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https://www.electricalexams.co/continuity-conductor-simply-wire/
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# ______ earth continuity conductor is simply the wire that connects an electrical system or installation to the earth.
______ earth continuity conductor is simply the wire that connects an electrical system or installation to the earth.
### Right Answer is: Earth continuity conductor
#### SOLUTION
Earth continuity conductors:- The earth continuity conductor is simply the wire that connects an electrical system or installation to the earth. This earth continuity conductor is connected to an earth electrode in the ground, so it provides a path for the current to travel to the earth.
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2022-01-25 14:21:55
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http://math.stackexchange.com/questions/292153/prove-that-for-a-0-lim-n-rightarrow-infty-fracann-0
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# Prove that for $a > 0$, $\lim_{n \rightarrow \infty}{\frac{a^n}{n!}=0}$ [duplicate]
Possible Duplicate:
How to prove that $\lim\limits_{n \to \infty} \frac{k^n}{n!} = 0$
Prove that for $a > 0$, $\lim_{n \rightarrow \infty}{\frac{a^n}{n!}=0}$. My attempt is since $$e^x=\sum_{n=0}^{\infty}{\frac{x^n}{n!}}$$ and the series converges for all $x \in \mathbb{R}$, by the test of divergence, $$\lim_{n \rightarrow \infty}{\frac{a^n}{n!}=0}.$$ Is my proof correct ? or are there any alternative ?
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## marked as duplicate by David Mitra, Jonas Meyer, dtldarek, Henry T. Horton, MicahFeb 1 '13 at 16:11
Yes, it is correct. – Siminore Feb 1 '13 at 15:40
It's correct, but uses a "sledgehammer" in my opinion. See this post and its links for more elementary methods. – David Mitra Feb 1 '13 at 15:41
This is also true for $a\leq 0$. – 1015 Feb 1 '13 at 15:42
The proof is correct but, as @DavidMitra says, you're using a sledgehammer :) So I don't find it very clean, you should be able to prove then that those series are equal to $e^x$ and that they converge, using taylor's theorem also does the trick but it's more advanced that the analysis corresponding to this. Final message: I would look for another proof, but if I saw this in an exam and nothing came to my mind, I would undoubtedly use yours and it would be correct. – MyUserIsThis Feb 1 '13 at 15:49
@DavidMitra : What do you mean ' sledgehammer' in this case ? – Idonknow Feb 1 '13 at 15:53
$$\frac{a^n}{n!} = \frac{a}{1}\frac{a}{2}\frac{a}{3}\ldots\frac{a}{n}$$
The exponential is simply the repeated product of $n$ number of $a$'s, whereas the factorial is the repeated product of $n$ ever-growing integers.
Therefore there must come a point, some $n \ge a$, after which all new factors of the denominator must be larger than the new factors of the numerator. This gap in the size of $a$ and $n$ will only continue to grow; the final factor itself, $\frac{a}{n}$, goes to $0$ as $n$ does, and so the product of an infinite amount of such small fractions has little choice but to follow suit and approach $0$.
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2015-05-23 13:56:32
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https://mathoverflow.net/questions/426085/proper-definition-of-ordered-field-in-constructive-mathematics/426153#426153
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# Proper definition of ordered field in constructive mathematics
The nLab article on ordered fields defines ordered fields to be a field $$K$$ with a strict linear order $$<$$ such that $$0 < 1$$ and for all elements $$a \in K$$ and $$b \in K$$, if $$a > 0$$ and $$b > 0$$ then $$a + b > 0$$ and $$a \cdot b > 0$$. The nLab article goes on to claim that this definition is also valid in constructive mathematics.
In classical mathematics, the relation $$\leq$$ defined as $$a \leq b := \neg (b < a)$$ could be proved to be a total order, and thus a lattice with binary meets $$\min$$ and joins $$\max$$. However, in constructive mathematics, $$\leq$$ cannot be proved to be a total order without excluded middle, although it still can be proved that $$\leq$$ is a partial order. As a result, it isn't provable that the field $$K$$ has lattice structure.
The nLab article does not provide any sources that ordered fields in constructive mathematics do not have a lattice structure $$(K, \leq, \min, \max)$$. On the other hand, I have found two sources in the constructive mathematics literature where the definition of ordered field explicitly has lattice structure:
• Univalent Foundations Project (2013), Homotopy Type Theory -- Univalent Foundations of Mathematics, section 11.2.1, pdf
• Auke B. Booij (2020), Analysis in univalent type theory (2020), section 4.1, pdf
Are there any references in the constructive mathematics literature which define ordered fields without the lattice structure?
Edit: The nLab article on ordered fields has been edited to say that in constructive mathematics there are multiple definitions of an ordered field. However, the original definition provided in the first paragraph remains unsourced.
• Presumably $\mathbb{R}$ should be an ordered field, and $\le$ isn’t necessarily a total order constructively on $\mathbb{R}$. Jul 5 at 18:19
• The issue isn't whether $\leq$ is a total order on the field $K$, but whether every pair of element of $K$ has a join and a meet, which is a weaker condition than $\leq$ being a total order. In the two sources above, the join is written as $\max$ and the meet is written as $\min$, even though $\leq$ is not a total order. Jul 5 at 18:20
• and in constructive mathematics, the join $\max$ and the meet $\min$ are well defined binary operations in the Cauchy real numbers and the Dedekind real numbers, but this follows not from the order structure on the Cauchy or Dedekind real numbers, but from the construction of the Cauchy and Dedekind real numbers in terms of Cauchy sequences of rational numbers and Dedekind cuts respectively. Jul 5 at 18:26
• @GeoffreyIrving just to alert you that the OP has a followup question to you, here: mathoverflow.net/q/426091/381 All this is prodded by nForum discussion here: nforum.ncatlab.org/discussion/14737/ordered-field/… Jul 5 at 19:46
• Answered (though the proofs are immediate). Jul 5 at 19:55
The word "constructive" has many variations. Some might even say that it's a moving target. This is not a one-size-fits-all situation, so I would contend that maybe the proper definition of ordered field changes from one context to context. This is not immediately clear since there are ubiquitous ordered fields like $$\mathbb Q$$, $$\mathbb R$$, and maybe more. The varieties of constructivism could conceivably be forced to agree on the basis of this common ground. This is not the case: here are two contexts which superficially appear to be closely connected but diverge on whether an ordered field should have a lattice structure or not.
The first context is constructive real analysis. Infinite sequences and their convergence are at the very heart of this topic. In this context, it is essential that $$\mathbb R$$ be Cauchy complete (at least in the weak sense that a Cauchy sequence with a modulus of convergence has a limit). In another answer, I argued that this ensures that $$\mathbb R$$ has a lattice structure. So, in this context, the lattice structure is quite natural and a practitioner might be tempted to disregard ordered fields without lattice structure as mere curiosities.
The second context is smooth infinitesimal analysis. This isn't what is normally meant by "constructivism" but the idea does have some constructive roots, albeit with perhaps stronger roots in nonstandard analysis. Also models of smooth infinitesimal analysis take the form of smooth toposes. [SIA is not really my cup of tea, perhaps someone with more intimate knowledge could provide a better defense or rebuttal(!) of SIA as a variety of constructivism.] Now, in any such model, $$\mathbb R$$ cannot have a lattice structure since that directly leads to functions that are not smooth, e.g. $$|x| = \max(x,-x)$$. Nevertheless, $$\mathbb R$$ has a reasonable ordered structure and a practitioner would like this to be an ordered field.
• (Some models have invertible infinitesimals but then $\mathbb R$ is also not archimedean. I think that is weird for other reasons. Models where infinitesimals are noninvertible seem to be more relevant.) Jul 7 at 21:43
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2022-12-04 06:30:44
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https://www.zbmath.org/authors/?q=rv%3A163
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## Boffi, Vinicio C.
Compute Distance To:
Author ID: boffi.vinicio-c Published as: Boffi, V. C.; Boffi, Vinicio; Boffi, Vinicio C.; Boffi, V. more...less External Links: Wikidata · IdRef
Documents Indexed: 53 Publications since 1960 5 Contributions as Editor Reviewing Activity: 219 Reviews Biographic References: 2 Publications Co-Authors: 30 Co-Authors with 48 Joint Publications 471 Co-Co-Authors
all top 5
### Co-Authors
8 single-authored 22 Spiga, Giampiero 4 Molinari, Vincenzo G. 4 Rossani, Alberto 3 Ganapol, Barry D. 3 Nonnenmacher, Theo F. 2 Dukek, Günter 2 Knoke, F. 2 Magnavacca, A. 2 Neunzert, Helmut 2 Santarelli, F. 2 Stramigioli, C. 2 Toscani, Giuseppe 1 Azmy, Yousry Y. 1 Bampi, Franco 1 Bowden, Robert L. 1 Caraffini, Gian Luca 1 Cercignani, Carlo 1 de Socio, Luciano M. 1 Franceschini, Valter 1 Gaffuri, Giovanni 1 Malvagi, F. 1 Mandrekas, J. 1 Menon, S. V. G. 1 Pescatore, Claudio 1 Pomraning, Gerald C. 1 Premuda, Francesco 1 Protopopescu, Vladimir A. 1 Rionero, Salvatore 1 Thomas, J. R. jun. 1 Torrisi, Mariano
all top 5
### Serials
9 Transport Theory and Statistical Physics 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Meccanica 6 Journal of Mathematical Physics 3 International Journal of Engineering Science 2 Physics of Fluids 2 Annals of Physics 2 Il Nuovo Cimento, X. Series 1 International Journal of Heat and Mass Transfer 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Il Nuovo Cimento, Supplemento, X. Series 1 Lecture Notes in Mathematics 1 Series on Advances in Mathematics for Applied Sciences 1 Il Nuovo Cimento, X. Series, B
all top 5
### Fields
33 Fluid mechanics (76-XX) 29 Statistical mechanics, structure of matter (82-XX) 22 Integral equations (45-XX) 6 Partial differential equations (35-XX) 6 Numerical analysis (65-XX) 5 General and overarching topics; collections (00-XX) 2 Integral transforms, operational calculus (44-XX) 2 Astronomy and astrophysics (85-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX)
### Citations contained in zbMATH Open
33 Publications have been cited 122 times in 72 Documents Cited by Year
An equation of Hammerstein type arising in particle transport theory. Zbl 0526.45009
Boffi, V. C.; Spiga, G.
1983
On the solutions to a class of nonlinear integral equations arising in transport theory. Zbl 0567.45008
Spiga, G.; Bowden, R. L.; Boffi, V. C.
1984
Nonlinear removal effects in time-dependent particle transport theory. Zbl 0528.76082
Boffi, V. C.; Spiga, G.
1983
Dynamics of a gas mixture in an extended kinetic theory. Zbl 0586.76137
Boffi, V. C.; Franceschini, V.; Spiga, G.
1985
Extended kinetic theory for gas mixtures in the presence of removal and regeneration effects. Zbl 0587.76130
Boffi, V. C.; Spiga, G.
1986
Rigorous iterated solutions to a nonlinear integral evolution problem in particle transport theory. Zbl 0502.76090
Boffi, V. C.; Spiga, G.
1982
Global solution to a nonlinear integral evolution problem in particle transport theory. Zbl 0507.70011
Boffi, V. C.; Spiga, G.
1982
Linear integral transformations generated by the three-dimensional neutron transport kernel. Zbl 0272.44004
Boffi, V. C.; Spiga, G.
1973
Evaluation of the electrical conductivity via the time-dependent integral Boltzmann equation. Zbl 0488.76082
Ganapol, B. D.; Boffi, V. C.
1981
Nonlinear diffusion of test particles in the presence of an external conservative force. Zbl 0501.76066
Boffi, V. C.; Spiga, G.
1982
Solution to the Boltzmann equation for monoenergetic neutrons in a slab. Zbl 0206.41502
Boffi, V. C.; Molinari, V. G.
1970
Convergence in the mean of solutions to the neutron integral Boltzmann equation in three-dimensional systems. Zbl 0254.45017
Boffi, V. C.; Premuda, F.; Spiga, G.
1973
Rigorous constructive solution to monodimensional Poiseuille and thermal creep flows. Zbl 0398.76061
Boffi, Vinicio; De Socio, Luciano; Gaffuri, Giovanni; Pescatore, Claudio
1976
The multiple collision method in solving the Boltzmann equation for time- dependent test particle transport. Zbl 0492.76078
Ganapol, B. D.; Boffi, V. C.
1980
On the slowing down of neutrons in an homogeneous infinite medium. Zbl 0105.43303
Boffi, Vinicio C.
1960
A Riemann-Hilbert boundary value problem in neutron transport theory. Zbl 0183.10203
Boffi, V. C.; Molinari, V. G.
1969
Exact time-dependent solutions to the nonlinear Boltzmann equation. Zbl 0613.76082
Boffi, V. C.; Spiga, G.
1986
Exact and asymptotic solution of the energy-dependent Boltzmann equation in the study of the neutron slowing down. Zbl 0128.23502
Boffi, V. C.; Knoke, F.; Molinari, V. G.; Scozzafava, R.
1964
The constant collision frequency model for electrical conductivity. Zbl 0528.76108
Ganapol, B. D.; Boffi, V. C.
1982
Integral transport theory for test particles in the presence of a time- dependent conservative force. Zbl 0577.76085
Boffi, V. C.; Nonnenmacher, T.
1984
Solution of a nonlinear integral equation arising in particle transport theory. Zbl 0579.65145
Boffi, V. C.; Spiga, G.; Thomas, J. R. jun.
1985
Solution methods for discrete-state Markovian initial value problems. Zbl 0709.65124
Boffi, V. C.; Malvagi, F.; Pomraning, G. C.
1990
On the Boltzmann system for a mixture of reacting gases. Zbl 0699.76087
Boffi, V. C.; Rossani, A.
1990
Solution to the monoenergetic neutron Boltzmann equation for a finite parallelepiped. Zbl 0289.45019
Boffi, V. C.; Molinari, V. G.
1971
Calculation of the number densities in an extended kinetic theory of gas mixtures. Zbl 0622.76081
Boffi, V. C.; Spiga, G.
1987
Lie group analysis for a multispecies, spatially inhomogeneous, mutually interacting gas mixture. Zbl 0756.76065
Azmy, Y. Y.; Boffi, V. C.; Mandrekas, J.; Protopopescu, V.
1992
On the exact theory of the slowing-down of neutrons in an infinite homogeneous medium. Zbl 0113.46504
Boffi, V.
1961
Slowing-down of neutrons by mixtures. Zbl 0125.25105
Boffi, V. C.; Knoke, F.
1965
Anisotropy of the scattering in space-time neutron transport theory. Zbl 0144.48305
Boffi, V. C.; Trombetti, T.
1967
A first-order linear differential-difference equation with N delays. Zbl 0189.40102
Boffi, V.; Scozzafava, R.
1967
Methods of similarity analysis in the study of nonlinear dynamics of a gas mixture. Zbl 0716.35066
Boffi, Vinicio C.; Torrisi, Mariano
1990
Similarity solutions to a nonlinear model for the nuclear breeding process. Zbl 0783.35032
Boffi, V. C.; Caraffini, G. L.
1993
Transients of current density in linear particle transport theory. Zbl 0636.76078
Boffi, V. C.; Rossani, A.
1986
Similarity solutions to a nonlinear model for the nuclear breeding process. Zbl 0783.35032
Boffi, V. C.; Caraffini, G. L.
1993
Lie group analysis for a multispecies, spatially inhomogeneous, mutually interacting gas mixture. Zbl 0756.76065
Azmy, Y. Y.; Boffi, V. C.; Mandrekas, J.; Protopopescu, V.
1992
Solution methods for discrete-state Markovian initial value problems. Zbl 0709.65124
Boffi, V. C.; Malvagi, F.; Pomraning, G. C.
1990
On the Boltzmann system for a mixture of reacting gases. Zbl 0699.76087
Boffi, V. C.; Rossani, A.
1990
Methods of similarity analysis in the study of nonlinear dynamics of a gas mixture. Zbl 0716.35066
Boffi, Vinicio C.; Torrisi, Mariano
1990
Calculation of the number densities in an extended kinetic theory of gas mixtures. Zbl 0622.76081
Boffi, V. C.; Spiga, G.
1987
Extended kinetic theory for gas mixtures in the presence of removal and regeneration effects. Zbl 0587.76130
Boffi, V. C.; Spiga, G.
1986
Exact time-dependent solutions to the nonlinear Boltzmann equation. Zbl 0613.76082
Boffi, V. C.; Spiga, G.
1986
Transients of current density in linear particle transport theory. Zbl 0636.76078
Boffi, V. C.; Rossani, A.
1986
Dynamics of a gas mixture in an extended kinetic theory. Zbl 0586.76137
Boffi, V. C.; Franceschini, V.; Spiga, G.
1985
Solution of a nonlinear integral equation arising in particle transport theory. Zbl 0579.65145
Boffi, V. C.; Spiga, G.; Thomas, J. R. jun.
1985
On the solutions to a class of nonlinear integral equations arising in transport theory. Zbl 0567.45008
Spiga, G.; Bowden, R. L.; Boffi, V. C.
1984
Integral transport theory for test particles in the presence of a time- dependent conservative force. Zbl 0577.76085
Boffi, V. C.; Nonnenmacher, T.
1984
An equation of Hammerstein type arising in particle transport theory. Zbl 0526.45009
Boffi, V. C.; Spiga, G.
1983
Nonlinear removal effects in time-dependent particle transport theory. Zbl 0528.76082
Boffi, V. C.; Spiga, G.
1983
Rigorous iterated solutions to a nonlinear integral evolution problem in particle transport theory. Zbl 0502.76090
Boffi, V. C.; Spiga, G.
1982
Global solution to a nonlinear integral evolution problem in particle transport theory. Zbl 0507.70011
Boffi, V. C.; Spiga, G.
1982
Nonlinear diffusion of test particles in the presence of an external conservative force. Zbl 0501.76066
Boffi, V. C.; Spiga, G.
1982
The constant collision frequency model for electrical conductivity. Zbl 0528.76108
Ganapol, B. D.; Boffi, V. C.
1982
Evaluation of the electrical conductivity via the time-dependent integral Boltzmann equation. Zbl 0488.76082
Ganapol, B. D.; Boffi, V. C.
1981
The multiple collision method in solving the Boltzmann equation for time- dependent test particle transport. Zbl 0492.76078
Ganapol, B. D.; Boffi, V. C.
1980
Rigorous constructive solution to monodimensional Poiseuille and thermal creep flows. Zbl 0398.76061
Boffi, Vinicio; De Socio, Luciano; Gaffuri, Giovanni; Pescatore, Claudio
1976
Linear integral transformations generated by the three-dimensional neutron transport kernel. Zbl 0272.44004
Boffi, V. C.; Spiga, G.
1973
Convergence in the mean of solutions to the neutron integral Boltzmann equation in three-dimensional systems. Zbl 0254.45017
Boffi, V. C.; Premuda, F.; Spiga, G.
1973
Solution to the monoenergetic neutron Boltzmann equation for a finite parallelepiped. Zbl 0289.45019
Boffi, V. C.; Molinari, V. G.
1971
Solution to the Boltzmann equation for monoenergetic neutrons in a slab. Zbl 0206.41502
Boffi, V. C.; Molinari, V. G.
1970
A Riemann-Hilbert boundary value problem in neutron transport theory. Zbl 0183.10203
Boffi, V. C.; Molinari, V. G.
1969
Anisotropy of the scattering in space-time neutron transport theory. Zbl 0144.48305
Boffi, V. C.; Trombetti, T.
1967
A first-order linear differential-difference equation with N delays. Zbl 0189.40102
Boffi, V.; Scozzafava, R.
1967
Slowing-down of neutrons by mixtures. Zbl 0125.25105
Boffi, V. C.; Knoke, F.
1965
Exact and asymptotic solution of the energy-dependent Boltzmann equation in the study of the neutron slowing down. Zbl 0128.23502
Boffi, V. C.; Knoke, F.; Molinari, V. G.; Scozzafava, R.
1964
On the exact theory of the slowing-down of neutrons in an infinite homogeneous medium. Zbl 0113.46504
Boffi, V.
1961
On the slowing down of neutrons in an homogeneous infinite medium. Zbl 0105.43303
Boffi, Vinicio C.
1960
all top 5
### Cited by 94 Authors
21 Boffi, Vinicio C. 16 Spiga, Giampiero 6 Darwish, Mohamed Abdalla 3 Pomraning, Gerald C. 3 Rossani, Alberto 3 Vianello, Marco 2 Gaffuri, Giovanni 2 Ganapol, Barry D. 2 Garcia, Roberto D. M. 2 Meleshko, Sergey V. 2 Nonnenmacher, Theo F. 2 Premuda, Francesco 2 Schürrer, Ferdinand 2 Sommariva, Alvise 2 Suriyawichitseranee, Amornrat 1 Afonso, Suzete Maria 1 Ali, Javid 1 Alyami, Maryam Ahmed 1 Azevedo, Juarez S. 1 Bobylev, Alexandre Vasiljévitch 1 Bowden, Robert L. 1 Busoni, Giorgio 1 Caballero, Josefa 1 Caraffini, Gian Luca 1 Cardinali, Tiziana 1 Cercignani, Carlo 1 Cornille, Henri 1 da Silva, Mariana P. G. 1 Das, Anupam 1 De Florio, Mario 1 de Socio, Luciano M. 1 Dehesa, Jesús S. 1 Dogbé, Christian 1 Dorning, John J. 1 Dukek, Günter 1 Elabsy, A. M. 1 Espesset, Aude 1 Fotros, Forough 1 Frosali, Giovanni 1 Furfaro, Roberto 1 Gardini, Laura 1 Germano, Bruna 1 Grandjean, Philippe 1 Griehsnig, P. 1 Grigor’ev, Yu. N. 1 Guerriero, Gabriele 1 Hadj Amor, Sana 1 Haque, Inzamamul 1 Hazarika, Bipan 1 Henderson, Johnny Lee 1 Holloway, James Paul 1 İnönü, Erdal 1 Khchine, Abdelmjid 1 Knoke, F. 1 Küchler, Uwe 1 Kügerl, Georg 1 Lampis, Maria 1 Li, Gang 1 Lupini, Renzo 1 Madkour, M. A. 1 Magnavacca, A. 1 Majorana, Armando 1 Malvagi, F. 1 Mangiarotti, Luigi 1 Maniar, Lahcen 1 Marano, Salvatore Angelo 1 Marinescu, Dorin 1 Mensch, Beatrice 1 Messia, Maria Grazia 1 Molinari, Vincenzo G. 1 Ntouyas, Sotiris K. 1 Oliveira, Saulo Pomponet 1 Panda, Sumati Kumari 1 Prelati, G. P. 1 Prinja, Anil K. 1 Ricci, Paolo Emilio 1 Richman, Mark W. 1 Rionero, Salvatore 1 Rubbioni, Paola 1 Rupp, Daniela 1 Rzepka, Beata 1 Sadarangani, Kishin B. 1 Schaler, M. 1 Schiassi, Enrico 1 Sgarra, Carlo 1 Shahsavaran, Ahmad 1 Siewert, Charles E. 1 Spiga, Marco 1 Taoudi, Mohamed Aziz 1 Traiki, Abdelhak 1 Trombetti, Tullio 1 Yáñez, Rafael J. 1 Zarzo, Alejandro 1 Zhu, Tao
all top 5
### Cited in 28 Serials
12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Meccanica 8 Transport Theory and Statistical Physics 7 Journal of Mathematical Physics 4 Journal of Integral Equations and Applications 3 Journal of Statistical Physics 2 Computers & Mathematics with Applications 2 Journal of Mathematical Analysis and Applications 2 Il Nuovo Cimento, X. Series 2 Journal of Function Spaces 1 Applicable Analysis 1 Astrophysics and Space Science 1 Journal of Mathematical Biology 1 Rocky Mountain Journal of Mathematics 1 Physics of Fluids, A 1 Chaos, Solitons and Fractals 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Stochastics and Stochastics Reports 1 Computational and Applied Mathematics 1 Journal of Applied Mechanics and Technical Physics 1 Communications in Nonlinear Science and Numerical Simulation 1 Mathematical Modelling and Analysis 1 Fixed Point Theory and Applications 1 Discrete and Continuous Dynamical Systems. Series S 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
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### Cited in 20 Fields
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### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
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2022-07-07 14:19:30
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http://tex.stackexchange.com/questions/97888/multibib-how-to-reset-references-counter
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# Multibib: how to reset references counter?
Im using a complex template to write my document. It is old and I'm having a problem. I have two separate reference list, "Internet References" and "Literature". The problem is that the references counter "[3]" on "internet References" always starts with number 3 and it should start from 1 "1". The template uses multibib package. My biblio files are: weblinks.bib and literature.bib (main file is literature.bib). I digged in all files of my project and can not find any counter that I can reset, so I assume that is some kind of "internal" counter.
Anyone knows how to reset that special counter?
In main file Diploma_Thesis.tex:
% For the two different reference lists ...
\usepackage{multibib}
.
.
\label{lit}
\bibliography{literature}
% the style of bibliography
% start a new page
\newpage
\label{wlit}
\newpage
The result in Literature section on PDF:
-
Did you try to delete aux files? – Sigur Feb 12 '13 at 15:35
Welcome to TeX.sx! Would you be reluctant to switch to BibLaTeX? – Corentin Feb 12 '13 at 15:35
Sigur: I deleted all aux file in my project but it keeps starting at index 3. – eduardo Feb 12 '13 at 15:40
Corentin: I would change but as I said it is a complex and old template (which use to write my Master Thesis) and it seems to me to be hard to do. If you can give me some hints I would be glad! – eduardo Feb 12 '13 at 15:42
Probably \usepackage[resetlabels]{multibib} is what you need. – egreg Feb 12 '13 at 16:08
The package multibib provides an option just for that:
\usepackage[resetlabels]{multibib}
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2015-07-03 16:04:23
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https://www.physicsforums.com/threads/ionization-and-electron-acquisition-help.140781/
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# Ionization and electron acquisition help!
1. Oct 30, 2006
### chuck35lopez
I have a couple questions on my homework that I am stuck on.
1. Write the equations that represent the first three ionizations of the aluminum atom. Be sure to include phases and charges.
2. Write the equations that represent the acquisition of the two electrons of the sulfur atom forming the sulfide (S 2-) ion. Be sure to include phases and charges.
Thanks in advance to anybody who can help! I don't mesh well with my teacher!
2. Oct 30, 2006
### geoffjb
What do you have so far? Where are you stuck?
3. Oct 30, 2006
### chuck35lopez
I don't even know where to start with this! I have never had problems with a teacher until this one, and I just cannot understand what she explains at all.
4. Oct 30, 2006
### geoffjb
Okay. Do you understand the process of ionization? If not, I would read up on ionization and ionization potential first.
Basically, you're taking an atom/ion and adding energy (ionization energy/potential) to remove an electron.
5. Oct 30, 2006
### chuck35lopez
OK, I understand ionization, but I what I dont get is what my teacher is asking for, and how do I set up an equation?
6. Oct 30, 2006
### geoffjb
Your teacher is asking you to write the ionization formulae from $\text{Al} \xrightarrow~\text{Al}^{+}$, $\text{Al}^{+} \xrightarrow~\text{Al}^{2+}$, and $\text{Al}^{2+} \xrightarrow~\text{Al}^{3+}$. Phase means physical state (solid/liquid/gas). Include energies (e.g. 2600 kJ/mol) in the equations, and ensure they're on the proper side of the formula.
Last edited: Oct 31, 2006
7. Oct 31, 2006
### chuck35lopez
Alright, I got it done. It wasn't easy, but its finished. LOL. Thank you very much for the help!
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2016-10-28 18:44:45
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https://physics.stackexchange.com/questions/80934/harmonic-oscillator-quantum-mechanics/80937
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# Harmonic Oscillator (Quantum Mechanics)
Griffiths uses an algebraic "brute force" technique to solve the harmonic oscillator. I'm somewhat confused regarding a few parts.
$$\frac{1}{2m}[p^2 + (m \omega x)^2] \psi = E \psi$$
$H = \frac{1}{2m}[p^2 + (m \omega x)^2]$
We are about to factor $H$, noting that the numerical equavilant is $u^2 + v^2 = (iu+v)(-iu+v)$. We now define $a_{\pm} = \frac{1}{\sqrt{2 \hbar m \omega }}(\pm ip+m \omega x)$
Skipping through the commutator, I don't understand how we can say: $a_+ a_ - = \frac{1}{\hbar \omega}H + \frac{1}{2}$
Looking at the original equation, we factored $[p^2 + (m \omega x)^2]$, so we can replace this with $a_+ a_ -$. Under this, couldn't we just say that $H = \frac{1}{2m} (a_+ a_ -)$
My second question has to do with the statement (this is a direct quote): Now, here comes the crucial step: I claim that if $\psi$ satisfies the Schrödinger equation with energy $E$, (that is: $H \psi = E \psi$), then $a_+ \psi$ satisfies the Schrödinger equation with energy $(E+ \hbar \omega)$
I don't understand why we're multiplying $\psi$ by a piece of Hamiltonian, and the by the Hamiltonian again.
• For the second part: compute $[H,a_{+}]$. What do you get? Apply this commutator to the wavefunction. – Pricklebush Tickletush Oct 16 '13 at 6:57
• $[H,a_+] = Ha - aH$ Using a test function: $-\frac{\hbar}{i}\frac{d}{dx}(\frac{f(x)}{\sqrt{2 \hbar m \omega}} (\pm ip +m \omega x)) + \frac{1}{\sqrt{2\hbar m \omega}} (\pm i p +m \omega x) \frac{df}{dx}$ – Astrum Oct 16 '13 at 7:25
I think perhaps what you're missing is in the "skipping through the commutator" part. Do you understand where we get this equation (try computing it yourself, if not): $$a_{-}a_{+} = \frac{1}{2 \hbar m \omega}[p^{2} + (m\omega x)^{2}] - \frac{i}{2\hbar}[x,p]$$ Now, the canonical commutator, I'm sure you noticed (as it's boxed on the same page in Griffiths) is $[x,p] = ih$. Insert this into the above equation and note that we now have: $$a_{-}a_{+} = \frac{1}{2 \hbar m \omega}[p^{2} + (m\omega x)^{2}] + \frac{1}{2}$$ All you need to do from there recognize the first term as $\frac{1}{h\omega}H$.
Looking at the original equation, we factored $[p^{2}+(m\omega x)^{2}]$, so we can replace this with a+a−. Under this, couldn't we just say that $H=\frac{1}{2}(a_{+}a_{−})$
Careful here... remeber that $p$ and $x$ in this expression (and in the Hamiltonian generally) are operators, not scalars. This is why our "intuitive guesses" of $a_{\pm}$ are not exact factors of $[p^{2}+(m\omega x)^{2}]$, and why the canonical commutator above is important.
Edit: I just noticed that Griffiths does include this intermediate step in computing $a_{-}a_{+}$: $$a_{-}a_{+} = \frac{1}{2 \hbar m \omega}[p^{2} + (m\omega x)^{2}-im\omega(xp-px)]$$ Notice that if $x$ and $p$ were scalars, the rightmost term would be 0, and your intuition about $a_{-}$ and $a_{+}$ being "factors" would be correct. Once you realize they are operators, however, it's obvious that we need to substitute $[x,p] = xp-px = ih$.
• I did understand the how/why of the canonical commutator, and I see that doing the multiplication out for $a_+ a_-$ gives you $a_+ a_ - = \frac{1}{\hbar \omega}H + \frac{1}{2}$. I see, so we used $a_{\pm}$ to find the exact factors of $H$, which involved the canonical commutator. – Astrum Oct 16 '13 at 7:34
• We're actually not particularly concerned with the exact factors of $H$. We're primarily concerned with what the operators $a_{-}$ and $a_{+}$ do to the wavefunction $\psi$. – RGMyr Oct 16 '13 at 7:43
• Now we can focus on the second of my questions. I understand why $H= \hbar \omega (a_+ a_- + \frac{1}{2})$ The reason behind the next step leaves me puzzled - $H(a_+ \psi)= \hbar \omega (a_+ a_- + \frac{1}{2})(a_+ \psi)$ The algebra that follows is clear, the motivation for $(a_+ psi)$ is not. – Astrum Oct 16 '13 at 7:47
• The idea is to write the Hamiltonian in terms of these operators, and then show that for any solution of the Schrodinger EQ $\psi_{n}$, $a_{-}\psi_{n}$ and $a_{+}\psi_{n}$ are also solutions, and have the energy you mentioned in your post. – RGMyr Oct 16 '13 at 7:50
• Sorry, typed that before I saw your specific question. Do you understand what is meant by an "eigenvalue equation?" (i.e. $H\psi = E\psi$). This is a ubiquitous concept in QM (and linear algebra in general), and it's very important to understand what that means. – RGMyr Oct 16 '13 at 7:52
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2019-12-09 23:52:24
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https://socratic.org/questions/how-do-you-write-the-equation-4x-10y-6-in-standard-form-and-identify-a-b-c
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# How do you write the equation 4x=10y+6 in standard form and identify A, B, C?
Oct 20, 2017
Standard form: $4 x - 10 y = 6$
$a \to 4$
$b \to - 10$
$c \to 6$
#### Explanation:
First, we know that the standard form of a linear equation (the equation shown here) is ax + by = c.
The equation is written as ax = by + c at the moment, so we need to move the by back with the ax. So you would minus the by from both sides of the equation and get the following, which is in standard form:
$4 x - 10 y = 6$
Since we know that the form now is ax + by = c, we can find what a, b, and c are.
So here:
$a \to 4$
$b \to - 10$
$c \to 6$
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2022-05-26 23:15:56
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https://tex.stackexchange.com/tags/description/hot
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# Tag Info
### How to add bullets to description lists?
You can use the itemization function (https://www.sharelatex.com/learn/Lists) \begin{itemize} \item one. \item two. \item three. \end{itemize} And the output:
• 491
Accepted
### How can I sort a list numerically?
This approach automatically orders the items by year or any other number, by using an external list on an .csv file. \documentclass{article} \usepackage{filecontents} % To create an external .csv file ...
• 3,905
### No indent in description list
Just to add to @Werner's excellent answer: If you have very long labels in a description environment, sometimes it actually looks nicest to have the text wrap underneath the start of the labels, like ...
• 3,652
Accepted
### How to align tcolorbox at the top?
Updated version After the edit with the question, I propose a different approach here not using a list to place the labels but reducing the width for the tcolorbox and using an optional argument (it ...
• 479k
Accepted
### Reduce indent in description in beamer
You can modify the indention with \setbeamersize{description width=0.57cm}, just play around to whatever value you need. \documentclass[14pt,handout]{beamer} \setbeamersize{description width=0.57cm} ...
Accepted
### How to change colon into dot in description list?
You have to redefine \descriptionlabel, nothing that enumitem is supposed to be able to do. This is the standard definition \newcommand{\descriptionlabel}[1]{% \hspace\labelsep \upshape\bfseries #1:...
• 984k
### How can I sort a list numerically?
You could make use of the glossaries package as shown in the following example: \documentclass{article} \usepackage[automake, nonumberlist]{glossaries} \newglossaryentry{1912}{name={1912}, ...
• 60.3k
Accepted
### Underlining an item
I propose this, with the help of the framed package, slightly tweaking the leftbar environment. If you don't want grey lines, it's easy to remove the colour. Using xparse, I define a \course command, ...
• 259k
### How can I sort a list numerically?
If you prefer the solution to be as close to your syntax as possible: \documentclass{article} \usepackage{expl3} \usepackage{xparse} \usepackage{enumitem} \usepackage{xcolor} \begin{document} \...
• 4,600
Accepted
### Redefining the item command of the description environment
In his answer, egreg has explained the problems with your current definition and a way to ammend it. However, I'd suggest you to use the nextline style for desciption offered by the enumitem package: ...
• 479k
Accepted
### How to set leftmargin of description to width of a particular label in enumitem?
Here are two ways: \documentclass{article} \usepackage{enumitem} \usepackage{calc} \begin{document} \begin{description}[labelwidth =\widthof{\bfseries9999}, leftmargin = !] \item[1987]Something ...
• 259k
Accepted
### Left aligned labels in descripton
As beamer does not like the package enumitem, you will have to define your own "description item". % arara: pdflatex \documentclass[handout]{beamer} \defbeamertemplate{description item}{align left}{\...
• 42.1k
### glossaries: How to customize list of symbols with additional column for units?
Just adding to Christian's answer: to use the unit macros inside the \si{unit} command defined by siunitx such as \metre and \kilo\watt used in his MWE, one should add the command \glssetnoexpandfield{...
• 7,497
### Line break after description label
Adding \leavevmode also has the desired effect and looks reasonably clean. \documentclass{article} \begin{document} \begin{description} \item[Animals:]\leavevmode \begin{itemize} \item Dog \...
• 2,473
### Using \lstinline inside a \item
If you're happy with a new command, here is something I am using now (inspired by the previous answer): \newcommand*{\lstitem}[1]{ \setbox0\hbox{\lstinline{#1}} \item[\usebox0] % \item[\...
• 465
Accepted
### right-alignment with enumitem
\documentclass{article} \usepackage{enumitem,xcolor} \usepackage{showframe} \begin{document} \begin{description}[font=\color{black},before=\color{blue},nosep] \raggedleft %%...
• 1,410
Accepted
### line break in description label
Hide the depth of the parbox: \documentclass{beamer} \usetheme{Madrid} \mode<handout>{ \usecolortheme{seahorse} \usecolortheme{rose} } \useinnertheme{circles} \usefonttheme[mathonly]{serif} \...
• 292k
Accepted
### Should I write \begin{quote} ... \end{quote} or \quote ... \endquote?
Always use the \begin \end syntax, some environments might work using the underlying commands but most will not. It also helps editors to offer syntax highlighting and context sensitive file ...
• 665k
### How do I align enumerate items inside empty description?
You could also just do \begin{enumerate} \item[] \item A1. \item A2. \item A3. \end{enumerate} instead of the above. Works equally well (and looks better in my opinion).
Accepted
### Automatically set description list labelwidth based on widest label?
Solution Here is a solution that uses the eqparbox package to measure item label widths. It avoids some of the limitations of the solution described in Gonzalo Medina's answer (see the bottom of this ...
• 10.4k
### How to align tcolorbox at the top?
I want suggest another possibility. It still needs some work but let me know if it's interesting. \tcolorboxes have upper and lower parts which can be placed side by side. Therefore instead of trying ...
• 127k
### lstlisting environment as item in description
Adding a \leavevmode helps here: \documentclass{article} \usepackage{xcolor} \usepackage{listings} % fancy code listings \usepackage{caption} % fancy chapters for fancy code listings \...
• 91.7k
Accepted
### Numbered description list with dot leaders?
Simply change the descripton environment for an enumerate environment: \documentclass[12pt, letter]{article} \newenvironment{specifications}{% \let\olditem\item% \renewcommand\item[2][]{\olditem#...
• 3,406
Accepted
### Reduce the space between label and item in a description list
\documentclass[12pt]{article} \usepackage{enumitem} \begin{document} \begin{description}[labelsep=\fontdimen2\font] \item[Video recordings] arguably produced the richest part of the data set. ...
• 44.7k
Accepted
### How to make enumerate indent like description
Just use [leftmargin=*, align=left] as your enumerate parameters. The output is identical but the values printed of the lengths are different because of the way the default description values are ...
• 201k
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2022-05-18 22:38:20
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http://eprint.iacr.org/2008/395
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## Cryptology ePrint Archive: Report 2008/395
New Applications of Differential Bounds of the SDS Structure
Jiali Choy and Khoongming Khoo
Abstract: In this paper, we present some new applications of the bounds for the differential probability of a SDS (Substitution-Diffusion-Substitution) structure by Park et al. at FSE 2003. Park et al. have applied their result on the AES cipher which uses the SDS structure based on MDS matrices. We shall apply their result to practical ciphers that use SDS structures based on {0,1}-matrices of size n times n. These structures are useful because they can be efficiently implemented in hardware. We prove a bound on {0,1}-matrices to show that they cannot be MDS and are almost-MDS only when n=2,3 or 4. Thus we have to apply Park's result whenever {0,1}-matrices where $n \geq 5$ are used because previous results only hold for MDS and almost-MDS diffusion matrices. Based on our bound, we also show that the {0,1}-matrix used in E2 is almost-optimal among {0,1}-matrices. Using Park's result, we prove differential bounds for E2 and an MCrypton-like cipher, from which we can deduce their security against boomerang attack and some of its variants. At ICCSA 2006, Khoo and Heng constructed block cipher-based universal hash functions, from which they derived Message Authentication Codes (MACs) which are faster than CBC-MAC. Park's result provides us with the means to obtain a more accurate bound for their universal hash function. With this bound, we can restrict the number of MAC's performed before a change of MAC key is needed.
Category / Keywords: secret-key cryptography /
Publication Info: Updated version of a paper presented at the ISC 2008 conference
Date: received 16 Sep 2008, last revised 22 Sep 2008
Contact author: kkhoongm at gmail com
Available format(s): PDF | BibTeX Citation
Note: This is a corrected version of a paper presented at the ISC 2008 conference. It was claimed in the conference paper that we proved the security of MCrypton against boomerang attack. In this paper, we corrected the claim to say that we prove the security of a variant of MCrypton, which we call MCrypton-x, against boomerang attack. Moreover, some typos were also corrected.
Short URL: ia.cr/2008/395
[ Cryptology ePrint archive ]
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2016-07-26 10:36:17
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http://www.chegg.com/homework-help/questions-and-answers/let-p-denote-statement-july-14th-bastille-day-let-q-denote-statement-mississippi-river-wri-q914315
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Symbolic Logic
Let p denote the statement "July 14th is Bastille Day" and let q denote the statement "Mississippi is a river." Write out the following statements in proper English sentences. Do NOT use DeMorgan's Law in your translation (i.e. write translation with ONE negation not two):
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2013-06-18 04:34:23
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https://www.aimsciences.org/article/doi/10.3934/jmd.2020004
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# American Institute of Mathematical Sciences
2020, 16: 81-107. doi: 10.3934/jmd.2020004
## Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics
Department of Mathematics, Stanford University, 450 Jane Stanford Way, Stanford, CA 94305-2125, USA
Received April 20, 2019 Revised October 06, 2019 Published April 2020
We show that the number of square-tiled surfaces of genus $g$, with $n$ marked points, with one or both of its horizontal and vertical foliations belonging to fixed mapping class group orbits, and having at most $L$ squares, is asymptotic to $L^{6g-6+2n}$ times a product of constants appearing in Mirzakhani's count of simple closed hyperbolic geodesics. Many of the results in this paper reflect recent discoveries of Delecroix, Goujard, Zograf, and Zorich, but the approach considered here is very different from theirs. We follow conceptual and geometric methods inspired by Mirzakhani's work.
Citation: Francisco Arana-Herrera. Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics. Journal of Modern Dynamics, 2020, 16: 81-107. doi: 10.3934/jmd.2020004
##### References:
[1] J. Athreya, A. Bufetov, A. Eskin and M. Mirzakhani, Lattice point asymptotics and volume growth on Teichmüller space, Duke Math. J., 161 (2012), 1055-1111. doi: 10.1215/00127094-1548443. Google Scholar [2] J. S. Athreya, A. Eskin and A. Zorich, Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\Bbb C\rm P^1$, Ann. Sci. Éc. Norm. Supér. (4), 49 (2016), 1311–1386. Google Scholar [3] F. Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math., 92 (1988), 139-162. doi: 10.1007/BF01393996. Google Scholar [4] F. Bonahon, Geodesic laminations on surfaces, in Laminations and Foliations in Dynamics, Geometry and Topology (Stony Brook, NY, 1998), Contemp. Math., vol. 269, Amer. Math. Soc., Providence, RI, 2001, 1–37. doi: 10.1090/conm/269/04327. Google Scholar [5] V. Delecroix, E. Goujard, P. Zograf and A. Zorich, Square-tiled surfaces of fixed combinatorial type: Equidistribution, counting, volumes of the ambient strata, arXiv e-prints, 2016, arXiv: 1612.08374. Google Scholar [6] V. Delecroix, E. Goujard, P. Zograf and A. Zorich, Enumeration of meanders and Masur–Veech volumes, arXiv e-prints, 2017, arXiv: 1705.05190. Google Scholar [7] V. Delecroix, E. Goujard, P. Zograf and A. Zorich, Masur–Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves, arXiv e-prints, 2019, arXiv: 1908.08611. Google Scholar [8] A. Eskin and A. Okounkov, Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math., 145 (2001), 59-103. doi: 10.1007/s002220100142. Google Scholar [9] V. Erlandsson, H. Parlier and J. Souto, Counting curves, and the stable length of currents, arXiv e-prints, 2016, arXiv: 1612.05980. Google Scholar [10] V. Erlandsson, A remark on the word length in surface groups, Trans. Amer. Math. Soc., 372 (2019), 441-455. doi: 10.1090/tran/7561. Google Scholar [11] V. Erlandsson and J. Souto, Counting curves in hyperbolic surfaces, Geom. Funct. Anal., 26 (2016), 729-777. doi: 10.1007/s00039-016-0374-7. Google Scholar [12] V. Erlandsson and C. Uyanik, Length functions on currents and applications to dynamics and counting, arXiv e-prints, 2018, arXiv: 1803.10801. Google Scholar [13] A. Fathi, F. Laudenbach and V. Poénaru, Thurston's Work on Surfaces, Translated from the 1979 French original by Djun M. Kim and Dan Margalit, Mathematical Notes, vol. 48, Princeton University Press, Princeton, NJ, 2012. Google Scholar [14] B. Farb and D. Margalit, A Primer on Mapping Class Groups, Princeton Mathematical Series, vol. 49, Princeton University Press, Princeton, NJ, 2012. Google Scholar [15] F. P. Gardiner, Teichmüller Theory and Quadratic Differentials, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1987. Google Scholar [16] F. P. Gardiner and H. Masur, Extremal length geometry of Teichmüller space, Complex Variables Theory Appl., 16 (1991), 209-237. doi: 10.1080/17476939108814480. Google Scholar [17] J. Hubbard and H. Masur, Quadratic differentials and foliations, Acta Math., 142 (1979), 221-274. doi: 10.1007/BF02395062. Google Scholar [18] J. H. Hubbard, Teichmüller Theory and Applications to Geometry, Topology, and Dynamics. Vol. 2. Surface Homeomorphisms and Rational Functions, Matrix Editions, Ithaca, NY, 2016. Google Scholar [19] S. P. Kerckhoff, The asymptotic geometry of Teichmüller space, Topology, 19 (1980), 23-41. doi: 10.1016/0040-9383(80)90029-4. Google Scholar [20] M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys., 147 (1992), 1-23. doi: 10.1007/BF02099526. Google Scholar [21] G. Levitt, Foliations and laminations on hyperbolic surfaces, Topology, 22 (1983), 119-135. doi: 10.1016/0040-9383(83)90023-X. Google Scholar [22] E. Lindenstrauss and M. Mirzakhani, Ergodic theory of the space of measured laminations, Int. Math. Res. Not. IMRN, 2008 (2008), Art. ID rnm126, 49pp. doi: 10.1093/imrn/rnm126. Google Scholar [23] G. A. Margulis, On Some Aspects of the Theory of Anosov Systems, With a survey by Richard Sharp: Periodic orbits of hyperbolic flows, Translated from the Russian by Valentina Vladimirovna Szulikowska, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2004. doi: 10.1007/978-3-662-09070-1. Google Scholar [24] B. Martelli, An introduction to geometric topology, arXiv e-prints, 2016, arXiv: 1610.02592. Google Scholar [25] H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2), 115 (1982), 169–200. doi: 10.2307/1971341. Google Scholar [26] H. Masur, Ergodic actions of the mapping class group, Proc. Amer. Math. Soc., 94 (1985), 455-459. doi: 10.1090/S0002-9939-1985-0787893-5. Google Scholar [27] M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math., 167 (2007), 179-222. doi: 10.1007/s00222-006-0013-2. Google Scholar [28] M. Mirzakhani, Ergodic theory of the earthquake flow, Int. Math. Res. Not. IMRN, 2008 (2008), Art. ID rnm116, 39pp. doi: 10.1093/imrn/rnm116. Google Scholar [29] M. Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Ann. of Math. (2), 168 (2008), 97–125. doi: 10.4007/annals.2008.168.97. Google Scholar [30] M. Mirzakhani, Counting Mapping Class group orbits on hyperbolic surfaces, arXiv e-prints, 2016, arXiv: 1601.03342. Google Scholar [31] L. Monin and V. Telpukhovskiy, On normalizations of Thurston measure on the space of measured laminations, Topology Appl., 267 (2019), 106878, 12 pp. doi: 10.1016/j.topol.2019.106878. Google Scholar [32] A. Papadopoulos, Geometric intersection functions and Hamiltonian flows on the space of measured foliations on a surface, Pacific J. Math., 124 (1986), 375-402. doi: 10.2140/pjm.1986.124.375. Google Scholar [33] R. C. Penner and J. L. Harer, Combinatorics of Train Tracks, Annals of Mathematics Studies, vol. 125, Princeton University Press, Princeton, NJ, 1992. doi: 10.1515/9781400882458. Google Scholar [34] I. Rivin, Geodesics with one self-intersection, and other stories, Adv. Math., 231 (2012), 2391-2412. doi: 10.1016/j.aim.2012.07.018. Google Scholar [35] K. Rafi and J. Souto, Geodesic currents and counting problems, Geom. Funct. Anal., 29 (2019), 871-889. doi: 10.1007/s00039-019-00502-7. Google Scholar [36] W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. (2), 115 (1982), 201–242. doi: 10.2307/1971391. Google Scholar [37] U. Wolf, The action of the mapping class group on the pants complex, preprint, 2009. Google Scholar [38] S. Wolpert, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math., 107 (1985), 969-997. doi: 10.2307/2374363. Google Scholar [39] M. Wolf, On realizing measured foliations via quadratic differentials of harmonic maps to $\mathbf R$-trees, J. Anal. Math., 68 (1996), 107-120. doi: 10.1007/BF02790206. Google Scholar [40] U. Wolf, Die Aktion der Abbildungsklassengruppe auf dem Hosenkomplex, Ph.D. thesis, 2009. Google Scholar
show all references
##### References:
[1] J. Athreya, A. Bufetov, A. Eskin and M. Mirzakhani, Lattice point asymptotics and volume growth on Teichmüller space, Duke Math. J., 161 (2012), 1055-1111. doi: 10.1215/00127094-1548443. Google Scholar [2] J. S. Athreya, A. Eskin and A. Zorich, Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\Bbb C\rm P^1$, Ann. Sci. Éc. Norm. Supér. (4), 49 (2016), 1311–1386. Google Scholar [3] F. Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math., 92 (1988), 139-162. doi: 10.1007/BF01393996. Google Scholar [4] F. Bonahon, Geodesic laminations on surfaces, in Laminations and Foliations in Dynamics, Geometry and Topology (Stony Brook, NY, 1998), Contemp. Math., vol. 269, Amer. Math. Soc., Providence, RI, 2001, 1–37. doi: 10.1090/conm/269/04327. Google Scholar [5] V. Delecroix, E. Goujard, P. Zograf and A. Zorich, Square-tiled surfaces of fixed combinatorial type: Equidistribution, counting, volumes of the ambient strata, arXiv e-prints, 2016, arXiv: 1612.08374. Google Scholar [6] V. Delecroix, E. Goujard, P. Zograf and A. Zorich, Enumeration of meanders and Masur–Veech volumes, arXiv e-prints, 2017, arXiv: 1705.05190. Google Scholar [7] V. Delecroix, E. Goujard, P. Zograf and A. Zorich, Masur–Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves, arXiv e-prints, 2019, arXiv: 1908.08611. Google Scholar [8] A. Eskin and A. Okounkov, Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math., 145 (2001), 59-103. doi: 10.1007/s002220100142. Google Scholar [9] V. Erlandsson, H. Parlier and J. Souto, Counting curves, and the stable length of currents, arXiv e-prints, 2016, arXiv: 1612.05980. Google Scholar [10] V. Erlandsson, A remark on the word length in surface groups, Trans. Amer. Math. Soc., 372 (2019), 441-455. doi: 10.1090/tran/7561. Google Scholar [11] V. Erlandsson and J. Souto, Counting curves in hyperbolic surfaces, Geom. Funct. Anal., 26 (2016), 729-777. doi: 10.1007/s00039-016-0374-7. Google Scholar [12] V. Erlandsson and C. Uyanik, Length functions on currents and applications to dynamics and counting, arXiv e-prints, 2018, arXiv: 1803.10801. Google Scholar [13] A. Fathi, F. Laudenbach and V. Poénaru, Thurston's Work on Surfaces, Translated from the 1979 French original by Djun M. Kim and Dan Margalit, Mathematical Notes, vol. 48, Princeton University Press, Princeton, NJ, 2012. Google Scholar [14] B. Farb and D. Margalit, A Primer on Mapping Class Groups, Princeton Mathematical Series, vol. 49, Princeton University Press, Princeton, NJ, 2012. Google Scholar [15] F. P. Gardiner, Teichmüller Theory and Quadratic Differentials, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1987. Google Scholar [16] F. P. Gardiner and H. Masur, Extremal length geometry of Teichmüller space, Complex Variables Theory Appl., 16 (1991), 209-237. doi: 10.1080/17476939108814480. Google Scholar [17] J. Hubbard and H. Masur, Quadratic differentials and foliations, Acta Math., 142 (1979), 221-274. doi: 10.1007/BF02395062. Google Scholar [18] J. H. Hubbard, Teichmüller Theory and Applications to Geometry, Topology, and Dynamics. Vol. 2. Surface Homeomorphisms and Rational Functions, Matrix Editions, Ithaca, NY, 2016. Google Scholar [19] S. P. Kerckhoff, The asymptotic geometry of Teichmüller space, Topology, 19 (1980), 23-41. doi: 10.1016/0040-9383(80)90029-4. Google Scholar [20] M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys., 147 (1992), 1-23. doi: 10.1007/BF02099526. Google Scholar [21] G. Levitt, Foliations and laminations on hyperbolic surfaces, Topology, 22 (1983), 119-135. doi: 10.1016/0040-9383(83)90023-X. Google Scholar [22] E. Lindenstrauss and M. Mirzakhani, Ergodic theory of the space of measured laminations, Int. Math. Res. Not. IMRN, 2008 (2008), Art. ID rnm126, 49pp. doi: 10.1093/imrn/rnm126. Google Scholar [23] G. A. Margulis, On Some Aspects of the Theory of Anosov Systems, With a survey by Richard Sharp: Periodic orbits of hyperbolic flows, Translated from the Russian by Valentina Vladimirovna Szulikowska, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2004. doi: 10.1007/978-3-662-09070-1. Google Scholar [24] B. Martelli, An introduction to geometric topology, arXiv e-prints, 2016, arXiv: 1610.02592. Google Scholar [25] H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2), 115 (1982), 169–200. doi: 10.2307/1971341. Google Scholar [26] H. Masur, Ergodic actions of the mapping class group, Proc. Amer. Math. Soc., 94 (1985), 455-459. doi: 10.1090/S0002-9939-1985-0787893-5. Google Scholar [27] M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math., 167 (2007), 179-222. doi: 10.1007/s00222-006-0013-2. Google Scholar [28] M. Mirzakhani, Ergodic theory of the earthquake flow, Int. Math. Res. Not. IMRN, 2008 (2008), Art. ID rnm116, 39pp. doi: 10.1093/imrn/rnm116. Google Scholar [29] M. Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Ann. of Math. (2), 168 (2008), 97–125. doi: 10.4007/annals.2008.168.97. Google Scholar [30] M. Mirzakhani, Counting Mapping Class group orbits on hyperbolic surfaces, arXiv e-prints, 2016, arXiv: 1601.03342. Google Scholar [31] L. Monin and V. Telpukhovskiy, On normalizations of Thurston measure on the space of measured laminations, Topology Appl., 267 (2019), 106878, 12 pp. doi: 10.1016/j.topol.2019.106878. Google Scholar [32] A. Papadopoulos, Geometric intersection functions and Hamiltonian flows on the space of measured foliations on a surface, Pacific J. Math., 124 (1986), 375-402. doi: 10.2140/pjm.1986.124.375. Google Scholar [33] R. C. Penner and J. L. Harer, Combinatorics of Train Tracks, Annals of Mathematics Studies, vol. 125, Princeton University Press, Princeton, NJ, 1992. doi: 10.1515/9781400882458. Google Scholar [34] I. Rivin, Geodesics with one self-intersection, and other stories, Adv. Math., 231 (2012), 2391-2412. doi: 10.1016/j.aim.2012.07.018. Google Scholar [35] K. Rafi and J. Souto, Geodesic currents and counting problems, Geom. Funct. Anal., 29 (2019), 871-889. doi: 10.1007/s00039-019-00502-7. Google Scholar [36] W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. (2), 115 (1982), 201–242. doi: 10.2307/1971391. Google Scholar [37] U. Wolf, The action of the mapping class group on the pants complex, preprint, 2009. Google Scholar [38] S. Wolpert, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math., 107 (1985), 969-997. doi: 10.2307/2374363. Google Scholar [39] M. Wolf, On realizing measured foliations via quadratic differentials of harmonic maps to $\mathbf R$-trees, J. Anal. Math., 68 (1996), 107-120. doi: 10.1007/BF02790206. Google Scholar [40] U. Wolf, Die Aktion der Abbildungsklassengruppe auf dem Hosenkomplex, Ph.D. thesis, 2009. Google Scholar
Example of a quadratic differential in the principal stratum of $\textbf{Re}^{-1}([\gamma_1]) \subseteq Q\mathcal{M}_{2,0}$ for a (non-separating) simple closed curve $\gamma_1$ in $S_{2,0}$
No escape of mass property in the real period coordinate chart (b) associated to the polygon representation (a), representing a flat pillowcase in the principal stratum of $\mathrm{Re}^{-1}(\gamma_1) \subseteq Q\mathcal{T}_{0,4}$. The blue region covers $K_\epsilon$ and the gray region covers $\widehat{E}(\gamma_1) \backslash K_\epsilon$
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2021-10-17 07:37:23
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8033813238143921, "perplexity": 3725.1715872800155}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585121.30/warc/CC-MAIN-20211017052025-20211017082025-00268.warc.gz"}
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https://answers.ros.org/question/351810/what-are-the-differents-between-turtlebot2_kobuki-and-turtlebot_burger-above-on-odometry-topic/
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What are the differents between turtlebot2_kobuki and turtlebot_burger above on Odometry topic?
Hello, I'm using ROS kinetic with Ubuntu 16.04.
It is clear that turtlebot2 is different from turtlebot3, but when I launch turtlebot2 with gazebo simulation and give it velocity topic, and also it collides with the wall, and still give velocity topic continuously, the position of its/odom increases infinitely at the crushed position.
In the case of turtlebot3_burger, the /odom does not increase anymore.
Anyone who knows this reason?
If so, would you happen to please give me the proper explanation?
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2021-09-20 09:35:17
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http://mathhelpforum.com/algebra/58159-compound-interest.html
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1. ## Compound interest
Lily invest $2500 at simple interst for 9 months. The amt that she will receive is$2650. If she invests \$2500 at the same rate for 9 months but compounded monthly, how much more interest would she receive?
2. The interest I lily gained by the simple interest is:
$I = 2650-2500 = 150$
Recall that simple interest $I = Prt$. Given principal P, time t, and interest I, you can solve for rate r. Note that the rate here is per month, so you may have to multiply by 12 to switch it to annual for convenience.
Recall that the compounded amount formula is:
$A = P\left(1+\frac{r}{m}\right)^{mt}$
Simply find the compounded amount and subtract the principal from it to find the interest. Remember to switch the time to years. Then find out how much more interest she would receive.
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2017-08-21 16:23:25
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https://eshelohad.co.il/uk-gpm-qduanx/t68xvz.php?tag=difference-between-machine-learning-and-convolutional-neural-network-b087af
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אוהד אשל- צמיחה עסקית לחברות וארגונים
difference between machine learning and convolutional neural network
Thus, the models can identify the patterns in the data. Without this context, it is sometimes difficult to decide which specific framework, or architecture is required for a particular application. Thus deciding what a channel means is very important, since each channel has its own set of filters. Setting a video as a 3D input with the temporal dimension as channel may not be the best option since in that way, the order in which temporal frames come does not matter (the outputs for the filters of each channel are summed up) resulting in losing the intrinsic temporal dynamics of the input data . The input for a convolutional layer has the following shape: input_shape = (batch_size,input_dims,channels), Input shape for conv1D: (batch_size,W,channels), Example: 1 second stereo voice signal sampled at 44100 Hz, shape: (batch_size,44100,2), Input shape for conv2D: (batch_size,(H,W),channels), Example: 32x32 RGB image, shape: (batch_size,32,32,3), Input shape for conv3D: (batch_size,(H,w,D),channels), Example (more tricky): 1 second video of 32x32 RGB images at 24 fps, shape: (batch_size,32,32,3,24). Machine Learning enables a system to automatically learn and progress from experience without being explicitly programmed. They keep learning until it comes out with the best set of features to obtain a satisfying predictive performance. Neural Networks are essentially a part of Deep Learning, which in turn is a subset of Machine Learning. Neural networks demand skills like data modelling, Mathematics, Linear Algebra and Graph Theory, programming, and probability and statistics. The main difference between CNN and RNN is the ability to process temporal information or data that comes in sequences. In this way, a Neural Network functions similarly to the neurons in the human brain. While a Machine Learning model makes decisions according to what it has learned from the data, a Neural Network arranges algorithms in a fashion that it can make accurate decisions by itself. If the dataset is not a computer vision one, then DBNs can most definitely perform better. The key difference between neural network and deep learning is that neural network operates similar to neurons in the human brain to perform various computation tasks faster while deep learning is a special type of machine learning that imitates the learning approach humans use to gain knowledge.. Neural network helps to build predictive models to solve complex problems. What are the differences between Convolutional1D, Convolutional2D, and Convolutional3D? If the same problem was solved using Convolutional Neural Networks, then for 50x50 input images, I would develop a network using only 7 x 7 patches (say). As explained here, each the 3x3 kernel moves across the image and does matrix multiplication with every 3x3 part of the image, emphasizing some features and smoothing others.. Haar-Features are good at detecting edges and lines. Differences Between Machine Learning vs Neural Network. Random Forests vs Neural Network - data preprocessing In theory, the Random Forests should work with missing and categorical data. Machine Learning vs Neural Network: Key Differences. The only difference is the dimensionality of the input space. Neural Networks, on the other hand, are used to solve numerous business challenges, including sales forecasting, data validation, customer research, risk management, speech recognition, and character recognition, among other things. Are there some links or references to show their use cases? rev 2020.12.3.38123, The best answers are voted up and rise to the top, Data Science Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. To learn more, see our tips on writing great answers. This way, a Neural Network features likewise to the nerve cells in the human mind. What is the difference between a Fully-Connected and Convolutional Neural Network? MathJax reference. Convolutional neural networks can be either feed-forward or recurrent. Stochastic Gradient Descent 2. The nervous system contains cells which are referred to as neurons. Machine Learning uses advanced algorithms that parse data, learns from it, and use those learnings to discover meaningful patterns of interest. Convolutional Nets are pretty much hardwired. The first layer is the input layer, followed by a hidden layer, and then finally an output layer. A neural network (Convolutional Neural Network): It does convolution (In signal processing it's known as Correlation) (Its a mathematical operation) between the previous layer's output and the current layer's kernel ( a small matrix ) and then it passes data to the next layer by … “Stationarity of statistics” and “locality of pixel dependencies”, How does the “skip” method work for upsampling? Demystifying Neural Networks, Deep Learning, Machine Learning, and Artificial Intelligence. After an employee has been terminated, how long should you wait before taking away their access to company email? What are the relationships/differences between Bias, Variance and Residuals? Thanks for contributing an answer to Data Science Stack Exchange! It will be interesting to see how (if) Nvidia manages to carve a niche for itself in the growing video-conf market with its AI features. Posted by 4 years ago. Machine Learning is an application or the subfield of artificial intelligence (AI). Close. What does it mean the term variation for an image dataset? or that: - "Backpropagation" is about neural networks, not deep learning… Convolutional neural networks are widely used in computer vision and have become the state of the art for many visual applications such as image classification, and have also found success in natural language processing for text classification. Neural network is a machine learning method like other ML methods. Your email address will not be published. Machine-Learning-Neural-Networks. Learn more about the, 7. In this article at OpenGenus, we have present the most insightful and MUST attempt questions on Convolutional Neural Network.To get an overview of this topic before going into the questions, you may go through the following articles: Overview of Different layers in Convolutional Neural Networks (CNN) by Piyush Mishra. 1. Each convolution traverses the voice to find meaningful patterns by employing a cost function. The two core ML methods are supervised learning and unsupervised learning. Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. One better approach (depending on the application) is to process the RGB images with 2D convolutions in a recurrent neural network. The convolutional layer apply different filters for each channel, thus, the weights of the conv layer have the following shape: Convolutional layer with 12 filters and square kernel matrix of size of 3. The Overflow Blog Podcast 261: Leveling up with Personal Development Nerds By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. The firms of today are moving towards AI and incorporating machine learning as their new technique. neural-networks machine-learning convolutional-neural-networks comparison Is it illegal to carry someone else's ID or credit card? Why was the mail-in ballot rejection rate (seemingly) 100% in two counties in Texas in 2016? © 2015–2020 upGrad Education Private Limited. This post is divided into five parts; they are: 1. Read: Deep Learning vs Neural Network. With the huge transition in today’s technology, it takes more than just Big Data and Hadoop to transform businesses. - There's a difference between a technology that works and one that has a viable business model. Making statements based on opinion; back them up with references or personal experience. They are also known as shift invariant or space invariant artificial neural networks (SIANN), based on their shared-weights architecture and translation invariance characteristics. How much did the first hard drives for PCs cost? Convolutional neural networks are the standard of today’s deep machine learning and are used to solve the majority of problems. What is the difference between horizontal and vertical ensemble? An ML model works in a simple fashion – it is fed with data and learns from it. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Variant: Skills with Different Abilities confuses me. It is especially well-suited for machine vision applications that have challenging classification requirements. Many people are familiar with the term, Deep Learning, as it has gained widespread attention as a reliable way to tackle difficult and computationally expensive problems. Use MathJax to format equations. How does steel deteriorate in translunar space? ... (or probably even THE biggest) impact that machine learning has on the world right now, yet I barely hear about it on this sub (I hope I'm wrong on this). Nvidia is up against Teams and Zoom, both of which have a strong backbone and access to AI research. 5. Namely, 1D, 2D & 3D. What are the differences between these three layers? I'll show you why. What are the key differences between cellular neural networks and convolutional neural networks in terms of working principle, implementation, potential performance, and applicability? Deep learning has been a topic of great interest and much discussion recently in the world of machin e vision.. In it, the data passes through several layers of interconnected nodes, wherein each node classifies the characteristics and information of the previous layer before passing the results on to other nodes in subsequent layers. For the first examples, it seems straightforward to decide that the stereo signals and the RGB images are different channels... they are commonly named like that (stereo channels, RGB channels) indeed. Podcast 291: Why developers are demanding more ethics in tech, Tips to stay focused and finish your hobby project, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…. 6. A convolutional neural network, or CNN, is a deep learning neural network designed for processing structured arrays of data such as images. Supervised learning methods offer inherent advantages over convolutional neural networks Dr. Jon Vickers. Machine Learning seeks to build intelligent systems or machines that can automatically learn and train themselves through experience, without being explicitly programmed or requiring any human intervention. In the examples given previously: 1 second stereo voice signal sampled at 44100 Hz, kernel_size = 3, 12 x 2 = 24 one-dimensional filters, 12 filter for each channel, 12 x 3 = 36 two-dimensional filters, 12 filter for each channel, 1 second video of 32x32 RGB images at 24 fps, kernel_size = (3,3,3), 24 x 12 = 288 three-dimensional filters, 12 filter for each channel. How do I orient myself to the literature concerning a research topic and not be overwhelmed? How are recovery keys possible if something is encrypted using a password? It is inspired by the idea of how the nervous system operates. In this sense, Machine Learning is a continuously evolving activity. Huang et al. Cite. 4. 3. Machine learning aims to understand the data structure of the dataset at hand and accommodate the data into ML models that can be used by companies and organizations. Difference Between Machine Learning and Pattern Recognition. If you’re interested to learn more about machine learning, check out IIIT-B & upGrad’s PG Diploma in Machine Learning & AI which is designed for working professionals and offers 450+ hours of rigorous training, 30+ case studies & assignments, IIIT-B Alumni status, 5+ practical hands-on capstone projects & job assistance with top firms. I received stocks from a spin-off of a firm from which I possess some stocks. I've been learning about Convolutional Neural Networks. Machine Learning vs Neural Network: Trick Distinctions. Difference between Deep Learning and Neural Network Concept – Neural network, also called artificial neural network, is an information processing model that stimulates the mechanism of learning biological organisms. Is "ciao" equivalent to "hello" and "goodbye" in English? MLP with more than one hidden layer is one type of deep neural network. These layers usually have more parameters to be learnt than the previous layers. Our task is to recognize an image and identify it as one of the ten classes. Each layer contains one or more neurons. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. It is essentially a Machine Learning model (more precisely, Deep Learning) that is used in unsupervised learning. It is important to note that a signal with an input dimension D can be regarded as a signal of D+1 dimension with one channel, but the resulting feature space may be less representative/useful: Conv1D is used for input signals which are similar to the voice. In theory, DBNs should be the best models but it is very hard to estimate joint probabilities accurately at the moment. Strictly speaking, a neural network (also called an “artificial neural network”) is a type of machine learning model that is usually used in supervised learning. 1. Machine Learning and NLP | PG Certificate, Full Stack Development (Hybrid) | PG Diploma, Full Stack Development | PG Certification, Blockchain Technology | Executive Program, Machine Learning & NLP | PG Certification, Machine Learning vs Neural Network: Key Differences. A lot of students have misconceptions such as: - "Deep Learning" means we should study CNNs and RNNs. What Is a Batch? However, Neural Networks can be classified into feed-forward, recurrent, convolutional, and modular Neural Networks. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. This makes it especial effective in face detection. This use case is very popular. Let’s look at the core differences between Machine Learning and Neural Networks. What is/are the default filters used by Keras Convolution2d()? The key thing is to think about what the channel means for our input data. Simple. Are there more layer types like convolution layers and fully connected layers? So, let’s try to understand them at the basic level. The main difference is that convolution is an operation that is designed to extract features from the input, while sub-sampling's purpose is just to reduce the dimensions of the input. By employing them you can find patterns across the signal. Is it more efficient to send a fleet of generation ships or one massive one? 4. Artificial Intelligence (AI), Machine Learning (ML), and Deep Learning (DL) have become so deeply entwined in our day-to-day lives and so fast that we’ve become accustomed to them without even knowing their connotations. In this case, each convolutional filter should be a three-dimensional filter to be convolved, cross-correlated actually, with the image to find appropriate patterns across the image. However, even in a simple Neural Network model, there are multiple layers. 5. Neural networks do not require human intervention as the nested layers within pass the data through hierarchies of various concepts, which eventually makes them capable of learning through their own errors. What are the exact differences between Deep Learning, Deep Neural Networks, Artificial Neural Networks and further terms? Neural networks have been shown to outperform a number of machine learning algorithms in many industry domains. 3. For most people, AI, ML, and DL are all the same. How to draw random colorfull domains in a plane? proposed an Extreme Learning Machine (ELM) as a training algorithm for a Single hidden-Layer Feed-forward Neural Network (SLFN) .The core components of the ELM training are a randomly generated input weight from an arbitrary continuous distribution and the minimum norm least-squares solution, which is calculated by using the Moore–Penrose inverse. So, Neural Networks are nothing but a highly advanced application of Machine Learning that is now finding applications in many fields of interest. The Difference Between Machine Learning and Neural Networks. In deep learning, a convolutional neural network (CNN, or ConvNet) is a class of deep neural networks, most commonly applied to analyzing visual imagery. But, there is a difference between knowing the name of something and knowing (and understanding) something. Where are the 60 million params of AlexNet? However, I would prefer Random Forests over Neural Network, because they are easier to use. With time, the ML model becomes more mature and trained as it continually learns from the data. When looking at Keras examples, I came across three different convolution methods. Therefore, in this article, I define both neural networks and deep learning, and look at how they differ. This project implements neural network and convolutional neural network. Image 2: Haar-features represented numerically. The task is to carry out classification on Fashion-MNIST dataset. What are their use cases? A Neural Network is a web of interconnected entities known as nodes wherein each node is responsible for a simple computation. On the contrary, the structure of a Neural Network is quite complicated. Machine Learning is applied in areas like. By increasing the number of hidden layers within a Neural Network model, you can increase its computational and problem-solving abilities. 3. What should I do when I am demotivated by unprofessionalism that has affected me personally at the workplace? Since Machine Learning models are adaptive, they are continually evolving by learning through new sample data and experiences. I've been learning about Convolutional Neural Networks. Neural networks or connectionist systems are the systems which are inspired by our biological neural network. Moreover, convolutional neural networks and recurrent neural networks are used for completely different purposes, and there are differences in the structures of the neural networks themselves to fit those different use cases. Your email address will not be published. Convolutional neural networks perform better than DBNs. Fields are marked *, PG DIPLOMA in Machine Learning and also Networks. Differences between deep Learning ) that is now finding applications in many industry domains relationships/differences. Of interest – it is inspired by the idea of how the nervous system operates with and. Out with the best set of features to obtain a satisfying predictive performance employing them you can patterns! Random Forests should work with missing and categorical data and look at the moment each channel very to!, Convolutional2D, and probability and statistics of Machine Learning is an application or subfield. What does it mean the term variation for an image dataset they have innate differences is little for! For a simple computation a large company with deep pockets from rebranding my MIT project and killing me off function. Vaccines are basically just dead '' viruses, then why does it often take so much to... Long should you Choose they are: 1 making statements based on opinion ; them. A firm from which I possess some stocks PG DIPLOMA in Machine Learning falls the! And then finally an Output layer each convolution traverses the voice to find meaningful patterns by employing a cost.. This project implements Neural Network functions similarly to the field, there is little for... Framework, or responding to other answers 100 % in two counties in Texas in 2016 tensorflow CNN or your. Long should you Choose why does it mean the term variation for an image and identify it as of... Within a Neural Network unsupervised Learning models one that has a viable business model, this. Design / logo © 2020 Stack Exchange Inc ; user contributions licensed under cc by-sa variation an. Between horizontal and vertical ensemble basically just dead '' viruses, then DBNs most. Company with deep pockets from rebranding my MIT project and killing me off wherein each node is responsible for simple. Consists of an assortment of algorithms used in unsupervised Learning efficient to a..., because they are: 1 deep learning… Huang et al viruses, then DBNs can most definitely difference between machine learning and convolutional neural network.! Marked *, PG DIPLOMA in Machine Learning for data modelling using graphs of neurons marked... Gains are short or long-term a technology that works and one that has a viable business model the differences! Exchange Inc ; user contributions licensed under cc by-sa both algorithms and each of them has own. Application ) is supervised Learning and also Neural Networks and further terms in Texas in 2016 or CNN is... Today are moving towards AI and incorporating Machine Learning enables a system to automatically learn and progress from experience being! Systems which are referred to as neurons predictive performance is essentially a part of deep Learning has terminated! You wait before taking away their access to company email solve the majority of.. Is now finding applications in many industry domains system to automatically learn and progress from experience without being explicitly.! ( HL2 - Output which is the input space the standard of today are moving towards AI incorporating. Implements Neural Network view '' equivalent to hello '' and goodbye '' English... That: - deep Learning, which in turn is a continuously evolving activity consists of an assortment algorithms! For our input data difference between machine learning and convolutional neural network structure of a firm from which I possess stocks..., there is little concern for how these systems were originally developed to understand them at the workplace do! A lot of students have misconceptions such as: - Backpropagation '' is about Neural Networks usually for!, both of which have a voice signal and you have a convolutional layer some or., Linear Algebra and Graph theory, the structure of the ten classes ” method for. Learn from data, in the human brain for this layer will 12... Study CNNs and RNNs that have challenging classification requirements Backpropagation '' is about Neural Networks CNN is... goodbye '' in English or connectionist systems are the exact differences between Machine Learning models, though these are! Networks are nothing but a highly advanced application of Machine Learning as their new technique have innate.... Similarly to the field, there is little concern for how these systems were originally developed depending the. Rbm instead of AutoEncoder ) is about Neural Networks by Keras Convolution2d )! Larger canvas of Artificial Intelligence ( AI ) Learning uses advanced algorithms that parse data, this. In sequences goodbye '' in English ten classes Learning falls under the larger canvas of Artificial.. Wait before taking away their access to company email from rebranding my MIT project and killing me?! A number of hidden layers within a Neural Network strong backbone and access to company email,!
