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## Journal of Mathematics of Kyoto University

 Short Title: J. Math. Kyoto Univ. Publisher: Kyoto University, Department of Mathematics ISSN: 0023-608X; 2154-3321/e Online: http://www.math.kyoto-u.ac.jp/journal/bn.htmlhttp://projecteuclid.org/kjm Predecessor: Memoirs of the College of Science, University of Kyoto, Series A Successor: Kyoto Journal of Mathematics Comments: No longer indexed
 Documents Indexed: 1,842 Publications (1961–2009)
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### Latest Issues

 49, No. 4 (2009) 49, No. 3 (2009) 49, No. 2 (2009) 49, No. 1 (2009) 48, No. 4 (2008) 48, No. 3 (2008) 48, No. 2 (2008) 48, No. 1 (2008) 47, No. 4 (2007) 47, No. 3 (2007) 47, No. 2 (2007) 47, No. 1 (2007) 46, No. 4 (2006) 46, No. 3 (2006) 46, No. 2 (2006) 46, No. 1 (2006) 45, No. 4 (2005) 45, No. 3 (2005) 45, No. 2 (2005) 45, No. 1 (2005) 44, No. 4 (2004) 44, No. 3 (2004) 44, No. 2 (2004) 44, No. 1 (2004) 43, No. 4 (2004) 43, No. 3 (2003) 43, No. 2 (2003) 43, No. 1 (2003) 42, No. 4 (2002) 42, No. 3 (2002) 42, No. 2 (2002) 42, No. 1 (2002) 41, No. 4 (2001) 41, No. 3 (2001) 41, No. 2 (2001) 41, No. 1 (2001) 40, No. 4 (2000) 40, No. 3 (2000) 40, No. 2 (2000) 40, No. 1 (2000) 39, No. 4 (1999) 39, No. 3 (1999) 39, No. 2 (1999) 39, No. 1 (1999) 38, No. 4 (1998) 38, No. 3 (1998) 38, No. 2 (1998) 38, No. 1 (1998) 37, No. 4 (1997) 37, No. 3 (1997) 37, No. 2 (1997) 37, No. 1 (1997) 36, No. 4 (1996) 36, No. 3 (1996) 36, No. 2 (1996) 36, No. 1 (1996) 35, No. 4 (1995) 35, No. 3 (1995) 35, No. 2 (1995) 35, No. 1 (1995) 34, No. 4 (1994) 34, No. 3 (1994) 34, No. 2 (1994) 34, No. 1 (1994) 33, No. 4 (1993) 33, No. 3 (1993) 33, No. 2 (1993) 33, No. 1 (1993) 32, No. 4 (1992) 32, No. 3 (1992) 32, No. 2 (1992) 32, No. 1 (1992) 31, No. 4 (1991) 31, No. 3 (1991) 31, No. 2 (1991) 31, No. 1 (1991) 30, No. 4 (1990) 30, No. 3 (1990) 30, No. 2 (1990) 30, No. 1 (1990) 29, No. 4 (1990) 29, No. 3 (1989) 29, No. 2 (1989) 29, No. 1 (1989) 28, No. 4 (1988) 28, No. 3 (1988) 28, No. 2 (1988) 28, No. 1 (1988) 27 (1987) 26 (1986) 25 (1985) 24 (1984) 23 (1983) 22 (1982/1983) 21 (1981) 20 (1980) 19 (1979) 18 (1978) 17 (1977) 16 (1976) ...and 19 more Volumes
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### Authors

 30 Kono, Akira 23 Matsumoto, Makoto 20 Nagata, Masayoshi 18 Miyanishi, Masayoshi 16 Taniguchi, Masahiko 15 Hirai, Takeshi 15 Mimura, Mamoru 15 Toda, Hirosi 15 Watanabe, Shinzo 14 Nishitani, Tatsuo 14 Shiga, Tokuzo 13 Goto, Shiro 13 Ōkaji, Takashi 13 Sakamoto, Reiko 12 Nishino, Toshio 11 Kitagawa, Keiichiro 11 Kono, Norio 11 Suzuki, Satoshi 10 Hamanaka, Hiroaki 10 Iriye, Kouyemon 10 Kozima, Kazumoto 10 Nakajima, Kazufumi 9 Morisugi, Kaoru 9 Yamaguchi, Kohhei 9 Yokota, Ichiro 8 Fukui, Kazuhiko 8 Igari, Katsuju 8 Imanishi, Hideki 8 Kishimoto, Daisuke 8 Matsumoto, Waichiro 8 Miyatake, Sadao 8 Mizohata, Sigeru 8 Nishida, Goro 8 Nishimura, Jun-ichi 8 Sainouchi, Yoshikazu 8 Sato, Eiichi 8 Shimomura, Hiroaki 7 Adachi, Masahisa 7 Asakura, Fumioki 7 Gotoh, Yasuhiro 7 Horiuchi, Toshio 7 Izumi, Shuzo 7 Kasahara, Yuji 7 Mochizuki, Kiyoshi 7 Nakaoka, Akira 7 Ninomiya, Haruki 7 Nishimura, Osamu 7 Niwa, Toshio 7 Shiga, Hiroshige 7 Yamaguchi, Hiroshi 6 Akiba, Tomoharu 6 Biswas, Indranil 6 Hirai, Etsuko 6 Kajitani, Kunihiko 6 Maitani, Fumio 6 Moriwaki, Atsushi 6 Ohtake, Hiromi 6 Sadamatsu, Takashi 6 Shiba, Masakazu 6 Shimakura, Norio 6 Shin’ya, Hitoshi 6 Urabe, Jiichiroh 6 Yamada, Toshio 6 Yamashita, Hiroshi 6 Zaharescu, Alexandru 5 Fuji’i’e, Tatsuo 5 Fujita, Osamu 5 Gyoja, Akihiko 5 Hara, Shin-ichiro 5 Hoshiro, Toshihiko 5 Ichijyō, Yoshihiro 5 Ikebe, Teruo 5 Ikeda, Nobuyuki 5 Itaya, Nobutoshi 5 Kusunoki, Yukio 5 Makino, Tetu 5 Maruyama, Masaki 5 Matsui, Kunihiko 5 Miyamoto, Munemi 5 Murai, Masafumi 5 Nakanishi, Nobutada 5 Ngô Viêt Trung 5 Nishida, Takaaki 5 Ohsita, Akihiro 5 Onishi, Hidekazu 5 Rung, Donald C. 5 Shimoda, Yasuhiro 5 Suto, Kiyokazu 5 Tatsuuma, Nobuhiko 5 Ueda, Tetsuo 5 Uemura, Hideaki 5 Ukai, Seiji 5 Yamasaki, Aiichi 4 Alexandru, Victor 4 Aoyama, Yoichi 4 Colombini, Ferruccio 4 Fujimoto, Yoshio 4 Furutani, Kenro 4 Gurjar, Rajendra Vasant 4 Hasegawa, Yukiko ...and 1,009 more Authors
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### Fields

 337 Partial differential equations (35-XX) 238 Algebraic geometry (14-XX) 188 Probability theory and stochastic processes (60-XX) 172 Algebraic topology (55-XX) 142 Manifolds and cell complexes (57-XX) 130 Functions of a complex variable (30-XX) 126 Commutative algebra (13-XX) 120 Several complex variables and analytic spaces (32-XX) 110 Topological groups, Lie groups (22-XX) 102 Differential geometry (53-XX) 83 Number theory (11-XX) 73 Global analysis, analysis on manifolds (58-XX) 57 Group theory and generalizations (20-XX) 57 Operator theory (47-XX) 56 Functional analysis (46-XX) 53 Fluid mechanics (76-XX) 50 Nonassociative rings and algebras (17-XX) 41 Abstract harmonic analysis (43-XX) 39 Ordinary differential equations (34-XX) 38 Dynamical systems and ergodic theory (37-XX) 27 Associative rings and algebras (16-XX) 23 Field theory and polynomials (12-XX) 21 Potential theory (31-XX) 19 Biology and other natural sciences (92-XX) 18 Measure and integration (28-XX) 17 Quantum theory (81-XX) 17 Statistical mechanics, structure of matter (82-XX) 16 $$K$$-theory (19-XX) 13 Category theory; homological algebra (18-XX) 13 Real functions (26-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 10 Special functions (33-XX) 9 Numerical analysis (65-XX) 8 General topology (54-XX) 8 Mechanics of deformable solids (74-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 5 Difference and functional equations (39-XX) 5 Approximations and expansions (41-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Sequences, series, summability (40-XX) 4 Integral transforms, operational calculus (44-XX) 4 Integral equations (45-XX) 4 Mechanics of particles and systems (70-XX) 4 Systems theory; control (93-XX) 3 Mathematical logic and foundations (03-XX) 3 Combinatorics (05-XX) 3 Optics, electromagnetic theory (78-XX) 3 Astronomy and astrophysics (85-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 2 Computer science (68-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

