. As an application we give the first examples for which the volume conjecture of Chen and the third named author\,\cite{Chen-Yang} is verified. Namely, we show that the asymptotics of the Turaev-Viro invariants of the Figure-eight knot and the Borromean rings complement determine the corresponding hyperbolic volumes. Our calculations also exhibit new phenomena of asymptotic behavior of values of the colored Jones polynomials that seem not to be predicted by neither the Kashaev-Murakami-Murakami volume conjecture and various of its generalizations nor by Zagier's quantum modularity conjecture. We conjecture that the asymptotics of the Turaev-Viro invariants of any link complement determine the simplicial volume of the link, and verify it for all knots with zero simplicial volume. Finally we observe that our simplicial volume conjecture is stable under connect sum and split unions of links. Authors: Award ID(s): Publication Date: NSF-PAR ID: 10156667 Journal Name: Quantum topology Volume: 9 Issue: 4 Page Range or eLocation-ID: 775-813 ISSN: 1663-487X 1. We establish a relation between the "large r" asymptotics of the Turaev-Viro invariants $TV_r$and the Gromov norm of 3-manifolds. We show that for any orientable, compact 3-manifold $M$, with (possibly empty) toroidal boundary, $log\|TVr(M)\|$ is bounded above by a function linear in $r$ and whose slope is a positive universal constant times the Gromov norm of $M$. The proof combines TQFT techniques, geometric decomposition theory of 3-manifolds and analytical estimates of $6j$-symbols. We obtain topological criteria that can be used to check whether the growth is actually exponential; that is one has $log\|TVr(M)\|\geq B r$, for some $B>0$. We use these criteria to construct infinite families of hyperbolic 3-manifolds whose $SO(3)$- Turaev-Viro invariants grow exponentially. These constructions are essential for the results of article [3] where we make progress on a conjecture of Andersen, Masbaum and Ueno about the geometric properties of surface mapping class groups detected by the quantum representations. We also study the behavior of the Turaev-Viro invariants under cutting and gluing of 3-manifolds along tori. In particular, we show that, like the Gromov norm, the values of the invariants do not increase under Dehn filling and we give applications of this result on the question ofmore »	2023-02-04T18:32:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7709686160087585, "perplexity": 300.80236284935665}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500151.93/warc/CC-MAIN-20230204173912-20230204203912-00161.warc.gz"}
https://gateway.ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Sheaf_of_modules.html	# Sheaf of modules In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module and the restriction maps F(U) →F(V) are compatible with the restriction maps O(U) →O(V): the restriction of fs is the restriction of f times that of s for any f in O(U) and s in F(U). The standard case is when X is a scheme and O its structure sheaf. If O is the constant sheaf , then a sheaf of O-modules are the same as a sheaf of abelian groups (i.e., abelian sheaf). If X is the prime spectrum of a ring R, then any R-module defines an OX-module (called an associated sheaf) in a natural way. Similarly, if R is a graded ring and X is the Proj of R, then any graded module defines an OX-module in a natural way. O-modules arising in such a fashion are examples of quasi-coherent sheaves, and in fact, on affine or projective schemes, all quasi-coherent sheaves are obtained this way. Sheaves of modules over a ringed space form an abelian category.[1] Moreover, this category has enough injectives,[2] and consequently one can and does define the sheaf cohomology as the i-th right derived functor of the global section functor .[3] ## Operations Let (X, O) be a ringed space. If F and G are O-modules, then their tensor product, denoted by or , is the O-module that is the sheaf associated to the presheaf (To see that sheafification cannot be avoided, compute the global sections of where O(1) is Serre's twisting sheaf on a projective space.) Similarly, if F and G are O-modules, then denotes the O-module that is the sheaf .[4] In particular, the O-module is called the dual module of F and is denoted by . Note: for any O-modules E, F, there is a canonical homomorphism , which is an isomorphism if E is a locally free sheaf of finite rank. In particular, if L is locally free of rank one (such L is called an invertible sheaf or a line bundle),[5] then this reads: implying the isomorphism classes of invertible sheaves form a group. This group is called the Picard group of X and is canonically identified with the first cohomology group (by the standard argument with Čech cohomology). If E is a locally free sheaf of finite rank, then there is an O-linear map given by the pairing; it is called the trace map of E. For any O-module F, the tensor algebra, exterior algebra and symmetric algebra of F are defined in the same way. For example, the k-th exterior power is the sheaf associated to the presheaf . If F is locally free of rank n, then is called the determinant line bundle (though technically invertible sheaf) of F, denoted by det(F). There is a natural perfect paring: Let f: (X, O) →(X', O') be a morphism of ringed spaces. If F is an O-module, then the direct image sheaf is an O'-module through the natural map O'f*O (such a natural map is part of the data of a morphism of ringed spaces.) If G is an O'-module, then the module inverse image of G is the O-module given as the tensor product of modules: where is the inverse image sheaf of G and is obtained from by adjuction. There is an adjoint relation between and : for any O-module F and O'-module G, as abelian group. There is also the projection formula: for an O-module F and a locally free O'-module E of finite rank, ## Properties Let (X, O) be a ringed space. An O-module F is said to be generated by global sections if there is a surjection of O-modules: . Explicitly, this means that there are global sections si of F such that the images of si in each stalk Fx generates Fx as Ox-module. An example of such a sheaf is that associated in algebraic geometry to an R-module M, R being any commutative ring, on the spectrum of a ring Spec(R). Another example: according to Cartan's theorem A, any coherent sheaf on a Stein manifold is spanned by global sections. (cf. Serre's theorem A below.) In the theory of schemes, a related notion is ample line bundle. (For example, if L is an ample line bundle, some power of it is generated by global sections.) An injective O-module is flasque (i.e., all restrictions maps F(U) → F(V) are surjective.)[6] Since a flasque sheaf is acyclic in the category of abelian sheaves, this implies that the i-th right derived functor of the global section functor in the category of O-modules coincides with the usual i-th sheaf cohomology in the category of abelian sheaves.[7] ## Sheaf associated to a module Let M be a module over a ring A. Put X = Spec A. For each pair , by the universal property of localization, there is a natural map which has the property that . Then is a contravariant functor from the category whose objects are the sets D(f) and morphisms the inclusions of sets to the category of abelian groups. One can show[8] it is in fact a B-sheaf (i.e., it satisfies the gluing axiom) and thus defines the sheaf on X called the sheaf associated to M. The most basic example is the structure sheaf on X; i.e., . Moreover, has the structure of and thus one gets the exact functor from ModA, the category of modules over A to the category of modules over . It defines an equivalence from ModA to the category of quasi-coherent sheaves on X, with the inverse , the global section functor. When X is Noetherian, the functor is an equivalence from the category of finitely generated A-modules to the category of coherent sheaves on X. The construction has the following properties: for any A-modules M, N, • .[9] • For any prime ideal p of A, as Op = Ap-module. • .[10] • If M is finitely presented, .[10] • , since the equivalence between ModA and the category of quasi-coherent sheaves on X. • ;[11] in particular, taking a direct sum and ~ commute. ## Sheaf associated to a graded module There is a graded analog of the construction and equivalence in the preceding section. Let R be a graded ring generated by degree-one elements as R0-algebra (R0 means the degree-zero piece) and M a graded R-module. Let X be the Proj of R (so X is a projective scheme). Then there is an O-module such that for any homogeneous element f of positive degree of R, there is a natural isomorphism as sheaves of modules on the affine scheme ;[12] in fact, this defines by gluing. Example: Let R(1) be the graded R-module given by R(1)n = Rn+1. Then is called Serre's twisting sheaf (the dual of the tautological line bundle.) If F is an O-module on X, then, writing , there is a canonical homomorphism: , which is an isomorphism if and only if F is quasi-coherent. ## Computing sheaf cohomology Main article: sheaf cohomology Sheaf cohomology has a reputation for being difficult to calculate. Because of this, the next general fact is fundamental for any practical computation: Theorem Let X be a topological space, F an abelian sheaf on it and an open cover of X such that for any i, p and 's in . Then for any i, where the right-hand side is the i-th Čech cohomology. Serre's theorem A states that if X is a projective variety and F a coherent sheaf on it, then, for sufficiently large n, F(n) is generated by finitely many global sections. Moreover, (a) For each i, Hi(X, F) is finitely generated over R0, and (b) (Serre's theorem B) There is an integer n0, depending on F, such that . ## Sheaf extension Let (X, O) be a ringed space, and let F, H be sheaves of O-modules on X. An extension of H by F is a short exact sequence of O-modules As with group extensions, if we fix F and H, then all equivalence classes of extensions of H by F form an abelian group (cf. Baer sum), which is isomorphic to the Ext group , where the identity element in corresponds to the trivial extension. In the case where H is O, we have: for any i ≥ 0, since both the sides are the right derived functors of the same functor Note: Some authors, notably Hartshorne, drop the subscript O. Assume X is a projective scheme over a Noetherian ring. Let F, G be coherent sheaves on X and i an integer. Then there exists n0 such that .[13] ## Notes 1. Vakil, Math 216: Foundations of algebraic geometry, 2.5. 2. Hartshorne, Ch. III, Proposition 2.2. 3. This cohomology functor coincides with the right derived functor of the global section functor in the category of abelian sheaves; cf. Hartshorne, Ch. III, Proposition 2.6. 4. There is a canonical homomorphism: which is an isomorphism if F is of finite presentation (EGA, Ch. 0, 5.2.6.) 5. For coherent sheaves, having a tensor inverse is the same as being locally free of rank one; in fact, there is the following fact: if and if F is coherent, then F, G are locally free of rank one. (cf. EGA, Ch 0, 5.4.3.) 6. Hartshorne, Ch III, Lemma 2.4. 7. Hartshorne, Ch. II, Proposition 5.1. 8. EGA I, Ch. I, Proposition 1.3.6. 9. EGA I, Ch. I, Corollaire 1.3.12. 10. EGA I, Ch. I, Corollaire 1.3.9. 11. Hartshorne, Ch. II, Proposition 5.11. 12. Hartshorne, Ch. III, Proposition 6.9. ## References This article is issued from Wikipedia - version of the 8/24/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.	2021-11-27T02:38:09	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9550645351409912, "perplexity": 545.8300340640182}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358078.2/warc/CC-MAIN-20211127013935-20211127043935-00242.warc.gz"}
https://www.ssa.gov/OACT/NOTES/as115/as115_VI_D.html	Short-Range Actuarial Projections of the Old-Age, Survivors, and Disability Insurance Program, 2001 Actuarial Study No. 115 Chris Motsiopoulos and Tim Zayatz, A.S.A. # Appendix ### D. DISABLED WORKER TERMINATIONS Terminations are tabulated as of calendar age-the integral age attained in the year disability benefits are terminated. For example, beneficiaries born in 1965 and terminated in 2000 are considered to be age 35 regardless of whether or not they had a birthday. As discussed in section III.A, benefit termination can occur for a number of reasons. The four major categories include: automatic conversion to old-age benefits upon attainment of normal retirement age; death of the beneficiary; medical recovery or return-to-work; and all other reasons. As it relates to termination, exposure is the estimated amount of time-measured in life-years-that individuals on the disability rolls are exposed to the possibility of benefit termination. This quantity is estimated by observing the activity of the rolls for a particular birth cohort. For example, consider a period during which disabled workers born in 1965 are observed for termination during 2000, at calendar age 35. The model assumes that each beneficiary already on the rolls as of the beginning of the year will be exposed for 12 months. An adjustment is then made for the amount of time contributed by new awards. Under the assumption that awards are uniformly distributed throughout the year, each new beneficiary will be exposed for an average of 6 months. Alternatively, termination exposure for a given calendar age in a particular year can be defined as the average number of beneficiaries on the rolls during the year. This can be estimated by adding one-half of the awards to those already in force at the beginning of the year. As shown in the following examples, this method is equivalent to calculating exposure using the "life-years" concept. Finally, historical termination rates are computed as terminations divided by exposure. For future years, terminations are computed by multiplying projected termination rates by projected exposure. ### Disabled Worker Termination Rate-Male Age 35 in 2000 (1965 Birth Cohort) • Death terminations (SSA administrative records): 702 • Recovery terminations (SSA administrative records): 1,263 • "All other" terminations (SSA administrative records): 67 • Awards (SSA administrative records): 4,146 • In force on January 1: 33,787 • Termination exposure: $33,787 +$1/2(4,146) = 35,860 aggregate life-years • Death rate: $702 / 35,860 = 0.01958$ • Recovery rate: $1,263 / 35,860 = 0.03522$ • "All other" rate: $67 / 35,860 = 0.00187$ ### Disabled Worker Terminations-Male Age 45 in 2010 (1965 Birth Cohort) • Projected death rate: 0.02708 • Projected recovery rate: 0.01135 • Projected "all other" rate: 0.00117 • Projected awards: 7,900 • Projected in force on January 1: 69,797 • Projected termination exposure: $69,797 +$1/2(7,900) = 73,747 • Projected death terminations: $0.02708 x 73,747 = 1,997$ • Projected recovery terminations: $0.01135 x 73,747 = 837$ • Projected "all other" terminations: $0.00117 x 73,747 = 86$ List of Studies December 26, 2001	2019-09-17T12:25:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3373202085494995, "perplexity": 7882.970089079719}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573071.65/warc/CC-MAIN-20190917121048-20190917143048-00244.warc.gz"}
http://lammps.sandia.gov/doc/compute_heat_flux.html	# compute heat/flux command ## Syntax compute ID group-ID heat/flux ke-ID pe-ID stress-ID • ID, group-ID are documented in compute command • heat/flux = style name of this compute command • ke-ID = ID of a compute that calculates per-atom kinetic energy • pe-ID = ID of a compute that calculates per-atom potential energy • stress-ID = ID of a compute that calculates per-atom stress ## Examples compute myFlux all heat/flux myKE myPE myStress ## Description Define a computation that calculates the heat flux vector based on contributions from atoms in the specified group. This can be used by itself to measure the heat flux into or out of a reservoir of atoms, or to calculate a thermal conductivity using the Green-Kubo formalism. See the fix thermal/conductivity command for details on how to compute thermal conductivity in an alternate way, via the Muller-Plathe method. See the fix heat command for a way to control the heat added or subtracted to a group of atoms. The compute takes three arguments which are IDs of other computes. One calculates per-atom kinetic energy (ke-ID), one calculates per-atom potential energy (pe-ID), and the third calculates per-atom stress (stress-ID). Note These other computes should provide values for all the atoms in the group this compute specifies. That means the other computes could use the same group as this compute, or they can just use group “all” (or any group whose atoms are superset of the atoms in this compute’s group). LAMMPS does not check for this. The Green-Kubo formulas relate the ensemble average of the auto-correlation of the heat flux J to the thermal conductivity kappa: Ei in the first term of the equation for J is the per-atom energy (potential and kinetic). This is calculated by the computes ke-ID and pe-ID. Si in the second term of the equation for J is the per-atom stress tensor calculated by the compute stress-ID. The tensor multiplies Vi as a 3x3 matrix-vector multiply to yield a vector. Note that as discussed below, the 1/V scaling factor in the equation for J is NOT included in the calculation performed by this compute; you need to add it for a volume appropriate to the atoms included in the calculation. Note The compute pe/atom and compute stress/atom commands have options for which terms to include in their calculation (pair, bond, etc). The heat flux calculation will thus include exactly the same terms. Normally you should use compute stress/atom virial so as not to include a kinetic energy term in the heat flux. This compute calculates 6 quantities and stores them in a 6-component vector. The first 3 components are the x, y, z components of the full heat flux vector, i.e. (Jx, Jy, Jz). The next 3 components are the x, y, z components of just the convective portion of the flux, i.e. the first term in the equation for J above. The heat flux can be output every so many timesteps (e.g. via the thermo_style custom command). Then as a post-processing operation, an autocorrelation can be performed, its integral estimated, and the Green-Kubo formula above evaluated. The fix ave/correlate command can calculate the autocorrelation. The trap() function in the variable command can calculate the integral. An example LAMMPS input script for solid Ar is appended below. The result should be: average conductivity ~0.29 in W/mK. Output info: This compute calculates a global vector of length 6 (total heat flux vector, followed by convective heat flux vector), which can be accessed by indices 1-6. These values can be used by any command that uses global vector values from a compute as input. See this section for an overview of LAMMPS output options. The vector values calculated by this compute are “extensive”, meaning they scale with the number of atoms in the simulation. They can be divided by the appropriate volume to get a flux, which would then be an “intensive” value, meaning independent of the number of atoms in the simulation. Note that if the compute is “all”, then the appropriate volume to divide by is the simulation box volume. However, if a sub-group is used, it should be the volume containing those atoms. The vector values will be in energy*velocity units. Once divided by a volume the units will be that of flux, namely energy/area/time units none	2017-10-16T22:16:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8902316093444824, "perplexity": 1544.8499180309016}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820466.2/warc/CC-MAIN-20171016214209-20171016234209-00286.warc.gz"}