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2022-05-22 20:19:49
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https://zbmath.org/?q=an:0593.35054
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zbMATH — the first resource for mathematics
On parabolic systems with variational structure. (English) Zbl 0593.35054
The author deals with the parabolic system of the second order for a vector function $$u=(u^ 1,...,u^ N)$$, $$N>1$$, $u^ i_ t=\sum_{\alpha,\beta}D_{\alpha}(a_{\alpha,\beta}(x,u)D_{\beta}u^ i)+a^ i_ 0(x,u\quad,\nabla u),\quad i=1,...,N,$ in the cylinder $$Q=\Omega \times (0,T)$$, where $$\Omega \subset R^ n$$ is a bounded Lipschitz domain. The functions $$a_{\alpha,\beta}$$, $$a^ i_ 0$$ are Lipschitz, $$a_{\alpha,\beta}$$-bounded, $$a^ i_ 0(x,u,p)$$ having quadratic growth in p. Uniform ellipticity in second order term and the variational structure of the system is assumed. Moreover a one-sided condition is imposed: $$a_ 0(x,u(x),\nabla u(x)):$$ $$u\geq -\mu | \nabla u(x)|^ 2-K$$, for each $$u\in L_{\infty}(\Omega)\cap W^ 1_ 2(\Omega)$$ and a.e. $$x\in \Omega$$ $$(\mu,K>0)$$. Employing the method of continuation the existence of a solution is considered for the Cauchy- Dirichlet problem $u(x,0)=u_ 0(x),\quad x\in \Omega;\quad u(x,t)=g(x),\quad x\in \partial \Omega,$ with g small in $$L_{\infty}(\partial \Omega)$$-norm. The main result yields (under some regularity conditions on $$u_ 0,g)$$ a solution-Hölder continuous in $$\bar Q,$$ for the case $$n=2$$. For general $$n\geq 2$$ the problem is reduced to a certain condition which is proved to hold for $$n=2$$.
Reviewer: P.Polacik
MSC:
35K55 Nonlinear parabolic equations 35K45 Initial value problems for second-order parabolic systems 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
Full Text:
References:
[1] ARONSON, D.G.: Non-negative solutions of linear parabolic equations; Ann. Sc. Norm. Sup. Pisa,22(1968), 607-694 · Zbl 0182.13802 [2] EELLS, J., J.H. SAMPSON: Harmonic mappings of Riemannian manifolds; Am. J. Math.86(1964), 109-160 · Zbl 0122.40102 [3] FREHSE, J.: On Two-Dimensional Quasi-Linear Elliptic Systems, manusc. math.28(1979), 21-49 · Zbl 0415.35025 [4] GIAQUINTA, M., M. STRUWE: An optimal regularity result for a class of quasilinear parabolic systems, manusc. math.36(1981), 223-239 · Zbl 0475.35026 [5] GILBARG, D., N.S. TRUDINGER: Elliptic Partial Differential Equations of Second Order, Springer Grundlehren 224, Berlin, Heidelberg, New York, Tokyo, 2nd edition, 1983 · Zbl 0562.35001 [6] HAMILTON, R.S.: Harmonic Maps of Manifolds with Boundary, Springer Lecture Notes 471, Berlin, Heidelberg, New York, 1975 · Zbl 0308.35003 [7] HILDEBRANDT, S., H. KAUL, K.-O. WIDMAN: An Existence Theorem for Harmonic Mappings of Riemannian Manifolds, Acta Math.138 (1977), 1-16 · Zbl 0356.53015 [8] JOST, J.: Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses; manusc. math.34(1981), 17-25 · Zbl 0459.58013 [9] LADYSHENSKAYA, O.A., V.A. SOLONNIKOV, N.N. URAL’CEVA: Linear and Quasilinear Equations of Parabolic Type; Transl. Math. Monogr. 23, AMS, Providence, 1968 [10] LIONS, J.L.: Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod, Paris, 1969 [11] MORREY, C.B. Jr.: Multiple Integrals in the Calculus of Variations, Springer, New York, 1966 · Zbl 0142.38701 [12] STRUWE, M.: On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems; manusc. math.35(1981), 125-145 · Zbl 0519.35007 [13] STRUWE, M.: Some regularity results for quasilinear parabolic systems, to appear in: Commentat. Math. Univ. Carol. [14] STRUWE, M.: On the evolution of harmonic mappings, to appear in: Comm. Math. Helv. · Zbl 0595.58013 [15] TOLKSDORF, P.: On some parabolic variational problems with quadratic growth, to appear in: Ann. Sc. Norm. Sup. Pisa [16] WAHL, W. VON: Verhalten der Lösungen parabolischer Gleichungen für t?? mit Lösbarkeit im Großen; Nachr. Akad. Wiss. Göttingen5(1981) · Zbl 0492.35035 [17] WIEGNER, M.: On two-dimensional elliptic systems with a one-sided condition, Math. Z.178(1981), 493-500 · Zbl 0474.35046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-10-16 12:52:10
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https://mathoverflow.net/questions/24307/locus-of-equal-area-hyperbolic-triangles
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# Locus of equal area hyperbolic triangles
Henry Segerman and I recently considered the following question:
Given a fixed area $A < \pi$ and two fixed points in the upper half-plane model for hyperbolic $2$-space, what is the locus of points which give rise to a hyperbolic triangle of the given area?
We found it a fun exercise in hyperbolic geometry to show that the answer is a Euclidean straight line, or an arc of a Euclidean circle. As this requires only elementary properties of hyperbolic geometry, we strongly suspect it should be known, but have thus far been unable to find a reference for it. Does anyone know whether it's known, and if so, where one can find it?
• Very nice! I'm now wondering idly what can be said about higher dimensions and spherical geometry...
– j.c.
May 12, 2010 at 2:24
• @Will: They seem to be equidistant curves only. A related question would be: Does the geodesic with the same endpoints have any significance? May 12, 2010 at 17:27
• @Will: The endpoints of the locus are actually distinct from the geodesic through the two fixed points, and hence define a separate geodesic (which necessarily does not intersect the first, even on the boundary). If, say, the two fixed points lie on a vertical line, we get one "banana" curve to the right of the line, and its reflection on the other side, but these do not share endpoints. May 12, 2010 at 20:43
• There is one special case, take the two points as $0$ and $\infty$ along the imaginary axis, area $\pi / 2 .$ Then the third point has real and imaginary parts equal. That is, if both your original points are on the "boundary," in this case the equidistant curve meets them. Specific value of the area should not matter, the "angles" at $0$ and $\infty$ are $0,$ so we are fixing the third angle, a diffeent third angle giving a different slope. May 13, 2010 at 0:01
• Yes, and in fact the same is true for any area: once you have one vertex $v$ giving the right area, with $0$ and $\infty$, the locus is the straight line through $0$ and $v$. The proof we constructed actually used this as a warm-up case, and the proof when all vertices are non-ideal is built from this. May 13, 2010 at 0:11
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2022-11-27 05:33:00
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https://www.bookofproofs.org/branches/extensional-relation/
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Welcome guest
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## Definition: Extensional Relation
Let $V$ be a set and let $R\subseteq V\times V$ be a binary relation. $R$ is called extensional if all elements of $x\in V$ are uniquely determined by ordered pairs $(z,x)\in R,$ formally
$$\{z\in V\mid zRx\}=\{z\in V\mid zRy\} \Rightarrow x=y,$$
or, by contraposition,
$$\{z\in V\mid zRx\}\neq \{z\in V\mid zRy\} \Rightarrow x\neq y.$$
| | | | | created: 2019-02-01 08:03:02 | modified: 2019-02-16 17:11:14 | by: bookofproofs | references: [8055]
(none)
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2019-02-17 17:28:19
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http://forum.math.toronto.edu/index.php?PHPSESSID=vr7acj5rroo41qop46p208c185&action=profile;u=4;area=showposts;start=1320
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### Show Posts
This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.
### Messages - Victor Ivrii
Pages: 1 ... 87 88 [89] 90 91 ... 93
1321
##### Home Assignment 2 / Re: Problem 3
« on: September 29, 2012, 03:13:13 PM »
What is meaning of "method of continuation"? I read the textbook and find it define the odd function to solve the problem, can I use that method?
See also Lecture 8 and note that it could be either odd or even
1322
##### Home Assignment 2 / Re: problem 1 typo?
« on: September 29, 2012, 03:10:20 PM »
Professor I have a question for part (c). Does the solution have to be continuous? For example I have f(x) on x>2t, g(x) on -2t<x<2t and h(x) on -3t<x<-2t. Should f(2t) = g(2t) and g(-2t)=h(-2t) (so the overall solution is continuous)?
My problem is that some of the f, g, h involve a constant K and I was wondering if I should use continuity to specify what K is.
Thanks a lot!
You should be able to find constants from initial and boundary conditions. Solutions may be discontinuous along lines you indicated
1323
##### APM346 Announcements / Re: Please register ASAP
« on: September 29, 2012, 02:42:53 PM »
Also again: select username whatever you want (make it short enough to save yourself a time while logging in) but change DisplayName (open Profile > Modify Profile > Account Settings and there will be Username and the next Name) matching to one on BlackBoard.
Credits for active and useful forum participation will be given only to those who are easily identified. Well, for identifying those who behaves badly I would go an extra mile
1324
##### Home Assignment 2 / Re: Problem 2
« on: September 29, 2012, 02:36:32 PM »
for the last part, can we just assume the same solution as c) but state a few assumptions instead? it's because I dont think the general solution of the equation would vary since no other IC were stated.
You should check when and if the general solution is continuous at $r=0$ and adjust it respectively
1325
##### Home Assignment 2 / Re: problem 1 typo?
« on: September 29, 2012, 09:04:56 AM »
Can we assume that for part (C) of Problem 1 that the Cauchy conditions are evenly reflected for x < 0?
Sure, you can but it will not be useful as your domain is $x>vt$ rather than $x>0$. Just use the general solution.
1326
##### Misc Math / Re: Example 8b
« on: September 28, 2012, 05:36:19 PM »
If we are looking for $t>0$ then we are interested in $0<x<ct$ and $x>ct$ because the original problem is dealing with $x>0$. Continuation is the method to reduce it to IVP but we need to come back
Transitions in (9), (12) from the middle to the r.h. expression is due to the trigonometric formulae. Everything is ok
PS. Please use \sin, \cos etc instead of sin, cos in LaTeX code as those are predefined macros.
PPS. In Lecture 9 we use \erf but as this is not a predefined macro, we define it by ourselves
1327
##### Home Assignment 2 / Re: Problem 2
« on: September 28, 2012, 05:23:56 PM »
I think in the new variant (just posted) it will be more clear
1328
##### APM346 Misc / Re: Midterm conflicts with schedule!
« on: September 28, 2012, 02:33:17 PM »
Just to open up the headline a bit:
Both midterm exams conflict with my schedule. So, what am I supposed to do?
There is now a poll attached to the announcement. Vote in it
http://forum.math.toronto.edu/index.php?topic=27.0
1329
##### APM346 Misc / Re: TA office hours
« on: September 28, 2012, 02:31:54 PM »
What are the TA office hours? On the course outline they are still listed as TBD....
Working on it. Meanwhile you can drop to my office hours
1330
##### Misc Math / Re: 1-D Wave equation derivation
« on: September 28, 2012, 02:20:57 PM »
Starting with
$$\frac{\partial}{\partial x} \left[ T(x,t) \sin{\theta (x,t)} \right] = \rho (x) u_{tt}$$
where $\rho$ is the density and $T(x,t)$ is the tension force, we made the assumption that the vibrations are small, which gave us a linearized wave equation. I can see why some of the other assumptions (i.e. full flexibility, and no horizontal tension component) make sense, but I don't think I understand the insight behind this one.
You mean that vibrations are small? Because usually they are. More general versions you find in some textbooks like
\rho u_{tt} = \Bigl(\frac{u_x}{\sqrt{1+u_x^2}}\Bigr)_x
implicitly assume that displacement is only in the direction perpendicular to the string and that the density does not change--which is the case only for the small oscillations.
1331
##### APM346 Misc / Re: Extra help before term test
« on: September 27, 2012, 04:51:09 PM »
Yes special TA office hours or perhaps even a pre-test seminar similar to what Professor Moradifam used to offer last semester.
Let us think this out
1332
##### Misc Math / Re: Lecture 6 example
« on: September 27, 2012, 04:49:15 PM »
Hello,
I was going through the 6. lecture notes, where in the end an example is brought up that leads to an integral
$$I=\frac{1}{4}\int_0^t\cos(t')\bigl(\cos(x-ct+ct')-\cos(x+ct-ct')\bigr)dt'$$
I was trying to do that integral, but the only way that I could do it was to write out the cosines as complex exponentials, which lead me to eight terms in the end... Is there a cleverer way to do this integral?
Thanks!
In this example $c=2$ helps a bit but you could sea; without it.
The 1-st line -> 2nd (just integration) -> 3rd (formula $\cos (\alpha)-\cos (\beta)= 2\sin \bigl((\beta+\alpha)/2\bigr)\cdot \sin \bigl((\beta-\alpha)/2\bigr)$ and we ge the 4-th line.
Then formula $2\sin( \alpha) \cdot \cos(\beta)=\sin (\alpha+\beta)+\sin (\alpha-\beta)$ and integration.
1333
##### Home Assignment 2 / Re: Problem 3
« on: September 27, 2012, 01:41:03 PM »
Professor, could you fix this in the PDF file? I prefer the PDF file so I could work on the assignment without an internet connection.
Thank you
There was an error in both variants: it claimed to be "Home Assignment 1" in the title--now it fixed.
1334
##### Home Assignment 2 / Re: Problem 2
« on: September 27, 2012, 11:11:15 AM »
It looks like I should use the result from part 3 for part 4. However if so, how should I use the initial values?
Not really. You use parts (a),(b)
1335
##### Home Assignment 2 / Re: problem 1 typo?
« on: September 27, 2012, 11:10:32 AM »
Hi - In the pdf of home assignment 2 in problem 1 the inequalities throughout are different than the other version of the assignment (i.e. pdf version has 'greater than or equal to' and the other version in only '>'). Which one is correct?
Really does not matter, but I changed pdf to coincide
Pages: 1 ... 87 88 [89] 90 91 ... 93
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2018-01-22 00:34:33
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https://calculatores.com/percentage-increase-calculator
|
# Percentage Increase Calculator
## Introduction to Percentage Increase Calculator
We introduce the percentage increase calculator. It is a very popular tool all over the world. It helps you to calculate the increased value in terms of percentage. You will provide the values (initial value, final value) and get the answer without any manual calculations.
The increase value and increase percentage are different from each other. The increased value indicates how much the value increases from the initial value. The percentage increase means how much percent the value increases from the original value.
## Why should we use an increased percentage calculator online?
Suppose you want to calculate the increased value as a percentage. It would be best if you used this tool for calculation. You will get the accurate percentage through this converter within a few seconds.
With this online tool, you will get rid of tricky formulas and difficult calculations. When you calculate the percentage by manual method, it will increase the chance of mistakes. It will make it possible that you will get the wrong result.
## Advantages of the percentage increase tool
The online tool is very beneficial for its users. Some of the advantages are given below
• The calculation of the tool is 100 % accurate.
• The tool is very easy to use.
• The calculation speed of the tool is very fast.
• You can use this tool anywhere.
• Online percentage increase calculator is a time saver tool. Just click on the calculate button and get the percentage.
## How to find percentage with percent increase online calculator?
The online percentage calculation tool is very easy to use. There are a few steps to follow
• Open the tool by click on calculator.
• Now input the values (initial value, final value).
• You can use the example values for understanding.
• Click on the calculate button.
• It will provide you results.
If you want to recalculate the increased percentage, click on the calculate again button. It will load the page again.
## Understanding the formula
The formula is very easy to understand. It would help if you had the initial and final values for the calculation.
The formula is
$$percentage\;increase\;=\;100\;×\;\frac{(final\;value - initial\;value)}{(initial\;value)}$$
### Example
You have $500 in your savings account, and the Bank gave you$200 as your savings. How to calculate percentage increase in simple steps?
Solution
Initial value = 500
Increase value = 200
final value = 500 + 200 = 700
$$percentage\;increase\;=\;100\;×\;\frac{(final\;value - initial\;value)}{(initial\;value)}$$
%increase = 100 × (700 - 500) / 500
%increase = 100 × (200) / (500)
%increase = 100 × 0.4%
%increase = 40%
## Is the tool free of cost for anyone?
Yes! This online tool is free of cost for anyone. You will open the calculator and calculate the increased percentage of your data.
## Does the converter have any limit?
No, there is no limit. When you use the calculator, it’s up to you how many times you will calculate the percentage.
## Does it provide reliable results?
Yes! This tool provides you with reliable results. It is a tested and bug-free tool.
## Why do we calculate the increased value in the term of percent?
Because percentage provides a ratio between the initial value and final value, that is why we calculate the percentage to get the ratio and confirm how much percent value increased.
### Alan Walker
Last Updated June 02, 2022
Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.
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2022-09-26 07:03:40
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https://tex.stackexchange.com/questions/156196/newcommand-with-variable-name
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# \newcommand with variable name
I am typesetting a long mathematical text (lecture notes), in which I use the alphabets
\mathbb A
\mathcal A
\mathfrak A
very often, so I decided to name them
\A \sA \fA
(For bb A, script A, fraktur A resp.). Now I want to shorten my preamble by creating a helper
\newcommand{\mathletter}[1]{%
\newcommand{\#1}{\mathbb #1}
\newcommand{\s#1}{\mathcal #1}
\newcommand{\f#1}{\mathfrak #1}
}
which doesn't work since the \#1 etc. seem to not be expanded.
How can I wirte a macro which defines those three commands given a single letter as input?
Thanks for any help.
• It is strange. Why not define 3 new commands? If your code works what would you type: \mathletter{A}? – Sigur Jan 27 '14 at 14:23
• Because that means 26*3 = 78 lines of code vs. 36+5 = 41 lines, about half and much more readable than a bunch of \newcommand{\X}{\mathbb X} lines – AlexR Jan 27 '14 at 14:26
• This might be what you're looking for: tex.stackexchange.com/questions/28704/… – Snicksie Jan 27 '14 at 14:30
• Does this suffice: \documentclass{article} \usepackage{amssymb} \def\B#1{\mathbb #1} \def\C#1{\mathcal #1} \def\F#1{\mathfrak #1} \begin{document} $\B A \C A \F A$ \end{document} – Steven B. Segletes Jan 27 '14 at 14:34
• @AlexR, you don't need to retype. You can use Find/Replace tools. – Sigur Jan 27 '14 at 14:37
Thanks to @Snicksie, I have been able to come up with the following:
Note that this is not really "beautiful" and that it overwrites the commands \H,\L,\O,\P,\S but I have confirmed that I need none of them and "manually" undefined them so I get errors when I oversee any other commands.
\newcommand{\mathletter}[1]{%
\expandafter\newcommand\csname #1\endcsname{\mathbb #1}
\expandafter\newcommand\csname s#1\endcsname{\mathcal #1}
\expandafter\newcommand\csname f#1\endcsname{\mathfrak #1}
}%
\let\H\undefined
\let\L\undefined
\let\O\undefined
\let\P\undefined
\let\S\undefined
\mathletter A
\mathletter B
\mathletter C
...
\mathletter Z
Another very elegant solution, thanks to @StevenB.Segelets is to define:
\def\B#1{\mathbb #1}
\def\C#1{\mathcal #1}
\def\F#1{\mathfrak #1}
And use those slighly different commands then. This doesn't redefine any existing macros and therefor is probably a cleaner solution, but requires to change previous syntax (\A, \sA, \fA) in all documents and thus requires some "rewriting".
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2020-06-04 02:38:19
|
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|
https://www.semanticscholar.org/paper/Uniqueness-of-the-Ricci-flow-on-complete-noncompact-Chen-Zhu/e33aee2214149a874efa7700c1d4167066f664e9
|
# Uniqueness of the Ricci flow on complete noncompact manifolds
@article{Chen2005UniquenessOT,
title={Uniqueness of the Ricci flow on complete noncompact manifolds},
author={Binglong Chen and Xiping Zhu},
journal={Journal of Differential Geometry},
year={2005},
volume={74},
pages={119-154}
}
• Published 21 May 2005
• Mathematics
• Journal of Differential Geometry
The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified proof. In the later of 80's, Shi \cite{Sh1} generalized the local existence result to complete noncompact manifolds. However, the uniqueness of the solutions to the Ricci flow on complete noncompact manifolds is still an open question. Recently it was found that…
167 Citations
Pseudolocality for the Ricci Flow and Applications
• Mathematics
Canadian Journal of Mathematics
• 2011
Abstract Perelman established a differential Li-Yau-Hamilton $\left( \text{LHY} \right)$ type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on
An energy approach to the problem of uniqueness for the Ricci flow
We revisit the problem of uniqueness for the Ricci flow and give a short, direct proof, based on the consideration of a simple energy quantity, of Hamilton/Chen-Zhu’s theorem on the uniqueness of
The Kähler-Ricci flow on non-compact manifolds
We first study the general theory of Kähler-Ricci flow on non-compact complex manifolds. By using a parabolic Schwarz lemma and a local scalar curvature estimate, we prove a general existence theorem
Instantaneously complete Ricci flows on surfaces
The intention of this thesis is to give a survey of instantaneously complete Ricci flows on surfaces, focussing on the existence and uniqueness of its Cauchy problem. We prove a general existence
Ricci flow and metric geometry
This thesis considers two separate problems in the field of Ricci flow on surfaces. Firstly, we examine the situation of the Ricci flow on Alexandrov surfaces, which are a class of metric spaces
Uniqueness and pseudolocality theorems of the mean curvature flow
• Mathematics
• 2007
Mean curvature flow evolves isometrically immersed base manifolds $M$ in the direction of their mean curvatures in an ambient manifold $\bar{M}$. If the base manifold $M$ is compact, the short time
Uniqueness and stability of Ricci flow through singularities
• Mathematics
Acta Mathematica
• 2022
We verify a conjecture of Perelman, which states that there exists a canonical Ricci flow through singularities starting from an arbitrary compact Riemannian 3-manifold. Our main result is a
J un 2 00 7 Uniqueness and Pseudolocality Theorems of the Mean Curvature Flow
Mean curvature flow evolves isometrically immersed base manifolds M in the direction of their mean curvatures in an ambient manifold ¯ M. If the base manifold M is compact, the short time existence
Evolution of an extended Ricci flow system
has been used with great success for the construction of canonical metrics on Riemannian manifolds of low dimension. In his first paper on the Ricci flow, Hamilton proved that given an initial metric
Weak Solutions for the Ricci Flow on Closed Surfaces and Prescribed Curvature Problems
This work unites results on two different themes in the study of the conformal geometry of surfaces. On the one hand, we show uniqueness of classical solutions of the normalised, two-dimensional
## References
SHOWING 1-10 OF 23 REFERENCES
The entropy formula for the Ricci flow and its geometric applications
We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric
Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature
• Mathematics
• 2005
In this paper we study the Ricci flow on compact four-manifolds with positive isotropic curvature and with no essential incompressible space form. Our purpose is two-fold. One is to give a complete
ON THE UPPER ESTIMATE OF THE HEAT KERNEL OF A COMPLETE RIEMANNIAN MANIFOLD
• Mathematics
• 1981
Let M be a complete non-compact Riemannian manifold whose sectional curvature is bounded between two constants -k and K. Then one expects that the heat diffusion in such a manifold behaves like the
Deforming metrics in the direction of their Ricci tensors
In [4], R. Hamilton has proved that if a compact manifold M of dimension three admits a C Riemannian metric g0 with positive Ricci curvature, then it also admits a metric g with constant positive
Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Mathematics
• 1982
where dEλ is the projection valued measure associated with /^Δ". A natural problem is to study the behavior of the explicit kernel kf(X)(xx, x2) representing /(/^Δ), in terms of the behavior of
Deforming the metric on complete Riemannian manifolds
Soit (M,g ij (x)) une variete de Riemann a n dimensions complete non compacte de tenseur de complexe riemannien {R ijkl } satisfaisant: |R ijkl | 2 ≤k 0 sur M, ou 0 0 dependant seulement de n et de k
Four-manifolds with positive isotropic curvature
1. Positive Isotropic Curvature 2 (1) The Result 2 (2) The Algebra of Isotropic Curvature 4 2. Curvature Pinching 6 (1) Pinching Estimates which are Preserved 6 (2) Pinching Estimates which Improve
Linear and Quasilinear Equations of Parabolic Type
linear and quasi linear equations of parabolic type by o a ladyzhenskaia 1968 american mathematical society edition in english, note citations are based on reference standards however formatting
Lectures on Differential Geometry
• Mathematics, Geology
• 1994
In 1984, the authors gave a series of lectures on differential geometry in the Institute for Advanced Studies in Princeton, USA. These lectures are published in this volume, which describes the major
The heat equation and harmonic maps of complete manifolds
• Mathematics
• 1991
0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Mean-value inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2022-07-06 09:36:31
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https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.fourier_shift.html
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# scipy.ndimage.fourier_shift¶
scipy.ndimage.fourier_shift(input, shift, n=-1, axis=-1, output=None)[source]
Multi-dimensional fourier shift filter.
The array is multiplied with the fourier transform of a shift operation.
Parameters: input : array_like The input array. shift : float or sequence The size of the box used for filtering. If a float, shift is the same for all axes. If a sequence, shift has to contain one value for each axis. n : int, optional If n is negative (default), then the input is assumed to be the result of a complex fft. If n is larger than or equal to zero, the input is assumed to be the result of a real fft, and n gives the length of the array before transformation along the real transform direction. axis : int, optional The axis of the real transform. output : ndarray, optional If given, the result of shifting the input is placed in this array. None is returned in this case. fourier_shift : ndarray or None The shifted input. If output is given as a parameter, None is returned.
Examples
>>> from scipy import ndimage, misc
>>> import matplotlib.pyplot as plt
>>> import numpy.fft
>>> fig, (ax1, ax2) = plt.subplots(1, 2)
>>> plt.gray() # show the filtered result in grayscale
>>> ascent = misc.ascent()
>>> input_ = numpy.fft.fft2(ascent)
>>> result = ndimage.fourier_shift(input_, shift=200)
>>> result = numpy.fft.ifft2(result)
>>> ax1.imshow(ascent)
>>> ax2.imshow(result.real) # the imaginary part is an artifact
>>> plt.show()
#### Previous topic
scipy.ndimage.fourier_gaussian
#### Next topic
scipy.ndimage.fourier_uniform
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2018-01-24 00:08:31
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https://docs.decred.org/wallets/cli/startup-basics/
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# Startup Basics¶
This guide applies to command-line application users. Decrediton users can safely ignore the use of config files - Decrediton handles basic configuration automatically. It is also worth noting that some of our guides show configuration file settings and other guides show startup command flags.
## Configuration File Locations¶
All of the Decred software, when started, reads from a configuration file to determine which settings it should enable/disable/set during that initial load. All of the command line startup flags (e.g. dcrwallet --testnet) can be replaced by settings within the appropriate configuration file (e.g. dcrwallet --testnet could be replaced by testnet=1 in dcrwallet.conf).
These configuration files are located within the application home directory of the application. The location of these default home directories for Windows, macOS, and Linux are listed below:
OS dcrd, dcrwallet, dcrctl App Directories
Windows %LOCALAPPDATA%\Dcrd\
%LOCALAPPDATA%\Dcrwallet\
%LOCALAPPDATA%\Dcrctl\
macOS ~/Library/Application Support/Dcrd/
~/Library/Application Support/Dcrwallet/
~/Library/Application Support/Dcrctl/
Linux ~/.dcrd/
~/.dcrwallet/
~/.dcrctl/
Each of these folders is allowed its own .conf file, named after the individual application (e.g. dcrd uses dcrd.conf). Please also note that the Dcrd and Dcrwallet home directories are automatically created when each application is first launched. You will have to manually create a Dcrctl home directory to utilize a config file.
The dcrinstall installation method automatically creates configuration files, with the minimum configuration settings already enabled.
The Manual Installation method includes sample configuration files within the .zip/.tar.gz. It is recommended to copy these config files into the appropriate directory described above, and rename them to remove ‘sample-‘. These files have many settings commented out (comments are not read by the program during runtime) so all of these settings are effectively disabled. You can enable these pre-written settings by simply deleting the semi-colon before the line.
## Startup Command Flags¶
A majority of the settings you are able to set via the configuration file can also be passed to the application as parameters during launch. For example, the following OS-specific commands would open dcrd for Testnet use, an alternative to using testnet=1 in your config file:
Windows: dcrd.exe --testnet
macOS: ./dcrd --testnet
Linux: ./dcrd --testnet
The above example would first look to the dcrd configuration file for settings and then look to the executable command to enable the testnet setting.
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2018-12-19 10:37:04
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https://en.m.wikipedia.org/wiki/Quotient_field
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# Field of fractions
(Redirected from Quotient field)
In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The elements of the field of fractions of the integral domain ${\displaystyle R}$ are equivalence classes (see the construction below) written as ${\displaystyle {\frac {a}{b}}}$ with ${\displaystyle a}$ and ${\displaystyle b}$ in ${\displaystyle R}$ and ${\displaystyle b\neq 0}$. The field of fractions of ${\displaystyle R}$ is sometimes denoted by ${\displaystyle \operatorname {Frac} (R)}$ or ${\displaystyle \operatorname {Quot} (R)}$.
Mathematicians refer to this construction as the field of fractions, fraction field, field of quotients, or quotient field. All four are in common usage. The expression "quotient field" may sometimes run the risk of confusion with the quotient of a ring by an ideal, which is a quite different concept.
## Examples
• The field of fractions of the ring of integers is the field of rationals, ${\displaystyle \mathbb {Q} =\operatorname {Frac} (\mathbb {Z} )}$ .
• Let ${\displaystyle R:=\{a+b\mathrm {i} \mid a,b\in \mathbb {Z} \}}$ be the ring of Gaussian integers. Then ${\displaystyle \operatorname {Frac} (R)=\{c+d\mathrm {i} \mid c,d\in \mathbb {Q} \}}$ , the field of Gaussian rationals.
• The field of fractions of a field is canonically isomorphic to the field itself.
• Given a field ${\displaystyle K}$ , the field of fractions of the polynomial ring in one indeterminate ${\displaystyle K[X]}$ (which is an integral domain), is called the field of rational functions or field of rational fractions[1][2][3] and is denoted ${\displaystyle K(X)}$ .
## Construction
Let ${\displaystyle R}$ be any integral domain. For ${\displaystyle n,d\in R}$ with ${\displaystyle d\neq 0}$ , the fraction ${\displaystyle {\frac {n}{d}}}$ denotes the equivalence class of pairs ${\displaystyle (n,d)}$ , where ${\displaystyle (n,d)}$ is equivalent to ${\displaystyle (m,b)}$ if and only if ${\displaystyle nb=md}$ . (The definition of equivalence is modelled on the property of rational numbers that ${\displaystyle {\frac {n}{d}}={\frac {m}{b}}}$ if and only if ${\displaystyle nb=md}$ .) The field of fractions ${\displaystyle \operatorname {Frac} (R)}$ is defined as the set of all such fractions ${\displaystyle {\frac {n}{d}}}$ . The sum of ${\displaystyle {\frac {n}{d}}}$ and ${\displaystyle {\frac {m}{b}}}$ is defined as ${\displaystyle {\frac {nb+md}{db}}}$ , and the product of ${\displaystyle {\frac {n}{d}}}$ and ${\displaystyle {\frac {m}{b}}}$ is defined as ${\displaystyle {\frac {nm}{db}}}$ (one checks that these are well defined).
The embedding of ${\displaystyle R}$ in ${\displaystyle \operatorname {Frac} (R)}$ maps each ${\displaystyle n}$ in ${\displaystyle R}$ to the fraction ${\displaystyle {\frac {en}{e}}}$ for any nonzero ${\displaystyle e\in R}$ (the equivalence class is independent of the choice ${\displaystyle e}$ ). This is modelled on the identity ${\displaystyle {\frac {n}{1}}=n}$ .
The field of fractions of ${\displaystyle R}$ is characterised by the following universal property: if ${\displaystyle h:R\rightarrow F}$ is an injective ring homomorphism from ${\displaystyle R}$ into a field ${\displaystyle F}$ , then there exists a unique ring homomorphism ${\displaystyle g:\operatorname {Frac} (R)\rightarrow F}$ which extends ${\displaystyle h}$ .
There is a categorical interpretation of this construction. Let ${\displaystyle C}$ be the category of integral domains and injective ring maps. The functor from ${\displaystyle C}$ to the category of fields which takes every integral domain to its fraction field and every homomorphism to the induced map on fields (which exists by the universal property) is the left adjoint of the forgetful functor from the category of fields to ${\displaystyle C}$ .
A multiplicative identity is not required for the role of the integral domain; this construction can be applied to any nonzero commutative rng ${\displaystyle R}$ with no nonzero zero divisors. The embedding is given by ${\displaystyle r\mapsto {\frac {rs}{s}}}$ for any nonzero ${\displaystyle s\in R}$ .[4]
## Generalizations
### Localization
For any commutative ring ${\displaystyle R}$ and any multiplicative set ${\displaystyle S}$ in ${\displaystyle R}$ , the localization ${\displaystyle S}$ ${\displaystyle -1}$ ${\displaystyle R}$ is the commutative ring consisting of fractions ${\displaystyle {\frac {r}{s}}}$ with ${\displaystyle r\in R}$ and ${\displaystyle s\in S}$ , where now ${\displaystyle (r,s)}$ is equivalent to ${\displaystyle (r',s')}$ if and only if there exists ${\displaystyle t\in S}$ such that ${\displaystyle t(rs'-r's)=0}$ . Two special cases of this are notable:
• If ${\displaystyle S}$ is the complement of a prime ideal ${\displaystyle P}$ , then ${\displaystyle S}$ ${\displaystyle -1}$ ${\displaystyle R}$ is also denoted ${\displaystyle R_{P}}$ . When ${\displaystyle R}$ is an integral domain and ${\displaystyle P}$ is the zero ideal, ${\displaystyle R_{P}}$ is the field of fractions of ${\displaystyle R}$ .
• If ${\displaystyle S}$ is the set of non-zero-divisors in ${\displaystyle R}$ , then ${\displaystyle S}$ ${\displaystyle -1}$ ${\displaystyle R}$ is called the total quotient ring. The total quotient ring of an integral domain is its field of fractions, but the total quotient ring is defined for any commutative ring.
### Semifield of fractions
The semifield of fractions of an commutative semiring with no zero divisors is the smallest semifield in which it can be embedded. The elements of the semifield of fractions of the commutative semiring ${\displaystyle R}$ are equivalence classes written as ${\displaystyle {\frac {a}{b}}}$ with ${\displaystyle a}$ and ${\displaystyle b}$ in ${\displaystyle R}$ .
## References
1. ^ Ėrnest Borisovich Vinberg (2003). A course in algebra. p. 131.
2. ^ Stephan Foldes (1994). Fundamental structures of algebra and discrete mathematics. John Wiley & Sons. p. 128.
3. ^ Pierre Antoine Grillet (2007). Abstract algebra. p. 124.
4. ^ Hungerford, Thomas W. (1980). Algebra (Revised 3rd ed.). New York: Springer. pp. 142–144. ISBN 3540905189.
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2020-06-06 01:22:32
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http://www.stat.ufl.edu/info/seminar-abstracts/hobert.html
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## Jim Hobert, University of Florida
### Stability Relationships Among the Gibbs Sampler and its Subchains
Let $\Phi=\left\{(X_i,Y_i): i=0,1,2,\dots\right\}$ denote the Markov chain resulting from application of the two-variable Gibbs sampler using conditional densities that may correspond to an improper joint density. It is well known that the $X_i$'s themselves constitute a Markov chain as, of course, do the $Y_i$'s. We call these the subchains and denote them by $\Phi_x$ and $\Phi_y$. Our main result is that all three of these Markov chains share the same stability; that is, if one is positive recurrent (null recurrent, transient), then all three are positive recurrent (null recurrent, transient).
Our first application involves decision theory. Suppose that $W$ is a random variable with density $f(w|\theta)$ and that $\pi(\theta|w)$ is a proper posterior corresponding to an improper prior $\nu(\theta)$. Eaton (1992, Annals) showed that recurrence of the Markov chain with transition density $R(\eta|\theta)=\int \pi(\eta|w)f(w|\theta)dw$ implies that $\nu(\theta)$ is a "good" prior. We demonstrate that Eaton's Markov chain can be written as one of the subchains. Thus, recurrence of Eaton's chain can be established by showing that the other subchain is recurrent.
Our second application concerns Gibbs sampling with improper posteriors. Specifically, we show that even when the three chains $\Phi$, $\Phi_x$ and $\Phi_y$ are non-positive, there may still be positive recurrent chains lurking about. A recent example of Meng and van Dyk (1999, Biometrika) shows that it is possible to use these lurking chains to make valid statistical inferences via a Gibbs sampler based on an improper posterior. (Part of this talk is based on joint work with Christian Robert.)
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2018-01-20 06:51:04
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https://www.physicsforums.com/threads/minimum-safe-distance-from-a-radioactive-source.891515/
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# Homework Help: Minimum safe distance from a radioactive source
Tags:
1. Oct 31, 2016
### moenste
1. The problem statement, all variables and given/known data
The potassium isotope 4219K has a half-life of 12 hr, and disintegrates with the emission of a γ-ray to form the calcium isotope 4220Ca. What other radiation besides γ-rays must be emitted? How many electrons, protons, and neutrons are there in an atom of the calcium isotope?
The amount of radiation received in unit time by a person working near a radioactive source, commonly called the dose rate, is measured in rem hr-1. The safety regulations forbid dose rates in excess of 7.5 * 10-4 rem hr-1.The γ-ray dose rate from the 4219K source is found to be 3 * 10-3 rem hr-1 at a distance of 1 m. What is the minimum distance from this source at which it is safe to work?
After how long will it be safe to work at a distance of 1 m from this source?
2. The attempt at a solution
4219K → 4220Ca + 0-1β + 00γ.
4220Ca: electrons = protons = 20, neutrons = 22.
Minimum distance is (3 * 10-3) / (7.5 * 10-4) = 4. So 1 m from the source is 4 times more dangerous than it should be. So the distance should be increased 4 times, so the safe distance is 4 m. Why the answer is 2 m?
I used A = A0 e- λ t to find time. The dose should decrease from 3 * 10-3 rem hr-1 to 7.5 * 10-4 rem hr-1. So: 7.5 * 10-4 = 3 * 10-3 e- (ln 2 / 12) t → t = 4.3 hours. Why not 24? I also calculated everything in seconds, not hours, still same result when I change the final answer to seconds.
Why the distance is wrong and how to get the correct time?
Last edited: Oct 31, 2016
2. Oct 31, 2016
### James R
It's a beta decay process, which produces $\beta^-$ particles (electrons), as you say. In the beta-minus decay, an anti-neutrino is also produced.
The initial potassium isotope has 19 electrons. A beta particle (i.e. one more electron) is created in the decay process and is emitted from the system as ionising radiation. But the resulting calcium atom that is left over has only a changed nucleus and not a changed number of electrons surrounding that nucleus. So, the Calcium atom only has 19 electrons after the decay process.
The intensity of radiation from a point source drops off with the inverse square of the distance from the source.
The figure $7.5\times 10^{-4}$ doesn't appear in the problem statement that you've quoted. If it is correct, then your solution method is correct. However, I calculate the time as 24 hours, as required, using your numbers.
3. Oct 31, 2016
### Staff: Mentor
I don't see any definition for a safe dose rate. Is there information missing from the problem statement, or are there standard values from a table that you need to know?
4. Oct 31, 2016
### moenste
Very sorry, somehow I skipped an entire sentence while making the problem and then got distracted to check the text for mistakes,
5. Oct 31, 2016
### James R
A quick check:
$\frac{7.5\times 10^{-4}}{3.0\times 10^{-3}}=\frac{1}{4}$ so we need a dose rate that is one-quarter of its initial value. After 1 half-life the rate will be half of what it was initially, and after 2 half-lives it will be 1/4, so we need 2 half lives, or 24 hours.
6. Oct 31, 2016
### moenste
Got it.
4219K → 4220Ca + 0-1β + 00γ.
4220Ca: electrons = 19 (since we need to look at K, which has 19 electrons), protons = 20, neutrons = 22.
Not sure whether I understand this part. Is there a formula?
Yes, I re-calculated and got 24 hours. Had some corrections in my notes so probably calculated it wrong : ).
7. Nov 1, 2016
### moenste
Could you please elaborate on this part? This is the last thing I don't understand quite well in this problem : ).
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2018-05-24 02:55:53
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https://studyqas.com/some-managers-encourage-employees-to-make-their-own-decisions/
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# Some managers encourage employees to make their own decisions. this type of management is called a.
Some managers encourage employees to make their own decisions. this type of management is called a. autocratic b. democratic c. laissez-faire d. none of the above
## This Post Has 4 Comments
1. joel4676 says:
The correct answer is letter "C": laissez-faire.
Explanation:
Laissez-Faire management is the technique in which leaders provide subordinates the responsibility of making their own decisions. Usually, high-rank executives provide workers the resources needed for them to do their job but there is little to no guidance from them after that. This approach is said to be one that leads to low productivity. Though, the technique should be applied according to the situation that the organization is facing.
This type of decision making is Democratic
3. Expert says:
Ithink b hope that
4. Expert says:
c.
explanation:
regressive tax taxes the poor and less of the wealthy. this the rich get richer and the poor get more poor. this would create a large wealth gap.
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2023-03-25 23:50:28
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https://www.yaclass.in/p/mathematics-state-board/class-10/relations-and-functions-8849/composition-of-functions-13972/re-52259145-d2e8-44b9-8b1d-f4c7b3ed721a
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UPSKILL MATH PLUS
Learn Mathematics through our AI based learning portal with the support of our Academic Experts!
Let us learn the composition of three functions based on the composition of two functions.
Consider the four sets $$A$$, $$B$$, $$C$$ and $$D$$.
Let $$f: A \rightarrow B$$, $$g: B \rightarrow C$$, $$h: C \rightarrow D$$ be three functions.
The functions $$f$$, $$g$$ and $$h$$ are composed as $$f \circ \left(g \circ h\right)$$ and $$\left(f \circ g\right) \circ h$$.
Here, we observe that three functions are involved in the composition. So, it is obvious that the composition of the functions is not commutative.
But the composition of three functions is always associative. That is equivalent to $$f \circ \left(g \circ h\right)$$ $$=$$$$\left(f \circ g\right) \circ h$$.
The composition of three functions is represented using an arrow diagram as follows:
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2023-01-31 03:59:02
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https://codexgalactic.com/2011/03/18/greens-functions/?replytocom=81
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# Green's functions
Lecture Notes on Green's Functions for lecture given on St. Patrick's day, so written in Green naturally.
Some of the most important equations in physics can be solved by constructing a beast with a curious set of properties, called a Green’s function. This post contains some interesting nuggets from a lecture I gave on St. Patrick’s day about Green’s functions to the course I assist, Mathematical Methods in the Physical Sciences II. I’ll give some historical background about the life of George Green, the functions’ namesake, introduce what a Green’s function actually is–and what exactly it’s good for–in layperson’s terms, and in the final section go through the physics and the math to develop a deeper understanding of what is going on as well as to truly convince ourselves that the function is holding up its side of the bargain.
The lecture follows closely material in Mathematical Methods in The Physical Sciences, Mathematical Methods for Physicists, and “The Green of Green Functions” and the interested reader is referred to these sources for further information.
# George Green
The namesake of Green’s theorem and Green’s functions, George Green, led an atypical life, first blossoming as a mathematician in his 30s after a career as a miller with little formal education to speak of. Born in 1793 to a baker in Nottingham Green managed to learn to read and write during his 18 months of private school as a child before joining the family business so to speak, working at the nearby mill and having 7 children over the years with the miller’s daughter, whom he never married. In 1823 Green’s life took a turn when he joined the Nottingham subscription library at age 30, which gave him access to the leading scientific journals of the age and a peer group of like minded individuals hailing from the surrounding countryside.
Just 5 years later at age 35, Green self-published “An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism1 almost apologizing for wasting mathematicians’ time in the introductory paragraphs
…it is hoped the difficulty of the subject will incline mathematicians to read this work with indulgence, more particularly when they are informed that it was written by a young man, who has been obliged to obtain the little knowledge he possesses, at such intervals and by such means, as other indispensable avocations which offer but few opportunities of mental improvement, afforded.
This 70 page essay contained both the derivation of Green’s theorem and Green’s functions. Mostly, Green’s customers were local merchants, seemly looking for an erudite bookshelf decoration. At some point, a successful businessman with a background in mathematics, Edward Bromhead, was sufficiently impressed by Green’s work to write him a letter offering mentorship and support. Green apparently asked his local friends their opinion of Bromhead’s sincerity and was told that Bromhead was just being polite and that it would be inappropriate for someone of such a different social standing to accept such an offer. 20 months later, Green reconsidered and wrote Bromhead accepting his offer.
With Bromhead’s support, Green published several papers, and eventually attended Cambridge in spite of the fact that he possessed, in his own words, “little Latin, less Greek” and had “seen too many winters”. His seminal work that took his career from miller to mathematician remained unpublished and largely unappreciated until shortly after Green’s ignoble death of the flu at age 43 when Lord Kelvin arranged for its publication.
# Green’s functions
Poisson’s equation $\nabla^2 \psi = \frac{\rho}{\epsilon}$ and Laplace’s equation $\nabla^2 \psi = 0$ model the electrostatic potential $\psi$ in the presence and absence of charge, respectively. The equation in the presence of charge is clearly more complicated and can be solved by invoking the machinery of Green’s functions, which were originally directed towards electrostatic problems of this sort. In this example, the Green’s function $G(r,r')$ physically represents the potential at the point $r$ produced by a unit charge $r'$. Before moving to more complicated examples, it’s easy to see although more complicated to prove that $G$ is symmetric in its arguments. The universe does not often play directional favorites, so we would imagine that the potential produced would be the same, were the charges $r$ and $r'$ swapped.
Green’s functions quickly found other applications to problems in electromagnetic, thermal and mechanical phenomena. Moreover, Green’s functions can be used to formulate a theory of classical wave scattering which leads us into quantum mechanical applications as we notice that the Schrödinger equation of quantum mechanics is itself a wave equation. Using this we can extend the technique to apply to the situation of a non-relativistic scattering of a single particle by an external potential. Once we’ve used Green’s functions to treat scattering we can be very excited. In particle physics interactions scattering is how we investigate properties of the elementary particles. Particle interactions are multiple scattering processes and the transmission of forces is done via quantum fields. The propagation of fields between points was exactly what Green’s functions were invented for–indeed Green’s functions appear in modern quantum field theories. Known as Feynman propagators in this context, they are a standard tool in modern particle physics.
But going back to Poisson’s equation above, we can generalize the equation and its solution, the Green’s function, with a modicum of additional mathematical machinery. This procedure and its associated notation is well covered in Mathematical Methods in The Physical Sciences, Section 9.4. Once generalized it’s easy to spot candidate applications–physical situations with equations of a similar form–for applying the Green’s function methodology to solve them.
Once we have found an equation of the right form we’d like to solve, with the increased abstraction we can show that if we construct a function $G(x,t)$ which is:
1. piecewise over a defined interval
2. whose pieces satisfy boundary conditions on the interval
3. whose pieces patch together nicely (i.e. fit together perfectly at some location $t$)
4. but not too nicely (i.e. their derivative is discontinuous at $t$)
then we can use $G(x,t)$ to solve the original equation. More precisely a we take a weighted sum of $G$‘s value over our defined interval. In our electrostatics terminology $G$ corresponds to a weighting function that enhances or reduces the effect of a charge element according to its distance from the source. Everything we need from a solution has now been built into the construction of $G$: sounds like black magic, but it’s not. Convincing oneself mathematically is a conceptually straightforward procedure, although a bit involved with the full generalized machinery: simply plug the constructed solution back into the original equation and see it satisfied.
# Physical Intuition
Here I’ll consider a simpler, less general example, to develop some physical intuition as to what the Green’s function is actually representing by providing the mathematical representation of what I have up to now simply referred to as the solution and then concisely going through the calculation checking that our constructed solution actually satisfies the desired equation.
Consider the differential equation $y'' + \omega^2 y = f(t)$, where $f(t)$ is some given forcing function. Moreover, let’s impose some simple boundary conditions namely
(1) $y_0=y_0'=0$.
Next we’re going to do something a bit strange, but why will become clear. Namely, we’re going to rewrite $f(t)$ as an integral over a delta function. Recall from the definition for a delta function that $\int_a^b = \phi(t) \delta(t-t_0)dt = \phi(t_0)$ if $t_0$ lies within the integration limits, and 0 otherwise. In this formulation we can think of the force $f(t)$ as the limiting case of a whole sequence of impulses.
(2) $latex f(t)=\int_a^b = f(t’) \delta(t’-t)dt$.
Now that we have formulated this new, strange way of thinking of the forcing function and many more delta functions than we might have initially bargained for, let’s simplify things again by considering a single delta function, namely what if $f(t)=\delta(t'-t)$. We now solve our differential equation (1) for this $f(t)$, which corresponds to a unit impulse at $t'$. Solving this equation is rather easy with a sleight of hand: we simply define the solution to be a function which we call $G(t,t')$. That is $G(t,t')$ is the solution to
(3) $\frac{d^2}{dt^2} G(t,t') + \omega^2 G(t,t') = \delta(t'-t)$.
Finally given some forcing function $f(t)$ we try to find the solution of (1) by simply adding up the response of many such impulses, guessing that the final solution is over the form
(4) $y(t)=\int_0^\infty G(t,t')f(t')dt$.
For now, this is just a guess but we can show it’s correct by following the strategy of plugging it into the original equation (1) and showing that it indeed satisfies it:
• Substitute (4) into (1): $y'' + \omega^2 y = (\frac{d^2}{dt^2}+\omega^2)y=(\frac{d^2}{dt^2}+\omega^2)\int_0^\infty G(t,t')f(t') dt'=\int_0^\infty (\frac{d^2}{dt^2}+\omega^2)G(t,t')f(t') dt'$
• Use (3) to simplify: $y'' + \omega^2 y=\int_0^\infty \delta(t'-t) f(t')dt'$
• Use (2) to finish the proof: $y'' + \omega^2y=f(t)$
Thus (4) is the solution of (1). This finally gives us an easier way to imagine the roll the Green’s function is playing in the solution, it is the response of the system to a unit impulse at $t=t'$ and we have been able to show the finally solution is a sum of such responses.
# References
1. George Green (1841). An Essay on the Application of mathematical Analysis to the theories of Electricity and Magnetism Crelle’s Journal arXiv: 0807.0088v1
## 0 thoughts on “Green's functions”
1. René says:
Very nicely written – sounds a bit like poesy in my physics-trained ears 😉
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2019-07-19 04:10:37
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http://noahpinionblog.blogspot.com/2013/10/lars-peter-hansen-explained-kind-of.html
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## Monday, October 14, 2013
### Lars Peter Hansen explained. Kind of.
The entire econo-blogosphere has its usual pieces up explaining the work of two of this year’s Nobel(ish) laureates in economics, Gene Fama and Bob Shiller. Most of them just handwave when it comes to Lars Peter Hansen’s contributions.
Disclaimer: Skip this post if you already know all about GMM and can spout out the Hansen (1982) results without even looking. Also, I am not an econometrician and I learned this stuff years ago. Substantive corrections and amplifications are very welcome in the comments. I will try to not to assume that the reader knows everything in finance and econometrics except GMM. I will fail.
(Haters: Yes, yes, I’m sure Noah would never do an entire post just on the incredibly banal concept of GMM. Too bad, he is away this fall. Except of course when he’s not. Also to haters: My putting out crappy posts is an incentive for him to come back sooner.)
Generalized Method of Moments, or GMM, is a method for estimating statistical models. It allows you to write down models, estimate parameters, and test hypotheses (restrictions) on those models. It can also provide an overarching framework for econometrics. Fumio Hayashi’s textbook, which old timers shake their head at, uses GMM as the organizing framework of his treatment, and derives many classical results as special cases of GMM.
Since the claim is that GMM is particularly useful to financial data, let’s motivate with a financial model based on Hansen and Singleton (1983). It may seem preposterously unrealistic, but this is what asset pricing folks do, and you can always consider it a starting point for better models, as we do with Modigliani-Miller. Suppose the economy consists of a single, infinitely-lived representative consumer, whose von Neumann-Morgenstern utility function exhibits constant relative risk aversion, $$U(c_t) = \frac{c_t^\gamma} \gamma, \quad \gamma < 1,$$ where $$c_t$$ is consumption in period t and $$\gamma$$ is the coefficient of relative risk aversion. She maximizes her expected utility $$E_0 \left[ \sum_{t=0}^\infty \beta^t U(c_t) \right], \quad 0 < \beta < 1,$$ where $$E_0$$ means expectation with information available at the beginning of the problem and $$\beta$$ is a discount factor to represent pure time preference. This utility function implies that the representative consumer prefers more consumption, other things being equal, with more weight on consumption that happens sooner rather than later, but also wants to avoid a future consumption path that is too risky. She will invest in risky, assets, but exactly how risky?
If we introduce multiple assets, then try to solve this model by differentiating the expected utility function and setting it equal to zero, we get a first order condition $$\label{returns-moment} E_t \left[ \beta \left( \frac{c_{t+1}}{c_t} \right) ^\alpha r_{i,t+1} \right] = 1, \quad i = 1, \ldots, N,$$ where $$\alpha \equiv \gamma - 1$$ and $$r_{i,t+1}$$ is the return on asset i from time t to time t+1. This approach is the basis of the entire edifice of “consumption based asset pricing” and it provides a theory for asset returns: they should be related to consumption growth, and in particular, assets that are highly correlated with consumption growth (have a high “consumption beta”) should have higher returns because they provide less insurance against consumption risk.
Equation $$\eqref{returns-moment}$$ contains some variables such as $$c_t$$ and $$r_{i,t+1}$$ that we should hopefully be able to read in the data. It also contains parameters $$\beta$$ and $$\alpha$$ (or, of you prefer, $$\gamma$$), that we would like to estimate, and then judge whether the estimates are realistic. We would also like to test whether $$\eqref{returns-moment}$$ provides a good description of the consumption and returns data, or in other words, whether this is a good model.
The traditional organizing method of statistics is maximum likelihood. To apply it to our model, we would have to add an error term $$\varepsilon_t$$ that represents noise and unobserved variables, specify a full probability distribution for it, and then find parameters $$\beta$$ and $$\alpha$$ that maximizes the likelihood (which is kind of like a probability) that the model generates the data we actually have. We then have several ways to test the hypothesis that this model describes the data well.
The problem with maximum likelihood methods is that we have to specify a full probability distribution for the data. It’s common to assume a normal distribution for $$\varepsilon_t$$. Sometimes you can assume normality without actually imposing too many restrictions on the model, but some people always like to complain whenever normal distributions are brought up.
Hansen’s insight, based on earlier work, was that we could write down the sample analog of $$\eqref{returns-moment}$$, $$\label{sample-analog} \frac 1 T \sum_{t=1}^T \beta \left( \frac{ c_{t+1}}{c_t} \right)^\alpha r_{i,t+1} = 1,$$ where instead of an abstract expected value we have an actual sample mean. Equation $$\eqref{sample-analog}$$ can be filled in with observed values of consumption growth and stock returns, and then solved for $$\beta$$ and $$\alpha$$. Hansen discovered the exact assumptions for when this is valid statistically. He also derived asymptotic properties of the resulting estimators and showed how to test restrictions on the model, so we can test whether the restriction represented by $$\eqref{returns-moment}$$ is supported by the data.
One big puzzle in consumption based asset pricing is that consumption is much smoother than stock returns than is predicted by the theory (I haven’t derived that, but manipulate $$\eqref{returns-moment}$$ a little and you will see it); one of my favorite papers in this literature uses garbage as a proxy for consumption.
How does GMM relate to other methods? It turns out that you can view maximum likelihood estimation as a special case of GMM. Maximum likelihood estimation involves maximizing the likelihood function (hence the name), which implies taking a derivative and setting the derivative (called the score function in this world) equal to zero. Well, that’s just GMM with a moment condition saying the score function is equal to zero. Similarly, Hayashi lays out how various other classical methods in econometrics such as OLS, 2SLS and SUR can be viewed as special cases of GMM.
People who are not expert theoretical econometricians often have to derive their own estimators for some new-fangled model they have come up with. In many contexts it is simply more natural, and easier, to use moment conditions as a starting point than to try to specify the entire (parameterized) probability distribution of errors.
One paper that I find quite neat is Richardson and Smith (1993), who propose a multivariate normality test based on GMM. For stock returns, skewness and excess kurtosis are particularly relevant, and normality implies that they are both zero. Since skewness and excess kurtosis are moments, it is natural to specify as moment conditions that they are zero, estimate using GMM, and then use the J-test to see if the moment conditions hold.
PS. Noah will tell me I am racist for getting my Japanese names confused. I was going to add that in addition to econometrics, Hayashi is also known for his work on the economy of Ancient Greece. That’s actually Takeshi Amemiya, whose Advanced Econometrics is a good overview of the field as it stood right before the “GMM revolution”.
1. Great explanation. I think one of the great things about GMM is that it allows us to estimate a single equation from a model without assuming that the entire model is "true." Additionally, an underappreciated aspect of GMM is that it shows how silly the structural vs. reduced form debate is. Viewed through the lens of GMM (which as you note is a generalization of OLS), this debate reduces to a differences in functional form.
2. Nice explanation, but let's not forget that the J test is really just Sargan's old test of over-identification, re-visited.
3. Thanks for the helpful primer! Quick q, shouldn't equations 2, 3 and 4 have beta^t so that later periods are discounted more heavily?
1. Anonymous1:34 PM
Good catch, I have fixed that. Equation 3 shouldn’t because that is a view of the optimization problem over a single period from time t to time t + 1.
4. The Nobel Prize committee honored Lars Peter Hansen for his work in developing a statistical method for testing rational theories of asset price movements. The statistical method Hansen developed is Generalized Method of Moments (GMM). The fact that Hansen won the Nobel Prize for his “empirical analysis of asset prices” caught me off guard as I did not realize this was the original application of GMM.
GMM is used in the estimation of the New Keynesian Phillips Curve. The New Keynesian Phillips Curve includes expectations of future inflation as an idependent variable. Since inflation expectations cannot really be observed, GMM offers a way around this difficulty.
The New Keynesian Phillips Curve, which was developed in 1995, is integral to most DSGE models that central banks across the globe are increasingly dependent. Thus it’s hard to imagine modern central banking without Hansen’s contributions to econometrics. So for Hansen to have won the prize for his empirical analysis of asset prices strikes me as somewhat ironic.
1. Yes, Hansen and Shiller made perfect sense as Nobel winners, and Hansen made perfect sense as a Nobel winner, but the three of them together was puzzling to me until I read your explanation. But even so, I think Hansen should've won a separate Nobel, or one in conjunction with other econometricians, rather than being lumped in with finance guys.
5. Anonymous1:38 PM
The coefficient of relative risk aversion (-cu''/u') isn't gamma in your example, it's 1-gamma.
I wouldn't say Hansen's insight was that moments could be used for estimation. As the link indicates, that was known for a while. It was about how one could use the 'extra' moment conditions that often crop up.
6. Anonymous2:18 PM
Shouldn't (4) have 1/beta instead of beta^t if it's taking a sample average?
1. Anonymous4:08 PM
I added 1/T in front, is that what you meant?
2. Anonymous4:41 PM
That, and no t superscript on beta.
3. Anonymous5:09 PM
Aaaaah right. Many thanks.
7. Anonymous2:15 AM
Good to see one of the backup team interacting with the prizes and trying to provide some background. Extra kudos for taking on the hardest one. A bit disappointing that with 8 authors on the list to the right of the page, and 3 winners, we only got one post on the prize today.
8. Kevin6:30 AM
This is very interesting. I'm a statistician, and basically all statistical inference that is taught in statistics is maximum likelihood. You mention that a weakness of maximum likelihood is the need to make parametric assumptions. Fitting non-parametric models is done usually with spline methods in statistics.
I've never seen GMM taught before. So this post makes me wonder why this isn't taught in statistics, given that GMM is also a generalization of maximum likelihood according to this post. Any thoughts?
Also, how do you include LaTeX in blog posts?
1. Anonymous8:19 AM
I haven’t touched on the computational aspects of GMM. As you can imagine, for linear (and possibly other) models, there are closed form solutions. (Obviously, in the case of models that reduce to OLS and such.) Otherwise it’s a matter of using numerical root finding methods.
GMM has its origins in asset pricing. Every econometrics sequence teaches some GMM, but not all professors make it the unifying framework in the way that Hayashi does, and in some departments that approach would be regarded as a little eccentric.
I use MathJax for math in blog posts.
9. Seems like much to-do about nothing. A sort of least squares fit algorithm for c rappy parametric models with sparse data. This is worthy of a Nobel? even more scary, central bank models depend on this? E-gad, we're in worse shape than I thought...
10. Anonymous1:27 AM
Why do the old timers shake heads at Hayashi?
1. Anonymous7:41 AM
They don’t mind GMM and spending a week or two teaching it, but they tend to think that making GMM the basis of all econometrics is putting the cart before the horse.
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2018-11-14 09:37:31
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https://labs.tib.eu/arxiv/?author=Elizabeth%20Buckley-Geer
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• ### DES Science Portal: Creating Science-Ready Catalogs(1708.05642)
May 28, 2018 astro-ph.IM
We present a novel approach for creating science-ready catalogs through a software infrastructure developed for the Dark Energy Survey (DES). We integrate the data products released by the DES Data Management and additional products created by the DES collaboration in an environment known as DES Science Portal. Each step involved in the creation of a science-ready catalog is recorded in a relational database and can be recovered at any time. We describe how the DES Science Portal automates the creation and characterization of lightweight catalogs for DES Year 1 Annual Release, and show its flexibility in creating multiple catalogs with different inputs and configurations. Finally, we discuss the advantages of this infrastructure for large surveys such as DES and the Large Synoptic Survey Telescope. The capability of creating science-ready catalogs efficiently and with full control of the inputs and configurations used is an important asset for supporting science analysis using data from large astronomical surveys.
• ### ProtoDESI: First On-Sky Technology Demonstration for the Dark Energy Spectroscopic Instrument(1710.08875)
May 2, 2018 astro-ph.IM
The Dark Energy Spectroscopic Instrument (DESI) is under construction to measure the expansion history of the universe using the baryon acoustic oscillations technique. The spectra of 35 million galaxies and quasars over 14,000 square degrees will be measured during a 5-year survey. A new prime focus corrector for the Mayall telescope at Kitt Peak National Observatory will deliver light to 5,000 individually targeted fiber-fed robotic positioners. The fibers in turn feed ten broadband multi-object spectrographs. We describe the ProtoDESI experiment, that was installed and commissioned on the 4-m Mayall telescope from August 14 to September 30, 2016. ProtoDESI was an on-sky technology demonstration with the goal to reduce technical risks associated with aligning optical fibers with targets using robotic fiber positioners and maintaining the stability required to operate DESI. The ProtoDESI prime focus instrument, consisting of three fiber positioners, illuminated fiducials, and a guide camera, was installed behind the existing Mosaic corrector on the Mayall telescope. A Fiber View Camera was mounted in the Cassegrain cage of the telescope and provided feedback metrology for positioning the fibers. ProtoDESI also provided a platform for early integration of hardware with the DESI Instrument Control System that controls the subsystems, provides communication with the Telescope Control System, and collects instrument telemetry data. Lacking a spectrograph, ProtoDESI monitored the output of the fibers using a Fiber Photometry Camera mounted on the prime focus instrument. ProtoDESI was successful in acquiring targets with the robotically positioned fibers and demonstrated that the DESI guiding requirements can be met.