1,295 Publications have been cited 11,293 times in 9,471 Documents Cited by Year
The initial value problem for the equations of motion of viscous and heat-conductive gases. Zbl 0429.76040
Matsumura, Akitaka; Nishida, Takaaki
1980
On the uniqueness of solutions of stochastic differential equations. Zbl 0236.60037
1971
On the decomposition numbers of the Hecke algebra of $$G(m,1,n)$$. Zbl 0888.20011
Ariki, Susumu
1996
Equivariant completion. Zbl 0277.14008
Sumihiro, Hideyasu
1974
Characterizations of complex projective spaces and hyperquadrics. Zbl 0261.32013
Kobayashi, Shoshichi; Ochiai, Takushiro
1973
The behavior of solutions of some non-linear diffusion equations for large time. Zbl 0408.35053
Uchiyama, Kohei
1978
Convergence of solutions of one-dimensional semilinear parabolic equations. Zbl 0387.35008
Matano, Hiroshi
1978
Moduli of stable sheaves. II. Zbl 0395.14006
Maruyama, Masaki
1978
Rational equivalence of O-cycles on surfaces. Zbl 0184.46603
Mumford, D.
1969
A mapping of Riemannian manifolds which preserves harmonic functions. Zbl 0421.31006
Ishihara, Toru
1979
On the associated graded ring of a local Cohen-Macaulay ring. Zbl 0353.13017
Sally, Judith D.
1977
A limit theorem of branching processes and continuous state branching processes. Zbl 0159.46201
Watanabe, S.
1968
Foxby equivalence over associative rings. Zbl 1154.16007
Holm, Henrik; White, Diana
2007
On differential systems, graded Lie algebras and pseudo-groups. Zbl 0206.50503
Tanaka, Noboru
1970
Moduli of stable sheaves. I. Zbl 0374.14002
Maruyama, Masaki
1977
Compactness in Boltzmann’s equation via Fourier integral operators and applications. I, II. Zbl 0831.35139
Lions, P. L.
1994
Affine surfaces containing cylinderlike open sets. Zbl 0445.14017
Miyanishi, Masayoshi; Sugie, Tohru
1980
The incompressible limit and the initial layer of the compressible Euler equation. Zbl 0618.76074
Ukai, Seiji
1986
On the differentiation of De Rham cohomology classes with respect to parameters. Zbl 0165.54802
Katz, N. M.; Oda, T.
1968
On some relations between the harmonic measure and the Levy measure for a certain class of Markov processes. Zbl 0118.13401
Ikeda, N.; Watanabe, S.
1962
Branching Markov processes. I. Zbl 0233.60068
Ikeda, Nobuyuki; Nagasawa, Masao; Watanabe, Shinzo
1968
On stationary solutions of a stochastic differential equation. Zbl 0131.16402
Ito, K.; Nisio, M.
1964
Entropies, convexity, and functional inequalities: on $$\Phi$$-entropies and $$\Phi$$-Sobolev inequalities. Zbl 1079.26009
Chafaï, Djalil
2004
Multi-dimensional diffusion and the Markov process on the boundary. Zbl 0219.60057
Sato, K.-i.; Ueno, T.
1965
On the automorphisms of hypersurfaces. Zbl 0141.37401
Matsumura, H.; Monsky, P.
1964
Derivatives of Wiener functionals and absolute continuity of induced measures. Zbl 0476.28008
Shigekawa, Ichiro
1980
Infinite dimensional stochastic differential equations and their applications. Zbl 0462.60061
Shiga, Tokuzo; Shimizu, Akinobu
1980
Global solutions to the initial value problem for the equations of one- dimensional motion of viscous polytropic gases. Zbl 0478.76097
Kawashima, Shuichi; Nishida, Takaaki
1981
Semi-homogeneous vector bundles on an abelian variety. Zbl 0417.14029
Mukai, Shigeru
1978
Limiting absorption method and absolute continuity for the Schrödinger operator. Zbl 0257.35022
Ikebe, Teruo; Saito, Yoshimi
1972
Generalized divisors on Gorenstein curves and a theorem of Noether. Zbl 0613.14008
Hartshorne, Robin
1986
Residual intersections in Cohen-Macaulay rings. Zbl 0263.14019
Artin, M.; Nagata, M.
1972
On the uniqueness of solutions of stochastic differential equations. II. Zbl 0229.60039
1971
Mixed problems for hyperbolic equations. I: Energy inequalities. Zbl 0203.10001
Sakamoto, Reiko
1970
Some remarks on the Cauchy problem. Zbl 0104.31903
Mizohata, Sigeru
1961
Imbedding of an abstract variety in a complete variety. Zbl 0109.39503
Nagata, M.
1962
A winding problem for a resonator driven by a white noise. Zbl 0119.34701
McKean, H. P. jun.
1963
Branching Markov processes. III. Zbl 0233.60070
Ikeda, Nobuyuki; Nagasawa, Masao; Watanabe, Shinzo
1969
On a comparison theorem for solutions of stochastic differential equations and its applications. Zbl 0277.60047
1973
Perturbation of drift-type for Levy processes. Zbl 0281.60064
Tanaka, Hiroshi; Tsuchiya, Masaaki; Watanabe, Shinzo
1974
On a generalization of complete intersections. Zbl 0332.14019
Mori, Shigefumi
1975
A theorem of characterization of residual transcendental extensions of a valuation. Zbl 0689.12017
Alexandru, Victor; Popescu, Nicolae; Zaharescu, Alexandru
1988
Equivariant completion. II. Zbl 0331.14008
Sumihiro, Hideyasu
1975
Some basic results on canonical modules. Zbl 0515.13011
Aoyama, Yoichi
1983
On the Cauchy problem for Schrödinger type equations and the regularity of solutions. Zbl 0807.35026
Doi, Shin-ichi
1994
Intersections of quotient rings of an integral domain. Zbl 0166.30601
Gilmer, R.; Heinzer, W. J.
1967
Openness of a family of torsion free sheaves. Zbl 0404.14004
Maruyama, Masaki
1976
On the equations of one-dimensional motion of compressible viscous fluids. Zbl 0529.76070
1983
On the generalized local cohomology and its duality. Zbl 0618.13008
Suzuki, Naoyoshi
1978
Invariants of a group in an affine ring. Zbl 0146.04501
Nagata, M.
1964
Capillary-gravity waves for an incompressible ideal fluid. Zbl 0548.76018
Yosihara, Hideaki
1983
On the neighborhood of a compact complex curve with topologically trivial normal bundle. Zbl 0519.32019
Ueda, Tetsuo
1983
Certain numerical characters of singularities. Zbl 0214.20003
Hironaka, H.
1970
Compactness in Boltzmann’s equation via Fourier integral operators and applications. III. Zbl 0884.35124
Lions, P. L.
1994
Notes on liaison and duality. Zbl 0506.13012
Schenzel, Peter
1982
Stochastic differential equations of jump type and Lévy processes in diffeomorphisms group. Zbl 0575.60065
Fujiwara, Tsukasa; Kunita, Hiroshi
1985
De Rham-Hodge-Kodaira’s decomposition on an abstract Wiener space. Zbl 0611.58006
Shigekawa, Ichiro
1986
Eine Verallgemeinerung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie. Zbl 0275.13028
1973
Characteristic polyhedra of singularities. Zbl 0159.50502
Hironaka, H.
1967
A generalization of the imbedding problem of an abstract variety in a complete variety. Zbl 0223.14011
Nagata, Masayoshi
1963
On conformal transformations of Finsler metrics. Zbl 0328.53014
Hashiguchi, Masao
1976
On the free boundary value problem for compressible viscous fluid motion. Zbl 0499.76061
Tani, Atusi
1981
Rings of constants for $$k$$-derivations in $$k[x_ 1,\dots ,x_ n]$$. Zbl 0665.12024
Nowicki, Andrzej; Nagata, Masayoshi
1988
Sur les ondes de surface de l’eau avec une justification mathématique des équations des ondes en eau peu profonde. Zbl 0419.76013
1979
On the successive approximation of solutions of stochastic differential equations. Zbl 0484.60053
1981
On the branching process for Brownian particles with an absorbing boundary. Zbl 0134.34401
Watanabe, S.
1965
Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves. Zbl 0798.14006
Yokogawa, Kôji
1993
Toward a definition of moduli of complexes of coherent sheaves on a projective scheme. Zbl 1063.14013
Inaba, Michi-aki
2002
Local structure of analytic transformations of two complex variables. I. Zbl 0611.32001
Ueda, Tetsuo
1986
Homological invariants associated to semi-dualizing bimodules. Zbl 1096.16001
Araya, Tokuji; Takahashi, Ryo; Yoshino, Yuji
2005
Branching Markov processes. II. Zbl 0233.60069
Ikeda, Nobuyuki; Nagasawa, Masao; Watanabe, Shinzo
1968
Conservation law with discontinuous flux. Zbl 1063.35114
2004
On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstein series. Zbl 0822.11041
Ikeda, Tamotsu
1994
A slope of a mountain is a Finsler surface with respect to a time measure. Zbl 0677.53028
Matsumoto, Makoto
1989
Self-intersection local time of fractional Brownian motions – via chaos expansion. Zbl 1008.60091
Hu, Yaozhong
2001
Diffusion processes with generators of generalized divergence form. Zbl 0657.35073
1987
Mixed problem for hyperbolic equation of second order. Zbl 0281.35052
1973
Complete reducibility of rational representations of a matric group. Zbl 0106.25201
Nagata, Masayoshi
1961
Decaying solution of a Navier-Stokes flow without surface tension. Zbl 1382.35190
Hataya, Yasushi
2009
On Finsler spaces with Randers’ metric and special forms of important tensors. Zbl 0295.53034
Matsumoto, Makoto
1974
On a characterization of the Sobolev spaces over an abstract Wiener space. Zbl 0614.46028
Sugita, Hiroshi
1985
On stochastic differential equations for multi-dimensional diffusion processes with boundary conditions. Zbl 0212.20203
Watanabe, S.
1971
On invariant tensors of $$\beta$$-changes of Finsler metrics. Zbl 0541.53017
Shibata, Chōkō
1984
A conjecture of Nagata on graded Cohen-Macaulay rings. Zbl 0278.13013
Matijevic, Jacob; Roberts, Paul
1974
Multiplicity for ideals of maximal analytic spread and intersection theory. Zbl 0816.13019
Achilles, Rüdiger; Manaresi, Mirella
1993
The homotopy groups of Lie groups of low rank. Zbl 0171.44101
Mimura, Mamoru
1967
A duality theorem for locally compact groups. I - IV. Zbl 0184.17402
Tatsuuma, N.
1967
Local smooth solutions of the relativistic Euler equation. Zbl 0833.35086
Makino, Tetu; Ukai, Seiji
1995
Sobolev spaces of Wiener functionals and Malliavin’s calculus. Zbl 0581.46026
Sugita, Hiroshi
1985
The decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators. Zbl 0673.10021
Ueda, Masaru
1988
Sur l’existence des solutions locales de l’équation d’Euler-Poisson pour l’évolution d’étoiles gazeuses. (Local existence of solutions for Euler-Poisson’s equation for the evolution of gazeous stars). Zbl 0657.35113
Makino, Tetu; Ukai, Seiji
1987
On general boundary value problem for parabolic equations. Zbl 0143.13902
Arima, Reiko
1964
On tensor products of Gorenstein rings. Zbl 0193.34804
Watanabe, K.-i.; Ishikawa, Takeshi; Tachibana, Sadao; Otsuka, Kayo
1969
On automorphism groups of ruled surfaces. Zbl 0213.47803
Maruyama, Masaki
1971
Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise. Zbl 1056.60057
Brzeźniak, Zdzisław; van Neerven, Jan
2003
On Rees algebras over Buchsbaum rings. Zbl 0473.13010
Goto, Shiro; Shimoda, Yasuhiro
1980
Excursions in a cone for two-dimensional Brownian motion. Zbl 0582.60048
Shimura, Michio
1985
Global in time behavior of viscous surface waves: horizontally periodic motion. Zbl 1095.35028
Nishida, Takaaki; Teramoto, Yoshiaki; Yoshihara, Hideaki
2004
On compactifications. Zbl 0106.15601
Tamano, Hisahiro
1962
Solutions nulles et solutions non analytiques. Zbl 0106.29601
Mizohata, Sigeru
1962
Decaying solution of a Navier-Stokes flow without surface tension. Zbl 1382.35190
Hataya, Yasushi
2009
A shallow water approximation for water waves. Zbl 1421.76020
Iguchi, Tatsuo
2009
Some results on local cohomology modules defined by a pair of ideals. Zbl 1174.13024
Chu, Lizhong; Wang, Qing
2009
Gorenstein flat dimension of complexes. Zbl 1234.16003
Iacob, Alina
2009
A variational representation for random functionals on abstract Wiener spaces. Zbl 1194.60037
Zhang, Xicheng
2009
Almost periodic models of impulsive Hopfield neural networks. Zbl 1177.34058
Stamov, Gani Tr.
2009
The Fano surface of the Klein cubic threefold. Zbl 1207.14045
Roulleau, Xavier
2009
Brownian motion conditioned to stay in a cone. Zbl 1192.60091
Garbit, Rodolphe
2009
On a result of H. Fujimoto. Zbl 1193.30035
Bai, Xiaotian; Han, Qi; Chen, Ang
2009
Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions. Zbl 1205.60082
Cohen, Serge; Dombry, Clément
2009
A construction of processes with one dimensional martingale marginals, based upon path-space Ornstein-Uhlenbeck processes and the Brownian sheet. Zbl 1203.60122
Hirsch, Francis; Yor, Marc
2009
Composition factors of polynomial representation of DAHA and $$q$$-decomposition numbers. Zbl 1214.20004
Enomoto, Naoya
2009
A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet. Zbl 1191.60040
Hirsch, Francis; Yor, Marc
2009
The relation between stationary and periodic solutions of the Navier-Stokes equations in two or three dimensional channels. Zbl 1180.35414
Kobayashi, Teppei
2009
The rationality problem for four-dimensional linear actions. Zbl 1188.13004
Kitayama, Hidetaka; Yamasaki, Aiichi
2009
On the critical values of $$L$$-functions of tensor product of base change for Hilbert modular forms. Zbl 1251.11031
Virdol, Cristian
2009
On localizing subcategories of derived categories. Zbl 1198.13011
Takahashi, Ryo
2009
Locally nilpotent derivations on modules. Zbl 1180.14057
Tanaka, Mikiya
2009
A Lane-Emden-Fowler type problem with singular nonlinearity. Zbl 1184.35133
Covei, Dragos-Patru
2009
Central limit theorem for linear stochastic evolutions. Zbl 1171.60005
Nakashima, Makoto
2009
Exponential decay of correlations for surface semiflows with an expanding direction. Zbl 1184.37008
Obayashi, Ippei
2009
An intrinsic characterization of the direct product of balls. Zbl 1190.32016
Kodama, Akio; Shimizu, Satoru
2009
Certain multiple orthogonal polynomials and a discretization of the Bessel equation. Zbl 1194.33012
Takata, Tomohiro
2009
$$p$$-compact groups as subgroups of maximal rank of Kac-Moody groups. Zbl 1173.55006
2009
On the cortex of a nilpotent Lie group. (Sur le cortex d’un groupe de Lie nilpotent.) Zbl 1170.22004
Kédim, Imed; Hatem, Megdiche
2009
Wegner estimate for a generalized alloy type potential. Zbl 1185.35047
Takahara, Jyunichi
2009
On parabolic geometry. II. Zbl 1185.53028
Biswas, Indranil
2009
Flips and variation of moduli scheme of sheaves on a surface. Zbl 1196.14037
2009
The quadratic variations of local martingales and the first-passage times of stochastic integrals. Zbl 1204.60034
Kaji, Shunsuke
2009
Generalized $$\mathcal L$$-geodesic and monotonicity of the generalized reduced volume in the Ricci flow. Zbl 1195.53092
Hsu, Shu-Yu
2009
A note on strong unique continuation for normal elliptic systems with Gevrey coefficients. Zbl 1188.35066
Tamura, Mitsuji
2009
An asymptotic estimate for the hitting time of a half-line by two-dimensional Brownian motion. Zbl 1195.60109
Isozaki, Yasuki
2009
The elliptic hypergeometric functions associated to the configuration space of points on an elliptic curve. I: Twisted cycles. Zbl 1184.14055
Ito, Ko-Ki
2009
Free-fall and heteroclinic orbits to triple collisions in the isosceles three-body problem. Zbl 1225.70009
Shibayama, Mitsuru
2009
On Samelson products in Sp($$n$$). Zbl 1184.55005
Nagao, Tomoaki
2009
Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential. Zbl 1175.35138
Mizumachi, Tetsu
2008
Necessary and sufficient conditions such that extended mean values are Schur-convex or Schur-convave. Zbl 1153.26307
Chu, Yuming; Zhang, Xiaoming
2008
Gorenstein cohomology in abelian categories. Zbl 1172.18004
Sather-Wagstaff, Sean; Sharif, Tirdad; White, Diana
2008
A computation of universal weight function for quantum affine algebra $$U_q(\widehat{\mathfrak {gl}}_n)$$. Zbl 1221.17016
Khoroshkin, Sergey; Pakuliak, Stanislav
2008
Effective calculation of the geometric height and the Bogomolov conjecture for hyperelliptic curves over function fields. Zbl 1248.11046
Yamaki, Kazuhiko
2008
The Nielsen-Thurston classification of mapping classes is determined by TQFT. Zbl 1195.57065
Andersen, Jørgen Ellegaard
2008
A global approach to the theory of special Finsler manifolds. Zbl 1170.53057
Youssef, Nabil Labib; Abed, Sayed Hassan; Soleiman, Amr
2008
Fundamental groups of symmetric sextics. Zbl 1172.14020
Degtyarev, Alex
2008
On the finiteness of co-associated primes of local homology modules. Zbl 1174.13028
Nam, Tran Tuan
2008
The Smith sets of finite groups with normal Sylow 2-subgroups and small nilquotients. Zbl 1157.55004
Koto, Akihiro; Morimoto, Masaharu; Qi, Yan
2008
Complex algebraic plane curves via Poincaré-Hopf formula. III: Codimension bounds. Zbl 1174.14028
Borodzik, Marciej; Żołądek, Henryk
2008
Mod $$p$$ decompositions of non-simply connected Lie groups. Zbl 1155.55003
Kishimoto, Daisuke; Kono, Akira
2008
Asymptotic expansions for functionals of a Poisson random measure. Zbl 1281.60051
Hayashi, Masafumi
2008
The global profile of blow-up at space infinity in semilinear heat equations. Zbl 1184.35078
Shimojō, Masahiko
2008
Estimates on the effective resistance in a long-range percolation on $$\mathbb{Z}^d$$. Zbl 1183.60038
Misumi, Jun
2008
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2008
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Ikoma, Hideaki
2008
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2008
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Holm, Henrik; White, Diana
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Asymptotic stability of small solitons for 2D nonlinear Schrödinger equations with potential. Zbl 1146.35085
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2007
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Takagi, Satoshi
2007
Logarithmic sheaves attached to arrangements of hyperplanes. Zbl 1156.14015
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2007
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Positive Toeplitz operators on pluriharmonic Bergman spaces. Zbl 1158.32001
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2007
Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces. Zbl 1156.46034
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2007
Functional limit theorems for occupation times of Lamperti’s stochastic processes in discrete time. Zbl 1143.60027
Fujihara, Etsuko; Kawamura, Yumi; Yano, Yuko
2007
On entire curves tangent to foliation. Zbl 1147.32019
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2007
On a class of multiplicity-free nilpotent $$K_{\mathbb C}$$-orbits. Zbl 1148.22010
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2007
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2007
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2007
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2007
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2007
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2007
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### Cited by 8,433 Authors