http://www.popflock.com/learn?s=Computation_of_radiowave_attenuation_in_the_atmosphere	Computation of Radiowave Attenuation in the Atmosphere Get Computation of Radiowave Attenuation in the Atmosphere essential facts below. View Videos or join the Computation of Radiowave Attenuation in the Atmosphere discussion. Add Computation of Radiowave Attenuation in the Atmosphere to your PopFlock.com topic list for future reference or share this resource on social media. Computation of Radiowave Attenuation in the Atmosphere The computation of radiowave attenuation in the atmosphere is a series of radio propagation models and methods to estimate the path loss due to attenuation of the signal passing through the atmosphere by the absorption of its different components. There are many well-known facts on the phenomenon and qualitative treatments in textbooks.[1] A document published by the International Telecommunication Union (ITU) [2] provides some basis for a quantitative assessment of the attenuation. That document describes a simplified model along with semi-empirical formulas based on data fitting. It also recommended an algorithm to compute the attenuation of radiowave propagation in the atmosphere. NASA also published a study on a related subject.[3] Free software from CNES based on ITU-R recommendations is available for download and is available to the public. ## The model and the ITU recommendation Derivation of the optical invariant, a measure of the light propagating through an optical system. The document ITU-R pp. 676-78 of the ITU-R section considers the atmosphere as being divided into spherical homogeneous layers; each layer has a constant refraction index. By the use of trigonometry, a couple of formulas and an algorithm were derived. Through the use of an invariant, the same results can be directly derived: An incident ray at A under the angle ? hits the layer B at the angle θ. From basic Euclidean geometry: ${\displaystyle \|CK\|=R\sin u=r\sin \theta .}$ By Snell's law: ${\displaystyle n_{1}\sin \Phi =n_{2}\sin u,}$ so that ${\displaystyle n_{1}R\sin \Phi =n_{2}r\sin \theta =INV}$ Notes: • One proof[1] starts from the Fermat's principle. As a result, one gets proof of the Snell's law along with this invariance. This invariant is valid in a more general situation; the spherical radius is then replaced by the radius of curvature at points along the ray. It is also used in equation (4) of the 2005 NASA's report[3] in an application of satellite tracking. • The assumption of the refraction index varying with the latitude is not strictly compatible with the notion of layers. However the variation of the index is very small, this point is usually ignored in practice. The ITU recommended algorithm consists of launching a ray from a radio source, then at each step, a layer is chosen and a new incidence angle is then computed. The process is iterated until the altitude of the target is reached. At each step, the covered distance dL is multiplied by a specific attenuation coefficient g expressed in dB/km. All the increments g dL are added to provide the total attenuation. Note that the algorithm does not guaranty that the target is actually reached. For this, a much harder boundary value problem would have to be solved. ## The eikonal equation This equation is discussed in the references.[4][5][6] The equation is highly non-linear. Given that a smooth data fitting curve n(altitude) is provided by the ITU[7] for the refraction index n, and that the values of n differs from 1 only by something of the order 10−4, a numerical solution of the eikonal equation can be considered. Usually the equation is presented under the self-adjoint form, a more tractable equation for the ray head position vector r[6] is given in generic parametric form: ${\displaystyle {\ddot {\mathbf {r} }}=n\operatorname {grad} n}$ ## Implementations Three implementations to compute the attenuations exist: • Take the ray to be a straight line. • Use the optical invariant and apply the ITU recommendation.[2] • Solve the eikonal equation. The first two are only of 1st order approximation (see Orders of approximation). For the eikonal equation, many numerical schemes are available.[6] Here only a simple second order scheme was chosen. For most standard configurations of source-target, the three methods differ little from each other. It is only in the case of rays grazing the ground that the differences are meaningful. The following was used for testing: At the latitude of 10°, when a ray starts at 5 km altitude with an elevation angle of −1° to hit a target at the same longitude but at latitude 8.84° and altitude 30 km. At 22.5 GHz, the results are: The linear path is the highest on the figure, the eikonal is the lowest.[clarification needed] dB implementation distance covered finale altitude 30.27 Eikonal 761.11 30.06 29.20 Optical invariant 754.24 30.33 23.43 Linear Trace Off Note that 22.5 GHz is not a practical frequency[1] but it is the most suitable for algorithms comparison. In the table, the first column gives the results in dB, the third gives the distance covered and the last gives the final altitude. Distances are in km. From the altitude 30 km up, the attenuation is negligible. The paths of the three are plotted: Note: A MATLAB version for the uplink (Telecommunications link) is available from the ITU[2] ## The boundary value problem When a point S communicates with a point T, the orientation of the ray is specified by an elevation angle. In a naïve way, the angle can be given by tracing a straight line from S to T. This specification does not guarantee that the ray will reach T: the variation of refraction index bends the ray trajectory. The elevation angle has to be modified[3] to take into account the bending effect. For the eikonal equation, this correction can be done by solving a boundary value problem. As the equation is of second order, the problem is well defined. In spite of the lack of a firm theoretical basis for the ITU method, a trial-error by dichotomy (or binary search) can also be used. The next figure shows the results of numerical simulations. The curve labeled as bvp is the trajectory found by correcting the elevation angle. The other two are from a fixed step and a variable step (chosen in accordance with the ITU recommendations[6]) solutions without the elevation angle correction. The nominal elevation angle for this case is -0.5-degree. The numerical results obtained at 22.5 GHz were: Attenuation Elevation angle ITU steps 15.40 -0.50° Fix step 15.12 -0.50° BVP 11.33 -0.22° Note the way the solution bvp bents over the straight line. A consequence of this property is that the ray can reach locations situated below the horizon of S. This is consistent with observations.[8] The trajectory is a Concave function is a consequence of the fact that the gradient of the refraction index is negative, so the Eikonal equation implies that the second derivative of the trajectory is negative. From the point where the ray is parallel to ground, relative to the chosen coordinates, the ray goes down but relative to ground level, the ray goes up. Often engineers are interested in finding the limits of a system. In this case, a simple idea is to try some low elevation angle and let the ray reach the desired altitude. This point of view has a problem: if suffice to take the angle for which the ray has a tangent point of lowest altitude. For instance with the case of a source at 5 km altitude, of nominal elevation angle -0.5-degree and the target is at 30 km altitude; the attenuation found by the boundary value method is 11.33 dB. The previous point of view of worst case leads to an elevation angle of -1.87-degree and an attenuation of 170.77 dB. With this kind of attenuation, every system would be unusable! It was found also for this case that with the nominal elevation angle, the distance of the tangent point to ground is 5.84 km; that of the worst case is 2.69 km. The nominal distance from source to target is 6383.84 km; for the worst case, it is 990.36 km. There are many numerical methods to solve boundary value problems.[9] For the Eikonal equation, due to the good behavior of the refraction index just a simple Shooting method can be used. ## References 1. ^ a b c Antennas and radiowave propagation. Robert E. Collin. McGraw-Hill College, 1985 2. ^ a b c ITU recommendation ITU-R pp. 676-78, 2009[clarification needed] 3. ^ a b c http://trs-new.jpl.nasa.gov/dspace/handle/2014/41145 Archived 23 April 2010 at the Wayback Machine. NASA progress report 4. ^ Microwave and optical ray geometry. S. Cornbleet, Wiley, 1984 5. ^ Light transmission optics. Detrich Marcuse, Van Nostrand, 1982 6. ^ a b c d Methods in Electromagnetic Wave Propagation. D. S. Jones, Oxford, 1987 7. ^ ITU recommendation ITU-R pp. 835-4, 2009[clarification needed] 8. ^ ITU recommendation ITU-R pp. 834-36, 2007[clarification needed] 9. ^ Initial Value Methods for Boundary Value Problems. Mayer. Academic Press, 1973 This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.	2020-10-31T00:03:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6628991961479187, "perplexity": 874.5446951705621}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107911792.65/warc/CC-MAIN-20201030212708-20201031002708-00467.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S010DT&home=sumtabM	# $({\boldsymbol \tau}_{{{\boldsymbol K}^{+}}}–{\boldsymbol \tau}_{{{\boldsymbol K}^{-}}})/{\boldsymbol \tau}_{\mathrm {average}}$ INSPIRE search This quantity is a measure of $\mathit CPT$ invariance in weak interactions. VALUE (%) DOCUMENT ID TECN $\bf{ 0.10 \pm0.09 }$ OUR AVERAGE Error includes scale factor of 1.2. $-0.4$ $\pm0.4$ 2008 KLOE $0.090$ $\pm0.078$ 1969 CNTR $0.47$ $\pm0.30$ 1967 CNTR Conservation Laws: $\mathit CPT$ INVARIANCE References: AMBROSINO 2008 JHEP 0801 073 Measurement of the Charged Kaon Lifetime with the KLOE Detector LOBKOWICZ 1969 PR 185 1676 Precise Measurement of the ${{\mathit K}^{+}}/{{\mathit K}^{-}}$ Lifetime Ratio FORD 1967 PRL 18 1214 Comparison of the ${{\mathit K}^{+}}$ and ${{\mathit K}^{-}}$ Decay Rates into the ${{\mathit \tau}}$ and ${{\mathit K}_{{\mu2}}}$ Modes	2021-03-09T07:52:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4051057696342468, "perplexity": 8527.108378591702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389472.95/warc/CC-MAIN-20210309061538-20210309091538-00618.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=Q007TVP	${\boldsymbol {\boldsymbol t}}$-quark EW Couplings ${{\mathit W}}$ helicity fractions in top decays. ${{\mathit F}_{{0}}}$ is the fraction of longitudinal and ${{\mathit F}_{{+}}}$ the fraction of right-handed ${{\mathit W}}$ bosons. ${{\mathit F}_{{{V+A}}}}$ is the fraction of $\mathit V+\mathit A$ current in top decays. The effective Lagrangian (cited by ABAZOV 2008AI) has terms f${}^{L}_{1}$ and f${}^{R}_{1}$ for $\mathit V−\mathit A$ and $\mathit V+\mathit A$ couplings, f${}^{L}_{2}$ and f${}^{R}_{2}$ for tensor couplings with b$_{R}$ and b$_{L}$ respectively. ${{\boldsymbol F}_{{+}}}$ INSPIRE search VALUE CL% DOCUMENT ID TECN COMMENT $\bf{ 0.002 \pm0.011}$ OUR AVERAGE $< 0.036 \pm0.006$ 95 1 2017 BB ATLS ${{\mathit F}_{{+}}}$ = ${{\mathit f}_{{1}}}{{\mathit f}_{{1}}^{+}}$ $-0.004$ $\pm0.005$ $\pm0.014$ 2 2016 BU CMS ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $-0.045$ $\pm0.044$ $\pm0.058$ 3 2013 D CDF ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $0.008$ $\pm0.012$ $\pm0.014$ 4 2013 BH CMS ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $0.01$ $\pm0.05$ 5 2012 BG ATLS ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $0.023$ $\pm0.041$ $\pm0.034$ 6 2011 C D0 ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $0.11$ $\pm0.15$ 7 2000 B CDF ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}}_{+}$ ${{\mathit b}}$ ) • • • We do not use the following data for averages, fits, limits, etc. • • • $-0.033$ $\pm0.034$ $\pm0.031$ 8 2012 Z TEVA ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $-0.01$ $\pm0.02$ $\pm0.05$ 9 2010 Q CDF Repl. by AALTONEN 2013D $-0.04$ $\pm0.04$ $\pm0.03$ 10 2009 Q CDF Repl. by AALTONEN 2010Q $0.119$ $\pm0.090$ $\pm0.053$ 11 2008 B D0 Repl. by ABAZOV 2011C $0.056$ $\pm0.080$ $\pm0.057$ 12 2007 D D0 ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $0.05$ ${}^{+0.11}_{-0.05}$ $\pm0.03$ 13 2007 I CDF ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $<0.26$ 95 13 2007 I CDF ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $<0.27$ 95 14 2006 U CDF ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $0.00$ $\pm0.13$ $\pm0.07$ 15 2005 L D0 ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $<0.25$ 95 15 2005 L D0 ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) $<0.24$ 95 16 2005 D CDF ${{\mathit F}_{{+}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{+}}}{{\mathit b}}$ ) 1 AABOUD 2017BB based on 20.2 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Triple-differential decay rate of top quark in the ${{\mathit t}}$-channel single-top production is used to simultaneously determine five generalized ${{\mathit W}}{{\mathit t}}{{\mathit b}}$ couplings as well as the top polarization. No assumption is made for the other couplings. The authors reported ${{\mathit f}_{{1}}}$ = $0.30$ $\pm0.05$ and ${{\mathit f}_{{1}}^{+}}$ $<$ $0.120$ which we converted to ${{\mathit F}_{{+}}}$ = ${{\mathit f}_{{1}}}{{\mathit f}_{{1}}^{+}}$. See this paper for constraints on other couplings not included here. 2 KHACHATRYAN 2016BU based on 19.8 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV using ${{\mathit t}}{{\overline{\mathit t}}}$ events with ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$4 jets(${}\geq{}$2 ${{\mathit b}}$). The result is consistent with the NNLO SM prediction of $0.0017$ $\pm0.0001$ for ${\mathit m}_{{{\mathit t}}}$ = $172.8$ $\pm1.3$ GeV. 3 Based on 8.7 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV using ${{\mathit t}}{{\overline{\mathit t}}}$ events with ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$4 jets(${}\geq{}$1 ${{\mathit b}}$), and under the constraint F$_{0}$ + F$_{+}$ + F$_{-}$ = 1. The statstical errors of F$_{0}$ and F$_{+}$ are correlated with correlation coefficient $\rho (F_{0},F_{+}$) = $-0.69$. 4 Based on 5.0 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2013BH studied events with large $\not E_T$ and ${{\mathit \ell}}$ +${}\geq{}$4 jets using a constrained kinematic fit. 5 Based on 1.04 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. AAD 2012BG studied events with large $\not E_T$ and either ${{\mathit \ell}}$ +${}\geq{}$4j or ${{\mathit \ell}}{{\mathit \ell}}$ +${}\geq{}$2j. 6 Results are based on 5.4 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at 1.96 TeV, including those of ABAZOV 2008B. Under the SM constraint of ${{\mathit f}_{{0}}}$ = 0.698 (for ${\mathit m}_{{{\mathit t}}}$ = 173.3 GeV, ${\mathit m}_{{{\mathit W}}}$ = 80.399 GeV), ${{\mathit f}_{{+}}}$ = $0.010$ $\pm0.022$ $\pm0.030$ is obtained. 7 AFFOLDER 2000B studied the angular distribution of leptonic decays of ${{\mathit W}}$ bosons in ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ events. The ratio $\mathit F_{0}$ is the fraction of the helicity zero (longitudinal) ${{\mathit W}}~$bosons in the decaying top quark rest frame. B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}}_{+}$ ${{\mathit b}}$ ) is the fraction of positive helicity (right-handed) positive charge ${{\mathit W}}~$bosons in the top quark decays. It is obtained by assuming the Standard Model value of $\mathit F_{0}$. 8 Based on 2.7 and 5.1 fb${}^{-1}$ of CDF data in ${{\mathit \ell}}$ + jets and dilepton channels, and 5.4 fb${}^{-1}$ of D0 data in ${{\mathit \ell}}$ + jets and dilepton channels. ${{\mathit F}_{{0}}}$ = $0.682$ $\pm0.035$ $\pm0.046$ if ${{\mathit F}_{{+}}}$ = 0.0017(1), while ${{\mathit F}_{{+}}}$ = $-0.015$ $\pm0.018$ $\pm0.030$ if ${{\mathit F}_{{0}}}$ = 0.688(4), where the assumed fixed values are the SM prediction for ${\mathit m}_{{{\mathit t}}}$ = $173.3$ $\pm1.1$ GeV and ${\mathit m}_{{{\mathit W}}}$ = $80.399$ $\pm0.023$ GeV. 9 Results are based on 2.7 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. ${{\mathit F}_{{0}}}$ result is obtained by assuming ${{\mathit F}_{{+}}}$ = 0, while ${{\mathit F}_{{+}}}$ result is obtained for ${{\mathit F}_{{0}}}$ = 0.70, the SM value. Model independent fits for the two fractions give ${{\mathit F}_{{0}}}$ = $0.88$ $\pm0.11$ $\pm0.06$ and ${{\mathit F}_{{+}}}$ = $-0.15$ $\pm0.07$ $\pm0.06$ with correlation coefficient of $-0.59$. The results are for ${\mathit m}_{{{\mathit t}}}$ = 175 GeV. 10 Results are based on 1.9 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. ${{\mathit F}_{{0}}}$ result is obtained assuming ${{\mathit F}_{{+}}}$ = 0, while ${{\mathit F}_{{+}}}$ result is obtained for ${{\mathit F}_{{0}}}$ = 0.70, the SM values. Model independent fits for the two fractions give ${{\mathit F}_{{0}}}$ = $0.66$ $\pm0.16$ $\pm0.05$ and ${{\mathit F}_{{+}}}$ = $-0.03$ $\pm0.06$ $\pm0.03$. 11 Based on 1 fb${}^{-1}$ at $\sqrt {s }$ = 1.96 TeV. 12 Based on 370 pb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV, using the ${{\mathit \ell}}$ + jets and dilepton decay channels. The result assumes ${{\mathit F}_{{0}}}$ = 0.70, and it gives ${{\mathit F}_{{+}}}$ $<$ 0.23 at 95$\%$ CL. 13 Based on 318 pb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV. 14 Based on 200 pb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV. ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit b}}$ (${{\mathit \ell}}$ = ${{\mathit e}}$ or ${{\mathit \mu}}$). The errors are stat + syst. 15 ABAZOV 2005L studied the angular distribution of leptonic decays of ${{\mathit W}}$ bosons in ${{\mathit t}}{{\overline{\mathit t}}}$ events, where one of the ${{\mathit W}}$'s from ${{\mathit t}}$ or ${{\overline{\mathit t}}}$ decays into ${{\mathit e}}$ or ${{\mathit \mu}}$ and the other decays hadronically. The fraction of the +'' helicity ${{\mathit W}}$ boson is obtained by assuming ${{\mathit F}_{{0}}}$ = 0.7, which is the generic prediction for any linear combination of V and A currents. Based on $230$ $\pm15$ pb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV. 16 ACOSTA 2005D measures the ${{\mathit m}^{2}}_{ {{\mathit \ell}} {+} {{\mathit b}} }$ distribution in ${{\mathit t}}{{\overline{\mathit t}}}$ production events where one or both ${{\mathit W}}$'s decay leptonically to ${{\mathit \ell}}$ = ${{\mathit e}}$ or ${{\mathit \mu}}$, and finds a bound on the V+A coupling of the ${{\mathit t}}{{\mathit b}}{{\mathit W}}$ vertex. By assuming the SM value of the longitudinal ${{\mathit W}}$ fraction ${{\mathit F}_{{0}}}$ = B( ${{\mathit t}}$ $\rightarrow$ ${{\mathit W}_{{0}}}{{\mathit b}}$ ) = 0.70, the bound on ${{\mathit F}}_{+}$ is obtained. If the results are combined with those of AFFOLDER 2000B, the bounds become ${{\mathit F}}_{V+A}$ $<$ 0.61 (95$\%$ CL) and ${{\mathit F}_{{+}}}$ $<$ 0.18 (95 $\%$CL), respectively. Based on $109$ $\pm7$ pb${}^{-1}$ of data at $\sqrt {s }$ = 1.8 TeV (run I). References: AABOUD 2017BB JHEP 1712 017 Analysis of the $\mathit W_{tb}$ Vertex from the Measurement of Triple-Differential Angular Decay Rates of Single Top Quarks Produced in the t-Channel at $\sqrt {s }$ = 8 TeV with the ATLAS Detector KHACHATRYAN 2016BU PL B762 512 Measurement of the ${{\mathit W}}$ Boson Helicity Fractions in the Decays of Top Quark Pairs to Lepton + Jets Final States Produced in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV AALTONEN 2013D PR D87 031104 Measurement of $\mathit W$-Boson Polarization in Top-Quark Decay using the Full CDF Run II Data Set CHATRCHYAN 2013BH JHEP 1310 167 Measurement of the ${{\mathit W}}$-Boson Helicity in Top-Quark Decays from ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production in Lepton+Jets Events in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV JHEP 1206 088 Measurement of the ${{\mathit W}}$ Boson Polarization in Top Quark Decays with the ATLAS Detector AALTONEN 2012Z PR D85 071106 Combination of CDF and ${D0}$ Measurements of the ${{\mathit W}}$ Boson Helicity in Top Quark Decays ABAZOV 2011C PR D83 032009 Measurement of the $\mathit W$ Boson Helicity in Top Quark Decays using 5.4 fb${}^{-1}$ of ${{\mathit p}}{{\overline{\mathit p}}}$ Collision Data AALTONEN 2010Q PRL 105 042002 Measurement of ${{\mathit W}}$-Boson Polarization in Top-Quark Decay in Collisions at $\sqrt {s }$ = 1.96$~$TeV AALTONEN 2009Q PL B674 160 Measurement of ${{\mathit W}}$-Boson Helicity Fractions in Top-Quark Decays using cos $\theta {}^{*}$ ABAZOV 2008B PRL 100 062004 Model-Independent Measurement of the ${{\mathit W}}$ Boson Helicity in Top Quark Decays at ${D0}$ ABAZOV 2007D PR D75 031102 Measurement of the ${{\mathit W}}$ Boson Helicity in Top Quark Decays at ${D0}$ ABULENCIA 2007I PR D75 052001 Measurement of the Helicity Fractions of ${{\mathit W}}$ Bosons from top Quark Decays using Fully Reconstructed ${\mathit {\mathit t}}$ ${\mathit {\overline{\mathit t}}}$ Events with CDF II ABULENCIA 2006U PR D73 111103 Measurement of the Helicity of $\mathit W$ Bosons in top-Quark Decays ABAZOV 2005L PR D72 011104 Search for Right-Handed ${{\mathit W}}$ Bosons in top Quark Decay ACOSTA 2005D PR D71 031101 Measurement of the ${{\mathit W}}$ Boson Polarization in top Decay at CDF at $\sqrt {s }$ = 1.8 TeV AFFOLDER 2000B PRL 84 216 Measurement of the Helicity of ${{\mathit W}}$ Bosons in Top Quark Decays	2020-09-21T09:55:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9368104934692383, "perplexity": 1936.7810554216242}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400201601.26/warc/CC-MAIN-20200921081428-20200921111428-00275.warc.gz"}
https://zbmath.org/authors/?q=ai%3Anehari.zeev	## Nehari, Zeev Compute Distance To: Author ID: nehari.zeev Published as: Nehari, Zeev; Nehari, Z.; Weissbach, Willi more...less External Links: MGP · Wikidata · IdRef Documents Indexed: 91 Publications since 1938, including 4 Books Biographic References: 1 Publication Co-Authors: 6 Co-Authors with 6 Joint Publications 81 Co-Co-Authors all top 5 ### Co-Authors 85 single-authored 1 Duffin, Richard James 1 Leighton, Walter jun. 1 Moore, Richard A. 1 Netanyahu, Elisha 1 Schwarz, Binyamin 1 Singh, Vikramaditya all top 5 ### Serials 12 Transactions of the American Mathematical Society 11 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 9 Proceedings of the American Mathematical Society 8 Journal d’Analyse Mathématique 6 Duke Mathematical Journal 5 American Journal of Mathematics 4 Bulletin of the American Mathematical Society 3 Journal of Mathematical Analysis and Applications 3 Journal of Differential Equations 3 Journal of the London Mathematical Society 2 Archive for Rational Mechanics and Analysis 2 Pacific Journal of Mathematics 1 American Mathematical Monthly 1 Acta Mathematica 1 Illinois Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Zeitschrift 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Irish Academy. Section A, Mathematical and Physical Sciences 1 Annals of Mathematics. Second Series 1 Journal of Mathematics and Mechanics 1 Proceedings of the London Mathematical Society. Second Series 1 Annals of Mathematics Studies 1 Journal of Rational Mechanics and Analysis all top 5 ### Fields 13 Ordinary differential equations (34-XX) 4 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Numerical analysis (65-XX) 1 Systems theory; control (93-XX) ### Citations contained in zbMATH Open 69 Publications have been cited 1,872 times in 1,610 Documents Cited by Year Conformal mapping. Zbl 0048.31503 Nehari, Zeev 1952 The Schwarzian derivative and schlicht functions. Zbl 0035.05104 Nehari, Zeev 1949 On bounded bilinear forms. Zbl 0077.10605 Nehari, Zeev 1957 On a class of nonlinear second-order differential equations. Zbl 0097.29501 Nehari, Zeev 1960 On the oscillation of solutions of self-adjoint linear differential equations of the fourth order. Zbl 0084.08104 Leighton, Walter; Nehari, Zeev 1959 Characteristic values associated with a class of nonlinear second-order differential equations. Zbl 0099.29104 Nehari, Zeev 1961 Nonoscillation theorems for a class of non-linear differential equations. Zbl 0089.06902 Moore, Richard A.; Nehari, Zeev 1959 Oscillation criteria for second-order linear differential equations. Zbl 0078.07602 Nehari, Zeev 1957 Disconjugate linear differential operators. Zbl 0183.09101 Nehari, Zeev 1967 On a nonlinear differential equation arising in nuclear physics. Zbl 0124.30204 Nehari, Zeev 1963 Some inequalities in the theory of functions. Zbl 0051.31204 Nehari, Zeev 1953 Some criteria of univalence. Zbl 0057.31102 Nehari, Zeev 1954 On the zeros of solutions of second-order linear differential equations. Zbl 0055.31501 Nehari, Zeev 1954 On the coefficients of meromorphic schlicht functions. Zbl 0079.10004 Nehari, Zeev; Netanyahu, E. 1957 Green’s functions and disconjugacy. Zbl 0339.34036 Nehari, Zeev 1976 Some eigenvalue estimates. Zbl 0091.08201 Nehari, Zeev 1959 A property of convex conformal maps. Zbl 0334.30006 Nehari, Zeev 1976 A nonlinear oscillation problem. Zbl 0181.09702 Nehari, Zeev 1969 Oscillation theorems for systems of linear differential equations. Zbl 0259.34042 Nehari, Zeev 1969 On the singularities of Legendre expansions. Zbl 0071.06502 Nehari, Zeev 1956 On an inequality of Lyapunov. Zbl 0113.07303 Nehari, Zeev 1962 Non-oscillation criteria for $$n$$-th order linear differential equations. Zbl 0134.07301 Nehari, Zeev 1965 Univalence criteria depending on the Schwarzian derivative. Zbl 0412.30012 Nehari, Zeev 1979 Inequalities for the coefficients of univalent functions. Zbl 0183.34403 Nehari, Zeev 1969 On the zeros of solutions of $$n$$-th order linear differential equations. Zbl 0125.04504 Nehari, Zeev 1964 A nonlinear oscillation theorem. Zbl 0385.34011 Nehari, Zeev 1975 On the coefficients of Bieberbach-Eilenberg functions. Zbl 0207.07703 Nehari, Z. 1970 Nonlinear techniques for linear oscillation problems. Zbl 0314.34040 Nehari, Zeev 1975 A generalization of Schwarz’ lemma. Zbl 0029.12302 Nehari, Zeev 1947 Inverse Hölder inequalities. Zbl 0182.38401 Nehari, Zeev 1968 Some function-theoretic aspects of linear second-order differential equations. Zbl 0182.10101 Nehari, Zeev 1967 On the principal frequency of a membrane. Zbl 0086.19204 Nehari, Zeev 1958 Disconjugacy criteria for linear differential equations. Zbl 0208.35302 Nehari, Z. 1968 The kernel function and canonical conformal maps. Zbl 0035.05301 Nehari, Zeev 1949 On a class of non-linear integral equations. Zbl 0092.10903 Nehari, Zeev 1959 Introduction to complex analysis. Zbl 0125.04001 Nehari, Zeev 1961 The elliptic modular function and a