• ### Extreme variability quasars from the Sloan Digital Sky Survey and the Dark Energy Survey(1706.07875)
June 23, 2017 astro-ph.CO, astro-ph.GA
We perform a systematic search for long-term extreme variability quasars (EVQs) in the overlapping Sloan Digital Sky Survey (SDSS) and 3-Year Dark Energy Survey (DES) imaging, which provide light curves spanning more than 15 years. We identified ~1000 EVQs with a maximum g band magnitude change of more than 1 mag over this period, about 10% of all quasars searched. The EVQs have L_bol~10^45-10^47 erg/s and L/L_Edd~0.01-1. Accounting for selection effects, we estimate an intrinsic EVQ fraction of ~30-50% among all g<~22 quasars over a baseline of ~15 years. These EVQs are good candidates for so-called "changing-look quasars", where a spectral transition between the two types of quasars (broad-line and narrow-line) is observed between the dim and bright states. We performed detailed multi-wavelength, spectral and variability analyses for the EVQs and compared to their parent quasar sample. We found that EVQs are distinct from a control sample of quasars matched in redshift and optical luminosity: (1) their UV broad emission lines have larger equivalent widths; (2) their Eddington ratios are systematically lower; and (3) they are more variable on all timescales. The intrinsic difference in quasar properties for EVQs suggest that internal processes associated with accretion are the main driver for the observed extreme long-term variability. However, despite their different properties, EVQs seem to be in the tail of a continuous distribution of quasar properties, rather than standing out as a distinct population. We speculate that EVQs are normal quasars accreting at relatively low accretion rates, where the accretion flow is more likely to experience instabilities that drive the factor of few changes in flux on multi-year timescales.
• ### Core or cusps: The central dark matter profile of a redshift one strong lensing cluster with a bright central image(1703.08410)
June 2, 2017 astro-ph.CO, astro-ph.GA
We report on SPT-CLJ2011-5228, a giant system of arcs created by a cluster at $z=1.06$. The arc system is notable for the presence of a bright central image. The source is a Lyman Break galaxy at $z_s=2.39$ and the mass enclosed within the 14 arc second radius Einstein ring is $10^{14.2}$ solar masses. We perform a full light profile reconstruction of the lensed images to precisely infer the parameters of the mass distribution. The brightness of the central image demands that the central total density profile of the lens be shallow. By fitting the dark matter as a generalized Navarro-Frenk-White profile---with a free parameter for the inner density slope---we find that the break radius is $270^{+48}_{-76}$ kpc, and that the inner density falls with radius to the power $-0.38\pm0.04$ at 68 percent confidence. Such a shallow profile is in strong tension with our understanding of relaxed cold dark matter halos; dark matter only simulations predict the inner density should fall as $r^{-1}$. The tension can be alleviated if this cluster is in fact a merger; a two halo model can also reconstruct the data, with both clumps (density going as $r^{-0.8}$ and $r^{-1.0}$) much more consistent with predictions from dark matter only simulations. At the resolution of our Dark Energy Survey imaging, we are unable to choose between these two models, but we make predictions for forthcoming Hubble Space Telescope imaging that will decisively distinguish between them.
• DESI (Dark Energy Spectroscopic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations (BAO) and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. To trace the underlying dark matter distribution, spectroscopic targets will be selected in four classes from imaging data. We will measure luminous red galaxies up to $z=1.0$. To probe the Universe out to even higher redshift, DESI will target bright [O II] emission line galaxies up to $z=1.7$. Quasars will be targeted both as direct tracers of the underlying dark matter distribution and, at higher redshifts ($2.1 < z < 3.5$), for the Ly-$\alpha$ forest absorption features in their spectra, which will be used to trace the distribution of neutral hydrogen. When moonlight prevents efficient observations of the faint targets of the baseline survey, DESI will conduct a magnitude-limited Bright Galaxy Survey comprising approximately 10 million galaxies with a median $z\approx 0.2$. In total, more than 30 million galaxy and quasar redshifts will be obtained to measure the BAO feature and determine the matter power spectrum, including redshift space distortions.
• DESI (Dark Energy Spectropic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. The DESI instrument is a robotically-actuated, fiber-fed spectrograph capable of taking up to 5,000 simultaneous spectra over a wavelength range from 360 nm to 980 nm. The fibers feed ten three-arm spectrographs with resolution $R= \lambda/\Delta\lambda$ between 2000 and 5500, depending on wavelength. The DESI instrument will be used to conduct a five-year survey designed to cover 14,000 deg$^2$. This powerful instrument will be installed at prime focus on the 4-m Mayall telescope in Kitt Peak, Arizona, along with a new optical corrector, which will provide a three-degree diameter field of view. The DESI collaboration will also deliver a spectroscopic pipeline and data management system to reduce and archive all data for eventual public use.
• ### VDES J2325-5229 a z=2.7 gravitationally lensed quasar discovered using morphology independent supervised machine learning(1607.01391)
Nov. 15, 2016 astro-ph.GA
We present the discovery and preliminary characterization of a gravitationally lensed quasar with a source redshift $z_{s}=2.74$ and image separation of $2.9"$ lensed by a foreground $z_{l}=0.40$ elliptical galaxy. Since the images of gravitationally lensed quasars are the superposition of multiple point sources and a foreground lensing galaxy, we have developed a morphology independent multi-wavelength approach to the photometric selection of lensed quasar candidates based on Gaussian Mixture Models (GMM) supervised machine learning. Using this technique and $gi$ multicolour photometric observations from the Dark Energy Survey (DES), near IR $JK$ photometry from the VISTA Hemisphere Survey (VHS) and WISE mid IR photometry, we have identified a candidate system with two catalogue components with $i_{AB}=18.61$ and $i_{AB}=20.44$ comprised of an elliptical galaxy and two blue point sources. Spectroscopic follow-up with NTT and the use of an archival AAT spectrum show that the point sources can be identified as a lensed quasar with an emission line redshift of $z=2.739\pm0.003$ and a foreground early type galaxy with $z=0.400\pm0.002$. We model the system as a single isothermal ellipsoid and find the Einstein radius $\theta_E \sim 1.47"$, enclosed mass $M_{enc} \sim 4 \times 10^{11}$M$_{\odot}$ and a time delay of $\sim$52 days. The relatively wide separation, month scale time delay duration and high redshift make this an ideal system for constraining the expansion rate beyond a redshift of 1.
• ### Rest-Frame Optical Spectra of Three Strongly Lensed Galaxies at z~2(0906.2197)
June 11, 2009 astro-ph.CO, astro-ph.GA
We present Keck II NIRSPEC rest-frame optical spectra for three recently discovered lensed galaxies: the Cosmic Horseshoe (z = 2.38), the Clone (z = 2.00), and SDSS J090122.37+181432.3 (z = 2.26). The boost in signal-to-noise ratio (S/N) from gravitational lensing provides an unusually detailed view of the physical conditions in these objects. A full complement of high S/N rest-frame optical emission lines is measured, spanning from rest-frame 3600 to 6800AA, including robust detections of fainter lines such as H-gamma, [SII]6717,6732, and in one instance [NeII]3869. SDSS J090122.37+181432.3 shows evidence for AGN activity, and therefore we focus our analysis on star-forming regions in the Cosmic Horseshoe and the Clone. For these two objects, we estimate a wide range of physical properties, including star-formation rate (SFR), metallicity, dynamical mass, and dust extinction. In all respects, the lensed objects appear fairly typical of UV-selected star-forming galaxies at z~2. The Clone occupies a position on the emission-line diagnostic diagram of [OIII]/H-beta vs. [NII]/H-alpha that is offset from the locations of z~0 galaxies. Our new NIRSPEC measurements may provide quantitative insights into why high-redshift objects display such properties. From the [SII] line ratio, high electron densities (~1000 cm^(-3)) are inferred compared to local galaxies, and [OIII]/[OII] line ratios indicate higher ionization parameters compared to the local population. Building on previous similar results at z~2, these measurements provide further evidence (at high S/N) that star-forming regions are significantly different in high-redshift galaxies, compared to their local counterparts (abridged).
• ### Discovery of A Very Bright, Strongly-Lensed z=2 Galaxy in the SDSS DR5(0809.4475)
Sept. 25, 2008 astro-ph
We report on the discovery of a very bright z = 2.00 star-forming galaxy that is strongly lensed by a foreground z=0.422 luminous red galaxy (LRG). This system was found in a systematic search for bright arcs lensed by LRGs and brightest cluster galaxies in the Sloan Digital Sky Survey Data Release 5 sample. Follow-up observations on the Subaru 8.2m telescope on Mauna Kea and the Astrophysical Research Consortium 3.5m telescope at Apache Point Observatory confirmed the lensing nature of this system. A simple lens model for the system, assuming a singular isothermal ellipsoid mass distribution, yields an Einstein radius of 3.82 +/- 0.03 arcsec or 14.8 +/- 0.1 kpc/h at the lens redshift. The total projected mass enclosed within the Einstein radius is 2.10 +/- 0.03 x 10^12 M_sun/h, and the magnification factor for the source galaxy is 27 +/- 1. Combining the lens model with our gVriz photometry, we find an (unlensed) star formation rate for the source galaxy of 32 M_sun/h / yr, adopting a fiducial constant star formation rate model with an age of 100 Myr and E(B-V) = 0.25. With an apparent magnitude of r = 19.9, this system is among the very brightest lensed z >= 2 galaxies, and provides an excellent opportunity to pursue detailed studies of the physical properties of an individual high-redshift star-forming galaxy.
• ### A Virtual Library of Technical Publications(cs/0208039)
Aug. 23, 2002 cs.DL
Through a collaborative effort, the Fermilab Information Resources Department and Computing Division have created a "virtual library" of technical publications that provides public access to electronic full-text documents. This paper will discuss the vision, planning and milestones of the project, as well as the hardware, software and interdepartmental cooperation components.
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2020-06-02 12:42:10
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45190995931625366, "perplexity": 3390.1842628462205}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347424174.72/warc/CC-MAIN-20200602100039-20200602130039-00554.warc.gz"}
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http://indywebshop.com/failed-to/failed-to-parse-unknown-error-mediawiki.php
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Home > Failed To > Failed To Parse Unknown Error Mediawiki
# Failed To Parse Unknown Error Mediawiki
## Contents
Then, as root, I copied /usr/local/bin/gs to /usr/bin/gs and it works now! The error messages returned are below. It just seem that the latex and dvips command won't start if they are called from php. On selinux-enabled systems, it is a good idea to check for records in the selinux log files. http://indywebshop.com/failed-to/failed-to-parse-unknown-error.php
Is intelligence the "natural" product of evolution? Apache Chroot Help needed on getting texvc to work with a chrooted apache. On one system where texvc was failing to work properly, the shell script was able to create files in the file system normally, but unable to write any contents to these Despite following the instructions as precisely as possible, testing three different versions of mediawiki, and googling extensively, I still get the error "Failed to parse (unknown error)" for even the simplest https://www.mediawiki.org/wiki/Manual_talk:Troubleshooting_math_display_errors
## Failed To Parse Missing Code Texvc Code Executable Please See Math Readme To Configure
Errors with convert For those of you who are having problems with convert, something like "Unable to temporary file", it seems to be convert, for some odd reason, trying to create Selinux On Linux systems with selinux support, such as recent versions of Fedora Core, restrictions enacted by selinux can result in puzzling manifestations. The last attempted database query was: (SQL query hidden) from within function "MathRenderer::_recall".
overleftrightarrow The token "\overleftrightarrow" is not handled correctly by Texvc. Increase the amount by setting $wgMaxShellMemory in LocalSettings.php until there is enough memory available. Therefore, table "math" is empty. Download Texvc Is your LaTeX installation correct? Tedious.$wgUseTeX = true; $wgUploadDirectory = "{$IP}/images"; $wgUploadPath = "{$wgScriptPath}/images"; $wgMathPath = "{$wgUploadPath}/math"; $wgMathDirectory = "{$wgUploadDirectory}/math"; $wgTmpDirectory = "{$wgUploadDirectory}/tmp"; $wgTexvc = "{$IP}/math/texvc"; share|improve this answer answered Mar 24 '11 at 11:12 Failed To Parse Png Conversion Failed Check For Correct Installation Of Latex Dvips Gs And Convert If not, see the previous section. See here Nginx: Execute texvc as root with sudo After we changed over from Apache to Nginx I found that the texvc binary would no longer produce the PNG file. latin1) You have probably upgraded from some older MediaWiki version to a newer one.
In this way, the latex and dvips executables know their own directory and will search the immediate parents for the relevent teTeX configuration files. Mediawiki Texvc Windows see the math/ directory Do you have LaTeX, dvips, gs and convert (ImageMagick)? Note that the above conversation may have been edited or added to since the transfer. share|improve this answer answered Sep 4 '09 at 3:31 Paradius 2,10992334 add a comment| up vote 1 down vote Adding this to LocalSettings solved it for me.
## Failed To Parse Png Conversion Failed Check For Correct Installation Of Latex Dvips Gs And Convert
Thanks, - Sonali. ______________________________________________________________________ This email has been scanned by the MessageLabs Email Security System. http://stackoverflow.com/questions/1296390/latex-failed-to-parseunknown-error-on-mediawiki You need GNU make to compile texvc. Failed To Parse Missing Code Texvc Code Executable Please See Math Readme To Configure Any ideas? Latex Error: File `cancel.sty' Not Found. See the Selinux section below.
Something like P ( r ) α r n − 1 exp ( − k r 2 / 2 σ 2 ) {\displaystyle P(r)\alpha r^{n-1}\exp(-kr^{2}/2\sigma ^{2})} renders beautifully whereas replacing http://indywebshop.com/failed-to/failed-to-parse-wsdl-document-xml-parser-error-createxmldoc.php Here's what I've tried: (1) compiled and tested texvc system -- it works fine from the command line (2) ensured that dvips, convert, and latex were in the default path -- Another possibility is that you wrote that wiki page before compiling texvc, and haven't rerendered any math since. Home | Browse | FAQ | Advertising | Blog | Feedback | MarkMail™ Legalese | About MarkLogic Server Mediawiki Math Extension
1. It should be straightforward.
3. Assuming this worked, we should get a cryptic line of output, This is dvips(k) 5.95a Copyright 2005 Radical Eye Software (www.radicaleye.com) ' TeX output 2005.07.23:0928' -> . [1] l4e053ca66cfc79a2397c40aa34c66a25
4. The parser assumes that the function is part of the normal TeX distribution, whereas it is actually a part of ams-math.
5. Failed to parse (Unknown error) What helped me was a recompilation of the ocaml stuff via cd /var/www/mediawiki/mywiki/math make clean make Good luck --Sigbert 17:33, 18 September 2009 (UTC) Stupid failure
6. Did you check for permissions/ownership of the director(ies)? -- Kowey 07:20, 9 August 2006 (UTC) I'm having a similar problem.
7. someone needs to make a math.php which can run in safe_mode. --207.109.251.117 05:01, 3 November 2005 (UTC) I made a patch, its mentioned on Problems_with_texvc --134.58.253.130 22:42, 2 February 2006 (UTC)
8. If that is not installed, latex will not render a dvi from the generated tex files and consequently no png can be rendered.
9. it's a modern post apocalyptic magical dystopia with Unicorns and Gryphons How is the Heartbleed exploit even possible?
10. Make all the statements true House of Santa Claus Need book id. Change the line to let cmd_convert tmpprefix finalpath = "convert -quality 100 -density 120 " ^ tmpprefix ^ ".ps " ^ finalpath ^ " >/dev/null 2>/tmp/wiki_convert_error" and run make. PHP Check that it works from the command line. http://indywebshop.com/failed-to/failed-to-parse-unknown-error-texvc.php If you are running selinux, it may be denying permission to httpd to execute the file.
I am not running in safe_mode. Mediawiki Mathjax On debian 7 with mediawiki 1.23.2 and Math 1.2.0 it will be: let cmd_dvips tmpprefix = "/usr/bin/dvips -q -R -E " ^ tmpprefix ^ ".dvi -f >" ^ tmpprefix ^ ".ps" It indicates, that the directories with the programs mentioned are not reachable for the texvc program.
## http://www.cs.wisc.edu/~ghost/doc/AFPL/get851.htm The error message stayed the same.
The directory images/tmp is defined to be owned by the root user and root group. What is the MediaWiki version that you're using? But the "directory" accorind to "$wgScriptPath" is "/~name/wiki". Mathoid The environment under Apache/PHP is different that the shell. let cmd_dvips tmpprefix = "/home/wiki/local/teTeX/bin/x86-unknown-linux-gnu/dvips ... If you try this, please be advised file /root/.texmf-var/web2c/latex.fmt is only created when you run the texvc command above. If the absolute path of the texvc is changed to the relative with command$wgTexvc = '/math/texvc' then the error message changes to Failed to parse (Missing texvc executable; please see http://indywebshop.com/failed-to/failed-to-parse-java-home-setting-error.php Remember that page renderings are aggressively cached; run your tests in a preview and try varying texts.
Then run make in the math directory again. Final comments: I've followed every troubleshooting method that I could find through web search and nothing has worked. If, after the assignment of variable $wgUseTeX value true, the diagnostics suggests to revise the latex, dvips, gs and convert, this can be done in the following way. Then check if your problem is listed below: Wrong collation / charset (usually utf8 vs. PATH variable may be different; use absolute paths in render.ml if you can't fix it. let cmd_latex tmpprefix = "env latex ... Therefore, if you do not have any other ams-math functions within the math tags, then it will not be rendered. Good Term For "Mild" Error (Software) Why is the spacesuit design so strange in Sunshine? more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed For FreeBSD, the file is found at '/usr/local/share/texmf-var/web2c/latex.fmt'. some weird PHP restriction is preventing you from accessing the file... Error: Failed to parse (Missing texvc executable) Failed to parse (Missing texvc executable); please see math/README to configure.) That error is returned in response to this test: if( function_exists( 'is_executable' ) function wfMkdirParents($fullDir, $mode ) {$parts = explode( "/", $fullDir );$path = ""; $dir2=""; foreach ($parts as $dir ) { if ($dir=="images") {$dir2="images";} if ($dir2=="images") { \$path = If you see these commands at command line with commands which latex which dvips which gs which convert then, perhaps, nothing can be done: this software is not compatible with your Here, for example, we see that what we are dealing with is a math_image_error: languages/LanguageFr.php:"math_image_error" => "La conversion en PNG a échouée, vérifiez l'installation de Latex, dvips, gs et convert", Localise
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2017-11-18 23:33:41
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7540469169616699, "perplexity": 9729.160435217625}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805114.42/warc/CC-MAIN-20171118225302-20171119005302-00313.warc.gz"}
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http://www.physicsforums.com/showthread.php?p=1892684
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# matlab-compute the distribution of the noise signal
by phoebus
Tags: distribution, matlabcompute, noise, signal
P: 4 my professor gave me this equation to compute the distribution of the noise signal but I have no ideal what it is, so can someone explain this for me 1/√(2πσ)*e^((x-μ)^2/2σ^2 ) thanks
Mentor P: 16,477 IIRC, that is the probability density function of a normally distributed random variable with mean μ and standard deviation σ. But I could be wrong.
Related Discussions Chemistry 1 Math & Science Software 5 Math & Science Software 2 Calculus & Beyond Homework 0 Introductory Physics Homework 3
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2014-04-20 21:31:00
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https://socratic.org/questions/what-is-the-area-of-a-45-45-90-triangle-with-a-hypotenuse-of-8mm-in-length
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# What is the area of a 45-45-90 triangle, with a hypotenuse of 8mm in length?
Nov 14, 2015
$4 m {m}^{2}$
#### Explanation:
The formula for calculating the area of a triangle is $\frac{1}{2} b a s e \cdot h e i g h t$.
Thanks to the fact that this is a 45-45-90 triangle the base of the triangle and the height of the triangle are equal. So we simply need to find the values of the two sides and plug them into the formula.
We have the length of the hypotenuse, so we can use the pythagorean theorem to calculate the length of the two sides.
(we know the area is going to be measured in $m {m}^{2}$ so we'll leave units out of the equations for now)
${a}^{2} + {b}^{2} = {8}^{2}$
$a = b$
We can simplify here, because we know the two remaining sides are equal. So we're just going to solve for
${a}^{4} = 16$
${a}^{2} = 8$
$a = \sqrt{8}$
Both non-hypotenuse sides of the triangle are $\sqrt{8 m m}$ long. Now we can use the triangle area formula so solve.
$a r e a = \frac{1}{2} b a s e \cdot h e i g h t = \frac{1}{2} \cdot \sqrt{8} \cdot \sqrt{8} = \frac{1}{2} \cdot 8 = 4 m {m}^{2}$
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2023-03-31 19:15:57
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https://bib-pubdb1.desy.de/collection/Contribution2book?ln=en
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# Contribution to a book
2021-06-0912:05 [PUBDB-2021-02585] Contribution to a book Melskens, J. ; Podraza, N. J. ; Stuckelberger, M. E. Infrared Optical Properties: Hydrogen Bonding and Stability The World Scientific Reference of Amorphous Materials: Structure, Properties, Modeling and Main Applications(In 3 Volumes)Volume 1: Structure, Properties, Modeling and Applications of Amorphous ChalcogenidesVolume 2: Structure, Properties and Applications of Oxide GlassesVolume 3: Structure, Properties, and Applications of Tetrahedrally Bonded Thin-Film Amorphous Semiconductors / Taylor, P Craig {Colorado School of MinesUSA} ; : World Scientific, 2021, ; ISBN: 978-981-12-1555-1=978-981-12-1593-3 ; doi:10.1142/11697-vol3 Singapore : World Scientific 85-128 (2021) [10.1142/9789811215612_0003] Restricted: PDF PDF (PDFA); 2021-06-0214:22 [PUBDB-2021-02546] Contribution to a conference proceedings/Contribution to a book Weber, T. ; Riebisch, M. ; Borras, K. ; et al Modelling for Quantum Error Mitigation [DESY-21-054; arXiv:2104.07320] 18th IEEE International Conference on Software Architecture Workshops, ICSAW, Video onlyVideo only, virtual world, 22 Mar 2021 - 26 Mar 2021 IEEE Xplore 102-105 (2021) [10.1109/ICSA-C52384.2021.00026] While we expect quantum computers to surpass their classical counterparts in the future, current devices are prone to high error rates and techniques to minimise the impact of these errors are indispensable. There already exists a variety of error mitigation methods addressing this quantum noise that differ in effectiveness, and scalability. [...] Restricted: PDF PDF (PDFA); 2021-06-0214:13 [PUBDB-2021-02545] Contribution to a conference proceedings/Contribution to a book Tian, W. ; Cirmi, G. ; Canalias, C. ; et al Multi-cycle terahertz generation in a periodically poled Rb:KTP crystal Conference on Lasers and Electro-Optics : [Proceedings] - OSA Washington, D.C., 2020. - ISBN 978-1-943580-76-7 - doi:10.1364/CLEO_SI.2020.STu3G.6CLEO: Science and Innovations, WashingtonWashington, USA, 10 May 2020 - 15 May 2020 OSA Washington, D.C. STu3G.6 (2020) [10.1364/CLEO_SI.2020.STu3G.6] We investigate multi-cycle 0.5-Terahertz generation in a periodically poled Rb-doped potassium titanyl phosphate (PPKTP) crystal. Up to 0.65-gJ terahertz energy was obtained at 77 K with maximum internal optical-to-terahertz efficiency of 0.09%.. Restricted: PDF PDF (PDFA); 2021-05-1218:18 [PUBDB-2021-02270] Journal Article/Contribution to a conference proceedings/Contribution to a book Shevyrtalov, S. ; Barannikov, A. ; Palyanov, Y. N. ; et al Synthetic single crystal diamonds for X-ray optics EUV and X-ray Optics, Sources, and Instrumentation : [Proceedings] - SPIE, 2021. - ISBN 97815106438649781510643871 - doi:10.1117/12.2589702EUV and X-ray Optics, Sources, and Instrumentation, Online OnlyOnline Only, Czech Republic, 19 Apr 2021 - 24 Apr 2021 Proceedings of SPIE 11776, 117760G (2021) [10.1117/12.2589702] special issue: "SPIE Optics + Optoelectronics" In the manuscript we report on characterization of single-crystalline (111) plates prepared from type Ib diamonds with nitrogen content of 100-150 ppm and (100) plates prepared from IIa diamond by means of high-resolution rocking curve imaging (RCI). Contrary to a common opinion about intrinsic poor diffraction quality of type Ib diamonds, RCI showed the presence of nearly defect-free areas of several mm2 in the central part of the (111)-oriented diamond plates. [...] Restricted: PDF PDF (PDFA); 2021-05-0416:36 [PUBDB-2021-02154] Journal Article/Contribution to a conference proceedings/Contribution to a book Tu, Z. ; H1 Collaboration ; ZEUS Collaboration HERA data on azimuthal decorrelation and charged particle multiplicity spectra probing QCD dynamics and quantum entanglement effects [arXiv:2011.02875] Proceedings of 40th International Conference on High Energy physics — PoS(ICHEP2020) - Sissa Medialab Trieste, Italy, 2021. - ISBN - doi:10.22323/1.390.051340th International Conference on High Energy Physics, ICHEP2020, PraguePrague, virtual meeting, 28 Jul 2020 - 6 Aug 2020 The azimuthal decorrelation angle between the leading jet and scattered lepton in deep inelastic scattering is studied with the ZEUS detector at HERA. The data was taken in the HERA II data-taking period and corresponds to an integrated luminosity of 330 pb$^{-1}$. [...] OpenAccess: PDF PDF (PDFA); External link: Fulltext 2021-04-2111:11 [PUBDB-2021-01890] Contribution to a conference proceedings/Contribution to a book Rehm, F. ; Vallecorsa, S. ; Saletore, V. ; et al Reduced Precision Strategies for Deep Learning: A High Energy Physics Generative Adversarial Network Use Case [arXiv:2103.10142] Proceedings of the 10th International Conference on Pattern Recognition Applications and Methods - SCITEPRESS - Science and Technology Publications, 2021. - ISBN 978-989-758-486-2 - doi:10.5220/001024500251025810th International Conference on Pattern Recognition Applications and Methods, Online StreamingOnline Streaming, virtual world, 4 Feb 2021 - 6 Feb 2021 SCITEPRESS - Science and Technology Publications, 1852251 251-258 (2021) [10.5220/0010245002510258] Deep learning is finding its way into high energy physics by replacing traditional Monte Carlo simulations. However, deep learning still requires an excessive amount of computational resources. [...] Restricted: PDF PDF (PDFA); External link: Fulltext 2021-03-0414:31 [PUBDB-2021-01317] Contribution to a conference proceedings/Contribution to a book Walasek-Höhne, B. ; Forck, P. ; Ischebeck, R. ; et al Screen materials for high precision measurements 8th International Beam Instrumentation Conference, IBIC2019, MalmöMalmö, Sweden, 8 Sep 2019 - 12 Sep 2019 JACoW Publishing, Geneva, Switzerland 7 pp. (2019) [10.18429/JACOW-IBIC2019-TUBO01] Scintillation screens made of various inorganic materials are widely used for transverse beam profile diagnostics at all kinds of accelerators. The monitor principle is based on the particles¿ energy loss and its conversion to visible light. [...] OpenAccess: PDF PDF (PDFA); 2021-02-2214:56 [PUBDB-2021-01040] Journal Article/Contribution to a conference proceedings/Contribution to a book Husung, N. A. ; Nada, A. ; Sommer, R. Yang Mills short distance potential and perturbation theory [DESY-20-012] 37th International Symposium on Lattice Field Theory, Lattice 2019, WuhanWuhan, China, 16 Jun 2019 - 22 Jun 2019 Proceedings of Science / International School for Advanced Studies (LATTICE2019), 263 (2020) [10.22323/1.363.0263] We compute the coupling $\alpha_\mathrm{qq}$ defined in terms of the static quark force by simulating the $\mathrm{SU}(3)$ Yang-Mills theory at lattice spacings down to $10^{-2}$~fm, keeping the volume large. In order to systematically improve the approach to the continuum, we subtract the leading cutoff effects in Symanzik's effective theory, resumming theleading $\log(a/r)$-term by renormalization group improvement. [...] OpenAccess: PDF PDF (PDFA); 2021-02-0910:39 [PUBDB-2021-00883] Journal Article/Contribution to a conference proceedings/Contribution to a book Sasikumar, K. S. ; List, J. ; Berggren, C. M. ; et al The ILC as a natural SUSY discovery machine and precision microscope: From light higgsinos to tests of unification The European Physical Society - High Energy Physics Conference 2019, EPS-HEP 2019, Ghent, BelgiumGhent, Belgium, Belgium, 10 Jul 2019 - 17 Jul 2019 Proceedings of Science / International School for Advanced Studies (EPS-HEP2019), 596 (2020) [10.22323/1.364.0596] The requirement of electroweak naturalness in simple supersymmetric models motivates the existence of a cluster of four light higgsinos with mass $100 - 300$ GeV, the lighter the better. While such light compressed spectra may be challenging to observe at the LHC, future $e^+e^-$ colliders with $\sqrt{s} > 2$m(higgsino) would serve as both a SUSY discovery machine and a precision microscope. [...] OpenAccess: PDF PDF (PDFA); 2021-02-0322:51 [PUBDB-2021-00818] Journal Article/Contribution to a conference proceedings/Contribution to a book Filozova, I. ; Zaikina, T. ; Shestakova, G. ; et al JINR Open Access Repository based on the JOIN² Platform Supplementary Proceedings of the XXII International Conference on Data Analytics and Management in Data Intensive Domains (DAMDID/RCDL 2020)Data Analytics and Management in Data Intensive Domains 2020, eedings of the XXII International Conference on Data Analytics and Management in Data Intensive Domains (, VoronezhVoronezh, Russia, 13 Oct 2020 - 16 Oct 2020 CEUR workshop proceedings 2790, 142-155 (2020) [10.3204/PUBDB-2021-00818] In recent years, Open Scientific Infrastructures have become an important tool for providing researchers and society with scientific information. Research institutes and universities worldwide actively plan and implement archivesof their scientific output [...] OpenAccess: PDF PDF (PDFA); External link: Fulltext
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2021-07-25 20:00:25
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https://www.impetus-afea.com/support/manual/?command=INITIAL_MATERIAL_DIRECTION_WRAP
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#### Command list
• Input handling
• Solution control and techniques
• Output
• Mesh commands
• Nodes and connectivity
• Material properties
• Initial conditions
• Boundary conditions
• Contact and tied interfaces
• Rigid bodies
• Connectors
• Parameters and functions
• Geometries
• Sets
• Coordinate system
• Particle
• SPH
### INITIAL_MATERIAL_DIRECTION_WRAP
###### Initial conditions
*INITIAL_MATERIAL_DIRECTION_WRAP
coid, entype, enid
$x_0$, $y_0$, $z_0$, $\hat{u}_x$, $\hat{u}_y$, $\hat{u}_z$, $\alpha$
#### Parameter definition
VariableDescription
coid Command ID
entype Entity type
options: P, PS
enid Entity ID
$x_0$, $y_0$, $z_0$ Coordinate used for definition of the ply location
$\hat{u}_x$, $\hat{u}_y$, $\hat{u}_z$ Vector used for definition of the ply orientation
$\alpha$ Angle used for definition of fiber direction
#### Description
This command is used to define local material directions in anisotropic materials such as fiber composites. The user defines the location and orientation of a "ply" in space. This ply is then wrapped around the component.
Note that models with more than one element in thickness direction require special consideration. For such models the wrapping algorithm requires a mesh with elements that are larger in-plane than in thickness direction.
The ply first needs to be projected onto the component. This projection generates intermediate in-plane directions $\bar{\mathbf x}$ and $\bar{\mathbf y}$.
$\displaystyle{ \bar{\mathbf y} = \frac{\hat{\mathbf z} \times \hat{\mathbf u}}{\vert \hat{\mathbf z} \times \hat{\mathbf u} \vert}}$
$\displaystyle{ \bar{\mathbf x} = \bar{\mathbf y} \times \hat{\mathbf z}}$
where $\hat{\mathbf z}$ is the local face surface normal direction. The local fiber direction $\hat{\mathbf x}$ and the orthogonal direction $\hat{\mathbf y}$ can now be defined by rotating the intermediate directions with the angle $\alpha$.
$\displaystyle{ \hat{\mathbf x} = \cos (\alpha) \bar{\mathbf x} + \sin (\alpha) \bar{\mathbf y}}$
$\displaystyle{ \hat{\mathbf y} =-\sin (\alpha) \bar{\mathbf x} + \cos (\alpha) \bar{\mathbf y}}$
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2019-09-21 23:56:13
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https://stacks.math.columbia.edu/tag/0GF8
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Lemma 68.17.2. Let $S$ be a scheme. Let $f : Y \to X$ be a morphism of algebraic spaces over $S$. Let $\mathcal{F}$ be a quasi-coherent sheaf on $Y$. Let $\mathcal{I}$ be a quasi-coherent sheaf of ideals on $X$. If $f$ is affine then $\mathcal{I}f_*\mathcal{F} = f_*(f^{-1}\mathcal{I}\mathcal{F})$ (with notation as explained in the proof).
Proof. The notation means the following. Since $f^{-1}$ is an exact functor we see that $f^{-1}\mathcal{I}$ is a sheaf of ideals of $f^{-1}\mathcal{O}_ X$. Via the map $f^\sharp : f^{-1}\mathcal{O}_ X \to \mathcal{O}_ Y$ on $Y_{\acute{e}tale}$ this acts on $\mathcal{F}$. Then $f^{-1}\mathcal{I}\mathcal{F}$ is the subsheaf generated by sums of local sections of the form $as$ where $a$ is a local section of $f^{-1}\mathcal{I}$ and $s$ is a local section of $\mathcal{F}$. It is a quasi-coherent $\mathcal{O}_ Y$-submodule of $\mathcal{F}$ because it is also the image of a natural map $f^*\mathcal{I} \otimes _{\mathcal{O}_ Y} \mathcal{F} \to \mathcal{F}$.
Having said this the proof is straightforward. Namely, the question is étale local on $X$ and hence we may assume $X$ is an affine scheme. In this case the result is a consequence of the corresponding result for schemes, see Cohomology of Schemes, Lemma 30.13.2. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
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2023-01-27 21:52:45
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http://publications.eng.cam.ac.uk/1290500/
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Balanced truncation of k-positive systems
Grussler, C and Damm, T and Sepulchre, R (2021) Balanced truncation of k-positive systems. IEEE Transactions on Automatic Control. ISSN 0018-9286
Full text not available from this repository.
Abstract
This paper considers balanced truncation of discrete-time Hankel <formula><tex>$k$</tex></formula>-positive systems, characterized by Hankel matrices whose minors up to order k are nonnegative. Our main result shows that if the truncated system has order <formula><tex>$k$</tex></formula> or less, then it is Hankel totally positive (<formula><tex>$\infty$</tex></formula>-positive), meaning that it is a sum of first order lags. This result can be understood as a bridge between two known results: the property that the first-order truncation of a positive system is positive (<formula><tex>$k=1$</tex></formula>), and the property that balanced truncation preserves state-space symmetry. It provides a broad class of systems where balanced truncation is guaranteed to result in a minimal internally positive system.
Item Type: Article UNSPECIFIED Div F > Control Cron Job 07 May 2021 22:14 02 Sep 2021 05:30 10.1109/TAC.2021.3075319
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2021-12-05 01:55:26
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https://me.gateoverflow.in/1848/gate2020-me-2-30
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A thin-walled cylinder of radius $r$ and thickness $t$ is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.
The material of the cylinder has Young’s modulus $E$, Poisson’s ratio $v$, and coefficient of thermal expansion $\alpha$. What is the minimum rise in temperature $\Delta T$ of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of $p$ above the atmosphere?
1. $\Delta T = \dfrac{3vpr}{2 \alpha t E} \\$
2. $\Delta T = \big( v – \dfrac{1}{4} \big) \dfrac{pr}{ \alpha t E} \\$
3. $\Delta T = \dfrac{vpr}{\alpha t E} \\$
4. $\Delta T = \big( v + \dfrac{1}{2} \big) \dfrac{pr}{ \alpha t E}$
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2022-09-26 23:42:34
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http://math.stackexchange.com/questions/114964/polynomials-on-the-complex-numbers
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# polynomials on the complex numbers
Let p be a complex polynomial $p\left( {a + bi} \right) = p\left( z \right):{\Bbb C} \to {\Bbb C}$ How can I prove the following? $$\lim_{\lVert z\rVert\to\infty} \Vert p(z)\rVert = \infty.$$
I can't use any important result about complex numbers, only the definition, and properties of $\mathbb{R}$ , how can I prove it?
-
Well, it is possible to show it for $p(z)=z^n$, and $$a_0+a_1 z + a_2 z^2 + \dots + a_n z^n = z^n \left( {a_0 \over z^n}+\dots+{a_{n-1}\over z} + a_n\right)$$
Of course you have to assume that $p$ is not constant. If $p(z)=\sum_{k=0}^na_kz^k$ where $a_n\neq 0$ and $n\geq 1$, then using the inequality $|a-b|\geq |a|-|b|$ for complex numbers we have $$|p(z)|\geq |a_n||z|^n-\sum_{k=0}^n|a_k||z|^k=|z|^n\left(|a_n|-\sum_{k=0}^{n-1}|a_k||z|^{k-n}\right),$$ and for $|z|\geq R$ where $R>0$ is such that $\sum_{k=0}^{n-1}|a_k||z|^{k-n}\leq \frac{|a_n|}2$ get
$$|p(z)|\geq |z|^n\frac{|a_n|}2,$$ so the result follows.
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2014-04-17 01:30:41
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https://www.zbmath.org/?q=an%3A0918.57001
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# zbMATH — the first resource for mathematics
A factorization of the Conway polynomial. (English) Zbl 0918.57001
The author shows that the Conway polynomial of a link is a product of two factors, the first of which is the Conway polynomial of an associated knot and the second factor is determined by the $$\widetilde\mu$$-invariants of the link.
Reviewer: A.Dimca (Bordeaux)
##### MSC:
57M25 Knots and links in the $$3$$-sphere (MSC2010)
##### Keywords:
Alexander polynomial; $$\widetilde\mu$$-invariants
Full Text:
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2021-03-06 06:00:22
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https://tex.stackexchange.com/tags/labels/info
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{labels} is about customizing the labels of {diagrams} and mathematical constructs like {matrices}. Please do not confuse questions about \label or similar commands with {labels}, use {cross-referencing} instead.
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2022-06-27 05:51:23
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https://en.wikipedia.org/wiki/Multiclass_classification
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# Multiclass classification
Jump to: navigation, search
Not to be confused with multi-label classification.
In machine learning, multiclass or multinomial classification is the problem of classifying instances into one of the more than two classes (classifying instances into one of the two classes is called binary classification).
While some classification algorithms naturally permit the use of more than two classes, others are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies.
Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance.
## General strategies
This section discusses strategies for reducing the problem of multiclass classification to multiple binary classification problems.
### One-vs.-rest
The one-vs.-rest[1]:182, 338 (or one-vs.-all, OvA or OvR, one-against-all, OAA) strategy involves training a single classifier per class, with the samples of that class as positive samples and all other samples as negatives. This strategy requires the base classifiers to produce a real-valued confidence score for its decision, rather than just a class label; discrete class labels alone can lead to ambiguities, where multiple classes are predicted for a single sample.[1]:182[note 1]
In pseudocode, the training algorithm for an OvA learner constructed from a binary classification learner L is as follows:
Inputs:
• L, a learner (training algorithm for binary classifiers)
• samples X
• labels y where yi ∈ {1, … K} is the label for the sample Xi
Output:
• a list of classifiers fk for k ∈ {1, …, K}
Procedure:
• For each k in {1, …, K}
• Construct a new label vector z where zi = 1 if yi = k and zi = 0 otherwise
• Apply L to X, z to obtain fk
Making decisions means applying all classifiers to an unseen sample x and predicting the label k for which the corresponding classifier reports the highest confidence score:
${\displaystyle {\hat {y}}=\arg \max _{k\in 1\ldots K}f_{k}(x)}$
Although this strategy is popular, it is a heuristic that suffers from several problems. Firstly, the scale of the confidence values may differ between the binary classifiers. Second, even if the class distribution is balanced in the training set, the binary classification learners see unbalanced distributions because typically the set of negatives they see is much larger than the set of positives.[1]:338
### One-vs.-one
In the one-vs.-one (OvO) reduction, one trains K (K − 1) / 2 binary classifiers for a K-way multiclass problem; each receives the samples of a pair of classes from the original training set, and must learn to distinguish these two classes. At prediction time, a voting scheme is applied: all K (K − 1) / 2 classifiers are applied to an unseen sample and the class that got the highest number of "+1" predictions gets predicted by the combined classifier.[1]:339
Like OvR, OvO suffers from ambiguities in that some regions of its input space may receive the same number of votes.[1]:183
## Notes
1. ^ In multi-label classification, OvR is known as binary relevance and the prediction of multiple classes is considered a feature, not a problem.
## References
1. Bishop, Christopher M. (2006). Pattern Recognition and Machine Learning. Springer.
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2016-08-29 21:03:11
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https://www.alibabacloud.com/help/doc-detail/191454.htm
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This topic describes the ST_DateTime function, which obtains the time information of a raster or band.
## Syntax
``````text ST_DateTime(raster raster_obj);
timetamp ST_DateTime(raster raster_obj,integer band);``````
## Parameters
Parameter Description
raster_obj The raster whose time information you want to obtain.
band The sequence number of the band whose time information you want to obtain. Valid values start from 0.
## Description
This function obtains the time information of a raster or band. If you specify the band parameter, this function returns the time information of the specified band. Otherwise, this function returns the time information of all bands of the raster by using a JSON-formatted string.
## Examples
``````SELECT ST_DateTime(raster_obj)
FROM raster_table;
st_datetime
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
{"0":"Mon Dec 31 00:00:00 2018","1":"Mon Dec 31 01:00:00 2018","2":"Mon Dec 31 02:00:00 2018","3":"Mon Dec 31 03:00:00 2018","4":"Mon Dec 31 04:00:00 2018","5":"Mon Dec 31 05:00:00 2018","6":"Mon Dec 31 06:00:00 2018",".
.7":"Mon Dec 31 07:00:00 2018","8":"Mon Dec 31 08:00:00 2018","9":"Mon Dec 31 09:00:00 2018","10":"Mon Dec 31 10:00:00 2018","11":"Mon Dec 31 11:00:00 2018","12":"Mon Dec 31 12:00:00 2018","13":"Mon Dec 31 13:00:00 2018".
.,"14":"Mon Dec 31 14:00:00 2018","15":"Mon Dec 31 15:00:00 2018","16":"Mon Dec 31 16:00:00 2018","17":"Mon Dec 31 17:00:00 2018","18":"Mon Dec 31 18:00:00 2018","19":"Mon Dec 31 19:00:00 2018","20":"Mon Dec 31 20:00:00 .
.2018","21":"Mon Dec 31 21:00:00 2018","22":"Mon Dec 31 22:00:00 2018","23":"Mon Dec 31 23:00:00 2018"}
SELECT ST_DateTime(raster_obj, 0)
FROM raster_table;
datetime
---------------------------
"Mon Dec 31 00:00:00 2018"``````
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2021-12-01 13:43:42
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https://s18612.gridserver.com/jesus-said-zeyp/permutation-without-repetition-example-problems-7bb4cc
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= 9! After choosing, say, number "14" we can't choose it again. ways Each digit is chosen from 0-9, and a digit can be repeated. In our case, as we have 3 balls, 3! Permutations with Repetition. Divide the factorial of the total by the denominator, as described above: 3,628,800/17,280. I explained in my last post that phone numbers are permutations because the order is important. There is a subset of permutations that takes into account that there are double objects or repetitions in a permutation problem. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Mathematics | Some theorems on Nested Quantifiers, Inclusion-Exclusion and its various Applications, Mathematics | Partial Orders and Lattices, Mathematics | Introduction and types of Relations, Discrete Mathematics | Representing Relations, Mathematics | Representations of Matrices and Graphs in Relations, Mathematics | Closure of Relations and Equivalence Relations, Number of possible Equivalence Relations on a finite set, Mathematics | Classes (Injective, surjective, Bijective) of Functions, Mathematics | Total number of possible functions, Discrete Maths | Generating Functions-Introduction and Prerequisites, Mathematics | Generating Functions – Set 2, Mathematics | Sequence, Series and Summations, Mathematics | Independent Sets, Covering and Matching, Mathematics | Rings, Integral domains and Fields, Mathematics | PnC and Binomial Coefficients, Number of triangles in a plane if no more than two points are collinear, Mathematics | Sum of squares of even and odd natural numbers, Finding nth term of any Polynomial Sequence, Discrete Mathematics | Types of Recurrence Relations – Set 2, Mathematics | Graph Theory Basics – Set 1, Mathematics | Graph Theory Basics – Set 2, Mathematics | Euler and Hamiltonian Paths, Mathematics | Planar Graphs and Graph Coloring, Mathematics | Graph Isomorphisms and Connectivity, Betweenness Centrality (Centrality Measure), Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph, Graph measurements: length, distance, diameter, eccentricity, radius, center, Relationship between number of nodes and height of binary tree, Mathematics | L U Decomposition of a System of Linear Equations, Mathematics | Eigen Values and Eigen Vectors, Mathematics | Mean, Variance and Standard Deviation, Bayes’s Theorem for Conditional Probability, Mathematics | Hypergeometric Distribution model, Mathematics | Limits, Continuity and Differentiability, Mathematics | Lagrange’s Mean Value Theorem, Mathematics | Graph theory practice questions, Easiest way to find the closure set of attribute, Difference between Spline, B-Spline and Bezier Curves, Newton's Divided Difference Interpolation Formula, Write Interview Permutations Without Repetition ... Permutations - Problem Solving Challenge Quizzes Permutations: Level 1 Challenges ... for sending signals. Solution: Since the arrangement has no repetitions, we find the permutation without repetitions. Variation without Repetition: choose k from n: "get me Margherita, then Gin-Tonic, then Bloody Mary" The special and the very special case. Reklamy sú pre nás jediným zdrojom príjmov, čo nám umožňuje poskytovať Vám obsah bez poplatkov, zadarmo. The permutation and combination question we have done so far are basically about selecting objects. To import permutations() – from itertools import permutations . The permutation of the elements of set A is any sequence that can be formed from its elements. Selection with Repetition. By using our site, you The following subsections give a slightly more formal definition of permutation and deal with the problem of counting the number of possible permutations of objects. A lock has a 5 digit code. Determine their number. = 3*2*1 = 6. This means that there are 210 different ways to combine the books on a shelf, without repetition and where order doesn't matter. Another example with repetitive numbers are bits and bytes. I tried to find an easy scheme, but couldn't. In how many ways if order does/doesn't matter? From how many elements, we can create 720 permutations without repetition? Na vašem počítači je tedy velice pravděpodobně nainstalován software sloužící k blokování reklam. Start with an example problem where you'll need a number of permutations without repetition. Permutation Solved Problems Example 1: What is the total number of possible 3-letter arrangements of the letters r, i, g, h, t if each letter is used only once in each arrangement? Each signal consists of one, two, or three flags where repetition in flag color is allowed. An addition of some restrictions gives rise to a situation of permutations with restrictions. What happens if Lisa instead has some ornaments that are identical? This example will help explaining the problem better. n! A byte is a sequence of bits and eight bits equal on… 1.Define and characterize permutations and permutations with repetition. is defined as: Each of the theorems in this section use factorial notation. It is called a permutation of X. Oct 08, 20 02:49 PM. Prerequisite – Permutation and Combination. Solution: 6 * 6 * 6 = 216. Exercises Answers 3. We have moved all content for this concept to for better organization. Let us suppose a finite set A is given. In other words we have 4! This is an example of permutation with repetition because the elements are repeated and their order is important. 6.If the number of members increments by 2, the number of possible variations with k=3 increments by 384. 125. A permutation is an arrangement, or listing, of objects in which the order is important. 4 people is a sequential problem. Solution: In the first place with repetition, we can arrange the number as 2,3 and 4 … For example, if $A=\{1,2,3\}$ and $k=2$, there are $6$ different possibilities: From a given set M = {a,b,c,d} enumerate the permutations with and without repetition for k=2. x 2! For example, the factorial of 5, 5! VCP equation Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0; N-gon Povolení reklamy na této stránce lze docílit aktivací volby "Nespouštět AdBlock na stránkách na této doméně", nebo "Vypnout AdBlock na priklady.eu", případně jinou podobnou položkou v menu vašeho programu na blokování reklam. Total number of letters in the word ‘GEEKSFORGEEKS’ = 13 In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical. Permutations A permutation is an ordered sequence of k elements selected from a given finite set of n numbers, without repetitions, and not necessarily using all n elements of the given set. The number of ways in which n things can be arranged, taken all at a time, n P n = n!, called ‘n factorial.’ Factorial Formula. Don’t stop learning now. Please update your bookmarks accordingly. Then we need to assign a person to the second place. Example-3 : How many different ways are there to arrange your first three classes if they are math, science, and language arts? Formula’s Used : 1. 5.From how many numbers 240 permutations can be made if the number of elements to be selected is 2? Attention reader! Then we need to assign a person to the second place. P(n, n) = n! Suppose three people are in a room. Example 1: How many 3 digit numbers can you make using the digits 1, 2 and 3 without repetitions? In how many ways could the gold, silver and bronze prizes be awarded? Covers permutations with repetitions. 216. In how many ways can 8 C++ developers and 6 Python Developers be arranged for a group photograph if the Python Developers are to sit on chairs in a row and the C++ developers are to stand in a row behind them ? Permutations with repetition. A five digit phone number has 10x10x10x10x10 or 10^5 equals 100 000 permutations. (e.g. For example, on some locks to houses, each number can only be used once. A permutation is an ordered sequence of k elements selected from a given finite set of n numbers, with repetitions, and not necessarily using all n elements of the given set. There are 3 possible ways to do this, because one person has already been assigned. For example, given that we have 5 different colored marbles (blue, green, red, yellow, and purple), if we choose 2 marbles at a time, once we pick the blue marble, the next marble cannot be blue. In a permutation, the order that we arrange the objects in is important. ways to arrange the trucks, 3! Explanation : Ex2 : All permutations made with the letters a, b, c taking all at a time are:( abc, acb, bac, bca, cab, cba) Number of Permutations: Number of all permutations of n things, taken r … Elements If the number of elements is decreased by two the number of permutations is decreased 30 times. Permutations with Repetition These are the easiest to calculate. Permutations A permutation is an ordered sequence of k elements selected from a given finite set of n numbers, without repetitions, and not necessarily using all n elements of the given set. method (1) listing all possible numbers using a tree diagram. Permutations with Repetition. Factorial of a number n is defined as the product of all the numbers from n to 1. Solve the equation to find the number of permutations. b) the selected ticket is returned to the pocket. The most common types of restrictions are that we can include or exclude only a small number of objects. In this case, we have to reduce the number of available choices each time. P(n, r) = n! = 9! Explanation : I need to create a function without the use of itertools which will create a permutation list of tuples with a given set of anything. našim systémem bylo detekováno odmítnutí zobrazení reklamy. An arrangement (or ordering) of a set of objects is called a permutation. If you want to crack this concept of Permutation and Combination Formula, first of all, you should learn what are definitions of terminology used in this concept and need to learn formulas, then finally learn factorial calculation, which is the most important to get a result for the given problem. Permutation With Repetition Problems With Solutions - Practice questions. Nowadays from Permutation and Combination is a scoring topic and definite question in any exams. Example-1 : How many 4-letter words, with or without meaning, can be formed out of the letters of the word, ‘GEEKSFORGEEKS’, if repetition of letters is not allowed ? /7! Solution: Formula’s Used : 1. / (n-r)! We need to assign a person to the first place. Permutation can be done in two ways, Permutation with repetition: This method is used when we are asked to make different choices each time and with different objects. Covers permutations with repetitions. Explanation : Question 1: Find the number of permutations if n = 9 and r = 2. Example: what order could 16 pool balls be in? Exercises Answers 3. = 5*4*3*2*1 = 120. Figure 1 So, we should really call this a "Permutation Lock"! The number of ways in which n things can be arranged, taken all at a time, n P n = n!, called ‘n factorial.’ Factorial Formula. java recursion sequence permutation. Get hold of all the important CS Theory concepts for SDE interviews with the CS Theory Course at a student-friendly price and become industry ready. OR It also involves rearranging the ordered elements. If we fix 0 at the thousand’s place, we need to arrange the remaining 9 digits by taking 3 at a time. Permutations without Repetition. For example, the factorial of 5, 5! 216. Start with an example problem where you'll need a number of permutations without repetition. How many members are there? The number of total permutation possible is equal to the factorial of length (number of elements). Consider arranging 3 letters: A, B, C. How many ways can this be done? Factorial Example 1: How many 3 digit numbers can you make using the digits 1, 2 and 3 without repetitions? Example-2 : 123, 132, 213, 231, 312, 321. We need to assign a person to the first place. Experience. P(n, n) = n! A permutation is an arrangement of objects in a definite order. How many 4-digit numbers are there with distinct digits ? Permutations with and without Repetition 1. The teacher wants to select a boy and a girl to represent the … A five digit phone number has 10x10x10x10x10 or 10^5 equals 100 000 permutations. How many 4-letter words, with or without meaning, can be formed out of the letters of the word, ‘GEEKSFORGEEKS’, if repetition of letters is not allowed ? How many postcards did they send together? This kind of problem... 2. ways to arrange the sedans and 1! = 288 ways. Factorial of a number n is defined as the product of all the numbers from n to 1. D. 320. How many different codes can you have? Each signal consists of one, two, or three flags where repetition in flag color is allowed. A permutation without repetition of objects is one of the possible ways of ordering the objects. Prosíme, odblokujte ho. Question 1 : 8 women and 6 men are standing in a line. a) n - without repetition b) m - with repetition; Cards How many ways can give away 32 playing cards to 7 player? Thanks matlab cell combinations permutation without repetition. 2. A permutation without repetition is also simply called a permutation. Example-4 : Explanation : Such as, in the above example of selection of a student for a particular post based on the restriction of the marks attained by him/her. Recall from the Factorial section that n factorial (written n!\displaystyle{n}!n!) Elements If the number of elements is decreased by two the number of permutations is decreased 30 times. There are 4 possible ways to do this. A permutation without repetition of objects is one of the possible ways of ordering the objects. A permutation is an ordered sequence of k elements selected from a given finite set of n numbers, without repetitions, and not necessarily using all n elements of the given set. Cross-power operation of parallel streams, Equations without the change of oxidation states, Calculations of fragments and percentage of elements, Assigning the oxidation states of elements. A bit is a single binary number like 0 or 1. Permutations Without Repetition ... Permutations - Problem Solving Challenge Quizzes Permutations: Level 1 Challenges ... for sending signals. You have 6 different tickets in your pocket marked with numbers 1-6. If the order does not matter then we can use combinations. Permutation With Repetition Problems With Solutions : In this section, we will learn, how to solve problems on permutations using the problems with solutions given below. How about permutations without repetition? Since all the words must begin with C. So, we need to fix the C at the first place. A permutation of a set is an arrangement of all of the set’s elements in a row, that is, a list without repetition that uses every element of the set. I… We have moved all content for this concept to for better organization. /(9-2)! The permutation of the elements of set A is any sequence that can be formed from its elements. It is otherwise called as arrangement number or order. 7. Solution: Given n = 9 and r = 2. Number of possible permutations: Permutations with repetition Let us suppose a finite set A is given. The same rule applies while solving any problem in Permutations. But I would like to do this without recursion, if this is possible. Answers were $$P(n,r)$$ and $$C(n,r)$$. 8 C++ Developers can stand behind in a row in 8P8 = 8! Calculating Permutations without Repetition 1. The remaining 7 letters can be arranged in 7P7 = 7! The same rule applies while solving any problem in Permutations. Permutation is used when we are counting without replacement and the order matters. For example, red, yellow \text{red, yellow} red, yellow and blue , blue, red \text{blue, blue, red} blue, blue, red are two possible signals. Thus, the total number of ways, Explanation : Next similar math problems: Variations 3rd class From how many elements we can create 13,800 variations 3rd class without repeating? Please use ide.geeksforgeeks.org, (We can also arrange just part of the set of objects.) Options: A. Practice Permutation and Combination Problems with Solutions for CAT exam. Solved Examples on Permutation and Combination. Permutation Solved Problems Example 1: What is the total number of possible 3-letter arrangements of the letters r, i, g, h, t if each letter is used only once in each arrangement? Download CAT Quant Questions PDF Instructions Directions for the next two questions: … There are 16 possible characters (six letters and 10 numbers) and we’re choosing 6 so there are 16 6 = 16777216 possible hexadecimal colors! In a class there are 10 boys and 8 girls. Permutations without repetition A permutation is an arrangement, or listing, of objects in which the order is important. Permutations without repetition - Each element can only appear once in the order. Writing code in comment? There are 3 possible ways to do this, because one person has already been assigned. Permutation and Combination Problems with Solutions PDF for CAT Download important CAT Permutation and Combination Problems with Solutions PDF based on previously asked questions in CAT exam. 6 Python Developers can sit on chairs in a row in 6P6 = 6! how many bitstrings with $$r$$ ones?) How many members are there? And Type Formulas Explanation of Variables Example Permutation with repetition choose (Use permutation formulas when order matters in the problem.) There are 7 members in a committee. Where n is the number of things to choose from, and you r of them. = 72. The following subsections give a slightly more formal definition of permutation and deal with the problem of counting the number of possible permutations of objects. I drew a graph/tree for it and this screams to use recursion. Type 1: How to Solve Quickly Permutation and Combination Different ways to arrange (with repetition) Question 1.How many 3 letter words with or without meaning can be formed out of the letters of the word MONDAY when repetition of words is allowed? Ďakujeme za pochopenie, tím Priklady.eu. Ex1 : All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb). And D. 320. Na vašom počítači je teda veľmi pravdepodobne nainštalovaný softvér slúžiaci na blokovanie reklám. Permutation without repetition (Use permutation formulas when order matters in the problem.) Example-1 : P(n) = n! A permutation is an arrangement of a set of objects in an ordered way. What is the probability that there is at least one shared birthday … How many elements are? n! Solution: 6 * 6 * 6 = 216. Solution (ii) Three men have 4 coats, 5 waist coats and 6 caps. For example, if $A=\{1,2,3\}$ and $k=2$, there are $6$ different possibilities: Consider the same setting as above, but now repetition is not allowed. A 4-digit number. ) poplatkov, zadarmo subset of permutations with repetition counting using. Problems using permutations and combinations - Aptitude questions, Shortcuts and Useful tips to improve your skills problems... 16 permutation without repetition example problems balls be in r { \displaystyle n }! n! / ( )! Coats, 5 Iterable – here, we have to pass the Iterable of whose permutations we want increase the... Therefore, the order is important plug your numbers in which the order of elements ) r! From the factorial of the set of n elements once, and you r of them elements ) taken... In the problem. ) you can see the following notation for the next two questions: … with... Repetitions, we have to reduce the number of things to choose a,! Two the number of possible permutations: Level 1 Challenges... for sending signals the in... Where you 'll need a number of things to choose a chairman, deputy chairman, secretary and cash... ) ones? je tedy velice pravděpodobně nainstalován software sloužící k blokování.... Of things to choose from, and our … in a row in 8P8 =!. Asked to reduce 1 from the previous term for each time stand behind a... That n factorial ( written n! \displaystyle { n }! n! \displaystyle { n }!!! If they are math, science, and only once below permutation example with. 5.From how many elements, we can also arrange just part of the same setting as above but. Make permutation without repetition example problems numbers using 3 digits and without repetitions of the number of without. Moved all content for this concept to for better organization marked with numbers.. A, b, permutation without repetition example problems, d } enumerate the permutations with and repetition! 0 or 1 create 990 combinations 2nd class without repeating for this concept to for better organization digits! Repetitions, we looked at examples of the theorems in this section use factorial notation: order! Permutation possible is equal to the first place, C, d } enumerate the permutations with counting... } enumerate the permutations with repetition choose ( use permutation formulas when order.! The C at the first place ticket is returned to the second.. Návštěvníku Priklady.eu, našim systémom bolo detekované odmietnutie zobrazenie reklamy class without?... Umožňuje Vám poskytovat obsah bez poplatkov, zadarmo scoring topic and definite question in Exams! Where repetition in this section use factorial notation, zadarmo how you calculate the number elements... To use recursion numbers are bits and bytes pass the Iterable of whose permutation without repetition example problems we want of... Repetition of objects in is important examples of the elements of set a is any sequence that can repeated! Elements, we have 3 permutation without repetition example problems, 3 2 and 3 without repetitions of the same setting as above but! ( use permutation formulas when order matters Formula of Permutation- M = { a, b, C d... And select \ ( r\ ) ones? basically about selecting objects. ) 4-letter words above, now. Permutation is used when we are asked to reduce the number of ways, explanation: total number of to! Its elements only a small number of permutations of Variables example permutation with repetition problems with or. Blokování reklam differ just in the order does n't matter you make using the digits,... Be arranged in 7P7 = 7 better organization only appear once in the number of possible with... After choosing, say, number 14 '' we ca n't choose again! Total by the denominator, as described above: 3,628,800/17,280 Formula of Permutation-,,... Or listing, of objects is one of the possible ways of ordering the.! What happens if Lisa instead has some ornaments that are identical, each can... Elements once, and you r of them using permutation Formula solve the equation to find the permutation combination... Of ways, explanation: Since the arrangement has no repetitions, we can include or exclude only a number... Pass the Iterable of whose permutations we want - Aptitude questions, Shortcuts and Useful tips to your., což nám umožňuje poskytovať Vám obsah bez poplatků, zdarma could n't otherwise called as arrangement number order. 1.2.0, 1.0.2, permutation without repetition example problems, 2.1.0 a pemutation is a scoring topic and question. Different pool balls calculate the number of objects is one of the theorems in this case we... Their order is important permutation Lock '' repetition... permutations - problem Challenge!, number 14 '' we ca n't choose it again have to the. From how many ways can this be done with C. so, we have balls. Matter then we can use combinations: Since the arrangement has no repetitions, we really. Three flags where repetition in this case, as we have to pass the Iterable of whose permutations we.. But phone numbers may also contain duplicate numbers or repeated numbers like 11 234 here. After choosing, say, number 14 '' we ca n't choose it.... K blokování reklam * 1 = 120 has 10x10x10x10x10 or 10^5 equals 100 000 permutations numbers may also duplicate. Factorial section that n factorial ( written n! / ( n−r ) ways of selecting the reduces! Better organization of a number of permutations with repetition Formula: n P r = 2 by 384, three. Possible is equal to the second place term for each time any Exams order does n't matter – from import! On a shelf, without repetition is allowed the following notation for the next questions! C ( n, r ) \ ) and \ ( n\ objects. N r: Solved examples using permutation Formula in this case permutation without repetition example problems have! Diagram above different values, 0 to 9 restrictions gives rise to a situation of that. Also contain duplicate numbers or repeated numbers permutation without repetition example problems 11 234, here number 1 is repeated can! Tickets in your pocket marked with numbers 1-6 ) and \ ( r\ ) ones? blokování reklam at! Našim systémom bolo detekované odmietnutie zobrazenie reklamy a problem involving a permutation thousand s! 3 balls, 3 three flags where repetition in flag color is allowed involving a is. Návštěvníku Priklady.eu, našim systémom bolo detekované odmietnutie zobrazenie reklamy selected ticket is returned to the place...: Level 1 Challenges... for sending signals n't obvious repetition ( permutation... - each element can only appear once in the problem. ) can also arrange just part the. 2, the result obtained are permutations with repetition problems with solution for your.... Recall from the previous term for each time if the order does n't matter we ’ re solving problem..., if this is possible the denominator, as we have to reduce the of... Elements we can create 13,800 variations 3rd class without repeating letters can be formed from its elements!! Since all the elements of set a is any sequence that can be composed from digits?! Out of 16 different pool balls be in in permutations order does not matter then need... With an example of permutation with repetition these are the easiest to calculate say... Possible variations with k=3 increments by 384 books on a shelf, without repetition of objects in which no is... A postcard each other r } n't choose it again 7P7 = 7 is. 3 possible ways of ordering the objects. ) and bronze prizes be awarded have to the. R of them n to 1 8 C++ Developers can stand behind in permutation. A set of objectsin an ordered way some locks to permutation without repetition example problems, each number can only be once! Question we have moved all content for this concept to for better organization,!! Their order is important ways if order does/does n't matter defined as the product of all the numbers n! With distinct digits Quizzes permutations: permutations with repetition permutations without repetition... permutations - solving! P r = n P r = n P r = 2 byte a! Without recursion, if this is an arrangement, or listing permutation without repetition example problems of objects in which digit... ’ = 13 Therefore, the result obtained are permutations with repetition příjmů, což nám umožňuje Vám. To do this without recursion, if this is an example of permutation repetition... Bit is a subset of permutations permutations ( ) – from itertools import permutations ( –. Can be composed from digits 0,1,2 objects. ) CAT Quant questions PDF Instructions Directions the! Solving Challenge Quizzes permutations: Level 1 Challenges... for sending signals method ( )., secretary and a digit can be made if the number of things to choose from, and language?... Easiest to calculate total permutation possible is equal to the first place can.: given n = 9 and r permutation without repetition example problems n P r = 2 color! Using permutations and combinations - Aptitude questions, Shortcuts and Useful tips to your! Subset of permutations of n things taken n at a time import permutations ( ) – from import...: 6 Python Developers can sit on chairs in a permutation without repetition repetition and where order n't. Bitstrings with \ ( r\ ) of them each element from a given set =... Make using the Formula of Permutation- are that we can use combinations r! 3 digits and without repetitions use combinations can stand behind in a class there are double objects repetitions... ) ones? does/does n't matter Therefore, the number of ways of ordering the..
Hotel Collection Waffle Weave Robe, 100% Turkish Cotton, Christmas In French, Land Before Time Song If We Hold On Together, Time Compression Ff8, Accident In Hereford This Afternoon,
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2021-04-23 02:56:28
|
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|
https://electronics.stackexchange.com/questions/492739/why-am-i-getting-weird-behavior-when-building-4-bit-down-counter
|
# Why am I getting weird behavior when building 4-bit down counter?
I'm attempting to build a 4-bit modulo-10 down-counter (i.e 9,8,7...,1,0,9,8,7...0). Here is my code so far:
LIBRARY IEEE;
USE IEEE.STD_LOGIC_1164.ALL;
USE IEEE.NUMERIC_STD.ALL;
ENTITY downcounter is
PORT (
enable : in std_logic;
reset : in std_logic;
clk : in std_logic;
count : out std_logic_vector(3 downto 0));
END downcounter;
ARCHITECTURE Behavior OF downcounter IS
COMPONENT Tflipflop
PORT (
clk : in std_logic;
T : in std_logic;
Q : out std_logic);
ENDCOMPONENT;
SIGNAL Q0 : std_logic := '1';
SIGNAL Q1 : std_logic := '0';
SIGNAL Q2 : std_logic := '0';
SIGNAL Q3 : std_logic := '1';
SIGNAL TFF2IN : std_logic;
SIGNAL TFF3IN : std_logic;
SIGNAL TFF4IN : std_logic;
BEGIN
TFF1: Tflipflop PORT MAP (clk, enable, Q0);
TFF2IN <= (NOT Q0) AND enable;
TFF2: Tflipflop PORT MAP (clk, TFF2IN, Q1);
TFF3IN <= (NOT Q1) AND TFF2IN;
TFF3: Tflipflop PORT MAP (clk, TFF3IN, Q2);
TFF4IN <= (NOT Q2) AND TFF3IN;
TFF4: Tflipflop PORT MAP (clk, TFF4IN, Q3);
PROCESS (clk)
BEGIN
IF FALLING_EDGE(clk) THEN
IF reset = '0' OR (Q3='1' AND Q1='1') OR (Q3='1' AND Q2='1') THEN
count <= "1001";
ELSE
count <= Q3 & Q2 & Q1 & Q0;
END IF;
END IF;
END PROCESS;
END Behavior;
I'm currently testing it in model-sim, but I'm getting this weird behavior:
The counter works from 9 to 0, but then when it reaches 9 again, it just stops there. Then after the same amount of time each time, it begins to work again!
I've tried my best to figure it out but I just can't. Any help is appreciated!
Edit: if a schematic helps, I'm basically doing this: except the enable is connected and AND-ed with each input of each T Flip Flop.
• To debug a circuit like this, you can't just look at the top-level signals. You have to go down into the hierarchy and add internal signals to your waveform. Then you can see what is all happening. – Oldfart Apr 13 '20 at 7:21
• It's doing what you asked it. – user_1818839 Apr 13 '20 at 10:43
• @BrianDrummond After your remark I suddenly noticed the error. – Oldfart Apr 13 '20 at 12:15
• @BrianDrummond how? – Sami Jr Apr 13 '20 at 22:10
• You're asking the counter (Q3..Q0) to keep counting until it rolls over at 15, while holding the output (confusingly, called "count") at 9. – user_1818839 Apr 13 '20 at 22:21
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2021-04-22 13:34:46
|
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|
http://tex.stackexchange.com/questions/88204/no-letters-of-certain-fonts-using-winfonts-package
|
# No letters of certain fonts using winfonts package [closed]
I am trying to use the winfonts package on Windows 8. I installed according to instructions—copied them to texmf-local, edited local config files, update the file names and map files. When I compile this test file under pdflatex,
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{winfonts}
\begin{document}
\fontfamily{georgia}\selectfont
abcdefg
\fontfamily{arial}\selectfont
abcdefg
\fontfamily{times-ttf}\selectfont
abcdefg
\fontfamily{verdana}\selectfont
abcdefg
\fontfamily{franklingothic}\selectfont
abcdefg
\fontfamily{impact}\selectfont
abcdefg
\end{document}
three of the fonts display correctly (Georgia, Franklin Gothic and Impact) while the other three are displayed only as ▯▯▯▯▯▯. What is the cause of this?
I'm using TeXLive 2012, last updated on 2012-12-26.
The log file is very long, but there is something interesting
pdfTeX warning: pdflatex.exe (file c:/Windows/fonts/verdana.ttf): glyph a' not found
-
Show the log-file. – Ulrike Fischer Dec 26 '12 at 10:20
An alternative would be to use XeLaTeX or LuaLaTeX and use fontspec to load systems fonts. – Guido Dec 26 '12 at 11:12
@Guido: I know that. But pdflatex is much faster. This is not an urgent matter, but it would be better to have a faster compilation. – C.R. Dec 26 '12 at 12:27
This probably means that your verdana.ttf version doesn't contains glyph names and you will need (at least) an .enc file which uses the uniXXXX` notation. See tug.org/TUGboat/Articles/tb30-1/tb94thanh.pdf. (I can't make tests, I don't have windows8 and it works fine with my version of the fonts.) – Ulrike Fischer Dec 26 '12 at 13:00
C. R. Do you already solve this problem with winfonts package on windows 8 ? I have the same problem. Can you help me? – Henrique Jun 30 at 10:00
|
2013-12-07 10:43:56
|
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|
https://tex.stackexchange.com/questions/503806/continuous-vertical-line-using-booktabs-in-tabularx-table
|
# Continuous vertical line using booktabs in tabularx table?
How can we draw a continuous vertical line using booktabs in table? What is the simplest method to maximise the width of a table? There are lots of methods, very confusing.
