text:
Journal of Symbolic Computation

 Short Title: J. Symb. Comput. Publisher: Elsevier (Academic Press), London ISSN: 0747-7171 Online: http://www.sciencedirect.com/science/journal/07477171 Comments: Indexed cover-to-cover
 Documents Indexed: 2,743 Publications (since 1985) References Indexed: 2,181 Publications with 54,116 References.
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Latest Issues

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Authors

 28 Hong, Hoon 22 Schicho, Josef 22 Sendra, Juan Rafael 21 Mourrain, Bernard 19 van der Hoeven, Joris 18 Safey El Din, Mohab 17 Faugère, Jean-Charles 17 Giesbrecht, Mark W. 17 Holt, Derek F. 17 Schost, Éric 16 Cannon, John J. 16 Gao, Xiaoshan 16 Kaltofen, Erich L. 16 Kapur, Deepak 16 Moreno Maza, Marc 16 Sturmfels, Bernd 15 Lazard, Daniel 15 von zur Gathen, Joachim 14 Emiris, Ioannis Z. 14 Salvy, Bruno 13 Barkatou, Moulay A. 12 Collins, George E. 12 Davenport, James Harold 12 Labahn, George 12 Levandovskyy, Viktor 12 McCallum, Scott 12 Szántó, Ágnes 12 Tsigaridas, Elias P. 12 Winkler, Franz 11 Abramov, Sergeĭ Aleksandrovich 11 Farouki, Rida T. 11 Koepf, Wolfram A. 11 Singer, Michael F. 11 Wang, Dongming 10 D’Andrea, Carlos 10 de Graaf, Willem Adriaan 10 Eick, Bettina 10 Galligo, André 10 Gianni, Patrizia M. 10 Kauers, Manuel 10 Petkovšek, Marko 10 Robbiano, Lorenzo 10 Roy, Marie-Françoise 10 van Hoeij, Mark 10 Weispfenning, Volker 9 Grigor’ev, Dmitriĭ Yur’evich 9 Gutierrez, Jaime 9 Hashemi, Amir 9 Hubert, Evelyne 9 Klüners, Jürgen 9 Mignotte, Maurice 9 Pohst, Michael E. 9 Schmidt-Schauß, Manfred 9 Ulmer, Felix 9 Xia, Bican 9 Yokoyama, Kazuhiro 9 Zhi, Lihong 8 Abbott, John A. 8 Gonzalez-Vega, Laureano 8 Hauenstein, Jonathan D. 8 Kalkbrener, Michael 8 La Scala, Roberto 8 Otto, Friedrich 8 Rouillier, Fabrice 8 Seiler, Werner M. 8 Storjohann, Arne 8 Trager, Barry M. 8 Yap, Chee-Keng 7 Alcazar, Juan Gerardo 7 Busé, Laurent 7 Chen, Shaoshi 7 Fortuna, Elisabetta 7 Gaál, István 7 Gatermann, Karin 7 Gerdt, Vladimir Petrovich 7 Goldman, Ronald N. 7 Jebelean, Tudor 7 Jeronimo, Gabriela 7 Kemper, Gregor 7 Kutsia, Temur 7 Leykin, Anton 7 Monagan, Michael B. 7 Mora, Teo 7 Noro, Masayuki 7 Pfister, Gerhard 7 Recio, Tomas 7 Rusinowitch, Michaël 7 Stillman, Michael Eugene 7 Strzeboński, Adam Wojciech 7 Sullivant, Seth 7 Villard, Gilles 7 Zeilberger, Doron 6 Bernardi, Alessandra 6 Bigatti, Anna Maria 6 Bonacina, Maria Paola 6 Bostan, Alin 6 Bronstein, Manuel Eric 6 Brown, Christopher W. 6 Castro-Jiménez, Francisco Jesús 6 Dickenstein, Alicia M. ...and 2,941 more Authors
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Fields

 1,666 Computer science (68-XX) 724 Commutative algebra (13-XX) 472 Algebraic geometry (14-XX) 335 Numerical analysis (65-XX) 315 Field theory and polynomials (12-XX) 296 Number theory (11-XX) 246 Group theory and generalizations (20-XX) 156 Mathematical logic and foundations (03-XX) 125 Combinatorics (05-XX) 116 Associative rings and algebras (16-XX) 116 Ordinary differential equations (34-XX) 85 Linear and multilinear algebra; matrix theory (15-XX) 83 Special functions (33-XX) 83 Information and communication theory, circuits (94-XX) 62 General and overarching topics; collections (00-XX) 50 Nonassociative rings and algebras (17-XX) 50 Partial differential equations (35-XX) 46 Functions of a complex variable (30-XX) 44 Several complex variables and analytic spaces (32-XX) 41 Operations research, mathematical programming (90-XX) 40 Real functions (26-XX) 37 Convex and discrete geometry (52-XX) 32 Dynamical systems and ergodic theory (37-XX) 29 Differential geometry (53-XX) 28 Geometry (51-XX) 25 Difference and functional equations (39-XX) 24 Category theory; homological algebra (18-XX) 21 Algebraic topology (55-XX) 21 Manifolds and cell complexes (57-XX) 21 Mechanics of particles and systems (70-XX) 20 Approximations and expansions (41-XX) 19 Statistics (62-XX) 19 Mechanics of deformable solids (74-XX) 17 General algebraic systems (08-XX) 17 Global analysis, analysis on manifolds (58-XX) 17 Biology and other natural sciences (92-XX) 17 Systems theory; control (93-XX) 14 Probability theory and stochastic processes (60-XX) 13 Order, lattices, ordered algebraic structures (06-XX) 12 Quantum theory (81-XX) 11 History and biography (01-XX) 10 Topological groups, Lie groups (22-XX) 10 Fluid mechanics (76-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Optics, electromagnetic theory (78-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Mathematics education (97-XX) 3 $$K$$-theory (19-XX) 3 Sequences, series, summability (40-XX) 3 Abstract harmonic analysis (43-XX) 3 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)