 36 Goto, Shiro 33 Tan, Zhong 27 Biswas, Indranil 26 Nishitani, Tatsuo 23 Ballico, Edoardo 23 Chen, Zhen-Qing 23 Xin, Zhouping 23 Zhang, Xicheng 22 Kono, Akira 21 Shen, Wenxian 21 Shibata, Yoshihiro 20 Feireisl, Eduard 20 Nualart, David 19 Li, Hailiang 19 Miyanishi, Masayoshi 19 Takahashi, Ryo 19 Tayebi, Akbar 19 Yang, Tong 18 Guo, Boling 18 Heinzer, William J. 18 Lasiecka, Irena 18 Ngô Viêt Trung 18 Qin, Yuming 18 Ulrich, Bernd 18 Zhu, Changjiang 17 Dawson, Donald Andrew 17 Gurjar, Rajendra Vasant 17 Hayashi, Nakao 16 Dubouloz, Adrien 16 Laterveer, Robert 16 Röckner, Michael 15 Brion, Michel 15 Gudmundsson, Sigmundur 15 Li, Jing 15 Perkins, Edwin A. 15 Sather-Wagstaff, Sean 15 Vasconcelos, Wolmer V. 14 Kawashima, Shuichi 14 Krutitskii, Pavel A. 14 Morimoto, Yoshinori 14 Novotný, Antonín 14 Ukai, Seiji 14 Wang, Feng-Yu 14 Wang, Weike 14 Wang, Yanjin 14 Xu, Jiang 14 Yao, Zhengan 13 Bove, Antonio 13 Fayers, Matthew 13 Greven, Andreas 13 Huang, Xiangdi 13 Huneke, Craig L. 13 Kruglikov, Boris S. 13 Matsumura, Akitaka 13 Mazorchuk, Volodymyr 13 Mirò-Roig, Rosa Maria 13 Ohsawa, Takeo 13 Theriault, Stephen D. 13 Wu, Guochun 13 Yor, Marc 12 Beznea, Lucian 12 Chu, Yuming 12 Cossart, Vincent 12 Danchin, Raphaël 12 Das, Mrinal Kanti 12 Fiedler, Bernold 12 Hamel, François 12 Jang, Juhi 12 Kishimoto, Daisuke 12 Li, Zenghu 12 Mandal, Satya 12 Naumkin, Pavel Ivanovich 12 Poláčik, Peter 12 Rocha, Carlos 12 Schenzel, Peter 12 Song, Renming 12 Tani, Atusi 12 Yan, Litan 12 Zhang, Jianwen 12 Zhao, Huijiang 11 Bogdan, Krzysztof 11 Ginzburg, David 11 Glöckner, Helge 11 Herrmann, Manfred 11 Isaev, Alexander 11 Isozaki, Hiroshi 11 Jiang, Song 11 Kojima, Hideo 11 Li, Yeping 11 Liu, Zhong-kui 11 Mytnik, Leonid 11 Nečasová, Šárka 11 Russell, Peter K. 11 Soleiman, Amr 11 Vega, Luis 11 Wang, Dehua 11 Xu, Chao-Jiang 10 Albeverio, Sergio A. 10 Alexandre, Radjesvarane 10 Andersen, Jørgen Ellegaard ...and 8,333 more Authors
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### Cited in 646 Journals