\documentclass{article}
\usepackage{makecell} % for bold in table using \small
\renewcommand\theadfont{\small} % for bold in table using \small
\usepackage{tabularx, ragged2e}
\usepackage{booktabs}
\begin{document}
\begin{table}[!ht]
\centering
\begin{tabularx}{\textwidth}{l>{\raggedright\arraybackslash}ccc|ccc}
\toprule
& \multicolumn{3}{c|}{\textbf{Paired Differences1}} & \multicolumn{3}{c}{\textbf{Paired Differences2}}\\
\cmidrule{2-7}
& \small {\textbf{Statistic}}
& \small {\textbf{Statistic}}
& \thead{\small {\textbf{Sig.}}} \\
\midrule
Difference & 44.20 & 14.36 & 4.54 & .957 & 10 & .746\\
\bottomrule
\end{tabularx}
\caption{Testing Testing Testing%
\label{tab:test1234}%
}
\end{table}
\end{document}
• A tabularx environment requires at least one X column to make sense. This answers you second question. As to the first, booktabs is not adapted to vertical rules. For which reason do you ue it? – Bernard Aug 11 '19 at 17:27
• To quote from the booktabs manual: "You will not go far wrong if you remember two simple guidelines at all times: 1. Never, ever use vertical rules. [...]" Therefore, I'd recommend to either stick to this rule, or, if you prefer vertical lines, use \hline instead of teh booktabs horizontal lines. – leandriis Aug 11 '19 at 17:39
• Regarding "the simplest method to maximise the width of a table" where would you like the extra white space to be? Between column 1 and 2, or 4 and 5 or equally distributed between all columns? Are there entries in the first column that are wider than the shown one? Why would wou even want your table to be wieder than it currently is? – leandriis Aug 11 '19 at 17:48
• Regarding the vertical lines, you might also want to have a loom at Vertical table lines are discontinuous with booktabs – leandriis Aug 11 '19 at 17:49
Here is my suggestion. I have used tabular* in combination with @{\extracolsep{\fill}} to make the table as wide as the textwidth and to evenly distribute the excess white space between the columns. I have also removed the vertical line and replaced the single \cmidrule by two adjacent ones with a small white space inbetween. In order to clean up the code, I have also removed the repeated occurences ot \small and \textbf and instead added \bfseries to \thedfont:
\documentclass{article}
\usepackage{makecell} % for bold in table using \small
\renewcommand\theadfont{\small\bfseries} % for bold in table using \small
\usepackage{tabularx, ragged2e}
\usepackage{booktabs}
\begin{document}
\begin{table}[!ht]
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lcccccc}
\toprule
& \multicolumn{3}{c}{\textbf{Paired Differences1}} & \multicolumn{3}{c}{\textbf{Paired Differences2}}\\
\cmidrule(r){2-4} \cmidrule(l){5-7}
\midrule
Difference & 44.20 & 14.36 & 4.54 & .957 & 10 & .746\\
\bottomrule
\end{tabular*}
\caption{Testing Testing Testing%
\label{tab:test1234}%
}
\end{table}
\end{document}
With combination of S and X columns type, without vertical lines, with rounded numbers ... :
\documentclass{article}
\usepackage{booktabs, tabularx}
\usepackage{xparse}
\NewExpandableDocumentCommand\mcx{O{1}m}
{\multicolumn{#1}{>{\Centering\small\bfseries\hsize=#1\hsize}X}{#2}}
\usepackage{ragged2e}
\usepackage{siunitx}
\begin{document}
\begin{table}[ht]
\centering
\setlength\tabcolsep{0pt}
\sisetup{round-integer-to-decimal,
round-mode=places,
table-format=2.2}
\begin{tabularx}{\linewidth}{l *{6}{S} }
\toprule
& \mcx[3]{Paired Differences 1}
& \mcx[3]{Paired Differences 2} \\
\cmidrule(r){2-4}\cmidrule(l){5-7}
& \mcx{Statistic} & \mcx{df} & \mcx{Sig.}
& \mcx{Statistic} & \mcx{df} & \mcx{Sig.} \\
\midrule
Difference
& 44.20 & 14.36 & 4.54 & 0.957 & 10 & 0.746 \\
\bottomrule
\end{tabularx}
\caption{Testing Testing Testing}
\label{tab:test1234}
\end{table}
\end{document}
I would rather replace the vertical line with a supplementary empty column to have a clear separation between the two group of columns. Another possibility, aesthetically, might be to delete the vertical padding of horizontal rules, and replace it with the \makegapedcells command from makecell, which adds a vertical space at the top and bottom of all cells. As a demonstration, I replaced the vertical line with thick, light grey vrule, which I find more pleasing to the eye than the default thin, black, vertical rule.
\documentclass{article}
\usepackage{makecell} % for bold in table using \small
\renewcommand\theadfont{\small\bfseries} % for bold in table using \small
\usepackage{tabularx, ragged2e}
\usepackage{booktabs}
\usepackage[table, svgnames]{xcolor}
\begin{document}
\begin{table}[!ht]
\centering
\begin{tabularx}{\textwidth}{X>{\raggedright\arraybackslash}ccccccc}
\toprule
& \multicolumn{3}{c}{\textbf{Paired Differences1}} & & \multicolumn{3}{c}{\textbf{Paired Differences2}}\\
\cmidrule(lr){2-4} \cmidrule(lr){6-8}
& \thead{ Sig. }
\midrule
Difference & 44.20 & 14.36 & 4.54 & & .957 & 10 & .746\\
\bottomrule
\end{tabularx}
\caption{Testing Testing Testing%
\label{tab:test1234}%
}
\end{table}
\begin{table}[!ht]
\centering
\setlength{\aboverulesep}{0pt}
\setlength{\belowrulesep}{0pt}
\setcellgapes{3pt}\makegapedcells
\begin{tabularx}{\textwidth}{X>{\raggedright\arraybackslash}ccc!{\color{Gainsboro!50!Lavender}\vline width 0.75em}ccc}
\toprule
& \multicolumn{3}{c!{\color{Gainsboro!50!Lavender}\vline width 0.75em}}{\textbf{Paired Differences1}} & \multicolumn{3}{c}{\textbf{Paired Differences2}}\\\noalign{\vskip -0.033em}
\cmidrule(lr{1.33em}){2-4} \cmidrule(lr){5-7}
`
|
2021-07-28 14:05:17
|
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|
https://www.ttp.kit.edu/preprints/1997/ttp97-35?rev=1458209039&do=diff
|
# Differences
This shows you the differences between two versions of the page.
— preprints:1997:ttp97-35 [2016/03/17 11:03] (current) Line 1: Line 1: + ====== TTP97-35 Lepton pair production by a high energy photon in a strong electromagnetic field ====== + + + Using impact-factor representation, we consider the + lepton pair production by an incident + high-energy + photon in a strong electromagnetic + field of a nucleus. By summing leading terms of + perturbation series, we obtain a + simple formula for the amplitude, valid + to all orders in ${\cal O}(\alpha Z)$ + and arbitrary field of the nucleus. + Using these results, + we derive, in a simple manner, the results for the lepton + pair production by a virtual incident photon + in a Coulomb field. + For real incident photon our results coincide + with the known ones. + Also, a particular example of a + non-Coulomb potential is discussed in some detail. + + |**a high energy photon in a strong electromagnetic field** | + |** Phys. Rev. D 57 4025 1998 ** | + | {{preprints:1997:ttp97-35.pdf|PDF}} {{preprints:1997:ttp97-35.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9709352|arXiv]] | + | |
|
2020-08-07 02:29:28
|
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|
https://chemistry.stackexchange.com/questions/116686/calculating-mixing-enthalpy-in-gromacs
|
# Calculating Mixing Enthalpy in GROMACS
What is the most reliable way to calculate mixing enthalpy of binary solvent mixture using GROMACS?
[EDIT]
I have simulated two-component systems of water and organic solvent with GROMACS. In a research paper from my field of study, authors calculate 'enthalpy of mixing' with the software in order to compare it with experimental mixing enthalplies. Under the Experimental Section of the paper, authors show that they do this according to this term:
A comment added in the text says the following:
"The internal energy, U, of the liquid mixture was obtained directly from the potential energy (see Tables S1 and S2) during the simulation, and yi is the molar fraction of component i."
I am interested in calculating same thermodynamical properties for my systems. I am aware that I can do that with g_energy function in GROMACS, or at least some parts of it (Pressure, Volume, Potential Energy).
My question is: Firstly, is this an appropriate way of calculating enthalpy of mixing in GROMACS via this equation? Secondly, how can one specify with the g_energy function which of the liquid's U(or potential energy), P and V is calculated if I initiate the function with .edr files, i.e. how can I choose to calculate i'th component's properties?
Reference for the image and quote:
Aguilera-Segura, S. M.; Di Renzo, F.; Mineva, T. Structures, Intermolecular Interactions, and Chemical Hardness of Binary Water-Organic Solvents: A Molecular Dynamics Study. J. Mol. Model. 2018, 24 (10), 292. https://doi.org/10.1007/s00894-018-3817-2.
• BTW, the authors of that paper, according to your image, need an introductory course about scientific typography. – mhchem Jun 13 at 14:46
• mhchem, could you elaborate? Edit Do you mean there should be a space before gamma (or molar fraction in their case)? – Koryphae Jun 14 at 5:16
• @Koryphae There are several typographical flaws in that formula: 1. textual subscripts (liq, mix) should be upright; 2. minus sign doesn't look like one (vertically misaligned and has tight spacing on both sides); 3. use of asterisk * as multiplication sign; 4. inconsistent notations ("liq,1" but "liq2" without comma). Maybe @mhchem can find even more inaccuracies:) In defense of the authors, they use proper upright subscripts $(ΔH_\mathrm{mix})$ in the text, so it might as well be a journal editor to blame, but overall quality is indeed rather poor. – andselisk Jun 14 at 5:32
GROMACS won't be able to calculate the enthalpy of mixing directly but using the energy function in GROMACS you will be able to get energy, pressure, and volume of the simulations.
Going through the paper that you posted it looks like the ran multiple simulation boxes for the different components and mixtures. They did this because you will not be able to get U,P, and V for individual components in GROMACS. So in order to calculate the enthalpy of mixing for a 2 component mixture they ran 3 simulations: one of the mixture, and one of each component by themselves.
Once you have the simulation boxes for the different components and mixtures it should be pretty straight forward to calculate the enthalpy of mixing.
Just a side note: I am always a little nervous calculating thermodynamic expressions using pressure from GROMACS because the pressure will fluctuate so wildly. So if you're going to make sure you're careful about your equilibration run and your NPT equilibration run as well.
Below are the GROMACS manual for energy which you would use to get U,P, and V from your simulation. The next is a tutorial for an NPT run from Virginia Tech and their tutorials are really well written and should help as a starting point and finally the last is a chat between a user and GROMACS developer discussing pressure fluctuations in NPT.
http://manual.gromacs.org/documentation/current/onlinehelp/gmx-energy.html
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin/gmx-tutorials/lysozyme/07_equil2.html
https://mailman-1.sys.kth.se/pipermail/gromacs.org_gmx-users/2011-May/061370.html
• Thank you for your Answer, @dtg67. What is actually puzzling for me, is as far as I can understand, there is an option for g_energy to choose number of molecules (-nmol) for the calculations. If following the formula they suggest and you calculate mixing enthalpies for pure components and the mixture, shouldn't number of molecules in a system for pure components be exactly same i.e. if you have mixture of 2500 molecules then you calculate thermodynamic parameters for 2500 of both pure components as well and then make the calculations according to the formula of mixing enthalpy? – Koryphae Jun 14 at 7:55
• Authors have provided their system compositions in Supporting Information and they have all different sizes for all solvents they use. – Koryphae Jun 14 at 7:56
• Yes you should use -nmol but thermodynamically we don't need to have the same N in all the simulations. Looking at the SI I think that they ran all the simulations at the same volume which is why the Ns are different – dtg67 Jun 14 at 15:06
• Okay, yes I see it now, that the using the equation, it has molar fraction component to it. However, when I calculate potential energy in my pure ethanol system, without specifying with -nmol, I get value of -100 000 kJ/mol. The paper discussed has value of -40 kJ/mol. I guess this is when you specify for "-nmol 1"? But now question arises, what is appropriate -nmol for the mixture? Shouldn't they be comparable? – Koryphae Jun 15 at 12:02
• I can't comment on the differences between the result that your simulation has with literature value but all the -nmol flag does is divide energies by the number that you specify. – dtg67 Jun 15 at 22:53
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2019-10-14 03:13:21
|
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http://mathhelpforum.com/math-challenge-problems/153408-catalan-s-constant.html
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# Math Help - Catalan's Constant
1. ## Catalan's Constant
Show $\displaystyle \int_1^\infty \frac{\log x}{x^2+1}dx = G,$ where $\displaystyle G$ is Catalan's constant.
2. Setting $u=\frac{1}{x}$ the integral becomes...
$\displaystyle \int_{1}^{\infty} \frac{\ln x}{1+ x^{2}}\ dx = - \int_{0}^{1} \frac{\ln u}{1 + u^{2}}\ du$ (1)
Now with a little of patience You can demonstrated that in general is...
$\displaystyle \int_{0}^{1} u^{n}\ \ln u\ du = -\frac{1}{(n+1)^{2}}$ (2)
... so that, tacking into account that for $|u|<1$ is...
$\displaystyle \frac{1}{1+ u^{2}} = \sum_{n=0}^{\infty} (-1)^{n}\ u^{2n}$ (3)
is...
$\displaystyle \int_{1}^{\infty} \frac{\ln x}{1+ x^{2}}\ dx = \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2n+1)^{2}}$ (4)
This integral is very similar to the integral resolved here...
http://www.mathhelpforum.com/math-he...ls-151443.html
Kind regards
$\chi$ $\sigma$
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2014-07-28 21:49:26
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http://math.stackexchange.com/questions/85688/hartshorne-exercise-ii-5-12b
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# Hartshorne exercise II.5.12(b)
I've been working on the Hartshorne exercise in the title for quite a while, which goes like this: let $f : X \to Y$ and $g : Y \to Z$ be morphisms of schemes, $\mathscr{L}$ a very ample invertible sheaf on $X$ relative to $Y$, and $\mathscr{M}$ a very ample invertible sheaf on $Y$ relative to $Z$. Show that $\mathscr{L} \otimes f^*\mathscr{M}$ is a very ample invertible sheaf on $X$ relative to $Z$.
After getting thoroughly stuck, I found the corresponding statement in EGA, namely Proposition 4.4.10(ii). The reason I am asking this question is that in EGA the claim is proved under some hypotheses (namely that $Z$ is quasi-compact, $f$ is of finite type, and $g$ is quasi-compact), and the conclusion is weaker: one can only say that there exists $n \geq 0$ such that $\mathscr{L} \otimes f^*(\mathscr{M}^{\otimes m})$ is very ample relative to $Z$ for all $m \geq n$. So is Hartshorne wrong, or is EGA using unnecessary hypotheses to reach a weak conclusion (I find this harder to believe), or am I misinterpreting one of the two?
Edit: there is another possibility that just occurred to me: Hartshorne remarks that EGA uses a slightly different definition of very ample, and having consulted EGA I see that this is the case. So I should extend my question to ask if this is the reason for my difficulty, and if so how does it make a difference?
-
Without looking it up, if I recall correctly EGA only assumes a very ample sheaf is the pullback of $\mathcal{O}(1)$ from a projective bundle whereas Hartshorne requires it to come from $\mathbb{P}^n$. This is definitely weaker as a later Hartshorne exercise is to construct a projective bundle such $\mathcal{O}(1)$ is not very ample, so I believe they both are correct. I haven't worked it out in awhile, but I assume you can use some Segre embedding and chase the diagrams around to prove this exercise. Sorry. This comment probably isn't very useful. – Matt Nov 26 '11 at 3:29
Because $Z$ and ${\bf Z}$ look too much alike, I'm going to work instead with projective morphisms $f:X \rightarrow Y$ and $g:Y \rightarrow W$. Also, the little I have to say about the difference between EGA and Hartshorne I will put at the end of this answer (briefly, Hartshorne is not wrong and I suspect the hypotheses in EGA are necessary); from now on I'm going to stick to Hartshorne's definitions.
A natural way to think about this problem is the following: we know $X$ embeds in some projective space over $Y$, and $Y$ embeds in some projective space over $W$, and that each of these embeddings equips its domain with a particular line bundle (the restriction of the twisting sheaf for the embedding). Stability of closed embeddings under base change together with the Segre embedding $$\sigma:{\bf P}_{\bf Z}^m \times {\bf P}_{\bf Z}^n \hookrightarrow {\bf P}_{\bf Z}^{mn+m+n}$$ implies that $X$ embeds in a projective space over $W$, and we are simply left with the task of calculating the very ample bundle for this embedding in terms of the data we started with (in fact, proving only that $X$ is projective over $W$ without keeping track of the corresponding bundles is the content of Hartshorne's exercise II.4.9). The details are in the next paragraph.
First observe that the closed embedding $j:Y \hookrightarrow {\bf P}_W^n$ that we start with gives, by base extension, a closed embedding $$(j \times 1):{\bf P}^m_Y=Y \times_{{\bf Z}}{\bf P}^m_{{\bf Z}} \hookrightarrow (W \times_{\bf Z} {\bf P}^n_{\bf Z}) \times_{\bf Z} {\bf P}^m_{\bf Z}.$$ Similarly, base-changing the Segre embedding $\sigma:{\bf P}_{\bf Z}^m \times {\bf P}_{\bf Z}^n \hookrightarrow {\bf P}_{\bf Z}^{mn+m+n}$ gives a closed embedding $$(1 \times \sigma):W \times_{\bf Z} {\bf P}^n_{\bf Z} \times_{\bf Z} {\bf P}^m_{\bf Z} \hookrightarrow {\bf P}^{mn+m+n}_W$$ and composing these with the given embedding $i:X \hookrightarrow {\bf P}^m_Y$ we have obtained a closed embedding $$(1 \times \sigma) \circ (j \times 1) \circ i :X \hookrightarrow {\bf P}^{mn+m+n}_W.$$ A routine diagram chase (using the compatibilities of $i$ and $j$ with $f$ and $g$) shows that composing this embedding with the projection on $W$ gives the map $g \circ f$, proving that $g \circ f$ is a projective morphism.
Now use the facts that (1) the pullback by the Segre embedding $\sigma$ of $\mathcal{O}(1)$ is the tensor product $\pi_1^* \mathcal{O}(1) \otimes \pi_2^* \mathcal{O}(1)$ of the twisting sheaves of the factors, and (2) pullback of a tensor product is tensor product of the pullbacks to calculate $$((1 \times \sigma) \circ (j \times 1))^* \mathcal{O}(1)=\pi^* \mathscr{M} \otimes \mathcal{O}(1), \quad \hbox{where \pi:{\bf P}^m_Y \rightarrow Y is the projection,}$$ and then $$i^*(\pi^* \mathscr{M} \otimes \mathcal{O}(1))=f^* \mathscr{M} \otimes \mathscr{L}$$ as desired.
As you are probably aware, the most significant difference between's Harthshorne's definition and the EGA definition of projective morphism is that Hartshorne requires that the given map come from an embedding in some trivial projective space bundle, while EGA allows "twisting"---i.e., only requires that the morphism come from an embedding of the form $X \hookrightarrow P$ where $P$ is the projective bundle associated to some quasi-coherent $\mathcal{O}_Y$-module (the latter seems to be a more natural generality to me, but here we are in a situation where it seems to make the statement of some basic facts more complicated!). So as you suspected there is no obvious contradiction.
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2014-12-21 02:47:42
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https://questions.examside.com/past-years/jee/question/the-function-fleft-x-right-log-left-x-sq-2003-marks-4-edxalxbmmbyhc8s7.htm
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1
AIEEE 2003
+4
-1
The function $$f\left( x \right)$$ $$= \log \left( {x + \sqrt {{x^2} + 1} } \right)$$, is
A
neither an even nor an odd function
B
an even function
C
an odd function
D
a periodic function
2
AIEEE 2003
+4
-1
A function $$f$$ from the set of natural numbers to integers defined by $$f\left( n \right) = \left\{ {\matrix{ {{{n - 1} \over 2},\,when\,n\,is\,odd} \cr { - {n \over 2},\,when\,n\,is\,even} \cr } } \right.$$\$ is
A
neither one -one nor onto
B
one-one but not onto
C
onto but not one-one
D
one-one and onto both
3
AIEEE 2003
+4
-1
If $$f:R \to R$$ satisfies $$f$$(x + y) = $$f$$(x) + $$f$$(y), for all x, y $$\in$$ R and $$f$$(1) = 7, then $$\sum\limits_{r = 1}^n {f\left( r \right)}$$ is
A
$${{7n\left( {n + 1} \right)} \over 2}$$
B
$${{7n} \over 2}$$
C
$${{7\left( {n + 1} \right)} \over 2}$$
D
$$7n + \left( {n + 1} \right)$$
4
AIEEE 2003
+4
-1
Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is
A
(-1, 0)$$\cup$$(1, 2)$$\cup$$(2, $$\infty$$)
B
(1, 2)
C
(-1, 0) $$\cup$$ (1, 2)
D
(1, 2)$$\cup$$(2, $$\infty$$)
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
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EXAM MAP
Joint Entrance Examination
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2023-03-29 04:06:51
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http://openstudy.com/updates/4f4c7558e4b0acf2d9fdcab3
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## xEnOnn Group Title Suppose I have the following sequence in an event: BABCCABAA There are 9 elements in the sequence and I want to find the number of arrangements I get can out of this 9 elements. The order does matter but because there are repeated elements such as 4A's, 3B's, etc, it becomes not as easy as just 9 factorial. For example, the following 2 are the considered only one arrangement: $BA_3BCCA_4BA_1A_2$ and $BA_1BCCA_4BA_2A_3$ So how can I find the number of arrangements when there are such repeated elements in it? 2 years ago 2 years ago
1. FoolForMath Group Title
It's simple, $$\large \frac{9!}{4! \times 3! \times 2!} = 1260$$
2. jerwyn_gayo Group Title
permutation. . i'll go with FFM
3. xEnOnn Group Title
Does this come from a formula? What's the rationale behind this equation?
4. xEnOnn Group Title
Also, what if order does not matter? ie, combinations?
5. FoolForMath Group Title
Put separate stickers on each of the four 'A', three 'B', and one of the two C's, to distinguish them. Now there are 9 distinct letters can be arranged in 9! ways. Remove the stickers, of all A's, then all B's and then all C's. Each time we remove the stickers, 4! arrangements collapse into 1 for A's, 3! arrangement collapses to 1 for B's and 2! to 1 for C. So the number of arrangements the given 9 letters is $\large \frac{9!}{4! \times 3! \times 2!}$
6. xEnOnn Group Title
Based on your explanation, if the order does not matter, can I say it would then be this: $\large \frac{9!}{(4! \times 3! \times 2!) \times 3!}$
7. FoolForMath Group Title
No that is incorrect interpretation for my explanation.
8. xEnOnn Group Title
But if the order does not matter, then I need to divide away the number of stickers I remove too, right? Although I remove 9 stickers in total, I can't divide by 9! again. Otherwise the equation will become a fraction.
9. FoolForMath Group Title
What you mean by order does not matter, my answer assumes it means that A's and B's and C's are indistinguishable.
10. jerwyn_gayo Group Title
at xenon, i think you can only do that to combination problems, this is permutation. .
11. xEnOnn Group Title
@jerwyn gayo oh yea...I think you are right. Thanks FFM for the help!! :)
12. xEnOnn Group Title
Because I think if I want "order does not matter", it will just be 1.
13. FoolForMath Group Title
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2014-07-31 17:39:40
|
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https://zbmath.org/?q=an:0715.57013&format=complete
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# zbMATH — the first resource for mathematics
Natural transformations of Weil functors into bundle functors. (English) Zbl 0715.57013
Geometry and physics, Proc. 9th Winter Sch., Srní/Czech. 1989, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 22, 177-191 (1990).
[For the entire collection see Zbl 0699.00032.]
Natural transformations of the Weil functor $$T^ A$$ of A-velocities [I. Kolař, Commentat. Math. Univ. Carol. 27, 723-729 (1986; Zbl 0603.58001)] into an arbitrary bundle functor F are characterized. In the case where F is a linear bundle functor, the author deduces that the dimension of the vector space of all natural transformations of $$T^ A$$ into F is finite and is less than or equal to $$\dim (F_ 0{\mathbb{R}}^ k)$$. The spaces of all natural transformations of Weil functors into linear functors of higher order tangent bundles are determined.
Reviewer: J.Kubarski
##### MSC:
57R22 Topology of vector bundles and fiber bundles 55R10 Fiber bundles in algebraic topology 58A20 Jets in global analysis
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2021-10-21 23:45:33
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|
https://brilliant.org/problems/base-and-exponent-accuracy/
|
# Base and Exponent Accuracy!
Algebra Level 2
What is the value of x such that:
${ 4 }^{ 2 }\quad -\quad { x }^{ x }\quad -\quad { x }^{ x }\quad \approx \quad |\quad 434.01\quad \times \quad { x }^{ x }\quad |$
×
|
2017-01-22 10:27:07
|
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|
https://ncatlab.org/nlab/show/Planck+length
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# nLab Planck length
Contents
### Context
#### Gravity
gravity, supergravity
# Contents
## Idea
The fundamental physical unit of length.
In comparison to macorscopic physical units such as the meter, the approximate value of the Planck length is $\sim 1.6 \;10^{-35}$ meter.
## Definition
Two important physical units of length induced by a mass $m$ are
1. $\ell_m \coloneqq \frac{2 \pi \hbar}{m c}$
2. $r_m \coloneqq 2 m G/c^2$
where
Solving the equation
$\array{ & \ell_m &=& r_m \\ \Leftrightarrow & 2\pi\hbar / m c &=& 2 m G / c^2 }$
for $m$ yields the Planck mass
$m_{P} \coloneqq \tfrac{1}{\sqrt{\pi}} m_{\ell = r} = \sqrt{\frac{\hbar c}{G}} \,.$
The corresponding Compton wavelength $\ell_{m_{P}}$ is given by the Planck length $\ell_P$
$\ell_{P} \coloneqq \tfrac{1}{2\pi} \ell_{m_P} = \sqrt{ \frac{\hbar G}{c^3} } \,$
## References
• Max Planck, Über irreversible Strahlungsvorgänge, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin. 5: 440–480. pp. 478–80, 1899, (10.1002/andp.19003060105)
|
2020-01-21 15:01:40
|
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|
https://docs.opentitan.org/hw/ip/rv_core_ibex/doc/dv/
|
# Ibex RISC-V Core Wrapper DV document
## Goals
• Verify compliance with the RISC-V specifications used by OpenTitan.
• Verify Ibex’s security hardening features.
• Ensure correct functionality is maintained across all possible behaviours of Ibex’s external interfaces when integrated into OpenTitan.
• Verify additional features provided by the wrapper.
## Design features
rv_core_ibex wraps a dual core lockstep configuration of Ibex, an RV32IMC CPU with security hardening features. The wrapper adapts Ibex’s top-level interfaces to be suitable for use with OpenTitan. In addition rv_core_ibex provides some extra functionality controlled via bus accessible registers.
For more information please see the Ibex RISC-V Core Wrapper Technical Specification.
## Verification strategy
The main Ibex testbench is not contained in the OpenTitan repository. Verification is primarily done by the testbench in the Ibex repository, see the Ibex Testplan for more details.
The additional features provided by the RISC-V Core Wrapper are verified at a chip level only (See the Earlgrey Chip DV testplan. As they are simple features chip level only verification suffices to meet our goals.
Similarly there is no specific verification for the TL-UL <-> Ibex memory protocol wrappers (provided by the separate TLUL IP). These are exercised extensively by all chip-level testing that runs software on Ibex providing comprehensive verification.
## Coverage
Due to the simplicity of the additional rv_core_ibex features, the existence of self checking chip-level tests combined with code and expression coverage is sufficient to be confident of their verification without functional coverpoints.
The TL-UL <-> Ibex memory protocol contains minimal logic so again code and expression coverage will suffice with one exception. The iside and dside Ibex interfaces can have up to 8 or 2 outstanding requests respectively, we need to ensure these scenarios are seen. An SVA cover expression will be used to produce coverage for this.
|
2022-12-08 00:37:17
|
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|
http://meetings.aps.org/Meeting/MAR12/Event/163327
|
### Session P10: Invited Session: Quantum Simulations
8:00 AM–11:00 AM, Wednesday, February 29, 2012
Room: 210A
Chair: Markus Greiner, Harvard University
Abstract ID: BAPS.2012.MAR.P10.5
### Abstract: P10.00005 : Mixed Bose-Fermi Mott Phases and Phase Transitions
10:24 AM–11:00 AM
Preview Abstract View Presentation MathJax On | Off Abstract
#### Author:
Ehud Altman
(Weizmann Institute of Science)
A recent experiment with an ultra-cold mixture of $^174$Yb and $^173$Yb atoms in an optical lattice [S. Sugawa e. al. Nature Physics 7, 642 (2011)] found a remarkable quantum phase that can be described as a mixed Mott insulator. Such a an incompressible state established at integer combined filling of the two species, must have residual low energy Fermionic degrees of freedom associated with relative motion of the two species. I will discuss the novel quantum states formed by the composite Fermions in the mixed Mott insulator as well as the unconventional phase transitions separating these states from the compressible Bose-Fermi mixture established at weak interactions. Finally I will propose to utilize the mixed Mott insulator as a quantum simulator for models of the doped Mott insulator relevant to high Tc superconductivity. The new approach, where the bosonic atoms play the role of doped holes offers significant advantages over direct simulation of the Hubbard model. In particular the mixed Mott plateau naturally provides a flat trap potential to the doped holes, while the hole doping is easily tuned by varying the relative fraction of the bosons.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2012.MAR.P10.5
|
2014-07-23 18:04:08
|
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|
https://codegolf.stackexchange.com/questions/57327/lets-make-a-word-search/91560
|
# Let's make a word-search!
In this challenge, we will together create a word-search containing many programs in different languages.
I have started us off with a grid of 60-by-25 blanks (·), some of which are replaced by the characters of a Ruby program.
To answer, choose a language that was not yet used. Using your chosen language, write a program that reads a character, token, line, or all input from the console, and prints it. Then, insert your program into the word-search.
For example, suppose you choose Python 3 for your answer, and write the program print(input()). Now you have to insert that program into the grid.
···a·24··········
··z····t·········
Then you can just put your program in the second line, overlapping with the existing t:
···a·24··········
··zprint(input())
Note that you can place your program in any direction: forward, backward, upward, downward, or diagonally, as long as it's in a straight line.
But what if the existing grid looks like this:
···a·24··········
··z····q·········
There's no way to fit the print(input()) here without changing existing characters, which is forbidden. Instead, you can change the program:
print(
input())
This two-line program fits neatly:
···a·24·print(···
··z····q input())
Here you replace a blank (·) with a space (). However, a space is just like any other character, and can not be overwritten in future programs.
Just like a one-liner, a multi-line program can be placed in any direction. For example, in a larger grid, you could do the following, by rotating the program 135° clockwise.
··········
········ ·
·······i·p
······n·r·
·····p·i··
····u·n···
···t·t····
··(·(·····
·)········
)·········
## Scoring
Your score for each answer is thirty divided by the number of characters added. Do not count characters that already existed in the grid, even if you use them yourself.
Your total score is the sum of the scores for all of your answers, multiplied by the number of answers. Highest score wins.
# Rules
• Every answer must be written in a different language. Languages that differ only in version number (e.g., Python 2 and Python 3) are considered the same.
• Every answer must build off of the most recent valid answer. That is, take the grid of the most recent such answer, and insert your program into it.
• To insert your program, replace at least one of the blanks (·) with characters of your choice. You may use existing characters from the grid in your answer, but you may not change or move any of them.
• You may not insert more than 500 characters in total, across all your answers.
• All characters you insert must be part of your program.
• Your program may consist only of printable ASCII and newlines, but there may not be two or more consecutive newlines back-to-back.
• Newlines do not count towards your score.
• A full program, not just a function or snippet, is required.
• The same user may not write two consecutive answers.
• If someone's answer violates a rule, leave a comment. If the mistake is not fixed in 30 minutes, it should be deleted.
# Used language snippet
This is a Stack Snippet, made by ETHproductions, FryAmTheEggman, and Mauris, that keeps track of users' scores and the used languages. It was originally copied from Martin Büttner's amazing template.
New (experimental) version, using a modified formula:
• Eh, I would just rely on the community being cool enough not to do something that boring :) – Lynn Sep 9 '15 at 3:20
• I have a basic "leaderboard" snippet set up, copied from Martin's amazing template, that keeps track of the used languages. May I edit it into the post? – ETHproductions Sep 9 '15 at 3:24
• Alright, I've added the snippet. I only removed the unnecessary HTML portion, so feel free to shorten the CSS or JS. – ETHproductions Sep 9 '15 at 3:39
• I would suggest that the next time someone does something like this that they limit it to languages notable enough to have a Wikipedia entry, or something like that. It doesn't really feel like a real word search with dozens of one-two character entries from esoteric languages no one has ever heard of. – ThaddeusB Sep 9 '15 at 23:36
• Someone should extend the snippet to have a leaderboard listing the scores per author. – Lynn Sep 10 '15 at 2:42
# Batch file, 16 characters added (corrected)
sET /P A=
ECHO %A%
Yeah ... batch files going all diagonal on ya.
The grid is now
····························································
···········i········a·······································
··········?pio;·····l·······································
··········,u········e·······································
··········.t········r·······································
···········s········t·······································
··········· ··printf(·······································
···········g·· input('','s'))····························
···········e·····n··r·······································
·········E·s········m·······································
········C·E·········p·······································
·······H·T··········t·····················r·················
······O· ···········(·······································
····· ·/············)·······································
····%·P·············)·······································
···A· ······················································
··%·A·······················································
···=························································
····························································
····························································
····························································
····························································
····························································
····························································
• I'm not sure if this is how multi-line diagonal programs fit. In the question's example, there is space between the two lines of the diagonal program (like a checkerboard). – PhiNotPi Sep 8 '15 at 20:18
• @PhiNotPi - Edited, fixed, and undeleted. – AdmBorkBork Sep 8 '15 at 20:27
• @FryAmTheEggman No, not an issue. Batch doesn't really care about capitalization. Corrected for clarification, though. – AdmBorkBork Sep 8 '15 at 20:33
• If you want to be super-technical, the first character of the second line should be to the upper-left of the first character on the first line. (this is true in the example, but it's a bad example because the first character of the second line was a space). You could reposition the s to be the s in puts. – PhiNotPi Sep 8 '15 at 20:35
• Well, now somebody has already chained onto this, so it's probably too late to fix. – PhiNotPi Sep 8 '15 at 20:37
cat(scan(,''))
The grid is now
····························································
···········i········a·······································
··········?pio;·····l·······································
··········,u········e·······c·······························
··········.t········r·······a·······························
··········@s········t·······t·······························
··········· ··printf(·······(·······························
···········g·· input('','s'))····························
···········e·····n··r·······c·······························
·········E·s········m·······n·······························
········C·E·········p·······(·······························
·······H·T··········t·······,·············r·················
······O· ···········(·······'·······························
····· ·/············)·······'·······························
····%·P·············)·······)·······························
···A· ······················)·······························
··%·A·······················································
···=························································
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··························································}}
····························································
····························································
····························································
grep -m1 .
The new grid:
·········v---H\·············································
·········>qir@uH····a·······································
Get a chr!?pio;·····l·······································
Outputs it,u········e·······c·······························
and 'BZam..t········r·······a·······························
··········@s······s t=" " r t#50:20 w !,t,!·················
··········· ··printf(·······(·······························
···········g·· input('','s'))····························
···········e·····n··r·······c·········g·····················
·······))E·s········m·······n)········e·····················
········C·E·········p·······((········p·····················
·······H·T··········t·······,t········ ···r·················
······O· ···········(·······'u········-·····················
····· ·/············)·······'p········m·····················
····%·P·············)·······)n········1·····················
···A· ······················)i·······n ·····················
··%·A························(······-·.·····················
···=·························t····· ···$·d·················· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ·····························r··e···a·····················}} ·····························p·h···=························ ··································<························· ·································>·························· • but you missed the LISP answer...It should be fixed now – Gavin S. Yancey Sep 8 '15 at 23:33 # awk, 11 characters added {print;exit} The new grid: ·········v---H\············································· ·········>qir@uH····a······································· Get a chr!?pio;·····l······································· Outputs it,u········e·······c······························· and 'BZam..t········r·······a······························· ··········@s······s t=" " r t#50:20 w !,t,!················· ··········· ··printf(·······(······························· ···········g·· input('','s'))···························· ···········e·····n··r·······c·········g····················· ·······(write(read-host)····a)········r······ ·············· ·······))E·s········m·······n)········e····················· ········C·E·········p·······((·······{print;exit}····K······ ·······H·T··········t·······,t········ ···r················· ······O· ···········(·······'u········-····················· ····· ·/············)·······'p········m····················· ····%·P·············)·······)n········1····················· ···A· ······················)i·······n ····················· ··%·A························(······-·.····················· ···=·························t····· ···$·d··················
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
·····························r··e···a·····················}}
·····························p·h···=························
··································<·························
·································>··························
• :( I was about to post an awk answer – ThaddeusB Sep 8 '15 at 23:48
• Could have just used awk 1 – User112638726 Sep 9 '15 at 14:59
IaP.
The new grid:
·········v---H\·············································
·········>qir@uH···IaP.·····································
Get a chr!?pio;·····l·······································
Outputs it,u········e·······c·······························
and 'BZam..t········r·······a·······························
··········@s······s t=" " r t#50:20 w !,t,!·················
··········· ··printf(·······(·······························
···········g·· input('','s'))····························
···········e·····n··r·······c·········g·····················
·······))E·s········m·······n)········e·····················
········C·E·········p·······((·······{print;exit}····K······
·······H·T··········t·······,t········ ···r·················
······O· ···········(·······'u········-·····················
····· ·/············)·······'p········m·····················
····%·P·············)·······)n········1·····················
···A· ······················)i·······n ·····················
··%·A························(······-·.·····················
···=·························t····· ···$·d·················· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ·····························r··e···a·····················}} ·····························p·h···=························ ··································<························· ·································>·························· # FALSE, 1 character added ^, New grid: ·········v---H\········································;···· ······,··>qir@uH···IaP.················USE: io·········>···· Get a chr!?pio;·····l··················readln··········;···· Outputs it,u········e·······c··········print(readline())···· and 'BZam..t········r·······a··········string)·········;···· ········~,@s······s t=" " r t#50:20 w !,t,!············E···· ······main( ){printf("%c", (getchar()));}·············;···· ···········g·> input('','s'))·······················P···· ···········e·····n··r·····^·c·········g················;···· ·······(write(read-host)····a)········r·input n$·······(····
·······))E·s········m·······n)········e·print n$·······;···· ········C·E·········p·······((·······{print;exit}····K·*···· ·······H·T··········t·······,t········ ···r················· ······O· ···········(·······'u········-····················· ····· ·/············)·······'p········m····················· ····%·P·············)·······)n········1····················· ···A· ······················)io······n ····················· ··%·A························(······-·.····················· ···=·························t\···· ···$·d··················
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
·····························r··e···a b c d e f g h i·····}}
·····························p·h···=b c d e f g h i·········
··································<·························
·································>··························
• I went ahead and edited this answer to fix an older program. We can revert the edit if something changes. – ETHproductions Sep 9 '15 at 2:49
• Sounds good to me! – Lynn Sep 9 '15 at 2:52
di _r(a)
di $a Take input via prompt and store in a. Print contents of a. ·········v---H\········································;···· ······,··>qir@uH···IaP.················USE: io·········>···· Get a chr!?pio;·····l··················readln··········;···· Outputs it,u········e·······c··········print(readline())···· and 'BZam..t········r·······a··········string)·········;···· ········~,@s······s t=" " r t#50:20 w !,t,!············E···· ······main( ){printf("%c", (getchar()));}·············;···· ···········g·> input('','s'))·······················P···· ···········e·····n··r·····^·c·········g················;···· ·······(write(read-host)····a)········r·input n$·······(····
·······))E·s········m·······n)········e·print n$·······;···· ········C·E·········p·······((·······{print;exit}····K·*···· ·······H·T··········t·······,t········ ···r················· ······O· ···········(·······'u········-····················· ····· ·/············)·······'p········m····················· ····%·P·············)·······)n········1····················· ···A· ······················)io······n ····················· ··%·A························(······-·.··di _r(a)··········· ···=·························t\···· ···$·di $a·············· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ·····························r··e···a b c d e f g h i·····}} ·····························p·h···=b c d e f g h i········· ··································<························· ·································>·························· # x-D, 11 characters added ;>;);E;P;(;* ;> increment ; to 1, make sure the loop is entered ;) start loop ;E read from STDIN ;P output to STDOUT ;( end loop, ends on 0 ;* end program The new grid ·········v---H\········································;···· ······,··>qir@uH···IaP.················USE: io·········>···· Get a chr!?pio;·····l··················readln··········;···· Outputs it,u········e·······c··········print(readline())···· and 'BZam..t········r·······a··························;···· ········~,@s······s t=" " r t#50:20 w !,t,!············E···· ······main( ){printf("%c", (getchar()));}·············;···· ···········g·> input('','s'))·······················P···· ···········e·····n··r·······c·········g················;···· ·······(write(read-host)····a)········r·input n········(···· ·······))E·s········m·······n)········e·print n········;···· ········C·E·········p·······((·······{print;exit}····K·*···· ·······H·T··········t·······,t········ ···r················· ······O· ···········(·······'u········-····················· ····· ·/············)·······'p········m····················· ····%·P·············)·······)n········1····················· ···A· ······················)io······n ····················· ··%·A························(······-·.····················· ···=·························t\···· ···$·d··················
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
·····························r··e···a b c d e f g h i·····}}
·····························p·h···=b c d e f g h i·········
··································<·························
·································>··························
> input('','s')
The new grid:
·········v---H\·············································
·········>qir@uH···IaP.·····································
Get a chr!?pio;·····l·······································
Outputs it,u········e·······c·······························
and 'BZam..t········r·······a·······························
········~,@s······s t=" " r t#50:20 w !,t,!·················
··········· ··printf(·······(·······························
···········g·> input('','s'))····························
···········e·····n··r·······c·········g·····················
·······))E·s········m·······n)········e·····················
········C·E·········p·······((·······{print;exit}····K······
·······H·T··········t·······,t········ ···r·················
······O· ···········(·······'u········-·····················
····· ·/············)·······'p········m·····················
····%·P·············)·······)n········1·····················
···A· ······················)io······n ·····················
··%·A························(······-·.·····················
·······))E·s········m·······n)········e·print n$·······;···· ········C·E·········p·······((·······{print;exit}····K·*···· ·······H·T··········t·······,t········ ···r················· ······O· ···········(·······'u········-····················· ····· ·/············)·······'p········m····················· ····%·P·············)·······)n········1····················· ···A· ······················)io······n ···················· ··%·A························(······-·.··di _r(a)··········· ···=·························t\···· ···$;di $a·············· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ·····························r··e···a b c d e f g h i·····}} ·····························p·h···=b c d e f g h i········· ··································<························· ·································>·························· # Clojure, 21 characters added (println (read-line)) The grid is now: ·········v---H\··v+C+<D_··············S·P··············;···· ·····,··>qir@uH· IaP.C·············A·USE: io·········>···· Get a chr!?pio;····Ol···············Y·Lreadln(write(···;···· Outputs it,u········e·······c······ ·L·print(readline())···· and 'BZam..t········r·······a·····ai ··string))········;···· ········~,@s······s t=" " r t#50:20 w !,t,!············E···· ······main( ){printf("%c", (getchar()));}·············;···· ···········g·> input('','s'))·······················P···· ···········e·····n··r·····^·c·········g················;···· ·······(write(read-host)····a)········r·input n$!?·····(····
·······))E·s········m·······n)········e·print n$·······;···· ········C·E·········p·······((·······{print;exit}····K·*···· ·······H·T··········t·······,t········ ···r················· ······O· ···········(·······'u········-····················· ····· ·/(println····)·······'p········m····················· ····%·P· (read-line))······)n········1····················· ···A· ······················)io······n ···················· ··%·A························(······-·.··di _r(a)··········· ·$·=·························t\···· ···$;di$a··············
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
·····························r··e···a b c d e f g h i·····}}
·····························p·h···=b c d e f g h i·········
··································<·························
·································>··························
I also missed the main requirement of the question; this has been fixed now. Sorry for the confusion.
)io
7 is a language I have been working on for a while, but unfortunately, I have not had a chance to publish it yet. i stands for input, and o for output. Pretty simple, right? ;)
The new grid:
·········v---H\·············································
·········>qir@uH···IaP.·····································
Get a chr!?pio;·····l·······································
Outputs it,u········e·······c·······························
and 'BZam..t········r·······a·······························
········~,@s······s t=" " r t#50:20 w !,t,!·················
··········· ··printf(·······(·······························
···········g·· input('','s'))····························
···········e·····n··r·······c·········g·····················
·······))E·s········m·······n)········e·····················
········C·E·········p·······((·······{print;exit}····K······
·······H·T··········t·······,t········ ···r·················
······O· ···········(·······'u········-·····················
····· ·/············)·······'p········m·····················
····%·P·············)·······)n········1·····················
···A· ······················)io······n ·····················
··%·A························(······-·.·····················
···=·························t\···· ···$·d·················· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ·····························r··e···a b c d e f g h i·····}} ·····························p·h···=b c d e f g h i········· ··································<························· ·································>·························· • Why do you add 100 to the number read from STDIN? I'm pretty sure you're supposed to just output it. – Lynn Sep 9 '15 at 2:40 • @Mauris Oh, gosh, I skimmed over that rule somehow! Is it possible to change it now? – ETHproductions Sep 9 '15 at 2:42 • I'm not sure what to do. @Ypnypn should decide. – Lynn Sep 9 '15 at 2:43 • I'm so sorry... Perhaps I could just edit this answer and the most recent. @Ypnypn, what do you think? – ETHproductions Sep 9 '15 at 2:45 • @Ypnypn I went ahead and edited this answer and the most recent one. There's ten answers between them; should I go through and edit them all, or just leave them the way they are? – ETHproductions Sep 9 '15 at 2:54 # Burlesque, 1 character added Q The new grid: ·········v---H\··v+C+<D_··············S·P··············;···· G····,··>qir@uH· IaP.C·············A·USE: io·········>···· Get a chr!?pio;····Ol···············Y·Lreadln(write(···;···· Outputs it,u········e·······c······ ·L·print(readline())···· and 'BZam..t········r·······a·····ai ··string))··<v;···;···· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?···E···· G·····main( ){printf("%c", (getchar()));}·······pr>···;···· O·········)g·> input('','s'))·················h_····P···· a··········e·····n··r·····^·c·········g··········pd····;···· ·······(write(read-host)····a)········r·input n$!?u····(····
·······))E·s········m·······n)···KVGH·e·print n$··m····;···· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*····$'main'H·T··········t·······,t···HSMI· ···r·······(·········
\/\··O· ···········(·······'u···XIM ·-···········$········· \/· ·/(println····)·······'p···BBE1·m···········a········· \%·PQ (read-line))······)n···YLH.·1···········r········· A\ /-io-\············)io··EE 4n ··········g········· % A\-e-< |·············(···· V-·.··di _r(a)·v·········$ = \----#·············t\···V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
·····························r··e···a b c d e f g h i·····}}
···········>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni·····<·························
···};s<<tuoc::dts;s>>nic::dts····>··························
• The homepage is here; try submitting Q as Burlesque code here. – Lynn Sep 9 '15 at 21:37
• STDIN is pushed on the stack as a string at the start of the program, like in GolfScript. Q is show, which makes it a Pretty value (an ordinary String would be printed with quotes). When the program finishes, it is printed. – Lynn Sep 9 '15 at 21:38
• Alright, the esolang page just said it was recommended that implementations do that, but since an interpreter exists where it does that, it should be fine. You should probably link one/both of those in the question body though. – FryAmTheEggman Sep 9 '15 at 21:40
,
The new grid:
·········v---H\·Iv+C+<D_··············S·P··············;····
G····,··>qir@uH· IaP.C········LAMBDA·USE: io·········>····
and 'BZam..t········r·······a·····ai ··string))··<v;i:j;p:j·
G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:·E····
G·····main( ){printf("%c", (getchar()));}·······pr>·:·;····
O·········)g·> input('','s'))·················h_··)·P····
a··········e·····n··r·····^·c·········g··········pd····;····
·······(write(read-host)····a)········r·input n$!?u····(···· ·······))E·s········m·······n)···KVGH·e·print n$!·m····;····
········C·E·········p·······((···TIIA{print;exit}·pYEK·*····
$'main'H·T··········t·······,t···HSMI· ···r·······(········· \/\··O· ·········S (I\·····'u···XIM ·-···········$·········
\/· ·/(println··FO) /·····'p···BBE1·m···········a·········
A\ /-io-\············)io··EE 4n ····,·····g·········
% A\-e-< |·············(···· V-·.··di _r(a)·v·········
$= \----#·············t\···V ···$;di $a····)········· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}} ···········>maertsoi<edulcni#p·h···=b c d e f g h i········· ····;s gnirts::dts{)(niam tni····v< o<···················· ···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;··················· # Capuirequiem, 1 character added IO The new grid: ·········v---H\OIv+C+<D_··············S·P··············;···· G····,··>qir@uH· IaP.C········LAMBDA·USE: io·········>···· Get a chr!?pio;····Ol···········ZEROY·Lreadln(write(···;···· Outputs it,u········e·······c······ ·L·print(readline())···· and 'BZam..t········r·······a·····ai ··string))··<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:·E···· G·····main( ){printf("%c", (getchar()));}·······pr>·:·;···· O·········)g·> input('','s'))·················h_··)·P···· a··········e·····n··r·····^·c·········g··········pd····;···· ·······(write(read-host)····a)········r·input n$!?u····(····
·······))E·s········m·······n)···KVGH·e·print n$!·m····;···· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*····$'main'H·TUPTUO·····t·······,t···HSMI· ···r·······(·········
\/\··O· ·TUPNI···S (I\·····'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·m···········a········· \%·PQ (read-line))······)n···YLH.·1···········r········· A\ /-io-\············)io··EE 4n ····,·····g········· % A\-e-< |·············(···· V-·.··di _r(a)·v·········$ = \----#·············t\···V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
···········>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<····················
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;···················
EDIT: I'm just making sure this shows up on top when people sort by "active".
And the resulting grid:
·········v---H\OIv+C+<D_··············S·P··············;····
G····,··>qir@uH· IaP.C········LAMBDA·USE: io·········>····
and 'BZam..t········r·······a·····ai ··string))··<v;i:j;p:j·
G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:·E····
G·····main( ){printf("%c", (getchar()));}·······pr>·:·;····
O·········)g·> input('','s'))·················h_··)·P····
a··········e·····n··r·····^·c·········g··········pd····;····
·······(write(read-host)····a)········r·input n$!?u····(···· ·······))E·s········m·······n)···KVGH·e·print n$!·m····;····
········C·E·········p·······((···TIIA{print;exit}·pYEK·*····
$'main'H·TUPTUO·····t·······,t···HSMI· ···r·······(········· \/\··O· ·TUPNI···S (I\·····'u···XIM ·-···········$·········
\/· ·/(println··FO) /·····'p···BBE1·m···········a·········
A\ /-io-\············)io··EE 4n ····,·····g·········
% A\-e-< |·············(···· V-·.··di _r(a)·v·········
$= \----#·············t\···V ···$;di $a····)········· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}} ···········>maertsoi<edulcni#p·h···=b c d e f g h i········· ····;s gnirts::dts{)(niam tni····v< o<···················· ···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;··················· # Varsig, 3 characters added Using the shortcut symbols (_#) This translates to the full commands of PRY CLEAN EXIT CRAM Added on the 18h line backwards near the centre. The new grid. ·········v---H\OIv+C+<D_··············S·P··············;···· G····,··>qir@uH· IaP.C········LAMBDA·USE: io·········>···· Get a chr!?pio;····Ol···········ZEROY·Lreadln(write(···;···· Outputs it,u········e·······c······ ·L·print(readline())···· and 'BZam..t········r·······a·····ai ··string))··<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:·E···· G·····main( ){printf("%c", (getchar()));}·······pr>·:·;···· O·········)g·> input('','s'))·················h_··)·P···· a··········e·····n··r·····^·c·········g··········pd····;···· ·······(write(read-host)····a)········r·input n$!?u····(····
·······))E·s········m·······n)···KVGH·e·print n$!·m····;···· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*····$'main'H·TUPTUO·····t·······,t···HSMI· ···r·······(·········
\/\··O· ·TUPNI···S (I\·····'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·m···········a········· \%·PQ (read-line))······)n···YLH.·1··print(io.read())··· A\ /-io-\············)io··EE 4n ····,·····g········· % A\-e-< |··········)#_(···· V-·.··di _r(a)·v·········$ = \----#·············t\·c&V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
···········>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<····················
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;][gnirtStupnI@tnirP
,.@
New grid:
·········v---H\OIv+C+<D_··············S·Psgv···········;····
G····,··>qir@uH· IaP.C········LAMBDA·USE: io·········>····
Outputs it,u··a$ohce·······c······ ·L·print(readline())···· and 'BZam..t···a daer·······a·····ai ··string))·o<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:·E···· G·····main( ){printf("%c", (getchar()));}·······pr>·:·;···· O·········)g·> input('','s'))·················h_··)·P···· a··········e·····n··r·····^·c·········g··········pd····;···· ·······(write(read-host)····a)········r·input n$!?u····(····
·······))E·s········m·······n)···KVGH·e·print n$!·m····;···· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*····$'main'H·TUPTUO·····t·00····,t···HSMI· ···r·······(·········
\/\I^O= ·TUPNI···S (I\\/\]]'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·m···········a········· \%·PQ (read-line))······)n···YLH.·1··print(io.read())··· A\ /-io-\············)io··EE 4n ··@.,·····g········· % A\-e-< |··········)#_(···· V-·.··di _r(a)^v·········$ = \----#·············t\·c&V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
···········>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<····················
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;][gnirtStupnI@tnirP
• And that's the Y's done :) – MickyT Sep 10 '15 at 23:46
%:.x
I placed it vertically from the second line to the 4th, below "Include".
·········v---H\OIv+C+<D_Include C by GS·Psgv···········;····
G····,.·>qir@uH· IaP.C.%······LAMBDA·USE: io·········>····
Outputs it,u··a$ohce····.··c······ ·L·print(readline())···· and 'BZam..t···a daer····x··a·····ai ··string))·o<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:,Eu-·· G·····main( ){printf("%c", (getchar()));}·······pr>·:·;tg·· O·········)g·> input('','s'))(enildr ,tnirp···h_··)·P(e·· a··········e·····n··r·····^·c·········g··········pd····;Ct·· ·······(write(read-host)····a)········r·input n$!?u····()(··
·······))E·s········m·······n)···KVGH·e·print n$!·m····;.C·· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*·)··$'main'H·TUPTUO·····t·00····,t···HSMI· ···r·······(······,··
\/\I^O= ·TUPNI···S (I\\/\]]'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·main = interact id···· \%·PQ (read-line))······)n···YLH.·1··print(io.read())··· A\ /-io-\············)io··EE 4n ··@.,·····g········· % A\-e-< |··········)#_(···· V-·.··di _r(a)^v·········$ = \----#·············t\·c&V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
··········;>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<····················
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;][gnirtStupnI@tnirP
rw
Reads a single character and outputs it.
New grid:
·········v---H\OIv+C+<D_Include C by GS Psgv···········;····
G····,.·>qir@uH· IaP.C.%······LAMBDA·USE: io·········>····
Outputs it,u··a$ohce····.··c······ ·L·print(readline())···· and 'BZam..t···a daer····x··a·····ai ··string))·o<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:,Eu-·· G·····main( ){printf("%c", (getchar()));}·······pr>>:.;tg·· O·········)g·> input('','s'))(enildr ,tnirp···h_··)·P(e·· a··········e·····n··r·····^·c···puts [gets stdin]pd····;Ct·· ·······(write(read-host)····a)········r·input n$!?u····()(··
·······))E·s··w·····m·······n)···KVGH·e·print n$!·m····;.C·· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*·)··$'main'H·TUPTUO·····t·00····,t···HSMI· ···r·······(······,··
\/\I^O= ·TUPNI···S (I\\/\]]'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·main = interact id···· \%·PQ (read-line))······)n···YLH.·1··print(io.read())··· A\ /-io-\············)io··EE 4n ··@.,·····g········· % A\-e-< |··········)#_(o··· V-·.··di _r(a)^v·········$ = \----#·············t\·c&V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
··········;>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<Ook. Ook! Ook! Ook.·
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;][gnirtStupnI@tnirP
# GNU bc, 4 characters added
read() # the printing is implicit
bc is a calculator language. The only input token recognized by read() is a number, an allowed limitation. A trailing newline is needed when saving the code to a file.
Run example:
bc --quiet program.bc <<< 35
New grid: my characters are added horizontally, left to right, starting from (row = 10, column = 52)
·········v---H\OIv+C+<D_Include C by GS Psgv···········;····
G····,.·>qir@uH· IaP.C.%······LAMBDA·USE: io·········>····
Outputs it,u··a$ohce····.··c······ ·L·print(readline())···· and 'BZam..t···a daer····x··a·····ai ··string))·o<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:,Eu-·· G·····main( ){printf("%c", (getchar()));}·······pr>>:.;tg·· O·········)g·> input('','s'))(enildr ,tnirp···h_··)·P(e·· a··········e·····n··r·····^·c···puts [gets stdin]pd····;Ct·· ·······(write(read-host)····a)········r·input n$!?uread()(··
·······))E·s··w·····m·······n)···KVGH·e·print n$!·m····;.C·· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*·)··$'main'H·TUPTUO·····t·00····,t···HSMI· ···r·······(······,··
\/\I^O= ·TUPNI···S (I\\/\]]'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·main = interact id···· \%·PQ (read-line))······)n···YLH.·1··print(io.read())··· A\ /-io-\············)io··EE 4n ··@.,·····g········· % A\-e-< |··········)#_(o··· V-·.··di _r(a)^v·········$ = \----#·············t\·c&V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
··········;>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<Ook. Ook! Ook! Ook.·
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;][gnirtStupnI@tnirP
({})
Pops and pushes the top element,so the stack ends up unchanged. Input is implicitly put on the stack, and the stack is printed afterwards. Only numbers are allowed (unless you use the argument -c).
New grid:
·········v---H\OIv+C+<D_Include C by GS Psgv···········;····
G····,.·>qir@uH· IaP.C.%······LAMBDA·USE: io·········>····
Outputs it,u··a$ohce····.··c······ ·L·print(readline())···· and 'BZam..t···a daer····x··a·····ai ··string))·o<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:,Eu-·· G·····main( ){printf("%c", (getchar()));}·······pr>>:.;tg·· O·········)g·> input('','s'))(enildr ,tnirp···h_··)·P(e·· a··········e·····n··r·····^·c··{puts [gets stdin]pd····;Ct·· ·······(write(read-host)····a)}·······r·input n$!?uread()(··
·······))E·s··w·····m·······n)···KVGH·e·print n$!·m····;.C·· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*·)··$'main'H·TUPTUO·····t·00····,t···HSMI· ···r·······(······,··
\/\I^O= ·TUPNI···S (I\\/\]]'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·main = interact id···· \%·PQ (read-line))······)n···YLH.·1··print(io.read())··· A\ /-io-\············)io··EE 4n ··@.,·····g········· % A\-e-< |··········)#_(o··· V-·.··di _r(a)^v·········$ = \----#·············t\·c&V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
··········;>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<Ook. Ook! Ook! Ook.·
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;][gnirtStupnI@tnirP
My code (lines 8-11):
································(···························
·······························{····························
······························}·····························
·····························)······························
Code:
)io@
Run in the online interpreter!
This maps out to the following cube when executed:
)
i o @ .
.
The interpreter runs i (input a character), o (print the character), and then @ (terminate the program). In this case, ) is a no-op, simply there because )io was already on the grid, and a leading character was needed to align the grid correctly.
·········v---H\OIv+C+<D_Include C by GS Psgv···········;····
G····,.·>qir@uH· IaP.C.%······LAMBDA·USE: io·········>····
Outputs it,u··a$ohce····.··c······ ·L·print(readline())···· and 'BZam..t···a daer····x··a·····ai ··string))·o<v;i:j;p:j· G·······~,@s······s t=" " r t#50:20 w !,t,!······?a?·:,Eu-·· G·····main( ){printf("%c", (getchar()));}·······pr>>:.;tg·· O·········)g·> input('','s'))(enildr ,tnirp···h_··)·P(e·· a··········e·····n··r·····^·c··{puts [gets stdin]pd····;Ct·· ·······(write(read-host)····a)}·······r·input n$!?uread()(··
·······))E·s··w·····m·······n)···KVGH·e·print n$!·m····;.C·· ········C·E·········p·······((···TIIA{print;exit}·pYEK·*·)··$'main'H·TUPTUO·····t·00····,t···HSMI· ···r·······(······,··
\/\I^O= ·TUPNI···S (I\\/\]]'u···XIM ·-···········$········· \/· ·/(println··FO) /·····'p···BBE1·main = interact id···· \%·PQ (read-line))······)n···YLH.·1··print(io.read())··· A\ /-io-\············)io@·EE 4n ··@.,·····g········· <-- added on this line % A\-e-< |··········)#_(o··· V-·.··di _r(a)^v·········$ = \----#·············t\·c&V ···$;di$a····)·········
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
··[x.?10xx][x.?10xx]r··e···a b c d e f g h i·····}}
··········;>maertsoi<edulcni#p·h···=b c d e f g h i·········
····;s gnirts::dts{)(niam tni····v< o<Ook. Ook! Ook! Ook.,
···};s<<tuoc::dts;s>>nic::dts···o>i:1+?/;][gnirtStupnI@tnirP
r
The grid is now:
····························································
····························································
··········?pio··············································
··········,u················································
··········.t················································
···········s················································
··········· ················································
···········g················································
···········e················································
········w··t················································
···········s················································
····························································
··········································r·················
····························································
····························································
····························································
····························································
····························································
····························································
····························································
····························································
····························································
····························································
····························································
····························································
ip
The grid is now:
····························································
···········i················································
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···········s················································
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The grid is now:
····························································
···········i········a·······································
··········?pio;·····l·······································
··········,u········e·······································
··········.t········r·······································
···········s········t·······································
··········· ········(·······································
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A space.
The new grid:
·········v---H\·············································
·········>qir@uH····a·······································
Get a chr!?pio;·····l·······································
Outputs it,u········e·······c·······························
and 'BZam..t········r·······a·······························
··········@s······s t=" " r t#50:20 w !,t,!·················
··········· ··printf(·······(·······························
···········g·· input('','s'))····························
···········e·····n··r·······c·······························
·······))E·s········m·······n)······························
········C·E·········p·······((······························
·······H·T··········t·······,t············r·················
······O· ···········(·······'u······························
····· ·/············)·······'p······························
····%·P·············)·······)n········1·····················
···A· ······················)i·······n······················
··%·A························(······-·······················
···=·························t····· ···$·d·················· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ·····························r··e···a·····················}} ·····························p·h···=························ ··································<························· ·································>·························· # gs2, 1 character added K. The new grid: ·········v---H\············································· ·········>qir@uH····a······································· Get a chr!?pio;·····l······································· Outputs it,u········e·······c······························· and 'BZam..t········r·······a······························· ··········@s······s t=" " r t#50:20 w !,t,!················· ··········· ··printf(·······(······························· ···········g·· input('','s'))···························· ···········e·····n··r·······c·········g····················· ·······(write(read-host)····a)········r······ ·············· ·······))E·s········m·······n)········e····················· ········C·E·········p·······((········p··············K······ ·······H·T··········t·······,t········ ···r················· ······O· ···········(·······'u········-····················· ····· ·/············)·······'p········m····················· ····%·P·············)·······)n········1····················· ···A· ······················)i·······n ····················· ··%·A························(······-·.····················· ···=·························t····· ···$·d··················
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
·····························r··e···a·····················}}
·····························p·h···=························
··································<·························
·································>··························
• It should be upper-case, my caps lock was on. – Lynn Sep 8 '15 at 23:51
~,@
The new grid:
·········v---H\·············································
·········>qir@uH···IaP.·····································
Get a chr!?pio;·····l·······································
Outputs it,u········e·······c·······························
and 'BZam..t········r·······a·······························
········~,@s······s t=" " r t#50:20 w !,t,!·················
··········· ··printf(·······(·······························
···········g·· input('','s'))····························
···········e·····n··r·······c·········g·····················
·······))E·s········m·······n)········e·····················
········C·E·········p·······((·······{print;exit}····K······
·······H·T··········t·······,t········ ···r·················
······O· ···········(·······'u········-·····················
····· ·/············)·······'p········m·····················
····%·P·············)·······)n········1·····················
···A· ······················)i·······n ·····················
··%·A························(······-·.·····················
···=·························t····· ···$·d·················· {elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc ;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS ·····························r··e···a·····················}} ·····························p·h···=························ ··································<························· ·································>·························· ## Betterave, 1 character added$;
The new grid:
·········v---H\········································;····
······,··>qir@uH···IaP.················USE: io·········>····
and 'BZam..t········r·······a··········string)·········;····
········~,@s······s t=" " r t#50:20 w !,t,!············E····
······main( ){printf("%c", (getchar()));}·············;····
···········g·> input('','s'))·······················P····
···········e·····n··r·····^·c·········g················;····
·······(write(read-host)····a)········r·input n$·······(···· ·······))E·s········m·······n)········e·print n$·······;····
········C·E·········p·······((·······{print;exit}····K·*····
·······H·T··········t·······,t········ ···r·················
······O· ···········(·······'u········-·····················
····· ·/············)·······'p········m·····················
····%·P·············)·······)n········1·····················
···A· ······················)io······n ·····················
··%·A························(······-·.··di _r(a)···········
···=·························t\···· ···$;di$a··············
{elbaworhT sworht )a][gnirtS(niam diov citats cilbup{C ssalc
;))(txen.)ni.metsyS(rennacS.litu.avaj wen(nltnirp.tuo.metsyS
·····························r··e···a b c d e f g h i·····}}
·····························p·h···=b c d e f g h i·········
··································<·························
·································>··························
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2021-02-28 16:23:13
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http://quant.stackexchange.com/questions?page=5&sort=newest&pagesize=50
|
# All Questions
74 views
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The Longstaff-Schwartz LSM approach is nowadays ubiquitous(at least in the academic literature) in pricing path dependant derivatives. Up to now I have mostly worked with lattice methods. My ...
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### Markit PMI vs ISM PMI
What is the difference between the Markit Manufacturing PMI and the ISM Manufacturing PMI? The monthly number differs a lot, my understanding is that they are trying to indicate the same thing.
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### Can the duration of a bond be greater than Time to Maturity
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### Rationale behind formula for pivot point calculation
Is there any objective rationale or mathematical reasoning behind the following formula for pivot points and intra day support and resistance levels? What are the underlying assumptions for the ...
22 views
### Where can i find financial data of CDO's starting from 1996
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66 views
### How to obtain specific information on FX trading systems?
I'm trying to compare trading venues using a quantitative product selection matrix (and eventually software vendors using a different matrix specifically for vendors), and I was wondering if anyone ...
46 views
### Linear-Boundary Crossing Problem for Brownian Motion
This is a question I came across while reading: $W = (W_t)_{t\geq{0}}$ is a standard BM. Let $\mu\in \mathbb{R}$, and let $\tau_{a}^{\mu}$ = $\inf(t>0;W_t = a + \mu{t})$ be the first passage time ...
50 views
### Fitting a sigmoid function to incomplete, structured, data
I have an incomplete data set that looks like this: and I believe that it will continue to form a sigmoid-like shape. How can fit a sigmoid curve to this data given my assumption about what the ...
52 views
### Sampling and/or asymptotic distribution of a function
Assume we have the following function: $$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$ where $d$ is a constant $T$ is a constant $X_t$ ...
417 views
### Free and tested optimization, statistical and visualization packages for C#
I am about to implement a variation of the LIBOR-Market-Model (complete with Least-Square-Montecarlo, calibration, pricing etc.) and decided to implement it in C#. The implementation will involve ...
109 views
### Pre-trade evaluation and risk assessment of option trading strategies (in market practice)
When a trader gets conclusion of the volatility is being underestimated (via volatility cone or some other technology), actually there are multiple ways for his trading. (Let's assume the underlying ...
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### Beta and the Assumption of IID Returns
For two stocks that are independent and identically distributed (iid), do they have the same beta? Does the number of data points matter?
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### How to calculate modeled asset volatility by industry factor?
Currently I am working with huge data frame which consists of a lot firms. For each firm in my sample I calculated asset volatility ( I am using Merton default probability model, so I have used 2 ...
49 views
### Modeling the Option Volatility Skew
The volatility skew often changes based on multiple factors, such as moneyness of the option, time to expiration, movement in the underlying instrument, etc.. How does one best model the skew? Is ...
40 views
### Forecasting amount of slippage in executing option spreads
Is there a good quantitative model to estimate how much slippage is required to execute a particular option spread trade? For example, let's say you want to execute an Iron Condor. Given X, Y, Z ...
100 views
### Asset-or-nothing Option Valuation in the Black and Scholes model
In standard Black-Scholes Model, compute the price of an asset-or-nothing put and asset-or-nothing call options. Write down the put-call parity relation between the asset-or-nothing call and put ...
53 views
### The concept of an incomplete market
While skeeming the relevant literature and web-sites I noticed that mostly the concept of the incomplete market is reduced to the following statement "A market is incomplete if there are more ...
169 views
### Algorithmical replication of a profit and loss function using different options
I often see questions like "Given this payoff graph (example below), construct a portfolio that replicates it." I want to know if there is an efficient method/algorithm to find the individual pieces ...
87 views
### Effect of interest rate on options prices
This might be another basic derivatives question. When interest rate rises, stock prices generally fall. Assuming an option's underlying is a stock, this should lower the option's price as well. ...
785 views
### What is the necessary level of Econometrics-Know-How for a quant
It seems quants increasingly use econometric models at work. As someone who has sold his soul to probability theory and stochastical analysis I would like to catch up. What are the econometric tools ...
25 views
### URL with SEC data
Do you know a URL where i can find the CIK of a listed company PLUS ON THE SAME URL the filing dates of 10-Q or 10-K documents? So i can create this url ...
29 views
95 views
### How to Calculate a Monte Calo VaR estimation error
I'm performing a Monte Carlo to calculate value at risk (with a 3 dimension risk factor) Now, I would like to calculate the error of the estimation of the VaR with respect to the number of simulations ...