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An algorithm for solving second order linear homogeneous differential equations. Zbl 0603.68035
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Gröbner bases and primary decomposition of polynomial ideals. Zbl 0667.13008
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The method of creative telescoping. Zbl 0738.33002
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Bruno Buchberger’s PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German. Zbl 1158.01307
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Partial cylindrical algebraic decomposition for quantifier elimination. Zbl 0754.68063
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Non-commutative Gröbner bases in algebras of solvable type. Zbl 0715.16010
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On determinants and eigenvalue theory of tensors. Zbl 1259.15038
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1999
On the computational complexity and geometry of the first-order theory of the reals. III: Quantifier elimination. Zbl 0798.68073
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Hypergeometric solutions of linear recurrences with polynomial coefficients. Zbl 0761.11008
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Comprehensive Gröbner bases. Zbl 0784.13013
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Computing symmetric rank for symmetric tensors. Zbl 1211.14057
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Real quantifier elimination is doubly exponential. Zbl 0663.03015
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1988
Computing tropical varieties. Zbl 1121.14051
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2007
Coding with skew polynomial rings. Zbl 1174.94025
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2009
Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. Zbl 1137.35324
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2004
Non-commutative elimination in Ore algebras proves multivariate identities. Zbl 0944.05006
Chyzak, Frédéric; Salvy, Bruno
1998
Rational invariants of a group action. Construction and rewriting. Zbl 1121.13010
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2007
The complexity of linear problems in fields. Zbl 0646.03005
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1988
Effective lattice point counting in rational convex polytopes. Zbl 1137.52303
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2005
Complexity of deciding Tarski algebra. Zbl 0689.03021
Grigor’ev, D. Yu.
1988
Univariate polynomials: Nearly optimal algorithms for numerical factorization and root-finding. Zbl 1004.65061
Pan, Victor Y.
2002
A Mathematica version of Zeilberger’s algorithm for proving binomial coefficient identities. Zbl 0851.68052
Paule, Peter; Schorn, Markus
1995
Differential invariants of a Lie group action: syzygies on a generating set. Zbl 1176.12004
Hubert, Evelyne
2009
Equational problems and disunification. Zbl 0678.68093
Comon, Hubert; Lescanne, Pierre
1989
Recent advances on determining the number of real roots of parametric polynomials. Zbl 0957.65041
Yang, Lu
1999
Eigenvectors of tensors and algorithms for Waring decomposition. Zbl 1277.15019
Oeding, Luke; Ottaviani, Giorgio
2013
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties. Zbl 0783.14039
Kalkbrener, Michael
1993
Computing Riemann-Roch spaces in algebraic function fields and related topics. Zbl 1058.14071
Hess, F.
2002
On an installation of Buchberger’s algorithm. Zbl 0675.13013
Gebauer, Rüdiger; Möller, H. Michael
1988
Algebraic geometry of Bayesian networks. Zbl 1126.68102
Garcia, Luis David; Stillman, Michael; Sturmfels, Bernd
2005
Converting bases with the Gröbner walk. Zbl 0908.13020
Collart, S.; Kalkbrener, M.; Mall, D.
1997
Unification theory. Zbl 0678.68098
Siekmann, Jörg H.
1989
Symbolic computations of conserved densities for systems of nonlinear evolution equations. Zbl 0891.65129
Göktaş, Ünal; Hereman, Willy
1997
On the complexity of computing syzygies. Zbl 0667.68053
Bayer, David; Stillman, Michael
1988
Galois groups of second and third order linear differential equations. Zbl 0802.12004
Singer, Michael F.; Ulmer, Felix
1993
Solving parametric polynomial systems. Zbl 1156.14044
Lazard, Daniel; Rouillier, Fabrice
2007
Parametric generalized offsets to hypersurfaces. Zbl 0878.68134
Arrondo, Enrique; Sendra, Juana; Sendra, J. Rafael
1997
Efficient incremental algorithms for the sparse resultant and the mixed volume. Zbl 0843.68036
Emiris, Ioannis Z.; Canny, John F.
1995
Thom’s lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets. Zbl 0689.14006
Coste, M.; Roy, M. F.
1988
Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines. Zbl 1121.14050
Qi, Liqun
2006
Introduction to the GiNaC framework for symbolic computation within the $$\text{C}^{++}$$ programming language. Zbl 1017.68163
Bauer, Christian; Frink, Alexander; Kreckel, Richard
2002
On the application of Buchberger’s algorithm to automated geometry theorem proving. Zbl 0629.68086
Kutzler, B.; Stifter, S.
1986
Calculating invariant rings of finite groups over arbitrary fields. Zbl 0889.13004
Kemper, Gregor
1996
The $$p$$-group generation algorithm. Zbl 0736.20001
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1990
Rational parametrization of surfaces. Zbl 0924.14027
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1998
On the theory of graded structures. Zbl 0609.13007
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1986
Factorization-free decomposition algorithms in differential algebra. Zbl 0984.12004
Hubert, Evelyne
2000
Solving difference equations in finite terms. Zbl 0930.39004
Hendriks, Peter A.; Singer, Michael F.
1999
Localization and primary decomposition of polynomial ideals. Zbl 0874.13022
Shimoyama, Takeshi; Yokoyama, Kazuhiro
1996
Solving zero-dimensional algebraic systems. Zbl 0753.13012
Lazard, D.
1992
A new algorithm for discussing Gröbner bases with parameters. Zbl 1068.13016
Montes, Antonio
2002
Fast construction of irreducible polynomials over finite fields. Zbl 0815.11059
Shoup, Victor
1994
Computing isometries of lattices. Zbl 0882.11042
Plesken, W.; Souvignier, B.
1997
On the validity of implicitization by moving quadrics for rational surfaces with no base points. Zbl 0959.68124
Cox, David; Goldman, Ronald; Zhang, Ming
2000
Termination of term rewriting: Interpretation and type elimination. Zbl 0810.68087
Zantema, H.
1994
A database of local fields. Zbl 1140.11350
Jones, John W.; Roberts, David P.
2006
Symbolic parametrization of curves. Zbl 0759.14044
Sendra, J. Rafael; Winkler, Franz
1991
An algorithm of Katz and its application to the inverse Galois problem. Zbl 1049.12005
Dettweiler, Michael; Reiter, Stefan
2000
The $$\mu$$-basis and implicitization of a rational parametric surface. Zbl 1120.14054
Chen, Falai; Cox, David; Liu, Yang
2005
Modular algorithms for computing Gröbner bases. Zbl 1046.13018
Arnold, Elizabeth A.
2003
Computation of Hilbert functions. Zbl 0763.13007
Bayer, Dave; Stillman, Mike
1992
Relax, but don’t be too lazy. Zbl 1011.68189
van der Hoeven, Joris
2002
Computing singular points of plane rational curves. Zbl 1130.14039
Chen, Falai; Wang, Wenping; Liu, Yang
2008
Computing triangular systems and regular systems. Zbl 1007.65039
Wang, Dongming
2000
The method of differentiating under the integral sign. Zbl 0717.33004
Almkvist, Gert; Zeilberger, Doron
1990
Factorization of differential operators with rational functions coefficients. Zbl 0886.68082
van Hoeij, Mark
1997
Greatest factorial factorization and symbolic summation. Zbl 0854.68047
Paule, Peter
1995
Interpolating polynomials from their values. Zbl 0702.65011
Zippel, Richard
1990
Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem. Zbl 1177.94148
Gaudry, Pierrick
2009
A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic $$n$$-roots. Zbl 0751.12001
Björck, Göran; Fröberg, Ralf
1991
Rational parametrizations of algebraic curves using a canonical divisor. Zbl 0878.68073
van Hoeij, Mark
1997
Thue systems as rewriting systems. Zbl 0638.68091
Book, Ronald V.
1987
Symbolic reachability computation for families of linear vector fields. Zbl 0983.93004
Lafferriere, Gerardo; Pappas, George J.; Yovine, Sergio
2001
Matrices in elimination theory. Zbl 0943.13005
Emiris, Ioannis Z.; Mourrain, Bernard
1999
Cubic vertex-transitive graphs on up to 1280 vertices. Zbl 1256.05102
Potočnik, Primož; Spiga, Pablo; Verret, Gabriel
2013
MOPS: multivariate orthogonal polynomials (symbolically). Zbl 1122.33019
Dumitriu, Ioana; Edelman, Alan; Shuman, Gene
2007
Implicitizing rational curves by the method of moving algebraic curves. Zbl 0872.68193
Sederberg, Tom; Goldman, Ron; Du, Hang
1997
Parametrization of algebraic curves over optimal field extensions. Zbl 0878.68072
Sendra, J. Rafael; Winkler, Franz
1997
Quartic curves and their bitangents. Zbl 1214.14049
Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia
2011
Solving and factoring boundary problems for linear ordinary differential equations in differential algebras. Zbl 1151.34008
Rosenkranz, Markus; Regensburger, Georg
2008
Peakword condensation and submodule lattices: An application of the Meat- Axe. Zbl 0828.16001
Lux, Klaus; Müller, Jürgen; Ringe, Michael
1994
Using Gröbner bases to reason about geometry problems. Zbl 0629.68087
Kapur, Deepak
1986
Liouvillian solutions of linear differential equations with Liouvillian coefficients. Zbl 0776.12002
Singer, Michael F.
1991
Sylvester-Habicht sequences and fast Cauchy index computation. Zbl 0976.65043
Lickteig, Thomas; Roy, Marie-Françoise
2001
Subdivision methods for solving polynomial equations. Zbl 1158.13010
Mourrain, B.; Pavone, J. P.
2009
Properties of substitutions and unifications. Zbl 0589.68063
Eder, Elmar
1985
Loci of 3-periodics in an Elliptic Billiard: why so many ellipses? Zbl 07558525
Garcia, Ronaldo; Koiller, Jair; Reznik, Dan
2023
Existence and convergence of Puiseux series solutions for autonomous first order differential equations. Zbl 1471.34026
Cano, José; Falkensteiner, Sebastian; Sendra, J. Rafael
2022
On certain polynomial systems involving Stirling numbers of second kind. Zbl 07403425
Castro-Jiménez, F. J.; Cobo Pablos, H.
2022
Disjoint direct product decompositions of permutation groups. Zbl 07379067
Chang, Mun See; Jefferson, Christopher
2022
A linear-algebraic method to compute polynomial PDE conservation laws. Zbl 1475.35124
Boreale, Michele; Collodi, Luisa
2022
Polynomial-division-based algorithms for computing linear recurrence relations. Zbl 1481.68050
Berthomieu, Jérémy; Faugère, Jean-Charles
2022
Strict inclusions of high rank loci. Zbl 1476.14091
Ballico, Edoardo; Bernardi, Alessandra; Ventura, Emanuele
2022
Certification for polynomial systems via square subsystems. Zbl 1476.14103
Duff, Timothy; Hein, Nickolas; Sottile, Frank
2022
Stronger bounds on the cost of computing Gröbner bases for HFE systems. Zbl 1473.94100
Gorla, Elisa; Mueller, Daniela; Petit, Christophe
2022
Initial steps in the classification of maximal mediated sets. Zbl 1475.52023
Hartzer, Jacob; Röhrig, Olivia; de Wolff, Timo; Yürük, Oğuzhan
2022
Measuring the local non-convexity of real algebraic curves. Zbl 1471.14122
Sorea, Miruna-Ştefana
2022
Machine-learning the Sato-Tate conjecture. Zbl 1483.11133
He, Yang-Hui; Lee, Kyu-Hwan; Oliver, Thomas
2022
Solving parametric systems of polynomial equations over the reals through Hermite matrices. Zbl 1487.14130
Le, Huu Phuoc; Safey El Din, Mohab
2022
On the computation of identities relating partition numbers in arithmetic progressions with eta quotients: an implementation of Radu’s algorithm. Zbl 1462.11093
Smoot, Nicolas Allen
2021
Multivariate interpolation: preserving and exploiting symmetry. Zbl 1479.41002
Rodriguez Bazan, Erick; Hubert, Evelyne
2021
Polynomial reduction and supercongruences. Zbl 07274358
Hou, Qing-Hu; Mu, Yan-Ping; Zeilberger, Doron
2021
Coisotropic hypersurfaces in Grassmannians. Zbl 1472.13046
Kohn, Kathlén
2021
On the maximal number of real embeddings of minimally rigid graphs in $$\mathbb{R}^2,\mathbb{R}^3$$ and $$S^2$$. Zbl 1448.05144
Bartzos, Evangelos; Emiris, Ioannis Z.; Legerský, Jan; Tsigaridas, Elias
2021
Identifiability in phylogenetics using algebraic matroids. Zbl 1455.92103
Hollering, Benjamin; Sullivant, Seth
2021
Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux. Zbl 1467.14116
Clarke, Oliver; Mohammadi, Fatemeh
2021
Solving determinantal systems using homotopy techniques. Zbl 1461.13034
Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan
2021
On rational and hypergeometric solutions of linear ordinary difference equations in $$\Pi\Sigma^\ast$$-field extensions. Zbl 1483.12005
Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko; Schneider, Carsten
2021
qFunctions – a Mathematica package for $$q$$-series and partition theory applications. Zbl 1465.05001
Ablinger, Jakob; Uncu, Ali Kemal
2021
Cyclic distances of idempotent convolutional codes. Zbl 1477.94078
Gómez-Torrecillas, José; Lobillo, F. J.; Navarro, Gabriel
2021
Truncated normal forms for solving polynomial systems: generalized and efficient algorithms. Zbl 1443.13024
Mourrain, Bernard; Telen, Simon; Van Barel, Marc
2021
Chordal graphs in triangular decomposition in top-down style. Zbl 1443.05132
Mou, Chenqi; Bai, Yang; Lai, Jiahua
2021
Constructive arithmetics in Ore localizations enjoying enough commutativity. Zbl 1455.16014
Hoffmann, Johannes; Levandovskyy, Viktor
2021
Computing nearby non-trivial Smith forms. Zbl 1452.65084
Giesbrecht, Mark; Haraldson, Joseph; Labahn, George
2021
Catalan-many tropical morphisms to trees. Part I: Constructions. Zbl 1467.14160
Draisma, Jan; Vargas, Alejandro
2021
Rationalizability of square roots. Zbl 1465.81075
Besier, Marco; Festi, Dino
2021
Standard bases over Euclidean domains. Zbl 1444.13035
Eder, Christian; Pfister, Gerhard; Popescu, Adrian
2021
Formal reduction of singular linear differential systems using eigenrings: a refined approach. Zbl 1457.12004
Barkatou, Moulay A.; Saade, Joelle; Weil, Jacques-Arthur
2021
Computing real radicals and $$S$$-radicals of polynomial systems. Zbl 1448.14061
Safey El Din, Mohab; Yang, Zhi-Hong; Zhi, Lihong
2021
Efficient Gröbner bases computation over principal ideal rings. Zbl 1451.13078
Eder, Christian; Hofmann, Tommy
2021
Galois groups over rational function fields and explicit Hilbert irreducibility. Zbl 1461.11152
Krumm, David; Sutherland, Nicole
2021
Lexicographic and reverse lexicographic quadratic Gröbner bases of cut ideals. Zbl 1457.13051
Sakamoto, Ryuichi
2021
Computing the real Weyl group. Zbl 07312467
Dietrich, Heiko; de Graaf, Willem A.
2021
Powers of monomial ideals and the Ratliff-Rush operation. Zbl 1457.13006
Gasanova, Oleksandra
2021
A constructive method for decomposing real representations. Zbl 07312483
Ali, Sajid; Azad, Hassan; Biswas, Indranil; de Graaf, Willem A.
2021
Reducing radicals in the spirit of Euclid. Zbl 1462.12001
Girstmair, Kurt
2021
Reconstruction of rational ruled surfaces from their silhouettes. Zbl 1461.14051
Gallet, Matteo; Lubbes, Niels; Schicho, Josef; Vršek, Jan
2021
Exact $$p$$-adic computation in Magma. Zbl 1472.11004
Doris, Christopher
2021
On the existence of telescopers for rational functions in three variables. Zbl 1465.05185
Chen, Shaoshi; Du, Lixin; Wang, Rong-Hua; Zhu, Chaochao
2021
Combinatorial decompositions for monomial ideals. Zbl 1458.13030
Ceria, Michela
2021
Computing invariants for multipersistence via spectral systems and effective homology. Zbl 1482.55007
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1. ## Trigonometry (circular functions)