class of analytic functions first considered by Hurwitz. Zbl 0034.05201 Nehari, Zeev 1947 On weighted kernels. Zbl 0049.17603 Nehari, Zeev 1952 A differential inequality. Zbl 0139.05701 Nehari, Zeev 1965 Extremal problems for a class of functionals defined on convex sets. Zbl 0181.15901 Nehari, Zeev 1967 Nonoscillation and disconjugacy of systems of linear differential equations. Zbl 0275.34035 Nehari, Zeev 1973 A class of domain functions and some allied extremal problems. Zbl 0040.33002 Nehari, Zeev 1950 On bounded analytic functions. Zbl 0040.33101 Nehari, Zeev 1950 On the coefficients of univalent Laurent series. Zbl 0056.29903 Nehari, Zeev; Schwarz, Binyamin 1954 Note on polyharmonic functions. Zbl 0097.08504 Duffin, R. J.; Nehari, Zeev 1961 On the biharmonic Green’s function. Zbl 0057.33201 Nehari, Zeev 1954 Introduction to complex analysis. Revised ed. Zbl 0164.08202 Nehari, Zeev 1968 Sufficient conditions in the calculus of variations and in the theory of optimal control. Zbl 0273.49012 Nehari, Zeev 1973 On the accessory parameters of a Fuchsian differential equation. Zbl 0031.40001 Nehari, Zeev 1949 Univalent functions and linear differential equations. Zbl 0066.32602 Nehari, Zeev 1955 Une propriété des valeurs moyennes d’une fonction analytique. JFM 65.0333.03 Nehari, Z. 1939 Oscillatory properties of complex differential systems. Zbl 0292.34005 Nehari, Zeev 1973 Conjugate points, triangular matrices, and Riccati equations. Zbl 0303.34009 Nehari, Zeev 1974 Analytic functions possessing a positive real part. Zbl 0031.29805 Nehari, Zeev 1948 Conformal mapping of open Riemann surfaces. Zbl 0041.41201 Nehari, Zeev 1950 An integral equation associated with a function-theoretic extremal problem. Zbl 0065.30803 Nehari, Zeev 1955 On the coefficients of univalent functions. Zbl 0078.06402 Nehari, Zeev 1957 Bounds for the solutions of a class of nonlinear partial differential equations. Zbl 0117.07401 Nehari, Zeev 1963 On an inequality of P.R. Beesack. Zbl 0121.31105 Nehari, Zeev 1964 On analytic functions possessing certain properties of univalency. Zbl 0030.25102 Nehari, Zeev 1948 A disconjugacy criterion for selfadjoint linear differential equations. tions. Zbl 0231.34023 Nehari, Zeev 1971 A proof of $$\|a_4\|\leq 4$$ by Loewner’s method. Zbl 0299.30017 Nehari, Zeev 1974 Note on positive harmonic functions. Zbl 0035.16901 Nehari, Zeev 1950 Extremal problems in the theory of bounded analytic functions. Zbl 0042.08305 Nehari, Zeev 1951 Bounded analytic functions. Zbl 0044.08403 Nehari, Zeev 1951 On the numerical computation of mapping functions by orthogonalization. Zbl 0044.08404 Nehari, Zeev 1951 Dirichlet’s principle and some inequalities in the theory of conformal mapping. Zbl 0052.08201 Nehari, Zeev 1953 On the coefficients of $$R$$-univalent functions. Zbl 0067.05704 Nehari, Zeev 1955 On the derivative of an analytic function. Zbl 0090.04701 Nehari, Zeev 1960 Univalence criteria depending on the Schwarzian derivative. Zbl 0412.30012 Nehari, Zeev 1979 Green’s functions and disconjugacy. Zbl 0339.34036 Nehari, Zeev 1976 A property of convex conformal maps. Zbl 0334.30006 Nehari, Zeev 1976 A nonlinear oscillation theorem. Zbl 0385.34011 Nehari, Zeev 1975 Nonlinear techniques for linear oscillation problems. Zbl 0314.34040 Nehari, Zeev 1975 Conjugate points, triangular matrices, and Riccati equations. Zbl 0303.34009 Nehari, Zeev 1974 A proof of $$\|a_4\|\leq 4$$ by Loewner’s method. Zbl 0299.30017 Nehari, Zeev 1974 Nonoscillation and disconjugacy of systems of linear differential equations. Zbl 0275.34035 Nehari, Zeev 1973 Sufficient conditions in the calculus of variations and in the theory of optimal control. Zbl 0273.49012 Nehari, Zeev 1973 Oscillatory properties of complex differential systems. Zbl 0292.34005 Nehari, Zeev 1973 A disconjugacy criterion for selfadjoint linear differential equations. tions. Zbl 0231.34023 Nehari, Zeev 1971 On the coefficients of Bieberbach-Eilenberg functions. Zbl 0207.07703 Nehari, Z. 1970 A nonlinear oscillation problem. Zbl 0181.09702 Nehari, Zeev 1969 Oscillation theorems for systems of linear differential equations. Zbl 0259.34042 Nehari, Zeev 1969 Inequalities for the coefficients of univalent functions. Zbl 0183.34403 Nehari, Zeev 1969 Inverse Hölder inequalities. Zbl 0182.38401 Nehari, Zeev 1968 Disconjugacy criteria for linear differential equations. Zbl 0208.35302 Nehari, Z. 1968 Introduction to complex analysis. Revised ed. Zbl 0164.08202 Nehari, Zeev 1968 Disconjugate linear differential operators. Zbl 0183.09101 Nehari, Zeev 1967 Some function-theoretic aspects of linear second-order differential equations. Zbl 0182.10101 Nehari, Zeev 1967 Extremal problems for a class of functionals defined on convex sets. Zbl 0181.15901 Nehari, Zeev 1967 Non-oscillation criteria for $$n$$-th order linear differential equations. Zbl 0134.07301 Nehari, Zeev 1965 A differential inequality. Zbl 0139.05701 Nehari, Zeev 1965 On the zeros of solutions of $$n$$-th order linear differential equations. Zbl 0125.04504 Nehari, Zeev 1964 On an inequality of P.R. Beesack. Zbl 0121.31105 Nehari, Zeev 1964 On a nonlinear differential equation arising in nuclear physics. Zbl 0124.30204 Nehari, Zeev 1963 Bounds for the solutions of a class of nonlinear partial differential equations. Zbl 0117.07401 Nehari, Zeev 1963 On an inequality of Lyapunov. Zbl 0113.07303 Nehari, Zeev 1962 Characteristic values associated with a class of nonlinear second-order differential equations. Zbl 0099.29104 Nehari, Zeev 1961 Introduction to complex analysis. Zbl 0125.04001 Nehari, Zeev 1961 Note on polyharmonic functions. Zbl 0097.08504 Duffin, R. J.; Nehari, Zeev 1961 On a class of nonlinear second-order differential equations. Zbl 0097.29501 Nehari, Zeev 1960 On the derivative of an analytic function. Zbl 0090.04701 Nehari, Zeev 1960 On the oscillation of solutions of self-adjoint linear differential equations of the fourth order. Zbl 0084.08104 Leighton, Walter; Nehari, Zeev 1959 Nonoscillation theorems for a class of non-linear differential equations. Zbl 0089.06902 Moore, Richard A.; Nehari, Zeev 1959 Some eigenvalue estimates. Zbl 0091.08201 Nehari, Zeev 1959 On a class of non-linear integral equations. Zbl 0092.10903 Nehari, Zeev 1959 On the principal frequency of a membrane. Zbl 0086.19204 Nehari, Zeev 1958 On bounded bilinear forms. Zbl 0077.10605 Nehari, Zeev 1957 Oscillation criteria for second-order linear differential equations. Zbl 0078.07602 Nehari, Zeev 1957 On the coefficients of meromorphic schlicht functions. Zbl 0079.10004 Nehari, Zeev; Netanyahu, E. 1957 On the coefficients of univalent functions. Zbl 0078.06402 Nehari, Zeev 1957 On the singularities of Legendre expansions. Zbl 0071.06502 Nehari, Zeev 1956 Univalent functions and linear differential equations. Zbl 0066.32602 Nehari, Zeev 1955 An integral equation associated with a function-theoretic extremal problem. Zbl 0065.30803 Nehari, Zeev 1955 On the coefficients of $$R$$-univalent functions. Zbl 0067.05704 Nehari, Zeev 1955 Some criteria of univalence. Zbl 0057.31102 Nehari, Zeev 1954 On the zeros of solutions of second-order linear differential equations. Zbl 0055.31501 Nehari, Zeev 1954 On the coefficients of univalent Laurent series. Zbl 0056.29903 Nehari, Zeev; Schwarz, Binyamin 1954 On the biharmonic Green’s function. Zbl 0057.33201 Nehari, Zeev 1954 Some inequalities in the theory of functions. Zbl 0051.31204 Nehari, Zeev 1953 Dirichlet’s principle and some inequalities in the theory of conformal mapping. Zbl 0052.08201 Nehari, Zeev 1953 Conformal mapping. Zbl 0048.31503 Nehari, Zeev 1952 On weighted kernels. Zbl 0049.17603 Nehari, Zeev 1952 Extremal problems in the theory of bounded analytic functions. Zbl 0042.08305 Nehari, Zeev 1951 Bounded analytic functions. Zbl 0044.08403 Nehari, Zeev 1951 On the numerical computation of mapping functions by orthogonalization. Zbl 0044.08404 Nehari, Zeev 1951 A class of domain functions and some allied extremal problems. Zbl 0040.33002 Nehari, Zeev 1950 On bounded analytic functions. Zbl 0040.33101 Nehari, Zeev 1950 Conformal mapping of open Riemann surfaces. Zbl 0041.41201 Nehari, Zeev 1950 Note on positive harmonic functions. Zbl 0035.16901 Nehari, Zeev 1950 The Schwarzian derivative and schlicht functions. Zbl 0035.05104 Nehari, Zeev 1949 The kernel function and canonical conformal maps. Zbl 0035.05301 Nehari, Zeev 1949 On the accessory parameters of a Fuchsian differential equation. Zbl 0031.40001 Nehari, Zeev 1949 Analytic functions possessing a positive real part. Zbl 0031.29805 Nehari, Zeev 1948 On analytic functions possessing certain properties of univalency. Zbl 0030.25102 Nehari, Zeev 1948 A generalization of Schwarz’ lemma. Zbl 0029.12302 Nehari, Zeev 1947 The elliptic modular function and a class of analytic functions first considered by Hurwitz. Zbl 0034.05201 Nehari, Zeev 1947 Une propriété des valeurs moyennes d’une fonction analytique. JFM 65.0333.03 Nehari, Z. 1939 all top 5 ### Cited by 1,558 Authors 30 Nehari, Zeev 23 Chuaqui, Martin 16 Osgood, Brad G. 15 Crowdy, Darren Gregory 13 Agarwal, Ravi P. 13 Coffman, Charles V. 13 Duren, Peter Larkin 12 Schwarz, Binyamin 11 Elias, Uri 11 Kajikiya, Ryuji 10 Papamichael, Nicolas 9 Dubinin, Vladimir N. 9 Eloe, Paul W. 9 Erbe, Lynn Harry 9 Gröhn, Janne 9 Minda, David 8 Aouf, Mohamed Kamal 8 Henderson, Johnny Lee 8 Kühnau, Reiner 8 MacGregor, Thomas H. 8 Nasser, Mohamed M. S. 8 Özbekler, Abdullah 8 Pommerenke, Christian 8 Sangawi, Ali W. K. 8 Wick, Brett D. 7 Bell, Steven R. 7 Darus, Maslina 7 Goodman, Adolph-W. 7 Murid, Ali Hassan Mohamed 7 Peterson, Allan C. 7 Schiffer, Menahem Max 7 Schippers, Eric D. 7 Solynin, Alexander Yu. 7 Wong, James S. W. 7 Yamashita, Shinji 6 Aharonov, Dov 6 Breaz, Daniel V. 6 Heittokangas, Janne M. 6 Hernández, Rodrigo 6 Hummel, James A. 6 Krushkal, Samuel L. 6 Kwong, Man Kam 6 Li, Ji 6 Muldowney, James S. 6 Ponnusamy, Saminathan 6 Rättyä, Jouni 6 Regenda, Ján 6 Shapiro, Harold Seymour 6 Silva, Kaye O. 6 Sugawa, Toshiyuki 6 Vuorinen, Matti Keijo Kustaa 6 Zhou, Jianxin 5 Ali, Rosihan Mohamed 5 Bazighifan, Omar 5 Brevig, Ole Fredrik 5 Causey, William M. 5 Deng, Yinbin 5 Došlá, Zuzana 5 Duong, Xuan Thinh 5 Gustafson, Grant B. 5 Hartman, Philip 5 Headley, Velmer B. 5 Hedenmalm, Håkan 5 Kreith, Kurt 5 Kusano, Takaŝi 5 Lacey, Michael T. 5 Lions, Pierre-Louis 5 Martín, María J. 5 Mostafa, Adela Osman 5 Pfaltzgraff, John A. 5 Pinasco, Juan Pablo 5 Sadosky, Cora 5 Saker, Samir H. 5 Srivastava, Hari Mohan 5 Sugie, Jitsuro 5 Suzuki, Takashi 5 Tanaka, Kazunaga 5 Verzini, Gianmaria 5 Wong, Pui-Kei 5 Wu, Tsungfang 5 Yafaev, Dimitri R. 4 Adimurthi, A. 4 Arov, Damir Zyamovich 4 Avkhadiev, Farit Gabidinovich 4 Bandle, Catherine 4 Barnes, David Clarence 4 Bauer, Robert Otto 4 Ben Amara, Jamel 4 Bers, Lipman 4 Bulut, Serap 4 Cheng, Sui Sun 4 Cotlar, Mischa 4 DeLillo, Thomas K. 4 El-Ashwah, Rabha Mohamed 4 Felmer, Patricio L. 4 Friedland, Shmuel 4 Fritzsche, Bernd 4 Gaier, Dieter 4 Goyal, Vinod B. 4 Grunau, Hans-Christoph ...and 1,458 more Authors all top 5 ### Cited in 300 Serials 138 Journal of Mathematical Analysis and Applications 113 Proceedings of the American Mathematical Society 104 Transactions of the American Mathematical Society 80 Journal of Differential Equations 58 Journal d’Analyse Mathématique 35 Computational Methods and Function Theory 30 Archive for Rational Mechanics and Analysis 30 Journal of Functional Analysis 27 Mathematische Zeitschrift 26 Annali di Matematica Pura ed Applicata. Serie Quarta 25 Journal of Computational and Applied Mathematics 20 Mathematische Annalen 19 Integral Equations and Operator Theory 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Nonlinear Analysis. Theory, Methods & Applications 17 Computers & Mathematics with Applications 16 Applied Mathematics and Computation 16 Bulletin of the American Mathematical Society 15 Czechoslovak Mathematical Journal 14 The Journal of Geometric Analysis 13 Rocky Mountain Journal of Mathematics 13 Mathematische Nachrichten 12 Abstract and Applied Analysis 11 International Journal of Control 11 Israel Journal of Mathematics 11 Journal of Mathematical Physics 11 Mathematical Notes 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Applied Mathematics Letters 11 Kodai Mathematical Seminar Reports 10 Acta Mathematica 10 Journal of Approximation Theory 10 Journal of Soviet Mathematics 10 Systems & Control Letters 10 Calculus of Variations and Partial Differential Equations 9 Kodai Mathematical Journal 9 Results in Mathematics 9 Linear Algebra and its Applications 8 Ukrainian Mathematical Journal 8 Duke Mathematical Journal 8 Monatshefte für Mathematik 8 Journal of Mathematical Sciences (New York) 8 Complex Variables and Elliptic Equations 7 Advances in Mathematics 7 Archiv der Mathematik 7 Mathematica Slovaca 7 Siberian Mathematical Journal 7 Tohoku Mathematical Journal. Second Series 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Journal of Inequalities and Applications 7 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Communications in Mathematical Physics 6 International Journal of Mathematics and Mathematical Sciences 6 Numerische Mathematik 6 Discrete and Continuous Dynamical Systems 6 Communications on Pure and Applied Analysis 6 Advances in Difference Equations 5 Applicable Analysis 5 Mathematics of Computation 5 Automatica 5 Proceedings of the Japan Academy. Series A 5 MCSS. Mathematics of Control, Signals, and Systems 5 Annales Academiae Scientiarum Fennicae. Mathematica 5 Acta Mathematica Sinica. English Series 5 Complex Analysis and Operator Theory 5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 5 Analysis and Mathematical Physics 4 Studia Mathematica 4 Compositio Mathematica 4 Functional Analysis and its Applications 4 Manuscripta Mathematica 4 Nagoya Mathematical Journal 4 Rendiconti del Circolo Matemàtico di Palermo. Serie II 4 Zeitschrift für Analysis und ihre Anwendungen 4 Physica D 4 Constructive Approximation 4 Journal of Scientific Computing 4 Science in China. Series A 4 Journal of the Egyptian Mathematical Society 4 NoDEA. Nonlinear Differential Equations and Applications 4 Mathematical Problems in Engineering 4 The Ramanujan Journal 4 Conformal Geometry and Dynamics 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Afrika Matematika 4 AIMS Mathematics 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Computational Physics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Nuclear Physics. B 3 Arkiv för Matematik 3 Annales de l’Institut Fourier 3 Computing 3 Inventiones Mathematicae 3 Acta Applicandae Mathematicae 3 Journal of the American Mathematical Society 3 Mathematical and Computer Modelling 3 Japan Journal of Industrial and Applied Mathematics 3 Journal of Global Optimization 3 Geometric and Functional Analysis. GAFA ...and 200 more Serials all top 5 ### Cited in 56 Fields 532 Functions of a complex variable (30-XX) 383 Ordinary differential equations (34-XX) 260 Partial differential equations (35-XX) 153 Operator theory (47-XX) 50 Potential theory (31-XX) 50 Functional analysis (46-XX) 49 Numerical analysis (65-XX) 46 Several complex variables and analytic spaces (32-XX) 44 Systems theory; control (93-XX) 42 Special functions (33-XX) 37 Differential geometry (53-XX) 35 Harmonic analysis on Euclidean spaces (42-XX) 34 Global analysis, analysis on manifolds (58-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 30 Fluid mechanics (76-XX) 27 Probability theory and stochastic processes (60-XX) 24 Dynamical systems and ergodic theory (37-XX) 23 Real functions (26-XX) 23 Approximations and expansions (41-XX) 22 Difference and functional equations (39-XX) 21 Quantum theory (81-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 20 Mechanics of deformable solids (74-XX) 11 Integral equations (45-XX) 9 Number theory (11-XX) 8 Mechanics of particles and systems (70-XX) 8 Optics, electromagnetic theory (78-XX) 8 Operations research, mathematical programming (90-XX) 6 Geometry (51-XX) 6 Manifolds and cell complexes (57-XX) 5 Algebraic geometry (14-XX) 5 Integral transforms, operational calculus (44-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Relativity and gravitational theory (83-XX) 4 General and overarching topics; collections (00-XX) 4 Mathematical logic and foundations (03-XX) 4 Abstract harmonic analysis (43-XX) 4 Convex and discrete geometry (52-XX) 4 Computer science (68-XX) 3 Measure and integration (28-XX) 3 Biology and other natural sciences (92-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Associative rings and algebras (16-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 2 Sequences, series, summability (40-XX) 2 General topology (54-XX) 2 Statistics (62-XX) 2 Geophysics (86-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Algebraic topology (55-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-06-28T20:50:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42772871255874634, "perplexity": 3178.6033119851595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103617931.31/warc/CC-MAIN-20220628203615-20220628233615-00611.warc.gz"}
https://www.usgs.gov/center-news/first-photograph-k-lauea-volcano-60s	# First photograph of Kīlauea volcano in the 60s Release Date: Sometimes you just don't know what you're going to find, and when you do find it, you're not quite sure what it is. Photograph taken in the 1860s, perhaps on August 27, 1865, from Uwekahuna. The many changes between 1865 and 2004 result mainly from the addition of lava flows to the floor of Kīlauea's caldera and the widening of Halemaumau in 1924. Abbreviations are: O, outlet through low hills, present in both photos; SB, "south sulphur bank"; KP, pali southwest of Keanakakoi, present in both photos; C cliff in 1860s covered by lava flows by 2004; L, lineament present in both photos; H, Halemaumau; 82, September 1982 lava flow; SS, area now called "sand spit"; HP, Halemaumau parking lot. (Public domain.) Photograph taken on September 24, 2004 from approximately the same location. Refer to symbol descriptions above. (Public domain.) One afternoon last September, while thumbing through a binder containing old photographs in the HVO archive, a pale brown print almost jumped from the page. It looked vaguely familiar, like the childhood photo of a friend known only as an adult. Then it slowly became apparent. This was indeed an early image of a friend, Kīlauea's caldera, as viewed from Uwekahuna. But many features on the print don't match those seen today. When the print was turned over, there, lightly penciled in old-fashioned script, appeared the words, "First view of volcano in the 60s." It sure wasn't the 1960s that was meant. A photograph of Kīlauea's caldera in the 1860s-now that is something! Running outside with the print in one hand and a camera in the other, the place where the photographer stood was narrowed down to an area about halfway between HVO and the highest point at Uwekahuna, where the triangulation station is. Shadows tell that the photograph was taken in the afternoon. But the match between the features in the print and those we see today remains poor, because of all the changes that have occurred in the caldera since the 1860s. For one, Halemaumau is twice as wide today as it was then, but we knew that already, for the crater doubled in diameter during the explosions in 1924. The most striking difference, completely unexpected, was the presence in the 1860s of a cliff, probably 10-15 m (30-50 feet) high, beyond Halemaumau, as viewed from Uwekahuna. The cliff could be a caldera fault or the wall of an older version of Halemaumau. A large area of sulfur deposits mantled the northeast end of this cliff. Nineteenth-century visitors called this area the "southern sulphur bank" and noted that it was larger than the "northern sulphur bank" (today's Sulphur Banks). Lava flows from Halemaumau covered it by mid-1879 and apparently also covered the high cliff, for not a trace of the cliff remains today, unless the slope just east of the Halemaumau parking lot is one. Who took the photograph, and when during "the 60s" was it taken? We don't know the answer to either of these questions, but a little digging has led to a reasonable hypothesis. William T. Brigham, future director of the Bishop Museum, first visited the summit of Kīlauea in 1864, riding up the Kau trail. He reached Uwekahuna at about 1 p.m. and later wrote in his book, The Volcanoes of Kīlauea and Mauna Loa, that "from here in the afternoon is a favorable view of Kīlauea, perhaps the best." After another visit in early August 1865 to "make arrangements for a survey," Brigham rode from Hilo to the summit on August 22, 1865, bringing with him "surveying instruments and photograph apparatus (wet plate most unsuitable to the vicinity of sulphur fumes)." The weather was poor for a week, but Brigham and his party surveyed, nonetheless. Brigham wrote that "Sunday [August 27] was the first bright day I had had." He was visited by pulu pickers after the morning service, who "told him the names of the various parts of the crater, and legends of various eruptions. Monday was rainy,?and the remainder of the week was too stormy to take photographs." Brigham then returned to Hilo. Perhaps the photograph was taken on that bright Sunday afternoon of August 27, 1865. Brigham had a "photograph apparatus" uncommon in Hawaii in the 1860s, was chomping at the bit after a week of dull weather, was enthused by the information given him by the pulu pickers, and knew where to go to get "perhaps the best" afternoon view of Kīlauea. We asked the Bishop Museum whether Brigham left plates or prints when he retired, but it has none. So, we may never know if the above musings are correct. If any readers have relevant information, we'd certainly appreciate hearing it. ———————————————————————————————————————————————————————————————— ### Volcano Activity Update Eruptive activity at Puu Oo continues. Spatter cones in the crater of Puu Oo glow brightly on clear nights, but have not produced any lava flows for several months. The MLK vent area, at the southwest base of the cone, intermittently erupts small Pāhoehoe flows that stack up close to the vent. The PKK flow continues to host substantial breakouts from above the top of Pulama pali to the coastal plain. Lava is not entering the ocean. As of January 20, lava flows were active on the coastal plain, about 500 m (550 yd) inland of the shore at West Highcastle. The area of breakouts is about 2.5 km (1.5 mi) from the end of the pavement on Chain of Craters Road in Hawaii Volcanoes National Park. Expect a 1-to-1.5-hour walk each way and remember to bring lots of water. Stay well back from the sea cliff, regardless of whether there is an active ocean entry or not. Heed the National Park warning signs. During the week ending January 20, there were no earthquakes felt on Hawai`i Island. Mauna Loa is not erupting. The summit region continues to inflate. Since July 2004, the rate of inflation and number of deep earthquakes has increased. Weekly earthquake counts have varied from 5 to over 150. During the week ending January 20, fourteen earthquakes were recorded beneath the summit area. Nearly all are 30 km (18 mi) or more deep and half are the long-period type, with magnitudes less than 3.	2020-01-27T19:51:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29377952218055725, "perplexity": 3204.2508924032236}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251705142.94/warc/CC-MAIN-20200127174507-20200127204507-00457.warc.gz"}