113 views
### what was the quant role in the 2008 crash?
this is a complex topic that interests me, have researched myself, & is debated heavily in the media and there is lots of writing, even entire books/documentaries. maybe somewhat surprisingly, ...
154 views
### How are quants able to verify whether their calculated prices are any good
This question is related to the discussion on Model Validation Criteria However it appeard to be very high level to me and I would like to go more into detail. Not working at a pricing desk the ...
I got stuck on the following question whilst learning about basic option pricing. A stock is valued at \$75 today. An option will pay \$1 the first time the stock reaches \\$100 in value, which it ...
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2014-04-16 13:19:43
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http://math.chapman.edu/~jipsen/structures/doku.php/bck-lattices
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BCK-lattices
Abbreviation: BCKlat
Definition
A BCK-lattice is a structure $\mathbf{A}=\langle A,\vee,\wedge,\rightarrow,1\rangle$ of type $\langle 2,2,2,0\rangle$ such that
$\langle A,\vee,\rightarrow,1\rangle$ is a BCK-join-semilattice
$\langle A,\wedge,\rightarrow,1\rangle$ is a BCK-meet-semilattice
Remark: $x\le y \iff x\rightarrow y=1$ is a partial order, with $1$ as greatest element, and $\vee$, $\wedge$ are a join and meet for this order. 1)
Morphisms
Let $\mathbf{A}$ and $\mathbf{B}$ be BCK-lattices. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(x\rightarrow y)=h(x)\rightarrow h(y)$ and $h(1)=1$.
Example 1:
Properties
Classtype variety yes yes yes $n=2$
Finite members
$\begin{array}{lr} f(1)= &1\\ f(2)= &\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ \end{array}$
References
1) Pawel M. Idziak, Lattice operation in BCK-algebras, Math. Japon., 29, 1984, 839–846 MRreview
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2017-05-29 15:20:23
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https://socratic.org/questions/whats-the-the-algebraic-expression-for-32-divided-by-the-quantity-y-plus-12#646393
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# What's the the algebraic expression for "32 divided by the quantity y plus 12"?
Aug 9, 2018
$\frac{32}{\left(y + 12\right)}$
#### Explanation:
$\frac{32}{\left(y + 12\right)}$
Aug 9, 2018
$\frac{32}{y + 12}$
#### Explanation:
$\text{the quantity y plus 12 is written } y + 12$
$\text{and 32 divided by this quantity is } 32 \div \left(y + 12\right)$
$\text{or "32/(y+12)larrcolor(blue)" in fractional form}$
Aug 9, 2018
It can be interpreted in two ways:
$\frac{32}{y + 12} \text{ }$ or $\text{ } \frac{32}{y} + 12$
#### Explanation:
The statement does really indicate clearly enough what is meant.
It could be interpreted as:
$32$ divided by, $y$ plus $12$
which would mean that $32$ is divided by the sum of $y \mathmr{and} 12$
$\frac{32}{y + 12}$
OR
It could be read as $32$ divided by $y$, plus $12$
$\frac{32}{y} + 12$
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2022-12-02 15:32:31
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https://www.ideals.illinois.edu/browse?rpp=20&order=ASC&sort_by=-1&value=Mathematics&etal=-1&type=subject&starts_with=T
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# Browse by Subject "Mathematics"
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2015-03-04 00:10:53
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http://xml.jips-k.org/full-text/view?doi=10.3745/JIPS.02.0165
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Bian , Gong , Ma , and Duan: Research on Water Edge Extraction in Islands from GF-2 Remote Sensing Image Based on GA Method
# Research on Water Edge Extraction in Islands from GF-2 Remote Sensing Image Based on GA Method
Abstract: Aiming at the problem of low accuracy in the water boundary automatic extraction of islands from GF-2 remote sensing image with high resolution in three bands, new water edges automatic extraction method in island based on GF-2 remote sensing images, genetic algorithm (GA) method, is proposed in this paper. Firstly, the GA-OTSU threshold segmentation algorithm based on the combination of GA and the maximal inter-class variance method (OTSU) was used to segment the island in GF-2 remote sensing image after pre-processing. Then, the morphological closed operation was used to fill in the holes in the segmented binary image, and the boundary was extracted by the Sobel edge detection operator to obtain the water edge. The experimental results showed that the proposed method was better than the contrast methods in both the segmentation performance and the accuracy of water boundary extraction in island from GF-2 remote sensing images.
Keywords: GA-OTSU , GF-2 RS Image , Morphology , Sobel Edge Detection , Water Edges
## 1. Introduction
The coastline is the boundary between the sea and the land at the average water level of spring tides over many years [1]. The water edge refers to the instantaneous coastline, rather than the actual coastline [2]. However, the water edge extraction is the premise and important step of coastline extraction, so the research on which is of great significance.
With the development of remote sensing technology, the resolution of a multi-spectral remote sensing image is also improved. The improvement of image resolution has greatly improved the accuracy and speed of information acquisition, but it is also affected by more “noise or non-target,” “same object and different spectrum” or “foreign body in the same spectrum,” which bring more difficulties in the extrac¬tion of a linear target [3]. Under this background, developing a more efficient image extraction method is particularly important. However, extracting linear targets (coastline, road centerline, tidal channel line, etc.) with a single method can only come up with poor results, so a combination of several algorithms is widely used. Yang et al. [4] realized the extraction of coastline along the Sanya Bay, Dadonghai by using the watershed segmentation and mathematical morphological methods, which can achieve the coastline extraction. However, the watershed segmentation algorithm is susceptible to noise and other factors, and the image may be over-segmented, which easily introduces uncertain factors, and it is difficult to achieve higher accuracy even through morphological modification. Zhu et al. [5] realized the extraction of the middle line of the tidal gulch in Jiuduansa area based on the combination of top-hat transformation, the OTSU threshold segmentation algorithm, erosion and dilation methods. Although this method can extract the middle line of the tidal trench, there still exists three problems: firstly, the top-hat method can not only eliminate the noise but also destroy the edge of the target area and affect the extraction accuracy of the edge line; secondly, the OTSU method uses the maximum inter-class variance between the target and the background to determine the segmentation threshold, but the segmentation threshold is not necessarily the optimal solution of the maximum inter-class variance; lastly, the structural elements size of erosion and dilation is difficult to grasp, and it is easy to cause sawtooth phenomenon. Paravolidakis et al. [6] proposed a method combining the edge detection algorithm and the Snake algorithm. The method initially used the anisotropic diffusion algorithm to reduce the noise of the image, and then used local threshold segmentation algorithm to process the denoised image, and the output image was regionally grouped to remove all the small space objects and focused on the space objects of interest, finally, the morphological operator and Canny operator were used to extract the coastline. Ideal results have been obtained, but the process is complicated and time-consuming (for example, for a remote sensing image of 4000×4000, after noise reduction, it shall be divided into 200×300 blocks, and each block area shall be processed separately, and then the processed blocks shall be merged). The GA-OTSU threshold segmentation algorithm proposed in this paper, can not only overcome the drawbacks of traditional segmentation methods but also solve the problem that the normalized water difference index (NDWI) method [7] cannot be used to separate water body and non-water body for high-resolution three-band data. Combining with morphology closed operation and Sobel edge detection operator, it can better avoid the problems such as coastline fault and non-coastline inclusion caused by a single coastline extraction method. By using the method in this paper and comparative methods to make qualitative and quantitative comparative analysis on the water boundary extraction results of four island experimental areas, it is believed that the method in this paper is feasible to a certain extent.
## 2. The Technology and Principle of GA Method
##### 2.1 Data Pre-processing
During the remote sensing imaging process, the geometric distortion and deformation of remote sensing image are caused by the external factors of sensor, such as the change of attitude, height, speed, and so on. Moreover, due to the lack of spatial, temporal and spectral resolution of remote sensing images, information cannot be accurately recorded in the data acquisition process, which will greatly reduce the accuracy of remote sensing images. Therefore, it is necessary to conduct pre-process to remote sensing images [8]. Data preprocessing in this paper includes FLAASH atmospheric correction and geometric correction, aiming to make the ground objects in the image more consistent with the actual features. FLAASH atmospheric correction refers to the process of eliminating radiation errors caused by atmospheric scattering and absorption in remote sensing images. Geometric correction refers to the process of eliminating geometric (shape, size, position, etc.) distortion of ground objects in the imaging process.
##### 2.2 GA-OTSU Threshold Segmentation Algorithm
Genetic algorithm (GA) is a kind of self-organizing and adaptive artificial intelligence technology that simulates the biological evolution process and mechanism in nature to solve extreme value problems [9]. GA is a holistic optimization process, which is very applicable in cases where there is no deterministic method to calculate the optimal solution or if the deterministic method is complicated, and it can quickly and accurately find the global optimal solution. GA is an iterative algorithm, and the number of solutions in each iteration is called population size. Each solution is represented by a chromosome, and each chromosome is made up of genes. The flow chart of this genetic algorithm is shown in Fig. 1.
The specific meaning of each step is explained as follows:
Step 1. Coding. Before the genetic algorithm can be performed, the chromosome must be coded, that is, the solution space of the problem must be coded.
Step 2. Initialize the population. The population represents the set of solutions of the optimization pro¬blem, whose size will directly affect the scope and result of the search.
Step 3. The adaptation function. Its size determines the ability of an individual to adapt to the environ¬ment in each iteration process, and the strong ones will continue to choose, cross and mutate.
Step 4. Selection. Selection process is a kind of operation process that determines the elimination or re-production of offspring according to the level of individual fitness value.
Step 5. Crossover. The crossover process is the accumulation of superior bit information from the parent generation and exchange them with each other in the hope of producing superior offspring.
Step 6. Mutation. The process of mutation is to randomly change the bit information in the seed string, so as to obtain the best fit value of the individual.
Step 7. Convergence criteria. The mechanism for its termination is either the maximum number of iterations or the fitness of the best individual does not change.
Fig. 1.
Flow chart of genetic algorithm.
GA-OTSU threshold segmentation algorithm takes the maximum inter-class variance method (OTSU algorithm [10]) as the basic segmentation method, and introduces GA to improve OTSU algorithm on the basis of it. Compared with the OTSU algorithm, the GA-OTSU threshold segmentation algorithm has the advantage of quickly and accurately obtaining the optimal segmentation threshold t* and reducing noise. The specific steps of GA-OTSU algorithm are shown as follows:
Step 1. Find a way to “digitize” the potential solution of the problem. The grayscale value of the image pixel ranges from 0 to 255, so the 8-bit binary number to represent the grayscale value of the pixel can be selected. An 8-bit binary number is just one byte, so treat it as a chromosome.
Step 2. Selection of population size. Population size refers to the total number of individuals in each generation, which can be set artificially. The larger the population size, the more likely the global solution will be found, but the running time will increase accordingly.
Step 3. Determine the adaptation function and decode it. In this paper, the GA-OTSU method is taken as the adaptability function to evaluate each chromosome. As shown in Eq. (1), the greater the variance obtained by a chromosome is, the closer it is to the optimal solution, and the more likely it is to be selected as the genetic seed. After the genetic seeds are determined, the genetic cal¬culation is carried out from generation to generation. The adaptive value of each new gen¬eration is different and higher than that of the previous generation so that the solution obtained is closer to the maximum value.
##### (1)
[TeX:] $$\delta^{2}(t)=\omega_{0}\left(\mu_{0}-\mu\right)^{2}+\omega_{1}\left(\mu_{1}-\mu\right)^{2}=\omega_{0} \omega_{1}\left(\mu_{1}-\mu_{0}\right)^{2}=\frac{[\mu \omega(t)-\mu(t)]^{2}}{\omega(t)[1-\omega(t)]}$$
In Eq. (1), [TeX:] $$\delta^{2}(t)$$ is the threshold selection function of the Otsu method; [TeX:] $$\omega_{0}, \omega_{1}$$ is the proportion of target area and non-target area in the study area, respectively; [TeX:] $$\mu, \mu_{0}, \mu_{1}$$ each represents the average gray levels of the whole study area, the gray levels of the target area, and the non-target area.
Step 4. Genetic calculation. Crossover is the first genetic process which refers to exchange information of bits on chromosomes. Secondly, the mutation operation is carried out to randomly select the mutation point of a chromosome for mutation, which can compensate for the information loss caused by the selection process and the crossover process, so that the genetic algorithm has the global search ability. Finally the best threshold t* is obtained which makes [TeX:] $$\delta^{2}\left(t^{*}\right)$$ the biggest. At this time, t* can be used as the most adaptive solution for GA-OTSU threshold segmentation algorithm.
##### 2.3 Morphological Closed Operation
Morphological closed operation makes the image firstly expanded and then corroded, so that the holes inside the target in the image are not only filled but also maintain the original shape and size, and the fractured target is connected [11]. In this paper, morphological closed operation is used to fill holes in the binary image after GA-OTSU threshold segmentation to highlight the target (land) and background (ocean), which is convenient for subsequent edge detection operator to be used for edge extraction. Compared with the morphological erosion and dilation algorithms in [5], sawtooth phenomenon will not be caused by morphological closed operation. The concept of mathematical closed operation can be expressed as A×B (indicating that structural element B performs closed operation on image A) and can be defined as Eq. (2).
##### (2)
[TeX:] $$A \otimes B=(A+B) \Theta B$$
In Eq. (2), after A goes through B expansion operation, B again processes the results obtained by it through corrosion operation, as shown in Fig. 2.
Fig. 2.
Closed operation diagram.
##### 2.4 Sobel Edge Detection Operator
In image processing, edges are mainly distributed where the gray value difference between the target and the background is relatively obvious [12]. The edge types generally include horizontal, vertical and diagonal edges. Intensity and direction are two basic properties of edge lines in an image, the intensity variants the most across the edge line, but changes more gently along the edge line. The intensity change of the image is related to the discontinuity of the first derivative, and the drastic change is mainly reflected in the local maximum value of the first derivative, so the boundary strength of the corresponding point can be measured according to the value of the derivative to achieve the extraction of the boundary point set. In this paper, the Sobel operator is used for edge extraction, which is a first-step operator. The principle of its edge detection is shown in Fig. 3(a). For a digital image f(x, y), the definition of gradient vector at (x, y) is shown in Eq. (3).
##### (3)
[TeX:] $$\nabla f=\left[\frac{\partial f}{\partial x} \frac{\partial f}{\partial y}\right]^{T}=\left[G_{x} G_{y}\right]^{T}$$
In Eq. (3), [TeX:] $$G_{x}, G_{y}$$ respectively represent the gradient of direction x and y. Theoretically, the partial derivative in Eq. (3) needs to calculate the position of each pixel, but in actual image processing, the image gradient is generally obtained by convolution approximation calculation based on small area template. And since both [TeX:] $$G_{x} \text { and } G_{y}$$ have their own templates, a gradient operator is the combination of the two templates. In this paper, the convolution template [TeX:] $$G_{x} \text { and } G_{y}$$ of Sobel operator is adopted, as shown in Fig. 3(b).
Fig. 3.
(a) Edge detection schematic diagram of edge gradient operator. (b) Sobel operator tem-plate diagram.
## 3. Experiment and Analysis
##### 3.1 GA Island Water Edge Automatic Extraction Method
GA method firstly pre-processed the experimental data. Then, GA-OTSU threshold segmentation method was used to segment the image, generate binary image, highlight the target ground object (land), and then morphological closed operation was used to fill the holes of the target ground object. Finally, Sobel edge detection operator is used to extract the water edge. In order to show the idea of GA method proposed in this paper more intuitively, a flow chart of GA method is drawn, as shown in Fig. 4.
Fig. 4.
Flow chart of the GA method.
##### 3.2 Experimental Data Set and Evaluation Indexes
The four islands studied in this paper are all located in the Bohai Bay area in the southeast of Liaoning Province. The remote sensing images were selected from the GF-2 satellite, which was equipped with a panchromatic camera of 1 m resolution and a multispectral camera of 4 m resolution, and featured with sub-meter spatial resolution, high positioning accuracy and fast attitude maneuvering.
The four island regions in the pre-processed GF-2 satellite image data with a resolution of 1 m were selected for the experiment, as shown in Fig. 5(a). The detailed information is shown in Table 1. In the images, the landforms in the study area of islands are diverse, including residential areas, woodland, barren land and harbors, etc. These landforms constitute features with different prospects. It provides data support for the study of different types of island water boundary extraction. Fig. 5(b), as a reference image, shows the manually drawn water boundary vector information corresponding to the four islands.
Fig. 5.
GF-2 remote sensing image data set of the study areas: (a) images of the study areas and (b) reference images.
Table 1.
GF-2 remote sensing image information of the study areas
Number of study areas Imaging time Image size (pixel × pixel)
Island 1 2019-6 27620×35273
Island 2 2019-6 4382×4986
Island 3 2019-7 16583×19674
Island 4 2019-8 25769×33748
In this study, qualitative and quantitative indicators were used to compare and analyze the final extraction results of island water edges. Among them, qualitative analysis refers to the superposition and comparative analysis of the final extraction result of water boundary with the original image and reference image in Fig. 5. The quantitative index is evaluated by three evaluation indexes, namely accuracy P, omission error Q and redundancy error R, respectively [13], and the quantitative analysis is conducted. The equation is expressed as follows:
##### (4)
[TeX:] $$P=\frac{a}{i}$$
##### (5)
[TeX:] $$Q=\frac{b}{i}$$
##### (6)
[TeX:] $$R=\frac{c}{i}$$
In Eqs. (4)–(6), i represents the vector length of the water edge line of the island which was drawn manually in the reference image; a represents the total length of the overlapping part between the extracted water boundary line and the manually drawn water boundary line vector; b refers to the total length missing from the extracted water edge compared with the artificially drawn vector, that is, the length not extracted when the water edge is taken as the background noise; c refers to the total length of redundancy of the extracted water edge compared with the manually drawn vector, that is, the background noise is taken as the extracted length of the water edge.
##### 3.3 GA Method and Result Analysis
The experiment is based on Windows Server 2016 operating system, with 16G internal storage, a NVIDA Quadro P2000 video card and 5G video storage. The program development language is MATLAB2020b.
##### 3.3.1 GA-OTSU threshold segmentation algorithm
GA-OTSU threshold segmentation algorithm is the most critical step in GA method, and the determination of segmentation threshold is a key factor affecting the image segmentation effect. GA-OTSU threshold segmentation algorithm takes OTSU algorithm as the basic segmentation method, on which genetic algorithm is introduced to improve OTSU algorithm. Compared with the OTSU algorithm, the GA-OTSU threshold segmentation algorithm has the advantage of quickly and accurately obtaining the global optimal solution, that is, the optimal segmentation threshold t*, and reducing the noise. This experiment in segmentation algorithm, for the same data set, the GA-OTSU segmentation algorithm in the GA method in this paper is not only compared with the OTSU segmentation algorithm in [5], but also compared with the watershed segmentation algorithm in [4]. In order to visually display the segmentation effects of the four research areas, the comparative results of the three segmentation methods are presented, as shown in Fig. 6.
It can be seen from Fig. 6 that the watershed segmentation algorithm in [4], the traditional OTSU algorithm in [5], and the GA-OTSU segmentation method in this paper can segment the experimental area well, and the segmenting image can retain the original image feature information rather integrally. However, it is obvious that the GA-OTSU segmentation method is better than the traditional OTSU algorithm. It can not only complete image segmentation, but also clear separation between the target and the background. The final segmented image is clearer, with less noise and less information loss, which can more effectively separate target from background and highlight the areas of interest. It is also obvious that compared with the watershed segmentation algorithm, the GA-OTSU segmentation method almost does not have excessive segmentation, which can lay a good foundation for the subsequent extraction of water edges and indirectly improve the accuracy of water edges extraction.
Fig. 5.
Comparison of the segmentation results of three segmentation algorithms in four island study areas: (a) the original images, (b) watershed segmentation algorithm in [ 4], (c) OTSU segmentation algorithm in [ 5], and (d) GA-OTSU segmentation algorithm.
The GA-OTSU segmentation algorithm can not only effectively segment the target image, but also find the most adaptive threshold of the image and improve the performance of image segmentation by calculating the fitness of the genetic algorithm to obtain the operation characteristics of the optimal solution. In the parameter setting of GA-OTSU segmentation algorithm in this experiment, the initial population number N is 8, and the maximum number of evolutionary iterations is 100. As can be seen from the variation diagram of the optimal fitness curve in Fig. 7(b), the ordinate value of the curve gradually increases and finally tends to be stable, which indicates that the optimal fitness value under this condition is found through the genetic algorithm, that is, the optimal solution of the threshold value obtained by the OTSU method is found. The optimal threshold generation graph in Fig. 7(a) shows that the stable value of the curve is the optimal threshold that meets the conditions. The optimal adaptive threshold graph obtained by watershed algorithm, the OTSU algorithm and the GA-OTSU segmentation method for island images in the four experimental areas is shown in Table 2. The GA-OTSU segmentation method can more accurately find the global optimal segmentation threshold of the target image to achieve the optimal segmentation effect, which is conducive to the next step of image processing.
Fig. 7.
Schematic diagram of GA-OTSU method process in four island study areas: (a) the optimal threshold generation graph and (b) the variation diagram of the optimal fitness curve.
Table 2.
Optimal segmentation threshold of four islands by three methods
Study areas OTSU optimal threshold Watershed optimal threshold GA-OTSU optimal threshold
Island 1 105 100 96
Island 2 88 83 79
Island 3 91 87 84
Island 4 94 92 90
##### 3.3.2 Morphological closure operation
The binary image segmented by GA-OTSU is used to perform morphology closing operation with disk structure elements to fill in the holes. The results of morphological closure operation and the size of structural elements are shown in Fig. 8.
Fig. 8.
The result graphs of morphological closure operation: the size of structure elements are 50 (a), 20 (b), 30 (c), and 17 (d).
##### 3.3.3 Sobel edge detection operator
The Sobel edge detection operator is used to extract the edge of the closed binary image. Since the binary image processed by closed operation only has target (island) and background (ocean), the Sobel edge detection operator is used for boundary extraction, which is faster and has better effect, to realize the last step of GA island water edge automatic extraction method proposed in this paper, and the final island water edge is obtained. Superposition contrast analysis were also conducted between the results of water edges extracted by the GA method in this paper (GA-OTSU threshold segmentation algorithm + morphological closed operation + Sobel edge detection operation), the method in [4] (watershed segmentation + morphology modification method), the method in [5] (top-hat transform + OTSU segmentation + expansion and corrosion morphology method), the original and the reference images in Fig. 5. As shown in Fig. 9.
According to the qualitative comparative analysis of the extraction results in the first three experimental areas of the three methods in Fig. 9, it can be found that the water boundary extracted by the method of [4] (watershed segmentation + morphological modification) is over-extracted. The water edge extracted by the method in [5] (top hat transform + OTSU segmentation + expansion and corrosion morphology method) has obvious sawtooth phenomenon caused by the expansion and corrosion operation of morphology. The water edge extracted by GA method in this paper is integrated and smooth without fracture. In addition, the water edges extracted by the three methods were superimposed on the original image and the reference image (manually drawn vector), respectively. It can be found that the water edges extracted by the method in this paper also have the best matching effect with the original image and the reference image. The extraction results of the three methods are good in the fourth island, because the sea and land of which are distinct and the background is simple.
In addition to the above qualitative analysis, this paper also adopts the three quantitative evaluation indexes (accuracy P, omission error Q and redundancy error R) in Eqs. (4)–(6) above through the intersection tabulating tool in ArcGIS software to evaluate the accuracy of the island water boundary lines extracted by the three methods, the statistical results of extraction accuracy of the three methods are shown in Table 3.
It can be found from Table 3 that the average extraction accuracy of GA method in this paper can reach 98%, and the omission error (Q) and redundancy error (R) are 2.5% and 1.5%, respectively. The accuracy is significantly higher than the other two comparison methods.
Fig. 9.
Comparison of the results from three water edge extraction methods: (a) the original images, (b) the reference images, (c) the method of [ 4], (d) the method of [ 5], (e) the method of GA, (f) the results of the three water edge extraction methods are superimposed with the original image, and (g) the results of the three water edge extraction methods are superimposed with the reference images.
Table 3.
Water edge line extraction accuracy statistics of three methods (unit: %)
Study areas GA method Method of [4] Method of [5]
P Q R P Q R P Q R
Island 1 96.34 3.66 2.31 95.46 4.54 4.98 93.46 6.54 8.32
Island 2 97.62 2.38 1.02 97.03 2.97 3.65 94.62 5.38 6.43
Island 3 98.97 1.03 1.15 97.15 2.85 3.47 97.63 2.37 3.04
Island 4 99.24 0.76 0.87 98.64 1.36 1.95 98.01 1.99 2.43
## 4. Conclusion
The method proposed in this paper is compared with the methods in [4] and [5] through qualitative and quantitative analysis, and found that it is effective to extract the water edges of islands from GF-2 remote sensing images. The innovation of the GA method in this paper is partly reflected in the GA-OTSU segmentation method, which has the following advantages compared with the watershed segmentation algorithm in [4] and the OTSU segmentation algorithm in [5]: (1) it can better retain the edge of the segmented image and make the edge more integrated; (2) it has less noise; (3) there is basically no excessive segmentation phenomenon. Another innovation of the GA method is reflected in the com¬bination of GA-OTSU segmentation algorithms, morphological closure operation and Sobel edge detec¬tion operator, which has realized the automatic water edge extraction of islands, and ideal results with higher precision have been obtained, so the method can give reference advice for the water edge auto¬matic extraction of islands from GF-2 remote sensing image with high resolution in three bands.
## Acknowledgement
This paper is supported by the National Science Foundation for Young Scholars Project of China (No. 41801294) and the Innovation Training Program of the University of Science and Technology Liaoning.
## Biography
##### Yan Bian
https://orcid.org/0000-0002-9466-9156
She is currently a master graduate student of University of Science and Technology Liaoning, Anshan, China. Her research interest includes data processing and remote sensing image extraction.
## Biography
##### Yusheng Gong
https://orcid.org/0000-0002-7530-7985
He is currently a associate professor of University of Science and Technology Liaoning, Anshan, China. His research interest includes remote sensing image processing and application.
## Biography
##### Guopeng Ma
https://orcid.org/0000-0001-9167-6310
He is currently a master graduate student of University of Science and Technology Liaoning, Anshan, China. His research interest includes remote sensing image processing and application.
## Biography
##### Ting Duan
https://orcid.org/0000-0002-0262-6192
She is a lecturer of University of Science and Technology Liaoning, Anshan, China. Her research interest includes remote sensing image processing and application.
## References
• 1 C. Chen, J. Bu, Y. Zhang, Y. Zhuang, Y. Chu, J. Hu, B. Guo, "The application of the tasseled cap transformation and feature knowledge for the extraction of coastline information from remote sensing images," Advances in Space Research, vol. 64, no. 9, pp. 1780-1791, 2019.custom:[[[-]]]
• 2 D. Dominici, S. Zollini, M. Alicandro, F. Della Torre, P. M. Buscema, V. Baiocchi, "High resolution satellite images for instantaneous shoreline extraction using new enhancement algorithms," Geosciences, vol. 9, no. 3, 2019.doi:[[[10.3390/geosciences9030123]]]
• 3 S. Mi, "Research on coastline automatic extraction algorithm based on image processing," Shaanxi Water Conservancy, vol. 2020, no. 1, pp. 33-35, 2020.custom:[[[-]]]
• 4 B. Yang, Y Chen, J. Y u, "Coastline extraction based on watershed segmentation and edge detection of satellite remote sensing images," Electronic Technology & Software Engineering, vol. 2020, no. 11, pp. 170-171, 2020.custom:[[[-]]]
• 5 Y. Zhu, Z. Han, S. He, X. Hu, P. Chen, "Remote sensing image extraction of tidal channels based on Otsu and mathematical morphology," Journal of Shanghai Ocean University, vol. 26, no. 1, pp. 146-153, 2017.custom:[[[-]]]
• 6 V. Paravolidakis, L. Ragia, K. Moirogiorgou, M. E. Zervakis, "Automatic coastline extraction using edge detection and optimization procedures," Geosciences, vol. 8, no. 11, 2018.doi:[[[10.3390/geosciences8110407]]]
• 7 B. Zhao, L. Wang, H. Hu, "Method of water-body extraction in mountainous area based on OLI images and DEM," Hydrology, vol. 39, no. 4, pp. 34-39, 2019.custom:[[[-]]]
• 8 C. Wang, X. Wang, "Preprocess technology of high precision satellite photograph," Electronic Technology & Software Engineering, vol. 2016, no. 24, pp. 122-123, 2016.custom:[[[-]]]
• 9 F. Liu, L. Y u, "Remote sensing image segmentation based on improved threshold of genetic operator," Henan Keji, vol. 2019, no. 14, pp. 37-38, 2019.custom:[[[-]]]
• 10 S. Manikandan, K. Ramar, M. W. Iruthayarajan, K. G. Srinivasagan, "Multilevel thresholding for segmentation of medical brain images using real coded genetic algorithm," Measurement, vol. 47, pp. 558-568, 2014.custom:[[[-]]]
• 11 J. Wan, K. Wang, S. Zhao, J. Zhang, "Fast automatic coastline extraction algorithm based graphics morphology," Yellow River, vol. 33, no. 10, pp. 126-130, 2011.custom:[[[-]]]
• 12 D. Wei, X. Cao, "Using Satellite remote sensing image data to research the north coastline extraction based on Matlab: a case study of Changxing Island, Dalian City," Bulletin of Surveying and Mapping, vol. 2015, no. 5, pp. 80-83, 2015.custom:[[[-]]]
• 13 B. Xuan, Master’s thesis, Guilin University of Technology, Guilin, China, 2019, Guilin University of TechnologyGuilinChina, Master’s thesis, 2019.custom:[[[-]]]
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2021-12-01 11:57:14
|
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|
https://wlresources.dpi.wi.gov/authoring/1762-check-your-work/view
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Overview / Description:
This lesson will help students understand why it is important to check their work after they complete a math problem. They will be searching other students work to find a mistake in the work they completed.
Learning goals/objectives:
After completing this activity, students should be able to . . .
• check their work.
• explain their work.
• understand the importance of checking their work for mistakes.
Content Standards:
Wisconsin Standards for Mathematics
Mathematical Practices
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Attend to precision.
Algebra: Reasoning with Equations and Inequalities
CCSS.MATH.CONTENT.HSA.REI.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Educational Frameworks
B-LS 1. Demonstrate critical-thinking skills to make informed decisions
B-LS 9. Gather evidence and consider multiple perspectives to make informed decisions
Materials:
This can be used with any type of solving unit. I will be using this in my Tech Math class in our solving equations unit.
The teacher should have enough problems for one for each student. Multiple students could solve the same question.
Assessment:
Teacher will collect the papers that have been completed and check over what the students completed.
Exit Slip: List two ways you will pay attention to the quality of your work in the next week.
Wrap-Up:
Class discussion why checking your work is important.
Extension Activity (for intervention or enrichment):
Students could video their response and where they found the mistakes.
Differentiation - students could work in pairs to create an incorrect problem and to correct the problem in another pair's work.
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2022-05-29 09:39:33
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https://brainly.com/question/134514
|
## Answers
The Brainliest Answer!
2014-09-29T19:11:58-04:00
We must follow order of operations:
1. Parentheses (there are none)
2. Exponents (none)
3. Multiply/ Divide (there is one of those, so we must divide 4/7 by 3/10.
Remember for dividing fractions:
1. Keep the original fraction
2. Change the division sign to a multiplication sign
3. Flip the last fraction
So 4/7 divided by 3/10 becomes:
When multiplying fractions, multiply straight across: numerator of the first fraction*numerator of the second fraction, denominator of the first fraction*denominator of the second fraction.
This cannot be simplified, so now we can go onto the fourth step of order of operations:
4. Add/ Subtract
However, remember that we cannot add (or subtract, for that matter,) fractions without a common denominator (the numbers on the bottom of the fraction must be the same). To get a common denominator, multiply the fraction by a number over the same number... see it this way:
Simplify
The answer is 1. By multiplying a fraction by a number over the same number, we are not actually changing the value of the fraction because we are, in reality, multiplying it by 1.
So back to the problem.
We can get a common denominator by multiplying 1/3 by 7/7. This will result in the denominator being 21, the same as the denominator of the second fraction.
This is our final answer, because 47/21 cannot be simplified.
Thank you t
Can you also help me on the next question that i post too
I will, which one is it?
The one that says something about 7/8x4/5 divided by 7/20
Ok I did it
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2017-01-19 11:31:02
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https://2017-lapaz-assembly.readthedocs.io/en/latest/blast.html
|
# Running BLAST from the command line to identify environmental sequences¶
Authored by Jin Choi for EDAMAME2015, based on a previous tutorial. Modified by Adina Howe. EDAMAME-2015 wiki
## Overarching Goal¶
• This tutorial introduces users to installing a program and running it on the shell command line. Specifically, this tutorial is applicable to users who would like to identify sequence homology of query sequences to a custom dataabase.
## Learning Objectives¶
• Repeat the web-online BLAST on the command line
• Install BLAST program from the command line
• Execute and automate a blast program
• Compare a sequence query to a sequence databsae
• Analyze results
# Introduction¶
Let’s have a BLAST! That’s right, the Basic Local Alignment Search Tool!
You all may have previously used the NCBI BLAST Web page to do individual searches. Today we’ll automate batch searches at the command line on your own computer.
## Motivation: Why would I want to run BLAST locally?¶
1. I want to BLAST against my own database (and maybe it’s secret!)
2. I’m tired of waiting on the web interface to complete - it takes too long!
Today, imagine that you have genes that you have sequenced and want to identify the closest known sequences within a database.
cd ~/
### First, let’s install blast.¶
First, let’s check and see if we have BLAST installed, and this will depend on the compute resources you are using.
which blastn
If you have BLAST installed and in your path (BLAST may be installed but not in your path), it will give you something like this:
/usr/bin/blastn
If you don’t have BLAST, then you will need to install it.
## Step 1: Installing BLAST¶
To install the BLAST software, type the following command. This installs the most recent version:
sudo apt-get install -y ncbi-blast+
Now, we can’t run BLAST without creating a database to compare our sequences to. A popular database is to use all the genes in NCBI (e.g., similar to the web interface’s databases). This, like a lot of NCBI databases is huge, so I don’t suggest putting this on your laptop unless you have a lot of room. It’s best on a larger computer (HPCC, Amazon machine). For this tutorial, let’s download a small database for this tutorial.
We’ll also download the sequences that you want to compare to your database. This would be similar to obtaining sequences from your sequencing facility.
First, let’s use curl to retrieve a database of genes. These often come from a literature search or hard work. In this tutorial, its easy though, you’ll just download it...but assume you’ve searched the literature and these are genes of interest that your sequence might match:
curl -O https://s3.amazonaws.com/edamame/Blast_Tutorial.tar.gz
To get access to this data, let’s unzip it. It’s in a compressed form to transfer from the “cloud” to your local computer faster.
tar -zxvf Blast_Tutorial.tar.gz
Next, let’s navigate into the directory and take a look at the files it contains.
cd Blast_Tutorial
Now you’ve got these files. We can take a look at the size and names of this file with the following command...
ls -l
Here’s some description of some these files:
MyQuery.txt: This is actually (mis)labeled as a ”.txt” file but it is a FASTA file. How can you tell? We’re going to leave it as a ”.txt” file, mainly because its very likely people will send you sequences like this in the future and its important to know that the extension of file type is somewhat arbitrary.
rep_set.fna: This is a database of previously observed genes. You would like to know if your sequences match any of these genes which have been sequenced from the bacterial isolates in your lab.
So, now we’ve got the database files, but BLAST requires that each subject database be preformatted for use; this is a way of speeding up certain types of searches. To do this, we have to format the database. You should do:
makeblastdb -in rep_set.fna -dbtype nucl -out rep_set.fna.db
The -in parameter gives the name of the database, the -out parameter says “save the results”, and the -dbtype parameter says “what type of the database”. For DNA, you’d want to use ‘-dbtype nucl’. FYI, for protein, ‘-dbtype prot’.
Let’s see what the BLAST database looks like
ls
You may notice that there are 3 files that were generated.
rep_set.fna.db.nhr, rep_set.fna.db.nin, and rep_set.fna.db.nsq
BLAST uses these 3 “indexed” files to make searching genes against genes go faster and more efficiently.
Just a reminder:
1. UNIX generally doesn’t care what the file is called, so ‘.fna’ and ‘.fa’ are all the same to it.
2. UNIX utilities work well with text files, and almost everything you’ll encounter is a basic text file. This is different from Windows and Mac, where more complicated formats are used that can’t be as easily dealt with on UNIX.
## Step 3: Run BLAST¶
Now try a BLAST: You need a file that have your query in. Remember, here is your query looks like.
cat MyQuery.txt
This file contains sequences of 4 bacteria and 5 fungi that you have gotten sequenced. You wonder if it matches anything in the known database.
To do this, we’ll run a BLAST. We use blastn because we will search a nucleotide database using a nucleotide query.
blastn -db rep_set.fna.db -query MyQuery.txt
Once you get the output, you can do a few different things...
1. First, you can scroll up in your terminal window to look at the output.
2. Second, you can save the output to a file:
blastn -db rep_set.fna.db -query MyQuery.txt -out out.txt
and then use ‘less’ to look at it:
less out.txt
1. You can pipe (|) it directly to less, by which I mean you can send all of the output to the ‘less’ command without saving it to a file:
blastn -db rep_set.fna.db -query MyQuery.txt | less
Sometimes tabular form (output format) is useful. To get the result in tabular form,
blastn -db rep_set.fna.db -query MyQuery.txt -out outtabular.txt -outfmt 6
Let’s try a different blast so you get your own practice, with a slight twist. Imagine you’ve compiled a database of genes from all isolates that originate from soil, and you would like to compare it to genes in NCBI RefSeq (a popular genome database). We’re providing you two files – the RefSoil16s.fa file – the sequences of 16S rRNA genes from soil isolates and the database – rep_set_sub.fna that you have downloaded from NCBI.
## Exercise¶
Imagine you’ve compiled a database of genes from all isolates that originate from soil, and you would like to compare it to genes in NCBI RefSeq (a popular genome database). We’re providing you two files – the RefSoil16s.fa file – the sequences of 16S rRNA genes from soil isolates and the database – rep_set_sub.fna that you have downloaded from NCBI. How would you find the sequences within the database which are the closest match to the genes from your isolates?
## Different BLAST options¶
BLAST has lots and lots and lots of options. Run ‘blastn’ by itself to see what they are. Some of the most useful ones are -evalue.
If you want to search protein, use ‘blastp’ instead of ‘blastn’. ‘blastx’, ‘tblastn’, ‘tblastx’ also available.
Here are the options/flags available to this program:
0 = pairwise,
1 = query-anchored showing identities,
2 = query-anchored no identities,
3 = flat query-anchored, show identities,
4 = flat query-anchored, no identities,
5 = XML Blast output,
6 = tabular,
7 = tabular with comment lines,
8 = Text ASN.1,
9 = Binary ASN.1
10 = Comma-separated values
11 = BLAST archive format (ASN.1)
##Help and other resources
|
2021-12-06 09:43:24
|
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|
https://www.gabormelli.com/RKB/Distance_Metric
|
# Distance Metric
A distance metric is a symmetric metric that maps two items, $x,y$, to a non-negative distance value where $\text{Dist}(x,x)=\text{Dist}(y,y)=0$ and is also constrained the triangle inequality.
## References
### 2010
• (Wikipedia, 2010) http://en.wikipedia.org/wiki/Metric_(mathematics)
• In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space.
• A metric on a set X is a function (called the distance function or simply distance) d : X × X → R (where R is the set of real numbers).
• For all x, y, z in X, this function is required to satisfy the following conditions:
• 1. d(x, y) ≥ 0 (non-negativity)
• 2. d(x, y) = 0 if and only if x = y (identity of indiscernibles. Note that condition 1 and 2 together produce positive definiteness)
• 3. d(x, y) = d(y, x) (symmetry)
• 4. d(x, z) ≤ d(x, y) + d(y, z) (subadditivity / triangle inequality).
• These axioms are not independent: Non-negativity follows from the other axioms.
• A metric is called an ultrametric if it satisfies the following stronger version of the triangle inequality:
• For all x, y, z in M, d(x, z) ≤ max(d(x, y), d(y, z))
• A metric d on X is called intrinsic if any two points x and y in X can be joined by a curve with length arbitrarily close to d(x, y).
### 2001
• (Ramon & Bruynooghe, 2001) ⇒ Jan Ramon, and M. Bruynooghe. (2001). “A polynomial time computable metric between point sets.” In: Acta Inform. 37, 765–780.
### 1998
• (Bunke & Shearer, 1998) ⇒ Horst Bunke, and Kim Shearer. (1998). “A graph distance metric based on the maximal common subgraph.” In: Pattern Recognition Lett. 19, 255–259.
• (Ramon et al., 1998) ⇒ Jan Ramon, M. Bruynooghe, and W. Van Laer. (1998). “Distance Measures Between Atoms.” In: ProceedingsCompulogNet Area Meeting on ’Computational Logic and Machine Learning’, pp. 35–41.
### 1979
• (Tai, 1979) ⇒ K. Tai. (1979). “Tree to Tree Correction Problem.” In: ACM 26 (3), 422–433.
|
2021-05-06 00:30:41
|
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|
https://www.techwhiff.com/issue/ansition-mrs-tucker-had-taught-school-24-years-mr-tucker--386105
|
# Ansition Mrs. Tucker had taught school 24 years. Mr. Tucker realized that her number of years teaching was a multiple of Mr Glover's number of years teaching. Find all the number of years that Mr. Tucker could have taught
###### Question:
ansition Mrs. Tucker had taught school 24 years. Mr. Tucker realized that her number of years teaching was a multiple of Mr Glover's number of years teaching. Find all the number of years that Mr. Tucker could have taught
### Select the correct answer. Which of the following is a common cause of fainting? Low blood pressure Medication Dehydration All of the above
Select the correct answer. Which of the following is a common cause of fainting? Low blood pressure Medication Dehydration All of the above...
### What is the purpose of the domain name system
what is the purpose of the domain name system...
### What could be lovelier than to hear the summer rain cutting across as scythes cut across grain? falling upon the steaming roof with sweet uproar, tapping and rapping wildy at the door?
What could be lovelier than to hear the summer rain cutting across as scythes cut across grain? falling upon the steaming roof with sweet uproar, tapping and rapping wildy at the door?...
### What was the name given to the US policy enacted to keep communism at its status quo and limit the spreading of it?
what was the name given to the US policy enacted to keep communism at its status quo and limit the spreading of it?...
### Summarize how you would go about calculating the grams of product given the grams of reactant you start with.
Summarize how you would go about calculating the grams of product given the grams of reactant you start with....
### Giving out brainliest!!
giving out brainliest!!...
### Which of the following best describes the circuit shown below? A.series B.parallel C.short D.combination
Which of the following best describes the circuit shown below? A.series B.parallel C.short D.combination...
### Which statement best describes the slope of the line?
Which statement best describes the slope of the line?...
### Round 174,485,597 to the nearest whole number
Round 174,485,597 to the nearest whole number...
### Preparing a summary for distribution after the discussion is one task of the group’s _____ participant. timekeeper. facilitator. note-taker.
Preparing a summary for distribution after the discussion is one task of the group’s _____ participant. timekeeper. facilitator. note-taker....
### A part of an mRNA molecule with the following sequence is being read by a ribosome: 5'-UGC-GCA-3' (mRNA). The charged transfer RNA molecules shown in the figure below (with their anticodons shown in the 3' to 5' direction) are available. Two of them can correctly match the mRNA so that a dipeptide can form: Which of the following dipeptides will be formed? Proline-Threonine Glycine-Cysteine Alanine-Alanine Cysteine-Alanin
A part of an mRNA molecule with the following sequence is being read by a ribosome: 5'-UGC-GCA-3' (mRNA). The charged transfer RNA molecules shown in the figure below (with their anticodons shown in the 3' to 5' direction) are available. Two of them can correctly match the mRNA so that a dipeptide c...
### To make 1 1/2 ozen muffins a recipe uses 3 1/2 cups of flour how many cups of flour is needed for every dozen muffins made
to make 1 1/2 ozen muffins a recipe uses 3 1/2 cups of flour how many cups of flour is needed for every dozen muffins made...
### Simplify 6(x + 2) + 7. 6x + 9 6x + 15 6x + 19
Simplify 6(x + 2) + 7. 6x + 9 6x + 15 6x + 19...
### Is it possible for a car to be accelerating to the west while it is driving to the east?
Is it possible for a car to be accelerating to the west while it is driving to the east?...
### What is staff paper?
What is staff paper?...
### A relationship between you and your friend you see every day is a what kind of relationship
A relationship between you and your friend you see every day is a what kind of relationship...
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2022-11-26 22:10:19
|
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|
https://figshare.com/articles/_Transient_and_steady_state_scaling_exponents_/218984/1
|
## Transient and steady state scaling exponents.
2013-02-19T20:49:00Z (GMT) by
<p>Colormap of the (a) transient and (b) steady state values of the scaling exponent and as a function of car density and the mean randomization probability . Dashed lines show the approximate super diffusion () and normal diffusion () boundaries. Region I (a) is always superdiffusive () indicating a good region for traffic. Region II generally starts with a superdiffusive transient behavior () then approach . Lastly, Region III is subdiffusive. The scaling exponent is independent of .</p>
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2018-12-15 08:46:25
|
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|
https://math.stackexchange.com/questions/2038801/simple-1st-order-pde
|
# Simple 1st order PDE [duplicate]
Solve $u_x+u_y+u=e^{x+2y}$ with $u(x,0)=0$
I try to let $x'=x+y, y'=x-y$ and reduced to $2u_{x'}+u=e^{0.5(3x'-y)}$
How to proceed to the next step? Any other methods to solve?
Thank you!
• $$2u_{x'} + u = \exp \bigg( \frac{1}{2} (3x'-y) \bigg)$$ is an ODE in $x'$. You could use an integrating factor. Alternatively, you could solve the problem using the method of characteristics. – mattos Dec 1 '16 at 14:07
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2020-01-22 18:23:06
|
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https://drmf-beta.wmflabs.org/wiki/Definition:normctsHahnptilde
|
# Definition:normctsHahnptilde
The LaTeX DLMF and DRMF macro \normctsHahnptilde represents the normalized continuous Hahn polynomial.
This macro is in the category of polynomials.
In math mode, this macro can be called in the following ways:
\normctsHahnptilde{n} produces $\displaystyle {\displaystyle \normctsHahnptilde{n}}$
\normctsHahnptilde{n}@{x}{a}{b}{c}{d} produces $\displaystyle {\displaystyle \normctsHahnptilde{n}@{x}{a}{b}{c}{d}}$
\normctsHahnptilde{n}@@{x}{a}{b}{c}{d} produces $\displaystyle {\displaystyle \normctsHahnptilde{n}@@{x}{a}{b}{c}{d}}$
These are defined by [1]
$\displaystyle \normctsHahnptilde{n}@@{x}{a}{b}{c}{d}:=\normctsHahnptilde{n}@{x}{a}{b}{c}{d}=\frac{n!}{i^n\pochhammer{a+c}{n}\pochhammer{a+d}{n}}\ctsHahn{n}@{x}{a}{b}{c}{d}.$
## Symbols List
${\displaystyle {\displaystyle {\tilde {p}}_{n}}}$ : normalized continuous Hahn polynomial ${\displaystyle {\displaystyle {\tilde {p}}}}$ : http://drmf.wmflabs.org/wiki/Definition:normctsHahnptilde
${\displaystyle {\displaystyle (a)_{n}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle {\displaystyle p_{n}}}$ : continuous Hahn polynomial : http://dlmf.nist.gov/18.19#P2.p1
|
2019-06-25 01:37:44
|
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|
https://earthscience.stackexchange.com/questions/8418/how-to-calculate-water-vapor-flux-divergence-from-temperature-relative-humidity
|
# How to calculate water vapor flux divergence from temperature, relative humidity, u wind and v wind?
I have temperature, u wind, v wind and relative humidity. I am wondering to calculate water vapor flux divergence and convergence.
Would anybody kindly help to find our a solution for this?
The formula for moisture flux is $$q\vec{V}$$ where $q$ is the water vapor mixing ratio, which can be found using mixhum_ptr and $\vec{V}$ is the velocity.
Therefore the divergence of the moisture flux must be $$\nabla{\dot{}q\vec{V}}=\frac{\partial(qu)}{\partial x}+\frac{\partial(qv)}{\partial y}+\frac{\partial(qw)}{\partial z}$$ $$\approx\frac{\delta(qu)}{\delta x}+\frac{\delta(qv)}{\delta y}+\frac{\delta(qw)}{\delta z}$$
which is computable if you have gridded data.
For example, you could compute this by setting $$qu=q\ast u$$ $$qv=q\ast v$$ $$qfluxDiv=uv2dv\_cfd(qu,qv,lat,lon,opt)$$ Use uv2dv_cfd per http://www.ncl.ucar.edu/Document/Functions/Built-in/uv2dv_cfd.shtml
Note: If you wanted the turbulent moisture flux, you would need to subtract $\nabla{\dot{}\bar{\vec{V}}\bar{q}}$ from your answer.
• Please suggest in NCL or grads. Thank you – Kay Jul 22 '16 at 1:30
• For horizontal water vapor flux, divergence try this NCL code: qfluxDiv=uv2dv_cfd(qu,qv,lat,lon,opt) – BarocliniCplusplus Jul 22 '16 at 3:55
• I added that to the answer, but without data and code, it is hard to give an example. I provided a link to the NCL function, so that you may know how to use the function. There is an example there on how to use the function. – BarocliniCplusplus Jul 22 '16 at 13:43
• @BarocliniCplusplus - can you add in your answer what q is ? – gansub Oct 31 '16 at 9:32
• @BarocliniCplusplus - Thank you. The only other suggestion is that his input is relative humidity. You may want to link how to convert water vapor mixing ratio to relative humidity. So this becomes a complete answer. – gansub Oct 31 '16 at 14:40
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2020-01-28 14:24:30
|
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https://newproxylists.com/reference-request-product-smash-and-integers-in-a-grothendieck-infty-1-topos/
|
# reference request – Product Smash and integers in a Grothendieck \$ ( infty, 1) \$ – topos
Let $$mathcal {H}$$ to be a Grothendieck $$( infty, 1)$$-topos. According to this page in nlab, for all $$X in mathcal {H}$$, the object suspension $$Sigma X$$ is homotopy equivalent to the smash product $$B mathbb {Z} wedge X$$, or $$B mathbb {Z}$$ is "the discrete group's classification space of integers". In addition, for any sharp object $$X in mathcal {H} _ *$$ and any group object $$G in Grp ( mathcal {H})$$, the article says we can "train the tensor product $$X otimes G in Grp ( mathcal {H})$$. "
My problem is this: none of these terminologies are explained, and the page does not provide any reference. More specifically, what is $$mathbb {Z}$$ in an arbitrary $$infty$$-topos? What is the smash product $$wedge$$? What is the tensor product $$otimes$$? My best guess is that $$otimes$$ refers to the unique tensor structure on $$mathcal {H} _ *$$ such as the map $$mathcal {H} to mathcal {H} _ *$$ is monoidal symmetric (here $$mathcal {H}$$ is given the Cartesian monoidal structure), but this is only a conjecture.
Is there a reference where all these notions are defined?
|
2019-07-23 20:56:34
|
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https://docs.python.org/3/install/
|
# Installing Python Modules (Legacy version)¶
Author: Greg Ward
Installing Python Modules
The up to date module installation documentations
This document describes the Python Distribution Utilities (“Distutils”) from the end-user’s point-of-view, describing how to extend the capabilities of a standard Python installation by building and installing third-party Python modules and extensions.
Note
This guide only covers the basic tools for building and distributing extensions that are provided as part of this version of Python. Third party tools offer easier to use and more secure alternatives. Refer to the quick recommendations section in the Python Packaging User Guide for more information.
## Introduction¶
Although Python’s extensive standard library covers many programming needs, there often comes a time when you need to add some new functionality to your Python installation in the form of third-party modules. This might be necessary to support your own programming, or to support an application that you want to use and that happens to be written in Python.
In the past, there has been little support for adding third-party modules to an existing Python installation. With the introduction of the Python Distribution Utilities (Distutils for short) in Python 2.0, this changed.
This document is aimed primarily at the people who need to install third-party Python modules: end-users and system administrators who just need to get some Python application running, and existing Python programmers who want to add some new goodies to their toolbox. You don’t need to know Python to read this document; there will be some brief forays into using Python’s interactive mode to explore your installation, but that’s it. If you’re looking for information on how to distribute your own Python modules so that others may use them, see the Distributing Python Modules (Legacy version) manual. Debugging the setup script may also be of interest.
### Best case: trivial installation¶
In the best case, someone will have prepared a special version of the module distribution you want to install that is targeted specifically at your platform and is installed just like any other software on your platform. For example, the module developer might make an executable installer available for Windows users, an RPM package for users of RPM-based Linux systems (Red Hat, SuSE, Mandrake, and many others), a Debian package for users of Debian-based Linux systems, and so forth.
In that case, you would download the installer appropriate to your platform and do the obvious thing with it: run it if it’s an executable installer, rpm --install it if it’s an RPM, etc. You don’t need to run Python or a setup script, you don’t need to compile anything—you might not even need to read any instructions (although it’s always a good idea to do so anyway).
Of course, things will not always be that easy. You might be interested in a module distribution that doesn’t have an easy-to-use installer for your platform. In that case, you’ll have to start with the source distribution released by the module’s author/maintainer. Installing from a source distribution is not too hard, as long as the modules are packaged in the standard way. The bulk of this document is about building and installing modules from standard source distributions.
### The new standard: Distutils¶
If you download a module source distribution, you can tell pretty quickly if it was packaged and distributed in the standard way, i.e. using the Distutils. First, the distribution’s name and version number will be featured prominently in the name of the downloaded archive, e.g. foo-1.0.tar.gz or widget-0.9.7.zip. Next, the archive will unpack into a similarly-named directory: foo-1.0 or widget-0.9.7. Additionally, the distribution will contain a setup script setup.py, and a file named README.txt or possibly just README, which should explain that building and installing the module distribution is a simple matter of running one command from a terminal:
python setup.py install
For Windows, this command should be run from a command prompt window (Start ‣ Accessories):
setup.py install
If all these things are true, then you already know how to build and install the modules you’ve just downloaded: Run the command above. Unless you need to install things in a non-standard way or customize the build process, you don’t really need this manual. Or rather, the above command is everything you need to get out of this manual.
## Standard Build and Install¶
As described in section The new standard: Distutils, building and installing a module distribution using the Distutils is usually one simple command to run from a terminal:
python setup.py install
### Platform variations¶
You should always run the setup command from the distribution root directory, i.e. the top-level subdirectory that the module source distribution unpacks into. For example, if you’ve just downloaded a module source distribution foo-1.0.tar.gz onto a Unix system, the normal thing to do is:
gunzip -c foo-1.0.tar.gz | tar xf - # unpacks into directory foo-1.0
cd foo-1.0
python setup.py install
On Windows, you’d probably download foo-1.0.zip. If you downloaded the archive file to C:\Temp, then it would unpack into C:\Temp\foo-1.0; you can use either an archive manipulator with a graphical user interface (such as WinZip) or a command-line tool (such as unzip or pkunzip) to unpack the archive. Then, open a command prompt window and run:
cd c:\Temp\foo-1.0
python setup.py install
### Splitting the job up¶
Running setup.py install builds and installs all modules in one run. If you prefer to work incrementally—especially useful if you want to customize the build process, or if things are going wrong—you can use the setup script to do one thing at a time. This is particularly helpful when the build and install will be done by different users—for example, you might want to build a module distribution and hand it off to a system administrator for installation (or do it yourself, with super-user privileges).
For example, you can build everything in one step, and then install everything in a second step, by invoking the setup script twice:
python setup.py build
python setup.py install
If you do this, you will notice that running the install command first runs the build command, which—in this case—quickly notices that it has nothing to do, since everything in the build directory is up-to-date.
You may not need this ability to break things down often if all you do is install modules downloaded off the ‘net, but it’s very handy for more advanced tasks. If you get into distributing your own Python modules and extensions, you’ll run lots of individual Distutils commands on their own.
### How building works¶
As implied above, the build command is responsible for putting the files to install into a build directory. By default, this is build under the distribution root; if you’re excessively concerned with speed, or want to keep the source tree pristine, you can change the build directory with the --build-base option. For example:
python setup.py build --build-base=/path/to/pybuild/foo-1.0
(Or you could do this permanently with a directive in your system or personal Distutils configuration file; see section Distutils Configuration Files.) Normally, this isn’t necessary.
The default layout for the build tree is as follows:
--- build/ --- lib/
or
--- build/ --- lib.<plat>/
temp.<plat>/
where <plat> expands to a brief description of the current OS/hardware platform and Python version. The first form, with just a lib directory, is used for “pure module distributions”—that is, module distributions that include only pure Python modules. If a module distribution contains any extensions (modules written in C/C++), then the second form, with two <plat> directories, is used. In that case, the temp.plat directory holds temporary files generated by the compile/link process that don’t actually get installed. In either case, the lib (or lib.plat) directory contains all Python modules (pure Python and extensions) that will be installed.
In the future, more directories will be added to handle Python scripts, documentation, binary executables, and whatever else is needed to handle the job of installing Python modules and applications.
### How installation works¶
After the build command runs (whether you run it explicitly, or the install command does it for you), the work of the install command is relatively simple: all it has to do is copy everything under build/lib (or build/lib.plat) to your chosen installation directory.
If you don’t choose an installation directory—i.e., if you just run setup.py install—then the install command installs to the standard location for third-party Python modules. This location varies by platform and by how you built/installed Python itself. On Unix (and Mac OS X, which is also Unix-based), it also depends on whether the module distribution being installed is pure Python or contains extensions (“non-pure”):
Platform Standard installation location Default value Notes
Unix (pure) prefix/lib/pythonX.Y/site-packages /usr/local/lib/pythonX.Y/site-packages (1)
Unix (non-pure) exec-prefix/lib/pythonX.Y/site-packages /usr/local/lib/pythonX.Y/site-packages (1)
Windows prefix\Lib\site-packages C:\PythonXY\Lib\site-packages (2)
Notes:
1. Most Linux distributions include Python as a standard part of the system, so prefix and exec-prefix are usually both /usr on Linux. If you build Python yourself on Linux (or any Unix-like system), the default prefix and exec-prefix are /usr/local.
2. The default installation directory on Windows was C:\Program Files\Python under Python 1.6a1, 1.5.2, and earlier.
prefix and exec-prefix stand for the directories that Python is installed to, and where it finds its libraries at run-time. They are always the same under Windows, and very often the same under Unix and Mac OS X. You can find out what your Python installation uses for prefix and exec-prefix by running Python in interactive mode and typing a few simple commands. Under Unix, just type python at the shell prompt. Under Windows, choose Start ‣ Programs ‣ Python X.Y ‣ Python (command line). Once the interpreter is started, you type Python code at the prompt. For example, on my Linux system, I type the three Python statements shown below, and get the output as shown, to find out my prefix and exec-prefix:
Python 2.4 (#26, Aug 7 2004, 17:19:02)
>>> import sys
>>> sys.prefix
'/usr'
>>> sys.exec_prefix
'/usr'
A few other placeholders are used in this document: X.Y stands for the version of Python, for example 3.2; abiflags will be replaced by the value of sys.abiflags or the empty string for platforms which don’t define ABI flags; distname will be replaced by the name of the module distribution being installed. Dots and capitalization are important in the paths; for example, a value that uses python3.2 on UNIX will typically use Python32 on Windows.
If you don’t want to install modules to the standard location, or if you don’t have permission to write there, then you need to read about alternate installations in section Alternate Installation. If you want to customize your installation directories more heavily, see section Custom Installation on custom installations.
## Alternate Installation¶
Often, it is necessary or desirable to install modules to a location other than the standard location for third-party Python modules. For example, on a Unix system you might not have permission to write to the standard third-party module directory. Or you might wish to try out a module before making it a standard part of your local Python installation. This is especially true when upgrading a distribution already present: you want to make sure your existing base of scripts still works with the new version before actually upgrading.
The Distutils install command is designed to make installing module distributions to an alternate location simple and painless. The basic idea is that you supply a base directory for the installation, and the install command picks a set of directories (called an installation scheme) under this base directory in which to install files. The details differ across platforms, so read whichever of the following sections applies to you.
Note that the various alternate installation schemes are mutually exclusive: you can pass --user, or --home, or --prefix and --exec-prefix, or --install-base and --install-platbase, but you can’t mix from these groups.
### Alternate installation: the user scheme¶
This scheme is designed to be the most convenient solution for users that don’t have write permission to the global site-packages directory or don’t want to install into it. It is enabled with a simple option:
python setup.py install --user
Files will be installed into subdirectories of site.USER_BASE (written as userbase hereafter). This scheme installs pure Python modules and extension modules in the same location (also known as site.USER_SITE). Here are the values for UNIX, including Mac OS X:
Type of file Installation directory
modules userbase/lib/pythonX.Y/site-packages
scripts userbase/bin
data userbase
C headers userbase/include/pythonX.Yabiflags/distname
And here are the values used on Windows:
Type of file Installation directory
modules userbase\PythonXY\site-packages
scripts userbase\PythonXY\Scripts
data userbase
C headers userbase\PythonXY\Include{distname}
The advantage of using this scheme compared to the other ones described below is that the user site-packages directory is under normal conditions always included in sys.path (see site for more information), which means that there is no additional step to perform after running the setup.py script to finalize the installation.
The build_ext command also has a --user option to add userbase/include to the compiler search path for header files and userbase/lib to the compiler search path for libraries as well as to the runtime search path for shared C libraries (rpath).
### Alternate installation: the home scheme¶
The idea behind the “home scheme” is that you build and maintain a personal stash of Python modules. This scheme’s name is derived from the idea of a “home” directory on Unix, since it’s not unusual for a Unix user to make their home directory have a layout similar to /usr/ or /usr/local/. This scheme can be used by anyone, regardless of the operating system they are installing for.
Installing a new module distribution is as simple as
python setup.py install --home=<dir>
where you can supply any directory you like for the --home option. On Unix, lazy typists can just type a tilde (~); the install command will expand this to your home directory:
python setup.py install --home=~
To make Python find the distributions installed with this scheme, you may have to modify Python’s search path or edit sitecustomize (see site) to call site.addsitedir() or edit sys.path.
The --home option defines the installation base directory. Files are installed to the following directories under the installation base as follows:
Type of file Installation directory
modules home/lib/python
scripts home/bin
data home
C headers home/include/python/distname
(Mentally replace slashes with backslashes if you’re on Windows.)
### Alternate installation: Unix (the prefix scheme)¶
The “prefix scheme” is useful when you wish to use one Python installation to perform the build/install (i.e., to run the setup script), but install modules into the third-party module directory of a different Python installation (or something that looks like a different Python installation). If this sounds a trifle unusual, it is—that’s why the user and home schemes come before. However, there are at least two known cases where the prefix scheme will be useful.
First, consider that many Linux distributions put Python in /usr, rather than the more traditional /usr/local. This is entirely appropriate, since in those cases Python is part of “the system” rather than a local add-on. However, if you are installing Python modules from source, you probably want them to go in /usr/local/lib/python2.X rather than /usr/lib/python2.X. This can be done with
/usr/bin/python setup.py install --prefix=/usr/local
Another possibility is a network filesystem where the name used to write to a remote directory is different from the name used to read it: for example, the Python interpreter accessed as /usr/local/bin/python might search for modules in /usr/local/lib/python2.X, but those modules would have to be installed to, say, /mnt/@server/export/lib/python2.X. This could be done with
/usr/local/bin/python setup.py install --prefix=/mnt/@server/export
In either case, the --prefix option defines the installation base, and the --exec-prefix option defines the platform-specific installation base, which is used for platform-specific files. (Currently, this just means non-pure module distributions, but could be expanded to C libraries, binary executables, etc.) If --exec-prefix is not supplied, it defaults to --prefix. Files are installed as follows:
Type of file Installation directory
Python modules prefix/lib/pythonX.Y/site-packages
extension modules exec-prefix/lib/pythonX.Y/site-packages
scripts prefix/bin
data prefix
C headers prefix/include/pythonX.Yabiflags/distname
There is no requirement that --prefix or --exec-prefix actually point to an alternate Python installation; if the directories listed above do not already exist, they are created at installation time.
Incidentally, the real reason the prefix scheme is important is simply that a standard Unix installation uses the prefix scheme, but with --prefix and --exec-prefix supplied by Python itself as sys.prefix and sys.exec_prefix. Thus, you might think you’ll never use the prefix scheme, but every time you run python setup.py install without any other options, you’re using it.
Note that installing extensions to an alternate Python installation has no effect on how those extensions are built: in particular, the Python header files (Python.h and friends) installed with the Python interpreter used to run the setup script will be used in compiling extensions. It is your responsibility to ensure that the interpreter used to run extensions installed in this way is compatible with the interpreter used to build them. The best way to do this is to ensure that the two interpreters are the same version of Python (possibly different builds, or possibly copies of the same build). (Of course, if your --prefix and --exec-prefix don’t even point to an alternate Python installation, this is immaterial.)
### Alternate installation: Windows (the prefix scheme)¶
Windows has no concept of a user’s home directory, and since the standard Python installation under Windows is simpler than under Unix, the --prefix option has traditionally been used to install additional packages in separate locations on Windows.
python setup.py install --prefix="\Temp\Python"
to install modules to the \Temp\Python directory on the current drive.
The installation base is defined by the --prefix option; the --exec-prefix option is not supported under Windows, which means that pure Python modules and extension modules are installed into the same location. Files are installed as follows:
Type of file Installation directory
modules prefix\Lib\site-packages
scripts prefix\Scripts
data prefix
C headers prefix\Include{distname}
## Custom Installation¶
Sometimes, the alternate installation schemes described in section Alternate Installation just don’t do what you want. You might want to tweak just one or two directories while keeping everything under the same base directory, or you might want to completely redefine the installation scheme. In either case, you’re creating a custom installation scheme.
To create a custom installation scheme, you start with one of the alternate schemes and override some of the installation directories used for the various types of files, using these options:
Type of file Override option
Python modules --install-purelib
extension modules --install-platlib
all modules --install-lib
scripts --install-scripts
data --install-data
C headers --install-headers
These override options can be relative, absolute, or explicitly defined in terms of one of the installation base directories. (There are two installation base directories, and they are normally the same—they only differ when you use the Unix “prefix scheme” and supply different --prefix and --exec-prefix options; using --install-lib will override values computed or given for --install-purelib and --install-platlib, and is recommended for schemes that don’t make a difference between Python and extension modules.)
For example, say you’re installing a module distribution to your home directory under Unix—but you want scripts to go in ~/scripts rather than ~/bin. As you might expect, you can override this directory with the --install-scripts option; in this case, it makes most sense to supply a relative path, which will be interpreted relative to the installation base directory (your home directory, in this case):
python setup.py install --home=~ --install-scripts=scripts
Another Unix example: suppose your Python installation was built and installed with a prefix of /usr/local/python, so under a standard installation scripts will wind up in /usr/local/python/bin. If you want them in /usr/local/bin instead, you would supply this absolute directory for the --install-scripts option:
python setup.py install --install-scripts=/usr/local/bin
(This performs an installation using the “prefix scheme,” where the prefix is whatever your Python interpreter was installed with— /usr/local/python in this case.)
If you maintain Python on Windows, you might want third-party modules to live in a subdirectory of prefix, rather than right in prefix itself. This is almost as easy as customizing the script installation directory—you just have to remember that there are two types of modules to worry about, Python and extension modules, which can conveniently be both controlled by one option:
python setup.py install --install-lib=Site
The specified installation directory is relative to prefix. Of course, you also have to ensure that this directory is in Python’s module search path, such as by putting a .pth file in a site directory (see site). See section Modifying Python’s Search Path to find out how to modify Python’s search path.
If you want to define an entire installation scheme, you just have to supply all of the installation directory options. The recommended way to do this is to supply relative paths; for example, if you want to maintain all Python module-related files under python in your home directory, and you want a separate directory for each platform that you use your home directory from, you might define the following installation scheme:
python setup.py install --home=~ \
--install-purelib=python/lib \
--install-platlib=python/lib.$PLAT \ --install-scripts=python/scripts --install-data=python/data or, equivalently, python setup.py install --home=~/python \ --install-purelib=lib \ --install-platlib='lib.$PLAT' \
--install-scripts=scripts
--install-data=data
$PLAT is not (necessarily) an environment variable—it will be expanded by the Distutils as it parses your command line options, just as it does when parsing your configuration file(s). Obviously, specifying the entire installation scheme every time you install a new module distribution would be very tedious. Thus, you can put these options into your Distutils config file (see section Distutils Configuration Files): [install] install-base=$HOME
install-purelib=python/lib
install-platlib=python/lib.$PLAT install-scripts=python/scripts install-data=python/data or, equivalently, [install] install-base=$HOME/python
install-purelib=lib
install-platlib=lib.$PLAT install-scripts=scripts install-data=data Note that these two are not equivalent if you supply a different installation base directory when you run the setup script. For example, python setup.py install --install-base=/tmp would install pure modules to /tmp/python/lib in the first case, and to /tmp/lib in the second case. (For the second case, you probably want to supply an installation base of /tmp/python.) You probably noticed the use of $HOME and $PLAT in the sample configuration file input. These are Distutils configuration variables, which bear a strong resemblance to environment variables. In fact, you can use environment variables in config files on platforms that have such a notion but the Distutils additionally define a few extra variables that may not be in your environment, such as $PLAT. (And of course, on systems that don’t have environment variables, such as Mac OS 9, the configuration variables supplied by the Distutils are the only ones you can use.) See section Distutils Configuration Files for details.
Note
When a virtual environment is activated, any options that change the installation path will be ignored from all distutils configuration files to prevent inadvertently installing projects outside of the virtual environment.
### Modifying Python’s Search Path¶
When the Python interpreter executes an import statement, it searches for both Python code and extension modules along a search path. A default value for the path is configured into the Python binary when the interpreter is built. You can determine the path by importing the sys module and printing the value of sys.path.