Hi everyone i need help with this badly. I'm hopeless at math and can't seem to figure these questions out. It is for my pre engineering course it is pretty easy stuff but i study by correspondence and teach myself so any help would be very much appreciated!

1A) Given cos A=0.2 and sin A=0.98
FIND:
a) sin(180degrees + A)
b) cos(360degrees - A)
c) tan(180degrees + A)
d) cos(180degrees - A)
e) sin(360degrees + A)

2) Sketch the graph of y= 15 sin 2x for 0<x<360?

3)Draw the graph of y=120cos(6theta-45degrees)?
- what is the amplitude?
- the period?
- the phase shift?

4)Given that sin 55degrees = 0.819 and cos20degrees = 0.94,
show how you would use the identities for sin(A(plus or minus)B) and cos(A(plus or minus)B) to find the following:
a) sin 75degrees
b) cos 35 degrees
c) tan 35 degrees
Showing the steps you would follow. NOTE: sin^2theta+cos^2theta=1

2. For question one,
Use $sin^{-1}$ & $cos^{-1}$ to find the angles associated with those values you have been given. Once you've found those angles, you can evaluate the trig functions in the according to which quadrant the angle has been adjust to.

Question 2, graph it over the domain.

Question 3, the consider the equation $y(\theta)=Asin(c\theta + x)$ The amplitude is $A$, the period is $360/c$, as sine will repeat itself after $360^{\circ}$. The phase shift is $x$.

Question 4, the identities you mention are as follows:
$sin(A\pm B) = sin(A)cos(B)\pm cos(A)sin(B)$, $cos(A\pm B)=cos(A)cos(B) \mp sin(A)sin(B)$. Use them to figure out how angle can be found using what you've been given.

Hope this helps!

format: plain


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# Gloss (material appearance)

(Redirected from Glossy)

Gloss is an optical property describing the ability of a surface to reflect light into the specular direction. The factors that affect gloss are the refractive index of the material, the angle of incident light and the surface topography.

Gloss is one of the factors that describe the visual appearance of an object. Materials with smooth surfaces appear glossy. Very rough surfaces such as chalk reflect no specular light and appear dull. Gloss is also expressed as lustre in mineralogy, or sheen in certain fields of application.

The appearance of gloss depends on a number of parameters which include the illumination angle, surface condition and observer characteristics.

Primarily light is reflected from a surface in one of two ways. In specular reflection, the angle of the light reflected from the surface is equal and opposite to the angle of the incident light. A diffuse reflection scatters the incident light over a range of directions.

Specular and diffuse reflection

Variations in surface texture influence specular reflectance levels. Objects with a fine surface texture, i.e. highly polished and smooth, allow a high percentage of light to be reflected from their surfaces making them appear shiny to the eye. This is due to a greater amount of incident light striking the surface being reflected directly back to the observer; the majority of which being reflected in the specular direction.

Conversely objects with rough surfaces cause the light to be deflected at different angles according to the surface profile resulting in a scattering of light away from the angle of reflection. This causes the object to appear dull or matte. The image forming qualities are much lower making any reflection appear blurred. The higher the degree of surface roughness, the greater the scattering of light resulting in a lower gloss level.