http://dergipark.gov.tr/konuralpjournalmath/issue/28490/344416	Yıl 2017, Cilt 5, Sayı 2, Sayfalar 160 - 167 2017-10-15 \| \| \| \| ## ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM #### ABDELMOUMEN TIAIBA [1] ##### 74 136 In this paper, we study a class of non commutative strongly $l_{p}$-summing sublinear operators and characterize this class of operators by given the extension of the Pietsch domination theorem. Some new properties are shown. Banach lattice, Completely bounded operator, Operator space, Strongly $l_{p}-$summing operator, Sublinear operator • [1] D. Achour and L. Mezrag, Little Grothendieck's theorem for sublinear operators, J. Math. Anal. Appl. 296 (2004), 541-552. • [2] D. Achour, L. Mezrag and A. Tiaiba, On the strongly $p$-summing sublinear operators,Taiwanesse J. Math. 11 (2007), no. 4, 969-973. • [3] D. Blecher, The standard dual of an operator space, Paci c J. Math. 153 (1992), 15-30. • [4] D. Blecher and V. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292. • [5] J. S. Cohen, Absolutely p-summing, $p$-nuclear operators and their conjugates, Math. Ann. 201 (1973), 177-200. • [6] E. Effros, Z. J. Ruan, A new approach to operator spaces, Canadian Math. Bull, 34 (1991), 329-337. • [7] L. Mezrag, Comparison of non-commutative 2 and $p$-summing operators from B(l2) into OH, Zeitschrift fürr Analysis und ihre Anwendungen. Mathematical Analysis and its Applications 21 (2002), no. 3, 709-717. • [8] L. Mezrag, On strongly $l_{p}$-summing m-linear operators, Colloquim Mathematicum, 111 (2008), no 1, 59-70. • [9] G. Pisier, Non-commutative vector valued $L_{p}$-spaces and completely p-summing maps, Asterisque (Soc. Math. France) 247 (1998), 1-131. • [10] G. Pisier, The operator Hilbert space OH, complex interpolation and tensor norms. Memoirs Amer. Math. Soc. 122, 585 (1996), 1-103. • [11] A. Tiaiba, Characterization of $l_{p}$-summing sublinear operators, IAENG International Journal of Applied Mathematics, 39 (2009) no.4, 206-211. Konular Mühendislik Articles Yazar: ABDELMOUMEN TIAIBAÜlke: Algeria Bibtex @araştırma makalesi { konuralpjournalmath344416, journal = {Konuralp Journal of Mathematics}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {160 - 167}, doi = {}, title = {ON A CLASS OF STRONGLY L\$\_\{p\}\$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM}, key = {cite}, author = {TIAIBA, ABDELMOUMEN} } APA TIAIBA, A . (2017). ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM. Konuralp Journal of Mathematics, 5 (2), 160-167. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/28490/344416 MLA TIAIBA, A . "ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM". Konuralp Journal of Mathematics 5 (2017): 160-167 Chicago TIAIBA, A . "ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM". Konuralp Journal of Mathematics 5 (2017): 160-167 RIS TY - JOUR T1 - ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM AU - ABDELMOUMEN TIAIBA Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 160 EP - 167 VL - 5 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2017 ER - EndNote %0 Konuralp Journal of Mathematics ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM %A ABDELMOUMEN TIAIBA %T ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM %D 2017 %J Konuralp Journal of Mathematics %P -2147-625X %V 5 %N 2 %R %U ISNAD TIAIBA, ABDELMOUMEN . "ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM". Konuralp Journal of Mathematics 5 / 2 (Ekim 2017): 160-167.	2018-12-11T08:44:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41623857617378235, "perplexity": 9227.843601562845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823614.22/warc/CC-MAIN-20181211083052-20181211104552-00547.warc.gz"}
http://legisquebec.gouv.qc.ca/en/showversion/cs/I-0.4?code=se:26_4&pointInTime=20210106	### I-0.4 - Mining Tax Act 26.4. The amount that an operator may deduct for a fiscal year, as an additional allowance for a mine situated in Northern Québec, in computing its annual earnings from a mine under subparagraph h of subparagraph 2 of the fourth paragraph of section 8 must not exceed the lesser of (1) if the mine is situated (a) in the Near North, the amount by which \$2,000,000 exceeds the aggregate of all amounts each of which is an amount deducted by the operator in computing its annual earnings from the mine for a preceding fiscal year under subparagraph h of subparagraph 2 of the fourth paragraph of section 8, or (b) in the Far North, the amount by which \$5,000,000 exceeds the aggregate of all amounts each of which is an amount deducted by the operator in computing its annual earnings from the mine for a preceding fiscal year under subparagraph h of subparagraph 2 of the fourth paragraph of section 8; and (2) the part of the operator’s annual earnings from the mine for the fiscal year that is attributable to the operator’s eligibility period in respect of the mine. Despite the first paragraph, the operator may deduct an amount, as an additional allowance for a mine situated in Northern Québec, in computing its annual earnings from the mine for a fiscal year under subparagraph h of subparagraph 2 of the fourth paragraph of section 8 only if (1) the mine has come into production in reasonable commercial quantities after 30 March 2010; and (2) the operator may not deduct an amount, as an additional allowance for a northern mine, in computing its annual earnings from the mine for the fiscal year under subparagraph g of subparagraph 2 of the fourth paragraph of section 8. 2011, c. 6, s. 58.	2021-03-08T17:01:17	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8506131172180176, "perplexity": 2973.9411030009765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178385378.96/warc/CC-MAIN-20210308143535-20210308173535-00048.warc.gz"}
https://www.usgs.gov/center-news/photo-and-video-chronology-k-lauea-december-2-1997	# Photo and Video Chronology - Kīlauea - December 2, 1997 Release Date: Kilauea Volcano's east rift zone eruption continues: most lava travels through tubes from the vent area to the coast [Eruption updates are posted approximately every two weeks. More frequent updates will accompany drastic changes in activity or increased threat to residential areas.] For readers familiar with events of the past few months, recent changes include these: • The vent inside Puu Oo hasn't spilled lava across the crater floor for three weeks. Instead, the top of the magma column remains 10-20 m below the bounding rampart. Magma in the vent circulates below the crusted lava surface of the crater floor--out of sight except from the air. • Roars that emanate from vents on the southwest flank of Puu Oo are heard as far as 20 km distant. These roars, often likened to the sound of a jet engine or blast furnace, leave little outward sign of their passage except for scant rocky debris and a delicate mantle of Pele's hair near the vent. Recently, however, fallout of Pele's hair has been reported from residential districts 10 km north of the vent. • Lava from the south shield travels in tubes to the coast, an in-tube distance of about 10 km. Travel time for a particle of melt is probably about 3 hours from vent to ocean. Eruption rate is generally 500,000-600,000 cubic meters per day. Although lava will escape occasionally from the tube to form new surface flows, no such breakouts have occurred in the past four weeks. • Ocean entries remain situated at East Kamokuna and Wahaula, which are the distal ends of the tube system. At East Kamokuna, small collapses periodically destroy short segments of the bench. Each new embayment is slowly reoccupied by new lava as the bench attempts to maintain its seaward growth. Steam plumes rise as a nearly continuous curtain from the 500-m-long edge of the slowly prograding lava flows of the bench. • Sulfur dioxide gas emissions from vents in the Puu Oo area remain high, about 2,500 tons per day. The 55th episode of Kilauea's almost 15-year-long east rift zone eruption continues. This episode, which began February 24, 1997, was characterized in its early months by shifting vent locations on the west and southwest flanks of Puu Oo cone and by rapid enlargement of the episode 50-55 lava shield. The flow field expanded slowly until, in July, lava reached the sea. The supply of lava to the coast became restricted to tubes, and surface flow activity diminished greatly. During the last 17 weeks, eruptive activity has been concentrated at two main vents: the "crater vent" on the Puu Oo crater floor and the "south shield," a lava shield about 300 m south of the Puu Oo cone. The most obvious of these has been "crater vent," which originated as a spatter cone. In September, however, the spatter cone subsided into its own throat, leaving a pit. The pit is slowly enlarging and now is about 60 m in diameter. Lava froths and sloshes within this cauldron. All of these changes occurred within the already existing crater of Puu Oo. In the two weeks prior to November 3, magma issued nearly continuously from the throat of the crater vent, spilling eastward across the main crater floor. This activity has diminished greatly in the past four weeks. Indeed, during the past two weeks, the lava remains within the rampart that bounds the vent. It does circulate away from the vent, but most of the activity is hidden beneath the crust of the crater floor. The limited extent of incandescent lava has reduced the magnificent nighttime glow once so prominent from many vantage points on the east slope of Kilauea volcano. Perhaps the most remarkable activity during the past two weeks has been the numerous roars reported by residents and visitors throughout the area. These roars, which may be compared to the sound of a jet engine, issue from the throats of sporadically active vents on the southwest flank of Puu Oo. The few close-hand observations describe dust- to fist-size rocky debris being tossed a short distance during such an event. Lately the area near these small vents has received much Pele's hair, filamentous volcanic glass as long as several centimeters. Unusually widespread fallout occurred on the weekend of November 28-30, when Pele's hair was reported at Napau Crater campground, 5 km west-southwest of the vents, and in the Glenwood district, 10 km to the north. Our preliminary assessment explains these events as a consequence of sudden gas escape. The magma is gas rich and degasses constantly in the near-surface environment. If enough gas can coalesce to form a bubble, it may begin to rise through the magma. The roar results when the gas breaches the magma-air interface and escapes suddenly. If this boundary is below the ground surface in an open conduit, then the rush of escaping gas may rip rock from the conduit walls and thrust it upward. Pele's hair is spun from the magma as the gas escapes. The other main vent, the south shield, is the source of the flows entering the ocean at the Wahaula and East Kamokuna sites near the east boundary of Hawaii Volcanoes National Park. The flows are encased within lava tubes for most of their length and are visible only through skylights in the roof of the tube. The tubes discharge their lava at the shoreline. The hot lava, about 1,150 degrees Celsius when it reaches the ocean, generates dense plumes of steam upon contact with seawater. The new lava builds benches beyond the low seacliffs that bound the south coast of the Big Island. Small explosions periodically disrupt the rapidly chilling lava and throw it onto the bench, constructing low nearshore (littoral) cones. These small explosions pose a minor threat for visitors. A far greater threat exists, however; these benches may collapse into the sea without warning, triggering large steam explosions that hurl dense rock and molten spatter tens of meters inland. Such a collapse occurred in early November (four weeks ago), lopping 4.75 acres (1.92 hectares) of existing episode-55 bench into the ocean at East Kamokuna. (No one was on the bench, so only land, not life, was lost.) Since then, a new lava flow from the beheaded tube is building a shelf at the foot of the new cliffs created by the collapse. These features may be discernible in the previous photo. The righthand steam plume is at East Kamokuna. The new lava flow, 40-50 m wide, is adjacent on the right side of that steam plume. The word "cliffline" and a white leader point to the cliff that formed as a result of the collapse. Thus, the new lava flow is filling an embayment created during the abrupt destruction of unstable land. Steam plumes rise as a nearly continuous curtain from the 500-m-long edge of the slowly prograding lava flow. More recently, smaller collapses have pared slices of the newly emplaced lava flows. The largest occurred on Monday, Nov. 24, when 0.65 acres (0.26 ha) subsided into the ocean. A tour guide on site at the time shared with us his realization that these collapse events happen quickly--too quickly for visitors to escape if they're within the area of collapse. The situations just described should serve as ample warning: No one should venture onto the benches, no matter how stable the new land may appear. Eruption-viewing opportunities change constantly, so those readers planning a visit to the volcano should contact Hawaii Volcanoes National Park for the most current eruption information (808-985-6000). Additional photographs and descriptions of east rift eruptive activity may be found on the University of Hawaii's web site. On Sunday, November 16, east Hawaii and especially Hawai`i Volcanoes National Park were engulfed in one of the worst episodes of vog this year. Gentle southeasterly winds blew much of the sulfur dioxide (SO2) emissions from Kilauea's east rift zone--about 2800 tons per day (t/d)--directly across the heavily visited Kilauea caldera area of the National Park. The current SO2emission rate of 2500 t/d is about 40 percent higher than the average for the last several years during continuous eruption. Summit SO2 emissions from Kilauea remain in the range of 50-100 t/d.	2020-07-16T01:14:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2469566911458969, "perplexity": 7479.319991530247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657176116.96/warc/CC-MAIN-20200715230447-20200716020447-00102.warc.gz"}
https://pos.sissa.it/374/047/	Volume 374 - Light Cone 2019 - QCD on the light cone: from hadrons to heavy ions (LC2019) - Contributed High energy scattering in QCD: from low to high Bjorken $x$ J. Jalilian-Marian Full text: pdf Pre-published on: 2020 May 06 Published on: 2020 May 26 Abstract We generalize the Color Class Condensate formalism for particle production in the small Bjorken $x$ kinematics to include contribution of large $x$ gluons. We consider scattering of a quark from the color fields of small and large $x$ gluons of a target proton or nucleus and demonstrate that this leads to spin and angular asymmetries in high energy collisions as well as rapidity loss of the projectile quark. DOI: https://doi.org/10.22323/1.374.0047 Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2020-05-30T12:08:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3749052584171295, "perplexity": 2638.921756530895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347409171.27/warc/CC-MAIN-20200530102741-20200530132741-00210.warc.gz"}
https://geodynamics.org/cig/software/sw4/	Status: Actively adding features to support improved science or performance by community contributors. ## How to Cite Code changes: 0 commits this past month, 0 commits this past year. Community: Geodynamics Forum Bug reports: Github Issue Tracker # SW4 SW4 implements substantial capabilities for 3-D seismic modeling, with a free surface condition on the top boundary, absorbing super-grid conditions on the far-fi eld boundaries, and an arbitrary number of point force and/or point moment tensor source terms. Each source time function can have one of many predefined analytical time dependencies, or interpolate a user de fined discrete time series. SW4 supports a fully 3-D heterogeneous material model that can be specified in several formats. It uses a curvilinear mesh near the free surface to honor the free surface boundary condition on a realistic topography. The curvilinear mesh is automatically generated from the description of the topography. To make SW4 more computationally efficient, the seismic wave equations are discretized on a Cartesian mesh below the curvilinear grid. The Cartesian mesh, which extends to the bottom of the computational domain, is also generated automatically. SW4 solves the seismic wave equations in Cartesian coordinates. It is therefore appropriate for local and regional simulations, where the curvature of the earth can be neglected. Locations can be specified directly in Cartesian coordinates, or through geographic (latitude, longitude) coordinates. SW4 can be built to use the Proj.4 library for calculating the mapping between geographic and Cartesian coordinates, or use an approximate spheroidal mapping. SW4 can output synthetic seismograms in an ASCII text format, or in the SAC format [7]. It can also present simulation information as GMT scripts, which can be used to create annotated maps. SW4 can output the solution, derived quantities of the solution, as well as the material model along 2-D grid planes. Furthermore, SW4 can output the 3-D volumetric solution, or material model, in a binary file format. Visco-elastic behavior can be important when modeling the dissipative nature of realistic materials, especially for higher frequencies. SW4 uses the rheological model of standard linear solid (SLS) elements, coupled in parallel. The coefficients in each SLS are determined such that the resulting quality factors Qp and Qs, for the attenuation of P- and S-waves, become approximately constant as function of frequency. These quality factors can vary from grid point to grid point over the computational domain and are read in the same way as the elastic properties of the material model. While most of the SW4 code is written in C++, almost all numerical computations are implemented in Fortan-77. SW4 uses a distributed memory programming model, implemented with the C-bindings of the MPI library. Compatible versions of the C++ and Fortran-77 compilers as well as the MPI library must be available to build the code. We have built and tested SW4 on a variety of machines, ranging from single processor laptops to large super-computers with O(100,000) cores. ## Current Release ### Source Packages For source installation instructions, please refer to the SW4 Installation Guide. sw4-v2.01.tgz [2017-11-20] Version 2.01 of SW4 fixes a bug in the python testing script. It is in all other aspects identical to version 2.0, which implements mesh refinement with hanging nodes. Mesh refinement is currently supported in the Cartesian portion of the mesh, but can be used together with realistic topography and heterogeneous isotropic visco-elastic material models. ### View Prior Source Releases [show] [hide] sw4-v2.0.tgz [2017-11-10] Version 2.0 of SW4 implements mesh refinement with hanging nodes. Mesh refinement is currently supported in the Cartesian portion of the mesh, but can be used together with realistic topography and heterogeneous isotropic visco-elastic material models. sw4-v1.1.tgz [2014-10-22] Version 1.1. ## User Resources User Manual The SW4 user manual is available online. Community Wiki Visit the SW4 Wiki page for additional support with building, using, or modifying SW4. SW4 Publications List Research publications using SW4. Community Discussion Browse the CIG Mailing List Archive to find past discussions and previous troubleshooting help, or post to the CIG forum with questions or comments. ## Developer Resources Development Version If you are interested in getting the development version of this code from the CIG repository, use the following git command: git clone --recursive https://github.com/geodynamics/sw4.git You can also browse the history of modifications in the Git repository. Issue/Bug Tracker on Github Browse and/or submit new issues at our Github Issues Tracker. Doxygen Documentation Auto-generated Doxygen documentation is available for the Development and Release codebases. ## SW4 Users Map Shows location of all users who downloaded SW4 in the past year (image updated daily.) This image was generated using GMT: The Generic Mapping Tools which is released under the GNU LGPL3+. Location data is based on MaxMind's GeoLite database which is released under the Creative Commons CC-BY-SA 3.0.	2020-07-14T12:57:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31864407658576965, "perplexity": 2952.292018640889}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655880665.3/warc/CC-MAIN-20200714114524-20200714144524-00485.warc.gz"}
http://pdglive.lbl.gov/DataBlock.action?node=S044GNL	# ${{\boldsymbol Z}}$ COUPLINGS TO NEUTRAL LEPTONS Averaging over neutrino species, the invisible ${{\mathit Z}}$ decay width determines the effective neutrino coupling $\mathit g{}^{{{\mathit \nu}_{{{{\mathit \ell}}}}}}$. For $\mathit g{}^{{{\mathit \nu}_{{e}}}}$ and $\mathit g{}^{{{\mathit \nu}_{{\mu}}}}$, ${{\mathit \nu}_{{e}}}{{\mathit e}}$ and ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ scattering results are combined with $\mathit g{}^{{{\mathit e}}}_{\mathit A}$ and $\mathit g{}^{{{\mathit e}}}_{\mathit V}$ measurements at the ${{\mathit Z}}$ mass to obtain $\mathit g{}^{{{\mathit \nu}_{{e}}}}$ and $\mathit g{}^{{{\mathit \nu}_{{\mu}}}}$ following NOVIKOV 1993C. # $\boldsymbol g{}^{{{\boldsymbol \nu}_{{{{\boldsymbol \ell}}}}}}$ INSPIRE search VALUE DOCUMENT ID COMMENT $0.50076$ $\pm0.00076$ 1 2006 ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV 1 From invisible ${{\mathit Z}}$-decay width. References: LEP-SLC 2006 PRPL 427 257 Precision Electroweak Measurements on the ${{\mathit Z}}$ Resonance	2019-03-19T17:20:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8917073607444763, "perplexity": 3401.212039292818}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202003.56/warc/CC-MAIN-20190319163636-20190319185636-00210.warc.gz"}