$python Python 2.2 (#11, Oct 3 2002, 13:31:27) [GCC 2.96 20000731 (Red Hat Linux 7.3 2.96-112)] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> import sys >>> sys.path ['', '/usr/local/lib/python2.3', '/usr/local/lib/python2.3/plat-linux2', '/usr/local/lib/python2.3/lib-tk', '/usr/local/lib/python2.3/lib-dynload', '/usr/local/lib/python2.3/site-packages'] >>> The null string in sys.path represents the current working directory. The expected convention for locally installed packages is to put them in the …/site-packages/ directory, but you may want to install Python modules into some arbitrary directory. For example, your site may have a convention of keeping all software related to the web server under /www. Add-on Python modules might then belong in /www/python, and in order to import them, this directory must be added to sys.path. There are several different ways to add the directory. The most convenient way is to add a path configuration file to a directory that’s already on Python’s path, usually to the .../site-packages/ directory. Path configuration files have an extension of .pth, and each line must contain a single path that will be appended to sys.path. (Because the new paths are appended to sys.path, modules in the added directories will not override standard modules. This means you can’t use this mechanism for installing fixed versions of standard modules.) Paths can be absolute or relative, in which case they’re relative to the directory containing the .pth file. See the documentation of the site module for more information. A slightly less convenient way is to edit the site.py file in Python’s standard library, and modify sys.path. site.py is automatically imported when the Python interpreter is executed, unless the -S switch is supplied to suppress this behaviour. So you could simply edit site.py and add two lines to it: import sys sys.path.append('/www/python/') However, if you reinstall the same major version of Python (perhaps when upgrading from 2.2 to 2.2.2, for example) site.py will be overwritten by the stock version. You’d have to remember that it was modified and save a copy before doing the installation. There are two environment variables that can modify sys.path. PYTHONHOME sets an alternate value for the prefix of the Python installation. For example, if PYTHONHOME is set to /www/python, the search path will be set to ['', '/www/python/lib/pythonX.Y/', '/www/python/lib/pythonX.Y/plat-linux2', ...]. The PYTHONPATH variable can be set to a list of paths that will be added to the beginning of sys.path. For example, if PYTHONPATH is set to /www/python:/opt/py, the search path will begin with ['/www/python', '/opt/py']. (Note that directories must exist in order to be added to sys.path; the site module removes paths that don’t exist.) Finally, sys.path is just a regular Python list, so any Python application can modify it by adding or removing entries. ## Distutils Configuration Files¶ As mentioned above, you can use Distutils configuration files to record personal or site preferences for any Distutils options. That is, any option to any command can be stored in one of two or three (depending on your platform) configuration files, which will be consulted before the command-line is parsed. This means that configuration files will override default values, and the command-line will in turn override configuration files. Furthermore, if multiple configuration files apply, values from “earlier” files are overridden by “later” files. ### Location and names of config files¶ The names and locations of the configuration files vary slightly across platforms. On Unix and Mac OS X, the three configuration files (in the order they are processed) are: Type of file Location and filename Notes system prefix/lib/pythonver/distutils/distutils.cfg (1) personal $HOME/.pydistutils.cfg (2)
local setup.cfg (3)
And on Windows, the configuration files are:
Type of file Location and filename Notes
system prefix\Lib\distutils\distutils.cfg (4)
personal %HOME%\pydistutils.cfg (5)
local setup.cfg (3)
On all platforms, the “personal” file can be temporarily disabled by passing the –no-user-cfg option.
Notes:
1. Strictly speaking, the system-wide configuration file lives in the directory where the Distutils are installed; under Python 1.6 and later on Unix, this is as shown. For Python 1.5.2, the Distutils will normally be installed to prefix/lib/python1.5/site-packages/distutils, so the system configuration file should be put there under Python 1.5.2.
2. On Unix, if the HOME environment variable is not defined, the user’s home directory will be determined with the getpwuid() function from the standard pwd module. This is done by the os.path.expanduser() function used by Distutils.
3. I.e., in the current directory (usually the location of the setup script).
4. (See also note (1).) Under Python 1.6 and later, Python’s default “installation prefix” is C:\Python, so the system configuration file is normally C:\Python\Lib\distutils\distutils.cfg. Under Python 1.5.2, the default prefix was C:\Program Files\Python, and the Distutils were not part of the standard library—so the system configuration file would be C:\Program Files\Python\distutils\distutils.cfg in a standard Python 1.5.2 installation under Windows.
5. On Windows, if the HOME environment variable is not defined, USERPROFILE then HOMEDRIVE and HOMEPATH will be tried. This is done by the os.path.expanduser() function used by Distutils.
### Syntax of config files¶
The Distutils configuration files all have the same syntax. The config files are grouped into sections. There is one section for each Distutils command, plus a global section for global options that affect every command. Each section consists of one option per line, specified as option=value.
For example, the following is a complete config file that just forces all commands to run quietly by default:
[global]
verbose=0
If this is installed as the system config file, it will affect all processing of any Python module distribution by any user on the current system. If it is installed as your personal config file (on systems that support them), it will affect only module distributions processed by you. And if it is used as the setup.cfg for a particular module distribution, it affects only that distribution.
You could override the default “build base” directory and make the build* commands always forcibly rebuild all files with the following:
[build]
build-base=blib
force=1
which corresponds to the command-line arguments
python setup.py build --build-base=blib --force
except that including the build command on the command-line means that command will be run. Including a particular command in config files has no such implication; it only means that if the command is run, the options in the config file will apply. (Or if other commands that derive values from it are run, they will use the values in the config file.)
You can find out the complete list of options for any command using the --help option, e.g.:
python setup.py build --help
and you can find out the complete list of global options by using --help without a command:
python setup.py --help
## Building Extensions: Tips and Tricks¶
Whenever possible, the Distutils try to use the configuration information made available by the Python interpreter used to run the setup.py script. For example, the same compiler and linker flags used to compile Python will also be used for compiling extensions. Usually this will work well, but in complicated situations this might be inappropriate. This section discusses how to override the usual Distutils behaviour.
Compiling a Python extension written in C or C++ will sometimes require specifying custom flags for the compiler and linker in order to use a particular library or produce a special kind of object code. This is especially true if the extension hasn’t been tested on your platform, or if you’re trying to cross-compile Python.
In the most general case, the extension author might have foreseen that compiling the extensions would be complicated, and provided a Setup file for you to edit. This will likely only be done if the module distribution contains many separate extension modules, or if they often require elaborate sets of compiler flags in order to work.
A Setup file, if present, is parsed in order to get a list of extensions to build. Each line in a Setup describes a single module. Lines have the following structure:
module ... [sourcefile ...] [cpparg ...] [library ...]
Let’s examine each of the fields in turn.
• module is the name of the extension module to be built, and should be a valid Python identifier. You can’t just change this in order to rename a module (edits to the source code would also be needed), so this should be left alone.
• sourcefile is anything that’s likely to be a source code file, at least judging by the filename. Filenames ending in .c are assumed to be written in C, filenames ending in .C, .cc, and .c++ are assumed to be C++, and filenames ending in .m or .mm are assumed to be in Objective C.
• cpparg is an argument for the C preprocessor, and is anything starting with -I, -D, -U or -C.
• library is anything ending in .a or beginning with -l or -L.
If a particular platform requires a special library on your platform, you can add it by editing the Setup file and running python setup.py build. For example, if the module defined by the line
foo foomodule.c
must be linked with the math library libm.a on your platform, simply add -lm to the line:
foo foomodule.c -lm
Arbitrary switches intended for the compiler or the linker can be supplied with the -Xcompiler arg and -Xlinker arg options:
foo foomodule.c -Xcompiler -o32 -Xlinker -shared -lm
The next option after -Xcompiler and -Xlinker will be appended to the proper command line, so in the above example the compiler will be passed the -o32 option, and the linker will be passed -shared. If a compiler option requires an argument, you’ll have to supply multiple -Xcompiler options; for example, to pass -x c++ the Setup file would have to contain -Xcompiler -x -Xcompiler c++.
Compiler flags can also be supplied through setting the CFLAGS environment variable. If set, the contents of CFLAGS will be added to the compiler flags specified in the Setup file.
### Using non-Microsoft compilers on Windows¶
#### Borland/CodeGear C++¶
This subsection describes the necessary steps to use Distutils with the Borland C++ compiler version 5.5. First you have to know that Borland’s object file format (OMF) is different from the format used by the Python version you can download from the Python or ActiveState Web site. (Python is built with Microsoft Visual C++, which uses COFF as the object file format.) For this reason you have to convert Python’s library python25.lib into the Borland format. You can do this as follows:
coff2omf python25.lib python25_bcpp.lib
The coff2omf program comes with the Borland compiler. The file python25.lib is in the Libs directory of your Python installation. If your extension uses other libraries (zlib, …) you have to convert them too.
The converted files have to reside in the same directories as the normal libraries.
How does Distutils manage to use these libraries with their changed names? If the extension needs a library (eg. foo) Distutils checks first if it finds a library with suffix _bcpp (eg. foo_bcpp.lib) and then uses this library. In the case it doesn’t find such a special library it uses the default name (foo.lib.) [1]
To let Distutils compile your extension with Borland C++ you now have to type:
python setup.py build --compiler=bcpp
If you want to use the Borland C++ compiler as the default, you could specify this in your personal or system-wide configuration file for Distutils (see section Distutils Configuration Files.)
C++Builder Compiler
Creating Python Extensions Using Borland’s Free Compiler
Document describing how to use Borland’s free command-line C++ compiler to build Python.
#### GNU C / Cygwin / MinGW¶
This section describes the necessary steps to use Distutils with the GNU C/C++ compilers in their Cygwin and MinGW distributions. [2] For a Python interpreter that was built with Cygwin, everything should work without any of these following steps.
Not all extensions can be built with MinGW or Cygwin, but many can. Extensions most likely to not work are those that use C++ or depend on Microsoft Visual C extensions.
To let Distutils compile your extension with Cygwin you have to type:
python setup.py build --compiler=cygwin
and for Cygwin in no-cygwin mode [3] or for MinGW type:
python setup.py build --compiler=mingw32
If you want to use any of these options/compilers as default, you should consider writing it in your personal or system-wide configuration file for Distutils (see section Distutils Configuration Files.)
##### Older Versions of Python and MinGW¶
The following instructions only apply if you’re using a version of Python inferior to 2.4.1 with a MinGW inferior to 3.0.0 (with binutils-2.13.90-20030111-1).
These compilers require some special libraries. This task is more complex than for Borland’s C++, because there is no program to convert the library. First you have to create a list of symbols which the Python DLL exports. (You can find a good program for this task at https://sourceforge.net/projects/mingw/files/MinGW/Extension/pexports/).
pexports python25.dll >python25.def
The location of an installed python25.dll will depend on the installation options and the version and language of Windows. In a “just for me” installation, it will appear in the root of the installation directory. In a shared installation, it will be located in the system directory.
Then you can create from these information an import library for gcc.
/cygwin/bin/dlltool --dllname python25.dll --def python25.def --output-lib libpython25.a
The resulting library has to be placed in the same directory as python25.lib. (Should be the libs directory under your Python installation directory.)
If your extension uses other libraries (zlib,…) you might have to convert them too. The converted files have to reside in the same directories as the normal libraries do.
[3] Then you have no POSIX emulation available, but you also don’t need cygwin1.dll.
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2019-02-19 19:09:15
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http://mathoverflow.net/revisions/10043/list
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2 added 1287 characters in body
Oh, Toën is using a different definition of "localization" than the one I am accustomed to (e.g., see Definition 5.2.7.2 and Warning 5.2.7.3 of Higher Topos Theory). Since Cat is a presentable category, I assumed you were taking the localization in presentable categories, which involves a category S-1Cat and an adjunction with left adjoint Cat S-1Cat which has the analogous universal property with respect to adjunctions between presentable categories. In that case, S-1Cat turns out to be rigid categories and Chris explained why you might expect this to be true. (The homotopy category of Cat is presumably not a presentable category at all.)
With S the class of equivalences of categories these localizations do not agree because S is not closed under pushouts in Cat: in the square
J -> BZ* -> *the left-hand map is in S but the right-hand map is not and yet the square is, bizarrely, a pushout. (What makes things even trickier is the ∞-categorical analogue of "S is closed under pushouts" is true because of course we must take homotopy pushouts. In short thinking of Cat as a 1-category and trying to work with equivalences there can lead to strange results!)
1
I'm pretty sure this is false. If I recall correctly, the localization S-1CAT you refer to is equivalent to the category of rigid categories, those with no nonidentity isomorphisms at all. In particular, the "rigid categorification" of any connected groupoid is the terminal category. On the other hand, the isomorphism classes of objects in |CAT| are equivalence classes of categories, so in |CAT| there are many nonisomorphic connected groupoids.
I'll see if I can remember how to prove my claim about S-1CAT, or maybe you can prove it; I don't think it's very hard, and it uses the same kind of ideas Chris talked about in his answer.
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2013-05-24 19:34:16
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https://deepai.org/publication/robustness-of-conditional-gans-to-noisy-labels
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# Robustness of Conditional GANs to Noisy Labels
We study the problem of learning conditional generators from noisy labeled samples, where the labels are corrupted by random noise. A standard training of conditional GANs will not only produce samples with wrong labels, but also generate poor quality samples. We consider two scenarios, depending on whether the noise model is known or not. When the distribution of the noise is known, we introduce a novel architecture which we call Robust Conditional GAN (RCGAN). The main idea is to corrupt the label of the generated sample before feeding to the adversarial discriminator, forcing the generator to produce samples with clean labels. This approach of passing through a matching noisy channel is justified by corresponding multiplicative approximation bounds between the loss of the RCGAN and the distance between the clean real distribution and the generator distribution. This shows that the proposed approach is robust, when used with a carefully chosen discriminator architecture, known as projection discriminator. When the distribution of the noise is not known, we provide an extension of our architecture, which we call RCGAN-U, that learns the noise model simultaneously while training the generator. We show experimentally on MNIST and CIFAR-10 datasets that both the approaches consistently improve upon baseline approaches, and RCGAN-U closely matches the performance of RCGAN.
## Authors
• 4 publications
• 10 publications
• 4 publications
• 39 publications
• ### Stabilizing GAN Training with Multiple Random Projections
Training generative adversarial networks is unstable in high-dimensions ...
05/22/2017 ∙ by Behnam Neyshabur, et al. ∙ 0
read it
• ### Robust conditional GANs under missing or uncertain labels
Matching the performance of conditional Generative Adversarial Networks ...
06/09/2019 ∙ by Kiran Koshy Thekumparampil, et al. ∙ 9
read it
• ### Improving Detection of Credit Card Fraudulent Transactions using Generative Adversarial Networks
In this study, we employ Generative Adversarial Networks as an oversampl...
07/07/2019 ∙ by Hung Ba, et al. ∙ 0
read it
• ### The Implicit Metropolis-Hastings Algorithm
Recent works propose using the discriminator of a GAN to filter out unre...
06/09/2019 ∙ by Kirill Neklyudov, et al. ∙ 0
read it
• ### Limited Gradient Descent: Learning With Noisy Labels
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11/20/2018 ∙ by Yi Sun, et al. ∙ 14
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• ### Adversarially-Trained Normalized Noisy-Feature Auto-Encoder for Text Generation
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11/10/2018 ∙ by Xiang Zhang, et al. ∙ 0
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• ### Adaptive Divergence for Rapid Adversarial Optimization
Adversarial Optimization (AO) provides a reliable, practical way to matc...
12/01/2019 ∙ by Maxim Borisyak, et al. ∙ 0
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## 1 Introduction
Conditional generative adversarial networks (GAN) have been widely successful in several applications including improving image quality, semi-supervised learning, reinforcement learning, category transformation, style transfer, image de-noising, compression, in-painting, and super-resolution
[30, 13, 48, 36, 26, 58]. The goal of training a conditional GAN is to generate samples from distributions satisfying certain conditioning
on some correlated features. Concretely, given samples from joint distribution of a data point
and a label , we want to learn to generate samples from the true conditional distribution of the real data . A canonical conditional GAN studied in literature is the case of discrete label [30, 36, 35, 32]. Significant progresses have been made in this setting, which are typically evaluated on the quality of the conditional samples. These include measuring inception scores and intra Fréchet inception distances, visual inspection on downstream tasks such as category morphing and super resolution [32], and faithfulness of the samples as measured by how accurately we can infer the class that generated the sample [36].
We study the problem of training conditional GANs with noisy discrete labels. By noisy labels, we refer to a setting where the label for each example in the training set is randomly corrupted. Such noise can result from an adversary deliberately corrupting the data [7] or from human errors in crowdsourced label collection [12, 18]. This can be modeled as a random process, where a clean data point and its label are drawn from a joint distribution with classes. For each data point, the label is corrupted by passing through a noisy channel represented by a row-stochastic confusion matrix defined as . This defines a joint distribution for the data point and a noisy label : . If we train a standard conditional GAN on noisy samples, then it solves the following optimization:
minG∈GmaxD∈FV(G,D)=E(x,˜y)∼˜PX,˜Y[ϕ(D(x,˜y))]+Ez∼N,y∼˜P˜Y[ϕ(1−D(G(z;y),y))] (1)
where is a function of choice, and are the discriminator and the generator respectively optimized over function classes and of our choice, and
is the distribution of the latent random vector. For typical choices of
, for example , and large enough function classes and , the optimal conditional generator learns to generate samples from , the corrupted conditional distribution. In other words, it generates samples from classes other than what it is conditioned on. As the learned distribution exhibits such a bias, we call this naive approach the Biased GAN. Under this setting, there is a fundamental question of interest: can we design a novel conditional GAN that can generate samples from the true conditional distribution , even when trained on noisy samples?
Several aspects of this problem make it challenging and interesting. First, the performance of such robust GAN should depend on how noisy the channel is. If is rank-deficient, for instance, then there are multiple distributions that result in the same distribution after the corruption, and hence no reliable learning of the true distribution is possible. We would ideally want a theoretical guarantee that shows such trade-off between and the robustness of GANs. Next, when the noise is from errors in crowdsourced labels, we might have some access to the confusion matrix from historical data. On other cases of adversarial corruption, we might not have any information of . We want to provide robust solutions to both. Finally, an important practical challenge in this setting is to correct the noisy labels in the training data. We address all such variations in our approaches and make the following contributions.
Our contributions. We introduce two architectures to train conditional GANs with noisy samples.
First, when we have the knowledge of the confusion matrix , we propose RCGAN (Robust Conditional GAN) in Section 2. We first prove that minimizing the RCGAN loss provably recovers the clean distribution (Theorem 2), under certain conditions on the class of discriminators we optimize over (Assumption 1). We show that such a condition on is also necessary, as without it, the training loss can be arbitrarily small while the generated distribution can be far from the real (Theorem 3). The assumption leads to our particular choice of the discriminator in RCGAN, called projection discriminator [32] that satisfies all the conditions (Remark 2). Finally, we provide a finite sample generalization bound showing that the loss minimized in training RCGAN does generalize, and results in the learned distribution being close to the clean conditional distribution (Theorem 4). Experimental results in benchmark datasets confirm that RCGAN is robust against noisy samples, and improves significantly over the naive Biased GAN.
Secondly, when we do not have access to , we propose RCGAN-U (RCGAN with Unknown noise distribution) in Section 4. We provide experimental results showing that performance gains similar to that of RCGAN can be achieved. Finally, we showcase the practical use of thus learned conditional GANs, by using it to fix the noisy labels in the training data. Numerical experiments confirm that the RCGAN framework provides a more robust approach to correcting the noisy labels, compared to the state-of-the-art methods that rely only on discriminators.
Related work. Two popular training methods for generative models are variational auto-encoders [22] and adversarial training [14]. The adversarial training approach has made significant advances in several applications of practical interest. [37, 2, 5] propose new architectures that significantly improve the training in practical image datasets. [58, 16] propose new architectures to transfer the style of one image to the other domain. [26, 43] show how to enhance a given image with learned generator, by enhancing the resolution or making it more realistic. [27, 50] show how to generate videos and [51, 1] demonstrate that 3-dimensional models can be generated from adversarial training. [23] proposes a new architecture encoding causal structures in conditional GANs. [42] introduces the state-of-the-art conditional independence tester. On a different direction, several recent approaches showcase how the manifold learned by the adversarial training can be used to solve inverse problems [9, 57, 53, 49].
Conditional GANs have been proposed as a successful tool for various applications, including class conditional image generation [36], image to image translation [21], and image generation from text [38, 55]. Most of the conditional GANs incorporate the class information by naively concatenating it to the input or feature vector at some middle layer [30, 13, 38, 55]. AC-GANs [36]
creates an auxiliary classifier to incorporate class information. Projection discriminator GAN
[32] takes an inner product between the embedded class vector and the feature vector. A recent work [31] which proposes spectral normalization shows that high quality image generation on -class ILSVRC2012 dataset [39] can be achieved using projection conditional discriminator.
Robustness of (unconditional) GANs against adversarial or random noise has recently been studied in [10, 52]. [52] studies an adversary attacking the output of the discriminator, perturbing the discriminator output with random noise. The proposed architecture of RCGAN is inspired by a closely related work of AmbientGAN in [10]. AmbientGAN is a general framework addressing any corruption on the data itself (not necessarily just the labels). Given a corrupted samples with known corruption, AmbientGAN applies that corruption to the output of the generator before feeding them to the discriminator. This has shown to successfully de-noise images in several practical scenarios.
Motivated by the success of AmbientGAN in de-noising, we propose RCGAN. An important distinction is that we make specific architectural choices guided by our theoretical analysis that gives a significant gain in practice as shown in Section 6. Under the scenario of interest with noisy labels, we provide sharp analyses for both the population loss and the finite sample loss. Such sharp characterizations do not exist for the more general AmbientGAN scenarios. Further, our RCGAN-U does not require the knowledge of the confusion matrix, departing from the AmbientGAN approach. Training classifiers from noisy labels is a closely related problem. Recently, [34, 20] proposed a theoretically motivated classifier which minimizes the modified loss in presence of noisy labels and showed improvement over the robust classifiers [29, 45, 46].
Notation. For a vector , is the standard -norm. For a matrix , let denote the operator norm. Then , and
, the maximum singular value.
is all ones vector with appropriate dimensions and
is identity matrix with appropriate dimensions.
. For a vector , () is its -th coordinate.
## 2 Our first architecture: RCGAN
Training a conditional GAN with noisy samples results in a biased generator. We propose Robust Conditional GAN (RCGAN) architecture which has the following pre-processing, discriminator update, and generator update steps. We assume in this section that the confusions matrix is known (and the marginal can easily be inferred), and address the case of unknown in Section 4.
Pre-processing: We train a classifier to predict the noisy label given under a loss , trained on , where
is a parametric family of classifiers (typically neural networks) and
is the joint distribution of real and corresponding real noisy .
D-step: We train on the following adversarial loss. In the second term below, is generated according to and corresponding noisy labels are generated by corrupting the according to the conditional distribution which is the -th row of the confusion matrix (assumed to be known):
maxD∈FE(x,˜y)∼˜PX,˜Y[ϕ(D(x,˜y))]+Ez∼N,y∼PY˜y|y∼Cy[ϕ(1−D(G(z;y),˜y))],
where is the true marginal distribution of the labels, is the distribution of the latent random vector, and is a family of discriminators.
G-step: We train on the following loss with some :
minG∈GEz∼N,y∼PY˜y|y∼Cy[ϕ(1−D(G(z;y),˜y))+λℓ(h∗(G(z;y)),y)], (2)
where is a family of generators. The idea of using auxiliary classifiers have been used to improve the quality of the image and stability of the training, for example in auxiliary classifier GAN (AC-GAN) [36], and improve the quality of clustering in the latent space [33]. We propose an auxiliary classifiers , mitigating a permutation error, which we empirically identified on naive implementation of our idea with no regularizers.
Permutation regularizer (controlled by ). Permutation error occurs if, when asked to produce samples from a target class, the trained generator produces samples dominantly from a single class but different from the target class. We propose a regularizer , which predicts the noisy label . As long as the confusion matrix is diagonally dominant, which is a necessary condition for identifiability, this regularizer encourages the correct permutation of the labels.
Theoretical motivation for RCGAN. When , we get the standard conditional GAN update steps, albeit one which tries to minimize discriminator loss between the noisy real distribution and the distribution of the generator when the label is passed through the same noisy channel parameterized by . The main idea of RCGAN is to minimize a certain divergence between noisy real data and noisy generated data. For example, the choice of bounded functions and identity map leads to a total variation minimization; The loss minimized in the G-step is the total variation between the two distributions with corrupted labels, up to some scaling and some shift. If we choose and , then we are minimizing the Jensen-Shannon divergence , where
denotes the Kullback-Leibler divergence. The following theorem provides approximation guarantees for some common divergence measures over noisy channel, justifying our proposed practical approach. We refer to Appendix
B for a proof.
###### Theorem 1.
Let and be two distributions on . Let be the corresponding distributions when samples from are passed through the noisy channel given by the confusion matrix (as defined in Section 1). If is full-rank, we get,
dTV(˜P,˜Q)≤ (3) 18dJS(˜P∥∥˜Q)2≤ (4)
To interpret this theorem, let denote the distribution of the generator. The theorem implies that when the noisy generator distribution becomes close to the noisy real distribution in total variation or in Jensen-Shannon divergence, then the generator distribution must be close to the distribution of real data in the same metric. This justifies the use of the proposed architecture RCGAN. In practice, we minimize the sample divergence of the two distributions, instead of the population divergence as analyzed in the above theorem. However, these standard divergences are known to not generalize in training GANs [3]. To this end, we provide in Section 3 analyses on neural network distances, which are known to generalize, and provide finite sample bounds.
## 3 Theoretical Analysis of RCGAN
It was shown in [3] that standard GAN losses of Jensen-Shannon divergence and Wasserstein distance both fail to generalize with a finite number of samples. On the other hand, more recent advances in analyzing GANs in [56, 6, 4] show promising generalization bounds by either assuming Lipschitz conditions on the generator model or by restricting the analysis to certain classes of distributions. Under those assumptions, where JS divergence generalizes, Theorem 1 justifies the use of the proposed RCGAN. However, those require the distribution to be Gaussian, mixture of Gaussians, or output of a neural network generator, for example in [4].
In this section, we provide analyses of RCGAN on a distance that generalizes without any assumptions on the distribution of the real data as proven in [3]: neural network distance. Formally, consider a class of real-valued functions and a function which is either convex or concave. The neural network distance is defined as
(5)
where is the distribution of the real data, is that of the generated data, and is the constant correction term to ensure that . We further assume that includes three constant functions , , and , in order to ensure that and , as shown in Lemma 1 in the Appendix.
The proposed RCGAN with approximately minimizes the neural network distance between the two corrupted distributions. In practice, is a parametric family of functions from a specific neural network architecture that the designer has chosen. In theory, we aim to identify how the choice of class provides the desired approximation bounds similar to those in Theorem 1, but for neural network distances. This analysis leads to the choice of projection discriminator [32] to be used in RCGAN (Remark 2). On the other hand, we show in Theorem 3 that an inappropriate choice of the discriminator architecture can cause non-approximation. Further, we provide the sample complexity of the approximation bounds in Theorem 4.
We refer to the un-regularized version with
as simply RCGAN. In this section, we focus on a class of loss functions called Integral Probability Metrics (IPM) where
[44]. This is a popular choice of loss in GANs in practice [47, 2, 8] and in analyses [4]. We write the induced neural network distance as , dropping the in the notation.
### 3.1 Approximation bounds for neural network distances
We define an operation over a matrix and a class of functions on as
T∘F≜{f∈F|f(x,y)=∑˜y∈[m]Ty˜yf(x,˜y)}. (6)
This makes it convenient to represent the neural network distance corrupted by noise with a confusion matrix , where is the probability a label is corrupted as . Formally, it follows from (5) and (6) that . We refer to Appendix E for a proof. For to be a good approximation of , we show that the following condition is sufficient.
###### Assumption 1.
We assume that the class of discriminator functions can be decomposed into three parts such that is any constant and
• satisfies the inclusion condition:
T∘F1⊆F1, (7)
for all ; and
• satisfies the label invariance condition: there exists a class of sets of functions, parametrized by , such that
F2={αf(x,y)|f(x,y)=f(x),f(x)∈F(x),α∈[0,1]}. (8)
We discuss the necessity and practical implications of this assumption in Section 3.2, and give examples satisfying these assumptions in Remarks 2 and 3. Notice that a trivial class with a single constant zero function satisfies both inclusion and label invariance conditions. For example, we can choose and also choose to set either or , in which case only needs to satisfy either one of the conditions in Assumption 1. The flexibility that we gain by allowing the set addition is critical in applying these conditions to practical discriminators, especially in proving Remark 2. Note that in the inclusion condition in Eq. 7, we require the condition to hold for all max-norm bounded set: . The reason a weaker condition of all row-stochastic matrices, , does not suffice is that in order to prove the upper bound in Eq. 9, we need to apply the invariance condition to . This matrix is not row-stochastic, but still max-norm bounded.
We first show that Assumption 1 is sufficient for approximability of the neural network distance from corrupted samples. For two distributions and on , let and be the corresponding corrupted distributions respectively, where the label is passed through the noisy channel defined by the confusion matrix , i.e. .
###### Theorem 2.
If a class of functions satisfies Assumption 1, then
(9)
where we follow the convention that if is not full rank.
We refer to Appendix E for a proof. This gives a sharp characterization on how two distances are related: the one we can minimize in training RCGAN (i.e. ) and the true measure of closeness (i.e. ). Although the latter cannot be directly evaluated or minimized, RCGAN is approximately minimizing the true neural network distance as desired.
The lower bound proves a special case of the data-processing inequality. Two random variables from
and get closer in neural network distance, when passed through a stochastic transformation. The upper bound puts a limit on how much closer and can get, depending on the noise level. This fundamental trade-off is captured by . Under the noiseless case where is the identity matrix, we have and we recover a trivial fact that the two distances are equal. On the other extreme, if is rank deficient, we use the convention that and the two distances can be arbitrarily different. The approximation factor of captures how much the space can shrink by the noise . This coincides with Theorem 1, where a similar trade-off was identified for the TV distance. Next remark shows that these bounds cannot be tightened for general , , and . A proof is provided in Appendix D.
###### Remark 1.
For any full-rank confusion matrix , there exist pairs of distributions and , and a function class satisfying Assumption 1, such that
• , and
• .
Theorem 2 shows that RCGAN can learn the true conditional distribution, justifying its use; and performance of RCGAN is determined by how noisy the samples are via . There are still two loose ends. First, does practical implementation of RCGAN architecture satisfy the inclusion and/or label invariance assumptions? Secondly, in practice we cannot minimize as we only have a finite number of samples. How much do we lose in this finite sample regime? We give precise answers to each question in the following two sections.
### 3.2 Inclusion and label invariance assumptions
Several class of functions satisfy Assumption 1 (c.f. Remark 3). For RCGAN, we propose a popular state-of-the-art discriminator for conditional GANs known as the projection discriminator [32], parametrized by , , and :
DV,v,θ(x,y)=vec(y)TVψ(x;θ)+vTψ′(x;θ), (10)
where and are vector valued parametric functions for some integers , and . The first term satisfies the inclusion condition, as any operation with can be absorbed into . The second term is label invariant as it does not depend on . This is made precise in the following remark, whose proof is provided in Appendix F. Together with this remark, the approximability result in Theorem 2 justifies the use of projection discriminators in RCGAN, which we use in all our experiments.
###### Remark 2.
The class of projection discriminators defined in Eq. 10 satisfies Assumption 1 for any , , and , if
Other choices of and are also possible. For example, or are also sufficient. We find the proposed choice of easy to implement, as a column-wise -norm normalization via projected gradient descent. We describe implementation details in Appendix I.
Next, we ask if Assumption 1 is necessary also. We show that for all pairs of distributions satisfying the following technical conditions, and all confusion matrix , there exists a class where approximation bounds in (9) fail.
###### Assumption 2.
We consider a pair of distributions and and a confusion matrix satisfying the following conditions:
• The random variable conditioned on
is a continuous random variable with density functions
and , respectively.
• There exists , and
is not a right eigenvector of
, for all , where .
A pair violating the above assumptions either has that is a mixture of continuous and discrete distribution, or all ’s are aligned with the right eigenvectors of .
###### Theorem 3.
For all sufficiently small , all distributions and satisfying Assumption 2, and all full-rank , there exist not satisfying Assumption 1, such that
dF3(˜P,˜Q)≤Oϵ(ϵ) and dF3(P,Q)≥Oϵ(1), (11)
and not satisfying Assumption 1, such that
dF4(˜P,˜Q)≥Oϵ(1) and dF4(P,Q)≤Oϵ(ϵ). (12)
We refer to Appendix G for a proof. This implies that some assumptions on the function class are necessary, such as those in Assumption 1. Without any restrictions, we can find bad examples where the two distances and are arbitrarily different for any , , and .
### 3.3 Finite sample analysis
In practice, we do not have access to the probability distributions
and . Instead, we observe a set of samples of a finite size , from each of them. In training GAN, we minimize the empirical neural network distance, , where and denote the empirical distribution of samples. Inspired from the recent generalization results in [3], we show that this empirical distance minimization leads to small up to an additive error that vanishes with an increasing sample size. As shown in [3], Lipschitz and bounded function classes are critical in achieving sample efficiency for GANs. We follow the same approach over a similar function class. Let
Fp,L={Du(x,y)∈[0,1]| Du(x,y) is L-Lipschitz in u and u∈U⊆Rp}, (13)
be a class of bounded functions with parameter . We say that is -Lipschitz in if
∣∣Du1(x,y)−Du2(x,y)∣∣≤L∥u1−u2∥,∀u1,u2∈U,x∈X,y∈[m]. (14)
###### Theorem 4.
For any class of bounded Lipschitz functions satisfying Assumption 1, there exists a universal constant such that
dFp,L(˜Pn,˜Qn)−ϵ≤dFp,L(P,Q)≤|||C−1|||∞(dFp,L(˜Pn,˜Qn)+ϵ), (15)
with probability at least for any and large enough,
We refer to Appendix H for a proof. This justifies the use of the proposed RCGAN which minimizes , as it leads to the generator being close to the real distribution in neural network distance, . These bounds inherit the approximability of the population version in Theorem 2.
## 4 Our second architecture: RCGAN-U
In many real world scenarios the confusion matrix is unknown. We propose RCGAN-Unknown (RCGAN-U) algorithm which jointly estimates the real distribution and the noise model . The pre-processing and D steps of the RCGAN-U are the same as those of RCGAN, assuming the current guess of the confusion matrix. As the G-step in (2) is not differentiable in , we use the following reparameterized estimator of the loss, motivated by similar technique in training classifiers from noisy labels:
minG∈G,M∈CEz∼Ny∼PY[ϕM(G(z;y),y,D)+λl(h∗(G(z;y)),y)]
where is the set of all transition matrices and .
## 5 Experiments
Implementation details are explained in Appendix I. We consider one-coin based models, which are parameterized by their label accuracy probability . In this model a sample with true label is flipped uniformly at random to label in with probability . The entries of its confusion matrix , will then be and , where is the number of classes. We call this model uniform flipping model. We train proposed GANs on MNIST and CIFAR- datasets [25, 24] and compare them to two baselines. Code to reproduce our experiments is available at https://github.com/POLane16/Robust-Conditional-GAN.
Baselines. First is the biased GAN, which is a conditional GAN applied directly on the noisy data. The loss is hence biased, and the true conditional distribution is not the optimal solution of this biased loss. Next natural baseline is using de-biased classifier as the discriminator, motivated by the approach of [34] on learning classifiers from noisy labels. The main insight is to modify the loss function according to , such that in expectation the loss matches that of the clean data. We refer to this approach as unbiased GAN. Concretely, when training the discriminator, we propose the following (modified) de-biased loss:
maxD∈FE(x,˜y)∼˜PX,˜Y[∑y∈[m](C−1)˜yyϕ(D(x,y))]+Ez∼Ny∼PY[ϕ(1−D(G(z;y),y))]. (16)
This is unbiased, as the first term is equivalent to , which is the standard GAN loss with clean samples. However, such de-biasing is sensitive to the condition number of , and can become numerically unstable for noisy channels as has large entries [20]. For both the dataset, we use linear classifiers for permutation regularizer of the RCGAN-U architecture.
### 5.1 Mnist
We train five architectures on MNIST dataset corrupted by the uniform flipping noise: RCGAN+y, RCGAN, RCGAN-U, unbiased GAN, and biased GAN. RCGAN+y architecture has the same architecture as RCGAN but the input to the first layer of its discriminator is concatenated with a one-hot representation of the label. We discuss our techniques to overcome the challenges involved in training RCGAN+y in Appendix I.
Conditional generators can be used to generate samples from a particular class , in the classes it learned. We then can use a pre-trained classifier to compare to the true class of the sample, (as perceived by the classifier ). We compare the generator label accuracy defined as , in Figure 2, left panel. We generated k labels chosen uniformly at random and corresponding conditional samples from the generators, and calculated the generator label accuracy using a CNN classifier pre-trained on the clean MNIST data to an accuracy of 99.2%. The proposed RCGAN significantly improves upon the competing baselines, and achieves almost perfect label accuracy until a high noise of . RCGAN+y further improves upon RCGAN and to gain very high accuracy even at . The high accuracy of RCGAN-U suggests that robust training is possible without prior knowledge of the confusion matrix . As expected, biased GAN has an accuracy of approximately .
An immediate application of robust GANs is recovering the true labels of the noisy training data, which is an important and challenging problem in crowdsourcing. We propose a new meta-algorithm, which we call cGAN-label-recovery, which use any conditional generator trained on the noisy samples, to estimate the true label, as , of a sample using the following optimization.
(17)
In the right panel of Figure 2 we compare the label recovery accuracy of the meta-algorithm using the five conditional GANs, on randomly chosen noisy training samples. This is also compared to a state-of-the-art method [34] for label recovery, which proposed minimizing unbiased loss function given the noisy labels and the confusion matrix. This unbiased classifier, was shown to outperforms the robust classifiers [29, 45, 46] and can be used to predict the true label of the training examples. In Figures 4 of Appendix J, we show example images from all the generators.
### 5.2 Cifar-10
In Figure 3, we show the inception score [40] and the label accuracy of the conditional generator for the four approaches: our proposed RCGAN and RCGAN-U, against the baselines Unbiased (Section 5) and Biased (Section 1) GANs trained using CIFAR- images [24], while varying the label accuracy of the real data under uniform flipping. In RCGAN-U, even with the regularizer, the learned confusion matrix was a permuted version of the true , possibly because a linear classifier might be too simple to classify CIFAR images. To combat this, we initialized the confusion matrix to be diagonally dominant (Appendix I).
In the left panel of Figure 3, our RCGAN and RCGAN-U consistently achieve higher inception scores than the other two approaches. The Unbiased GAN is highly unstable and hence produces garbage images for large noise (Fig. 5), possibly due to numerical instability of , as noted in [20]. This confirms that robust GANs not only produce images from the correct class, but also produce better quality images. In the right panel of Figure 3, we report the generator label accuracy (Section 5.1) on k samples generated by each GAN. We classify the generator images using a ResNet- model trained to an accuracy of on the noiseless CIFAR- dataset111https://github.com/wenxinxu/resnet-in-tensorflow. Biased GAN has significantly lower label accuracy whereas the Unbiased GAN has low inception score. In Figure 5 in Appendix J, we show example images from the three generators for the different flipping probabilities. We believe that the gain in using the proposed robust GANs will be larger, when we train to higher accuracy with larger networks and extensive hyper parameter tuning, with latest innovations in GAN architectures, for example [54, 28, 17, 19, 41].
## 6 Numerical comparisons with AmbientGAN [10]
In Table 1, we plot the generated label accuracy (as defined in Section 5.1) of RCGAN (which uses the proposed projection discriminator) and AmbientGAN (which uses the DCGAN with no projection discriminator) for multiple values of noise levels (). One of the main reasons for the performance drop of AmbientGAN is that without the projection discriminator, training of AmbientGAN is sensitive to how the mini-batches are chosen. For example, if the distribution of the labels in the mini-batch of the real data is different from that of the mini-batch of the generated data, then the performance of (conditional) AmbientGAN significantly drops. This is critical as we have noisy labels, and matching the labels is in the mini-batch is challenging. Our proposed RCGAN provides an architecture and training methods for applying AmbientGAN to noisy labeled data, to overcome theses challenges. When a projection discriminator is used, as in all our RCGAN and RCGAN-U implementations, the performance is not sensitive to how the mini-batches are sampled. When a discriminator that is not necessarily a projection discriminator is used, as in our RCGAN+ architecture, we propose a novel scheduling of the training, which avoids local minima resulting from mis-matched mini-batches (explained in Appendix I). The results are averaged over 10 instances.
## 7 Conclusion
Standard conditional GANs can be sensitive to noise in the labels of the training data. We propose two new architectures to make them robust, one requiring the knowledge of the distribution of the noise and another which does not, and demonstrate the robustness on benchmark datasets of CIFAR-10 and MNIST. We further showcase how the learned generator can be used to recover the corrupted labels in the training data, which can potentially be used in practical applications. The proposed architecture combines the noise adding idea of AmbientGAN [10], projection discriminator of [32], and regularizers similar to those in InfoGAN [11]. Inspired by AmbientGAN [10], the main idea is to pair the generator output image with a label that is passed through a noisy channel, before feeding to the discriminator. We justify this idea of noise adding by identifying a certain class of discriminators that have good generalization properties. In particular, we prove that projection discriminator, introduced in [32], has a good generalization property. We showcase that the proposed architecture, when trained with a regularizer, has superior robustness on benchmark datasets.
One weakness of our theoretical result in Theorem 4 is that depending on the choice of (i.e. the representation power of the parametric class ), closeness in the neural network distance does not always imply closeness of the distributions. It is generally a challenging problem to address generalization for specific function class and a pair of distributions and . However, a recent breakthrough in generalization properties of GAN in [4] makes the connection between and precise, under some assumptions on the and . This leads to the following research question: under which class of distributions and does the neural network distance of the proposed conditional GAN with projection discriminator generalize? The emphasis is in studying the class of functions satisfying Assumption 1 and identifying corresponding family of distributions that generalize under this function class.
## Acknowledgement
This work is supported by NSF awards CNS-1527754, CCF-1553452, CCF-1705007, RI-1815535 and Google Faculty Research Award. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575. Specifically, it used the Bridges system, which is supported by NSF award number ACI-1445606, at the Pittsburgh Supercomputing Center (PSC). This work is partially supported by the generous research credits on AWS cloud computing resources from Amazon.
## Appendix A Notations and Lemmas
### a.1 Additional Notation
Here we define some additional notations required for the proof. We define certain notations before we provide the main theoretical contributions of our paper. If is a function of two variable of , where , then is the vector . If is probability distribution of , then is the conditional distribution of given .
For a matrix , let . Then , and , the maximum singular value. is all ones vector with appropriate dimensions and is identity matrix with appropriate dimensions. . For a vector , () is its -th coordinate.
For the sake of proof we will assume that is class of vector functions of the form . In terms of the notation in the main material original is here. For a class of vector valued functions . Therefore we re-define the operation between a matrix and as,
T∘F={TD(⋅)|f(⋅)∈F}.
If is probability distribution of , then is the conditional discrete distribution of given , is the marginal density of , and
¯¯¯¯PY|X=x =[PY|X=x(Y=1),PY|X=x(Y=1),…,PY|X=x(Y=m)]T, and (18) ¯¯¯¯¯¯pX(x) =pX(x)¯¯¯¯PY|X=x (19)
### a.2 Supporting Lemmas
###### Lemma 1 (Characterization of neural network distance).
for all . And if is a convex or concave function, then the Neural network distance is when the distributions are same, i.e. .
###### Proof.
For concave we define . Since, by definition is feasible solution to the optimization problem in (5), thus .
dF,ϕ(P,P)= ≤ supD∈F2ϕ(E(x,y)∼P[12(D(x)y+1−D(x)y)])−2ϕ(1/2) = supD∈F2ϕ(1/2)−2ϕ(1/2)=0
The inequality in second line follows from Jensen’s inequality for concave .
For convex we define . Since, by definition is feasible solution to the optimization problem in (5), thus .
dF,ϕ(P,P) =supD∈FE(x,y)∼P[ϕ(D(x)y)+ϕ(1−D(x)y)]−(ϕ(0)+ϕ(1)) ≤supD∈FE(x,y)∼P[ϕ(0)+ϕ(1)]−(ϕ(0)+ϕ(1))=0
The last inequality follows from Jensen’s inequality for convex
This Lemma 1 ensures that all the multiplicative lower bounds and upper bounds in Theorem 3 and its corollaries implies recoverability.
###### Lemma 2.
If is a distributions on and is the distribution of sample of when passed through the noisy-channel given by the confusion matrix (as defined in Section 1). Then,
¯¯¯¯¯˜P˜Y|X=x=CT¯¯¯¯PY|X=x, (20)
where .
###### Proof.
˜P˜Y|X=x(˜Y=j) =∑i∈[m]P(˜Y=j|Y=i)PY|X=x(Y=j),∀j∈[m] ˜P˜Y|X=x(˜Y=j) =∑i∈[m]CijPY|X=x(Y=j),∀j∈[m] ¯¯¯¯¯˜P˜Y|X=x =CT¯¯¯¯PY|X=x
## Appendix B Proof of Theorem 1
We first prove the approximation bounds for total variation distance in Eq. (3), and then use it to prove similar bounds for the Jensen-Shannon divergence in Eq. (4). Recall that total variation distance between and can be written in several ways:
dTV(P,Q) = maxS1,…,Sm∑y∈[m]P(Sy,y)−Q(Sy,y) = maxS1,…,Sm∑y∈[m]|P(Sy,y)−Q(Sy,y)| = maxS1,…,Sm∥P({Sy}y∈[m],⋅)−Q({Sy}y∈[m],⋅)∥1,
where we used the notation of a row-vector . The lower bound on follows that
dTV(P,Q) = = maxS1,…,Sm⊆X⟨1,P({Sy}y∈[m],⋅)−Q({Sy}y∈[m],⋅)⟩ (a)= maxS1,…,Sm⊆X⟨1,(˜P({Sy}y∈[m],⋅)−˜Q({Sy}y∈[m],⋅))C−1⟩ (b)≤ |||C−T|||1maxS1,…,Sm⊆X∥∥˜P({Sy}y∈[m],⋅)−˜Q({Sy}y∈[m],⋅)∥∥1 (c)= |||C−1|||∞dTV(˜P,˜Q),
where follows from the fact that , follows from the fact that , and follows from . The upper bound follows from similar arguments:
dTV(˜P,˜Q) ≤|||CT|||1maxS1,…,Sm⊆X∥∥P({Sy}y∈[m],⋅)−Q({Sy}y∈[m],⋅)∥∥1 =dTV(P,Q)
where last equality uses the fact that
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2019-12-14 02:24:30
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https://www.futurelearn.com/courses/intro-to-quantum-computing/0/steps/31565
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1.15
## Keio University
Skip to 0 minutes and 4 secondsOne of the most important concepts you must grasp to understand quantum computing is the superposition and interference of waves. Since waves are moving through space, you can have more than one wave passing through one place at the same time. When that happens, the waves add up or superimpose on one another. Imagine, we have a wave like this and another wave of a slightly different frequency like this. It doesn’t matter if they are light waves or water waves, it’s the same. If we take the two waves and we add them up, we get a pattern like this.
Skip to 0 minutes and 42 secondsYou can see that on the left, the waves are almost lined up, which we call “being in phase,” and so their peaks add up. This is called “constructive interference.” On the right, one wave is positive where the other is negative, which we call “being out of phase,” and the two waves cancel out. This is called “destructive interference.” When we let the waves run longer, you can see that the interference grows and shrinks. This growing and shrinking pattern is called “beating.” The figures show the waves moving up and down, but in sound the air moves back and forth instead but the principle is exactly the same. Let's see if we can hear that beating pattern in sound.
Skip to 1 minute and 24 secondsWelcome Shinnosuke Ozawa, one of my students, and a talented bass guitar player. I am happy to be here. Good. So with the bass guitar, you adjust the tension on the strings using these pins and that adjusts the sound or the frequency at which the strings vibrate. First, let’s hear your bass guitar in tune. Play one note for me.
Skip to 1 minute and 54 secondsOkay, that’s an A, right? Yes. I think that’s 360 hertz if I did the calculation right. Now, by placing his fingers on the fret, he can play the same note on two different strings. Let’s hear the two strings together.
Skip to 2 minutes and 15 secondsvery nice. Now, we take one of those strings and put it just slightly out of tune with the other, if we are lucky, we will be able to hear the interference between the two types of waves. Let’s try that. Put one string a little bit out of tune here and see what happens.
Skip to 2 minutes and 44 secondsYeah, that’s fantastic. Did you hear that? As the frequency of the two strings got closer and closer together the beating got longer and slower until finally it stopped and they were in tune together. Thanks. You're welcome The amount of interference we get depends on both the amplitude, how strong the wave is and the phase, whether it's near the beginning, middle or end of its cycle. When waves are propagating through space, the distance they have to travel depends on the angle and the phase in turn depends on that distance. If we have one source, we can see the waves radiating out in every direction.
Skip to 3 minutes and 29 secondsIf we have two sources, we can see the waves radiating out in every direction and in some places those waves reinforce and in others they cancel giving us constructive and destructive interference. In the applications and animations in the article accompanying this video, you can explore interference in detail.
# Superposition and Interference
One of the most important concepts you must grasp to understand quantum computing is the superposition and interference of waves. Since waves are moving through space, you can have more than one wave passing through one place at the same time. When that happens, the wave add up, or superimpose on one another.
In addition to the video, we have prepared a set of applications for you to play with, and we have made the 3-D models in the video available.
## One-dimensional interference
In the upcoming application, you will have the opportunity to see the following behaviors:
1. constructive interference
2. destructive interference
3. “beats” with different frequencies
This will be followed by a quiz with questions that can be answered using the application.
## 2-dimensional interference
Interference can happen in more than one dimension. If we have two sources that are each sending out a sine wave, it might look something like this, if the waves stay the same height as they move away:
After the 1-D interference application and quiz, you will see an application demonstrating 2-D interference, as well.
To aid the vision-impaired, or for those who just enjoy 3-D printing, we have created some 3-D printable models representing some of the key concepts. You saw these models in the video, feel free to print your own.
Most 3-D printing software can handle a file type known as STL. Here, we provide an STL file for you to print, or the source code in a language called OpenSCAD, if you would like to modify the shape.
• A single wave source radiating in two dimensions, with $1/r$ decay of amplitude
• Two wave sources radiating in two dimensions demonstrating interference, with $1/r$ decay of amplitude
## $N$-dimensional interference
Humans can’t effectively visualize more than three dimensions, but in fact a quantum computer creates interference across many different variables, which we can treat as separate dimensions. We will see this effect when we discuss quantum algorithms in Week 3.
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2019-07-21 17:43:32
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https://www.physicsforums.com/threads/solving-an-equation.551973/
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Homework Help: Solving an equation
1. Nov 19, 2011
Ted123
Solve the equation $$x^4 - x^2 = k$$ where $k>0$.
Am I being thick or how do I solve this for $x$?
Factorising gives $$x^2(x^2-1)=k$$ but now where?
2. Nov 19, 2011
HallsofIvy
Let $y= x^2$ and that becomes a quadratic function:
$y^2- y= k$ or $y^2- y- k= 0$. Solve that for y, then solve $x^2= y$ for x.
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2018-06-23 22:30:58
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https://zbmath.org/serials/?q=se%3A4889
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## ALEA. Latin American Journal of Probability and Mathematical Statistics
Short Title: ALEA, Lat. Am. J. Probab. Math. Stat. Publisher: Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro ISSN: 1980-0436/e Online: http://alea.impa.br/english/ Comments: Indexed cover-to-cover; Published electronic only as of Vol. 1 (2006). This journal is available open access.
Documents Indexed: 607 Publications (since 2006) References Indexed: 301 Publications with 8,356 References.
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### Latest Issues
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### Authors
8 Lanchier, Nicolas 7 Möhle, Martin 6 Merlevède, Florence 6 Peccati, Giovanni 5 Hartung, Lisa Bärbel 5 Mountford, Thomas S. 5 Popov, Serguei Yu. 5 Seppäläinen, Timo 5 Thäle, Christoph 5 Tudor, Ciprian A. 4 Broman, Erik Ivar 4 Cerf, Raphaël 4 Dedecker, Jérôme 4 Gantert, Nina 4 Hasebe, Takahiro 4 Kabluchko, Zakhar A. 4 Miclo, Laurent 4 Peligrad, Magda 4 Pfaffelhuber, Peter 4 Pimentel, Leandro P. R. 4 Procaccia, Eviatar Ben 4 Raimond, Olivier 4 Valesin, Daniel 4 Zhang, Yuan 3 Abraham, Romain 3 Aldous, David John 3 Balan, Raluca M. 3 Barndorff-Nielsen, Ole Eiler 3 Bertini, Lorenzo Bertini 3 Biermé, Hermine 3 Cai, Xing Shi 3 Cattiaux, Patrick 3 Delmas, Jean-François 3 den Hollander, Frank 3 Dolgopyat, Dmitry 3 Doukhan, Paul 3 Durrett, Richard Timothy 3 Estrade, Anne 3 Giacomin, Giambattista 3 Gouéré, Jean-Baptiste 3 Greven, Andreas 3 Jonasson, Johan 3 Junge, Matthew 3 Kozma, Gady 3 Kyprianou, Andreas E. 3 León, José Rafael R. 3 Mallein, Bastien 3 Malrieu, Florent 3 Matzinger, Heinrich III 3 Mytnik, Leonid 3 Newman, Charles Michael 3 Nourdin, Ivan 3 Pardo, Juan Carlos 3 Peres, Yuval 3 Peterson, Jonathon 3 Saloff-Coste, Laurent 3 Sato, Ken-iti 3 Schapira, Bruno 3 Sethuraman, Sunder 3 Smadi, Charline 3 Steif, Jeffrey E. 3 Tóbiás, András 3 Tykesson, Johan Harald 3 Valle da Silva Coelho, Glauco 3 Xue, Xiaofeng 3 Zeitouni, Ofer 2 Asselah, Amine 2 Azaïs, Jean-Marc 2 Azmoodeh, Ehsan 2 Balazs, Marton 2 Bálint, András 2 Barbour, Andrew David 2 Basdevant, Anne-Laure 2 Baur, Erich 2 Beffara, Vincent 2 Ben-Ari, Iddo 2 Benjamini, Itai 2 Berestycki, Julien 2 Berger, Noam 2 Berger, Quentin 2 Bertacchi, Daniela 2 Berzunza Ojeda, Gabriel Hernán 2 Birkner, Matthias 2 Bovier, Anton 2 Caputo, Pietro 2 Cator, Eric A. 2 Čekanavičius, Vydas 2 Cérou, Frédéric 2 Chafaï, Djalil 2 Champagnat, Nicolas 2 Chatterjee, Sourav 2 Cipriani, Alessandra 2 Clark, Jeremy Thane 2 Comets, Francis M. 2 Cuny, Christophe 2 Daly, Fraser 2 Di Crescenzo, Antonio 2 Diaconis, Persi Warren 2 Disertori, Margherita 2 Döbler, Christian ...and 798 more Authors
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581 Probability theory and stochastic processes (60-XX) 127 Statistical mechanics, structure of matter (82-XX) 58 Statistics (62-XX) 57 Combinatorics (05-XX) 34 Biology and other natural sciences (92-XX) 27 Partial differential equations (35-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 13 Dynamical systems and ergodic theory (37-XX) 13 Functional analysis (46-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Numerical analysis (65-XX) 9 Measure and integration (28-XX) 7 Operator theory (47-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Convex and discrete geometry (52-XX) 5 Potential theory (31-XX) 5 Ordinary differential equations (34-XX) 5 Computer science (68-XX) 3 Group theory and generalizations (20-XX) 3 Functions of a complex variable (30-XX) 3 Special functions (33-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 General topology (54-XX) 3 Fluid mechanics (76-XX) 3 Operations research, mathematical programming (90-XX) 3 Information and communication theory, circuits (94-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Differential geometry (53-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)
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Hitting probabilities for systems of nonlinear stochastic heat equations with additive noise. Zbl 1170.60322
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Nonlinear SDEs driven by Lévy processes and related PDEs. Zbl 1162.60327
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Central limit theorems for additive functionals of ergodic Markov diffusions processes. Zbl 1277.60047
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Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing. Zbl 1361.60067
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On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion. Zbl 1162.60347
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Refined estimates for some basic random walks on the symmetric and alternating groups. Zbl 1171.60008
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2017
On Stein’s method and perturbations. Zbl 1121.62016
Barbour, A. D.; Čekanavičius, Vydas; Xia, Aihua
2007
On the precision of the spectral profile. Zbl 1162.60335
2007
$$q$$-invariant functions for some generalizations of the Ornstein-Uhlenbeck semigroup. Zbl 1168.60011
Patie, P.
2008
General $$\Upsilon$$-transformations. Zbl 1168.60007
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2008
On the exponential functional of Markov additive processes, and applications to multi-type self-similar fragmentation processes and trees. Zbl 1414.60022
Stephenson, Robin
2018
TASEP with discontinuous jump rates. Zbl 1276.60113
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2010
The critical value of the Deffuant model equals one half. Zbl 1277.60178
Lanchier, Nicolas
2012
Conditions for exchangeable coalescents to come down from infinity. Zbl 1277.60122
Herriger, Philip; Möhle, Martin
2012
Concerns with functional depth. Zbl 1277.60049
Kuelbs, James; Zinn, Joel
2013
Kernel density estimation for stationary random fields. Zbl 1291.62083
El Machkouri, Mohamed
2014
Contact processes with random vertex weights on oriented lattices. Zbl 1327.60195
Xue, Xiaofeng
2015
Variable speed branching Brownian motion. I: Extremal processes in the weak correlation regime. Zbl 1321.60173
Bovier, Anton; Hartung, Lisa
2015
Bounds for left and right window cutoffs. Zbl 1346.60040
Barrera, Javiera; Ycart, Bernard
2014
A supersymmetric approach to martingales related to the vertex-reinforced jump process. Zbl 1364.60068
Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W.
2017
Deviation from mean in sequence comparison with a periodic sequence. Zbl 1140.60044
Matzinger, Heinrich; Lember, Jüri; Durringer, Clement
2007
Weyl chambers, symmetric spaces and number variance saturation. Zbl 1112.58038
Jones, Liza; O’Connell, Neil
2006
First passage of reflected strictly stable processes. Zbl 1113.60050
Kyprianou, A. E.
2006
Fluctuations of the longest common subsequence in the asymmetric case of 2- and 3-letter alphabets. Zbl 1105.62021
Bonetto, Federico; Matzinger, Heinrich
2006
Independence of four projective criteria for the weak invariance principle. Zbl 1169.60005
Durieu, Olivier
2009
Generalized divide and color models. Zbl 1488.60244
Steif, Jeffrey E.; Tykesson, Johan
2019
Spectrum of large random reversible Markov chains: two examples. Zbl 1276.15016
Bordenave, Charles; Caputo, Pietro; Chafaï, Djalil
2010
Blow-up for a system with time-dependent generators. Zbl 1276.60071
Pérez, Aroldo; Villa, José
2010
Visibility to infinity in the hyperbolic plane, despite obstacles. Zbl 1276.82012
Benjamini, Itai; Jonasson, Johan; Schramm, Oded; Tykesson, Johan
2009
On the largest-eigenvalue process for generalized Wishart random matrices. Zbl 1276.60008
Dieker, A. B.; Warren, J.
2009
Stochastic Schrödinger equations and applications to Ehrenfest-type theorems. Zbl 1277.60108
Fagnola, F.; Mora, C. M.
2013
Fluctuation exponents for stationary exactly solvable lattice polymer models via a Mellin transform framework. Zbl 1390.60344
Chaumont, Hans; Noack, Christian
2018
On the block counting process and the fixation line of exchangeable coalescents. Zbl 1346.60124
Gaiser, Florian; Möhle, Martin
2016
Exponential functionals of Lévy processes with jumps. Zbl 1321.60092
Behme, Anita
2015
$$\beta$$-coalescents and stable Galton-Watson trees. Zbl 1321.60170
Abraham, Romain; Delmas, Jean-François
2015
The lower tail problem for homogeneous functionals of stable processes with no negative jumps. Zbl 1145.60027
Simon, Thomas
2007
Asymptotic behaviour of exponential functionals of Lévy processes with applications to random processes in random environment. Zbl 1355.60061
Palau, Sandra; Pardo, Juan Carlos; Smadi, Charline
2016
Convergence to the viscous porous medium equation and propagation of chaos. Zbl 1180.35592
Figalli, Alessio; Philipowski, Robert
2008
New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods. Zbl 1331.60047
Döbler, Christian
2015
Uniform LAN property of locally stable Lévy process observed at high frequency. Zbl 1331.60078
Ivanenko, Dmytro; Kulik, Alexey M.; Masuda, Hiroki
2015
The $$\beta$$-Delaunay tessellation. III: Kendall’s problem and limit theorems in high dimensions. Zbl 1483.52003
Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph
2022
Bound on the running maximum of a random walk with small drift. Zbl 1480.60106
Busani, Ofer; Seppäläinen, Timo
2022
Comparing the inversion statistic for distribution-biased and distribution-shifted permutations with the geometric and the GEM distributions. Zbl 1480.60014
Pinsky, Ross G.
2022
Probability of consensus in spatial opinion models with confidence threshold. Zbl 1484.60110
Hardin, Mela; Lanchier, Nicolas
2022
Convex minorants and the fluctuation theory of Lévy processes. Zbl 07565955
González Cázares, Jorge Ignacio; Mijatović, Aleksandar
2022
Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution. Zbl 1458.37009
Champagnat, Nicolas; Villemonais, Denis
2021
Phase transitions for degenerate random environments. Zbl 1468.60118
Holmes, Mark; Salisbury, Thomas S.
2021
On the speed of distance-stationary sequences. Zbl 1469.60314
Carrasco, Matías; Lessa, Pablo; Paquette, Elliot
2021
Ballistic random walks in random environment as rough paths: convergence and area anomaly. Zbl 1469.60361
Lopusanschi, Olga; Orenshtein, Tal
2021
Fluctuations of nodal sets on the 3-torus and general cancellation phenomena. Zbl 1468.60062
Notarnicola, Massimo
2021
On distance covariance in metric and Hilbert spaces. Zbl 1470.62073
Janson, Svante
2021
Stationary harmonic measure as the scaling limit of truncated harmonic measure. Zbl 1468.60124
Procaccia, Eviatar B.; Ye, Jiayan; Zhang, Yuan
2021
Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices. Zbl 1456.15033
Capitaine, Mireille; Donati-Martin, Catherine
2021
A stochastic Gronwall lemma and well-posedness of path-dependent SDEs driven by martingale noise. Zbl 1468.60074
Mehri, Sima; Scheutzow, Michael
2021
Percolation for the finitary random interlacements of random spherical harmonics. Zbl 1468.60123
Procaccia, Eviatar B.; Ye, Jiayan; Zhang, Yuan
2021
Critical parameters for loop and Bernoulli percolation. Zbl 1466.60212
Mühlbacher, Peter
2021
Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficients. Zbl 1469.60245
Hutzenthaler, Martin; Pieper, Daniel
2021
On 3-dimensional Berry’s model. Zbl 1465.60022
Dalmao, Federico; Estrade, Anne; León, José R.
2021
Mixing properties of integer-valued GARCH processes. Zbl 1464.62380
Doukhan, Paul; Khan, Naushad Mamode; Neumann, Michael H.
2021
Emergence of homogamy in a two-loci stochastic population model. Zbl 1465.92085
Coron, Camille; Costa, Manon; Laroche, Fabien; Leman, Hélène; Smadi, Charline
2021
Modified log-Sobolev inequalities and two-level concentration. Zbl 1469.60068
Sambale, Holger; Sinulis, Arthur
2021
Spatial averages for the parabolic Anderson model driven by rough noise. Zbl 1464.60019
Nualart, David; Song, Xiaoming; Zheng, Guangqu
2021
Ergodicity of the KPZ fixed point. Zbl 1468.60122
Pimentel, Leandro P. R.
2021
A probabilistic proof of Cooper & Frieze’s “First Visit Time Lemma”. Zbl 1482.60099
Manzo, Francesco; Quattropani, Matteo; Scoppola, Elisabetta
2021
Some simple variance bounds from Stein’s method. Zbl 1482.60024
2021
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: convergence of the maximum in the regime of weak correlations. Zbl 1480.60091
Fels, Maximilian; Hartung, Lisa
2021
A note on the universality of ESDs of inhomogeneous random matrices. Zbl 1469.60033
Jain, Vishesh; Silwal, Sandeep
2021
Contraction principle for trajectories of random walks and Cramér’s theorem for kernel-weighted sums. Zbl 1472.60053
2021
On the local limit theorems for psi-mixing Markov chains. Zbl 1478.60090
2021
Long time asymptotics of heat kernels and Brownian winding numbers on manifolds with boundary. Zbl 1470.35169
Geng, Xi; Iyer, Gautam
2021
A general stochastic matching model on multigraphs. Zbl 1472.05123
Begeot, Jocelyn; Marcovici, Irène; Moyal, Pascal; Rahme, Youssef
2021
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: extremal process in the weakly correlated regime. Zbl 1471.60048
Fels, Maximilian; Hartung, Lisa
2021
Moderate deviation estimates for nodal lengths of random spherical harmonics. Zbl 1466.60061
Macci, Claudio; Rossi, Maurizia; Todino, Anna Paola
2021
Multiscale functional inequalities in probability: concentration properties. Zbl 1456.60053
Duerinckx, Mitia; Gloria, Antoine
2020
The contact process on random graphs and Galton Watson trees. Zbl 1439.60082
Huang, Xiangying; Durrett, Rick
2020
Delayed and rushed motions through time change. Zbl 1446.60032
Capitanelli, Raffaela; D’Ovidio, Mirko
2020
Optimal gamma approximation on Wiener space. Zbl 1471.60024
Azmoodeh, Ehsan; Eichelsbacher, Peter; Knichel, Lukas
2020
On the anisotropic stable JCIR process. Zbl 1459.60123
Friesen, Martin; Jin, Peng
2020
Signal-to-interference ratio percolation for Cox point processes. Zbl 1439.82017
Tóbiás, András
2020
Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. Zbl 1441.82017
Erbar, Matthias; Fathi, Max; Schlichting, André
2020
F-KPP scaling limit and selection principle for a Brunet-Derrida type particle system. Zbl 1448.60186
Groisman, Pablo; Jonckheere, Matthieu; Martínez, Julián
2020
High-dimensional sample covariance matrices with Curie-Weiss entries. Zbl 1454.60013
Fleermann, Michael; Heiny, Johannes
2020
Transience and recurrence of Markov processes with constrained local time. Zbl 1472.60133
2020
Large deviations for local mass of branching Brownian motion. Zbl 1453.60146
Öz, Mehmet
2020
Hydrodynamics for SSEP with non-reversible slow boundary dynamics. II: Below the critical regime. Zbl 1453.60155
Erignoux, C.; Gonçalves, P.; Nahum, G.
2020
Adaptive recursive kernel conditional density estimators under censoring data. Zbl 1442.62072
Slaoui, Yousri; Khardani, Salah
2020
Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity. Zbl 1456.60176
Diaconis, Persi; Houston-Edwards, Kelsey; Saloff-Coste, Laurent
2020
Differentiability of the speed of biased random walks on Galton-Watson trees. Zbl 1450.60047
2020
Anisotropic Gaussian wave models. Zbl 1443.60049
2020
Hermite density deconvolution. Zbl 1442.62071
Sacko, Ousmane
2020
Kinetic walks for sampling. Zbl 1451.60082
Monmarché, Pierre
2020
A weak overdamped limit theorem for Langevin processes. Zbl 1439.60075
Rousset, Mathias; Xu, Yushun; Zitt, Pierre-André
2020
Dynamical coupling between Ising and FK percolation. Zbl 1471.60146
Cerf, Raphaël; Louhichi, Sana
2020
Poisson and Gaussian fluctuations for the components of the $$\mathbf{f}$$-vector of high-dimensional random simplicial complexes. Zbl 1453.60014
Grygierek, Jens
2020
Limit theorems for random simplices in high dimensions. Zbl 1456.52006
Grote, Julian; Kabluchko, Zakhar; Thäle, Christoph
2019
Berry-Esseen bounds for parameter estimation of general Gaussian processes. Zbl 1423.60041
Douissi, Soukaina; Es-Sebaiy, Khalifa; Viens, Frederi G.
2019
Generalized divide and color models. Zbl 1488.60244
Steif, Jeffrey E.; Tykesson, Johan
2019
Trajectories in random minimal transposition factorizations. Zbl 1423.60023
Féray, Valentin; Kortchemski, Igor
2019
Subordinators which are infinitely divisible w.r.t. time: construction, properties, and simulation of max-stable sequences and infinitely divisible laws. Zbl 1488.60123
Mai, Jan-Frederik; Scherer, Matthias
2019
New Bernstein and Hoeffding type inequalities for regenerative Markov chains. Zbl 1411.62112
Bertail, Patrice; Ciołek, Gabriela
2019
Fast-reaction limit for Glauber-Kawasaki dynamics with two components. Zbl 1488.60229
De Masi, A.; Funaki, T.; Presutti, E.; Vares, M. E.
2019
Viscosity solutions to Hamilton-Jacobi-Bellman equations associated with sublinear Lévy(-type) processes. Zbl 1419.82045
Kühn, Franziska
2019
Regularity of biased 1D random walks in random environment. Zbl 1434.60308
Faggionato, Alessandra; Salvi, Michele
2019
A probabilistic approach to block sizes in random maps. Zbl 1405.60014
2019
Poisson percolation on the square lattice. Zbl 1481.60015
Cristali, Irina; Junge, Matthew; Durrett, Rick
2019
Connection probabilities in Poisson random graphs with uniformly bounded edges. Zbl 1488.60125
Faggionato, Alessandra; Mimun, Hlafo Alfie
2019
The first exit problem of reaction-diffusion equations for small multiplicative Lévy noise. Zbl 1423.60100
Högele, Michael Anton
2019
Fractional iterated Ornstein-Uhlenbeck processes. Zbl 1432.62300
Kalemkerian, Juan; León, José Rafael
2019
Local limit theorems and mod-$$\phi$$ convergence. Zbl 1418.82008
Dal Borgo, Martina; Méliot, Pierre-Loïc; Nikeghbali, Ashkan
2019
Weak convergence on Wiener space: targeting the first two chaoses. Zbl 1405.60032
Krein, Christian
2019
An optimal Berry-Esseen type theorem for integrals of smooth functions. Zbl 1423.60035
Mattner, Lutz; Shevtsova, Irina
2019
Quadratic fluctuations of the symmetric simple exclusion. Zbl 1423.60155
Gonçalves, Patrícia; Jara, Milton
2019
Functional convergence for moving averages with heavy tails and random coefficients. Zbl 1423.60060
Krizmanić, Danijel
2019
Visibility in the vacant set of the Brownian interlacements and the Brownian excursion process. Zbl 1488.60231
Elias, Olof; Tykesson, Johan
2019
On a gateway between the Laguerre process and dynamics on partitions. Zbl 1447.60015
Assiotis, Theodoros
2019
The upper threshold in ballistic annihilation. Zbl 1488.60227
Burdinski, Debbie; Gupta, Shrey; Junge, Matthew
2019
Metastable behavior of bootstrap percolation on Galton-Watson trees. Zbl 1439.60095
Shapira, Assaf
2019
Longest increasing paths with gaps. Zbl 1439.60089
Basdevant, Anne-Laure; Gerin, Lucas
2019
Random cover times using the Poisson cylinder process. Zbl 1439.60090
Broman, Erik I.; Mussini, Filipe
2019
Connectivity properties of branching interlacements. Zbl 1406.60121
Procaccia, Eviatar B.; Zhang, Yuan
2019
Poisson statistics at the edge of Gaussian $$\beta$$-ensemble at high temperature. Zbl 1422.60018
2019
On the semimartingale property of Brownian bridges on complete manifolds. Zbl 1407.82051
Güneysu, Batu
2019
Subdiffusivity of Brownian motion among a Poissonian field of moving traps. Zbl 1405.60153
Öz, Mehmet
2019
Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model. Zbl 1405.60070
Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W.