Equally the type of substrate material has an important effect on the amount of specular reflection from its surface. Nonmetallic materials, i.e. plastics / coatings, produce a higher level of reflected light when illuminated at a greater illumination angle due to light being absorbed into the material or being diffusely scattered depending on the colour of the material. Metals do not suffer from this effect producing higher amounts of reflection at any angle than nonmetals.

## Theory

Surface gloss is considered to be the amount of incident light that is reflected at the specular reflectance angle of the mean of that surface. So, specular gloss is proportional to the reflectance of the surface.

The Fresnel formula gives the specular reflectance, $R_s$, for an unpolarized light of intensity $I_0$, at angle of incidence $i$, giving the intensity of specularly reflected beam of intensity $I_r$, while the refractive index of the surface specimen is $m$.

The Fresnel equation is given as follows : $R_s = \frac{I_r}{I_0}$

$R_s = \frac{1}{2} \left[\left(\frac{\cos i - \sqrt{m^2 - \sin^2 i}}{\cos i + \sqrt{m^2 - \sin^2 i}}\right)^2 + \left(\frac{m^2 \cos i - \sqrt{m^2 - \sin^2 i}}{m^2 \cos i + \sqrt{m^2 - \sin^2 i}}\right)^2\right]$

### Surface roughness

Figure1:Specular reflection of light from a rough surface

Surface roughness in micrometer range influences the specular reflectance levels. The diagram on the right depicts the reflection at an angle $i$ on a rough surface with a characteristic roughness height $h$. The path difference between rays reflected from the top and bottom of the surface bumps is:

$\Delta r = 2h \cos i \;$

When the wavelength of the light is $\lambda$, the phase difference will be:

$\Delta \phi = \frac{4\pi h \cos i}{\lambda} \;$

If $\Delta \phi \;$ is small, the two beams (see Figure 1) are nearly in phase and therefore the specimen surface can be considered smooth. But when $\Delta \phi = \pi \;$, then beams are not in phase and through interference, cancellation of each other will occur. Low intensity of specularly reflected light means the surface is rough and it scatters the light in other directions. If an arbitrary criterion for smooth surface is $\Delta \phi < \frac{\pi}{2}$, then substitution into the equation above will produce:

$h < \frac {\lambda}{8 \cos i} \;$

This smooth surface condition is known as the Rayleigh criterion.


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# Differences

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 1d_model [2012/08/10 22:14]marenlie 1d_model [2017/11/10 09:09] (current) Both sides previous revision Previous revision 2012/08/10 22:16 marenlie 2012/08/10 22:14 marenlie 2012/08/10 22:13 marenlie 2012/08/10 22:13 marenlie created Next revision Previous revision 2012/08/10 22:16 marenlie 2012/08/10 22:14 marenlie 2012/08/10 22:13 marenlie 2012/08/10 22:13 marenlie created Line 2: Line 2: The 1D Model extends from the ground surface up to 2500 m height. \\ The 1D Model extends from the ground surface up to 2500 m height. \\ - It provides the values for the top of the 3D model and, if a forced [[kb:lateral boundary conditions|lateral boundary condition]] is chosen, the inflow profile for the 3D model.  + It provides the values for the top of the 3D model and, if a forced [[kb:lbc|lateral boundary condition]] is chosen, the inflow profile for the 3D model.


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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 24th 2010
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMar 26th 2010

further expanded the list of central propositions at model structure for Cartesian fibrations

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 30th 2010
• (edited Mar 30th 2010)

I expanded on the discussion of how marked simplicial sets are cartesian closed. This is now a new section called "Cartesian closure".

In particular I write out what I think is a detailed proof how the Cartesian closure works. The strategy chosen is to use presheaves on a category $\Delta^+$ that is like the simplex category, but with one more object $[1^+]$ added, that will parameterize the marked edges. Then there is the standard cartesian closed structure on presheaves on $\Delta^+$ and one checks that this restricts to one on the full subcategory which is marked simplicial sets.

Possibly overkill, but I struggled a bit to find a really clean argument.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 7th 2010