 379 Journal of Algebra 284 Journal of Differential Equations 253 Transactions of the American Mathematical Society 213 Journal of Pure and Applied Algebra 202 Journal of Functional Analysis 193 Stochastic Processes and their Applications 191 Advances in Mathematics 190 Journal of Mathematical Analysis and Applications 184 Mathematische Annalen 184 Mathematische Zeitschrift 178 Proceedings of the American Mathematical Society 170 Proceedings of the Japan Academy. Series A 165 Publications of the Research Institute for Mathematical Sciences, Kyoto University 136 Nagoya Mathematical Journal 128 Inventiones Mathematicae 113 Probability Theory and Related Fields 98 Annales de l’Institut Fourier 97 Manuscripta Mathematica 95 The Annals of Probability 94 Communications in Mathematical Physics 93 Compositio Mathematica 90 Archive for Rational Mechanics and Analysis 89 Duke Mathematical Journal 84 Tôhoku Mathematical Journal. Second Series 77 Proceedings of the Japan Academy 72 Kyoto Journal of Mathematics 69 Topology and its Applications 68 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 68 International Journal of Mathematics 66 Journal de Mathématiques Pures et Appliquées. Neuvième Série 63 SIAM Journal on Mathematical Analysis 60 Communications in Algebra 59 Journal of Algebra and its Applications 57 Osaka Journal of Mathematics 53 Journal of Geometry and Physics 51 Journal of Mathematical Physics 51 Journal of the Mathematical Society of Japan 51 Nonlinear Analysis. Real World Applications 50 Geometriae Dedicata 49 Journal of Number Theory 49 Statistics & Probability Letters 49 Potential Analysis 47 Israel Journal of Mathematics 47 Journal of Mathematical Fluid Mechanics 46 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 46 Discrete and Continuous Dynamical Systems 44 ZAMP. Zeitschrift für angewandte Mathematik und Physik 43 Differential Geometry and its Applications 43 Comptes Rendus. Mathématique. Académie des Sciences, Paris 42 The Journal of Geometric Analysis 41 Kodai Mathematical Journal 40 Archiv der Mathematik 39 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 39 Journal of Algebraic Geometry 39 Journal of Mathematical Sciences (New York) 38 Annali di Matematica Pura ed Applicata. Serie Quarta 37 Mathematical Methods in the Applied Sciences 37 Journal of Theoretical Probability 36 Rocky Mountain Journal of Mathematics 36 Journal of Soviet Mathematics 35 Journal of Statistical Physics 35 Bulletin des Sciences Mathématiques 35 Acta Mathematica Sinica. English Series 35 Science China. Mathematics 34 Rendiconti del Seminario Matematico della Università di Padova 34 Transformation Groups 33 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 32 Acta Applicandae Mathematicae 32 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 32 Communications in Partial Differential Equations 31 Journal d’Analyse Mathématique 31 Mathematical Notes 31 Mathematische Nachrichten 31 Michigan Mathematical Journal 29 Nonlinearity 29 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 29 Journal of Dynamics and Differential Equations 28 Nonlinear Analysis. Theory, Methods & Applications 27 Stochastics and Dynamics 26 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 26 Algebras and Representation Theory 25 The Annals of Applied Probability 25 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 25 Bernoulli 25 Bulletin of the American Mathematical Society 24 Bulletin de la Société Mathématique de France 24 Journal für die Reine und Angewandte Mathematik 24 Chinese Annals of Mathematics. Series B 24 Electronic Journal of Probability 23 Monatshefte für Mathematik 23 Japan Journal of Industrial and Applied Mathematics 22 Ukrainian Mathematical Journal 22 Applied Mathematics and Computation 22 Applied Mathematics and Optimization 22 Czechoslovak Mathematical Journal 22 Journal of the American Mathematical Society 21 Representation Theory 20 Communications on Pure and Applied Mathematics 20 Communications in Contemporary Mathematics 20 European Journal of Mathematics ...and 546 more Journals
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### Cited in 63 Fields

 2,527 Partial differential equations (35-XX) 1,980 Algebraic geometry (14-XX) 1,640 Probability theory and stochastic processes (60-XX) 1,064 Fluid mechanics (76-XX) 1,021 Commutative algebra (13-XX) 604 Several complex variables and analytic spaces (32-XX) 604 Differential geometry (53-XX) 391 Operator theory (47-XX) 390 Number theory (11-XX) 379 Global analysis, analysis on manifolds (58-XX) 376 Group theory and generalizations (20-XX) 316 Algebraic topology (55-XX) 315 Manifolds and cell complexes (57-XX) 286 Dynamical systems and ergodic theory (37-XX) 285 Associative rings and algebras (16-XX) 277 Topological groups, Lie groups (22-XX) 243 Functions of a complex variable (30-XX) 237 Ordinary differential equations (34-XX) 233 Quantum theory (81-XX) 231 Nonassociative rings and algebras (17-XX) 223 Statistical mechanics, structure of matter (82-XX) 213 Functional analysis (46-XX) 194 Category theory; homological algebra (18-XX) 186 Numerical analysis (65-XX) 167 Biology and other natural sciences (92-XX) 122 Potential theory (31-XX) 113 Combinatorics (05-XX) 109 Field theory and polynomials (12-XX) 99 Real functions (26-XX) 99 Systems theory; control (93-XX) 96 Measure and integration (28-XX) 85 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 83 General topology (54-XX) 77 Abstract harmonic analysis (43-XX) 72 Mechanics of deformable solids (74-XX) 70 Harmonic analysis on Euclidean spaces (42-XX) 61 Integral equations (45-XX) 60 Relativity and gravitational theory (83-XX) 59 Statistics (62-XX) 58 $$K$$-theory (19-XX) 55 Calculus of variations and optimal control; optimization (49-XX) 55 Classical thermodynamics, heat transfer (80-XX) 49 Special functions (33-XX) 39 Linear and multilinear algebra; matrix theory (15-XX) 38 Approximations and expansions (41-XX) 35 Optics, electromagnetic theory (78-XX) 32 Difference and functional equations (39-XX) 30 Convex and discrete geometry (52-XX) 28 Mechanics of particles and systems (70-XX) 27 Astronomy and astrophysics (85-XX) 22 Integral transforms, operational calculus (44-XX) 18 Computer science (68-XX) 18 Operations research, mathematical programming (90-XX) 17 Geophysics (86-XX) 15 History and biography (01-XX) 15 Geometry (51-XX) 13 Mathematical logic and foundations (03-XX) 13 Information and communication theory, circuits (94-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 8 General and overarching topics; collections (00-XX) 3 General algebraic systems (08-XX) 3 Sequences, series, summability (40-XX) 2 Mathematics education (97-XX)


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# Other Math

All new and solved questions in Other Math category

The volume of a cylindrical can is ( 4πxˆ3+28πxˆ2+65πx+50π) cmˆ3. the can is (x+2)cm high. what is the radius?...
##### Annual Cash Flow Analysis
The manager of a canned food processing plant is trying to decide between two labeling machines.Machine A Machine BInitial Cost $15,000$25,000Yearly Maintenanceand Operating Costs $1,600$400Annual Benefit $8,000$13,000Salvage Value $3,000$6,000Useful life, in years 7 10Assume an interest rate of...
##### Standard Deviation
Based on the service records from Visa, it generally takes ten minutes to answer a customer’s question on his/her financial charges, with the standard deviation ofthree minutes. In other words, the time to answer customers’ questions on financial charges follows a normal distribution of ...
##### Accounting
AP8-6APanda Manufacturing (PM) is a division of Worldwide Communications, Inc. PM produces pagers and other personal communication devices. These devices are sold to otherWorldwide divisions, as well as to other communication companies. PM was recently approached by the manager of the Personal Commu...
##### Unit convert
A surveyor needs to determine the height of a tree. She places a mirror on the ground and paces backwards until she sees the top of the tree reflected in the mirror.She marks where she is standing and then measures the distance from this spot to the mirror which is 11 feet. She then measures the dis...
##### Matrix method for area of triangle
This is for modern geometry I need to write the points ascolun vectors in a matrix and the area is half the absolute valueof determinant. can you help?USING THE FOLLOWING POINTS AS VERTICES OF A TRIANGLEFAND MATRIX METHOD, FIND THE AREAa) (0,0) (1,0) (0,1)b)(0,0) (2,0) (2,2)c) (-1,1) (0,-1) (8,0)d) ...
##### Caluclus for the Life Sciences
The amount of recyclable glass collected annually in a new community is given by g(p) = (sqrt{3.1p^2 + 49}) tons, where p isthe population of the community in thousands. It is estimated that t years from now, the population will be p(t) = 1.8 + 0.2t^2 thousand people.a) How many tons of glass is exp...
##### Discrete Math-Proof by Resolution
Discrete Math-Proof by Resolution...

format: plain


text:
Next Meeting: December 2: Social gathering Next Installfest: TBD Latest News: Nov. 18: Club officer elections Page last updated: 2002 Apr 19 16:19
Re: [vox-tech] LaTeX, DVI, PDF, LaTeX, fonts - HELP!

# Re: [vox-tech] LaTeX, DVI, PDF, LaTeX, fonts - HELP!

If you're not doing anything to specifically control fonts, the default is
Computer Modern (the distinct look behind most TeX documents)
for the 3 font families of roman, san serif, and typewriter.  The CM fonts
are not PostScript fonts.

I'm no expert, but the following simple fix will probably go a long way.
Insert \usepackage{times} in the preamble of your document.  It
will make Times, Helvetica, and Courier the roman, san serif, and
typewriter font family, respectively.  These are PostScript fonts and
the resulting output files should be much more compatible with PS
printers.

As for math symbols, I'll quote from "Math Into LaTeX" (an excellent
resource for typesetting mathematical documents with LaTeX):
"Looking at a mathematical article typeset with the Times text font,
you may find that the Computer Modern math symbols look too thin."
In your case, you may also find that your end-user is not getting the
desired "look."  Insert \usepackage{mathtime} in the preamble,
and you will get the MathTime PS fonts for math symbols; these
are a better match for Times and possibly more compatible with
PS printers (I don't know).  The MathTime fonts are in the
teTeX TeX distribution commonly distributed with Linux systems.

shawn.

On Friday 19 April 2002 03:12 pm, you wrote:
> I've just been informed that some documents that are being generated
> by LaTeX aren't printing properly on some printers.
>
> I think it's less a problem with the printers (HP-850s) and probably
> more a problem with Acrobat on the system (all of these are Windows boxes,
> BTW) that the printer happens to be connected to.
>
> On one box, printing to a laser printer, the document appears correctly.
> On the other box, printing to the HP-850, the fonts aren't right
>
>
> Is there some way of embedding the fonts into the PDF document so that
> Acrobat will work correctly?  Or perhaps is Acrobat missing something
> or misconfigured?
>
> I've tried sending "-dNOPLATFONTS" to my call to 'dvipdf', but the
> PDFs generated with and without that option were indentical in size.
> (Unfortunately, >I< don't have the problem, people on the other side
> of the country do, so this is mighty hard to test/debug. :^( )
>
> Thx!
>
> -bill!
> _______________________________________________
> vox-tech mailing list
> vox-tech@lists.lugod.org
> http://lists.lugod.org/mailman/listinfo/vox-tech
_______________________________________________
vox-tech mailing list
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Spotlight
A Fast, Consistent Kernel Two-Sample Test
Arthur Gretton · Kenji Fukumizu · Zaid Harchaoui · Bharath Sriperumbudur

Mon Dec 07 06:41 PM -- 06:42 PM (PST) @ None
A kernel embedding of probability distributions into reproducing kernel Hilbert spaces (RKHS) has recently been proposed, which allows the comparison of two probability measures P and Q based on the distance between their respective embeddings: for a sufficiently rich RKHS, this distance is zero if and only if P and Q coincide. In using this distance as a statistic for a test of whether two samples are from different distributions, a major difficulty arises in computing the significance threshold, since the empirical statistic has as its null distribution (where P=Q) an infinite weighted sum of $\chi^2$ random variables. The main result of the present work is a novel, consistent estimate of this null distribution, computed from the eigenspectrum of the Gram matrix on the aggregate sample from P and Q. This estimate may be computed faster than a previous consistent estimate based on the bootstrap. Another prior approach was to compute the null distribution based on fitting a parametric family with the low order moments of the test statistic: unlike the present work, this heuristic has no guarantee of being accurate or consistent. We verify the performance of our null distribution estimate on both an artificial example and on high dimensional multivariate data.

