text:
## Drafts in Hakyll

In the post about my switch to Hakyll I talked about the various features I implemented in my Hakyll blog. One feature that was sorely missing was support for drafts: posts which aren’t supposed to be published when the site is deployed.

I usually take my time writing posts. Sometimes it can take me days, during which I might want to deploy other minor changes to the site, or perhaps even a shorter, quicker post. Without a draft system, I’m forced to manually move the draft post out of the provider directory so that it doesn’t get generated and subsequently deployed.

A draft system is able to clearly distinguish draft posts from regular posts. This way, when it comes to deploying the site, draft posts aren’t deployed along with it.

## Considerations

I believe that the fundamental problem with draft systems in static site generators is that drafts, like regular posts, come to permeate the entire site. They accomplish this by showing up on index pages, tag pages, and any other place you might expect regular posts to show up in. This is something to keep in mind when creating a draft system because it means that simply deleting the compiled page won’t suffice, as there will still be traces in other pages.

One approach to this problem is to quarantine the draft posts such that they don’t show up on any of these things and instead only show them when you visit them directly. This is not an option for me because when I preview drafts I want to see how they will affect the entire site. I don’t preview drafts simply to check how my post is formatted.

## Examples

The following two draft system implementations exemplify the two approaches I can think of for a draft system. These are approaches taken by static site generators. There are other ad hoc solutions, such as creating a separate drafts branch in git.

Octopress had support for drafts hacked onto Jekyll by way of a plugin that allowed a metadata field published to be set that, if set to false, would establish an environment variable that would be detected on site generation in order to regenerate the site without the draft posts. This consequently meant that draft posts were stored in the same directory as regular posts.

Jekyll implemented support for this in its 1.0 version by allowing a new directory, _drafts/, to store draft posts which could be previewed by specifying the --drafts flag to most operations. However, it was right after Jekyll 1.0 was released that I decided to switch to Hakyll.

Octopress’ draft system was pretty straightforward in my opinion, despite being a pretty hack-ish implementation. I would create drafts in the same directory as all of the other posts, and would simply set metadata published: false. This would allow the draft to show up when I previewed the site, but not when it was ultimately deployed. This was accomplished by regenerating the site on deploy, this time without the preview posts.

The other solution I could think of consisted of detecting when the site was being previewed, and if that were the case, establish a different output directory and a different posts pattern which would include the posts in a separate drafts/ directory. When the site wasn’t being previewed, the regular output directory would be used.

## Implementation

Both approaches amount to hacks on top of Hakyll, but after some consideration, it seems to me that the second option is a lot less messy.

My solution consists of some code that runs before the Hakyll driver. The code extracts the first argument from the program arguments, which by convention is the action to perform, e.g. build, clean, preview, and checks to see if it’s the preview action.

main = do
(action:_) <- getArgs

If the preview action is being run, the Hakyll configuration data structure’s destinationDirectory field, i.e. the output directory, is changed to a separate one for previewing purposes. This implies that the field is set to the deployable output directory by default. This is important because it means that all actions other than preview will ignore drafts.

Furthermore, if we are previewing, the pattern used to fetch posts is changed to also include the posts in the drafts/ directory. This is achieved by using the .||. function to compose two Pattern types.

  let previewMode  = action == "preview"
hakyllConf   = if previewMode
then myHakyllConf { destinationDirectory = "generated/preview" }
else myHakyllConf
postsPattern = if previewMode
then "posts/*" .||. "drafts/*"
else "posts/*"

Finally, we need to make one modification to an existing action. The clean action removes the provider, cache, and destination (output) directories. However, we now have two separate destination directories and by default every other action only knows of the deployable destination directory, i.e. the one without drafts. For this reason, we have to detect if the action being run is clean, and if so, remove the preview output directory.

Note that this depends on System.Directory.

  when (action == "clean") $do putStrLn "Removing generated/preview..." removeDirectoryRecursive "generated/preview" Now that this is done, you simply have to be sure to use the hakyllConf that was created above, as well as postsPattern wherever you would have simply put "posts/*" before. Two places that come to mind are tag generation and posts compilation:  hakyllWith hakyllConf$ do
tags <- buildTags postsPattern (fromCapture "tags/*.html")

match postsPattern \$ do
-- etc.

## Usage

This drafts system is pretty straightforward. When you run ./site preview it’ll serve the site with drafts as well. Deployment carries on as usual, i.e. you shouldn’t have to modify your deployment routine. With this system, you’ll never accidentally deploy drafts because they won’t ever show up in that output directory to begin with.

June 5, 2013
18630dc — October 6, 2018

format: plain


text:
# Bold and Colored Image Caption

How can I color and bold an image's caption in \documentclass[12pt]{report}?

In this documentclass, as, I believe, in any documentclass, it is possible to use the caption package and the \textcolor command.

For example, if I want to color blue and bold the caption of a simple triangle drawn in TikZ in your documentclass, I can use the following code to achieve the following output, which I will break down below.