https://www.rba.gov.au/publications/rdp/2021/2021-09/appendix-d.html	# RDP 2021-09: Is the Phillips Curve Still a Curve? Evidence from the Regions Appendix D: Persistence in Unemployment Fluctuations As discussed in Section 7.2.3, Hazell et al's (2020) framework suggests that both the RBA's aggregate model and the baseline regional estimates in this paper may overstate the slope of the New Keynesian wage Phillips curve because they do not account for the persistence in unemployment fluctuations. To explore the importance of this point, we follow Hazell et al by estimating a regional panel regression that replaces the contemporaneous unemployment rate term in Equation (3) with the present discounted sum of realised unemployment rates over a five-year horizon into the future, (D1) $Δ w it =α+κ ∑ j=0 5 β j u i,t+j + θ i + ω t + ε it$ where the discount factor $\beta$ is calibrated to be 0.99. We instrument the forward sum of the unemployment rate with the first lag of the unemployment rate $\left({u}_{i,t-1}\right).$ The forward sums in Equation (D1) mean that we lose five years of observations at the end of our sample, and the instrument means we lose one observation at the start of our sample. We estimate Equation (D1) using 2SLS.[53] We find that the lagged unemployment rate is not a weak instrument, with a first-stage F value of 59.75. We estimate $\kappa$ to be –0.093 (p = 0.000), which is smaller than our estimate for $\delta$ of –0.227 using Equation (3) (Table 1).[54] Based on the framework of Hazell et al, the larger absolute size of the slope in Equation 3 reflects the fact that the unemployment rate is standing in for the entire future sum in Equation (D1). Since unemployment is persistent, time variation in the future sum is larger than the time variation in the unemployment rate, which leads to a smaller coefficient in Equation (D1) compared to Equation (3). Note, however, that this estimation approach is based on a theoretical model of the price Phillips curve, and we have not attempted to adapt Hazell et al's theory to the context of wage inflation. In that sense, the estimates in this appendix are only suggestive of a role for persistence. Overall, this suggests that while our regional estimates are helpful for examining the modelling assumptions in the RBA's aggregate models (as they both identify the same parameter), we should be cautious in interpreting these estimates as the structural slope of the New Keynesian wage Phillips curve. ## Footnotes We omit the lagged wages growth terms from the specification to increase comparability with Hazell et al's specification. Including lagged wages growth makes little difference to the conclusions in this appendix. [53] The impact of this adjustment is far smaller than found by Hazell et al, who find that the implied slope of the Phillips curve falls from 0.112 to 0.0062 when accounting for persistence in unemployment fluctuations. [54]	2021-11-28T23:42:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.758507251739502, "perplexity": 1112.5747374663597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358673.74/warc/CC-MAIN-20211128224316-20211129014316-00019.warc.gz"}
https://control.com/textbook/instrument-connections/electrical-signal-and-control-wiring/	# Electrical Signal and Control Wiring ## Chapter 10 - Instrument Connection and Communication There is much to be said for neatness of assembly in electrical signal wiring. Even though the electrons don’t “care” how neatly the wires are laid in place, human beings who must maintain the system certainly do. Not only are neat installations easier to navigate and troubleshoot, but they tend to inspire a similar standard of neatness when alterations are made. The following photographs illustrate excellent wiring practice. Study them carefully, and strive to emulate the same level of professionalism in your own work. Here we see 120 volt AC power distribution wiring. Note how the hoop-shaped “jumper” wires are all cut to (nearly) the same length, and how each of the wire labels is oriented such that the printing is easy to read: This next photograph shows a great way to terminate multi-conductor signal cable to terminal blocks. Each of the pairs was twisted together using a hand drill set to very slow speed. Note how the end of the cable is wrapped in a short section of heat-shrink tubing for a neat appearance: Beyond esthetic preferences for instrument signal wiring are several practices based on sound electrical theory. The following subsections describe and explain these wiring practices. ### Connections and wire terminations Many different techniques exist for connecting electrical conductors together: twisting, soldering, crimping (using compression connectors), and clamping (either by the tension of a spring or under the compression of a screw) are popular examples. Most industrial field wiring connections utilize a combination of compression-style crimp “lugs” (often referred to as ferrules or compression terminals) and screw clamps to attach wires to instruments and to other wires. The following photograph shows a typical terminal strip or terminal block array whereby twisted-pair signal cables connect to other twisted-pair signal cables. Metal bars inside each plastic terminal section form connections horizontally, so that wires fastened to the left side are connected to wires fastened to the right side: If you look closely at this photograph, you can see the bases of crimp-style ferrules at the ends of the wires, just where they insert into the terminal block modules. These terminal blocks use screws to apply force which holds the wires in close electrical contact with a metal bar inside each block, but metal ferrules have been crimped on the end of each wire to provide a more rugged tip for the terminal block screw to hold to. A close-up view shows what one of these ferrules looks like on the end of a wire: Also evident in this photograph is the dual-level connection points on the left-hand side of each terminal block. Two pairs of twisted signal conductors connect on the left-hand side of each terminal block pair, where only one twisted pair of wires connects on the right-hand side. This also explains why each terminal block section has two screw holes on the left but only one screw hole on the right. A close-up photograph of a single terminal block section shows how the screw-clamp system works. Into the right-hand side of this block a single wire (tipped with a straight compression ferrule) is clamped securely. No wire is inserted into the left-hand side: If another wire were secured by the screw clamp on the left-hand side of this terminal block, it would be made electrically common with the wire on the right-hand side by virtue of the metal bar joining both sides. Some terminal blocks are screwless, using a spring clip to make firm mechanical and electrical contact with the wire’s end: In order to extract or insert a wire end from or to a “screwless” terminal block, you must insert a narrow screwdriver into a hole in the block near the insertion point, then pivot the screwdriver (like a lever) to exert force on the spring clip. Screwless terminal blocks are generally faster to terminate and un-terminate than screw type terminal blocks, and the pushing action of the release tool is gentler on the body than the twisting action required to loosen and tighten screws. Many different styles of modular terminal blocks are manufactured to suit different wiring needs. Some terminal block modules, for example, have multiple “levels” instead of just one. The following photograph shows a two-level terminal block with screwless wire clamps: The next photograph shows a three-level terminal block with screw type clamps: Some multi-level terminal blocks provide the option of internal jumpers to connect two or more levels together so they will be electrically common instead of electrically isolated. This use of a multi-level terminal block is preferable to the practice of inserting multiple wires into the same terminal, when wires need to be made common to each other. Other modular terminal blocks include such features as LED indicator lamps, switches, fuses, and even resettable circuit breakers in their narrow width, allowing the placement of actual circuit components near connection points. The following photograph shows a swing-open fused terminal block module, in the open position: Modular terminal blocks are useful for making connections with both solid-core and stranded metal wires. The clamping force applied to the wire’s tip by the screw mechanism inside one of these blocks is direct, with no sliding or other motions involved. Some terminal blocks, however, are less sophisticated in design. This next photograph shows a pair of “isothermal” terminals designed to connect thermocouple wires together. Here you can see how the bare tip of the screw applies pressure to the wire inserted into the block: The rotary force applied to each wire’s tip by these screws necessitates the use of solid wire. Stranded wire would become frayed by this combination of forces. Many field instruments, however, do not possess “block” style connection points at all. Instead, they are equipped with pan-head machine screws designed to compress the wire tips directly between the heads of the screws and a metal plate below. Solid wires may be adequately joined to such a screw-head connection point by partially wrapping the bare wire end around the screw’s circumference and tightening the head on top of the wire, as is the case with the two short wire stubs terminated on this instrument: The problem with directly compressing a wire tip beneath the head of a screw is that the tip is subjected to both compressive and shear forces. As a result, the wire’s tip tends to become mangled with repeated connections. Furthermore, tension on the wire will tend to turn the screw, potentially loosening it over time. This termination technique is wholly unsuitable for stranded wire, because the shearing forces caused by the screw head’s rotation tends to “fray” the individual strands. The best way to attach a stranded wire tip directly to a screw-style connection point is to first crimp a compression-style terminal to the wire. The flat metal “lug” (ferrule) portion of the terminal is then inserted underneath the screw head, where it can easily tolerate the shearing and compressive forces exerted by the head. This next photograph shows five such stranded-copper wires connected to screw-style connection points on a field instrument using compression-style terminals: Compression-style terminals come in two basic varieties: fork and ring. An illustration of each type is shown here: Fork terminals are easier to install and remove, since they merely require loosening of the connector screw rather than removal of the screw. Ring terminals are more secure, since they cannot “fall off” the connection point if the screw ever accidently loosens. Just as direct termination underneath a screw head is wholly unsuitable for stranded wires, compression-style terminals are wholly unsuitable for solid wire. Although the initial crimp may feel secure, compression terminals lose their tension rapidly on solid wire, especially when there is any motion or vibration stressing the connection. Compression wire terminals should only be crimped to stranded wire! Properly installing a compression-type terminal on a wire end requires the use of a special crimping tool. The next photograph shows one of these tools in use: Note the different places on the crimping tool, labeled for different wire sizes (gauges). One location is used for 16 gauge to 10 gauge wire, while the location being used in the photograph is for wire gauges 22 through 18 (the wire inside of the crimped terminal happens to be 18 gauge). This particular version of a “crimping” tool performs most of the compression on the underside of the terminal barrel, leaving the top portion undisturbed. The final crimped terminal looks like this when viewed from the top: ### DIN rail An industry-standard structure for attaching terminal blocks and small electrical components to flat metal panels is something called a DIN rail. This is a narrow channel of metal – made of bent sheet steel or extruded aluminum – with edges designed for plastic components to “clip” on. The following photograph shows terminal blocks, relay sockets, fuses, and more terminal blocks mounted to a horizontal length of DIN rail in a control system enclosure: Two photographs of a terminal block cluster clipped onto a length of DIN rail – one from above and one from below – shows how specially-formed arms on each terminal block module fit the edges of the DIN rail for a secure attachment: The DIN rail itself mounts on to any flat surface by means of screws inserted through the slots in its base. In most cases, the flat surface in question is the metal subpanel of an electrical enclosure to which all electrical components in that enclosure are attached. An obvious advantage of using DIN rail to secure electrical components versus individually attaching those components to a subpanel with their own sets of screws is convenience: much less labor is required to mount and unmount a DIN rail-attached component than a component attached with its own set of dedicated screws. This convenience significantly eases the task of altering a panel’s configuration. With so many different devices manufactured for DIN rail mounting, it is easy to upgrade or alter a panel layout simply by unclipping components, sliding them to new locations on the rail, or replacing them with other types or styles of components. This next photograph shows some of the diversity available in DIN rail mount components. From left to right we see four relays, a power supply, and three HART protocol converters, all clipped to the same extruded aluminum DIN rail: As previously mentioned, DIN rail is available in both stamped sheet-steel and extruded aluminum forms. A comparison of the two materials is shown here, with sheet steel on the left and aluminum on the right: The form of DIN rail shown in all photographs so far is known as “top hat” DIN rail. A variation in DIN rail design is the so-called “G” rail, with a markedly different shape: Fortunately, many modular terminal blocks are formed with the ability to clip to either style of DIN rail, such as these two specialty blocks, the left-hand example being a terminal block with a built-in disconnect switch, and the right-hand example being a “grounding” terminal block whose termination points are electrically common to the DIN rail itself: If you examine the bottom structure of each block, you will see formations designed to clip either to the edges of a standard (“top hat”) DIN rail or to a “G” shaped DIN rail. Smaller DIN rail standards also exist, although they are far less common than the standard 35mm size: A nice feature of many DIN rail type terminal blocks is the ability to attach pre-printed terminal numbers. This makes documentation of wiring much easier, with each terminal connection having its own unique identification number: ### Cable routing In the interest of safety and longevity, one cannot simply route electrical power and signal cables randomly between different locations. Electrical cables must be properly supported to relieve mechanical stresses on the conductors, and protected from harsh conditions such as abrasion which might degrade the insulation. A traditional and rugged technique for cable routing is conduit, either metal or plastic (PVC). Conduit resembles piping used to convey fluids, except that it is much thinner-walled than fluid pipe and is not rated to withstand internal pressure as pipe is. In fact, threaded conduit uses the same thread pitch and diameter standards as NPT (National Pipe Taper) fluid pipe connections. Metal conduit naturally forms a continuously-grounded enclosure for conductors which not only provides a measure of protection against electrical shock (all enclosures and devices attached to the conduit become safely grounded through the conduit) but also shields against electrostatic interference. This is especially important for power wiring to and from devices such as rectifiers and variable-frequency motor drive (VFD) units, which have a tendency to broadcast large amounts of electromagnetic noise. Plastic conduit, of course, provides no electrical grounding or shielding because plastic is a non-conductor of electricity. However, it is superior to metal conduit with regard to chemical corrosion resistance, which is why it is used to route wires in areas containing water, acids, caustics, and other wet chemicals. Thin-wall conduit is made with metal so thin that threads cannot be cut into it. Instead, special connectors are used to join “sticks” of thin-wall conduit together, and to join thin-wall conduit to electrical enclosures. Several runs of thin-wall conduit appear in this next photograph. Two of those conduit runs have been severed following a wiring change, exposing the conductors inside: Installing cable into an electrical conduit is a task referred to as cable pulling, and it is something of an art. Cable “pulls” may be especially challenging if the conduit run contains many bends, and/or is close to capacity in terms of the number and size of conductors it already holds. A good practice is to always leave a length of nylon pull string inside each length of conduit, ready to use for pulling a new wire or cable through. When performing a wire “pull,” a new length of nylon pull string is pulled into the conduit along with the new wires, to replace the old pull string as it is pulled out of the conduit. Special lubricating “grease” formulated for electrical wiring may be applied to conductors pulled into a conduit, to reduce friction between those new conductors and the conductors already inside the conduit. When connecting electrical conduit to end-point devices, it is common to use flexible liquid-tight conduit as a connector between the rigid metal (or plastic) conduit and the final device. This provides some stress relief to the conduit in the event the device moves or vibrates, and also allows more freedom in positioning the device with respect to the conduit. Here, we see a motor-operated control valve with two runs of liquid-tight conduit routing conductors to it: Liquid-tight conduit comes in two general varieties: metallic and non-metallic. The metallic kind contains a spiraled metal sheath just underneath the plastic outer coating to provide a continuously-grounded shield much the same way that rigid metal conduit does. Non-metallic liquid-tight conduit is nothing more than plastic hose, providing physical protection against liquid exposure and abrasion, but no electrical grounding or shielding ability. Another technique for cable routing is the use of cable tray. Trays may be made of solid steel wire for light-duty applications such as instrument signal cabling or computer network cabling, or they may be made of steel or aluminum channel for heavy-duty applications such as electrical power wiring. Unlike conduit, cable trays are open, leaving the cables exposed to the environment. This often necessitates special cable insulation rated for exposure to ultraviolet light, moisture, and other environmental wear factors. A decided advantage of cable trays is ease of cable installation, especially when compared to electrical conduit. While cable tray does provide a continuously-grounded surface for electrical safety the same as metal conduit, cable tray does not naturally provide shielding for the conductors because it does not completely enclose the conductors the way metal conduit does. An example of light-duty cable tray appears here, used to support Ethernet cabling near the ceiling of a room at a college campus. The cable tray is made of solid steel wire, bent to form a “basket” to support dozens of yellow Ethernet cables: Heavy-duty cable tray appears throughout this next photograph, supporting large-gauge power conductors for electric generators at a gas turbine power plant. Here, the cable tray has the appearance of an aluminum ladder, with extruded metal rails and rungs providing physical support for the cables: Similar cables trays appear in the next photograph, supporting feeder cables from a stationary transformer and switchgear cabinets: A special form of wiring often seen in industrial facilities for power distribution is busway, also known as bus duct. These are rectangular sheet-metal tubes containing pre-fabricated copper busbars for the conduction of three-phase AC power. Special junction boxes, “tees,” and tap boxes allow busways to extend and branch to other busways and/or standard conductor wiring. Busways are used in indoor applications, often in motor control center (MCC) and power distribution center rooms to route electrical power to and from large disconnect switches, fuses, and circuit breakers. In this photograph, we see busway used to distribute power along the ceiling of an MCC room, alongside regular rigid conduit: As useful and neat in appearance as busways are, they are definitely limited in purpose. Busways are only used for electrical power distribution; not for instrumentation, control, or signaling purposes. Two materials useful for neatly routing power, signal, and instrumentation conductors inside an enclosure are wire duct and wire loom. Wire duct is a plastic channel with slotted sides, designed to be attached to the subpanel of an enclosure along with all electrical devices inside that enclosure. Wires pass from the devices to the duct through the slots (gaps) in the sides of the duct, and are enclosed by a removable plastic cover that snaps onto the top of the duct. A common brand name of wire duct in the industry is Panduit and so you will often hear people refer to wire duct as “Panduit” whether or not that particular brand is the one being used249. Wire loom is a loose spiral tube made of plastic, used to hold a group of individual wires together into a neat bundle. Wire loom is frequently used when a group of conductors must periodically flex, as is the case of a wire bundle joining devices inside a panel to other devices mounted on the hinging door of that panel. A photograph showing both wire duct and wire loom inside an instrumentation panel appears here. The wire duct is the grey-colored rectangular plastic channel set vertically and horizontally inside the panel, while the loom is a grey-colored plastic spiral surrounding the bundle of wires near the door hinge: ### Signal coupling and cable separation If sets of wires lie too close to one another, electrical signals may “couple” from one wire (or set of wires) to the other(s). This can be especially detrimental to signal integrity when the coupling occurs between AC power conductors and low-level instrument signal wiring such as thermocouple or pH sensor cables. Two mechanisms of electrical “coupling” exist: capacitive and inductive. Capacitance is a property intrinsic to any pair of conductors separated by a dielectric (an insulating substance), whereby energy is stored in the electric field formed by voltage between the wires. The natural capacitance existing between mutually insulated wires forms a “bridge” for AC signals to cross between those wires, the strength of that “bridge” inversely proportional to the capacitive reactance ($$X_C = {1 \over {2 \pi f C}}$$). Inductance is a property intrinsic to any conductor, whereby energy is stored in the magnetic field formed by current through the wire. Mutual inductance existing between parallel wires forms another “bridge” whereby an AC current through one wire is able to induce an AC voltage along the length of another wire. Capacitive coupling between an AC power conductor and a DC sensor signal conductor is shown in the following diagram: If the voltage-generating sensor happens to be a thermocouple and the receiving instrument a temperature indicator, the