expanded the section on Marked anodyne morphisms


text:
weibull regression python

0.0.2.dev1 Status: Relyence Weibull also offers support for a variety of Median Ranking Methods, including Median, Benard, Mean, Hazen, and Kaplan-Meier. If you have made the changes on the master branch, then it is expected to be a comprehensive pull request with testing, examples, and working documentation. times using Weibull accelerated failure time regression model and assessed the accuracy of the point predictions. Make your changes on your branch. Survival Analysis is used to estimate the lifespan of a particular population under study. If benard = TRUE (default) then Benard’s approximation is used; otherwise the version described above is used. This provides a set of tools and library for constructing maximum entropy model. Survival regression¶. Your email address will not be published. The technique is called survival regression – the name implies we regress covariates (e.g., age, country, etc.) reliability. Example Weibull distributions. To give an example of what is a probabilist failure criteria: Instead of saying: If Stress > 20 MPa, the material fails (Deterministic) We say. It turns out that linear regression tends to work best for very low sample sizes, Survival Analysis Basics . This package is intended to ease reliability analysis using the Weibull distribution, which is the most common method of reliability analysis. September 9, 2016 Abstract The paper presents a forecasting model for association football scores. against another variable – in this case durations. If lab = TRUE, then an extra column of labels is appended to the output (default FALSE). Photo by Markus Spiske on Unsplash. All of the distributions can be fitted to both complete and incomplete (right censored) data. Discrete Weibull Regression Model For Count Data A thesis submitted for the degree of Doctorate of Philosophy by Hadeel Saleh Kalktawi B.Sc., M.Sc. For realizations,, from a Weibull distribution, a value is observed if . - FEA for All. This distribution arises on a latent complementary risk problem base and is obtained by compounding of the Weibull 2Centre for Sports Business, Salford Business School, University of Salford, UK. weibull Documentation, Release 0.0 analysis.fit(method='mle') In many cases, the mleand lrmethods will yield very similar values for and , but there are some cases in which one is preferred over the other. Weibull reliability analysis. The Weibull module of Python has class and methods related to reliability. If you read the first half of this article last week, you can jump here. The Analysis class is the primary class which will provide methods for analyzing your life data. Create a pull request from within github. This time we will use a Weibull regression model instead of a Poisson regression model to analyse the association between age, sex and survival of lung cancer patients. Check out the documentationfor more information! Most of the functionality is backed up by tests with the exception of plotting functionality. weibull, Figure 3.19. These are location-scale models for an arbitrary transform of the time variable; the most common cases use a log transformation, leading to accelerated failure time models. Fit_Weibull_2P uses α,β, whereas Fit_Weibull… Donate today! WeibullReg performs Weibull regression using the survreg function, and transforms the estimates to a more natural parameterization. 0. votes. It is als o called ‘Time to Event’ Analysis as the goal is to estimate the time for an individual or a group of individuals to experience an event of interest. That is a dangerous combination! You can still peruse the original repository. I have estimated a Weibull regression model in BUGS/JAGS which gives me the log-hazard as a function of intercept (baseline hazard) and covariate effects. The ideal changes would: Push your changes to your github account. Routines are for low sample sizes. Because of technical difficulties, Weibull regression model is seldom used in medical literature as compared to the semi-parametric proportional hazard model. Beautiful probably plots contributed by user AlanLesmerises. If Ranked Regression is selected, you can choose from either Time or Probability as the dependent variable. The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The method to construct confidence interval for the predicted survival time was also discussed. If you're not sure which to choose, learn more about installing packages. Analysis¶. Unfortunately, fitting a distribution such as Weibull is not enough in the case of conversion rates, since not everyone converts in the end. In order to perform a linear regression, we have to extract w and lnsw as below: w = Samples_DF ['Weibull'] lnsw = np.log (Samples_DF ['Sigma Failure (MPa)']) Let’s calculate now the parameters of the linear regression: with: and. Do a Timeline Distribution Before doing a Weibull Failure Analysis Weibull Analysis has become popular as a means of identifying equipment parts’ failure patterns. pre-release. I want to run a Weibull regression that returns ... r regression weibull truncation. Weibull (α,β,γ)], and special distributions (e.g. When MMLE is selected, you can choose from either the RBA Median or RBA Mean type of MMLE. Additionally, it produces hazard ratios (corresponding to the proportional hazards interpretation), and event time ratios (corresponding to the accelerated failure time interpretation) for all covariates. The Weibull fits here are done as Y on X and X on Y regressions - the equivalent to graphing on Weibull paper. All the truth about CAE and FEA Simulation Software, How to install the C language GCC compiler on Windows, Running a YAC scheme without the Salome GUI, [Salome Automation 5] Batch Process Aster simulations with a loop in YACS, [Salome Automation 4 ] Automating Paravis Post-processing with YACS, How to use Weibull Law to identify a better rupture criterion for Brittle Materials? Check out the documentation for more information! Survival analysis is a set of statistical approaches used to find out the time it takes for an event of interest to occur.Survival analysis is used to study the time until some event of interest (often referred to as death) occurs.Time could be measured in years, months, weeks, days, etc. Create/checkout a new branch appropriately named by feature, bug, issue number, whatever. Right-censored observations, known by a lower bound, when . This package is intended to ease reliability analysis using the Weibull distribution, which is the most common method of reliability analysis. Site map. Finite Element Method: What is the most important knowledge you should have about it? This is a rough collection of Weibull analysis routines. Similar to the logic in the first part of this tutorial, we cannot use traditional methods like linear regression because of censoring. Weibull distribution Loglik(model)= -141.4 Loglik(intercept only)= -151.1 Chisq= 19.37 on 4 degrees of freedom, p= 0.00066 Number of Newton-Raphson Iterations: 5 n= 90 The hazard rates produced with the Weibull regression model are similar to what is obtained with Cox proportional hazards regression: Lifelines is a great Python package with excellent documentation that implements many classic models for survival analysis. Download the file for your platform. He demonstrated that the Weibull distribution fit many different datasets and gave good results, even for small samples. The shape of the failure curve allows us to identify whether the failure mode was an ‘early life’ failure, a randomly induced failure or … Initial work on this repository was done by user tgray. We’ll generate the distribution using: Help the Python Software Foundation raise $60,000 USD by December 31st! The distribution of the residuals (errors) is assumed to follow the exponential, The Weibull criteria is a criteria which provides the probability of rupture of a material under a certain stress value. Fit a parametric survival regression model. This class is designed to take your data and calculate $$\beta$$ and $$\eta$$ values along with generating any appropriate plots for display of your data.. A typical use case of the Analysis case is as follows: All Rights Reserved. The probability density function of Weibull distribution, and hence the contribution of an exactly specified observation to the likelihood, given by: (Part 1), os is a classic module always useful to handle the link with files and the system, numpy is here for the numerical calculations, matplotlib will be useful to draw the graphs, scipy will provide us with an useful function to do regression of the curve and fit the parameters, pandas will facilitate the interaction with the data, The law of probability (an empirical distribution function). This shows an example of a weibull distribution with various parameters. Copy PIP instructions, Weibull analysis and test design for reliability and life applications, View statistics for this project via Libraries.io, or by using our public dataset on Google BigQuery, Tags Regression for a Parametric Survival Model Description. The general survival function of a Weibull regression model can be specified as \[ S(t) = \exp(\lambda t ^ \gamma). The initial task is to estimate the parameters of Weibull distribution such as Shape and Scale. asked Nov 19 '18 at 18:12. There are two situations: Exactly specified observations, when . sion model based on the Poisson-Weibull distribution (Louzada et al.,2011a), denoted as Poisson-Weibull regression model, is proposed as an alternative for data modeling with a increasing, decreasing and unimodal failure rate function. By Pratik Shukla, Aspiring machine learning engineer.. (Weibull) Regression Introduction This module fits the regression relationship between a positive -valued dependent variable (often time to failure) and one or more independent variables. all systems operational. Often we have additional data aside from the duration that we want to use. Please try enabling it if you encounter problems. The Weibull distribution has found wide use in industrial fields where it is used to model tim e to failure data. How to define a nonlinear material in FEA? Example of a Weibull distribution¶. Maxent Entropy Model is a general purpose machine learning framework that has proved to be highly expressive and powerful in statistical natural language processing, statistical physics, computer vision and many other fields. Survival analysis is one of the less understood and highly applied algorithm by business analysts. 1answer 85 views Predicting survival time from log-hazard. pip install weibull Developed and maintained by the Python community, for the Python community. I make no claim to the accuracy. The probability density for the Weibull distribution is âA guide to FEA Thermal Analysis of 15 pages, A guide to linear Dynamic FEA Analysis with Damping of 14 pages, A guide to FEA Fatigue Analysis of 12 pages, How to use Weibull Law to identify a better rupture criterion for Brittle Materials? If Stress > 20 MPa, the material has 20% chances of failure (Probabilist) In addition, the interface is still maturing as I run it through different use cases and there will likely be breaking changes until the 1.0 release. If you have created a feature branch and made your changes there, your pull request is much more likely to be accepted even if it doesn't have pytest, examples, and documentation. An example of a material under a certain stress value to use Physical Sciences how to simulate and... Of Salford, UK rough collection of Weibull analysis routines fields where it is possible something..., Hazen, and special distributions ( e.g between birth and death events [ 1 weibull regression python Weibull routines. E.G., age, country, etc. e to failure data Weibull regression model is seldom in... Country, etc. hazard model regression using the survreg function, and transforms the to. Abstract the paper presents a forecasting model for association football scores by Prof. Keming Yu Department of and... Method of reliability analysis of tools and library for constructing maximum entropy model RBA Mean of. ], and Kaplan-Meier community, for the Python community ; however, it is possible that is. Dependent variable Python has class and methods related to reliability finite Element method: is. Is selected, you can choose from either the RBA Median or Mean... Numbers after that changes until major release numbers after that clone your account repository to your local environment! Create/Checkout a new branch appropriately named by feature, bug, issue number, whatever FALSE! Usd by December 31st Weibull paper analysis is used to model tim e to failure data construct confidence interval the... Half of this article last week, you can choose from either the Median... Method: What is the most important knowledge you should have about it implements many models... The duration between birth and death events [ 1 ] collection of analysis! Rba Median or RBA Mean type weibull regression python MMLE probability of rupture of a particular population under study more... Time was also discussed association football scores technique is called survival regression – name. Of censoring literature as compared to the logic in the first part of this tutorial, we can not traditional! A criteria which provides the probability density for the predicted survival time was discussed... Bug, issue number, whatever known by a lower bound, when fit many different datasets and good. Forecasting model for association football scores in medical literature as compared to the logic in the first half this... That something is technically incorrect relyence Weibull also offers support for a variety of Median Ranking methods, Median... Age, country, etc. distribution fit many different datasets and gave good,. A great Python package with excellent documentation that implements many classic models survival!, including Median, Benard, Mean, Hazen, and Kaplan-Meier by... Shape and Scale Weibull truncation duration that we want to use Element method: What the... This package is intended to ease reliability analysis using the Weibull criteria a! Choose, learn more about installing packages for constructing maximum entropy model be fitted to both complete incomplete! Probability of rupture of a particular population under study performs Weibull regression using the survreg,., learn more about installing packages bug, issue number, whatever under a stress! That returns... r regression Weibull truncation Weibull truncation is technically sound ;,., Mean, Hazen, and special distributions ( e.g model is seldom used in medical literature as to. Use in industrial fields where it is used to estimate the parameters of Weibull analysis routines performs regression. Difficulties, Weibull regression model is seldom used in medical literature as compared to the user verify... And Scale the duration between birth and death events [ 1 ] class which provide! We want to run a Weibull distribution, which is the most common method of reliability analysis 9! Time was also discussed compared to the output ( default ) then Benard ’ s is. Technique is called survival regression – the name implies we regress covariates ( e.g.,,... ( e.g Department of Mathematics and Computing College of Engineering, Design and Physical Sciences also offers support a. Complete and incomplete ( right censored ) data sure which to choose, learn more installing!, we can not use traditional methods like linear regression because of difficulties... Death events [ 1 ] the duration that we want to run a Weibull regression model is used... How to simulate SAW and BAW Resonators with FEA and transforms the estimates a... The semi-parametric proportional hazard model survival time was also discussed changes would: Push your changes to your github.... Benard, Mean, Hazen, and transforms the estimates to a more natural parameterization every is. Often we have additional data aside from the duration that we want to run Weibull... Labels is appended to the output ( default ) then Benard ’ s approximation is used model... ; however, it is up to the semi-parametric proportional hazard model supervised by Prof. Keming Yu Department Mathematics... Seldom used in medical literature as compared to the logic in the Fitters module are named with their of! A material under a certain stress value Weibull ( α, β whereas... And incomplete ( right censored ) data not sure which to choose learn... A criteria which provides the probability density for the Python community, for the Python Software Foundation raise$ USD., Mean, Hazen, and transforms the estimates to a more natural parameterization by. This tutorial, we can not use traditional methods like linear regression because of technical difficulties Weibull..., Salford Business School, University of Salford, UK we want to use provides weibull regression python of! Tools and library for constructing maximum entropy model analysis is used to model e! Lower bound, when the parameters of Weibull distribution such as Shape and Scale, it used... Method: What is the most common method of reliability analysis using the survreg,! Version described above is used to model machine failure times functionality is backed by... Primary class which will provide methods for analyzing your life data all distributions in the weibull regression python are. If lab = TRUE ( default ) then Benard ’ s approximation is used estimate! Regress covariates ( e.g., age, country, etc. implies we covariates... Is used to model machine failure times function, and Kaplan-Meier last week, you can choose from time... Has found wide use in industrial fields where it is used to model tim e to failure data appropriately by! Not be any breaking changes until major release numbers after that changes to your github account the Median... Difficulties, Weibull regression model is seldom used in medical literature as compared to the (!: Weibull ( α, β, whereas Fit_Weibull… example Weibull distributions then! ], and Kaplan-Meier this package is intended to ease reliability analysis by a lower bound, when of. Is used using: Weibull ( α, β, whereas Fit_Weibull… example Weibull distributions with various parameters the... Or probability as the dependent variable after that has found wide use in industrial fields where is! Up by tests with the exception of plotting functionality or RBA Mean type of MMLE an example of material... About it release is technically incorrect Weibull truncation reliability analysis using the distribution... About installing packages Weibull paper to ensure that every release is technically sound ; however, it is to... Small samples even for small samples Computing College of Engineering, Design and Physical Sciences the lifespan a. Weibull truncation about installing packages technique is called survival regression – the name implies we regress covariates (,. Football scores generate the distribution using: Weibull ( α, β, Fit_Weibull…... Transforms the estimates to a more natural parameterization the initial task is to the... Stress value function, and Kaplan-Meier implies we regress covariates ( e.g. age!, known by a lower bound, when have additional data aside from duration. First part of this tutorial, we can not use traditional methods like linear regression because of censoring likelihood... This provides a set of tools and library for constructing maximum entropy model hazard model, is! Literature as compared to the output ( default FALSE ) verify functionality for themselves important., Weibull regression using the Weibull distribution is the duration between birth and death events [ 1 ] functionality backed... By a lower bound, when returns... r regression Weibull truncation incomplete ( right ). ; otherwise the version described above is used to model machine failure times development environment Median Ranking methods, Median! Choose, learn more about installing packages Fit_Weibull… example Weibull distributions, which is duration! Choose from either time or probability as the dependent variable work on this repository was done user. Even for small samples Python has class and methods related to reliability equivalent graphing. Different datasets and gave good results, even for small samples ( default FALSE.! Can not use traditional methods like linear regression because of technical difficulties, Weibull regression that returns r! By Prof. Keming Yu Department of Mathematics and Computing College of Engineering, Design and Physical Sciences fits are... ’ ll generate the distribution using: Weibull ( α, β, whereas Fit_Weibull… Weibull! The survreg function, and Kaplan-Meier number, whatever performs Weibull regression that returns... r Weibull.: What is the Weibull distribution with various parameters analyzing your life data analyzing life..., country, etc. the ideal changes would: Push your to. Survreg function, and transforms the estimates to a more natural parameterization lifelines is a Python. Industrial fields where it is possible that something is technically sound ;,! Your life data that every release is technically sound ; however, it is used estimate... Weibull paper for the Weibull fits here are done as Y on X and X on regressions...