#### Author Information

##### Arthur Gretton (Gatsby Unit, UCL)

Arthur Gretton is a Professor with the Gatsby Computational Neuroscience Unit at UCL. He received degrees in Physics and Systems Engineering from the Australian National University, and a PhD with Microsoft Research and the Signal Processing and Communications Laboratory at the University of Cambridge. He previously worked at the MPI for Biological Cybernetics, and at the Machine Learning Department, Carnegie Mellon University. Arthur's recent research interests in machine learning include the design and training of generative models, both implicit (e.g. GANs) and explicit (high/infinite dimensional exponential family models), nonparametric hypothesis testing, and kernel methods. He has been an associate editor at IEEE Transactions on Pattern Analysis and Machine Intelligence from 2009 to 2013, an Action Editor for JMLR since April 2013, an Area Chair for NeurIPS in 2008 and 2009, a Senior Area Chair for NeurIPS in 2018, an Area Chair for ICML in 2011 and 2012, and a member of the COLT Program Committee in 2013. Arthur was program chair for AISTATS in 2016 (with Christian Robert), tutorials chair for ICML 2018 (with Ruslan Salakhutdinov), workshops chair for ICML 2019 (with Honglak Lee), program chair for the Dali workshop in 2019 (with Krikamol Muandet and Shakir Mohammed), and co-organsier of the Machine Learning Summer School 2019 in London (with Marc Deisenroth).


text:
# Let f(z) = {.Find the value of c such that f' (c) does not exist (Use symbolic notation and fractions

###### Question:

Let f(z) = {.Find the value of c such that f' (c) does not exist (Use symbolic notation and fractions where needed:) The f' (c) does not exist at â‚¬ â‚¬ help (fractions)

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##### (6 â‚¬8' LCl Sl uniueq JO aOU &uo JO sseU 84L) 'unuueq J0 swuoje ,zOl Sv' + J0 suuejf Ul SSeU &41 au/ujaiad
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PLEASE HELP WITH CHEMISTRY PROBLEM you need to treat your PCR product with Fnu4HI (final concentration = 0.1 U/µl) in NEB buffer 4 (final concentration = 1X). For a total reaction volume of 30µl, calculate the volumes of Fnu4HI stock and NEB buffer 4 stock that are needed. =============...
##### Fit to page C Page view ECG Chest x-ray CT of head 6. Treatment Identify drugs...
Fit to page C Page view ECG Chest x-ray CT of head 6. Treatment Identify drugs that are used to treat a patient with syncope and altered mental status. Complete the table using Deglin et al, Davis's Drug Guide for Nurses 12e, or other drug reference. Medication Indication Side Effect Nursing Imp...
##### Please answer all parts especially C and D. Thanks Before Christmas a 65kg student consumes 2500...
Please answer all parts especially C and D. Thanks Before Christmas a 65kg student consumes 2500 Cal each day and stays at the same weight. For three days in a row while visiting her parents she eats 3500 Cal and, wanting to keep from gaining weight decides to work off" the excess by jumping ...


text:
## Product knot invariants

Let $I_1(L)$ be a Reshetikhine-Turaev link invariant coming from the (quantum Lie) group $G_1$ and representation $\lambda_1$ having the S matrix $S_1$. Let $I_2(L)$ be a Reshetikhine-Turaev link invariant coming from the (quantum Lie) group $G_2$ and representation $\lambda_2$ having the S matrix $S_2$ (hooray for copy'n'paste!). Then, for now just by my experiments, there always exists an invariant $I(L)=I_1(L)*I_2(L)$ (good old multiplication) with the S matrix $S_1\otimes{S_2}$ (here the trouble already begins: you can have S in tensor from, or condensed to matrix form, or condensed with index swap - and "$\otimes$" may be correct only in one case) which surely comes from the group $G_1°G_2$ (Tensor product? Direct product? Product of my imagination? :-) and the representation $\lambda_1°\lambda_2$ (even worse - if I remember correctly, now there are even 3 kind of products to be considered).

Please help me out with the correct signs $*,\otimes,\times$ which I confuse all the time. I also like to know about sort of a converse: If $G=G_1°G_2$ (Tensor? Direct?), are the representations $\lambda$ of $G$ always of the form $\lambda_1°\lambda_2$?

-
If you are viewing the quantum groups as Hopf algebras, then you should use tensor product on both the quantum groups and the representations, where the Hopf algebras act component-wise on the representations. – S. Carnahan Aug 25 2011 at 9:57
@Hauke: you have asked many questions on similar topics before, and to be honest the answer to most of them is "it would be a good idea for you to learn abstract algebra in general at the undergraduate and beginning graduate level before thinking about such things." (Not that I blame you for being interested in this material; it is of course very interesting! But patience is a virtue in these matters.) – Qiaochu Yuan Aug 25 2011 at 22:45
@Qiaochu: I surely would do MO a favor, yes :-) And I'm not even especially stupid, I always had an A in school math. But, and this is a but of cosmic dimensions. I am 50. Each time I try myself on Harris&Fuller or comparable stuff I see I have no, NO talent for abstract math at all. I probably need 20 years of intensive study to be able to answer such questions myself. Which is a complete waste of my brilliancy :-) (I could never compete with a math pro, my talents are conjectures drawn from the hat, generalizing a pattern of 3 items to infinity and doing all with diagrams.) – Hauke Reddmann Aug 26 2011 at 10:57
@Hauke: forgive me my impertinency, but I don't necessarily think that being 50 is a barrier. It's all a matter of starting at the right level (Fulton and Harris, if that is what you were referring to, being absolutely the wrong level to start at). You should start by looking at books on general abstract algebra (I like Artin's Algebra), then moving on to books on the representation theory of finite groups (I like James and Liebeck's Representations and Characters of Groups) before tackling the harder stuff. – Qiaochu Yuan Aug 28 2011 at 4:42
Book tips are duely noted (in the lib, check.) I'm surely not the guy giving up fast. :-) (It's just that math is a building and if I run in yet another notion I'm unfamiliar with I know I still didn't start low enough.) For triangle geometry the situation is almost ideal, there exists "Hyacinthos" on Yahoo where you can discuss everything informally and it doesn't hurt much when you lack a proof or your result is aniticipated, about 1800. :-) I wish there were the same for knot theory, and in lack of that I tend to abuse MO... – Hauke Reddmann Aug 28 2011 at 17:22
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# SI defining constants

All units in the International System of Units (SI) are defined by the seven constants listed in Table 1. These constants are based on unchanging properties of nature. In the SI, each of the seven defining constants has a fixed exact numerical value. The defining constants can be expressed using SI coherent derived units, or with a combination of SI base units.

The defining constants have been chosen such that, when taken together, their units cover all of the units of the SI. Any SI unit is a product of powers of these seven constants and a dimensionless factor.

 Name Symbol Value Unit Expressed in terms of SI base units the Planck constant h 6.626 070 15 × 10−34 J s kg m2 s−1 the speed of light in vacuum c 299 792 458 m s−1 m s−1 the unperturbed ground state hyperfine transition frequency of the caesium 133 atom ΔνCs 9 192 631 770 Hz s−1 the elementary charge e 1.602 176 634 × 10−19 C s A the Boltzmann constant k 1.380 649 × 10−23 J K−1 kg m2 s−2 K−1 the Avogadro constant NA 6.022 140 76 × 1023 mol−1 mol−1 the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz Kcd 683 lm W−1 kg−1 m−2 s3 cd

These definitions specify the exact numerical value of each constant when its value is expressed in the corresponding SI unit. By fixing the exact numerical value the unit becomes defined, since the product of the numerical value {Q} and the unit [Q] has to equal the value Q of the constant, which is invariant: Q = {Q} [Q].

## SI defining constants expressed in terms of base units

From Table 1, it can be seen that each defining constant can be expressed as the product of powers of the SI base units:

kgα mβ sγ Aδ Kε molζ cdη

 Expressed in terms of SI base units 1 2 -1 0 0 0 0 kg m2 s−1 0 1 -1 0 0 0 0 m s−1 0 0 -1 0 0 0 0 s−1 0 0 1 1 0 0 0 s A 1 2 -2 0 -1 0 0 kg m2 s−2 K−1 0 0 0 0 0 -1 0 mol−1 -1 -2 3 0 0 0 1 kg−1 m−2 s3 cd

The exponents required for each defining constant are presented in rows in Table 2. For example, the exponents used for the Planck constant, h, are (1, 2, −1, 0, 0, 0, 0), giving the coherent unit kg1 m2 s−1 A0 K0 mol0 cd0. Exponent values of zero result in a factor of one, and can be discarded, so in this example the coherent unit is kg m2 s−1.

## SI base units expressed in terms of defining constants

The seven SI base units can be defined in terms of the seven defining constants. The exponent values in Table 2 constitute a 7 × 7 matrix. Inverting this matrix gives the exponents required to express each SI base unit in terms of the product of powers of the defining constants:

hα′ cβ′ ΔνCsγ′ eδ′ kε′ NAζ′ Kcdη′

 Expressed in terms of SI defining constants 1 -2 1 0 0 0 0 h c−2 ΔνCs 0 1 -1 0 0 0 0 c ΔνCs−1 0 0 -1 0 0 0 0 ΔνCs−1 0 0 1 1 0 0 0 ΔνCs e 1 0 1 0 -1 0 0 h ΔνCs k−1 0 0 0 0 0 -1 0 NA−1 1 0 2 0 0 0 1 h ΔνCs2 Kcd

The exponents required for each SI base unit are presented in rows in Table 3. For example, the exponents used for the kilogram, kg, are (1, −2, 1, 0, 0, 0, 0), giving the combined constant h1 c−2 ΔνCs1 e0 k0 NA0 Kcd0. Exponent values of zero result in a factor of one, and can be discarded, so in this example the combined constant is h c−2 ΔνCs.

## Scaling factors for the SI base unit definitions

Table 3 excludes scaling factors. The calculations to derive the exact scaling factor for each SI base unit definition are shown below. For each base unit, substituting the values from Table 1 into the left side of the equation, which is a combination of SI defining constants, gives us the right side, which is the value of the combination in the SI.