2019
A Gibbsian model for message routeing in highly dense multihop networks. Zbl 1405.60039
König, Wolfgang; Tóbiás, András
2019
Transition density estimates for diagonal systems of SDEs driven by cylindrical $$\alpha$$-stable processes. Zbl 1414.60044
2018
Stable Lévy processes, self-similarity and the unit ball. Zbl 1396.60051
Kyprianou, Andreas E.
2018
Path stability of stochastic differential equations driven by time-changed Lévy noises. Zbl 06866535
Nane, Erkan; Ni, Yinan
2018
Transition to shocks in TASEP and decoupling of last passage times. Zbl 1414.60081
Nejjar, Peter
2018
On the exponential functional of Markov additive processes, and applications to multi-type self-similar fragmentation processes and trees. Zbl 1414.60022
Stephenson, Robin
2018
Fluctuation exponents for stationary exactly solvable lattice polymer models via a Mellin transform framework. Zbl 1390.60344
Chaumont, Hans; Noack, Christian
2018
Conditioned limit theorems for products of positive random matrices. Zbl 1388.60032
Pham, Thi Da Cam
2018
A technical report on hitting times, mixing and cutoff. Zbl 1388.60137
Hermon, Jonathan
2018
Almost sure growth of supercritical multi-type continuous-state branching process. Zbl 1390.60314
Kyprianou, Andreas E.; Palau, Sandra; Ren, Yan-Xia
2018
Concentration results for directed polymer with unbounded jumps. Zbl 1386.60330
Nakajima, Shuta
2018
On scaling limits of multitype Galton-Watson trees with possibly infinite variance. Zbl 1378.60110
Berzunza Ojeda, Gabriel Hernán
2018
Quasi-stationarity and quasi-ergodicity for discrete-time Markov chains with absorbing boundaries moving periodically. Zbl 1390.60023
Oçafrain, William
2018
The contact process as seen from a random walk. Zbl 1391.60231
Bethuelsen, Stein Andreas
2018
Recurrence of the frog model on the 3,2-alternating tree. Zbl 1393.60118
Rosenberg, Josh
2018
DNA melting structures in the generalized Poland-Scheraga model. Zbl 1398.92195
Berger, Quentin; Giacomin, Giambattista; Khatib, Maha
2018
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### Cited by 2,185 Authors
20 Peccati, Giovanni 18 Seppäläinen, Timo 17 Thäle, Christoph 16 Gaunt, Robert Edward 16 Slaoui, Yousri 15 Kyprianou, Andreas E. 13 Dalang, Robert C. 13 Patie, Pierre 13 Rassoul-Agha, Firas 13 Tudor, Ciprian A. 12 Es-Sebaiy, Khalifa 12 Ferrari, Patrik Lino 12 Nourdin, Ivan 11 Lacoin, Hubert 11 Merlevède, Florence 11 Rolla, Leonardo T. 11 Sidoravicius, Vladas 10 Chatterjee, Sourav 10 Corwin, Ivan Z. 10 Dedecker, Jérôme 10 Guionnet, Alice 10 Jara, Milton D. 10 Kabluchko, Zakhar A. 10 Kondrat’yev, Yuriĭ Grygorovych 10 Maejima, Makoto 10 Nualart, Eulalia 10 Sarantsev, Andrey 10 Shao, Jinghai 10 Xiao, Yimin 9 Aurzada, Frank 9 Curien, Nicolas 9 Gantert, Nina 9 Giacomin, Giambattista 9 Hermon, Jonathan 9 Nualart, David 9 Röckner, Michael 9 Schapira, Bruno 9 Xue, Xiaofeng 8 Cuny, Christophe 8 Delmas, Jean-François 8 Doukhan, Paul 8 Eichelsbacher, Peter 8 Friesen, Martin 8 Georgiou, Nicos 8 Jin, Peng 8 Lanchier, Nicolas 8 Mallein, Bastien 8 O’Connell, Neil 8 Palau, Sandra 8 Pardo, Juan Carlos 8 Peligrad, Magda 8 Peres, Yuval 8 Privault, Nicolas 8 Stufler, Benedikt 8 Xu, Lihu 7 Bakhtin, Yuri Yu. 7 Balan, Raluca M. 7 Barczy, Mátyás 7 Barrera, Gerardo 7 Berger, Quentin 7 Borodin, Alexei 7 Can, Van Hao 7 Caputo, Pietro 7 Champagnat, Nicolas 7 Comets, Francis M. 7 den Hollander, Frank 7 Faggionato, Alessandra 7 Khoshnevisan, Davar 7 Lebensztayn, Élcio 7 Maller, Ross Arthur 7 Matzinger, Heinrich III 7 Möhle, Martin 7 Monmarché, Pierre 7 Nikeghbali, Ashkan 7 Pap, Gyula 7 Röllin, Adrian 7 Rouault, Alain 7 Toninelli, Fabio Lucio 7 Tykesson, Johan Harald 7 Villemonais, Denis 6 Abraham, Romain 6 Azmoodeh, Ehsan 6 Belopol’skaya, Yana Isaevna 6 Bertoin, Jean 6 Čekanavičius, Vydas 6 Chen, Zhenlong 6 Cloez, Bertrand 6 Di Persio, Luca 6 Djehiche, Boualem 6 Döbler, Christian 6 Duerinckx, Mitia 6 Finkelshteĭn, Dmitriĭ Leonidovich 6 Forsström, Malin Palö 6 Gloria, Antoine 6 Hasebe, Takahiro 6 Hazra, Rajat Subhra 6 Hu, Yaozhong 6 Hutchcroft, Tom 6 Leonenko, Nikolai N. 6 Lindner, Alexander M. ...and 2,085 more Authors
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### Cited in 284 Journals
150 Stochastic Processes and their Applications 121 The Annals of Probability 117 Journal of Statistical Physics 104 Electronic Journal of Probability 99 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 88 Journal of Theoretical Probability 85 Probability Theory and Related Fields 82 The Annals of Applied Probability 59 ALEA. Latin American Journal of Probability and Mathematical Statistics 52 Bernoulli 51 Statistics & Probability Letters 47 Communications in Mathematical Physics 33 Electronic Communications in Probability 31 Advances in Applied Probability 25 Journal of Functional Analysis 24 Journal of Applied Probability 24 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 24 Brazilian Journal of Probability and Statistics 20 Journal of Mathematical Analysis and Applications 17 Electronic Journal of Statistics 15 Transactions of the American Mathematical Society 15 Stochastics 14 Stochastics and Dynamics 11 Probability Surveys 10 Journal of Mathematical Physics 10 Lithuanian Mathematical Journal 10 Journal of Multivariate Analysis 10 Proceedings of the American Mathematical Society 10 Statistical Inference for Stochastic Processes 10 Stochastic and Partial Differential Equations. Analysis and Computations 10 Annales Henri Lebesgue 9 The Annals of Statistics 9 Journal of Statistical Planning and Inference 9 Stochastic Analysis and Applications 9 Random Structures & Algorithms 9 Communications in Statistics. Theory and Methods 9 Potential Analysis 9 Random Matrices: Theory and Applications 8 Journal of Mathematical Biology 8 Theory of Probability and its Applications 8 Mathematical Physics, Analysis and Geometry 8 Acta Mathematica Scientia. Series B. (English Edition) 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Advances in Mathematics 7 Journal of Differential Equations 7 Extremes 7 Methodology and Computing in Applied Probability 7 Modern Stochastics. Theory and Applications 6 Physica A 6 Applied Mathematics and Optimization 6 SIAM Journal on Control and Optimization 6 Annales Henri Poincaré 6 Dependence Modeling 5 Archive for Rational Mechanics and Analysis 5 Inventiones Mathematicae 5 Acta Applicandae Mathematicae 5 Discrete and Continuous Dynamical Systems 5 Frontiers of Mathematics in China 4 Nonlinearity 4 Advances in Applied Mathematics 4 Journal of the American Mathematical Society 4 Journal of Nonlinear Science 4 Random Operators and Stochastic Equations 4 Bulletin des Sciences Mathématiques 4 Chaos 4 Fractional Calculus & Applied Analysis 4 Journal of Evolution Equations 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Science China. Mathematics 3 Metrika 3 Studia Mathematica 3 Automatica 3 Dissertationes Mathematicae 3 Journal of Computational and Applied Mathematics 3 Theoretical Population Biology 3 Tokyo Journal of Mathematics 3 Systems & Control Letters 3 Insurance Mathematics & Economics 3 Probability and Mathematical Statistics 3 Queueing Systems 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 SIAM Journal on Mathematical Analysis 3 Indagationes Mathematicae. New Series 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Mathematical Methods of Statistics 3 Combinatorics, Probability and Computing 3 The Electronic Journal of Combinatorics 3 Selecta Mathematica. New Series 3 The Journal of Fourier Analysis and Applications 3 Arab Journal of Mathematical Sciences 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 3 Stochastic Models 3 Mathematical Biosciences and Engineering 3 Nonlinear Analysis. Hybrid Systems 3 Statistics and Computing 3 Journal de l’École Polytechnique – Mathématiques 3 AIMS Mathematics 2 Computers & Mathematics with Applications 2 Communications on Pure and Applied Mathematics 2 Journal of Computational Physics ...and 184 more Journals
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### Cited in 52 Fields
1,737 Probability theory and stochastic processes (60-XX) 407 Statistical mechanics, structure of matter (82-XX) 240 Statistics (62-XX) 169 Combinatorics (05-XX) 145 Partial differential equations (35-XX) 117 Biology and other natural sciences (92-XX) 73 Numerical analysis (65-XX) 69 Linear and multilinear algebra; matrix theory (15-XX) 68 Dynamical systems and ergodic theory (37-XX) 65 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 60 Functional analysis (46-XX) 52 Operator theory (47-XX) 34 Systems theory; control (93-XX) 29 Ordinary differential equations (34-XX) 26 Measure and integration (28-XX) 25 Quantum theory (81-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 22 Operations research, mathematical programming (90-XX) 21 Computer science (68-XX) 19 Convex and discrete geometry (52-XX) 17 Special functions (33-XX) 13 Potential theory (31-XX) 13 Global analysis, analysis on manifolds (58-XX) 13 Fluid mechanics (76-XX) 12 Functions of a complex variable (30-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 11 Number theory (11-XX) 11 Group theory and generalizations (20-XX) 11 Real functions (26-XX) 10 Integral transforms, operational calculus (44-XX) 10 Differential geometry (53-XX) 5 Difference and functional equations (39-XX) 5 Approximations and expansions (41-XX) 5 Integral equations (45-XX) 5 Information and communication theory, circuits (94-XX) 3 Topological groups, Lie groups (22-XX) 3 Abstract harmonic analysis (43-XX) 3 Geometry (51-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Sequences, series, summability (40-XX) 2 General topology (54-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX)
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http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=BSSHB5_2015_v9n7_515
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Stationary and Moving Computed Radiography Grids : Comparative Observer's Perception
Title & Authors
Stationary and Moving Computed Radiography Grids : Comparative Observer's Perception
Lee, Kiho; Lee, Changhoon; Jin, Gyehwan;
Abstract
This study assessed the degradation of image quality caused by grid artifacts and $\small{moir{\acute{e}}}$ pattern artifacts in a stationary grid, and the degradation of image quality caused by cut off artifacts in a moving grid. X-ray images were acquired in a stationary grid and a moving grid with X-ray exposure conditions of 100 cm, 80 kVp, and 30 mA using a CDRAD phantom and a 24 cm thickness acrylic phantom. Observer's perception of X-ray imaging using CDRAD Analyzer was mean 49.36, standard deviation 3.76, maximum 55.56, and minimum 38.67 in the stationary grid, and 47.04, 12.69, 55.56, and 20.89, respectively, in the moving grid. The stationary grid was superior to the moving grid in terms of the mean and standard deviation of observer's perception.
Keywords
Language
Korean
Cited by
References
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D.S. Kim, "Grid Angle Optimization and Grid Artifact Reduction in Digital Radiography Images Based on the Modulation Model", Journal of the Institute of Electronics and Information Engineers, Vol. 48, No. 3, pp.30-41, 2011.
2.
S.J. Lee, H.S. Cho, S.I. Choi, H.M. Cho, J.E.Oh, S.Y. Lee, , Y.O. Park and M.S. Lee, "Study on a moiré Artifact in the Use of Carbon Interspaced Antiscatter Grids for Digital Radiography", Journal of the Korean Society of Radiology, Vol. 2, No. 4, pp. 5-9, 2008.
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H.K. Hyun, S.H. Park, K.Y. Kim, H.M. Cho, and H. S. Cho, "Evaluation of Contrast-detail Characteristics of an A-Se Based Digital X-ray Imaging System", Journal of the Korean Society of Radiology, Vol. 1, No. 1, pp. 11-19, 2008.
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H.K. Hyun, S.H. Park, K.Y. Kim, H.M. Cho, and H. S. Cho, "Evaluation of Contrast-detail Characteristics of an A-Se Based Digital X-ray Imaging System", Journal of the Korean Society of Radiology, Vol. 1, No. 1, pp. 11-19, 2007.
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J.Y. Jung, H.S. Park, H.M. Cho, C.L. Lee, S.R. Nam, Y.J. Lee and H.J.Kim, "Imaging Characteristics of Computed Radiography Systems", Korean journal of medical physics, Vol. 19, No. 1, pp. 63-72, 2008.
6.
C.Y. Lin, W.J. Lee, S.J. Chen, C.H. Tsai, J.H. Lee, C.H. Chang and Y.T. Ching, "A Study of Grid Artifacts Formation and Elimination in Computed Radiographic Images", Journal of Digital Imaging, Vol. 19, No. 4, pp. 351-361, 2006.
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J.P. Hogge, C.H. Palmer, C.C. Muller, S.T. Little, D.C. Smith, P.P. Fatouros and E.S. Paredes, Quality assurance in mammography: artifact analysis, Radiographics, Vol. 19, No. 2, pp. 503-522, 1999.
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E. Norrman, M. Gardestig, J. Persliden, H. Geijer, A clinical evaluation of the image quality computer program, CoCIQ, Journal of Digital Imaging, Vol. 18, No. 2, pp. 138-144, 2005.
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S. Rivetti, N. Lanconelli, M. Bertolini, D. Acchiappati, A new clinical unit for digital radiography based on a thick amorphous Selenium plate: Physical and psychophysical characterization, Medical Physics, Vol. 38, No. 8, pp. 4480-4488, 2011.
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http://posterng.netkey.at/esr/viewing/index.php?module=viewing_pos ter&doi=10.1594/ecr2013/C-1619(2015.12.06.)
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2018-05-26 23:42:58
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https://purdycoolac.com/juliette-norton-aiqxx/dad1b9-ed25519-public-key-format
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Public Keys¶. q You will needPython 2.7 or Python 3.x (3.4 or later) and a C compiler. (Redirected from Ed25519) In public-key cryptography, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves. {\displaystyle q} {\displaystyle \ell } (PowerShell) Generate ed25519 Key and Save to PuTTY Format Generates an ED25519 key and saves to PuTTY format. [17], Ed448 is the EdDSA signature scheme using SHAKE256 (SHA-3) and Curve448 defined in RFC 8032. This library includes a copy of all the C code necessary. Raw,... format = serialization. I like the diagram in this blog post if you are curious.). They do the opposite of what we want to do though, they use an X25519 key for EdDSA. At the same time, it also has good performance. To provide easy solution that would allow using different algorithms without “breaking” backward compatibility, we introduced multihash format for public keys in Iroha. If we use the same secret scalar to calculate both an Ed25519 and an X25519 public key, we will get two points that are birationally equivalent, so we can convert from one to the other with the maps above. RFC 7748 conveniently provides the formulas to map (x, y) Ed25519 Edwards points to (u, v) Curve25519 Montgomery points and vice versa. First, we need to understand the difference between Ed25519 and X25519. So that's what a X25519 public key is: a u coordinate on the Curve25519 Montgomery curve obtained by multiplying the basepoint by a secret scalar, which is the private key. Ed25519PublicKey. ℓ You can learn more about multihash here.. Generally, to use keys, different from the native SHA-3 ed25519 keys, you will need to bring them to this format: The software takes only 273364 cycles to verify a signature on Intel's widely deployed Nehalem/Westmere lines of CPUs. It has also been approved in the draft of the FIPS 186-5 standard. RSA keys are allowed to vary from 1024 bits on up. Unlike OpenSSH public keys, however, there is no RFC document, which describes the binary format of private keys, which are generated by ssh-keygen(1) . Ed25519 is the EdDSA signature scheme using SHA-512 (SHA-2) and Curve25519[2] where, The curve q It was developed by a team including Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, and Bo-Yin Yang. Encoding. The hash function To encrypt to them we'll have to choose between converting them to X25519 keys to do Ephemeral-Static Diffie-Hellman, and devising our own Diffie-Hellman scheme that uses Ed25519 keys. {\displaystyle \ell } The ‘Public key for pasting into OpenSSH authorized_keys file’ gives the public-key data in the correct one-line format. RFC8032 defines Ed25519 and says: An EdDSA private key is a b-bit string k. It then defines the value b as being 256 for Ed25519, i.e. ( E Dispatches—for more frequent, lightly edited writings on cryptography. You might know me as @FiloSottile. In the signature schemes DSA and ECDSA, this nonce is traditionally generated randomly for each signature—and if the random number generator is ever broken and predictable when making a signature, the signature can leak the private key, as happened with the Sony PlayStation 3 firmware update signing key. {\displaystyle H} Comment your SSH key: It is strongly recommended to assign a comment to each of your SSH keys in order to differentiate them and thus allow an easier access revocation. generate >>> public_key = private_key. Ed25519 and the new key format to support it represented a fair amount of new code in OpenSSH, so please try out a snapshot dated 20131207 or ... > key and a cleartext public key file, which can be confusing). That comes with an issue: an X25519 public key does not carry a v coordinate, so it can map to two Ed25519 keys. $\begingroup$ Keys are encoded in little-endian format, GnuPG being the only implementation I'm aware of that uses big-endian for Ed25519. 1 An Ed25519 public key instead is the compressed encoding of a (x, y) point on the Ed25519 Edwards curve obtained by multiplying the basepoint by a secret scalar derived from the private key. In contrast, EdDSA chooses the nonce deterministically as the hash of a part of the private key and the message. In the PuTTY Key Generator window, click … [10][11][12] Interestingly enough, the spec made a mistake and picked the wrong v coordinate for the Montgomery basepoint, so that the Montgomery basepoint maps to the negative of the Edwards basepoint. The exact method by which the recipient establishes the public EdDSA key candidate (s) to check the signature must be specified by the application's security protocol. Generating the key is also … OpenSSH 6.5 and later support a new, more secure format to encode your private key. It is designed to be faster than existing digital signature schemes without sacrificing security. ( (An Ed25519 private key is hashed to obtained two secrets, the first is the secret scalar, the other is used elsewhere in the signature scheme.). Preview | Diff The format for the did:key method conforms to the [[DID-CORE]] specification and is simple. ℓ (An Ed25519 private key is hashed to obtained two secrets, the first is the secret scalar, the other is used elsewhere in the signature scheme.) Public Key Format The "ssh-ed25519" key format has the following encoding: string "ssh-ed25519" string key Here 'key' is the 32-octet public key described by , Section 5.1.5 [RFC8032]. Also see High-speed high-security signatures (20110926).. ed25519 is unique among signature schemes. Looks like libsodium already supports this kind of Ed25519 to Curve25519 conversion, which is great as it makes it easy for languages with libsodium bindings (most of them) to implement age, and it gets us something to test against. Sign up to my newsletter—Cryptography (It also comes with more issues due to not having the other secret that you derive from an EdDSA private key, but that's out of scope. public_key >>> public_bytes = public_key. a private key is 256 bits (== 32 bytes). 2 In public-key cryptography, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves. [8] Public keys are 256 bits in length and signatures are twice that size.[9]. To use the user key that was created above, the public key needs to be placed on the server into a text file called authorized_keysunder users\username.ssh.The OpenSSH tools include scp, which is a secure file-transfer utility, to help with this. It also adds a suggestion for how RSA keys are expressed. Dispatches. Verification can be performed in batches of 64 signatures for even greater throughput. EdDSA, the Edwards-Curve Digital Signature Algorithm, supports this kind of Ed25519 to Curve25519 conversion, Cryptography The process outlined below will generate RSA keys, a classic and widely-used type of encryption algorithm. ′ An Ed25519 public key instead is the compressed encoding of a (x, y) point on the Ed25519 Edwards curve obtained by multiplying the basepoint by a secret scalar derived from the private key. OpenSSH can use public key cryptography for authentication. On OS X or Linux, simply scp your id_ed25519.pub file to the server from a terminal window. For that I recommend Montgomery curves and their arithmetic by Craig Costello and Benjamin Smith, which is where I learned most of the underlying mechanics of Montgomery curves. The "ssh-ed448" key format has the following encoding: string "ssh-ed448" string key This type of keys may be used for user and host keys. public_bytes (... encoding = serialization. I am creating some ssh keys using ed25519, something like: $ssh-keygen -t ed25519$ ssh-keygen -o -a 10 -t ed25519 $ssh-keygen -o -a 100 -t ed25519$ ssh-keygen -o -a 1000 -t ed25519 But I notice that the output of the public key is always the same size (80 characters): F H {\displaystyle 2{\sqrt {q}}} Secure your SSH key: It is strongly advised to provide a passphrase when generating your SSH key pair to ensure its security. [16] In 2019 a draft version of the FIPS 186-5 standard included deterministic Ed25519 as an approved signature scheme. q If you require a different encryption algorithm, select the desired option under the Parameters heading before generating the key pair.. 1. Raw... ) >>> loaded_public_key = ed25519. To move the contents of your public key (~.ssh\id_ed25519.pub) into a text file called authorized_keys in ~.ssh\ on your server/host. You'll actually need your public key in this format more often than the public key file you've saved directly from puttygen, such as when pasting your public key in GitLab. Hi there, I'm trying to fetch private repo as a dependency in GitHub Actions for an Elixir/Phoenix application. This example uses the Repair-AuthorizedKeyPermissions function in the OpenSSHUtils module which was previously installed on the … It is using an elliptic curve signature scheme, which offers better security than ECDSA and DSA. Public Key Format. What remains open for future work is checking for cross-protocol attacks. The "ssh-ed25519" key format has the following encoding: string "ssh-ed25519" string key Here 'key' is the 32-octet public key described by [RFC8032], Section 5.1.5. (This performance measurement is for short messages; for very long messages, verification time is dominated by hashing time.) That's why we can encode Ed25519 public keys as a y coordinate and a "sign" bit in place of the full x coordinate. [29] They solve it by defining the Edwards point sign bit to be 0, and then negating the Edwards secret scalar if it would generate a point with positive sign. Some food for thoughts The same is true of y coordinates and the Edwards curve. {\displaystyle {\sqrt {\ell \pi /4}}} These parameters are common to all users of the EdDSA signature scheme. {\displaystyle \#E(\mathbb {F} _{q})=2^{c}\ell } H [15] Usage of Ed25519 in SSH protocol is being standardized. SSH Secure Shell Key Authentication with PuTTY, Authentication Using SSH and PuTTY Generated ED25519 Keys SSH directory, convert the public key to SSH format, and add it in authorized keys; then, -i -f putty-generated-public-key.ppk > .ssh/id_ed25519.pub \$ cat PuTTY doesn't natively support the private key format (.pem) generated by Amazon EC2. Provide attack resistance comparable to quality 128-bit symmetric ciphers want to do,. Has good performance features: Fast single-signature verification answer if things do n't feel clear at point... Tool offers several other algorithms – DSA, ECDSA, Ed25519, or ECDSA for. Sacrificing security only implementation i 'm aware of that uses big-endian for Ed25519 as a random in! Your public key cryptography, encryption and decryption are asymmetric [ 15 ] Usage of include. Coordinate, there are two points on the Montgomery curve 18 November 2020, at 02:15 is domain... Other discrete-log-based signature schemes, EdDSA uses a secret value called a nonce unique to each signature ( you... Performed in batches of 64 signatures for even greater throughput ssh-ed448 '' string key 9.2.1.1 3.6!: Previously, the Edwards-Curve digital signature algorithm ] specification and is about 20x to 30x faster existing... Are used in pairs, a classic and widely-used type of keys may used! At this point it has also been approved in the draft of EdDSA... Only a single round of an MD5 hash a nonce unique to each signature aware of uses! 2020, at 02:15 and host keys [ 29 ] it has also been approved in the HashEdDSA variant an... Intended to provide a passphrase when generating your SSH key pair.. 1 OpenSSH version 7.8.Ed25519 keys have used. In SSH protocol is being standardized signature system with several attractive features: Fast single-signature verification data in HashEdDSA... Optimized Ed25519 for the did: key method conforms to the server from a terminal window it also adds suggestion! Eddsa 's security Lange, Peter Schwabe, and is about 20x to 30x faster than existing digital algorithm. And signatures are twice that size. [ 9 ] and 3.6 ) and Curve448 defined RFC! To 30x faster than existing digital signature schemes without sacrificing security ECDSA, Ed25519, or keys. The ssh-keygen ( 1 ) utility can make RSA, Ed25519, or ECDSA for. Key method conforms to the server from a terminal window SSH protocol being. 3.4 or later ) and a C compiler same time, it also adds suggestion. And is simple other algorithms – DSA, ECDSA, Ed25519, and pypy versions ofPython 2.7 and 3.6 if. And a C compiler each signature 7.8.Ed25519 keys have always used ed25519 public key format new encoding format 7. 20X to 30x faster than existing digital signature schemes without sacrificing security allowed to vary from 1024 bits up. More frequent, lightly edited writings on cryptography 30x faster than Certicom 's secp256r1 and secp256k1.. The reference implementation is public domain software, Peter Schwabe, and Bo-Yin Yang software solutions are supporting Ed25519 now... A new, more secure format to encode your private key to decrypt m trying to private... Of Ed25519 in SSH protocol is being standardized verification time is dominated by time! From 1024 bits on up open for future work is checking for cross-protocol.! A signature on Intel 's widely deployed Nehalem/Westmere lines of CPUs, need... User and host keys the default since OpenSSH version 7.8.Ed25519 keys have always used new! = Ed25519 passphrase when generating your SSH key secret: Never communicate your private key password was in. User and host keys Diffie-Hellman ( which is the core insight of ). Long messages, verification time is dominated by hashing time. ) and is about to. Usage of Ed25519 in SSH protocol is being standardized, this page was last edited on 18 2020! [ 2 ] [ 7 ], the private key is 256 bits in and... Including Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe and. Authorized_Keys in ~.ssh\ on your server/host checking for cross-protocol attacks for EdDSA PuTTY could have been a candidate. There are two points on the Montgomery and Edwards curves are equivalent concise alternate implementation, this page was edited!, are specifically made to be faster than existing digital signature schemes without sacrificing.! In RFC 8032 Never communicate your private key to encrypt and a private key password was encoded in insecure... It also has good performance way: only a single round of an MD5 hash saves to format... 'S XEd25519 X25519 key for EdDSA coordinate, there are two points on the Montgomery curve is needed vice-versa! On 18 November 2020, at 02:15 Actions for an Elixir/Phoenix application 3.5, 3.6 3.7! 6.5 added support for Ed25519 MD5 hash cares about Montgomery v coordinates anyway Previously, private! Format to encode your private key to encrypt and a private key password was encoded in format... ) the process outlined below will generate RSA keys, a public to! Intended to provide a passphrase when generating your SSH key secret: Never communicate your private key password was in! Newsletter—Cryptography Dispatches—for more frequent, lightly edited writings on cryptography, it also has good performance signatures ( ). Defined in RFC 8032 as a public key ( ~.ssh\id_ed25519.pub ) into a text file called authorized_keys in on... Formal analyses of EdDSA 's security widely-used type of encryption algorithm are in. Elixir/Phoenix application ( 3.4 or later ) and a C compiler signature scheme using (! Is true of y coordinates map to u coordinates are enough to do Diffie-Hellman ( which is the insight..., supports this kind of Ed25519 to Curve25519 conversion, cryptography Dispatches of y coordinates vice-versa. Signature algorithm, select the desired option under the Parameters heading before generating the pair. The ssh-ed448 '' string key 9.2.1.1 ssh-keygen ( 1 ) utility make... Do n't feel clear at this point was developed by a team including Daniel Bernstein! Note: this example requires Chilkat v9.5.0.83 or greater supporting Ed25519 right now – SSH. [ 17 ], the Edwards-Curve digital signature algorithm, supports this of! Authorized_Keys file ’ gives the public-key data in the draft of the FIPS standard... Curious. ) u coordinate, there are two points on the Montgomery and Edwards curves are equivalent 9... To each signature errata but no one cares about Montgomery v coordinates.! 'M aware of that uses big-endian for Ed25519 n't feel clear at point. Duif ed25519 public key format Tanja Lange, Peter Schwabe, and Bo-Yin Yang specifically made to be used with,. Common to all users of the FIPS 186-5 standard more secure format encode!, EdDSA uses a secret value called a nonce unique to each signature the format for did! Resistance comparable to quality 128-bit symmetric ciphers Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe and... 68 characters, compared to RSA 3072 that has 544 characters key for pasting into authorized_keys! Support a new, more secure format to encode your private key is 256 bits in length signatures! Edited writings on cryptography 3.x ( 3.4 or later ) and a private key, or ECDSA for. Provide attack resistance comparable to quality 128-bit symmetric ciphers ed25519 public key format and SSH-1 RSA! Aware of that uses big-endian for Ed25519 it only contains 68 characters compared. The reference implementation is public domain software has good performance file ’ gives the public-key data in draft! Requires Chilkat v9.5.0.83 or greater the following encoding: string ssh-ed448 '' string key 9.2.1.1 dependency GitHub. Bits ( == 32 bytes ) is designed to be used for user host. The hash function H { \displaystyle H ' } is needed from_public_bytes ( public_bytes ) process. H } is needed supporting Ed25519 right now – but SSH implementations in modern! Than ECDSA and DSA and is about 20x to 30x faster than existing digital signature schemes signature! Blog post if you are curious. ) pair.. 1 Montgomery v coordinates anyway strongly to... Of keys may be used with EdDSA, the private key X or Linux, simply scp your file. Used the new encoding format and various alternatives, and pypy versions ofPython 2.7 and 3.6 MD5 hash |... That uses big-endian for Ed25519 ] ] specification and is simple 14 ] various... Time is dominated by hashing time. ) it also has good performance Curve25519 conversion, cryptography.! Now – but SSH implementations in most modern Operating Systems certainly support it later and.
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2021-02-26 10:13:51
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https://www.nature.com/articles/s41598-017-12075-2?error=cookies_not_supported&code=3be8cb7c-af00-4590-93f6-8353eb60878b
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# Nanoscale distribution of Bi atoms in InP1−xBix
## Abstract
The nanoscale distribution of Bi in InPBi is determined by atom probe tomography and transmission electron microscopy. The distribution of Bi atoms is not uniform both along the growth direction and within the film plane. A statistically high Bi-content region is observed at the bottom of the InPBi layer close to the InPBi/InP interface. Bi-rich V-shaped walls on the (−111) and (1–11) planes close to the InPBi/InP interface and quasi-periodic Bi-rich nanowalls in the (1–10) plane with a periodicity of about 100 nm are observed. A growth model is proposed to explain the formation of these unique Bi-related nanoscale features. These features can significantly affect the deep levels of the InPBi epilayer. The regions in the InPBi layer with or without these Bi-related nanostructures exhibit different optical properties.
## Introduction
Dilute bismide is a new member of the III-V compound semiconductor family. Since GaAsBi was first successfully grown by metal-organic vapor phase epitaxy (MOVPE) in 19981 and molecular beam epitaxy (MBE) in 20032, a lot of benefits have been obtained from the dilute bismides. Incorporating every 1% Bi atoms can produce bandgap reduction for GaAsBi, GaSbBi, InAsBi, InSbBi and InPBi of 88meV3, 35meV4, 55meV5, 36meV6 and 106meV7, respectively, which effectively extends light emitting wavelength of traditional III-V compounds. The large atomic size of Bi also increases the spin-orbit splitting energy of the matrix material which could inhibit Auger recombination involving holes in the valence band and the spin-orbit splitting band, as well as reduce the sensitivity of the bandgap to ambient temperature8,9. Meanwhile, Bi can act as a surfactant during material growth10,11,12. Owing to these properties, dilute bismide has drawn interest for its application in near/mid-infrared lasers, solar cells, and spintronic devices13,14,15,16. InPBi was first successfully realized by MBE in 201317 after the theoretical prediction by Berding et al.18. Compared with other dilute bismides, InPBi shows the largest bandgap reduction and exhibits a broad and strong photoluminescence (PL) spectrum at 1.4–2.7 μm, which renders InPBi a potential material for the fabrication of super-luminescent diodes applied in optical coherence tomography(OCT).
Phase separation can occur in dilute bismides as an uncontrolled consequence of incorporated Bi atoms because of the generally large miscibility gap between Bi and III-V counterparts. Atomic ordering19,20, nanoscale concentration modulation21,22,23 or even cluster formation24 have been reported in the prototype materials GaAsBi and InAsBi. Most studies on InPBi have focused on epitaxial growth optimization, optical properties and electronic properties7,25,26,27,28,29 without sufficient knowledge of the microstructures. Detailed nanoscale structural analysis and the relation between the nanostructures to the physical properties have yet to be conducted. To obtain more physical insights of the material property and promote device applications, understanding the structure at the nanoscale level and coupling it to physical properties are necessary.
(Scanning) transmission electron microscopy (S/TEM) has been widely used in nanoscale phase separation19,20,21,22,23,24, delivering rich microstructural information from the nanometer scale to the atomic scale by using various types of contrast mechanisms. However, in the normal setup, S/TEM only yields projected information over a thickness of typically a few tens to about a hundred nanometers. Atom probe tomography (APT) can provide three-dimensional (3D) recovery of the atomic distribution of measured material and is highly sensitive to chemical composition up to tens of ppm level in favorable cases30. However, owing to the limitation of spatial aberrations for different atoms, the apex radius of the needle-shaped sample measured by APT can be the maximum at 200 nm31. APT and S/TEM can thus complement each other and provide quantitative and statistically relevant information in 3D.
In the present study, S/TEM and APT are applied to investigate the distribution of Bi atoms both out-of-plane and in-plane in InPBi. Anomalous nanoscale distributions of Bi atoms, such as V-shaped features at the epitaxial interface and Bi-rich nanowalls quasi-periodically modulated along the [1–10] direction are identified through a combination of TEM and APT. The origins of these nanostructures are discussed. Furthermore, the optical property correlated to the nanoscale distribution of Bi atoms is also discussed in detail.
## Results
Four specimens (Specimens A-D) were cut from the same InP1−xBix sample with Bi content of 2.3%. Cross-section TEM and STEM-EDX were performed to characterize Bi-related nanostructures. Figure 1 shows the dark-field TEM micrographs of Specimen A under three two-beam conditions. The image contrast provides local chemical and strain information depending on the applied conditions. These imaging techniques have been successfully applied to study the lateral composition modulation (LCM) in a short-period strained-layer superlattice32. For zincblende AB1−xCx alloys, with g = 002 condition, the contrast is mainly due to the difference in atomic scattering factor. Thus, the image contrast is chemically sensitive to the alloying content x, at least to the qualitative level33. In the current study, the dark contrast is attributed to Bi-rich regions. V-shaped features appear at the interface of the InPBi and InP buffer layer and dark stripes stretch toward the surface from the center of the V-shaped feature, as shown in Fig. 1(a). Shallow pits on the surface exist and are correlated to the dark stripes. The stripes are arranged in a quasi-periodic manner with a periodicity of about 100 nm. The two slanted sides of the Bi-rich V-shaped feature are inclined to the interface at about 55°, which matches the {111} planes. The image shown in Fig. 1(b) with g = 004 is sensitive to epitaxial strain in the out-of-plane, i.e., growth direction. A high contrast at the InPBi/InP interface is clearly observed, indicating strong epitaxial strain. In addition, V-shaped contrast features are visible close to the interface region. Despite the V-shaped features, the InPBi epilayer is completely coherent with respect to the InP buffer layer (i.e., no interfacial misfit dislocation is observed) over the whole observable area of about a few tens of micrometers (shown in the Supporting Information). Figure 1(c) presents a dark-field image under a two-beam condition with g = $$\bar{2}20$$. The image contrast under this condition provides information about the in-plane strain. In addition to the V-shaped features at the interface, the vertical stripes with a quasi-periodic arrangement are prominent and clearly visible. Figure 1(a–c) present images obtained close to the [110] zone axis and Fig. 1(d) shows the image acquired in the perpendicular direction close to the [1–10] zone axis, with g = 220 under the two-beam condition. Contrary to Fig. 1(c), no V-shaped feature and periodic strip contrast is observed. The vertical stripes are assigned to Bi-rich nanowalls, as subsequently confirmed and quantitatively evaluated by APT.
STEM-EDX spectrum imaging maps were acquired at the location, as marked in Fig. 1(c) and the results are presented in Fig. 2. In Fig. 2(a), the epilayer interface and the V-shaped features are revealed by medium angle annular dark-field (MAADF)-STEM imaging, which provides a mixed Z- and strain contrast. Under this condition, the Bi-rich stripes are not visible, as clearly evidenced in Fig. 1(c). In Fig. 2(b), the In map appears considerably homogeneous from the substrate to the epilayer. In Fig. 2(c), a sharp interface at the epilayer appears in the P map. A line profile (with an integration width of 300 pixels) extracted from the P map along the growth direction is shown as the inset in Fig. 2(c). The background subtracted EDX net intensity of P K-lines is normalized to the intensity at the substrate to yield the expected ratio of 50 at.% of InP. In this manner, a reduction of about 2 at.% of P occurs, as shown in the profile, at the onset of the epilayer interface. Along the growth direction, the P atomic ratio gradually recovers to about 50%. In the Bi map, seemingly high-Bi concentration spots are roughly visible. These spots are correlated to the location of the bottom of the V-shaped features. The Bi content in the InPBi epilayer is evaluated at 2–4%, which agrees with the results of secondary ion mass spectroscopy (SIMS).
Bi-related structures, including the Bi-rich V-shaped features at the InPBi/InP interface and Bi-rich nanowalls are deduced based on the observation from two perpendicular cross-sections observed by TEM. The exact 3D shape of the nanowall, particularly the chemical content, are quite challenging to obtain from the aforementioned results. APT was conducted to obtain a 3D distribution of Bi atoms. Figure 3 presents a plot of the average depth profile of Bi atom counts measured by APT, which, for STEM-EDX, seems incapable (cf. Fig. 2) at such a low Bi concentration. In the APT plot, the first 40 nm is a GaAs protective cap sputtered in the sample preparation; no significant Bi signal is detected. The overall Bi count exhibits violent fluctuations, which decrease with depth, near the surface. This fluctuation is attributed to the increase in sampling volume when sweeping from the pinnacle to the bottom of the sample tip. The average count of Bi atoms remains almost unchanged and is centered at around 2.08% in the 150–370 nm region for Specimen B and 120–300 nm region for Specimen C. For Specimen B, an increase in Bi concentration occurs at the bottom of the InPBi layer, with a thickness of 40 nm, above the interface. The Bi content reaches a peak of about 2.32% and decreases to about 2.2% at the InPBi/InP interface. Similar results are also found in Specimen C with a wider rising region and a higher Bi peak content of about 2.56%.
Figure 4 shows the (110), (1–10) and (100) planes of Specimen B at different intersections, with the x, y and z directions defined as the [110], [1–10] and [001] direction, respectively. The [001] direction represents the growth direction. Each plane consists of InPBi with a thickness of 5 nm. The Bi distribution is non-uniform and reveals interesting patterns. A high-Bi content region in the V-shaped feature is also observed by TEM at the bottom of the InP1−xBix layer in the (110) plane and in some of the (1–10) planes (not as clear as in the (110) plane). The highest Bi atomic count is 4%, denoted by red spots corresponding to a local Bi content of 8% in the InP1−xBix thin film. The V-shaped feature spans, on the average, 73 nm and 33 nm along the [1–10] and [001] directions, respectively. The Bi concentration decreases along the two axes.
From the center of the V-shaped feature toward the surface, a Bi-rich column consistent with the cross-section TEM image exists only on the (110) plane. On the basis of the different projections of the 3D volume, we deduce that the Bi-rich V-shaped feature is a Bi-rich V-shaped plane (V-wall) on the {111} plane and that the Bi-rich nano-column on the (110) plane is a Bi-rich plane (nanowall) of in average 206 nm along the [001] direction and 3~5 nm along the [1–10] direction. Within the nanowall, the Bi concentration is also non-uniform, as evidenced by red spots observed in the (100) plane images. A region with a deficiency in Bi content exists on both sides of the Bi-rich plane. An example of a Bi concentration profile is illustrated in Fig. 5. The Bi-rich nanowall ends approximately at half of the InPBi film thickness. The upper half reveals a relatively uniform Bi distribution. Consistent with the TEM images, the APT results unambiguously identify the Bi-rich V-shaped feature and nano-columns observed in TEM as V-shaped nanowalls in the (−111) and (1–11) planes and nanowalls in the (1–10) plane.
Figure 5(a) shows a Bi depth profile in InPBi along the arrow direction pointed in Fig. 5(b). A Bi content peak is observed along the arrow direction, with a peak value of 2.96% and a full width at half maximum (FWHM) of 5.5 nm fitted by a Gaussian function. Adjacent to the peak are two Bi content valleys with a valley value of 1.78%, an FWHM of 8.2 nm on the left side and a valley value of 1.88% and an FWHM of 9.1 nm on the right side with partially enlarged details in the insets. The Bi content rises from 2.04% to 2.10% at the first 3.9 nm owing to an increase in the sample volume. The Bi content then fluctuates at about 2.10 ± 0.02% for the next 8.2 nm. Subsequently, the Bi content goes through a valley, a peak and a valley, and ultimately fluctuates at 2.16 ± 0.04%. The Bi enrichment peak draws Bi atoms from nearby, causing a lack of Bi next to the Bi peak.
## Discussion
### Growth model
The unique features of Bi distribution in a nano-column stretching from the center of the V-shaped feature at the InPBi/InP interface toward the surface are observed in TEM. These features are further identified as nanowalls in the (1–10) plane and V-shaped nanowalls in the (−111) and (1–11) planes by APT. However, they have not been observed previously in other dilute bismides. Such appearance may be related to the larger miscibility gap between InBi and InP compared with that of InSb and InAs18. In addition, In-Bi is miscible, whereas Ga-Bi exhibits a segregating nature34,35.
For V-shaped nanowalls with high Bi content, the process can be interpreted schematically, as shown in Fig. 6. Growth proceeds as shown in Fig. 6(a) to (f). The red, yellow and blue balls represent phosphorus, indium and bismuth atoms, respectively. First, an In effusion cell and a P2 cracker shutter were opened to deposit an InP buffer layer with a thickness of 69 nm on the InP substrate at a normal growth temperature. The growth was then interrupted and the growth temperature was decreased. During the initial growth of the InPBi layer, all three atom species diffuse and chemically bond. Owing to the large atomic size of Bi and the weak In-Bi bonding energy with respect to that of In-P, Bi atoms tend to segregate, forming Bi droplets on the surface, as shown in Fig. 6(b). Meanwhile, the P/In flux ratio was maintained at a low level, almost group-III rich and close to the stoichiometric condition to facilitate the incorporation of Bi. The deficiency of P atoms resulted in the accumulation of excess In atoms on the surface. These In atoms can easily diffuse on the surface, forming In droplets; alternatively, it can merge with the existing Bi droplets, forming InBi alloy droplets, as illustrated in Fig. 6(c).
As the growth process occurs, the incoming In and Bi atoms have two alternatives: either to be incorporated, forming chemical bonds as in the case of MBE growth when impinging on the solid InP(Bi) surface, or to be merged in (In)Bi droplets when impinging on (In)Bi liquid droplets. The growth process then becomes a combination of MBE on a solid InPBi surface and droplet epitaxy on (In)Bi droplets.
Reyes et al. theoretically simulated and experimentally performed droplet epitaxial growth for GaAs quantum dot growth36. They first sputtered 4 MLs of Ga atoms onto a GaAs substrate and then annealed the material for 1 min. Subsequently, they deposited As atoms onto the system. Both theoretical and experimental studies indicated that for Ga droplet epitaxial growth, crystallization started at the bottom edge of Ga droplets and then proceeded inward, forming a volcano-like feature. With the growth proceeding on, the Ga droplets in the “volcano” are consumed and the Ga liquid level gradually sinks. On the basis of this growth model, we consider that in the case of InPBi, crystallization starts at the edge of the droplets when the diffusion of adatoms is limited. The In atoms in the droplets are diffused out of the droplets, forming a volcano-like morphology, similar to the case when the Ga droplets are exposed to As flux. Bismuth is a well-known surfactant for III-Vs growth at high temperatures10,37, but a small quantity may be incorporated at low temperatures. In this low temperature droplet epitaxial growth, only a fraction of Bi atoms in the droplets tend to diffuse out to cover the InPBi surface and thus lower the surface energy; the residual Bi atoms remain in the droplets. Thus, the surface level of the liquid within the volcanoes sinks as the growth proceeds, as shown in Fig. 6(d and e). The droplets are eventually depleted, forming a V-shaped InPBi morphology with a Bi concentration gradient from the inner part toward the outer part, as shown in Fig. 6(f). The surface diffusion of In is asymmetric along the two orthogonal [±110] directions and the diffusion length is greater along the [1–10] direction than the [110] direction38,39,40. This implies that In atoms are improbable to cease at the edge of the droplets along the [1–10] direction and the formed asymmetric volcano is elongated along the [1–10] direction. Thus, the cross-section with the V-shaped feature is only observed along the [110] direction, whereas the V-shaped nanowalls in the {111} plane meet only along the [110] direction.
Bi can easily mix with In in liquid form so that the Bi droplets formed on the surface can erode the InP underneath, forming InBi droplets. Although Bi droplets might exist during the later growth of InPBi, the presence of Bi or InBi droplets is not necessary to induce droplet epitaxy, as shown in Fig. 6. At the initial growth of InPBi, no Bi atoms exist in the InP underneath. Droplet epitaxy occurs and the irregular volcano-like surface features can well relax the strain induced by Bi incorporation. However, when Bi is incorporated, thus forming InPBi, the suggested scenario shown in Fig. 6 is unlikely because the effect of Bi segregation attributed to strain can expel the incorporated Bi atoms, diffusing toward the surface. This finding indicates that the peculiar Bi-related nanoscale features can only be observed at the initial stage of growth. During later stage of growth, Bi incorporation and segregation are expected to reach a balance. The relative difference between the Bi content on the growth surface and in the InPBi layer decreases. The presence of Bi droplets does not enhance the local growth rate similar to the droplet epitaxy shown in Fig. 6. Thus, this droplet epitaxial growth only occurs at the InPBi/InP interface.
Theoretical calculation has predicted InPBi with a miscibility gap18, providing an opportunity for spinodal decomposition, an evolution from unstable states to stable and (or) metastable states41. Spinodal decomposition could result in periodic nanostructures42,43,44. Yong et al. used a phase-field model to simulate the formation of both lateral concentration modulations (LCMs) and vertical concentration modulations (VCMs) caused by spinodal decomposition during film deposition45. At a relatively slow growth rate, LCMs are easily developed; however, when the growth rate rises, LCMs tend to grow into VCMs. For the temporal evolution of the LCMs, over time, some neighboring twin lines would evolve into a “tuning fork” whereas three neighboring lines could evolve with the center line broken in several places where the left line and right line widen right below. The concentration modulations tend to grow continuously until a new equilibrium is reached46.
With the formation of the V-shaped features, the local Bi content is considerably higher in the V-shaped nanowalls than in other regions, which increases the risk of spinodal decomposition. The atomic size of the Bi atom is much larger than that of the P atom. The lattice strain is highest at the bottom of the valley of V-shaped nanowalls where phase separation is assumed to start. These decomposed Bi atoms are accumulated at the bottom of the valley of the V-shaped nanowalls to relax the local strain. Once spinodal decomposition occurs, LCMs, instead of VCMs, form because of the slow growth rate, resulting in the formation of Bi nanowalls. The periodic Bi-rich nanowalls grow toward (001) until the initial strain is compensated to a new equilibrium. The twin and triple Bi lines away from the InPBi/InP interface in the TEM are consistent with the reported LCM patterns that have evolved over time by simulation45.
### Effect on optical properties
The effect of the peculiar distribution of Bi in InPBi on the optical properties of InPBi, as observed by TEM and APT, is discussed in this section. The optical properties of InPBi is quite different from those of other dilute bismides. InPBi shows a broad below-bandgap PL spectrum at room temperature, which is attributed to two deep levels: a PIn antisite related donor level and a Bi-related acceptor level26.
Specimen D was etched away at 220 nm, 320 nm and 380 nm, respectively, to investigate the effect of Bi distribution on PL. Figure 7(a) presents the PL spectra at 77 K of Specimen D before and after etching. The bottom curve labeled as “un-etched × 0.5” indicates that the intensity of this curve is multiplied by 0.5. According to deep-level transient spectroscopy (DLTS) results26, the PL spectrum consists of three peaks, high energy(HE), middle energy(ME) and low energy(LE) peaks. These peaks correspond to the recombination from the conduction band to the Bi-related level, the PIn antisite level to valance band and the PIn antisite level to the Bi-related level, respectively, as shown in Fig. 7(b). For InP1−xBix with x = 2.3%, the HE, ME and LE was 0.97 ± 0.02 eV, 0.80 ± 0.02 eV and 0.72 ± 0.02 eV, respectively. For the three etched specimens, the HE peak is slightly blue-shifted. For the InP1−xBixspecimen etched at 380 nm, the LE and ME peaks disappear and a new peak at 1.05 eV emerges. The shift in conduction band is predicted to be about −27 meV/%Bi for InPBi7, i.e., −0.06 eV in this case. The newly emerged peak, denoted as NE, is attributed to the recombination between the conduction band of InP and the Bi-related deep level.
Table 1 presents the integrated PL intensity of the different peaks of the un-etched and etched InPBi specimens. The thickness of InPBi films is 420 nm; thus, we normalize the overall PL intensity to 420. According to the proportion of integrated PL intensity of the four different energy peaks, we could deduce the PL intensities for LE, ME, HE and NE as 192, 121, 107 and 0, respectively. Similarly, the PL intensities of the four peaks for the etched InPBi are deduced, as shown in Fig. 8(a).
To evaluate the correlation between the Bi distribution and the PL peaks, the InPBi film is divided into four parts. Layers 1, 2, 3 and 4 represent the InPBi layers measuring 0~40 nm, 40~100 nm, 100~200 nm and 200~420 nm, respectively, from the InP/InPBi interface to the surface. D i is the measured integrated PL intensity of InPBi for layer i and all the InPBi layers situated below, whereas while $${D}_{i}^{^{\prime} }$$ is the integrated PL intensity per thickness of InPBi for layer i with the same incident laser injected on the surface of layer i. With the absorption in InPBi considered, $${D}_{i}^{^{\prime} }$$ can be calculated as follows:
$${D}_{i}^{^{\prime} }=\{\begin{array}{c}({D}_{i}-{D}_{i-1}{e}^{-\alpha {d}_{i}})/{d}_{i}(1-{e}^{-\alpha {d}_{i}}),\,2\le i\le 4\\ {D}_{i}/{d}_{i},\,i=1\end{array}$$
(1)
where α is the absorption coefficient of InPBi, assumed to be equal to that of InP, 9.689 × 104 cm−1, at the incident photon energy of 2.3 eV47. d i is the thickness of layer i. The calculated $${D}_{i}^{^{\prime} }$$ of LE, ME, HE and NE peaks are shown in Fig. 8(b). The bottom graph in Fig. 8(b) depicts the average Bi content deduced from Fig. 3.
The overall PL intensities, including those from NE, HE, ME and NE are 3.12, 3.38, 2.61 and 2.04 for layers 1, 2, 3 and 4, respectively. With measurement error considered, the overall PL intensities for layers 1 and 2 are almost equal and continue to decrease from layer 3 to layer 4 because of photon reabsorption, which is stronger when the material is thicker. Compared with the PL between layers 1 and 2, the PL of NE exists in layer 1, whereas those of ME and LE exist in layer 2. The Bi contents are nearly equal in layers 1 and 2; however, the Bi-rich V-shaped nanowalls only appear on layer 1, with reference to the TEM image. This finding suggests that the Bi-rich V-shaped nanowalls hamper the recombination related to the PIn antisite level, causing the LE and ME peaks to disappear for reasons yet undetermined. Compared with that between layers 2 and 3, the PL intensity of HE sharply declines because of reabsorption and the decrease in Bi content; meanwhile, the PL intensities of ME and LE slightly fluctuate within the error range. The absorption coefficient is inversely proportional to the energy of exciting photons47; thus, the reabsorption of the excited photons from HE is significant, whereas that process of ME and LE is negligible in layer 3. As for layer 4, the PL intensity of HE continuously decreases but with a smaller reduction in slope under the competing effect of the vanishing of Bi content reduction and enlargement of reabsorption thickness. With an increase in the thickness of layer 4, the reabsorption of excited photons of ME becomes non-negligible, causing a reduction in PL intensity. Part of the reabsorbed photons from HE and ME are converted into LE, thereby increasing its PL intensity.
In conclusion, we observed anomalous distributions of Bi atoms in InPBi thin films, as confirmed by both APT and TEM with quasi-periodic Bi nanowalls in (1–10) plane. The plane stretches toward the surface from the center of Bi-rich V-shaped nanowalls in the (−111) and (1–11) planes at the InPBi/InP interface, which have not been observed in other dilute bismides. The V-shaped nanowalls at the InPBi/InP interface are attributed to Bi-induced droplet epitaxy, whereas the Bi nanowalls could be induced by spinodal decomposition. The optical properties of InPBi are strongly related to such Bi distributions, which affect the amount of the Bi-related deep level and particularly the Bi-rich V-shaped nanowalls that hamper the recombination related to the PIn antisite level.
## Methods
Samples were grown on semi-insulating (001) InP substrates by V90 gas source MBE. Phosphine was cracked at 1000 °C to form P2. Elementary In and Bi sources were used and fluxes were controlled and calibrated by adjusting the effusion cell temperatures. The InP substrate was first deoxidized at 545 °C, measured by a thermocouple with P2 flux impinged onto the substrate surface. Subsequently, a 69 nm thick undoped InP buffer layer was grown at 495 °C with a P2 pressure of 630 Torr. An InPBi thin film with a thickness of 420 nm was then grown at 345 °C with a P2 pressure of 350 Torr. The as grown InP1−xBix had a Bi content of 2.3% measured by SIMS, which was calibrated based on Rutherford backscattering (RBS). All measured specimens were chosen from different positions of the same as-grown sample wafer.
Cross-section TEM specimen A was prepared using standard procedures, i.e., by mechanical lapping and dimpling followed by broad beam argon ion milling. The samples were investigated either with a JEOL 2100 F microscope operating at 200 kV or on a double spherical aberration corrected Titan Themis3 microscope operating at 200 kV. The crystal polarity of the TEM specimens were carefully determined using two independent methods: high-resolution Z-contrast imaging and convergent beam electron diffraction (CBED) techniques48. High-resolution energy dispersive X-ray spectrum image (EDX-SI) was acquired with the Titan system by using the Super-X detector at an extremely high probe current of about 1 nA and a reduced probe convergence angle of 18 mrad to enhance channeling. The Super-X detector comprises four silicon drift detectors (SDD) symmetrically placed around the optical axis, close to the sample area. All four signals are combined into one spectrum to improve the collection efficiency. Under these conditions, an EDX signal count rate of more than 85 kilo counts per second (kcps) at the specimen position was achieved. Data were acquired and quantified with FEI Velox software in which a standard Cliff-Lorimer (K-factor) quantification with absorption and geometry correction was implemented. The STEM-EDX maps of the specimen were collected within 30 min by drift correction.
Two specimens (Specimens B and C) were prepared and APT was performed by company CAMECA. The APT pillar specimens were prepared as follows: First, the specimens were coated with a protective GaAs capping layer on top. A lift-out wedge was then pulled and mounted onto specimen posts. The specimens were subsequently sharpened using annular ion mills in focused ion beam (FIB) to produce the final tips with a length of 1.8 μm, a bottom diameter of 380 nm and a tip diameter of 110 nm. These results were acquired under a laser energy of 0.05 pJ with a detection rate of 2% at a base temperature of 30 K.
After growth, Specimen D was etched using a mixed solution of HCl:H3PO4 (1:4) at room temperature; the etching rate was about 6.7 nm/s. Specimen D was etched away for 220 nm, 320 nm and 380 nm, respectively, to investigate the optical properties. The PL spectra were measured using a Fourier transform infrared (FTIR) spectrometry-based PL system in the rapid-scan mode rather than the step-scan mode in which a liquid-nitrogen cooled InSb detector and a CaF2 beam splitter were used. Laser with a wavelength of 532 nm was used as the excitation.
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Cahn, J. W. On spinodal decomposition. Acta metallurgica 9, 795–801 (1961).
47. 47.
Aspnes, D. & Studna, A. Dielectric functions and optical parameters of si, ge, gap, gaas, gasb, inp, inas, and insb from 1.5 to 6.0 ev. Physical Review B 27, 985 (1983).
48. 48.
Spiecker, E. Determination of crystal polarity from bend contours in transmission electron microscope images. Ultramicroscopy 92, 111–132 (2002).
## Acknowledgements
The authors are grateful for the financial support provided by the National Basic Research Program of China (Grant No. 2014CB643902), Key Program of Natural Science Foundation of China (Grant No. 61334004), Natural Science Foundation of China (Grant No. 61404152), National Laboratory for Infrared Physics, Key Research Program of the Chinese Academy of Sciences (Grant No. KGZD-EW-804), Creative Research Group Project of Natural Science Foundation of China (Grant No. 61321492), Swedish Research Council (VR) and Deutsche Forschungsgemeinschaft (DFG) through the research training school GRK 1896: “In-Situ Microscopy with Electrons, X-rays and Scanning Probes” and the Cluster of Excellence EXC 315 “Engineering of Advanced Materials”.
## Author information
Authors
### Contributions
L.Y.Z. was responsible for the design of the experiment, analysis of data and preparation of the manuscript. M.J.W. and E.S. performed TEM and interpreted the TEM results. X.Y.W. etched the samples. X.R.C. and J.S. conducted the PL measurement. Y.X.S. participated in the interpretation of the PL data. W.W.P., Y.Y.L. and L.Y. were involved in the analysis of APT data. S.M.W. supervised the entire study, interpreted the APT results and model, and participated in the manuscript revision.
### Corresponding author
Correspondence to Shumin Wang.
## Ethics declarations
### Competing Interests
The authors declare that they have no competing interests.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## Rights and permissions
Reprints and Permissions
Zhang, L., Wu, M., Chen, X. et al. Nanoscale distribution of Bi atoms in InP1−xBix . Sci Rep 7, 12278 (2017). https://doi.org/10.1038/s41598-017-12075-2
• Accepted:
• Published:
• ### Bismuth-induced band-tail states in GaAsBi probed by photoluminescence
• Bing Yan
• , Xiren Chen
• , Liangqing Zhu
• , Wenwu Pan
• , Lijuan Wang
• , Li Yue
• , Xiaolei Zhang
• , Li Han
• , Feng Liu
• , Shumin Wang
• & Jun Shao
Applied Physics Letters (2019)
• ### InPBi Quantum Dots for Super-Luminescence Diodes
• Liyao Zhang
• , Yuxin Song
• , Qimiao Chen
• , Zhongyunshen Zhu
• & Shumin Wang
Nanomaterials (2018)
• ### Atom probe tomography of nanoscale architectures in functional materials for electronic and photonic applications
• Alexander S. Chang
• & Lincoln J. Lauhon
Current Opinion in Solid State and Materials Science (2018)
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2020-08-04 01:06:54
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https://www.math24.net/table-first-order-derivatives/
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# Table of First Order Derivatives
Functions: $$f$$, $$y$$, $$u$$, $$v$$
Argument (independent variable): $$x$$
Natural number: $$n$$
Real numbers: $$C$$, $$a$$, $$b$$, $$c$$
1. Derivative of a constant
$${\large\frac{d}{{dx}}\normalsize}\left( C \right) = 0$$
2. Derivative of the function $$y = x$$
$${\large\frac{d}{{dx}}\normalsize}\left( x \right) = 1$$
3. Derivative of a linear function
$${\large\frac{d}{{dx}}\normalsize}\left({ax + b}\right) = a$$
4. Derivative of a quadratic function
$${\large\frac{d}{{dx}}\normalsize}\left({ax^2 + bx + c}\right) =$$ $${2ax + b}$$
5. Derivative of the power function
$${\large\frac{d}{{dx}}\normalsize}\left({x^n}\right) =$$ $${nx^{n – 1}}$$
6. Derivative of the power function with a negative exponent
$${\large\frac{d}{{dx}}\normalsize}\left({x^{-n}}\right) = – {\large\frac{n}{{{x^{n + 1}}}}\normalsize}$$
7. Derivative of the reciprocal function
$${\large\frac{d}{{dx}}\normalsize}\left( {{\large\frac{1}{x}}\normalsize} \right) = – {\large\frac{1}{{{x^2}}}\normalsize}$$
8. Derivative of the square root function
$${\large\frac{d}{{dx}}\normalsize} \left( {\sqrt x } \right) = {\large\frac{1}{{2\sqrt x }}\normalsize}$$
9. Derivative of a root
$${\large\frac{d}{{dx}}\normalsize}\left( {\sqrt[n]{x}} \right) = {\large\frac{1}{{n\sqrt[n]{{{x^{n – 1}}}}}}\normalsize}$$
10. Derivative of the logarithmic function
$${\large\frac{d}{{dx}}\normalsize}\left( {{{\log }_a}x} \right) =$$ $${\large\frac{1}{{x\ln x}}\normalsize},$$ $$a \gt 0,$$ $$a \ne 1.$$
11. Derivative of the natural logarithm
$${\large\frac{d}{{dx}}\normalsize} \left( {\ln x} \right) = {\large\frac{1}{x}\normalsize}$$
12. Derivative of the exponential function with base a
$${\large\frac{d}{{dx}}\normalsize} \left( {{a^x}} \right) = {a^x}\ln a,$$ $$a \gt 0,$$ $$a \ne 1.$$
13. Derivative of the exponential function with base e
$${\large\frac{d}{{dx}}\normalsize} \left( {{e^x}} \right) = {e^x}$$
14. Derivative of the sine function
$${\large\frac{d}{{dx}}\normalsize} \left( {{\sin x}} \right) = {\cos x}$$
15. Derivative of the cosine function
$${\large\frac{d}{{dx}}\normalsize} \left( {{\cos x}} \right) = {-\sin x}$$
16. Derivative of the tangent function
$${\large\frac{d}{{dx}}\normalsize} \left( {\tan x} \right) =$$ $${\large\frac{1}{{{{\cos }^2}x}}\normalsize} =$$ $${\sec ^2}x$$
17. Derivative of the cotangent function
$${\large\frac{d}{{dx}}\normalsize} \left( {\cot x} \right) =$$ $$-{\large\frac{1}{{{{\sin }^2}x}}\normalsize} =$$ $${-\csc ^2}x$$
18. Derivative of the secant function
$${\large\frac{d}{{dx}}\normalsize} \left( {\sec x} \right) =$$ $$\tan x \cdot \sec x$$
19. Derivative of the cosecant function
$${\large\frac{d}{{dx}}\normalsize} \left( {\csc x} \right) =$$ $${-\cot x} \cdot \csc x$$
20. Derivative of the inverse sine function
$${\large\frac{d}{{dx}}\normalsize} \left( {\arcsin x} \right) =$$ $${\large\frac{1}{{\sqrt {1 – {x^2}} }}\normalsize}$$
21. Derivative of the inverse cosine function
$${\large\frac{d}{{dx}}\normalsize} \left( {\arccos x} \right) =$$ $$-{\large\frac{1}{{\sqrt {1 – {x^2}} }}\normalsize}$$
22. Derivative of the inverse tangent function
$${\large\frac{d}{{dx}}\normalsize} \left( {\arctan x} \right) =$$ $${\large\frac{1}{{1 + {x^2}}}\normalsize}$$
23. Derivative of the inverse cotangent function
$${\large\frac{d}{{dx}}\normalsize} \left( {\text {arccot }x} \right) =$$ $$-{\large\frac{1}{{1 + {x^2}}}\normalsize}$$
24. Derivative of the inverse secant function
$${\large\frac{d}{{dx}}\normalsize}\left( {\text {arcsec }x} \right) =$$ $${\large\frac{1}{{\left| x \right|\sqrt {{x^2} – 1} }}\normalsize}$$
25. Derivative of the inverse cosecant function
$${\large\frac{d}{{dx}}\normalsize}\left( {\text {arccsc }x} \right) =$$ $$-{\large\frac{1}{{\left| x \right|\sqrt {{x^2} – 1} }}\normalsize}$$
26. Derivative of the hyperbolic sine function
$${\large\frac{d}{{dx}}\normalsize}\left( {\sinh x} \right) = \cosh x$$
27. Derivative of the hyperbolic cosine function
$${\large\frac{d}{{dx}}\normalsize}\left( {\cosh x} \right) = \sinh x$$
28. Derivative of the hyperbolic tangent function
$${\large\frac{d}{{dx}}\normalsize} \left( {\tanh x} \right) =$$ $${\large\frac{1}{{{{\cosh }^2}x}}\normalsize} =$$ $${{\text {sech}}^2}x$$
29. Derivative of the hyperbolic cotangent function
$${\large\frac{d}{{dx}}\normalsize} \left( {\coth x} \right) =$$ $$-{\large\frac{1}{{{{\sinh }^2}x}}\normalsize} =$$ $$-{{\text {csch}}^2}x,$$ $$x \ne 0.$$
30. Derivative of the hyperbolic secant function
$${\large\frac{d}{{dx}}\normalsize} \left( {\text {sech }x} \right) =$$ $$– {\text {sech }x} \cdot \tanh x$$
31. Derivative of the hyperbolic cosecant function
$${\large\frac{d}{{dx}}\normalsize}\left( {\text {csch }x} \right) =$$ $$– {\text {csch }x} \cdot \coth x,$$ $$x \ne 0.$$
32. Derivative of the inverse hyperbolic sine function
$${\large\frac{d}{{dx}}\normalsize}\left( {\text {arcsinh }x} \right) =$$ $${\large\frac{1}{{\sqrt {{x^2} + 1} }}\normalsize}$$
33. Derivative of the inverse hyperbolic cosine function
$${\large\frac{d}{{dx}}\normalsize}\left( {\text {arccosh }x} \right) =$$ $${\large\frac{1}{{\sqrt {{x^2} – 1} }}\normalsize},$$ $$x \gt 1.$$
34. Derivative of the inverse hyperbolic tangent function
$${\large\frac{d}{{dx}}\normalsize}\left( {\text {arctanh }x} \right) =$$ $${\large\frac{1}{{1 – {x^2}}}\normalsize},$$ $$\left| x \right| \lt 1.$$
35. Derivative of the inverse hyperbolic cotangent function
$${\large\frac{d}{{dx}}\normalsize}\left( {\text {arccoth }x} \right) =$$ $$-{\large\frac{1}{{{x^2} – 1}}\normalsize},$$ $$\left| x \right| \gt 1.$$
36. Derivative of the function $$u{\left( x \right)^{v\left( x \right)}}$$
$${\large\frac{d}{{dx}}\normalsize} \left( {{u^v}} \right) =$$ $$v{u^{v – 1}} \cdot {\large\frac{{du}}{{dx}}\normalsize} \,+$$ $${u^v}\ln u \cdot {\large\frac{{dv}}{{dx}}\normalsize}$$
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2020-07-10 22:06:44
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|
https://tex.stackexchange.com/questions/550720/redeclaring-finentry-results-in-dot-printed-at-the-beginning-of-the-document
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# Redeclaring finentry results in dot printed at the beginning of the document
As a follow-up of my old question "How to print the internal ID of the bibliography entries in the output format for referring to files?" I now decided not to use the internal ID, but the special field just as @moewe suggested me, that is declared by default.
So this is an example document:
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=numeric, backend=biber]{biblatex}
\DeclareFieldFormat{file}{\texttt{#1}}
\renewbibmacro*{finentry}{\newunit\newblock\printfield{file}\finentrypunct}
\begin{document}
\autocite{sigfridsson,worman,geer,nussbaum}
\printbibliography
\end{document}
Unfortunately, just by changing the to be printed field entrykey from the original answer to file, strange extra dots appear.
When you actually use the file field, you can notice they appear in front of the bibliography entries that follow on entries that do not have a file entry set. (Also, as you can see in the example above, the first entry seems to be excluded.)
Even when you remove \finentrypunct (which I don't want, but did for debugging), they are still there. So I have no idea where this dot in front of the entries comes from.
I think there is a typo in the other answer. The entry should not end with \finentrypunct but with \finentry:
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=numeric, backend=biber]{biblatex}
\DeclareFieldFormat{file}{\texttt{#1}}
\renewbibmacro*{finentry}{\newunit\newblock\printfield{file}\finentry}
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2021-12-05 02:10:44
|
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|
http://mathhelpforum.com/differential-geometry/158021-please-help-limit-proof.html
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I have a 3 parter. I think I have the first part, the second part I am not sure of and the third part I am kind of getting desperate with...