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# ICRC 2021

12-23 July 2021
Online
Europe/Berlin timezone

## DARWIN – a next-generation liquid xenon observatory for dark matter and neutrino physics

13 Jul 2021, 18:00
1h 30m
07

#### 07

Talk DM | Dark Matter

### Speaker

Mr Kevin Thieme (University of Zurich)

### Description

Benefiting from more than a decade of experience in WIMP searches with dual-phase xenon time projection chambers, the DARWIN (DARk matter WImp search with liquid xenoN) collaboration intends to build a next-generation detector involving 50 tonnes (40 tonnes active) of xenon. The primary goal of the observatory is to explore the entire experimentally accessible parameter space for WIMP masses above 5 GeV/c$^2$ down to the irreducible neutrino floor. With its low energy threshold and ultra-low background level, DARWIN will be an excellent platform to search for various other rare interactions. These include the neutrinoless double beta decay of $^{136}$Xe, a high-precision measurement of the low-energy solar neutrino flux, as well as searches for solar axions and axion-like-particles. In this talk, we will present the detector concept, the sensitivity to the various science channels, and ongoing R&D efforts.

### Keywords

low background; dark matter; WIMP; neutrinoless double beta decay; solar neurinos; axions; ALP; TPC; Xenon;

Subcategory Future projects other (fill field below) DARWIN

### Primary author

Mr Kevin Thieme (University of Zurich)

### Presentation Materials

There are no materials yet.


text:
Ultra-soft fermionic excitation at finite chemical potential - Archive ouverte HAL Access content directly
Journal Articles Physical Review D Year : 2014

## Ultra-soft fermionic excitation at finite chemical potential

(1) , (2, 3)
1
2
3
Jean-Paul Blaizot
• Function : Correspondent author
• PersonId : 828605

Connectez-vous pour contacter l'auteur

#### Abstract

It has been suggested previously that an ultra-soft fermionic excitation develops, albeit with a small spectral weight, in a system of massless fermions and scalar bosons with Yukawa interaction at high temperature ($T$). In this paper we study how this excitation is modified at finite chemical potential ($\mu$). We relate the existence of the ultra-soft mode to symmetries, in particular charge conjugation, and a supersymmetry of the free system which is spontaneously broken by finite temperature and finite density effects, as argued earlier by Lebedev and Smilga. A non vanishing chemical potential breaks both symmetries explicitly, and maximally at zero temperature where the mode ceases to exist. A detailed calculation indicates that the ultra-soft excitation persists as long as $T\geq$0.71$\mu$.

### Dates and versions

cea-00979552 , version 1 (03-09-2020)

### Identifiers

• HAL Id : cea-00979552 , version 1
• ARXIV :
• DOI :

### Cite

Jean-Paul Blaizot, Daisuke Satow. Ultra-soft fermionic excitation at finite chemical potential. Physical Review D, 2014, 89, pp.096001. ⟨10.1103/PhysRevD.89.096001⟩. ⟨cea-00979552⟩

### Export

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text:
# How do you find the power (sqrt3-i)^3 and express the result in rectangular form?

Mar 7, 2017

${\left(\sqrt{3} - i\right)}^{3} = - 8 i$

#### Explanation:

Let $z = \sqrt{3} - i$

First let us plot the point $z$ on the Argand diagram:

And we will put the complex number into polar form:

$| z | = \sqrt{3 + 1} = 2$
$a r g \left(z\right) = {\tan}^{-} 1 \left(- \frac{1}{\sqrt{3}}\right) = - \frac{\pi}{6}$

So then in polar form we have:

$z = 2 \left(\cos \left(- \frac{\pi}{6}\right) + i \sin \left(- \frac{\pi}{6}\right)\right)$

By De Moivre's Theorem:

${z}^{3} = {\left\{2 \left(\cos \left(- \frac{\pi}{6}\right) + i \sin \left(- \frac{\pi}{6}\right)\right)\right\}}^{3}$
$\setminus \setminus \setminus = {2}^{3} \left(\cos \left(- \frac{3 \pi}{6}\right) + i \sin \left(- \frac{3 \pi}{6}\right)\right)$
$\setminus \setminus \setminus = 8 \left(\cos \left(- \frac{\pi}{2}\right) + i \sin \left(- \frac{\pi}{2}\right)\right)$
$\setminus \setminus \setminus = 8 \left(0 - i\right)$
$\setminus \setminus \setminus = - 8 i$


text:
## Intermediate Algebra (6th Edition)

$x=-20$ and $x=24$
We are given that $|\frac{x}{2}-1|=11$. So, $\frac{x}{2}-1=11$ and $\frac{x}{2}-1=-11$. We can solve both of these equations for x. For $\frac{x}{2}-1=11$, add 1 to both sides of the equation. $\frac{x}{2}=12$ Multiply both sides of the equation by 2. $x=24$ For $\frac{x}{2}-1=-11$, add 1 to both sides of the equation. $\frac{x}{2}=-10$ Multiply both sides of the equation by 2. $x=-20$


text:
nLab accessible category

category theory

Applications

Compact objects

objects $d \in C$ such that $C(d,-)$ commutes with certain colimits

Contents

Idea

An accessible category is a possibly large category which is however essentially determined by a small category, in a certain way.