### kilogram

$\dfrac{h \mspace{6mu} \Delta \nu _{Cs}}{c^2} = \dfrac{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2} \mspace{4mu} \text{kg}\\ \\ \\ 1 \mspace{4mu} \text{kg} \mspace{26mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{4mu} \dfrac{h \mspace{6mu} \Delta \nu _{Cs}}{c^2}\\ \\ \\ 1 \mspace{4mu} \text{kg} \mspace{26mu} = 1.475 \mspace{4mu} 521 \mspace{4mu} 399 \mspace{4mu} 735 \mspace{4mu} 270 \mspace{4mu} 916 \text{...} \times 10^{40} \mspace{4mu} \dfrac{h \mspace{6mu} \Delta \nu _{Cs}}{c^2}$

### metre

$\dfrac{c}{\Delta \nu _{Cs}} = \dfrac{299 \mspace{4mu} 792 \mspace{4mu} 458}{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770} \mspace{4mu} \text{m}\\ \\ \\ 1 \mspace{4mu} \text{m} \mspace{16mu} = \dfrac{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770}{299 \mspace{4mu} 792 \mspace{4mu} 458} \mspace{4mu} \dfrac{c}{\Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{m} \mspace{16mu} = 30.663 \mspace{4mu} 318 \mspace{4mu} 988 \mspace{4mu} 498 \mspace{4mu} 369 \mspace{4mu} 762 \text{...} \mspace{4mu} \dfrac{c}{\Delta \nu _{Cs}}$

### second

$\dfrac{1}{\Delta \nu _{Cs}} = \dfrac{1}{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770} \mspace{4mu} \text{s}\\ \\ \\ 1 \mspace{4mu} \text{s} \mspace{22mu} = 9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770 \mspace{4mu} \dfrac{1}{\Delta \nu _{Cs}}$

### ampere

$\Delta \nu _{Cs} \mspace{6mu} e = (9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}) \mspace{4mu} \text{A}\\ \\ \\ 1 \mspace{4mu} \text{A} \mspace{28mu} = \dfrac{1}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})} \mspace{4mu} \Delta \nu _{Cs} \mspace{6mu} e\\ \\ \\ 1 \mspace{4mu} \text{A} \mspace{28mu} = 6.789 \mspace{4mu} 686 \mspace{4mu} 817 \mspace{4mu} 250 \mspace{4mu} 553 \mspace{4mu} 926 \text{...} \times 10^{8} \mspace{4mu} \Delta \nu _{Cs} \mspace{6mu} e$

### kelvin

$\dfrac{h \mspace{6mu} \Delta \nu _{Cs}}{k} = \dfrac{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)}{1.380 \mspace{4mu} 649 \times 10^{-23}} \mspace{4mu} \text{K}\\ \\ \\ 1 \mspace{4mu} \text{K} \mspace{32mu} = \dfrac{1.380 \mspace{4mu} 649 \times 10^{-23}}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770))} \mspace{4mu} \dfrac{h \mspace{6mu} \Delta \nu _{Cs}}{k}\\ \\ \\ 1 \mspace{4mu} \text{K} \mspace{32mu} = 2.266 \mspace{4mu} 665 \mspace{4mu} 264 \mspace{4mu} 601 \mspace{4mu} 104 \mspace{4mu} 867 \text{...} \mspace{4mu} \dfrac{h \mspace{6mu} \Delta \nu _{Cs}}{k}$

### mole

$\dfrac{1}{N_A} \mspace{13mu} = \dfrac{1}{6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23}} \mspace{4mu} \text{mol}\\ \\ \\ 1 \mspace{4mu} \text{mol} = 6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23} \mspace{4mu} \dfrac{1}{N_A}$

### candela

$h \mspace{6mu} {\Delta \nu _{Cs}}^2 \mspace{6mu} K_{cd} = (6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2 (683) \mspace{4mu} \text{cd}\\ \\ \\ 1 \mspace{4mu} \text{cd} \mspace{66mu} = \dfrac {1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2 (683)} \mspace{4mu} h \mspace{6mu} {\Delta \nu _{Cs}}^2 \mspace{6mu} K_{cd}\\ \\ \\ 1 \mspace{4mu} \text{cd} \mspace{66mu} = 2.614 \mspace{4mu} 830 \mspace{4mu} 482 \mspace{4mu} 285 \mspace{4mu} 615 \mspace{4mu} 686 \text{...} \times 10^{10} \mspace{4mu} h \mspace{6mu} {\Delta \nu _{Cs}}^2 \mspace{6mu} K_{cd}$

## SI base units expressed in terms of defining constants

Table 4 presents the seven SI base units as defined by the product of powers of the SI defining constants.

 Name Symbol Scaling factor Constant kilogram kg 1.475 521 397 352 … × 1040 h c−2 ΔνCs metre m 30.663 318 988 498 … c ΔνCs−1 second s 9 192 631 770 ΔνCs−1 ampere A 6.789 686 817 250 … × 108 ΔνCs e kelvin K 2.266 665 264 601 … h ΔνCs k−1 mole mol 6.022 140 76 × 1023 NA−1 candela cd 2.614 830 482 285 … × 1010 h ΔνCs2 Kcd

Since all seven base units of the SI can be defined in terms of the seven defining constants, it follows that all other SI units can also be defined in terms of the seven defining constants.

The distinction between SI base units and SI derived units remains useful, but is not essential.


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# Highway Simulator

Posted 2016. 2. 23. 15:06

Video

A green robot is controlled with keyboard inputs where future trajectories are depicted with black circles with arrows indicating directions. Similar to adding building blocks, the whole track can be made by simply adding road segments using add_segment API

Lane Description

: Track consists of lanes with three types: straight, left turn, and right turn.

Code (MATLAB)

Highway.zip

#### 'Enginius > Matlab' 카테고리의 다른 글

 KNN-regression  (0) 2017.03.01 2016.11.21 2016.02.23 2016.01.15 2015.12.23 2015.07.05


text:
Select Page

# What are we learning ?

Competency in Focus: Representation of numbers in base 10 This problem from American Mathematics contest (AMC 8, 2013) is a digit problem .

# Next understand the problem

When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?
##### Source of the problem
American Mathematical Contest 2013, AMC 8 Problem 13
##### Key Competency
Representation of numbers in base 10
4/10
##### Suggested Book
Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics

Do you really need a hint ? Try it first!
Let the two digits be $a$ and $b$ that is total score of Clara is ab .
Now we know that any number in base 10 can be represented as ab=10 a+ b.  Given, when Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. So, Clara misinterpreted ab as ba . Again , ba= 10b+a .
The difference between the two is $|9a-9b|$ which factors into $|9(a-b)|$. So, what can we say from here?
Therefore, since the difference is a multiple of 9, the only answer choice that is a multiple of 9 that is 45.

# Connected Program at Cheenta

#### Amc 8 Master class

Cheenta AMC Training Camp consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams.

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+0

A castle and a bishop are placed on different squares of a chessboard. What is the probability that one piece threatens the other?

0
5
1155
7

A castle and a bishop are placed on different squares of a chessboard. What is the probability that one piece threatens the other?

Mar 10, 2015

#4
+1036
+10

A castle (usually known as a rook) moves laterally and a bishop moves diagonally. That means that they can never both threaten each other simultaneously. So the probability that one piece threatens the other is equal to the probability that the rook threatens the bishop, plus the probability that the bishop threatens the rook.

A rook placed anywhere on the board threatens 14 squares. The probability that the rook threatens the bishop is 14/63, or 2/9.

The bishop . . .

Threatens 7 squares when placed on one of the 28 edge squares.

Threatens 9 squares when placed on one of the 20 squares one square from the edge.

Threatens 11 squares when placed on one of the 12 squares two squares from the edge.

Threatens 13 squares when placed on one of the 4 center squares.

The average number of squares threatened by a bishop is

$$\dfrac{\left(7\times28 \right ) + \left(9\times20 \right ) + \left(11\times12 \right ) + \left (13\times4 \right )}{64}\; = \; \dfrac{35}4 \\\\ \small \text {The probability that the bishop threatens the rook} \;\dfrac{35}{4\times63} = \dfrac5{36}\\\\ \text {The probability that either threatens the other } \; \dfrac{5}{36}+ \dfrac{2}{9} \;=\; \dfrac{13}{36}\\$$

Here you can see that getting hooked by a rook is 62.5% more likely than getting buggered by a bishop.

I’m not sure where the knight came in. Maybe Cphill is taking a break from his quest.

Mar 11, 2015

#1
+21951
+5

A bishop only threatens a piece of the same color; a knight only threatens a piece of the opposite color. So, the probability that they threaten each other is zero.

Mar 10, 2015
#2
0

Is it decided that the bishop will be placed on a black square or a white square, or is it that it is put down at random and that it can be either a black squared or a white squared bishop ?

Mar 11, 2015
#3
+110208
+5

Geno, I do not get your answer.

do you mean that they both can't threaten each other at the same time?  That is true.

Assuming that there are no other peices in the way. And assuming that one is white and the other is black.

If a bishop is on any square it will be threatened if the castle is on the same row or the same column.

There are 7 squares left on the column and 7 on the same row and there are a total of 8*8-1=63 squares that the bishop could be on so

P(castle threatens bishop) =  $${\frac{{\mathtt{14}}}{{\mathtt{63}}}} = {\frac{{\mathtt{2}}}{{\mathtt{9}}}} = {\mathtt{0.222\: \!222\: \!222\: \!222\: \!222\: \!2}}$$

NOW

The probability that the bishop threatens the castle is more complicated.

I think I shall think about it later.  LOL

Mar 11, 2015
#4
+1036
+10

A castle (usually known as a rook) moves laterally and a bishop moves diagonally. That means that they can never both threaten each other simultaneously. So the probability that one piece threatens the other is equal to the probability that the rook threatens the bishop, plus the probability that the bishop threatens the rook.

A rook placed anywhere on the board threatens 14 squares. The probability that the rook threatens the bishop is 14/63, or 2/9.

The bishop . . .

Threatens 7 squares when placed on one of the 28 edge squares.

Threatens 9 squares when placed on one of the 20 squares one square from the edge.

Threatens 11 squares when placed on one of the 12 squares two squares from the edge.

Threatens 13 squares when placed on one of the 4 center squares.

The average number of squares threatened by a bishop is

$$\dfrac{\left(7\times28 \right ) + \left(9\times20 \right ) + \left(11\times12 \right ) + \left (13\times4 \right )}{64}\; = \; \dfrac{35}4 \\\\ \small \text {The probability that the bishop threatens the rook} \;\dfrac{35}{4\times63} = \dfrac5{36}\\\\ \text {The probability that either threatens the other } \; \dfrac{5}{36}+ \dfrac{2}{9} \;=\; \dfrac{13}{36}\\$$

Here you can see that getting hooked by a rook is 62.5% more likely than getting buggered by a bishop.

I’m not sure where the knight came in. Maybe Cphill is taking a break from his quest.

Nauseated Mar 11, 2015
#5
+110208
+5

Thanks Nauseated,

I wasn't about to just take your word for it so I also worked it out.

I got exactly the same answer but my working was a little different.