result of this capacitive coupling will be a “noisy” temperature signal interpreted by the instrument. This noise will be proportional to both the voltage and the frequency of the AC power. Inductive coupling between an AC power conductor and a DC sensor signal conductor is shown in the following diagram: Whereas the amount of noise induced into a low-level signal via capacitive coupling was a function of voltage and frequency, the amount of noise induced into a signal via inductive coupling is a function of current and frequency. A good way to minimize signal coupling is to simply separate conductors carrying incompatible signals. This is why electrical power conductors and instrument signal cables are almost never found in the same conduit or in the same ductwork together. Separation decreases capacitance between the conductors (recall that $$C = {A \epsilon \over d}$$ where $$d$$ is the distance between the conductive surfaces). Separation also decreases the coupling coefficient between inductors, which in turn decreases mutual inductance (recall that $$M = k \sqrt{L_1 L_2}$$ where $$k$$ is the coupling coefficient and $$M$$ is the mutual inductance between two inductances $$L_1$$ and $$L_2$$). In control panel wiring, it is customary to route AC power wires in such a way that they do not lay parallel to low-level signal wires, so that both forms of coupling may be reduced. If conductors carrying incompatible signals must cross paths, it is advisable to orient the conductors perpendicular to each other rather than parallel, like this: Perpendicular conductor orientation reduces both inter-conductor capacitance and mutual inductance by two mechanisms. Capacitance between conductors is reduced by means of minimizing overlapping area ($$A$$) resulting from the perpendicular crossing. Mutual inductance is reduced by decreasing the coupling coefficient ($$k$$) to nearly zero since the magnetic field generated perpendicular to the current-carrying wire will be parallel and not perpendicular to the “receiving” wire. Since the vector for induced voltage is perpendicular to the magnetic field (i.e. parallel with the current vector in the “primary” wire) there will be no voltage induced along the length of the “receiving” wire. The problem of power-to-signal line coupling is most severe when the signal in question is analog rather than digital. In analog signaling, even the smallest amount of coupled “noise” corrupts the signal. A digital signal, by comparison, will become corrupted only if the coupled noise is so great that it pushes the signal level above or below a detection threshold it should not cross. This disparity is best described through illustration. Two signals are shown here, coupled with equal amounts of noise voltage: The peak-to-peak amplitude of the noise on the analog signal is almost 20% of the entire signal range (the distance between the lower- and upper-range values), representing a substantial degradation of signal integrity. Analog signals have infinite resolution, which means any change in signal amplitude has meaning. Therefore, any noise whatsoever introduced into an analog signal will be interpreted as variations in the quantity that signal is supposed to represent. That same amount of noise imposed on a digital signal, however, causes no degradation of the signal except for one point in time where the signal attempts to reach a “low” state but fails to cross the threshold due to the noise. Other than that one incident represented in the pulse waveform, the rest of the signal is completely unaffected by the noise, because digital signals only have meaning above the “high” state threshold and below the “low” state threshold. Changes in signal voltage level caused by induced noise will not affect the meaning of digital data unless and until the amplitude of that noise becomes severe enough to prevent the signal’s crossing through a threshold (when it should cross), or causes the signal to cross a threshold (when it should not). From what we have seen here, digital signals are far more tolerant of induced noise than analog signals, all other factors being equal. If ever you find yourself in a position where you must route a signal wire near AC power conductors, and you happen to have the choice whether it will be an analog signal (e.g. 4-20 mA, 0-10 V) or a digital signal (e.g. EIA/TIA-485, Ethernet), your best option is to choose the digital signal to coexist alongside the AC power wires. ### Electric field (capacitive) de-coupling The fundamental principle invoked in shielding signal conductor(s) from external electric fields is that no substantial electric field can exist within a solid conductor. Electric fields exist due to imbalances of electric charge. If such an imbalance of charge ever were to exist within a conductor, charge carriers (typically electrons) in that conductor would quickly move to equalize the imbalance, thus eliminating the electric field. Another way of saying this is to state that electric fields only exist between points of different potential, and therefore cannot exist between equipotential points. Thus, electric flux lines may be found only in the dielectric (insulating media) between conductors, not within a solid conductor: This also means electric flux lines cannot span the diameter of a hollow conductor: The electrical conductivity of the hollow sphere’s wall ensures that all points on the circumference of the sphere are equipotential to each other. This in turn prohibits the formation of any electric flux lines within the interior air space of the hollow sphere. Thus, all points within the hollow sphere are shielded from any electric fields originating outside of the sphere. The only way to allow an external electric field to penetrate a hollow conductor from the outside is if that conductive shell is left “floating” with respect to another conductor placed within the shell. In this case the lines of electric flux do not exist between different points on the conductive sphere, but rather between the shell of the sphere and the conductor at the center of the sphere because those are the points between which a potential difference (voltage) exists. To illustrate: However, if we make the hollow shell electrically common to the negative side of the high-voltage source, the flux lines inside the sphere vanish, since there is no potential difference between the internal conductor and the conductive shell: If the conductor within the hollow sphere is elevated to a potential different from that of the high-voltage source’s negative terminal, electric flux lines will once again exist inside the sphere, but they will reflect this second potential and not the potential of the original high-voltage source. In other words, an electric field will exist inside the hollow sphere, but it will be completely isolated from the electric field outside the sphere. Once again, the conductor inside is shielded from external electrostatic interference: If conductors located inside the hollow shell are thus shielded from external electric fields, it means there cannot exist any capacitance between external conductors and internal (shielded) conductors. If there is no capacitance between conductors, there will never be capacitive coupling of signals between those conductors, which is what we want for industrial signal cables to protect those signals from external interference. All this discussion of hollow metal spheres is just an introduction to a discussion of shielded cable, where electrical cables are constructed with a conductive metal foil wrapping or conductive metal braid surrounding the interior conductors. Thus, the foil or braid creates a conductive tube which may be connected to ground potential (the “common” point between external and internal voltage sources) to prevent capacitive coupling between any external voltage sources and the conductors within the cable: The following photograph shows a set of signal cables with braided shield conductors all connected to a common copper “ground bus.” This particular application happens to be in the control panel of a 500 kV circuit breaker, located at a large electrical power substation where strong electric fields abound: This next photograph shows a four-conductor USB cable stripped at one end, revealing a metal-foil shield as well as silver-colored wire strands in direct contact with the foil, all wrapped around the four colored power and signal conductors: At the terminating end we typically twist the loose shield conductor strands together to form a wire which is then attached to a ground point to fix the cable’s shield at Earth potential. It is very important to ground only one end of a cable’s shield, or else you will create the possibility for a ground loop: a path for current to flow through the cable’s shield resulting from differences in Earth potential at the cable ends. Not only can ground loops induce noise in a cable’s conductor(s), but in severe cases it can even overheat the cable and thus present a fire hazard: An important characteristic of capacitively-coupled noise voltage is that it is common-mode in nature: the noise appears equally on every conductor within a cable because those conductors lie so close to each other (i.e. because the amount of capacitance existing between each conductor and the noise source is the same). One way we may exploit this characteristic in order to help escape the unwanted effects of capacitive coupling is to use differential signaling. Instead of referencing our signal voltage to ground, we let the signal voltage “float.” The following schematic diagram illustrates how this works: The lack of a ground connection in the DC signal circuit prevents capacitive coupling with the AC voltage from corrupting the measurement signal “seen” by the instrument. Noise voltage will still appear between either signal wire and ground as a common-mode voltage, but noise voltage will not appear between the two signal wires where our signal of interest exists. In other words, we side-step the problem of common-mode noise voltage by making common-mode voltage irrelevant to the sensor and to the signal receiver. Some industrial data communications standards such as EIA/TIA-485 (RS-485) use this technique to minimize the corrupting effects of electrical noise. To see a practical example of how this works in a data communications circuit, refer to the illustration in section beginning on page of this book. ### Magnetic field (inductive) de-coupling Magnetic fields, unlike electric fields, are exceedingly difficult to completely shield. Magnetic flux lines do not terminate, but rather loop. Thus, one cannot “stop” a magnetic field, only re-direct its path. A common method for magnetically shielding a sensitive instrument is to encapsulate it in an enclosure made of some material having an extremely high magnetic permeability ($$\mu$$): a shell offering much easier passage of magnetic flux lines than air. A material often used for this application is mu-metal, or $$\mu$$-metal, so named for its excellent magnetic permeability: This sort of shielding is impractical for protecting signal cables from inductive coupling, as mu-metal is rather expensive and must be layered relatively thick in order to provide a sufficiently low-reluctance path to shunt most of the external magnetic flux lines. The most practical method of granting magnetic field immunity to a signal cable follows the differential signaling method discussed in the electric field de-coupling section, with a twist (literally). If we twist a pair of wires rather than allow them to lie along parallel straight lines, the effects of electromagnetic induction are vastly minimized. The reason this works is best illustrated by drawing a differential signal circuit with two thick wires, drawn first with no twist at all. Suppose the magnetic field shown here (with three flux lines entering the wire loop) happens to be increasing in strength at the moment in time captured by the illustration: According to Lenz’s Law, a current will be induced in the wire loop in such a polarity as to oppose the increase in external field strength. In other words, the induced current tries to “fight” the imposed field to maintain zero net change. According to the right-hand rule of electromagnetism (tracing current in conventional flow notation), the induced current must travel in a counter-clockwise direction as viewed from above the wire loop in order to generate a magnetic field opposing the rise of the external magnetic field. This induced current works against the DC current produced by the sensor, detracting from the signal received at the instrument. When the external magnetic field strength diminishes, then builds in the opposite direction, the induced current will reverse. Thus, as the AC magnetic field oscillates, the induced current will also oscillate in the circuit, causing AC “noise” voltage to appear at the measuring instrument. This is precisely the effect we wish to mitigate. Immediately we see a remarkable difference between noise voltage induced by a magnetic field versus noise voltage induced by an electric field: whereas capacitively-coupled noise was always common-mode, here we see inductively-coupled noise as differential. If we twist the wires so as to create a series of loops instead of one large loop, we will see that the inductive effects of the external magnetic field tend to cancel: [Twisted wire pair physics] Not all the lines of flux go through the same loop. Each loop represents a reversal of direction for current in the instrument signal circuit, and so the direction of magnetically-induced current in one loop directly opposes the direction of magnetically-induced current in the next. So long as the loops are sufficient in number and spaced close together, the net effect will be complete and total opposition between all induced currents, with the result of no net induced current and therefore no AC “noise” voltage appearing at the instrument. In order to enjoy the benefits of magnetic and electric field rejection, instrument cables are generally manufactured as twisted, shielded pairs. The twists guard against magnetic (inductive) interference, while the grounded shield guards against electric (capacitive) interference. If multiple wire pairs are twisted within the same cable, the twist rates of each pair may be made different so as to avoid magnetic coupling from pair to pair. ### High-frequency signal cables Electronic signals used in traditional instrumentation circuits are either DC or low-frequency AC in nature. Measurement and control values are represented in analog form by these signals, usually by the magnitude of the electronic signal (how many volts, how many milliamps, etc.). Modern electronic instruments, however, often communicate process and control data in digital rather than analog form. This digital data takes the form of high-frequency voltage and/or current pulses along the instrument conductors. The most capable fieldbus instruments do away with analog signaling entirely, communicating all data in digital form at relatively high speeds. If the time period of a voltage or current pulse is less than the time required for the signal to travel down the length of the cable (at nearly the speed of light!), very interesting effects may occur. When a pulse propagates down a two-wire cable and reaches the end of that cable, the energy contained by that pulse must be absorbed by the receiving circuit or else be reflected back down the cable. To be honest, this happens in all circuits no matter how long or brief the pulses may be, but the effects of a “reflected” pulse only become apparent when the pulse time is short compared to the signal propagation time. In such short-pulse applications, it is customary to refer to the cable as a transmission line, and to regard it as a circuit component with its own characteristics (namely, a continuous impedance as “seen” by the traveling pulse). For more detail on this subject, refer to section 5.10 beginning on page . This problem has a familiar analogy: an “echo” in a room. If you step into a large room with hard wall, floor, and ceiling surfaces, you will immediately notice echoes resulting from any sound you make. Holding a conversation in such a room can be quite difficult, as the echoed sounds superimpose upon the most recently-spoken sounds, making it difficult to discern what is being said. The larger the room, the longer the echo delay, and the greater the conversational confusion. Echoes happen in small rooms, too, but they are generally too short to be of any concern. If the reflected sound(s) return quickly enough after being spoken, the time delay between the spoken (incident) sound and the echo (reflected) sound will be too short to notice, and conversation will proceed unhindered. We may address the “echo” problem in two entirely different ways. One way is to eliminate the echoes entirely by adding sound-deadening coverings (carpet, acoustic ceiling tiles) and/or objects (sofas, chairs, pillows) to the room. Another way to address the problem of echoes interrupting a conversation is to slow down the rate of speech. If the words are spoken slowly enough, the time delay of the echoes will be relatively short compared to the period of each spoken sound, and conversation may proceed without interference (albeit at a reduced speed). Both the problem of and the solutions for reflected signals in electrical cables follow the same patterns as the problem of and solutions for sonic echoes in a hard-surfaced room. If an electronic circuit receiving pulses sent along a cable receives both the incident pulse and an echo (reflected pulse) with a significant time delay separating those two pulses, the digital “conversation” will be impeded in the same manner that a verbal conversation between two or more people is impeded by echoes in a room. We may address this problem either by eliminating the reflected pulses entirely (by ensuring all the pulse energy is absorbed by an appropriate load placed at the cable’s end) or by slowing down the data transfer rate (i.e. longer pulses, lower frequencies) so that the reflected and incident pulse signals virtually overlap one another at the receiver. High-speed “fieldbus” instrument networks apply the former solution (eliminate reflections) while the legacy HART instrument signal standard apply the latter (slow data rate). Reflections are eliminated in high-speed data networks by ensuring the two furthest cable ends are both “terminated” by a resistance value of the proper size (matching the characteristic impedance of the cable). The designers of the HART analog-digital hybrid standard chose to use slow data rates instead, so their instruments would function adequately on legacy signal cables where the characteristic impedance is not standardized. The potential for reflected pulses in high-speed fieldbus cabling is a cause for concern among instrument technicians, because it represents a new phenomenon capable of creating faults in an instrument system. No longer is it sufficient to have tight connections, clean wire ends, good insulation, and proper shielding for a signal cable to faithfully convey a 4-20 mA DC instrument signal from one device to another. Now the technician must ensure proper termination and the absence of any discontinuities (sharp bends or crimps) along the cable’s entire length, in addition to all the traditional criteria, in order to faithfully convey a digital fieldbus signal from one device to another. Signal reflection problems may be investigated using a diagnostic instrument known as a time-domain reflectometer, or TDR. These devices are a combination of pulse generator and digital-storage oscilloscope, generating brief electrical pulses and analyzing the returned (echoed) signals at one end of a cable. If a TDR is used to record the pulse “signature” of a newly-installed cable, that data may be compared to future TDR measurements on the same cable to detect cable degradation or wiring changes. • Share Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License	2020-09-29T00:35:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38841691613197327, "perplexity": 1793.9330137856286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401617641.86/warc/CC-MAIN-20200928234043-20200929024043-00241.warc.gz"}