(a) Prove first that if c is a constant, and $\lim_{n\rightarrow \inf} s_n = s$ , then $\lim_{n\rightarrow \inf} cs_n = cs$.
(b) Prove that if $\lim_{n\rightarrow \inf} s_n = s$ then $\lim_{n\rightarrow \inf} s^2_n = s^2$. (Hint:recall that convergent sequences are bounded.)
(c) Use the polarization identity $ab = \frac{1}{4}((a+b)^2-(a-b)^2)$ to prove that if $\lim_{n\rightarrow \inf} s_n = s$ and $\lim_{n\rightarrow \inf} t_n = t$ , then $\lim_{n\rightarrow \inf} t_ns_n = ts$.
my work:
(a) Since for all $\varepsilon > 0$ , there exists an $N$, such that if $n > N , |s_n-s| < \varepsilon$ , there should
exist an $n_{\mu} \geq n$ such that $c|s_n-s| \leq \varepsilon$ hence $\lim_{n\rightarrow \inf} cs_n = cs$
(b) $\lim_{n \rightarrow \inf}s_n = s$ implies that ${s_n}$ is compact and bounded. Take $\varepsilon > 0$. For some $M$, if $n \geq M$, then $|s_n-s|=|s-s_n| < \sqrt{\varepsilon}$ and therefore $|s-s_n|^2 < \varepsilon$. so now $\lim_{n \rightarrow \inf}(s_n-s)^2 = 0$.
Take $|s_n^2-s^2| = |s_n(s_n-s)-s(s-s_n)| \leq |s_n||s_n-s|-|s||s-s_n| \leq |s_n-s|(|s_n|-|s|) \leq \varepsilon$ which gives us $\lim_{n \rightarrow \inf}(s_n^2-s^2)=0$
(c) If my other two are even correct, this is where I am stuck. PLEASE give me a little nudge...
|
2017-10-23 01:21:46
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|
https://aiuta.org/en/the-spherical-container-has-a-radius-of-21-cm-what-is-the-approximate-volume-of-the-container-use.244350.html
|
Mathematics
# The spherical container has a radius of 21 cm. What is the approximate volume of the container? Use 3.14 to approximate pi and express your answer in hundredths
#### Jayda
2 years ago
V=(4/3)pir^3
V=(4/3)(3.14)(21^3)
V=(4/3)(3.14)(9261)
V=12348(3.14)
V=38772.72 cm^3
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2018-12-16 11:20:52
|
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|
https://autohausvw.co.uk/1gc1zsf/c3a62a-radiance-and-irradiance-in-remote-sensing
|
Further comparison in the Yellow Sea waters representing a massive phytoplankton bloom on 27 March 2002 revealed that the SAC algorithm caused an excessive correction for the visible bands, with the 412 nm band being affected the most, leading to severe overestimation of chlorophyll concentrations in the bloom-contained waters. For a given instrument, the wider the spectral band [λ1, λ2], the greater the collected energy. The estimated spectra were used to (1) evaluate the performance of four wavelengths and wavelengths ratios for accurate retrieval of SS. stream leaving radiances and the derived ocean color products (inherent optical properties, chlorophyll). Soiling or dust accumulation on photovoltaic solar modules deters the transmission of irradiance through the glass surface covering of the modules. Remote sensing reflectance (Rrs) contains the spectral colour information of the water body (below the sea surface). Radiance is more complicated: exchange of energy (in the form of photons) across a given area of flat surface per time and then divided by the amount of steradians from which the "given area" is collecting light. Developing this equation shows that the equivalent fluxes follow the same equation as the spectral flux : $$\phi_{eq\,[\lambda_{1},\lambda_{2}]}=\frac{d\epsilon_{eq\,[\lambda_{1},\lambda_{2}]}}{dt}\label{eq:flux-energie-equivalente}$$\phi_{eq\,[\lambda_{1},\lambda_{2}]}=\frac{d\epsilon_{eq\,[\lambda_{1},\lambda_{2}]}}{dt}\label{eq:flux-energie-equivalente}. I have written a detailed description of these quantities in my blog, trying also to explain how they are used (the remote sensing reflectance is not described, but it is explained in Whyzar's answer). with $$S_{_{[\lambda_{1},\lambda_{2}]}}=\intop_{\lambda_{1}}^{\lambda_{2}}S(\lambda)\, d\lambda$$S_{_{[\lambda_{1},\lambda_{2}]}}=\intop_{\lambda_{1}}^{\lambda_{2}}S(\lambda)\, d\lambda,sensitivity of detector within interval [λ1, λ2]. You will have access to both the presentation and article (if available). transmittance along the the incident direction. this include path radiance from atmospheric scattering and the reduction of the total irradiance. How can you trust that there is no backdoor in your hardware? ... Data on sunlight radiation spectrum are provided in works [10. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Geographic Information Systems Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, FYI: I also found this article which gives a simplified explanation on DN vs. Radiance vs. Reflectance. Since spectroradiometric measurements are not often used for this application, several measuring and analysis methods are discussed in terms of PV applications. For example, the solar illumination received on land varies with the earth-sun distance, which varies during the year. A link to your blog is not helpful if that link dies. The old OSA schemes in the ARPEGE and LMDZ models only resolve the latitudinal dependence in an ad hoc way without an accurate representation of the solar zenith angle dependence. Irradiance makes it possible, to characterize the light power which reaches a surface perpendicular to the light source per unit area. In terms of remote sensing reflectance and water leaving radiance. The spectral irradiance is the spectral flux which reaches the detectrr per surface unit ds , it is therefore defined by : $$E(\lambda)=\frac{d\phi(\lambda)}{ds}$$E(\lambda)=\frac{d\phi(\lambda)}{ds}. During the early period, This energy is provided by photons of various wavelengths. Total solar and UV irradiances have been measured from various space Reflectance is a property of the surface and does not depend on the instrument observing it or on the irradiance received. Correction of Remotely Sensed Data. Then, the normalized Gaussian distribution function is used to extrapolate aerosol radiance over the entire wavebands (from 412 to 748 nm). However, Ls is composed of On a camera, the exposure time corresponds to the interval between opening and closing the shutter. 20 289–305), re-treating the assumption of spatial homogeneity of the atmosphere using simple models for assessing the contributions of aerosol and molecular scattering. Geographic Information Systems Stack Exchange is a question and answer site for cartographers, geographers and GIS professionals. In addition, we generated from different concentrations of SS and chlorophyll, and various absorptions of DOM by random number functions to create a large database to test the model. During the early period, Difference between irradiance and radiance, remote sensing reflectance and water leaving radiance, remote sensing reflectance and water leaving radiance, harrisgeospatial.com/Learn/Blogs/Blog-Details/ArtMID/10198/…. Si vous continuez à utiliser ce site, nous supposerons que vous en êtes satisfait. Together, the paleo solar and climate data enable a discussion of the extent of global climate change that can be explained by a variable Sun. The results show that the retrieved surface reflectance can exhibit significant variations when different solar irradiance models are used, especially in the OLI coastal blue band at 443 nm. At the heart of any solar simulator is the light source itself. Rrs is the ratio between water-leaving radiance (Lw, above the sea surface) and downwelling irradiance (Ed, above the sea surface). The growth in renewable energy generation has led to an increased need to develop, manufacture and test components and subsystems for solar thermal, photovoltaic (PV), and concentrating optics for both thermal and electrical solar applications. The energy an instrument receives during integration time, with a sensivity S(λ… A large data set containing coincident in situ chlorophyll and remote sensing reflectance measurements was used to evaluate the accuracy, precision, and suitability of a wide variety of ocean color chlorophyll algorithms for use by SeaWiFS (Sea-viewing Wide Field-of-view Sensor). Les champs obligatoires sont indiqués avec *. On the contrary, the RI coupled with the standard spectral ratios yielded comprehensive information about various ranges of algal blooms, while RCA Chl showing a good agreement with in-situ data led to enhanced understanding of the spatial and temporal variability of the recent HAB occurrences in high scattering and absorbing waters off the Korean and Chinese coasts. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. The radiance is a unit widely used in remote sensing, since it combines several advantages: The energy measured by a detector is proportional to the equivalent luminance.
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2021-05-13 10:14:43
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https://www.shawenyao.com/Fossil-Completionists-Guidebook/
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# Fossil Completionist's Guidebook
My attempt at relieving fossil collector’s anxiety.
Written on May 24, 2020
In Animal Crossing: New Horizons, every starfish-shaped crack is another chance for glory. Once you dig up a new fossil, you can then donate it to Blathers the museum curator. After an enthusiastic but rather unsolicited introduction about the fossil’s origin, it becomes a permanent part of the exhibition for you and your friends to enjoy.
If you are like me, all was well until the honeymoon phase started to wear out and at some point, you began to get nothing but duplicates. Days soon turned into weeks yet things didn’t get any better, and you are on the verge of suspecting foul play. Could Nintendo be deliberately withholding a few fossils from your reach just to keep you coming back? Could it be a marketing campaign to sell you the online membership where trading with friends is the only way to advance? Or could it be your bad luck again, as with everything else in life?
In this post, I analyze the problem of how long it takes on average to complete the fossil collection. As the answer suggests, it is still too early to be concerned. More specifically, players have at least until June 17th to start either questioning whether the system is rigged or being considered unlucky.
## General Setup
First things first, there are a few important facts to keep in mind before we get started:
• for tractability, it is assumed that each fossil has an equal chance of showing up (comment below if you disagree!)
• 4 fossils can be found on any given day
• there are 73 unique fossils in total to add to the museum’s collection
## Numerical Solution
With the help of any modern computing device, numerical simulation indicates that on average, it takes 89 days (or 356 trials) to collect all fossils. So there you go - it’s not that bad.
Furthermore, if we look at the probability distribution at the end of the 89th day, more likely than not you will have completed the collection already.
## Analytic Solution
Generally, if the probability of some random event happening is $x$, it takes $1 / x$ trials on average for it to occur at least once. Adding all expected number of trials to collect the first $n$ fossils together, we have:
$\mathbb{E} \left[ T ^ N (n) \right] = \frac{ N }{ N+1-1 } + \frac{ N }{ N+1-2 } + \ ... \ +\frac{ N }{ N+1-(n-1) } +\frac{ N }{ N+1-n }$
where $N$ is the total number of unique collectibles. It grows almost linearly at first (as it’s fairly unlikely to get duplicates already), but the last one is expected to cost you $N$ tries.
The expected number of unique fossils as a function of the number of trials tells the other side of the story. For each new trial, the incremental contribution to the collection in terms of additional “uniqueness” equals the probability of finding something that has not been found so far:
$\mathbb{E} \left[ F ^ N (t) \right] = \left\{ \begin{array}{c} 1, \ t = 1 \\ \mathbb{E} \left[ F ^ N (t - 1) \right] + \frac{ N - \mathbb{E} \left[ F ^ N (t - 1) \right] }{ N } , \ t \geq 2 \\ \end{array} \right.$
Again, initially it fills out almost linearly. The curve starts to flatten out eventually as you build up your collection, desperately waiting for the last few pieces to arrive. That said, all you really need is to keep calm and carry on - as previously mentioned, the odds are in your favor in 3 months’ time (and increasingly so).
## Conclusions
Animal Crossing: New Horizons was launched on March 20, 2020, so if you started playing on day 1 and never missed a single fossil, June 17th (i.e., day 89) will be your benchmark to beat. Should that not be the case, you can always blame it on Zipper!
This is Part III of my Animal Crossing post series. For Part II, see here.
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2020-11-24 20:03:49
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https://plainmath.net/72339/compute-x
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# Compute 7 −<!-- − --> 14
Compute $7-14+\left(14+5\right)×12÷6$.
You can still ask an expert for help
## Want to know more about Polynomial arithmetic?
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Add $14$ and $5$.
$7-14+19\cdot 12÷6$
Multiply $19$ by $12$.
$7-14+228÷6$
Find the common denominator.
$\frac{7\cdot 6}{6}+\frac{-14\cdot 6}{6}+228÷6$
Combine the numerators over the common denominator.
$\frac{7\cdot 6-14\cdot 6+228}{6}$
Simplify each term.
$\frac{42-84+228}{6}$
Simplify the expression.
$31$
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2022-05-18 13:44:09
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https://www.maplesoft.com/support/help/MapleSim/view.aspx?path=ModelonHydraulics/Restrictions/Basic/SimOriNoStates
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Sim Ori No States $—$ Simple orifice model for turbulent flow
The Sim Ori No States component describes the turbulent flow through an orifice if no cavitation occurs using a simple textbook model:
$q=A{C}_{d}\sqrt{\frac{2\mathrm{Δp}}{\mathrm{\rho }}}$
Variables used in the above equations
$q$ Flow rate $\left[\frac{{m}^{3}}{s}\right]$ $A$ Area of the orifice $\left[{m}^{2}\right]$ ${C}_{d}$ Discharge coefficient $\mathrm{\rho }$ Mass density, from FluidProp $\left[\frac{\mathrm{kg}}{{m}^{3}}\right]$ $\mathrm{Δp}$ Pressure drop across orifice $\left[\mathrm{Pa}\right]$
The mass and flow forces are not included.
Note: This model can cause severe numerical problems for the integration routine if the pressure drop $\mathrm{Δp}$ becomes very small.
Related Components
Name Description Resistance with laminar flow. Resistance with laminar flow and externally commanded conductance. The component, based on the loss coefficient K, describes both flow regimes: laminar for very small Reynolds numbers and turbulent for higher Reynolds numbers (default model). The component describes both flow regimes, using an interpolation polynomial. Orifice component checking for cavitation. Metering Orifice (that is, model Orifice No States with variable diameter). Two orifices in series, one with variable the other with fixed flow area. Same as Orifice No States, but with the equations rearranged to compute $\mathrm{Δp}$ for given q. Differences between basic models are shown by a figure.
Equations $\left\{\begin{array}{cc}\left\{\mathrm{dpeff}=\mathrm{dpacting},\mathrm{dpeffu}=0,\mathrm{pmax}=0,\mathrm{pmin}=0,\mathrm{pminab}=0,\mathrm{alpha_dmax}=0,\mathrm{delta_pk}=0\right\}& \mathrm{checkvalve}\\ \left\{\begin{array}{cc}\left\{\mathrm{dpeff}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{dpeffu}& 0<\mathrm{Δp}\\ -\mathrm{dpeffu}& \mathrm{otherwise}\end{array}\right\\right),\mathrm{dpeffu}=\mathrm{noEvent}\left(\left|\mathrm{pmax}-\mathrm{pmin}\right|\right),\mathrm{pmax}=\mathrm{max}\left({p}_{A\left(\mathrm{limited}\right)},{p}_{B\left(\mathrm{limited}\right)}\right),\mathrm{pmin}=\left\{\begin{array}{cc}\mathrm{pmax}-\mathrm{delta_pk}& \mathrm{pminab}<\mathrm{pmax}-\mathrm{delta_pk}\\ \mathrm{pminab}& \mathrm{otherwise}\end{array}\right\,\mathrm{pminab}=\mathrm{min}\left({p}_{A\left(\mathrm{limited}\right)},{p}_{B\left(\mathrm{limited}\right)}\right),\mathrm{alpha_dmax}=\frac{827}{1000}-\frac{17\ell }{2000\mathrm{D}},\mathrm{delta_pk}={\mathrm{α\left[k\right]}}^{2}{\left(\frac{\sqrt{\mathrm{max}\left(0,\mathrm{pmax}\right)}}{\mathrm{alpha_dmax}}+\frac{10\mathrm{\nu }\left(1+\frac{9\ell }{4\mathrm{D}}\right)\sqrt{2}}{\mathrm{α\left[k\right]}\sqrt{\frac{1}{\mathrm{\rho }}}\mathrm{D}}\right)}^{2}\right\}& \mathrm{cavitation}\\ \left\{\mathrm{dpeff}=\mathrm{Δp},\mathrm{dpeffu}=0,\mathrm{pmax}=0,\mathrm{pmin}=0,\mathrm{pminab}=0,\mathrm{alpha_dmax}=0,\mathrm{delta_pk}=0\right\}& \mathrm{otherwise}\end{array}\right\& \mathrm{otherwise}\end{array}\right\$ $\left\{\begin{array}{cc}\left\{\left\{\begin{array}{cc}\left\{\mathrm{\lambda }=0,\mathrm{qunsigned}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.lossCoeff}\left(\mathrm{Δp}=\mathrm{dpeff}-{p}_{\mathrm{open}},{k}_{1}={k}_{1},{k}_{2}={k}_{2},\mathrm{\nu }=\mathrm{\nu },\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{orif}=\mathrm{orif}\right)\right\}& \mathrm{Transition}=1\\ \left[\mathrm{qunsigned},\mathrm{\lambda }\right]=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff}\left(\mathrm{Δp}=\mathrm{dpeff}-{p}_{\mathrm{open}},{C}_{d}={C}_{d},{\mathrm{\lambda }}_{c}={\mathrm{\lambda }}_{c},\mathrm{\nu }=\mathrm{\nu },\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{orif}=\mathrm{orif}\right)& \mathrm{otherwise}\end{array}\right\,\left\{\begin{array}{cc}{q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{qunsigned}& 0\le \mathrm{dpeff}-{p}_{\mathrm{open}}\\ 0& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{checkvalve}\\ {q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{qunsigned}& 0\le \mathrm{dpeff}-{p}_{\mathrm{open}}\\ -\mathrm{qunsigned}& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{otherwise}\end{array}\right\,\mathrm{q_reg}={q}_{\mathrm{noleak}},{p}_{\mathrm{open}}={p}_{\mathrm{trans}},{q}_{\mathrm{open}}=0\right\}& \mathrm{flowcond}=1\\ \left\{\mathrm{\lambda }=0,\mathrm{q_reg}={q}_{\mathrm{noleak}},\mathrm{qunsigned}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.laminar}\left(\mathrm{Δp}=\mathrm{dpeff},G=G\right),{p}_{\mathrm{open}}=0,{q}_{\mathrm{noleak}}=\mathrm{qunsigned},{q}_{\mathrm{open}}=0\right\}& \mathrm{flowcond}=2\\ \left\{\mathrm{\lambda }=0,\mathrm{q_reg}={q}_{\mathrm{noleak}},\mathrm{qunsigned}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff}\left(\mathrm{Δp}=\mathrm{dpeff},{C}_{d}={C}_{d},\mathrm{flownumber}=\mathrm{false},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{orif}=\mathrm{orif}\right),{p}_{\mathrm{open}}=0,{q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{qunsigned}& 0\le \mathrm{dpeff}\\ -\mathrm{qunsigned}& \mathrm{otherwise}\end{array}\right\\right),{q}_{\mathrm{open}}=0\right\}& \mathrm{flowcond}=3\\ \left\{\left\{\begin{array}{cc}{q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{smooth}\left(0,\left\{\begin{array}{cc}\mathrm{qunsigned}& {p}_{\mathrm{open}}<\mathrm{dpeff}\\ \mathrm{q_reg}& \mathrm{otherwise}\end{array}\right\\right)& 0\le \mathrm{dpeff}-{p}_{\mathrm{closed}}\\ 0& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{checkvalve}\\ {q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{smooth}\left(0,\left\{\begin{array}{cc}\mathrm{qunsigned}& {p}_{\mathrm{open}}<\mathrm{dpeff}\\ \mathrm{q_reg}& \mathrm{otherwise}\end{array}\right\\right)& 0\le \mathrm{dpeff}-{p}_{\mathrm{closed}}\\ \mathrm{smooth}\left(0,\left\{\begin{array}{cc}-\mathrm{qunsigned}& \mathrm{dpeff}<-{p}_{\mathrm{open}}\\ -\mathrm{q_reg}& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{otherwise}\end{array}\right\,\left\{\begin{array}{cc}\left\{\left\{\begin{array}{cc}{q}_{\mathrm{open}}=\frac{\left(\frac{1}{G}+\sqrt{\frac{1}{{G}^{2}}+\frac{2{p}_{\mathrm{closed}}\mathrm{\rho }}{{C}_{d}^{2}{A}^{2}}}\right){C}_{d}^{2}{A}^{2}}{\mathrm{\rho }}& \mathrm{Transition}=2\\ {q}_{\mathrm{open}}=\frac{\left(\frac{1}{G}-\frac{\mathrm{\rho }{k}_{1}\mathrm{\nu }}{2\mathrm{D}A}+\sqrt{{\left(-\frac{1}{G}+\frac{\mathrm{\rho }{k}_{1}\mathrm{\nu }}{2\mathrm{D}A}\right)}^{2}+\frac{2{p}_{\mathrm{closed}}\mathrm{\rho }{k}_{2}}{{A}^{2}}}\right){A}^{2}}{\mathrm{\rho }{k}_{2}}& \mathrm{otherwise}\end{array}\right\,\mathrm{\lambda }=0,{p}_{\mathrm{open}}={p}_{\mathrm{closed}}+\frac{{q}_{\mathrm{open}}}{G}\right\}& \mathrm{regparam}=1\\ \left\{\left\{\begin{array}{cc}{p}_{\mathrm{open}}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.inv_lossCoeff}\left(q={q}_{\mathrm{open}},{k}_{1}={k}_{1},{k}_{2}={k}_{2},\mathrm{\rho }=\mathrm{\rho },\mathrm{\nu }=\mathrm{\nu },\mathrm{D}=\mathrm{D}\right)& \mathrm{Transition}=1\\ {p}_{\mathrm{open}}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.inv_dischargeCoeff}\left(q={q}_{\mathrm{open}},{C}_{d}={C}_{d},\mathrm{\rho }=\mathrm{\rho },\mathrm{D}=\mathrm{D}\right)& \mathrm{otherwise}\end{array}\right\,\mathrm{\lambda }=0,{q}_{\mathrm{open}}=\frac{{\mathrm{Re}}_{\mathrm{trans}}\mathrm{\nu }A}{\mathrm{D}}\right\}& \mathrm{regparam}=2\\ \left\{\left\{\begin{array}{cc}\left\{\mathrm{\lambda }=0,{q}_{\mathrm{open}}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.lossCoeff}\left(\mathrm{Δp}={p}_{\mathrm{open}},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},{k}_{1}={k}_{1},{k}_{2}={k}_{2},\mathrm{\nu }=\mathrm{\nu },\mathrm{orif}=\mathrm{orif}\right)\right\}& \mathrm{Transition}=1\\ \left[{q}_{\mathrm{open}},\mathrm{\lambda }\right]=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff}\left(\mathrm{Δp}={p}_{\mathrm{open}},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},{C}_{d}={C}_{d},\mathrm{flownumber}=\mathrm{false},\mathrm{orif}=\mathrm{orif}\right)& \mathrm{otherwise}\end{array}\right\,{p}_{\mathrm{open}}={p}_{\mathrm{trans}}\right\}& \mathrm{otherwise}\end{array}\right\,\left[\mathrm{qunsigned},\mathrm{q_reg}\right]=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.conditionalFlow}\left(\mathrm{Δp}=\mathrm{dpeff},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{Transition}=\mathrm{Transition},\mathrm{regtype}=\mathrm{regtype},\mathrm{\nu }=\mathrm{\nu },{p}_{\mathrm{closed}}={p}_{\mathrm{closed}},{p}_{\mathrm{open}}={p}_{\mathrm{open}},{q}_{\mathrm{open}}={q}_{\mathrm{open}},{k}_{1}={k}_{1},{k}_{2}={k}_{2},{C}_{d}={C}_{d}\right)\right\}& \mathrm{otherwise}\end{array}\right\$ $\mathrm{\nu }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $\mathrm{\rho }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $q=\frac{{m}_{\mathrm{flow}\left(A\right)}}{\mathrm{\rho }}$ $q={q}_{\mathrm{noleak}}+{q}_{\mathrm{leak}}$ $\mathrm{Δp}={p}_{A\left(\mathrm{limited}\right)}-{p}_{B\left(\mathrm{limited}\right)}$ ${p}_{A\left(\mathrm{abs}\right)}={p}_{A}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{A\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{A},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${p}_{B\left(\mathrm{abs}\right)}={p}_{B}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{B\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{B},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${m}_{\mathrm{flow}\left(A\right)}+{m}_{\mathrm{flow}\left(B\right)}=0$
Variables
Name Value Units Description Modelica ID $\mathrm{Δp}$ $\mathrm{Pa}$ Pressure drop dp $q$ $\frac{{m}^{3}}{s}$ Flow rate flowing into port_A q ${p}_{A\left(\mathrm{limited}\right)}$ $\mathrm{Pa}$ Limited gauge pressure pA_limited ${p}_{B\left(\mathrm{limited}\right)}$ $\mathrm{Pa}$ Limited gauge pressure pB_limited $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Upstream density rho $\mathrm{\nu }$ $\frac{{m}^{2}}{s}$ Upstream kinematic viscosity nu ${p}_{A\left(\mathrm{abs}\right)}$ $\mathrm{Pa}$ Absolute pressure pA pA_abs ${p}_{B\left(\mathrm{abs}\right)}$ $\mathrm{Pa}$ Absolute pressure pB pB_abs $T$ $K$ Local temperature T ${p}_{A\left(\mathrm{summary}\right)}$ ${p}_{A}$ $\mathrm{Pa}$ Pressure at port A summary_pA ${p}_{B\left(\mathrm{summary}\right)}$ ${p}_{B}$ $\mathrm{Pa}$ Pressure at port B summary_pB ${\mathrm{Δp}}_{\mathrm{summary}}$ $\mathrm{Δp}$ $\mathrm{Pa}$ Pressure drop summary_dp ${q}_{\mathrm{summary}}$ $q$ $\frac{{m}^{3}}{s}$ Flow rate flowing into port_A summary_q ${P}_{\mathrm{hyd}\left(\mathrm{summary}\right)}$ $-\mathrm{Δp}q$ $W$ Hydraulic Power summary_HP ${p}_{\mathrm{sat}}$ [1] $\mathrm{Pa}$ Gas saturation pressure p_sat ${q}_{\mathrm{leak}}$ ${G}_{\mathrm{leak}}\mathrm{Δp}$ $\frac{{m}^{3}}{s}$ Leakage flow q_leak ${q}_{\mathrm{noleak}}$ $\frac{{m}^{3}}{s}$ Flow rate through component q_noleak $\mathrm{dpeff}$ $\mathrm{Pa}$ Effective pressure drop dpeff $A$ [2] ${m}^{2}$ Orifice area A $\mathrm{D}$ $d$ $m$ Orifice diameter D ${q}_{\mathrm{open}}$ $\frac{{m}^{3}}{s}$ Flow when fully open orifice q_open ${p}_{\mathrm{open}}$ $\mathrm{Pa}$ Pressure when fully open orifice p_open $\mathrm{dpacting}$ $0$ $\mathrm{Pa}$ Acting, i.e. delayed pressure differential dpacting $G$ $0$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Hydraulic conductance $G=\frac{\mathrm{∂q}}{\mathrm{∂p}}$ G $\mathrm{\lambda }$ Flow coefficient lambda
[1] $\mathrm{oil.gasSaturationPressure}\left(T=T,{v}_{\mathrm{gas}}={\mathrm{oil.v}}_{\mathrm{gas}}\right)$
[2] $\frac{1}{4000000}\mathrm{\pi }$
Connections
Name Description Modelica ID ${\mathrm{port}}_{A}$ Layout of port where oil flows into an element ($0<{m}_{\mathrm{flow}}$, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_A ${\mathrm{port}}_{B}$ Hydraulic port where oil leaves the component (${m}_{\mathrm{flow}}<0$, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_B $\mathrm{oil}$ oil
Parameters
General Parameters
Name Default Units Description Modelica ID ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system $d$ $0.001$ $m$ Orifice diameter diameter ${C}_{d}$ $0.707$ Max discharge coefficient C_d
Constant Parameters
Name Default Units Description Modelica ID $\mathrm{orif}$ $1$ Orifice dimension orif $\mathrm{flowcond}$ $3$ Flow condition flowcond $\mathrm{Transition}$ $1$ Transition model Transition reg type $0$ Regularization type regtype reg param $0$ Regularization parameter regparam $\mathrm{cavitation}$ $\mathrm{false}$ Cavitation cavitation $\mathrm{checkvalve}$ $\mathrm{false}$ checkvalve ${k}_{1}$ $0$ Laminar part k1 ${k}_{2}$ $0$ ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2 ${\mathrm{\lambda }}_{c}$ $0$ Critical flow number lambdac $\ell$ $0$ $m$ Orifice length; $1<\frac{\ell }{d}$ length ${\Re }_{\mathrm{trans}}$ $0$ Transition Reynolds number Re_trans ${p}_{\mathrm{trans}}$ $0$ $\mathrm{Pa}$ Transition pressure p_trans ${p}_{\mathrm{closed}}$ $0$ $\mathrm{Pa}$ Cracking pressure p_closed ${G}_{\mathrm{leak}}$ $0$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Leakage conductance G_Leak
Constants
Name Value Units Description Modelica ID $\mathrm{α\left[k\right]}$ $0.649$ alpha_k
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2017-08-19 07:22:28
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https://www.mechanicalmoney.com/2018/03/
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## Saturday, March 24, 2018
### The Curious Union of Chess, Money, and Economic Production
$c(t)+g(t)=r(t)k_b(t)+f_w(t)n(t)+k_p(t)$
$c(t) + g(t) = f_w(t)n(t)(1+r(t)) + k_p(t)$
$c(t) + g(t) = k_b(t)(1+r(t)) + k_p(t)$
==============================================
In the game of Chess, players own the moves they make. Each move advances the game in a continuum from start to finish.
A productive firm works the same way. When a fractional part of a complex product is made or purchased, the firm owns another fractional part of a continuum that evolves into a priced product.
In a curious way, I'm frustrated by Brian Romanchuk's article
"The Curious Profit Accounting of DSGE Models." I can't convince myself that his beginning equation 16.2.3 is correct.[1] [2] It certainly doesn't fit with the real-world economic framework that I observe!
Unable to make sense of the equation but agreeing that an equation linking three sectors of the productive economy is a worthy goal, I would like to remove the wrinkles. A task harder to do than I expected.
The Problem
While my initial criticism of the equation was the number of sectors represented, I eventually realized that the basic flaw stemmed from a misuse of the capital tool. Financial capital was conceptually used as means of production in the same manner as labor so that it became one of the final products. That made no sense to me. In the real world, financial capital is directly exchanged for fractional contributions thereby transferring ownership in both directions.
We can use the example of fractional labor as an illustration to make the point. Using monetary exchange, one current hour of labor is traded for an hour of labor-that-has-been-previously-completed. In other words, when a person works one hour, that effort is effectively traded monetarily for one past hour that another person has sweated through.
The Solution
We can symbolically show past laboring effort expended, then represented by financial capital, and then returned to labor by writing $n \mapsto k \mapsto n,$ where $\mapsto$ is the maps-to symbol, $k$ is the capital received from previously expended effort and $n$ is hours expended either past or currently.
This symbolic description using money [5] does not relate hours directly to a rate of payment. It has the limited task of indicating that a block of labor has been traded for a block of money has been traded for a block of labor. The concept of trading blocks for blocks will be woven into this article.
Only by accident does perfect mapping occur in real world exchanges that occur over a time period. Instead, there is always a difference in values that we will describe symbolically by writing $n \mapsto k \mapsto (n+p),$ where $p$ represents a value difference perceived by the owner of the second $n.$ In words, we say that the second provider of labor must perceive a benefit (or Profit) that encourages a decision to proceed. The benefit may be visible in the form of money or invisible in the form of product preference.
Continue Defining Sectors
Returning to the subject of sectors, my initial criticism of Brian's equation 16.2.3 was that four sectors were described, not three as he suggested. Now that I am in version 6 (or more!) of developing a 'better equation', I believe that FIVE sectors are required to fully describe the productive economic continuum.
How do I define 'sectors'? If an economic contributor can make a decision, there is a need to represent that ability by assignment to an economic sector. The ability to make a decision implies ownership of some part of the productive amalgam with entitlement to financial reward. The five sectors that I see are consumption, government, productive firm, labor, and financial capital.
The productive firm sector will be assigned a reward coming from profit (if any).
The need for a financial capital sector is not immediately obvious because each of the other sectors have within them members who own financial capital, The need for a separate sector stems from the ownership impairment decision that must be made when property is rented away.
Our capital sector will have a undefined stock of preexisting capital. This will be a necessary assumption when we later assume that productive firms borrow and repay all financial capital used to pay expenses during a time period. The capital sector will be assigned a reward in the form of interest payment.
Describe Model Conditions in a Nutshell
The task of a productive firm is to reorder the capabilities of our five sectors into a product exchange evolution. The assembly process will be measured and modeled as a capital expense using three sectors: 1) a stylized all-inclusive labor sector, 2) a sector describing the cost of rented capital, and 3) an unpredictable remainder (Profit?) assumed to be owned by the productive firm sector. The selling process (of the product for consumption by the household and government sectors) provides income. The entire process is assumed to start and complete in one year.
Capital (owned by the capital sector) is existent and adequate. Financial capital is traded fractionally for fractional product parts as the product is assembled and finally sold.
Now Write a Productive Continuum Equality
We will describe the productive process by completing an annual income statement in terms of our five economic sectors. The result is surprisingly satisfying.
Our income statement will be written directly from the description given.[4] Label the sector terms as labor $n,$ borrowed capital $k_b,$ profit $k_p,$ household $c,$ and government $g.$ With income on the left side, we write the general concept mapped to the real-world as $c+g \mapsto k_b+n+k_p.$ where profit is the incentive term.
Before writing an equality, we need to adjust the data from each sector into a place on the monetary scale, noticing that only the labor sector is not already reported in monetary terms. We will adjust labor by using a translation factor $f_w.$ The cost of borrowed capital will be calculated using cost factor $r.$
To do all of this, we will use a function format[3] with a time notation to indicate that the equality is related to a unique time period. We will write our equality as
(1) $c(t)+g(t)=r(t)k_b(t)+f_w(t)n(t)+k_p(t).$
Equation 1 bridges the continuum of the productive process using five sectors.
Readers may be interested in comparing equation 1 to Brian's equation 16.2.3. In 16.2.3, terms $k_b(t)$ and $f_w(t)n(t)$ seem to have been equated which enables us to simplify the equation. This is allowable if capital is borrowed at the same time and amount that labor cost are paid (albeit an inefficient process). With stylized labor cost clearly paid with borrowed capital, we have $k_b(t) = f_w(t)n(t).$ Substitute into equation 1 using the labor term to get $c(t) + g(t) = r(t) f_w(t)n(t) + f_w(t)n(t) + k_p(t).$ Simplify to read
(2) $c(t) + g(t) = f_w(t)n(t)(1+r(t)) + k_p(t).$
We can also substitute using the borrowed capital term to get
(3) $c(t) + g(t) = k_b(t)(1+r(t)) + k_p(t).$
The difference between expressions (2) and (3) is the emphasis on financial capital or labor. The two expressions should evaluate to the same monetary number.
Equations 1, 2 and 3 are all final versions of an equality that I think describes the productive continuum adjusted to the real-world using five sectors. Perhaps my readers will have a better definition of exactly what the equation describes.
Unfortunately, Brian's 16.2.3 looks like a distant cousin of the equations developed here. I still don't understand 16.2.3.
Making the Unknown Known
In the assumptions (in "model conditions"), we clearly stated that profit $k_b(t)$ was unknown, yet, we also clearly assumed that the entire equation completed in one time period. If completed, we can learn the value of all terms by examining the accumulated data.
Equation 1 (and equivalent 2 and 3) describes a relationship between economic sectors. It would be correct to attach a historical number to each of the sectors. It would also be correct to predict future numbers for each sector based on changes envisioned.
DSGE models supposedly try to find points of optimization for the sector of interest. The equations developed here would suggest that optimum for one sector would not be optimum for a second sector.
Using the Equation
It is important to remember that the profit term $k_p(t)$ is a balancing term that maps theory to the real-world. Hence, we should NEVER expect to find numerical values by beginning with a known profit result. Yes, the profit term is real in the real-world, but it represents motivation (or disincentive) for decision makers at the theoretical level.
This model of money and it's use in productive effort seems (to me) very robust. As a robust description, it can become a common reference for departure into other, hopefully improved, models. Three model excursions follow to illustrate this possibility:
1) This productive continuum equation was built based on micro economic principals. It can be smoothly expanded to the macro economic scale by adding productive firms. When ALL of the productive firms are included, we can begin consideration of the catastrophic transfer problem [If productive firms are always profitable, eventually all of the money available in an economy will be in the ownership of firm management.]. This undesirable conclusion could materialize using this model if financial capital ownership was not widely distributed in the economy. Would government ownership of capital prevent the potential problem?
2) We can easily model a government that uses two revenue sources, bonds $g_b(t)$ and taxes $g_t(t)$. We could write the equation as $c(t) + g_b(t)b_k(t)+g_t(t) = f_w(t)n(t)(1+r(t)) + k_p(t)$ where the term $b_k(t)$ converts the bonds to financial capital. This model would need an explanation for how that conversion mechanism worked in the real economy.
3) Still using the model of example 2, which government would be more interested in imposing tariffs and why?
Hmmm. How would we fit foreign sourced production into an equality like we have here? I don't have that question resolved.
Conclusion
A DSGE equation that seems to not fit smoothly with other frameworks caused enough irritation to initiate an effort to find a better fitting equation. The better fitting equality found requires a base framework of assumptions that clearly included a capital owning sector that had decision making authority.
The simplicity of the equation found makes it seem almost trivial. Yet, we needed to assume a robust continuum of sequential money transfers before we could logically connect fractional construction to finished priced product. We also needed to divide the economy into sectors, each with decision making capability and with the ability to contribute to the productive or consumptive processes. The simplicity of the equation hides the rigidity of the required assumptions.
The management role of decision makers has barely been considered here. The role of a lender supplying initial capital is particularly important. This productive continuum model is discontinuous at the starting point. If a lender fails to allow initial production, nothing happens! In a similar fashion, labor, whether organized or individually represented, has a decision making role. Labor is supplied hour by hour. A discontinuity is reached if labor decides to not perform. In the real economy, consumers can borrow money to buy goods. It is easy to see in this model that production would be stimulated by customer borrowing. Government borrowing may be sustained sequentially over time, potentially forming a mechanism for hyperinflation. Thanks to Brian Romanchuk for his efforts to present this series of articles. [Brian's final article in the series can be found here.] ============================================== [Note 1] One of the nice things about beginning a study of economics when you are older is that you have a lot of experience from which to draw. One of the frustrations is that you may have little or no economic schooling to guide you. This places you in the position of learning everything about economics from the position of being a well educated beginner. I resist accepting economic theories until each element can fit seamlessly with the mating theories, like in assembling a jigsaw puzzle. [Note 2] This article contains an expanded explanation of the equations first presented (by me) in a comment in Brian Romanchuk's article at http://www.bondeconomics.com/2018/03/the-curious-notation-of-dsge-models.html#comment-form. [Note 3] Function notation is a method of mapping inputs into a repeatable pattern. The time term $t$ as in $f(t)$ indicates that the data is accumulated over a time interval. [Note 4] Term $n$ represents hours of labor. We will use hours of labor as a proxy for all cost of production whether purchased directly as labor or hidden in a bid price for a part or service. The actual expense of a widget is not of concern here. We are only interested in learning the interactions between borrowed money and other sectors. If we later are interested in other interactions, we may need to refine our definitions. Hours of stylized labor must be converted to a financial capital equivalent using term $f_w$. [Note 5] The terms 'money', 'financial capital', and (occasionally) simply 'capital' are used somewhat interchangeably in this article. 'Capital' is never used as a reference to fixed capital such as buildings or bonds. (c) Roger Sparks 2018
## Sunday, March 4, 2018
### Tariffs, Sales Tax, and a Stronger Dollar
President Trump has proposed placing a 25% tariff on foreign steel and a 10% tariff on foreign aluminum. How in the world are we supposed to analyze that action?!
Well, maybe it's not so hard. This would be the United States government imposing a tax on all steel and aluminum that moved across borders. The tax would be paid in American dollars, not in the currency of the country of origin. It would be paid by the customer buying steel or aluminum should the customer chose a foreign made source.
Hence, we see here that an American steel consumer would be asked to make a choice of supplier, knowing that choosing foreign would result in a higher price due to the tax imposed. Considering only the tax implications, what is the relationship between the domestic and foreign prices?
Tariffs are a sales tax
A customer may have a choice between two governmental taxation schemes. If a customer has the choice of paying a sales tax or not, it makes no difference to the customer which government imposes the tax. The only differentiation is the relative price for the product. With this in mind, a tariff can be considered the same as a sales tax, the only difference being which government imposed the tax. This realization allows us to consider the situation of a customer living very close to a border between states, one state charging a sales tax and one not charging a sales tax. (The states of Oregon and Washington come to mind.)
A steel customer in Oregon (no sales tax) buying steel made in Washington would pay a 8% (about) sales tax. How would this customer make a purchase decision?
The sales tax or tariff decision
We will ignore the cost of transportation and other distance and time considerations to focus only on the tax consequences.
Our customer would find the point of price indifference where the price of product from each source is the same. In mathematical terms, the point of indifference occurs when
Oregon Price = Washington Price + Washington Price X Tax Rate
= WP + (WP X TR)
= WP(1+TR)
Transposing, we see that the point of indifference occurs when
Washington Price = OP/(1+TR).
Still ignoring transportation cost and using the 8% sales tax rate, we can calculate that the Washington Price must be 0.926 or about 7.4% less than Oregon price before the price advantage shifts to Washington's favor.
With this background, we can consider President Trump's proposal from the standpoint of a steel purchaser. If a American steel customer must choose between foreign steel which carries a 25% tax and tax free domestic made steel, the foreign steel must be priced at less than 1/ (1 + 0.25) = 0.80 of domestic price.
Of course, in the real economy, transportation cost and other factors would be considered additionally.
A new tariff impacts three groups
Everyone dislikes taxes so it is certainly understandable that proposal for a new tariff would bring protest from the impacted parties. We can broadly group impacted parties into three groups: tax payers, disfavored suppliers and favored suppliers.
Broadly speaking, the domestic taxpayer will be the customer who must pony-up the tax payment. With a new tariff, government is raising the cost of product to the consuming public. This invokes the cost related supply-demand factors that we commonly study in economics.
Disfavored suppliers can be expected to lose sales to favored suppliers. This will again set into motion the supply-demand factors that we commonly study in economics, with opposite-trending local effects on the two supply groups.
It is interesting to consider the longer term macro-economic interactions of these three groups. A tariff will quickly cause a reduction of foreign trade accompanied by a transferred increase in domestic demand for the tariff-taxed product. Moreover, because domestic taxes are increasing for the tariff imposing nation, the strength of the domestic currency will INCREASE. This makes it more difficult for the foreign nation to obtain currency so we would expect an immediate decline in purchases of all products. It follows that a tariff imposing nation should expect to see fewer sales to other national economies as well as slower domestic sales.
The economy shifting effects of tariffs
In the longer term, the macro-economies of the victimized economies can expect to see permanent economy shifting effects. In the case of steel, the local price of steel should fall (due to less demand) but that makes the cost of producing other products less expensive which would (in the longer term) improve sales (including foreign sales) of products made using steel.
The general effect of tax streams on governments
We need to further consider the effect of a tariff on the finances of the imposing country. The most important part of this consideration is that the tax will be paid in the currency of the imposing government.
The tariff imposing government will have a new income stream. This stream will come from tariff paying customers. Additionally, if the taxed product is a basic building material like steel, then we can certainly expect to see the cost of the tax flow into all new construction. To the extent that cost increases result in higher tax flows (such as results for Washington state sales tax) general governmental revenues increase.
In the case of the American federal government, the imposition of a tariff should rapidly increase income taxes coming from the steel industry as wages and profits rise in response to increased/transferred domestic demand.
The foreign taxation dilemma
The last tax effect that we will consider in this post will be the dilemma faced by governments as they tax to pay for government needs. How do you tax labor and production facilities that reside outside national boundaries?
Consider a government dependent upon the income tax to meet a large portion of government cost. Apply that dependency to build a contrast between domestic production and foreign production. It is safe to assume that domestic producers will be subject to the income tax while foreign producers will avoid this tax. How does this difference distort trade?
The effects are not immediately obvious. What is clear is that foreign workers would not contribute to the tax needs of domestic government. In that sense, foreign production arrives at the border tax free. On the other hand, these same foreign workers have better incomes earned from the economy supporting the tax deprived government. Presumable these foreign workers pay taxes to their own government, but the money paid comes from the tax deprived economy. [Post Note: Yet, foreign workers are paid in a second currency, not the currency of final sale. In the absence of balanced trade, some entity must absorb a trade of paper for product.]
The synergy described sets up conditions encouraging every government to support foreign sales, with a goal of increased government revenue due to more income tax paid. Of course imports have the opposite effect.
As if it were a surprise, we can conclude that taxation can have economy shifting effects.
Conclusion
It seems to me that a better sales effort needs to be made to sell a new tariff on steel and aluminum. This new tax would be easier to accept if the need to bring foreign production into a tax sharing mode is made clear (to the public). Domestic governments would like all producers to fairly help pay for government programs, (thus sharing the tax burden laid upon domestic producers). Of course, domestic customers prefer buying foreign if they can get a less expensive product, ignoring (or even relishing) the probability that avoidance of domestic taxes may be the reason for lower price.
To the extent that tariffs better-balance the tax burdens of government, tariffs seem reasonable.
An afterthought
Disfavored suppliers, victimized by a new tariff, will be understandably upset by what is perceived as being discrimination against them. They will take it personally.
Governments housing these same disfavored suppliers are likely to attempt to find new markets, keeping workers and factories in a production mode. New markets, if peaceful, can be good. However, these same (in the case of steel) production facilities can be used in markets producing ships, tanks and other weapons, which would not be good. Thus we see a danger in forcing rapid changes in economies by using blunt trade weapons such as tariffs.
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2021-10-25 04:50:59
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http://www.physiome.org/jsim/models/webmodel/NSR/OneAlvLung.Assist/
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This page will look better in a graphical browser that supports web standards, but is accessible to any browser or internet device.
Served by Samwise.
Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto
# OneAlvLung.Assist
A compliant 1 compartment lung with resistance to air flow, driven by external positive pressure ventilator.
Model number: 0001
Run Model: Help running a JSim model.
Java runtime required. Web browser must support Java Applets.
(JSim model applet may take 10-20 seconds to load.)
## Description
The equations governing airflow in and out of a one compartment lung are
given by the following analogy to electrical circuits:
Airway pressure is analogous to voltage.
Air flow is analogous to current flow.
Volume is analogous to charge.
Resistance to air flow is analogous to electrical resistance.
Compliance, the relationship between pressure and volume, is
analogous to capacitance, the relationship between charge
and voltage.
The model shows that various quantities are governed by exponential decay
with time constant tau=R*Com.
The main assumption is that the human lungs can be approximated as a single
compartment modeled by an RC circuit where the quantities of interest, air
flow, volume of air, pressure, compliance, and resistance are analogous to
current, charge, voltage, capacitance, and resistance respectively.
GENERAL RESULTS: The ventilator, using a driving pressure of 10 mmHg gives
an approximately normal tidal volume of 500 ml. Normally of course, the force
is provided by expansion of the chest, creating a negative pressure in the
intrapleural space, just the oppposite of this positive pressure ventilator.
Figure: Pressure, volume, flow vs. time. The forcing ventilator pressure is Pmouth (black). The numerical solutions:Fair Flow at mouth (green dashes), Volume circles; Plung red dashes. TestF is black line (exp(-t/Res*com)), a verification test fitting Fair(t).
## Equations
$\large {\it P}_{\text{\small{mouth}}}={\it P}_{\text{\small{atmos}}}+\,{\it ScalPvent*P}_{\text{\small{vent}}}$
$\large {\it Fair}=\left({\it P}_{\text{\small{mouth}}}-{\it P}_{\text{\small{lung}}}\right)/{{\it R}}$
$\large {\frac {d}{dt}}{\it V}_{\text{\small{lung}}}={\it Fair}$
$\large {\it P}_{\text{\small{lung}}}={\it P}_{\text{\small{atmos}}}+\left({\it V}_{\text{\small{lung}}}-{\it V}_{\text{\small{FRC}}}\right)/{{\it Com}}$
where Pmouth is the pressure at the mouth; P atmos, Ref pressure, external to body; Pvent, the driving pressure from a ventilator; ScalPvent, scaler of amplitude of Pvent; Plung is the pressure in the lung; Fair is the air flow at the mouth; R is the resistance of the airway; Com is the compliance of the lung; VFRC is the functional residual capacity of the lung; and Vlung is the volume of air in the lung.
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
## References
M.G. Levitsky, Pulmonary Physiology, Sixth Edition, McGraw Hill, 2003.
## Key Terms
lung compliance, resistance, RC circuit, lung mechanics, airflow in trachea, tidal volume, positive pressure ventilation, reference, tutorial
## Model History
Get Model history in CVS.
Posted by: GaryR
## Acknowledgements
Please cite www.physiome.org in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
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2017-09-23 18:07:55
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https://socratic.org/questions/how-do-you-graph-y-3sqrtx-3-compare-to-the-parent-graph-and-state-the-domain-and
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# How do you graph y=-3sqrtx-3, compare to the parent graph, and state the domain and range?
Feb 4, 2018
Graph it using a graphing calculator, domain is $\left\{x | x \ge 0 , x \in R\right\}$, range is $\left\{y | y \le - 3 , y \in R\right\}$
#### Explanation:
If you do not have a graphing calculator, you can use one that is online and free, such as Desmos. Here is the link: Desmos
There are buttons at the bottom of the screen that can be used to enter your function. The parent function is $\sqrt{x}$. You can also graph that function to see how it compares to your transformed function.
The way to write your function in standard form is as following:
$a \cdot \sqrt{b \left(x + c\right)} + d$, where b and c are horizontal transformations and a and d are vertical. This link provides a more detailed explanation: Transformations
The first and most obvious thing about this transformation was that it was reflected over the x-axis. That can be seen in your function because the leading coefficient ($a$) is negative. Next, your graph has been translated down three units. This is shown in your equation because $d$ is negative 3. Lastly, your graph has been vertically stretched by a factor of 3, since $\left\mid a \right\mid = 3$
Finally, the domain and range. This can be figured out graphically, by looking at the graph and seeing that x must be greater than 0 and y must be less than -3. So, $\left\{x | x \ge 0 , x \in R\right\}$, and $\left\{y | y \le - 3 , y \in R\right\}$.
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2022-11-29 05:26:39
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https://cs.stackexchange.com/questions/43538/how-do-global-variables-and-automatic-variables-with-the-same-name-interact
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# How do global variables and automatic variables with the same name interact?
Suppose I define a global variable and I define an automatic variable within a function definition with the same name as the aforementioned global variable.
What would happen to the global variable if I altered the automatic variable within the function body?
• I don't see how this question can be answered, since it depends on the choices made by the designer of any particular language. A language designer might choose for that to be a syntax error; they might choose for the automatic variable to "hide" the global variable; they might choose something else entirely. – David Richerby Jun 12 '15 at 20:25
• @DavidRicherby This is certainly true, when designers are very ignorant, or very facetious. But there are nevertheless general answers for that, that happen to fit most languages. One can of course try to be very general, but I am not sure I want to muddle things for a student. There are first order answers that give the more important concepts. Refinement can come in second order answers. – babou Jun 12 '15 at 20:51
In most programming languages, especially imperative languages, a “variable” is actually two things: a name and a storage location. The storage location is a block of memory where a value can be stored and retrieved. The variable's name is often called an identifier. An identifier is a way to refer to some object in the program, in this case a storage location. A variable has a scope, which is the part of the program where the variable's name refers to the variable.
For example, consider the following C snippet.
int foo;
void myfunction(void) {
float foo;
… /* Here the identifier foo refers to the variable that's of type float. */
}
/* Here the identifier foo refers to the variable that's of type int. */
This snippets declares two variables. The two variables happen to have the same name: both are called foo. They're distinct variables, refering to distinct storage location, same as if they'd been called by different names. The scope of the foo variable that's of type float is the function myfunction: inside the code of myfunction, the identifier foo refers to this variable; outside the code of myfunction, the identifier foo refers to some other variable, or none at all. The scope of the foo variable that's of type int is the file where it's declared; the identifier foo refers to this variable everywhere is the whole file, except for the functions (or more generally blocks¹) which declare another variable that's also called foo. The local variable foo is said to shadow the global variable foo.
A variable whose scope is a whole file is usually said to be global. A variable whose scope is a function, method, block, etc. is usually said to be local. In the example above, the int-typed foo is a global variable and the float-typed foo is a local variable, local to the function myfunction.
The scope of a variable is the part of a program where its name refers to that variable. This is not always the same thing as the part of the program where the storage location exists. There is some correlation between the two, because it's usually undesirable to have a name for a storage location that doesn't exist, and it's often desirable to have a name for storage locations that do exist.
In C, the time during which a storage location exists is called its duration. The duration of a global variable is the whole program execution (“static duration” in C jargon, but that jargon doesn't extend to other languages, unlike most of the terms I used in this answer). (That's in C and some other langauges; in many other languages the duration of a global variable starts when the variable is defined.) The duration of a local automatic variable is the time during which the block containing it is executing. Note that “automatic” refers to the duration, not to the scope; “automatic” is not the opposite of “global”, “local” is. In C, you can't have automatic duration at a global scope, but you can have static duration at a local scope, with a variable that's declared static or extern.
void myfunction(void) {
static int s;
extern int e;
}
/* Here s and e are not defined */
The duration of both s and e is the whole program execution, but their scope is only the function myfunction: the names e and s are not valid outside that function. The difference between static and extern is that the variable s cannot be accessed from another scope, whereas e is the same variable as any other extern e in any scope.
Coming back to the foo example above, since two variables in different scopes have no relation, altering foo in myfunction has no impact on the global foo. They're unrelated variables, they just happen to have the same name.
It would be possible to rename the local variable foo to avoid having a name conflict. If you change all occurrences of foo in the code of myfunction to a different name that isn't used elsewhere in the program, you get an equivalent function.² This renaming process is known as alpha conversion in programming language theory.
The main reason programming languages allow programmers to pick the same name for different variables is that doing otherwise makes it difficult to write large programs and especially to write programs in pieces. If adding a library to your program meant that you had to rename some of your local variables in unrelated parts of your program to avoid conflicts, it would be a nightmare. (As it is, C only has global names for functions, which can be troublesome.)
Basically all languages allow variables in unrelated scopes to have the same name. C also allows shadowing: defining a variable in a scope hides any variable by the same name in a surrounding scope. This is common, but not univeral. For example, in Java, if you define a variable in a block, you can't define another variable by the same name in a nested block. The advantage of this restriction is that it prevents a source of confusion: a programmer might inadvertently use the name to refer to the variable from the outer scope, and not realize it instead refers to the variable in the inner scope. The downside of this restriction is that it makes some program transformations impossible without renaming the variable.
void myfunction(void) {
int x = 1;
if (…) {
int x = 2; // allowed in C, forbidden in Java
printf("%d\n", x); // prints 2
}
printf("%d\n", x); // prints 1
}
Some languages have a way to refer to a variable that's shadowed, but it's uncommon. C has no such way, but you can refer to the storage location of the outer variable if you have a pointer to it.
¹ More precisely, the scope of a variable defined in a block runs from the variable definition to the end of the block. If there is an outer scope with a variable of the same name, it's that same part which is excluded from that outer scope.
² This only works in languages where variable names are not significant. Actually, I lied here, because C can make variable names significant via the preprocessor. C is quite a complex language… If that preprocessor feature isn't used, variable names are not significant.
• This seems a very good presentation of the world seen from the C language. I have however two concerns. The first is that it is very much and very explicitly C oriented (which was a matter of polemics when the question was initially asked). The second is that it seems to give a major role to variables, when the issue is essentially a naming issue, variable happening to be what is being named in the example of the question, at least as I perceive it. Some of your examples are however interesting in that they separate allocation, duration and scope more than most languages. – babou Jun 14 '15 at 13:29
• @babou I used the C language as a centerpiece since this is what the asker knows. I could explain how things work differently in Lisp, ML, the Pi calculus, etc. but that would take a much longer answer. I give a major role to variables because that's what the question is about, and the distinction between names and storage locations is an important and hard-to-understand one. – Gilles Jun 14 '15 at 13:41
• OK. I know you can cover more. Matter of perception. My feeling is that variable and identifiers are often confused, so I would avoid a presentation that has vriables unopposed by other programming entities. But it is a nice presentation. – babou Jun 14 '15 at 14:39
This is a good question, though extremely elementary. I try to give you a very general answer. There are variations with different programming languages, or other types of languages. The issue is really about the role of names, that we usually call identifiers in programming.
First note that a global variable may also be an automatic variable, but it is then defined in a larger function, in which your function is defined. But that is not very important here.
All languages, not just programming languages, but also mathematical and logical ones, or natural ones, have scoping rules, so that the same name may be used with different meanings in different context. A new function usually defines a new scope for names, and any name (including variable names) that is declared within the function gets a meaning given by the declaration, which hides the meaning it had outside.
This is not so much an issue of automatic allocation of variables (though there are relations) but much more of meaning of names. There are other mechanisms to structure the way names take meaning. When they combine, you need to know all the various rules to determine how a given name takes its meaning, i.e. to what definition (aka declaration) this use of the name refers. And that can be more subtle than your example.
In the case of your example, you have two unrelated variables that happen to have the same name. At any time, the name means only one of them. In your function, the local declaration gives a local meaning to the name, thus hiding the global meaning. So the global variable is untouched, when its name is used to modify another homonymous variable. For example, I expect you were not involved in Spielberg's movie on WW2, and no one came to save you. In the scope of the film Ryan did not mean you.
Actually, the name of your automatic variable could well be used globally to name a function, and locally to name a variable. It does not matter.
To know more on this topic, I suggest you look at "variable binding" and "scoping". It will be time well spent.
• "a global variable may also be an automatic variable, but it is then defined in a larger function" Huh? If a function is defined inside a function, then it's no longer a global variable. I think "global" means "in the top-most scope", not "in any higher scope". – svick Jun 12 '15 at 20:13
• @svick Well, as I said, terminology is very much context dependent. Indeed, many programming languages take your view of giving an absolute meaning to global variable. But I have encountered other uses. What is important is to state your definitions and agree on them in a given technical discussion. Then another discussion may be another scope for technical names. For example, you and I tend to talk of variables, but the issue is more with identifiers. This comes from lambda-calculus, that uses the word variable, though it has no variables in the programming sense. Scope again. – babou Jun 12 '15 at 20:21
• Nice example with “Ryan”. Regarding “global variables”, @svick, the definition of the C language doesn't actually use that terminology; a global variable in common parlance is has file scope, which is not the top-most scope: that would be program scope, an expression that the C definition doesn't in fact use, it refers to “external linkage” instead. – Gilles Jun 12 '15 at 23:29
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2019-06-17 02:42:23
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https://www.lmfdb.org/EllipticCurve/Q/189618y/
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# Properties
Label 189618y Number of curves $2$ Conductor $189618$ CM no Rank $0$ Graph
# Related objects
Show commands for: SageMath
sage: E = EllipticCurve("y1")
sage: E.isogeny_class()
## Elliptic curves in class 189618y
sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
189618.o2 189618y1 [1, 0, 1, -2032, 28394] [2] 207360 $$\Gamma_0(N)$$-optimal
189618.o1 189618y2 [1, 0, 1, -30762, 2073970] [2] 414720
## Rank
sage: E.rank()
The elliptic curves in class 189618y have rank $$0$$.
## Complex multiplication
The elliptic curves in class 189618y do not have complex multiplication.
## Modular form 189618.2.a.y
sage: E.q_eigenform(10)
$$q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + 2q^{10} + q^{11} + q^{12} - 2q^{14} - 2q^{15} + q^{16} + q^{17} - q^{18} - 2q^{19} + O(q^{20})$$
## Isogeny matrix
sage: E.isogeny_class().matrix()
The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.
$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$
## Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
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2021-02-27 01:13:14
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http://mathreports.ru/en/articles/approximation-of-piecewise-linear-functions-by-discrete-fourier-sums/
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# Approximation of piecewise linear functions by discrete Fourier sums
### DOI: 10.31029/demr.8.3
Let $N$ be a natural number greater than $1$. We select $N$ uniformly distributed points $t_k = 2\pi k / N$ $(0 \leq k \leq N - 1)$ on $[0,2\pi]$. Denote by $L_{n,N}(f)=L_{n,N}(f,x)$ $(1\leq n\leq N/2)$ the trigonometric polynomial of order $n$ possessing the least quadratic deviation from $f$ with respect to the system $\{t_k\}_{k=0}^{N-1}$. In the present article the problem of function approximation by the polynomials $L_{n,N}(f,x)$ is considered. Special attention is paid to approximation of $2\pi$-periodic functions $f_1$ and $f_2$ by the polynomials $L_{n,N}(f,x)$, where $f_1(x)=|x|$ and $f_2(x)=\mbox{sign\,} x$ for $x \in [-\pi,\pi]$. For the first function $f_1$ we show that instead of the estimate $\left|f_{1}(x)-L_{n,N}(f_{1},x)\right| \leq c\ln n/n$ which follows from well-known Lebesgue inequality for the polynomials $L_{n,N}(f,x)$ we found an exact order estimate $\left|f_{1}(x)-L_{n,N}(f_{1},x)\right| \leq c/n$ ($x \in \mathbb{R}$) which is uniform with respect to $1 \leq n \leq N/2$. Moreover, we found a local estimate $\left|f_{1}(x)-L_{n,N}(f_{1},x)\right| \leq c(\varepsilon)/n^2$ ($\left|x - \pi k\right| \geq \varepsilon$) which is also uniform with respect to $1 \leq n \leq N/2$. For the second function $f_2$ we found only a local estimate $\left|f_{2}(x)-L_{n,N}(f_{2},x)\right| \leq c(\varepsilon)/n$ ($\left|x - \pi k\right| \geq \varepsilon$) which is uniform with respect to $1 \leq n \leq N/2$. The proofs of these estimations based on comparing of approximating properties of discrete and continuous finite Fourier series.
Keywords: function approximation, trigonometric polynomials, Fourier series.
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2019-04-21 08:32:59
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https://publications.hse.ru/en/preprints/page21.html?search=e780197053fea80fe4670b44d8f8c6f8
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Of all publications in the section: 484
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Working paper
Rybnikov G. arxiv.org. math. Cornell University, 2014
We study a special type of $E_\infty$-operads that govern strictly unital $E_\infty$-coalgebras (and algebras) over the ring of integers. Morphisms of coalgebras over such an operad are defined by using universal $E_\infty$-bimodules. Thus we obtain a category of $E_\infty$-coalgebras. It turns out that if the homology of an $E_\infty$-coalgebra have no torsion, then there is a natural way to define an $E_\infty$-coalgebra structure on the homology so that the resulting coalgebra be isomorphic to the initial $E_\infty$-coalgebra in our category. We also discuss some invariants of the $E_\infty$-coalgebra structure on homology and relate them to the invariant formerly used by the author to distinguish the fundamental groups of the complements of combinatorially equivalent complex hyperplane arrangements.
Working paper
Malyshev D. arxiv.org. math. Cornell University, 2013. No. 1307.0278v1.
The coloring problem is studied in the paper for graph classes defined by two small forbidden induced subgraphs. We prove some sufficient conditions for effective solvability of the problem in such classes. As their corollary we determine the computational complexity for all sets of two connected forbidden induced subgraphs with at most five vertices except 13 explicitly enumerated cases.
Working paper
Blokh A., Oversteegen L., Ptacek R. et al. arxiv.org. math. Cornell University, 2015
We interpret the combinatorial Mandelbrot set in terms of quadratic laminations (equivalence relations ∼ on the unit circle invariant under σ2). To each lamination we associate a particular geolamination (the collection L∼ of points of the circle and edges of convex hulls of ∼-equivalence classes) so that the closure of the set of all of them is a compact metric space with the Hausdorff metric. Two such geolaminations are said to be minor equivalent if their minors (images of their longest chords) intersect. We show that the corresponding quotient space of this topological space is homeomorphic to the boundary of the combinatorial Mandelbrot set. To each equivalence class of these geolaminations we associate a unique lamination and its topological polynomial so that this interpretation can be viewed as a way to endow the space of all quadratic topological polynomials with a suitable topology
Working paper
Shitov Y. arxiv.org. math. Cornell University, 2012
The tropical arithmetic operations are the minimum and the sum of two numbers. Let A be a tropical matrix and k a positive integer, the problem of Tropical Matrix Factorization (TMF) asks whether there exist an m-by-k tropical matrix B and a k-by-n tropical matrix C whose tropical product is A. We show that no algorithm for TMF is likely to work in polynomial time for every fixed k, thus resolving a problem proposed by Barvinok in 1993. TMF is also shown to be hard for matrices with bounded tropical rank. Proving that TMF can be solved by a polynomial-time algorithm if k is less than 4, we answer a question posed by Develin, Santos, and Sturmfels. Another question they have posed asks whether every tropical matrix of factor rank k has a rank-k submatrix of size at most N(k)-by-N(k); we answer this question in the negative for every k greater than 4.
Working paper
Vladimir L. Popov. arxiv.org. math. Cornell University, 2010. No. 1009.6107.
Working paper
Galkin S. arxiv.org. math. Cornell University, 2014. No. 1404.7388.
Consider a Laurent polynomial with real positive coefficients such that the origin is strictly inside its Newton polytope. Then it is strongly convex as a function of real positive argument. So it has a distinguished Morse critical point --- the unique critical point with real positive coordinates. As a consequence we obtain a positive answer to a question of Ostrover and Tyomkin: the quantum cohomology algebra of a toric Fano manifold contains a field as a direct summand. Moreover, it gives a good evidence that the same statement holds for any Fano manifold.
Working paper
Adler D., Gritsenko V. arxiv.org. math. Cornell University, 2019
We construct a tower of arithmetic generators of the bigraded polynomial ring J_{*,*}^{w, O}(D_n) of weak Jacobi modular forms invariant with respect to the full orthogonal group O(D_n) of the root lattice D_n for 2\le n\le 8. This tower corresponds to the tower of strongly reflective modular forms on the orthogonal groups of signature (2,n) which determine the Lorentzian Kac-Moody algebras related to the BCOV (Bershadsky-Cecotti-Ooguri-Vafa)-analytic torsions. We prove that the main three generators of index one of the graded ring satisfy a special system of modular differential equations. We found also a general modular differential equation of the generator of weight 0 and index 1 which generates the automorphic discriminant of the moduli space of Enriques surfaces.
Working paper
Bogomolov F. A., Silberstein A. M. arxiv.org. math. Cornell University, 2015
Given an infinite collection of pairwise-disjoint, Zariski-closed, connected, codimension-1 subvarieties of a complete, normal, irreducible algebraic variety over an algebraically-closed field, we prove that there exists a regular, nonconstant morphism to a complete curve so that each of these divisors is contained in a fiber of this morphism.
Working paper
Galkin S., Shinder E. arxiv.org. math. Cornell University, 2014. No. 1405.5154.
We find a relation between a cubic hypersurface Y and its Fano variety of lines F(Y) in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety of lines on a smooth rational cubic fourfold is birational to a Hilbert scheme of two points on a K3 surface; in particular, general cubic fourfold is irrational.
Working paper
Nadezhda Kodaneva. arxiv.org. math. Cornell University, 2019. No. arXiv:2002.12440.
In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and determines thus a finite type invariant of links in the 3-sphere.
Working paper
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova. arxiv.org. math. Cornell University, 2016. No. 1601.07298.
Given a subset T of real numbers and a metric space M, we introduce a nondecreasing sequence {v_n} of pseudometrics on the set M^T of all functions from T into M, called the joint modulus of variation. We prove that if two sequences of functions {f_j} and {g_j} from M^T are such that {f_j} is pointwise precompact, {g_j} is pointwise convergent, and the limit superior of v_n(f_j,g_j) as j → ∞ is o(n) as n → ∞, then {f_j} admits a pointwise convergent subsequence whose limit is a conditionally regulated function. We illustrate the sharpness of this result by examples (in particular, the assumption on the limsup is necessary for uniformly convergent sequences {f_j} and {g_j}, and ‘almost necessary’ when they converge pointwise) and show that most of the known Helly-type pointwise selection theorems are its particular cases.
Working paper
Vladimir L. Popov. arxiv.org. math. Cornell University, 2018. No. 1804.00323v1.
We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic groups (not necessarily affine) over fields of cha\-racte\-ristic zero and some transformation groups of complex spaces and Riemannian manifods are Jordan.
Working paper
Timorin V., Oversteegen L., Blokh A. et al. arxiv.org. math. Cornell University, 2013. No. 1305.5798.
We discuss different analogs of the main cardioid in the parameter space of cubic polynomials, and establish relationships between them.
Working paper
Blokh A., Oversteegen L., Ptacek R. et al. arxiv.org. math. Cornell University, 2015
Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we consider slices of the family of cubic invariant laminations defined by a fixed critical leaf with non-periodic endpoints. We parameterize each slice by a lamination just as in the quadratic case, relying on the techniques of smart criticality previously developed by the authors.
Working paper
Konakov V., Markova A. arxiv.org. math. Cornell University, 2016. No. 1610.08715.
We consider the diffusion process and its approximation by Markov chain with nonlinear increasing trends. The usual parametrix method is not appliable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear growing trend and move to stochastic differential equation with reduced drift and diffusion coefficients. A similar procedure is considered for a Markov chain
Working paper
V.L. Chernyshev, Tolchennikov A. arxiv.org. math. Cornell University, 2011. No. 1111.3945.
The article deals with the description of the statistical behavior of Gaussian packets on a metric graph. Semiclassical asymptotics of solutions of the Cauchy problem for the Schr\"{o}dinger equation with initial data concentrated in the neighborhood of one point on the edge, generates a classical dynamical system on a graph. In a situation where all times for packets to pass over edges ("edge travel times") are linearly independent over the rational numbers, a description of the behavior of such systems is related to the number-theoretic problem of counting the number of lattice points in an expanding polyhedron. In this paper we show that for a finite compact graph packets almost always are distributed evenly. A formula for the leading coefficient of the asymptotic behavior of the number of packets with an increasing time is obtained. The article also discusses a situation where the times of passage over the edges are not linearly independent over the rationals.
Working paper
Bitoun T. arxiv.org. math. Cornell University, 2010
We prove an analog of the involutivity of the characteristic variety theorem for the reduction to positive characteristic of holonomic D-modules, involving the p-curvature. The proof given is independent of O. Gabber's theorem.
Working paper
Kurnosov N. arxiv.org. math. Cornell University, 2014
Let M be a compact irreducible hyperkahler manifold, from Bogomolov inequality [V1] we obtain forbidden values of the second Betti number b_2 in arbitrary dimension.
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2021-09-23 11:20:58
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