I said that for 28 out of 64 squares the bishop would be a threat to 7 out of 63 squares

then  I said that for 20 out of 64 squares the bishop would be a threat to 9 out of 63 squares

then  I said that for 12 out of 64 squares the bishop would be a threat to 11 out of 63 squares

then  I said that for 4 out of 64 squares the bishop would be a threat to 13 out of 63 squares

So the probability that the bishop would be a threat to the rook is

$$\\\mbox{P(they are a threat to each other)}=0\\\\ \mbox{P(the rook is a threat to the bishop)}=\frac{2}{9}\\\\ \mbox{P(the bishop is a threat to the rook)}\\\\ =\frac{28}{64}\times\frac{7}{63}+\frac{20}{64}\times\frac{9}{63}+\frac{12}{64}\times\frac{11}{63}+\frac{4}{64}\times\frac{13}{63}\\\\ =\frac{(28*7)+(20*9)+(12*11)+(4*13)}{64*63}\\\\ =\frac{560}{4032}\\\\ =\frac{5}{36}\\\\ so\\ \mbox{P(that any threat is presented)}=\frac{2}{9}+\frac{5}{36}-0=\frac{13}{36}$$

Mar 12, 2015
#6
+110208
0

I do not think that this is correct - I need to rethink.

Mar 12, 2015
#7
+110208
+5

What Nauseated and I both forgot is that bishops can only ever be on one colour.

This will not change the answer but I will still make the working more accurate.

So there is not 64 squares that they can be on there is only 32 possible squares!

I wasn't about to just take your word for it so I also worked it out.

I got exactly the same answer but my working was a little different.

I said that for 14 out of 32 squares the bishop would be a threat to 7 out of 63 squares

then  I said that for 10 out of 32 squares the bishop would be a threat to 9 out of 63 squares

then  I said that for 6 out of 32 squares the bishop would be a threat to 11 out of 63 squares

then  I said that for 2 out of 32 squares the bishop would be a threat to 13 out of 63 squares

So the probability that the bishop would be a threat to the rook is

$$\\\mbox{P(they are a threat to each other)}=0\\\\ \mbox{P(the rook is a threat to the bishop)}=\frac{2}{9}\\\\ \mbox{P(the bishop is a threat to the rook)}\\\\ =\frac{14}{32}\times\frac{7}{63}+\frac{10}{32}\times\frac{9}{63}+\frac{6}{32}\times\frac{11}{63}+\frac{2}{32}\times\frac{13}{63}\\\\ =\frac{(14*7)+(10*9)+(6*11)+(2*13)}{32*63}\\\\ =\frac{280}{2016}\\\\ =\frac{5}{36}\\\\ so\\ \mbox{P(that any threat is presented)}=\frac{2}{9}+\frac{5}{36}-0=\frac{13}{36}$$

Mar 12, 2015


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# Partial derivative form question

It's my understanding the partial derivative can take the following form:

Where $$y_0$$ is held constant as a plane slicing and $$x_0$$ is the point where the derivative is taken with respect to $$x$$.

I'm confused by the following notation in a Rojas AI book:

In the third paragraph the partial derivative is taken with respect to $$a_i$$. I'm confused how this derivative is taken. I'm also confused also why $$f_i$$ is used when it is not part of the derivative of $$x^2$$. Can anyone provide guidance here?

The variables $$x_1,\cdots x_m$$ are integration variables that disappear after the integration on the given volume.

So the function $$E$$ is a function of the variable parameters $$a_i$$ and can be differentiatd with respect to these variables. Using the Leibniz's rule for differentiation under the integral sign the derivative can be calculated as : $$\frac{dE}{da_i}=\int_V \frac{\partial}{\partial a_i}F(a_i,x_j) dV$$

where $$F(a_i,x_j)=(f-(a_1f_1+a_2f_2+\cdots a_nf_n))^2$$

so: $$\frac{\partial F}{\partial a_1}=-2(f-(a_1f_1+a_2f_2+\cdots a_nf_n)) \cdot f_1$$ $$\frac{\partial F}{\partial a_2}=-2(f-(a_1f_1+a_2f_2+\cdots a_nf_n)) \cdot f_2$$

etc....

Maybe you are confused by the notation. The situation is as for function

$$F(x_1,x_2,y_1,y_2)= (f(x_1,x_2)-y_1f_1(x_1,x_2)-y_2f_2(x_1,x_2))^2$$

the derivative with respect to $$y_i$$ ( that is your $$a_i$$ ) can be evaluated considering the functions $$f_i$$ as constants, because there are not dependent form $$y_i$$, so, using the chain rule we have: $$\frac{\partial F}{\partial y_i}=$$ $$= 2(f(x_1,x_2)-y_1f_1(x_1,x_2)-y_2f_2(x_1,x_2)) \cdot \frac{\partial }{\partial y_i}(f(x_1,x_2)-y_1f_1(x_1,x_2)-y_2f_2(x_1,x_2))=$$ $$=2(f(x_1,x_2)-y_1f_1(x_1,x_2)-y_2f_2(x_1,x_2))(-f_i(x_1,x_2))$$

• where is $f_1$, $f_2$ coming from? – Nick Mar 2 '20 at 7:19
• $f_i$ is the ''coefficient'' of $a_i$. – Emilio Novati Mar 2 '20 at 9:18
• i'm still confused why the coefficient of $a_i$ is in the product after taking the derivative with respect to $a_1$. Am I missing something? – Nick Mar 2 '20 at 19:11
• I added to my answer. I hope it's useful :) – Emilio Novati Mar 2 '20 at 21:27
• I was missing the chain rule! Thanks – Nick Mar 3 '20 at 2:05

Maybe it's easier to see if we take a finite number of functions to expand upon. Let's say we take $$3$$ such functions $$f_1, f_2, f_3$$ and proceed to calculate the quadratic error as

$$E = \int_{V}(f-(a_1f_1+a_2f_2+a_3f_3))^2dV$$

Now we want to minimize the error, and so we calculate the derivative with respect to the expansion coefficients. For the first one

$$\frac{dE}{da_1} = \frac{d}{d a_1}\int_V(f-a_1f_1-a_2f_2-a_3f_3)^2dV = \int_V\frac{\partial}{\partial a_1}(f-a_1f_1-a_2f_2-a_3f_3)^2dV$$

so we just need to evaluate the partial derivative of the quantity in parenthesis. This is just the same as calculating the derivative of composite function like

$$\frac{d}{dt}g^2(t) = \color{red}{2}\color{green}{g(t)}\color{orange}{\frac{dg}{dt}}$$

and so

$$\frac{\partial}{\partial a_1}\overbrace{(f-a_1f_1-a_2f_2-a_3f_3)^2}^{g^2(a_1,a_2,a_3)} = \color{red}{2}\color{green}{(f-a_1f_1-a_2f_2-a_3f_3)}\color{orange}{\left[\frac{\partial}{\partial a_1}(f-a_1f_1-a_2f_2-a_3f_3)\right]}$$

We have to find the orange part which is the partial derivative wrt $$a_1$$ of the, no more squared, function. To make it easier I'll write it in the following manner, choosing

$$x = a_1f_1\qquad y=a_2f_2\qquad z=a_3f_3$$

this means that (remember that for the partial derivative, the $$f_i$$ are just coefficients, even though they are in practise functions)

$$f_1\frac{\partial}{\partial x} = f_1\frac{\partial}{f_1 \partial a_1} = \frac{\partial}{\partial a_1}$$

so that we can write the orange part as

$$\frac{\partial}{\partial a_1}(f-a_1f_1-a_2f_2-a_3f_3) = f_1\frac{\partial}{\partial x}(f-x-y-z) = -f_1$$

In the end what we get is

$$\frac{\partial}{\partial a_1}(f-a_1f_1-a_2f_2-a_3f_3)^2 = 2(f-a_1f_1-a_2f_2-a_3f_3)(-f_1) = -2f_1(f-a_1f_1-a_2f_2-a_3f_3)$$

You can do it by yourself for the other two coefficients and convince yourself that the result, indipendently of how many functions you expand on, the general result is given by

$$\frac{\partial}{\partial a_i}(f-a_1f_1-a_2f_2-a_3f_3-\cdots -a_nf_n)^2 = -2f_i(f-a_1f_1-a_2f_2-a_3f_3-\cdots -a_nf_n)$$

• I'm confused why $f_i$ in the final solution is appearing. Perhaps I'm overlooking something – Nick Mar 2 '20 at 7:18
• @Nick I'll add a explanation to my answer – Davide Morgante Mar 2 '20 at 8:26

If you differentiate

$$(p+qx+ry)^2$$ on $$q$$, you get $$2x(p+qx+ry).$$

Now consider $$p\leftrightarrow f$$, $$q\leftrightarrow-a_1$$, $$r\leftrightarrow-a_2$$, $$x\leftrightarrow f_1$$ and $$y\leftrightarrow f_2$$.


text:
Ask Your Question

# Revision history [back]

This ended up working for me, both in command line, and notebook:

cmd_folder = os.path.dirname(os.path.abspath('/home/william/pyserial-2.5/serial'))
if cmd_folder not in sys.path:
sys.path.insert(0, cmd_folder)
import serial

I found the solution here.


text:
# 3. Data Configuration¶

OpenMC relies on a variety of physical data in order to carry out transport simulations, depletion simulations, and other common tasks. As a user, you are responsible for specifying one or more of the following:

• Cross sections (XML) – A cross sections XML file (commonly named cross_sections.xml) contains a listing of other data files, in particular neutron cross sections, photon cross sections, and windowed multipole data. Each of those files, in turn, uses a HDF5 format (see Nuclear Data File Formats). In order to run transport simulations with continuous-energy cross sections, you need to specify this file.

• Depletion chain (XML) – A depletion chain XML file contains decay data, fission product yields, and information on what neutron reactions can result in transmutation. This file is needed for depletion/activation calculations as well as some basic functions in the openmc.data module.

• Multigroup cross sections (HDF5) – OpenMC can also perform transport simulations using multigroup data. In this case, multigroup cross sections are stored in a single HDF5 file. Thus, in order to run a multigroup transport simulation, this file needs to be specified.

Each of the above files can specified in several ways. In the Python API, a runtime configuration variable openmc.config can be used to specify any of the above and is initialized using a set of environment variables.

## 3.1. Runtime Configuration¶

Data sources for OpenMC can be specified at runtime in Python using the openmc.config variable. This variable acts like a dictionary and stores key-values pairs, where the values are file paths (strings or path-like objects) and the key can be one of the following:

"cross_sections"

Indicates the path to the cross sections XML file that lists HDF5 format neutron cross sections, photon cross sections, and windowed multipole data. At startup, this is initialized with the value of the OPENMC_CROSS_SECTIONS environment variable. Note that the openmc.Materials.cross_sections attribute will override this, if specified.

"chain_file"

Indicates the path to the depletion chain XML file that contains decay data, fission product yields, and what neutron reactions may result in transmutation of a target nuclide. At startup, this is initialized with the value of the OPENMC_CHAIN_FILE environment variable.