https://googology.wikia.org/wiki/Rathjen%27s_psi_function?oldid=324974	10,973 Pages Not to be confused with Rathjen's Psi function. Rathjen's $$\psi$$ function based on the least weakly Mahlo cardinal is an ordinal collapsing function.[1] A weakly Mahlo cardinal can be defined as a cardinal $$\text M$$ such that all normal functions closed in $$\text M$$ are closed under some regular ordinal $$<\textrm M$$. He uses this to diagonalise over the weakly inaccessible hierarchy. ## Definition Restrict $$\pi$$ and $$\kappa$$ to uncountable regular cardinals $$<M$$ only, for a function $$f$$ let $$\textrm{dom}$$ denote the domain of $$f$$, let $$\textrm{cl}_M(X)$$ denote $$X\cup\{\alpha<M:\alpha\textrm{ is a limit point of }X\}$$, and let $$\textrm{enum}(X)$$ denote the enumeration of $$X$$. An ordinal $$\alpha$$ is said to be to be strongly critical if $$\varphi_{\alpha}(0) = \alpha$$. For $$\alpha\in\Gamma_{M+1}$$ and $$\beta\in M$$: $$\beta\cup\{0,M\}\subseteq B^n(\alpha,\beta) \\ \gamma=\gamma_1+\cdots\gamma_k\land\gamma_1,\cdots,\gamma_k\in B^n(\alpha,\beta)\rightarrow\gamma\in B^{n+1}(\alpha,\beta) \\ \gamma=\varphi_{\gamma_0}(\gamma_1)\land\gamma_0,\gamma_1\in B^n(\alpha,\beta)\rightarrow\gamma\in B^{n+1}(\alpha,\beta) \\ \pi\in B^n(\alpha,\beta)\land\gamma<\pi\rightarrow\gamma\in B^{n+1}(\alpha,\beta) \\ \delta,\eta\in B^n(\alpha,\beta)\land\delta<\alpha\land\eta\in\textrm{dom}(\chi_\delta)\rightarrow\chi_\delta(\eta)\in B^{n+1}(\alpha,\beta) \\ B(\alpha,\beta):=\bigcup\{B^n(\alpha,\beta):n<\omega\} \\ \chi_\alpha=\textrm{enum}(\textrm{cl}_Μ(\{\kappa:\kappa\notin B(\alpha,\kappa)\land\alpha\in B(\alpha,\kappa)\}))$$ If $$\kappa = \chi_\alpha(\beta+1)$$ for some $$(\alpha,\beta) \in \Gamma_{M+1} \times M$$, define $$\kappa^- := \chi_\alpha(\beta)$$ using the unique $$(\alpha,\beta)$$. Otherwise if $$\kappa = \chi_\alpha(0)$$ for some $$\alpha \in \Gamma_{M+1}$$, then define $$\kappa^- := \textrm{sup}(\textrm{SC}_M(\alpha)\cup\{0\})$$ using the unique $$\alpha$$, where $$\textrm{SC}_M(\alpha)$$ is a set of strongly critical ordinals < M explicitly defined in the original source. For $$\alpha\in\Gamma_{M+1}$$: $$\kappa^-\cup\{\kappa^-,M\}\subset C_\kappa^n(\alpha) \\ \gamma=\gamma_1+\cdots\gamma_k\land\gamma_1,\cdots,\gamma_k\in C^n(\alpha)\rightarrow\gamma\in C^{n+1}(\alpha) \\ \gamma=\varphi_{\gamma_0}(\gamma_1)\land\gamma_0,\gamma_1\in C^n(\alpha,\beta)\rightarrow\gamma\in C^{n+1}(\alpha) \\ \pi\in C^n_\kappa(\alpha)\cap\kappa\land\gamma<\pi\land\pi\in\textrm R\rightarrow\gamma\in C^{n+1}_\kappa(\alpha) \\ \gamma=\chi_\delta(\eta)\land\delta,\eta\in C^n_\kappa(\alpha)\rightarrow\gamma\in C^{n+1}_\kappa(\alpha)$$ $$\gamma=\,$$$$\Phi$$‍‍$$_\delta(\eta)\land\delta,\eta\in C^n_\kappa(\alpha)\land 0<\delta\land\delta,\eta<M\rightarrow\gamma\in C^{n+1}_\kappa(\alpha)$$ $$\beta<\alpha\land\pi,\beta\in C^n_\kappa(\alpha)\land\beta\in C_\pi(\beta)\rightarrow\psi_\pi(\beta)\in C^{n+1}_\kappa(\alpha) \\ C_\kappa(\alpha):=\bigcup\{C^n_\kappa(\alpha):n<\omega\} \\ \psi_\kappa(\alpha):=\textrm{min}(\{\xi:\xi\notin C_\kappa(\alpha)\})$$ ## Ordinal notation It admits an associated ordinal notation $$T(\text{M})$$ whose limit (i.e. ordinal type) is $$\psi_{\Omega}(\chi_{\varepsilon_{\text{M}+1}}(0))$$, which is strictly greater than $$\textrm{PTO}(\textrm{KPM})$$ and is strictly smaller than the limit of countable ordinals expressed by Rathjen's $$\psi$$. The ordinal $$\textrm{PTO}(\textrm{KPM})$$, which is called "Rathjen's ordinal" in this community, means the proof-theoretic ordinal of $$\textbf{KPM}$$, where $$\textrm{KPM}$$ is Kripke–Platek set theory $$\textrm{KP}$$ augmented by the axiom schema "for any $$\Delta_0$$-formula $$H(x,y)$$ satifying $$\forall x, \exists y, H(x,y)$$, there exists an addmissible set $$z$$ satisfying $$\forall x \in z, \exists y, H(x,y)$$". It coincides with $$\psi_{\omega_1}(\psi_{\chi_{\varepsilon_{\text M+1}}(0)}(0))$$ in Rathjen's $$\psi$$ function.[2] ## Explanation Due to the complexity of the original notation, the one provided below has been simplified slightly, but still emulates the several properties of the ordinal collapsing function. In order to avoid the confusion similar to above ones, we emphasise that the simplified OCF below is different from the original one, and hence we do not necessarily have an ordinal notation associated to it. We restrict $$\pi$$ to uncountable regular ordinals. $$\text{enum}(X)$$ is the unique increasing function $$f$$ such that the range of $$f$$ is exactly $$X$$. $$\text{cl}(X)$$ is the closure of $$X$$; that is $$\text{cl}(X):=X\cup\{\beta \in \textrm{Lim} \mid \sup(X\cap\beta)=\beta\}$$, where $$\textrm{Lim}$$ denotes the class of non-zero limit ordinals. It is also the closure under the order topology, because every non-zero ordinal $$\alpha$$ admits the fundamental system $$\{(\alpha + 1) \setminus (\beta + 1) \mid \beta \in \alpha\}$$ of neighbourhoods in $$\textrm{On}$$. $$\text B_0(\alpha,\beta):=\beta\cup\{0,\text M\}$$ $$\text B_{n+1}(\alpha,\beta):=\{\gamma+\delta,\,$$$$\varphi$$$$_\gamma(\delta),\chi_\mu(\delta):\gamma,\delta,\mu\in\text B_n(\alpha,\beta)\wedge\mu<\alpha\}$$ $$\text B(\alpha,\beta):=\cup_{n<\omega}\text B_n(\alpha,\beta)$$ $$\chi_\alpha:=\text{enum}(\text{cl}(\{\pi:\text B(\alpha,\pi)\cap\text M\subseteq \pi\wedge\alpha\in\text B(\alpha,\pi)\}))$$ $$\text C_0(\alpha,\beta):=\beta\cup\{0,\text M\}$$ $$\text C_{n+1}(\alpha,\beta):=\{\gamma+\delta,\varphi_\gamma(\delta),\chi_\gamma(\delta),\psi_\pi(\mu):\gamma,\delta,\mu,\pi\in\text C_n(\alpha,\beta)\wedge\mu<\alpha\}$$ $$\text C(\alpha,\beta):=\cup_{n<\omega}\text C_n(\alpha,\beta)$$ $$\psi_\pi(\alpha):=\min\{\beta:\text C(\alpha,\beta)\cap\pi\subseteq\beta\wedge\alpha\in\text C(\alpha,\beta)\}$$ Rathjen originally defined the $$\psi$$ function in more complicated a way in order to create an ordinal notation associated to it. Therefore it is not certain whether the simplified OCF above yields an ordinal notation or not. The original $$\chi$$ functions used in Rathjen's original OCF are not so easy to understand, and differ from the $$\chi$$ functions defined above. Instead, we explain the $$\text I$$ functions, which is deeply related to the original $$\chi$$ functions. The $$\text I_0$$ function enumerates the uncountable cardinals less than $$\text M$$. The $$\text I_1$$ function enumerates the weakly inaccessible cardinals less than $$\text M$$, and their limits. Similarly, for each $$\alpha<\text M$$, $$\text I_{1+\alpha}$$ enumerates the weakly $$\alpha$$-inaccessible cardinals less than $$\text M$$ (and their limits, because the function is normal), and the function $$\text I_{\text M}$$ diagonalises over these, and enumerates the weakly hyper-inaccessible cardinals and their limits less than $$\text M$$. $$\text I_{\text M2}$$ enumerates the weakly hyper-hyper-inaccessible cardinals and their limits less than $$\text M$$, and so on and so fourth. Rathjen verified that $$\chi_{\alpha}(\beta)$$ (with respect to the original $$\chi$$ functions) coincides with $$\textrm I_{\alpha}(\beta)$$ for any $$\alpha < \Lambda_0 := \chi_{\chi_{\chi_{\cdot_{\cdot_{\cdot}}}(0)}(0)}(0)$$ and $$\beta < \text M$$. Although it may not be obvious why, the limits of these large cardinals are added to the $$\text I$$ function to make it much easier to notate, say, the suprenum of the first weakly inaccessible cardinal, the second weakly inaccessible cardinal, the third weakly inaccessible cardinal, $$\ldots$$, as values like these don't otherwise have any way of being notated easily. Be careful that some author denote by $$\text I_\alpha$$ the $$\alpha$$th weakly inaccessible cardinal, while Rathjen denoted by $$\text I_\alpha$$ a function. ## Common misconceptions Here is a list of common misconceptions in this community, originally pointed out by a Japanese Googology Wiki user p進大好きbot.[3] For more common misconceptions, see also the full list. Common misconception Fact Reason The limit of countable ordinals expressed by Rathjen's $$\psi$$ function is equal to $$\textrm{PTO}(\textrm{KPM})$$. These two ordinals aren't equal The former one is strictly greater than the limit of $$T(\text{M})$$, while the latter one is strictly smaller than it. Rathjen's $$\psi$$ and simplified Rathjen's $$\psi$$ are the same OCF Rathjen's $$\psi$$ function is often confounded with another simplified Rathjen's $$\psi$$, but they are distinct OCFs.[4] The former is known to admit an ordinal notation, while the latter isn't known to admit an ordinal notation. Rathjen's $$\psi$$ function is the same as another of Rathjen's works, a function symbol $$\psi$$. Rathjen's $$\psi$$ function is often confounded with another Rathjen's function symbol $$\psi$$, but they are distinct notions.[5] The former one is a published OCF, while the latter one is just a function symbol in an ordinal notation associated to an unpublished OCF. Rathjen's $$\psi$$ satisfies $$\psi(\psi_I(0))=\psi(\Omega_{\Omega_{\Omega_{\cdots}}})$$ where $$\psi$$ denotes $$\psi_\Omega$$, $$\Omega_{\Omega_{\Omega_{\cdots}}}$$ denotes the least Omega fixed point, and $$I$$ denotes the least inaccessible cardinal An OCF satisfying this equality must be different than Rathjen's $$\psi$$ Rathjen's $$\psi$$ satisfies $$\psi(\psi_I(0)) > \psi(\Omega_{\Omega_{\Omega_{\cdots}}})$$ The page 2000 steps uses $$\psi$$ to denote Rathjen's $$\psi$$ The OCFs are distinct, and also the OCF on the page is unspecified Rathjen's $$\psi$$ doesn't fit the analysis given on the page Several complicated conditions in the definition of Rathjen's $$\psi$$ function are droppable if we are interested only in googology They are important conditions that should be kept They're used to define and prove the isomorphism of the ordinal notation associated to it, which is required for computable googology, as OCFs aren't computable. It's possible to define the same OCF using only a single $$\text C$$ function instead of both $$\text B$$ and $$\text C$$ It's not guaranteed to be the same OCF This is not done in the original text, as it is more transparent and easier to manage values when the functions are defined separately. Moreover, such a "simplification" might not admit an ordinal notation associated to it if the replacement of the definition changes the behaviour of the functions. ## Sources 1. Rathjen, Michael. "Ordinal Notations Based on a Weakly Mahlo Cardinal", Archive for Mathematical Logic 29 (1990) 249--263. 2. Rathjen, Michael. "Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM", Archive for Mathematical Logic (1994), Volume 33, Issue 1, pp 35–55. 3. Rathjen, Michael. "The Realm of Ordinal Analysis" 4. Rathjen, Michael. "Proof-theoretic analysis of KPM", Archive for Mathematical Logic 30 (1991) 377--403. Community content is available under CC-BY-SA unless otherwise noted.	2021-07-24T02:09:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9826039671897888, "perplexity": 455.80955497469586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150067.87/warc/CC-MAIN-20210724001211-20210724031211-00039.warc.gz"}
http://pdglive.lbl.gov/Particle.action?node=M003&home=sumtabM	LIGHT UNFLAVORED MESONS($\boldsymbol S$ = $\boldsymbol C$ = $\boldsymbol B$ = 0) For $\mathit I = 1$ (${{\mathit \pi}}$, ${{\mathit b}}$, ${{\mathit \rho}}$, ${{\mathit a}}$): ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit d}}}$, ( ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit u}}}−$ ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit d}}})/\sqrt {2 }$, ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit u}}}$;for $\mathit I = 0$ (${{\mathit \eta}}$, ${{\mathit \eta}^{\,'}}$, ${{\mathit h}}$, ${{\mathit h}^{\,'}}$, ${{\mathit \omega}}$, ${{\mathit \phi}}$, ${{\mathit f}}$, ${{\mathit f}^{\,'}}$): ${\mathit {\mathit c}}_{{\mathrm {1}}}$( ${{\mathit u}}{{\overline{\mathit u}}}$ $+$ ${{\mathit d}}{{\overline{\mathit d}}}$ ) $+$ ${\mathit {\mathit c}}_{{\mathrm {2}}}$( ${{\mathit s}}{{\overline{\mathit s}}}$ ) INSPIRE search # ${{\boldsymbol f}_{{0}}{(980)}}$ $I^G(J^{PC})$ = $0^+(0^{+ +})$ See also the minireview on scalar mesons under ${{\mathit f}_{{0}}{(500)}}$. (See the index for the page number.) ${{\mathit f}_{{0}}{(980)}}$ MASS $990 \pm20$ MeV ${{\mathit f}_{{0}}{(980)}}$ WIDTH $10\text{ to }100$ MeV	2019-11-12T16:08:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9987121820449829, "perplexity": 685.3485457619731}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665575.34/warc/CC-MAIN-20191112151954-20191112175954-00020.warc.gz"}
https://www.usgs.gov/media/images/pollen-under-a-microscope	# Pollen Under a Microscope ### Detailed Description This image was taken through the eyepiece of a microscope. Pollen is mixed in with a few larger pieces of organic material. Public Domain.	2023-03-25T22:03:29	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8357505202293396, "perplexity": 8402.850519746427}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945372.38/warc/CC-MAIN-20230325191930-20230325221930-00168.warc.gz"}
https://mooseframework.inl.gov/newsletter/2018_11.html	## MOOSE Development Workflow We have slightly modified the way MOOSE changes are submitted+merged on GitHub. In general, nothing should change from the workflow you are use to. From now on, all pull requests will be into the "next" branch instead of "devel". We've changed the default github branch for MOOSE to be "next" - so it will be automatically selected when you create new pull requests. The "devel" branch still exists and has the exact meaning as before, and you should still branch from "devel" when working on changes to MOOSE. ## Automatic Differentiation Making use of the MetaPhysicL package, MOOSE now has forward mode automatic differentiation (AD) capabilities. Where this capability is perhaps most useful is in Jacobian computation, as demonstrated in classes inherited from ADKernel. These derivative classes only have to override the computeQpResidual method; the Jacobian is computed automatically by carrying derivatives through the residual computation. The ADKernel and ADMaterial classes have been designed such that derivative computation is only conducted during the Jacobian computation phase; while computing the residual, derivative computations are not carried out, saving substantial expense. More documentation will be added as AD percolates through the framework (e.g. addition of ADInterfaceKernel, ADDGKernel, ADIntegratedBC, ADNodalBC). For now the best documentation is the existing tests. Some example input files include: ad_material.i, ad_coupled_convection.i, and ad_simple_diffusion.i. For examples of writing ADKernels, see ADCoupledConvection.h, ADMatDiffusionTest.h headers and ADCoupledConvection.C, ADMatDiffusionTest.C source files. An example of an ADMaterial can be found in ADCoupledMaterial.h, ADCoupledMaterial.C. Moving forward, the idea is for application developers to be able to develop entire apps without writing a single Jacobian statement, having confidence that the automatically computed Jacobians are accurate. This has the potential to decrease application development time by order(s) of magnitude. In terms of computing performance, note that presently AD Jacobians are indeed slower to compute than hand-coded Jacobians, but they parallelize extremely well. ## Relationship Manager System Evolution In October, the Relationship Manager system gained several new capabilities ## Grain Tracker Enhancements The GrainTracker continues to be improved upon, with robustness enhacements and new functionality in several areas. The GrainTracker has been updated to utilize the latest improvments added to the Relationship Manager system. The GrainTracker now creates separate Geomateric and Algebraic Relationship Managers to ensure the proper amount of solution information is necessary in distributed simulations for stitching together separate grain regions. Other Grain Tracker enhancments added in October: • The GrainTracker has been enhanced to support "melt pool" simulations where the simulation may begin with zero grains. Previously the GrainTracker only supported simulations that began with a non-zero number of grains. • The GrainTracker no longer uses a recursive discovery method for identifying individual grain regions on each processor. Modern Linux and Mac operating system default to fairly small stack sizes (only a few Megabytes). If the GrainTracker is used on finer meshes or with larger grains, it was possible to run out of stack space creating a difficult to understand segmentation fault. Rather than require users to adjust stack spaces to use this common capability, the recursive algorithm was simply replaced with an iterative one, which allows for much larger recursive exploration of features. • Handles degenerative bounding boxes (e.g. 2D bounding boxes in 3D) for more robust fast intersection checking. • Additional algorithmic checks for difficult tracking cases involving nucleation and evolution in close proximity (e.g. more tracking robustness). ## Vector Initial Conditions Initial conditions can now be supplied for vector variables. Currently, only VectorConstantIC exists (see VectorConstantIC.h, VectorConstantIC.C, vector_constant_ic.i), but more can be easily added by overriding the value method. ## Action Refactor The MaterialOutputAction object and related objects were refactored and made simplier. Previously these tasks were designed as meta-actions. However, it was discovered that these Actions could be simplified by being converted into normal MooseObjectActions (more direct). ## New Enhacements • Enable Mac OS 10.14 (Mojave) support and debugging through code signing (entitlements) • CSVDiffer.py (CSVDiff Tester) can now compare a subset of columns (more enhancements coming) • Migrate to the improved RandomIC in all tests (remove all deprecated tests from the framework and modules) • Don't update the "failed tests" list when running only failed tests (–failed-tests). ## Bug Fixes • Avoid unecessary data structure copies (multiple) in SystemBase • Explicity set the current subdomain in ElementalVariableValue postprocessor (avoid assertion) • Avoid duplicate runs of mesh adaptivity and mesh modifiers when running MOOSE using a pre-split mesh fixes (https://github.com/idaholab/moose/issues/12084 and https://github.com/idaholab/moose/issues/12304)	2019-02-19T21:41:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34171929955482483, "perplexity": 6295.58026132635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247492825.22/warc/CC-MAIN-20190219203410-20190219225410-00526.warc.gz"}
https://directorioicc.gov.co/event-created/year/2019	D L M M J V S 1 4 5 D L M M J V S D L M M J V S D L M M J V S 20 21 D L M M J V S D L M M J V S 22 23 24 25 26 27 28 29 30 D L M M J V S 1 2 3 4 5 6 8 9 D L M M J V S 11 D L M M J V S D L M M J V S 12 13 14 15 D L M M J V S 23 24 D L M M J V S 8 22 23 24 25 26 27 28 29 30 31	2021-12-04T21:12:25	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9642824530601501, "perplexity": 6377.012492485724}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363006.60/warc/CC-MAIN-20211204185021-20211204215021-00482.warc.gz"}
https://pos.sissa.it/256/243/	Volume 256 - 34th annual International Symposium on Lattice Field Theory (LATTICE2016) - Applications Beyond QCD Numerical simulation of Dirac semimetals V.V. Braguta, M.I. Katsnelson, A.Y. Kotov,* A.A. Nikolaev *corresponding author Full text: pdf Pre-published on: 2017-02-03 12:57:35 Published on: 2017-03-24 10:20:24 Abstract Dirac semimetals are recently discovered materials with low energy electronic excitation spectrum similar to the massless two favour 3+1 Dirac fermions. The interaction between quasiparticles in Dirac semimetals is instantaneous Coulomb with large effective coupling constant $\alpha \sim 1$. In this report we present results of study of the phase diagram of Dirac semimetals within lattice simulation with rooted staggered fermions. In particular, we calculate the chiral condensate as a function of effective coupling constant and Fermi velocity anisotropy and thus determine the position of semimetal-insulator transition in Dirac semimetals. Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2017-11-22T16:47:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.602350652217865, "perplexity": 10945.84893768222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806615.74/warc/CC-MAIN-20171122160645-20171122180645-00721.warc.gz"}
https://www.itl.nist.gov/div898/handbook/prc/section2/prc21.htm	7. Product and Process Comparisons 7.2. Comparisons based on data from one process ## Do the observations come from a particular distribution? Data are often assumed to come from a particular distribution. Goodness-of-fit tests indicate whether or not it is reasonable to assume that a random sample comes from a specific distribution. Statistical techniques often rely on observations having come from a population that has a distribution of a specific form (e.g., normal, lognormal, Poisson, etc.). Standard control charts for continuous measurements, for instance, require that the data come from a normal distribution. Accurate lifetime modeling requires specifying the correct distributional model. There may be historical or theoretical reasons to assume that a sample comes from a particular population, as well. Past data may have consistently fit a known distribution, for example, or theory may predict that the underlying population should be of a specific form. Hypothesis Test model for Goodness-of-fit Goodness-of-fit tests are a form of hypothesis testing where the null and alternative hypotheses are $$H_0$$: Sample data come from the stated distribution. $$H_a$$: Sample data do not come from the stated distribution. Parameters may be assumed or estimated from the data One needs to consider whether a simple or composite hypothesis is being tested. For a simple hypothesis, values of the distribution's parameters are specified prior to drawing the sample. For a composite hypothesis, one or more of the parameters is unknown. Often, these parameters are estimated using the sample observations. A simple hypothesis would be: $$H_0$$: Data are from a normal distribution, $$\mu=0$$ and $$\sigma=1$$. A composite hypothesis would be: $$H_0$$: Data are from a normal distribution, unknown $$\mu$$ and $$\sigma$$. Composite hypotheses are more common because they allow us to decide whether a sample comes from any distribution of a specific type. In this situation, the form of the distribution is of interest, regardless of the values of the parameters. Unfortunately, composite hypotheses are more difficult to work with because the critical values are often hard to compute. Problems with censored data A second issue that affects a test is whether the data are censored. When data are censored, sample values are in some way restricted. Censoring occurs if the range of potential values are limited such that values from one or both tails of the distribution are unavailable (e.g., right and/or left censoring - where high and/or low values are missing). Censoring frequently occurs in reliability testing, when either the testing time or the number of failures to be observed is fixed in advance. A thorough treatment of goodness-of-fit testing under censoring is beyond the scope of this document. See D'Agostino & Stephens (1986) for more details. Three types of tests will be covered Three goodness-of-fit tests are examined in detail: 1. Chi-square test for continuous and discrete distributions; 2. Kolmogorov-Smirnov test for continuous distributions based on the empirical distribution function (EDF); 3. Anderson-Darling test for continuous distributions. A more extensive treatment of goodness-of-fit techniques is presented in D'Agostino & Stephens (1986). Along with the tests mentioned above, other general and specific tests are examined, including tests based on regression and graphical techniques.	2018-06-22T22:50:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6833053827285767, "perplexity": 597.4925843908187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864822.44/warc/CC-MAIN-20180622220911-20180623000911-00460.