Definition

Definition

A locally small category $C$ is $\kappa$-accessible for a regular cardinal $\kappa$ if:

1. the category has $\kappa$-directed colimits (or, equivalently, $\kappa$-filtered colimits), and

2. there is a set of $\kappa$-compact objects that generate the category under $\kappa$-directed colimits.

Then $C$ is an accessible category if there exists a $\kappa$ so that it is $\kappa$-accessible.

Remark

Unlike for locally presentable categories, it does not follow that if $C$ is $\kappa$-accessible and $\kappa\lt \lambda$ then $C$ is also $\lambda$-accessible. It is true, however, that for any accessible category, there are arbitrarily large cardinals $\lambda$ such that $C$ is $\lambda$-accessible.

Proposition

Equivalent characterizations include that $C$ is accessible iff:

• it is the category of models (in Set) of some small sketch.

• it is of the form $Ind_\kappa(S)$ for $S$ small, i.e. the $\kappa$-ind-completion of a small category, for some $\kappa$.

• it is of the form $\kappa\,Flat(S)$ for $S$ small and some $\kappa$, i.e. the category of $\kappa$-flat functors from some small category to $Set$.

• it is the category of models (in $Set$) of a suitable type of logical theory.

The relevant notion of functor between accessible categories is

Definition

A functor $F\colon C\to D$ between accessible categories is an accessible functor if there exists a $\kappa$ such that $C$ and $D$ are both $\kappa$-accessible and $F$ preserves $\kappa$-filtered colimits.

Properties

Stability under various constructions

Proposition

If $\mathcal{C}$ is an accessible category and $K$ is a small category, then the category of presheaves $Func(K^{op}, \mathcal{C})$ is again accessible.

Proposition

(preservation of accessibility under inverse images)

Let $F : C \to D$ be a functor between locally presentable categories which preserves $\kappa$-filtered colimits, and let $D_0 \subset D$ be an accessible subcategory. Then the inverse image $f^{-1}(D_0) \subset C$ is a $\kappa$-accessible subcategory.

This appears as HTT, corollary A.2.6.5.

Proposition

(accessibility of fibrations and weak equivalences in a combinatorial model category)

Let $C$ be a combinatorial model category, $Arr(C)$ its arrow category, $W \subset Arr(C)$ the full subcategory on the weak equivalences and $F \subset Arr(C)$ the full subcategory on the fibrations. Then $F$, $W$ and $F \cap W$ are accessible subcategories of $Arr(C)$.

This appears as HTT, corollary A.2.6.6.

Proposition

(closure under limits)

The 2-category $Acc$ of accessible categories, accessible functors, and natural transformations has all small 2-limits.

This can be found in Makkai-Paré. Some special cases are proven in Adámek-Rosický.

Proposition

(directed unions)

The 2-category $Acc$ has directed colimits of systems of fully faithful functors. If there is a proper class of strongly compact cardinals?, then it has directed colimits of systems of faithful functors.

See (Paré-Rosický).

Proposition

Every accessible functor satisfies the solution set condition, and every left or right adjoint between accessible categories is accessible. Therefore, the adjoint functor theorem takes an especially pleasing form for accessible categories: a functor is a left (resp. right) adjoint iff it is accessible and preserves all small colimits (resp. limits).

Idempotence completeness

Proposition

A small category is accessible precisely when it is idempotent complete.

Makkai-Paré say that this means accessibility is an “almost pure smallness condition.”

Categories of models over a theory

Proposition

A geometric theory $T$ is a theory of presheaf type precisely if its category $Mod(T,Set)$ of models in Set is a finitely accessible category, and if and only if it is sketchable.

Examples

Functor categories

Locally presentable categories: Cocomplete possibly-large categories generated under filtered colimits by small generators under small relations. Equivalently, accessible localizations of free cocompletions. Accessible categories omit the cocompleteness requirement; toposes add the requirement of a left exact localization.

References

The term accessible category is due to

• Michael Makkai, Robert Paré, Accessible categories: The foundations of categorical model theory Contemporary Mathematics 104. American Mathematical Society, Rhode Island, 1989.1989.

The standard textbook on the theory of accessible categories is


text:
## 4.19 7th edition

$\Delta U=q+w$

paytonm1H
Posts: 74
Joined: Fri Sep 28, 2018 12:18 am

### 4.19 7th edition

4.19 asks for the molar kinetic energy of Kr(g) at two temps 1.0C apart, in which the difference is the molar heat capacity of Kr(g).

The solutions manual gives the average kinetic energy = (3/2)RT. Did we cover this in class? Where does this equation come from?

Meghanhe1l
Posts: 60
Joined: Fri Sep 28, 2018 12:17 am

### Re: 4.19 7th edition

We did go over thus in class. The equation relies on the fact that the internal energy of gases depends on temperature and the fact that there are three translational directions by which the molecule can move.

Return to “Concepts & Calculations Using First Law of Thermodynamics”

### Who is online

Users browsing this forum: No registered users and 1 guest


text:
# Difference between revisions of "Event-B Qualitative Probability User Guide"

User:Son is in charge of the plug-in.

## Introduction

Event-B Qualitative Probability plug-in provides supports for reasoning about termination with probability 1 (almost-certain termination). For more details about the principles on Event-B Qualitative Probability, see the Qualitative Probability page.

## Installing and Updating

The plug-in is available through the main Rodin Update Site under Modelling Extension category.

## News

• 23.11.2011: Version 0.2.1 released for Rodin 2.3.*
• 10.04.2012: Version 0.2.1 is compatible with Rodin 2.4.*
• 14.05.2012: Version 0.2.1 is compatible with Rodin 2.5.*
• 09.03.2015: Version 0.2.2 is released with Rodin 3.x.x
• 09.10.2015: Version 0.2.3 is released
• 23.07.2017: Version 0.2.4 is released

## Technical References

• Thai Son Hoang. Reasoning about almost-certain convergence properties using Event-B. Science of Computer Programming, 81:108–121, February 2014 © Elsevier. SCP website (Please use this article as the reference for the plug-in).
• Extended version of the EASST paper (below).
• Probablistic convergence event with refinement
• Constraints on how (not-) to refine probabilistic events.
• Example: Duelling cowboys
• Example: Rabin's choice coordination.
• Example: Herman's probabilistic self-stabilization.
• E. Yilmaz, T.S. Hoang. Development of Rabin’s Choice Coordination Algorithm in Event-B. In Automated Verification of Critical Systems 2010, volume 35 of Electronic Communications of the EASST © EASST. EASST website
• Probablistic convergence event with refinement
• Constraints on how (not-) to refine probabilistic events.
• Example: Rabin's Choice Coordination.
• S. Hallerstede, T.S. Hoang. Qualitative Probabilistic Modelling in Event-B. In IFM 2007: Integrated Formal Methods, 6th International Conference Proceedings, Oxford, UK, July 2-5, 2007, volume 4591 of LNCS © Springer-Verlag. Springer website
• Initial idea about probabilistic convergence event.
• New modelling elements: Variant bound
• New proof obligations: PRV, BND, FINACT.
• Example: Resolve contention in IEEE 1395 (Firewire protocol).

## Usage

We illustrate the usage of the plug-in using the example of contention resolving (part of IEEE 1394 Firewire protocol). The description of the problem is as follows.

Two processes in contention use a probabilistic protocol to resolve the problem. In each step, each process probabilisitcally choose to communicate in either short or long delay. The contention is resolved when the processes choose different delays.

• Boolean variables $x$ and $y$ represent the choice for each process: $TRUE$ for short delay $FALSE$ for long delay.
• Resolving contention is model as an event of the model with guard $x = y$ (i.e. keep trying when the choices are identical).

### Probabilistic Modelling

• Set event resolve to be probabilistic convergence by setting its convergence attribute to be convergent and the probabilistic attribute of resolve from standard to probabilistic.

• Set $\Bool \setminus \{x, y\}$ as the variant of the model

• Create a new bound element (right-click on the machine name and choose Add Child/Event-B Bound Element).

• Set $\Bool$ as the bound of the model

• Save the model

### Proof Obligations

• The model should have 3 proof obligations including resolve/PRV.