"mg_cross_sections"

Indicates the path to an HDF5 file that contains multigroup cross sections. At startup, this is initialized with the value of the OPENMC_MG_CROSS_SECTIONS environment variable. Note that the openmc.Materials.cross_sections attribute will override this if specified.

If you want to persistently set the environment variables used to initialized the configuration, export them from your shell profile (.profile or .bashrc in bash).

## 3.2. Continuous-Energy Cross Sections¶

### 3.2.1. Using Pregenerated Libraries¶

Various evaluated nuclear data libraries have been processed into the HDF5 format required by OpenMC and can be found at https://openmc.org. Unless you have specific data needs, it is highly recommended to use one of the pregenerated libraries. You can find both libraries generated by the OpenMC development team as well as libraries based on ACE files distributed elsewhere. To use these libraries, download the archive file, unpack it, and then specify the path of the cross_sections.xml file contained in the unpacked directory as described in Runtime Configuration.

### 3.2.2. Manually Creating a Library from ACE files¶

If you have ACE format data that was produced with NJOY, such as that distributed with MCNP or Serpent, it can be converted to the HDF5 format using the using the Python API. Several sources provide openly available ACE data including the ENDF/B, JEFF, and TENDL libraries as well as the LANL Nuclear Data Team.

The openmc.data module in the Python API enables users to directly convert ACE data to OpenMC’s HDF5 format and create a corresponding cross_sections.xml file. For those who prefer to use the API directly, the openmc.data.IncidentNeutron and openmc.data.ThermalScattering classes can be used to read ACE data and convert it to HDF5. For continuous-energy incident neutron data, use the IncidentNeutron.from_ace() class method to read in an existing ACE file and the IncidentNeutron.export_to_hdf5() method to write the data to an HDF5 file.

u235 = openmc.data.IncidentNeutron.from_ace('92235.710nc')
u235.export_to_hdf5('U235.h5')

If you have multiple ACE files for the same nuclide at different temperatures, you can use the IncidentNeutron.add_temperature_from_ace() method to append cross sections to an existing IncidentNeutron instance:

u235 = openmc.data.IncidentNeutron.from_ace('92235.710nc')
for suffix in [711, 712, 713, 714, 715, 716]:
u235.export_to_hdf5('U235.h5')

Similar methods exist for thermal scattering data:

light_water = openmc.data.ThermalScattering.from_ace('lwtr.20t')
for suffix in range(21, 28):
light_water.export_to_hdf5('lwtr.h5')

Once you have created corresponding HDF5 files for each of your ACE files, you can create a library and export it to XML using the openmc.data.DataLibrary class:

library = openmc.data.DataLibrary()
library.register_file('U235.h5')
library.register_file('lwtr.h5')
...
library.export_to_xml()

At this point, you will have a cross_sections.xml file that you can use in OpenMC.

Hint

The IncidentNeutron class allows you to view/modify cross sections, secondary angle/energy distributions, probability tables, etc. For a more thorough overview of the capabilities of this class, see the example notebook.

### 3.2.3. Manually Creating a Library from ENDF files¶

If you need to create a nuclear data library and you do not already have suitable ACE files or you need to further customize the data (for example, adding more temperatures), the IncidentNeutron.from_njoy() and ThermalScattering.from_njoy() methods can be used to create data instances by directly running NJOY. Both methods require that you pass the name of ENDF file(s) that are passed on to NJOY. For example, to generate data for Zr-92:

zr92 = openmc.data.IncidentNeutron.from_njoy('n-040_Zr_092.endf')

By default, data is produced at room temperature, 293.6 K. You can also specify a list of temperatures that you want data at:

zr92 = openmc.data.IncidentNeutron.from_njoy(
'n-040_Zr_092.endf', temperatures=[300., 600., 1000.])

The IncidentNeutron.from_njoy() method assumes you have an executable named njoy available on your path. If you want to explicitly name the executable, the njoy_exec optional argument can be used. Additionally, the stdout argument can be used to show the progress of the NJOY run.

To generate a thermal scattering file, you need to specify both an ENDF incident neutron sub-library file as well as a thermal neutron scattering sub-library file; for example:

light_water = openmc.data.ThermalScattering.from_njoy(
'neutrons/n-001_H_001.endf', 'thermal_scatt/tsl-HinH2O.endf')

Once you have instances of IncidentNeutron and ThermalScattering, a library can be created by using the export_to_hdf5() methods and the DataLibrary class as described in Manually Creating a Library from ACE files.

### 3.2.4. Enabling Resonance Scattering Treatments¶

In order for OpenMC to correctly treat elastic scattering in heavy nuclides where low-lying resonances might be present (see Energy-Dependent Cross Section Model), the elastic scattering cross section at 0 K must be present. If the data you are using was generated via IncidentNeutron.from_njoy(), you will already have 0 K elastic scattering cross sections available. Otherwise, to add 0 K elastic scattering cross sections to an existing IncidentNeutron instance, you can use the IncidentNeutron.add_elastic_0K_from_endf() method which requires an ENDF file for the nuclide you are modifying:

u238 = openmc.data.IncidentNeutron.from_hdf5('U238.h5')
u238.export_to_hdf5('U238_with_0K.h5')

With 0 K elastic scattering data present, you can turn on a resonance scattering method using Settings.resonance_scattering.

Note

The process of reconstructing resonances and generating tabulated 0 K cross sections can be computationally expensive, especially for nuclides like U-238 where thousands of resonances are present. Thus, running the IncidentNeutron.add_elastic_0K_from_endf() method may take several minutes to complete.

### 3.2.5. Photon Cross Sections¶

Photon interaction data is needed to run OpenMC with photon transport enabled. Some of this data, namely bremsstrahlung cross sections from Seltzer and Berger, mean excitation energy from the NIST ESTAR database, and Compton profiles calculated by Biggs et al. and available in the Geant4 G4EMLOW data file, is distributed with OpenMC. The rest is available from the NNDC, which provides ENDF data from the photo-atomic and atomic relaxation sublibraries of the ENDF/B-VII.1 library.

Most of the pregenerated HDF5 libraries available at https://openmc.org already have photon interaction data included. If you are building a data library yourself, it is possible to use the Python API directly to convert photon interaction data from an ENDF or ACE file to an HDF5 file. The openmc.data.IncidentPhoton class contains an IncidentPhoton.from_ace() method that will generate photon data from an ACE table and an IncidentPhoton.export_to_hdf5() method that writes the data to an HDF5 file:

u = openmc.data.IncidentPhoton.from_ace('92000.12p')
u.export_to_hdf5('U.h5')

Similarly, the IncidentPhoton.from_endf() method can be used to read photon data from an ENDF file. In this case, both the photo-atomic and atomic relaxation sublibrary files are required:

u = openmc.data.IncidentPhoton.from_endf('photoat-092_U_000.endf',
'atom-092_U_000.endf')

Once the HDF5 files have been generated, a library can be created using the DataLibrary class as described in Manually Creating a Library from ACE files.

## 3.3. Chain Files¶

Pregenerated depletion chain XML files can be found at https://openmc.org. Additionally, depletion chains can be generated using the openmc.deplete.Chain class. In particular, the from_endf() method allows a chain to be generated starting from a set of ENDF incident neutron, decay, and fission product yield sublibrary files. Once you’ve downloaded or generated a depletion chain XML file, make sure to specify its path as described in Runtime Configuration.

## 3.4. Windowed Multipole Data¶

OpenMC is capable of using windowed multipole data for on-the-fly Doppler broadening. A comprehensive multipole data library containing all nuclides in ENDF/B-VII.1 is available on GitHub. To obtain this library, download and unpack an archive (.zip or .tag.gz) from GitHub. Once unpacked, you can use the openmc.data.DataLibrary class to register the .h5 files as described in Manually Creating a Library from ACE files.

The official ENDF/B-VII.1 HDF5 library includes the windowed multipole library, so if you are using this library, the windowed multipole data will already be available to you.

## 3.5. Multigroup Cross Sections¶

Multigroup cross section libraries are generally tailored to the specific calculation to be performed. Therefore, at this point in time, OpenMC is not distributed with any pre-existing multigroup cross section libraries. However, if a multigroup library file is downloaded or generated, the path to the file needs to be specified as described in Runtime Configuration. For an example of how to create a multigroup library, see the example notebook.


text:
Q

# Show that the function given by f (x) is equal to sin x is increasing in 0 to pie by 2

3. a) Show that the function given by f (x) = $\sin x$ is  increasing in $\left ( 0 , \pi /2 \right )$

Views

Given f(x) = sinx
$f^{'}(x) = \cos x$
Since,     $\cos x > 0 \ for \ each \ x\ \epsilon \left ( 0,\frac{\pi}{2} \right )$
$f^{'}(x) > 0$
Hence, f(x) = sinx is strictly increasing in   $\left ( 0,\frac{\pi}{2} \right )$

Exams
Articles
Questions


text:
## MWC '15 #7 P3: Blue and Green

View as PDF

Points: 15 (partial)
Time limit: 2.5s
Memory limit: 16M

Author:
Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Blue and Green is a fictitious sandbox game where you have a line of blue and green marbles. There exists a currency in this game, which you can use to change the assortment of marbles. Each move has its own cost. The following moves are:

• set the colour of a single marble at a cost of
• rotate all the marbles to the left by 1 (the left-most marble moves to the right end, and everything else moves one place to the left) at a cost of
• rotate all the marbles to the right by 1 (the right-most marble moves to the left end, and everything else moves one place to the right) at a cost of
• invert the colour of all the marbles at a cost of

Find the number of different arrangements of blue and green marbles that can be achieved by using or less currency units. All blue marbles are not distinguishable from each other and the same goes for green marbles. This means that if you have the arrangement GBGBGB and you rotate it twice to get GBGBGB, the original and final arrangements are indistinguishable (equivalent).

Hint: try the steps in the listed order for efficiency.

#### Input Specification

The first line contains two space separated integers , the number of marbles and , the amount of currency.

The second line contains four space separated integers , , and .

The third line contains a string with characters, B for a blue marble or G for a green marble.

Note: Test cases are reasonable.

#### Output Specification

A single integer - the number unique marble arrangements achievable with the amount of currency.

#### Sample Input 1

2 1
1 2 2 2
BB

#### Sample Output 1

3

#### Explanation for Sample Output 1

You can only afford to set the colour of one marble. Thus, you can change the colour of the first or second marble to get the possible arrangements: BB, GB and BG.

#### Sample Input 2

4 1
1 1 1 1
BGGG

#### Sample Output 2

8

#### Explanation for Sample Output 2

You can afford one of the moves. Thus, we get the following unique arrangements:

• BGGG original
• GGGG setting the first marble to green
• BBGG setting the second marble to blue
• BGBG setting the third marble to blue
• BGGB setting the fourth marble to blue
• GBGG rotating the marbles right once
• GGGB rotating the marbles left once
• GBBB inverting all the colours

#### Sample Input 3

5 5
3 4 4 2
BGGBB

#### Sample Output 3

14