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Adavis.martin-d	# zbMATH — the first resource for mathematics ## Davis, Martin David Compute Distance To: Author ID: davis.martin-d Published as: Davis, M.; Davis, M. D.; Davis, Martin; Davis, Martin D.; Davis, Martin David Homepage: https://www.cs.nyu.edu/cs/faculty/davism/ External Links: MGP · Wikidata · dblp · GND Documents Indexed: 80 Publications since 1953, including 17 Books Biographic References: 4 Publications all top 5 #### Co-Authors 50 single-authored 4 Putnam, Hilary Whitehall 3 Weyuker, Elaine J. 2 Robinson, Julia 2 Schonberg, Edmond 1 Blum, Lenore 1 Fechter, Ronald 1 Feferman, Solomon 1 Gaal, Lisl 1 Gale, David 1 Gottlieb, Allan 1 Henkin, Leon Albert 1 Insall, Matt 1 Kelly, James M. 1 Lehmer, Derrick Henry 1 Logemann, George 1 Loveland, Donald W. 1 Mac Lane, Leslie Saunders 1 Matiyasevich, Yuriĭ Vladimirovich 1 Niven, Ivan Morton 1 Pitcher, Everett 1 Post, Emil Leon 1 Putman, Hilary 1 Schwartz, Jacob Theodore 1 Scott, Elizabeth L. 1 Trotskaia Lehmer, Emma all top 5 #### Serials 4 Notices of the American Mathematical Society 2 Communications on Pure and Applied Mathematics 2 Illinois Journal of Mathematics 2 Information and Control 2 The Journal of Symbolic Logic 2 Proceedings of the American Mathematical Society 2 The Bulletin of Symbolic Logic 1 American Mathematical Monthly 1 Artificial Intelligence 1 Computers & Mathematics with Applications 1 International Journal of Theoretical Physics 1 Applied Mathematics and Computation 1 The Computer Journal. Section A / Section B 1 Journal of the Association for Computing Machinery 1 Kiberneticheskiĭ Sbornik. Novaya Seriya 1 Journal of Logic and Computation 1 Games and Economic Behavior 1 Communications of the ACM 1 Journal of Mathematical Sciences (New York) 1 Annals of Mathematics. Second Series 1 Higher-Order and Symbolic Computation 1 Nexus Network Journal all top 5 #### Fields 33 Mathematical logic and foundations (03-XX) 27 Computer science (68-XX) 21 History and biography (01-XX) 8 Number theory (11-XX) 7 General and overarching topics; collections (00-XX) 2 Quantum theory (81-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) #### Citations contained in zbMATH 52 Publications have been cited 1,444 times in 1,114 Documents Cited by Year A machine program for theorem-proving. Zbl 0217.54002 Davis, M.; Logemann, G.; Loveland, D. 1962 A computing procedure for quantification theory. Zbl 0212.34203 Davis, M.; Putnam, H. 1960 Computability and unsolvability. Zbl 0080.00902 Davis, Martin 1958 Hilbert’s tenth problem is unsolvable. Zbl 0277.02008 Davis, Martin 1973 The decision problem for exponential diophantine equations. Zbl 0111.01003 Davis, Martin; Putnam, Hilary; Robinson, Julia 1961 Applied nonstandard analysis. Zbl 0359.02060 Davis, Martin 1977 Hilbert’s tenth problem: Diophantine equations: Positive aspects of a negative solution. Zbl 0346.02026 Davis, Martin; Matijasevic, Yuri; Robinson, Julia 1976 Computability, complexity, and languages. Fundamentals of theoretical computer science. Zbl 0569.68042 Davis, Martin D.; Weyuker, Elaine J. 1983 The mathematics of non-monotonic reasoning. Zbl 0435.68075 Davis, Martin 1980 Arithmetical problems and recursively enumerable predicates. Zbl 0051.24509 Davis, Martin 1953 Automata studies. Zbl 0074.11204 Shannon, Claude E. (ed.); McCarthy, John (ed.); Kleene, S. C.; von Neumann, J.; Culbertson, James T.; Minsky, M. L.; Moore, Edward F.; Shannon, Claude E.; McCarthy, John; Davis, M. D.; de Leeuw, K.; Shapiro, N.; Ashby, W. Ross; MacKay, D. M.; Uttley, Albert M. 1956 Why Goedel didn’t have Church’s thesis. Zbl 0519.03033 Davis, Martin 1982 The undecidable. Basic papers on undecidable propositions, unsolvable problems and computable functions. Corrected reprint of the 1965 original. Zbl 1099.03002 Davis, Martin (ed.) 2004 A relativity principle in quantum mechanics. Zbl 0392.03040 Davis, Martin 1978 Eliminating the irrelevant from mechanical proofs. Zbl 0131.01201 Davis, Martin 1963 Why there is no such discipline as hypercomputation. Zbl 1103.68555 Davis, Martin 2006 The universal computer. The road from Leibniz to Turing. Zbl 0960.01001 Davis, Martin 2000 Computability and unsolvability. (Enl. version of the orig. publ. McGraw- Hill Book Company, New York 1958). Zbl 0553.03024 Davis, Martin 1982 An explicit Diophantine definition of the exponential function. Zbl 0222.10017 Davis, Martin 1971 The definition of universal Turing machine. Zbl 0084.01003 Davis, Martin 1958 Solvability, provability, definability. The collected works of Emil L. Post. Zbl 0823.03001 Post, Emil L.; Davis, Martin (ed.) 1993 On the number of solutions of Diophantine equations. Zbl 0275.02042 Davis, Martin 1972 Diophantine sets over polynomial rings. Zbl 0113.00604 Davis, M.; Putnam, H. 1963 Extensions and corollaries of recent work on Hilbert’s tenth problem. Zbl 0112.24603 Davis, M. 1963 What did Gödel believe and when did he believe it? Zbl 1108.03003 Davis, Martin 2005 The early history of automated deduction. Zbl 1011.68511 Davis, Martin 2001 Engines of logic. Mathematicians and the origin of the computer. Corrected reprint paperback ed. of the original with the title “The universal computer. The road from Leibniz to Turing”. Zbl 1035.01002 Davis, Martin 2000 Metamathematical extensibility for theorem verifiers and proof-checkers. Zbl 0418.68079 Davis, Martin; Schwartz, Jacob T. 1979 The effect of antibody-dependent enhancement, cross immunity, and vector population on the dynamics of dengue fever. Zbl 1406.92577 Hu, K.; Thoens, C.; Bianco, S.; Edlund, S.; Davis, M.; Douglas, J.; Kaufman, J. H. 2013 The universal computer. The road from Leibniz to Turing. Turing centenary edition. Zbl 1243.68013 Davis, Martin 2012 The Church-Turing thesis: Consensus and opposition. Zbl 1145.03300 Davis, Martin 2006 A free variable version of the first-order predicate calculus. Zbl 0754.03004 Davis, Martin; Fechter, Ronald 1991 A formal notion of program-based test data adequacy. Zbl 0537.68025 Davis, Martin D.; Weyuker, Elaine J. 1983 One equation to rule them all. Zbl 0316.02051 Davis, Martin 1968 Conceptual confluence in 1936: Post and Turing. Zbl 1400.01008 Davis, Martin; Sieg, Wilfried 2015 Pragmatic Platonism. Zbl 1338.03004 Davis, Martin 2014 American logic in the 1920s. Zbl 0858.01025 Davis, Martin 1995 A first course in functional analysis. Zbl 0199.17901 Davis, Martin 1966 Diophantine equations and recursively enumerable sets. Zbl 0199.03901 Davis, M. 1966 Computable functionals of arbitrary finite type. Zbl 0085.24803 Davis, Martin 1959 Reductions of Hilbert’s tenth problem. Zbl 0085.24802 Davis, Martin; Putman, Hilary 1959 From linear operators to computational biology. Essays in memory of Jacob T. Schwartz. Zbl 1252.92002 Davis, Martin (ed.); Schonberg, Edmond (ed.) 2013 Representation theorems for recursively enumerable sets and a conjecture related to Poonen’s large subring of $$\mathbb Q$$. Zbl 1345.03021 Davis, M. 2010 Computability, computation, and the real world. Zbl 1188.68132 Davis, Martin 2006 The incompleteness theorem. Zbl 1100.03003 Davis, Martin 2006 From logic to computer science and back. Zbl 0930.03003 Davis, Martin 1999 Influences of mathematical logic on computer science. Zbl 0663.68012 Davis, Martin 1988 Metric space-based test-data adequacy criteria. Zbl 0632.68031 Davis, Martin; Weyuker, Elaine 1988 Julia Bowman Robinson 1919-1985. Zbl 0571.01026 Henkin, L.; Lehmer, D. H.; Lehmer, Emma; Scott, E.; Kelley, J.; Gaal, L.; Gale, D.; Davis, M.; MacLane, S.; Niven, I.; Pitcher, E.; Blum, L.; Feferman, S. 1985 Unsolvable problems: A review. Zbl 0129.25703 Davis, M. 1963 Applications of recursive function theory to number theory. Zbl 0192.05301 Davis, M. 1962 A program for Presburgers algorithm. Zbl 0171.27101 Davis, M. 1960 Conceptual confluence in 1936: Post and Turing. Zbl 1400.01008 Davis, Martin; Sieg, Wilfried 2015 Pragmatic Platonism. Zbl 1338.03004 Davis, Martin 2014 The effect of antibody-dependent enhancement, cross immunity, and vector population on the dynamics of dengue fever. Zbl 1406.92577 Hu, K.; Thoens, C.; Bianco, S.; Edlund, S.; Davis, M.; Douglas, J.; Kaufman, J. H. 2013 From linear operators to computational biology. Essays in memory of Jacob T. Schwartz. Zbl 1252.92002 Davis, Martin (ed.); Schonberg, Edmond (ed.) 2013 The universal computer. The road from Leibniz to Turing. Turing centenary edition. Zbl 1243.68013 Davis, Martin 2012 Representation theorems for recursively enumerable sets and a conjecture related to Poonen’s large subring of $$\mathbb Q$$. Zbl 1345.03021 Davis, M. 2010 Why there is no such discipline as hypercomputation. Zbl 1103.68555 Davis, Martin 2006 The Church-Turing thesis: Consensus and opposition. Zbl 1145.03300 Davis, Martin 2006 Computability, computation, and the real world. Zbl 1188.68132 Davis, Martin 2006 The incompleteness theorem. Zbl 1100.03003 Davis, Martin 2006 What did Gödel believe and when did he believe it? Zbl 1108.03003 Davis, Martin 2005 The undecidable. Basic papers on undecidable propositions, unsolvable problems and computable functions. Corrected reprint of the 1965 original. Zbl 1099.03002 Davis, Martin (ed.) 2004 The early history of automated deduction. Zbl 1011.68511 Davis, Martin 2001 The universal computer. The road from Leibniz to Turing. Zbl 0960.01001 Davis, Martin 2000 Engines of logic. Mathematicians and the origin of the computer. Corrected reprint paperback ed. of the original with the title “The universal computer. The road from Leibniz to Turing”. Zbl 1035.01002 Davis, Martin 2000 From logic to computer science and back. Zbl 0930.03003 Davis, Martin 1999 American logic in the 1920s. Zbl 0858.01025 Davis, Martin 1995 Solvability, provability, definability. The collected works of Emil L. Post. Zbl 0823.03001 Post, Emil L.; Davis, Martin (ed.) 1993 A free variable version of the first-order predicate calculus. Zbl 0754.03004 Davis, Martin; Fechter, Ronald 1991 Influences of mathematical logic on computer science. Zbl 0663.68012 Davis, Martin 1988 Metric space-based test-data adequacy criteria. Zbl 0632.68031 Davis, Martin; Weyuker, Elaine 1988 Julia Bowman Robinson 1919-1985. Zbl 0571.01026 Henkin, L.; Lehmer, D. H.; Lehmer, Emma; Scott, E.; Kelley, J.; Gaal, L.; Gale, D.; Davis, M.; MacLane, S.; Niven, I.; Pitcher, E.; Blum, L.; Feferman, S. 1985 Computability, complexity, and languages. Fundamentals of theoretical computer science. Zbl 0569.68042 Davis, Martin D.; Weyuker, Elaine J. 1983 A formal notion of program-based test data adequacy. Zbl 0537.68025 Davis, Martin D.; Weyuker, Elaine J. 1983 Why Goedel didn’t have Church’s thesis. Zbl 0519.03033 Davis, Martin 1982 Computability and unsolvability. (Enl. version of the orig. publ. McGraw- Hill Book Company, New York 1958). Zbl 0553.03024 Davis, Martin 1982 The mathematics of non-monotonic reasoning. Zbl 0435.68075 Davis, Martin 1980 Metamathematical extensibility for theorem verifiers and proof-checkers. Zbl 0418.68079 Davis, Martin; Schwartz, Jacob T. 1979 A relativity principle in quantum mechanics. Zbl 0392.03040 Davis, Martin 1978 Applied nonstandard analysis. Zbl 0359.02060 Davis, Martin 1977 Hilbert’s tenth problem: Diophantine equations: Positive aspects of a negative solution. Zbl 0346.02026 Davis, Martin; Matijasevic, Yuri; Robinson, Julia 1976 Hilbert’s tenth problem is unsolvable. Zbl 0277.02008 Davis, Martin 1973 On the number of solutions of Diophantine equations. Zbl 0275.02042 Davis, Martin 1972 An explicit Diophantine definition of the exponential function. Zbl 0222.10017 Davis, Martin 1971 One equation to rule them all. Zbl 0316.02051 Davis, Martin 1968 A first course in functional analysis. Zbl 0199.17901 Davis, Martin 1966 Diophantine equations and recursively enumerable sets. Zbl 0199.03901 Davis, M. 1966 Eliminating the irrelevant from mechanical proofs. Zbl 0131.01201 Davis, Martin 1963 Diophantine sets over polynomial rings. Zbl 0113.00604 Davis, M.; Putnam, H. 1963 Extensions and corollaries of recent work on Hilbert’s tenth problem. Zbl 0112.24603 Davis, M. 1963 Unsolvable problems: A review. Zbl 0129.25703 Davis, M. 1963 A machine program for theorem-proving. Zbl 0217.54002 Davis, M.; Logemann, G.; Loveland, D. 1962 Applications of recursive function theory to number theory. Zbl 0192.05301 Davis, M. 1962 The decision problem for exponential diophantine equations. Zbl 0111.01003 Davis, Martin; Putnam, Hilary; Robinson, Julia 1961 A computing procedure for quantification theory. Zbl 0212.34203 Davis, M.; Putnam, H. 1960 A program for Presburgers algorithm. Zbl 0171.27101 Davis, M. 1960 Computable functionals of arbitrary finite type. Zbl 0085.24803 Davis, Martin 1959 Reductions of Hilbert’s tenth problem. Zbl 0085.24802 Davis, Martin; Putman, Hilary 1959 Computability and unsolvability. Zbl 0080.00902 Davis, Martin 1958 The definition of universal Turing machine. Zbl 0084.01003 Davis, Martin 1958 Automata studies. Zbl 0074.11204 Shannon, Claude E. (ed.); McCarthy, John (ed.); Kleene, S. C.; von Neumann, J.; Culbertson, James T.; Minsky, M. L.; Moore, Edward F.; Shannon, Claude E.; McCarthy, John; Davis, M. D.; de Leeuw, K.; Shapiro, N.; Ashby, W. Ross; MacKay, D. M.; Uttley, Albert M. 1956 Arithmetical problems and recursively enumerable predicates. Zbl 0051.24509 Davis, Martin 1953 all top 5 #### Cited by 1,477 Authors 20 Shlapentokh, Alexandra 16 Matiyasevich, Yuriĭ Vladimirovich 10 Giunchiglia, Enrico 8 Davis, Martin David 8 Plaisted, David Alan 8 Szeider, Stefan 8 Van Gelder, Allen 7 Katz, Mikhail G. 7 Lauria, Massimo 7 Lierler, Yuliya 7 Manyà, Felip 7 Marques-Silva, João P. 7 Zafiris, Elias 6 Becker, Bernd 6 Biere, Armin 6 Bonacina, Maria Paola 6 Eisenträger, Kirsten 6 Pasten, Hector V. 6 Schaub, Torsten H. 5 Ábrahám, Erika 5 Beyersdorff, Olaf 5 Chen, Jian-er 5 Demeyer, Jeroen 5 Doria, Francisco Antonio 5 Eggers, Andreas 5 Fränzle, Martin 5 Goldberg, Eugene L. 5 Kramosil, Ivan 5 Li, Chumin 5 Lynch, Christopher A. 5 Maratea, Marco 5 Nieuwenhuis, Robert 5 Pheidas, Thanases 5 Selman, Bart 5 Siekmann, Jörg H. 5 Soare, Robert I. 5 Stuckey, Peter James 5 Tacchella, Armando 5 Weidenbach, Christoph 4 Bruni, Renato 4 Costa, José Félix 4 Da Costa, Newton Carneiro Affonso 4 de Moura, Leonardo 4 Glaßer, Christian 4 Gomes, Carla P. 4 Hirsch, Edward A. 4 Hooker, John N. jun. 4 Ibaraki, Toshihide 4 Itsykson, Dmitry M. 4 Jones, James P. 4 Kanovei, Vladimir G. 4 Kullmann, Oliver 4 Kupferschmid, Stefan 4 Lê Văn Băng 4 Lu, Shuwang 4 Lynce, Inês 4 Marquis, Pierre 4 Otto, Friedrich 4 Purdom, Paul Walton jun. 4 Sabharwal, Ashish 4 Saïs, Lakhdar 4 Su, Shenghui 4 Teige, Tino 4 Tinelli, Cesare 4 Vardi, Moshe Y. 4 Vidaux, Xavier 4 Zhang, Hantao 3 Armando, Alessandro 3 Beame, Paul W. 3 Beggs, Edwin J. 3 Benhamou, Belaid 3 Brown, Cynthia A. 3 Buchberger, Bruno 3 Cimatti, Alessandro 3 Cooper, Stuart Barry 3 De Mol, Liesbeth 3 Dershowitz, Nachum 3 Dose, Titus 3 Dubois, Olivier 3 Farmer, William M. 3 Franco, John V. 3 Gebser, Martin 3 Gent, Ian Philip 3 Grégoire, Éric 3 Griggio, Alberto 3 Hernando, Antonio 3 Heule, Marijn J. H. 3 Hutchinson, George K. 3 Järvisalo, Matti 3 Johannsen, Jan 3 Jonsson, Peter A. 3 Kaufmann, Benjamin 3 Kleine Büning, Hans 3 Kremer, Gereon 3 Miller, Russell G. 3 Minker, Jack 3 Monasson, Rémi 3 Myhill, John R. 3 Narendran, Paliath 3 Nordström, Jakob ...and 1,377 more Authors all top 5 #### Cited in 230 Serials 94 Theoretical Computer Science 58 Artificial Intelligence 52 Journal of Automated Reasoning 35 Discrete Applied Mathematics 32 The Journal of Symbolic Logic 29 Annals of Pure and Applied Logic 29 Annals of Mathematics and Artificial Intelligence 26 Transactions of the American Mathematical Society 25 Information Processing Letters 23 Journal of Computer and System Sciences 18 Proceedings of the American Mathematical Society 17 Journal of Symbolic Computation 15 Information and Computation 14 Journal of Mathematical Sciences (New York) 13 International Journal of Theoretical Physics 13 Applied Mathematics and Computation 13 Information Sciences 12 The Bulletin of Symbolic Logic 12 Constraints 11 Theory and Practice of Logic Programming 9 Journal of Soviet Mathematics 8 Israel Journal of Mathematics 8 Journal of Algebra 8 Annals of Operations Research 8 Formal Methods in System Design 7 Journal of Number Theory 7 Studia Logica 7 Synthese 6 International Journal of General Systems 5 Acta Informatica 5 Archiv für Mathematische Logik und Grundlagenforschung 5 Journal of Mathematical Physics 5 The Mathematical Intelligencer 5 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 5 Computers & Operations Research 5 European Journal of Operational Research 5 Foundations of Science 4 Mathematical Notes 4 Computing 4 Journal of Mathematical Economics 4 Kybernetika 4 SIAM Journal on Computing 4 Journal of Computer Science and Technology 4 Formal Aspects of Computing 4 JETAI. Journal of Experimental & Theoretical Artificial Intelligence 4 Bulletin of the American Mathematical Society. New Series 4 Archive for Mathematical Logic 4 Journal of Applied Non-Classical Logics 4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Journal of Applied Mathematics 4 Journal of Applied Logic 4 Bulletin of the American Mathematical Society 3 Computers & Mathematics with Applications 3 Discrete Mathematics 3 Journal of the Franklin Institute 3 Journal of Mathematical Analysis and Applications 3 Advances in Mathematics 3 Inventiones Mathematicae 3 Journal of Philosophical Logic 3 Mathematische Annalen 3 Mathematical Social Sciences 3 Operations Research Letters 3 History and Philosophy of Logic 3 International Journal of Parallel Programming 3 Mathematical and Computer Modelling 3 RAIRO. Informatique Théorique et Applications 3 Journal of Logic, Language and Information 3 Mathematical Logic Quarterly (MLQ) 3 The Journal of Logic and Algebraic Programming 3 Natural Computing 3 Foundations of Physics 3 Logica Universalis 3 Formalized Mathematics 3 Prikladnaya Diskretnaya Matematika 2 Archive for Rational Mechanics and Analysis 2 International Journal of Systems Science 2 Chaos, Solitons and Fractals 2 Algebra and Logic 2 BIT 2 Fuzzy Sets and Systems 2 International Journal of Computer & Information Sciences 2 Mathematische Nachrichten 2 Mathematica Slovaca 2 Notre Dame Journal of Formal Logic 2 Programming and Computer Software 2 Siberian Mathematical Journal 2 Advances in Applied Mathematics 2 Science of Computer Programming 2 Algorithmica 2 Random Structures & Algorithms 2 MSCS. Mathematical Structures in Computer Science 2 Historia Mathematica 2 Expositiones Mathematicae 2 Mathematical Programming. Series A. Series B 2 Computational Complexity 2 Mathematical Problems in Engineering 2 Topoi 2 Abstract and Applied Analysis 2 Journal of Scheduling 2 New Journal of Physics ...and 130 more Serials all top 5 #### Cited in 53 Fields 669 Computer science (68-XX) 438 Mathematical logic and foundations (03-XX) 112 Number theory (11-XX) 67 Operations research, mathematical programming (90-XX) 44 History and biography (01-XX) 34 Quantum theory (81-XX) 33 Combinatorics (05-XX) 29 Information and communication theory, circuits (94-XX) 22 General and overarching topics; collections (00-XX) 21 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Field theory and polynomials (12-XX) 20 Probability theory and stochastic processes (60-XX) 17 Category theory; homological algebra (18-XX) 16 Group theory and generalizations (20-XX) 16 Real functions (26-XX) 16 Numerical analysis (65-XX) 14 Order, lattices, ordered algebraic structures (06-XX) 14 Algebraic geometry (14-XX) 10 Ordinary differential equations (34-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Biology and other natural sciences (92-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Functional analysis (46-XX) 7 General topology (54-XX) 6 General algebraic systems (08-XX) 6 Topological groups, Lie groups (22-XX) 6 Statistics (62-XX) 6 Systems theory; control (93-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Measure and integration (28-XX) 5 Differential geometry (53-XX) 4 Commutative algebra (13-XX) 4 Associative rings and algebras (16-XX) 4 Functions of a complex variable (30-XX) 4 Partial differential equations (35-XX) 4 Operator theory (47-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Approximations and expansions (41-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Geometry (51-XX) 3 Convex and discrete geometry (52-XX) 3 Mechanics of particles and systems (70-XX) 3 Fluid mechanics (76-XX) 3 Relativity and gravitational theory (83-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 Potential theory (31-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-04-16T01:04:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.594227135181427, "perplexity": 8669.844702218295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038088264.43/warc/CC-MAIN-20210415222106-20210416012106-00134.warc.gz"}
http://mathonline.wikidot.com/z-nz-is-isomorphic-to-zn	Z/nZ is Isomorphic to Zn Table of Contents Z/nZ is Isomorphic to Zn Recall that $(\mathbb{Z}/n\mathbb{Z}, +)$ denotes the group of integers $\{0, 1, 2, ..., n - 1\}$ modulo $n$, and $\mathbb{Z}_n$ denotes the cyclic subgroup of order $n$. We have already noted that $\mathbb{Z}/n\mathbb{Z}$ is isomorphic to $\mathbb{Z}_n$ via an explicit isomorphism. We will now prove this fact against using The First Group Isomorphism Theorem. Proposition 1: For each $n \in \mathbb{N}$, $\mathbb{Z}/n\mathbb{Z}$ is isomorphic to $\mathbb{Z}_n$. • Proof: Let $\mathbb{Z}_n = \langle x \rangle$ where $x^n = 1$. Let $\phi : \mathbb{Z} \to \mathbb{Z} \to \mathbb{Z}_n$ be defined for all $x \in \mathbb{Z}$ by: (1) \begin{align} \quad \phi(m) = x^{m \pmod n} \end{align} • Observe that $\phi$ is indeed a homomorphism from $\mathbb{Z}$ since for all $m_1, m_2 \in \mathbb{Z}$ we have that: (2) \begin{align} \quad \phi(m_1 + m_2) = x^{m_1 + m_2 \pmod n} = x^{m_1 \pmod n} x^{m_2 \pmod n} = \phi(m_1) \phi(m_2) \end{align} • Now observe that: (3) \begin{align} \quad \ker(\phi) = \{ m \in \mathbb{Z} : x^{m \pmod n} = 1 \} = \{ m \in \mathbb{Z} : n \mid m \} = n\mathbb{Z} \end{align} • So by The First Group Isomorphism Theorem we have that: (4) \begin{align} \quad \mathbb{Z}/n\mathbb{Z} = \mathbb{Z}/\ker(\phi) \cong \phi(G) \end{align} • But $\phi$ is surjective, since for all $x^t \in G = \langle x \rangle$, $1 \leq t \leq n$, we have that $\phi(t) = x^t$. So $\phi(G) = \mathbb{Z}_n$ and thus from above: (5) \begin{align} \quad \mathbb{Z}/n\mathbb{Z} \cong \mathbb{Z}_n \quad \blacksquare \end{align} Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License	2022-05-18T06:57:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 5, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998972415924072, "perplexity": 787.6314467550759}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521152.22/warc/CC-MAIN-20220518052503-20220518082503-00592.warc.gz"}
http://indico.vecc.gov.in/conferenceDisplay.py/openMenu%3FcurrentURL=http%253A%252F%252Findico.vecc.gov.in%252Findico%252FcontributionDisplay.py%253FcontribId%253D144%2526confId%253D1&confId=1.html	# ICPAQGP-2010 5-10 December 2010 6th International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP 2010) Home > Timetable > Contribution details Thermal photons in QGP and non-ideal effects Content: We investigate the thermal photon production-rates using one dimensional boost-invariant second order relativistic hydrodynamics to find proper time evolution of the energy density and the temperature. The effect of bulk-viscosity and non-ideal equation of state are taken into account in a manner consistent with recent lattice QCD estimates. It is shown that the \textit{non-ideal} gas equation of state i.e $\varepsilon-3\,P\,\neq 0$ behaviour of the expanding plasma, which is important near the phase-transition point, can significantly slow down the hydrodynamic expansion and thereby increase the photon production-rates. Inclusion of the bulk viscosity may also have similar effect on the hydrodynamic evolution. However the effect of bulk viscosity is shown to be significantly lower than the \textit{non-ideal} gas equation of state. We also analyze the interesting phenomenon of bulk viscosity induced cavitation making the hydrodynamical description invalid. It is shown that ignoring the cavitation phenomenon can lead to a very significant over estimation of the photon flux. It is argued that this feature could be relevant in studying signature of cavitation in relativistic heavy ion collisions. Id: 144 Place: Room: Main Auditorium Starting date: --not yet scheduled-- Duration: 00' Primary Authors: Mr. V., Sreekanth (Physical Research Laboratory) Co-Authors: Prof. BHATT, Jitesh (Physical Research Laboratory) Mr. MISHRA, Hiranmaya (Physical Research Laboratory) Presenters: Mr. V., Sreekanth	2021-10-24T17:49:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7222738862037659, "perplexity": 2341.8615052600894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587593.0/warc/CC-MAIN-20211024173743-20211024203743-00301.warc.gz"}

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