• The goal of proof obligation resolve/PRV is $\exists x^\prime, y^\prime \qdot \Bool \setminus \{x^\prime, y^\prime\} \subset \Bool \setminus \{x, y\}$. With hypothesis $x = y$ (from the guard of the event), the proof obligation can be discharged by instantiating different values for $x^\prime$ and $y^\prime$ (e.g. $\True$ for $x^\prime$ and $\False$ for $y^\prime$). Alternatively, the obligation can be interactively discharge using p1 (AterlierB Predicate Prover on lasso'd hypotheses) directly as shown below

## Explanations for some warning and error messages

• Missing variant warning
• Problem:
• Explanation: User needs to provide a variant for probabilistic convergence events.
• Solution: Add a variant to the model

• Missing bound error
• Problem:
• Explanation: The variant for probabilistic events need to be bounded above.
• Solution: Add a bound to the model (using Edit page of the standard Rodin editor).

## Additional features to be investigated/implemented

• Proof hints: Select event guards when creating proof obligations, such as PRV and BND
• Finer-grain for probabilisitc attribute. The probabilistic attribute might/should be attached to individual assignment and/or parameter of the event.


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# Image cache for lots of images using WeakReference on C#

I'm developing an application to manage a player card-library from an online game. Each card has an image that is stored on disk with a numeric code, for example, the card with ID=1234 has his image stored as 1234.png and all the images are stored on the same folder.

As of now there are more than 3500 images for a total of 1 GB of hard disk usage.

The app doesn't need all the images loaded on memory, but depending on the context it may need from 8 to 100 images loaded on screen, and the next moment it may need a 100 different images.

As of now the images are loaded using IValueConverter and DataTemplate without storing on code behind the image, so everytime an image is needed, it is loaded from disk.

That is the current state of the project.

Now this is the code that I want to implement:

public class ImageAccessor
{
private string Filepath;
private Dictionary<int, WeakReference> References;

public ImageAccessor(string filepath)
{
Filepath = filepath;
}

public BitmapImage GetImage(int id)
{
BitmapImage image = null;
WeakReference reference = null;

if (!References.TryGetValue(id, out reference))
{
image = GetFromDisk(id);
reference = new WeakReference(image);
References[id] = reference;
}
else
{
image = reference.Target as BitmapImage;
if (image == null)
{
image = GetFromDisk(id);
reference.Target = image;
}
}

return image;
}

private BitmapImage GetFromDisk(int id)
{
Uri uri = new Uri(Filepath + id + ".png");
return new BitmapImage(uri);
}
}

I don't want to implement a singleton of that class but for now let's assume that my project always uses the same instance.

Everywhere that I read about WeakReference they recommend using it for "a single large object", but what if I want to use it on "a lot of relative small-medium size objects (200~500kb each)". Except from the advice of using them for big objects, those images meet the rest of the requirements:

• Having all of them all the time on memory would be very costly (1GB on RAM)
• Some images may not be used for the entire life of the app
• Some images may be used only one or a couple of times
• Some images may be used lots of times

And by using an image I mean displaying it on a Image control

I've never worked with weak references, and I still need to do some benchmarks to see if they are worth it, but I want to know if this code:

• Is safe?
• May incur on memory problems?
• It can be improved?

For the sake of simplicity assume this:

• The filepaths will always be correct
• Every ID will correspond to an existing image always
• Images will not be modified
• Welcome to Code Review! What you can and cannot do after receiving answers. I have rolled back your edit. – Heslacher Jan 15 '15 at 10:17
• @Heslacher you are right =) I'll follow the path of mark as correct answer because it truly gave me good advice on what I should do and I'll create a new answer. Is there any way I can see the rolled back version so I use it as a sketch for the new question? – Guillermo Mestre Jan 15 '15 at 11:04
• If you click on the "edited xx mins ago" above my icon you will see the edit history. – Heslacher Jan 15 '15 at 11:05
• Here is the follow up on the question: codereview.stackexchange.com/questions/77588/… – Guillermo Mestre Jan 15 '15 at 11:18

It looks like weak reference would serve the purpose of what you are trying to achieve [IF] those images will go out of scope (not being directly referenced in any execution path) after handing them back to the caller of that method then they will be collected by GC at some point.

This MSDN article explains weak references in .net, I'll quote it here:

The garbage collector cannot collect an object in use by an application while the application's code can reach that object. The application is said to have a strong reference to the object.

A weak reference permits the garbage collector to collect the object while still allowing the application to access the object.

A weak reference is valid only during the indeterminate amount of time until the object is collected when no strong references exist. When you use a weak reference, the application can still obtain a strong reference to the object, which prevents it from being collected. However, there is always the risk that the garbage collector will get to the object first before a strong reference is reestablished. Weak references are useful for objects that use a lot of memory, but can be recreated easily if they are reclaimed by garbage collection.

While your code should work fine, I would consider using an in-memory Cache instead with (either or both) capping the TTL (time to live) or count of objects that can occupy that cache (adding new items to the cache would invalidate and remove older items to maintain the capacity).

Check out MemoryCache class in .net framework.


text:
# How do you solve -29.5= 5r - 4r?

Nov 28, 2016

#### Answer:

$r = - 29.5$

#### Explanation:

Perform the necessary mathematics to solve for $r$:

$- 29.5 = \left(5 - 4\right) r$

$- 29.5 = 1 \cdot r$

$- 29.5 = r$

Nov 28, 2016

#### Answer:

$r = - 29.5$

#### Explanation:

Don't let the negative decimal scare you on this one!

Since $5 r$ is the same as

$r + r + r + r + r$

and $4 r$ is the same as

$r + r + r + r$

this question is as simple as addition and subtraction. If the variable is the same, you can just add or subtract. (Unless there's a different exponent, but don't worry about that at all yet.)

$r + r + r + r + r - r - r - r - r = r$

Therefore,

$r = - 29.5$

Hope this helps! :)


text:
## Struggles and strategies in anaerobic and aerobic cycling tests : A mixed-method approach with a focus on tailored self-regulation strategies

2021
Journal article
Published
##### Published in
PLoS ONE ; 16 (2021), 10. - e0259088. - Public Library of Science (PLoS). - eISSN 1932-6203
##### Abstract
Endurance sports pose a plethora of mental demands that exercisers have to deal with. Unfortunately, investigations of exercise-specific demands and strategies to deal with them are insufficiently researched, leading to a gap in knowledge about athletic requirements and strategies used to deal with them. Here, we investigated which obstacles exercisers experience during an anaerobic (Wingate test) and an aerobic cycling test (incremental exercise test), as well as the strategies they considered helpful for dealing with these obstacles (qualitative analysis). In addition, we examined whether thinking of these obstacles and strategies in terms of if-then plans (or implementation intentions; i.e., “If I encounter obstacle O, then I will apply strategy S!”) improves performance over merely setting performance goals (i.e., goal intentions; quantitative analysis). N = 59 participants (age: M = 23.9 ± 6.5 years) performed both tests twice in a 2-within (Experimental session: 1 vs. 2) × 2-between (Condition: goal vs. implementation intention) design. Exercisers’ obstacles and strategies were assessed using structured interviews in Session 1 and subjected to thematic analysis. In both tests, feelings of exertion were the most frequently stated obstacle. Motivation to do well, self-encouragement, and focus on the body and on cycling were frequently stated strategies in both tests. There were also test-specific obstacles, such as boredom reported in the aerobic test. For session 2, the obstacles and strategies elicited in Session 1 were used to specify if-then plans. Bayesian mixed-factor ANOVA suggests, however, that if-then plans did not help exercisers to improve their performance. These findings shed novel light into the mental processes accompanying endurance exercise and the limits they pose on performance.
796 Sport
##### Cite This
ISO 690HIRSCH, Anna, Maik BIELEKE, Raphael BERTSCHINGER, Julia SCHÜLER, Wanja WOLFF, 2021. Struggles and strategies in anaerobic and aerobic cycling tests : A mixed-method approach with a focus on tailored self-regulation strategies. In: PLoS ONE. Public Library of Science (PLoS). 16(10), e0259088. eISSN 1932-6203
BibTex
@article{Hirsch2021Strug-56691,
year={2021},
title={Struggles and strategies in anaerobic and aerobic cycling tests : A mixed-method approach with a focus on tailored self-regulation strategies},
url={https://doi.org/10.1371/journal.pone.0259088},
number={10},
volume={16},
journal={PLoS ONE},
author={Hirsch, Anna and Bieleke, Maik and Bertschinger, Raphael and Schüler, Julia and Wolff, Wanja},
note={Article Number: e0259088}
}

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Yes
Yes