\documentclass[12pt]{report}

\usepackage{tikz}
\usepackage[labelfont={color=blue,bf}]{caption}

\begin{document}

\begin{figure}[h!]
\centering
\begin{tikzpicture}
\draw[black, very thick] (0,0) -- (3,2) -- (4,0) -- cycle;
\end{tikzpicture}
\caption{\textbf{\textcolor{blue}{A triangle.}}}
\label{fig:triangle}
\end{figure}

\end{document}

I began by declaring your documentclass of choice. Next, I called in tikz for the triangle and caption to change the color of "Figure 1:". I modified caption with two constraints under one modifier (labelfont), namely declaring the color to be blue (although it could be many others) and "bf" for boldface.

Then, down in the actual figure, I used \textbf{\textcolor{<color>}{<caption>}}. This combines the two separate commands to color the caption, itself.

Hope this helps!

• The problem, is that any cross-reference to this figure will also be in blue and boldface… – Bernard Jul 7 at 21:39
• @Bernard, not really, only cross reference will be only bold and not colored. – Zarko Jul 7 at 21:46
• @Zarko: really? In any case, it is preferable to do that through the caption package. – Bernard Jul 7 at 22:07

\documentclass[12pt]{report}
\usepackage{graphicx}
\usepackage{xcolor}
\usepackage{caption}
\captionsetup{font={color=blue,bf}} % <---

\begin{document}

\begin{figure}[htb]
\centering
\includegraphics[width=0.8\linewidth]{example-image-duck}
\caption{A triangle.}
\label{fig:myfig}
\end{figure}
See figure~\ref{fig:myfig}   % <---

\end{document}


text:
# Unit Impulse funciton FT

How is FT of $\delta$(t) equal to 1 ? Normal FT gives the result $\infty$. Can someone please explain? I did the normal integration and substituted the limits.

Is it because $\delta$(t) is a unit impulse function so as it's height is large it's width is very small so no matter what the FT will always be equal to 1 ? (I'm just trying to figure out the logic)

If follows directly from the definition of the Dirac delta distribution. It is defined so that

$$\int_\mathbb{R} \delta(x) f(x) dx := f(0)$$

for any test function $f(x)$. In other words, the Dirac distribution is the generator of the linear functional that extracts a single function value.

With this definition the Fourier transform of the Dirac distribution is simply: $$\int_\mathbb{R} \delta(t) \exp(-2\pi i \omega t) dt=\exp(-2\pi i \omega\cdot 0)=\exp(0)=1$$

It doesn't make much sense to say the Dirac distribution is infinitely high or infinitely narrow. Just use the definition given above and apply it. If you really need to, you can understand the distribution as the limit of a sequence of certain functions, but it's not a function itself. And specifically it doesn't have a graph.

• You do need $f(x)$ to be continuous at $0$. – Dilip Sarwate Aug 10 '14 at 16:14
• @DilipSarwate, I see that you need continuity if you define it using measure theory or even weak $C^\infty$ if you come from general distribution theory. But I don't see the requirement of f being continuous at 0 if you just define the linear functional $\delta(f):=f(0)$ without further context. Do you see this differently? – Jazzmaniac Aug 10 '14 at 16:40
• If you want to use the Dirac delta in Fourier transform applications, which is the context here, then it is perhaps best to include the continuity requirement without insisting on the non-necessity of including such a requirement. You might want to raise this question on math.SE if you want a complete answer as to whether the more general definition that you are using is adequate for use in the context of Fourier transforms. – Dilip Sarwate Aug 11 '14 at 0:40
• @DilipSarwate, this is a good example on, just at a pragmatic level, that people from a background discipline of mathematics will not see things the same way as people from an engineering or physics background. the continuity requirement for $f(0)$ is necessary for the "nascent delta" definition (which uses a limit and what engineers often see) of the dirac delta. but from the "distribution" definition, no such requirement is needed. but then $\delta(t)$ is not a function in the strict mathematical sense, so viewing $f(t) \cdot \delta(t)$ by itself (not inside an integral) makes no sense. – robert bristow-johnson Oct 3 '14 at 2:18
• Robert, please don't change notation just because you like it better. The use of $\exp()$ has nothing to do with the availablility of $e$ as a symbol. I strongly prefer the function notation for several reasons and I also find it easier to read. – Jazzmaniac Oct 3 '14 at 9:36


text:
Mapping class group of the Torus (intuitive/visual proof)

I am giving a talk in a graduate seminar soon and would like show that the mapping class group of the torus is $SL_2(\mathbb{Z})$.The proof I was going to present lacks geometric intuition and is kind of long. I was wondering if anyone had an intuitive/visual proof of this fact or knew where I might be able to find such a proof.

-
An easy proof that the mapping class group contains $SL_2(Z)$ is by looking at what an orientation preserving diffeomorphism must do to $H^1(T^2)$. –  Jason DeVito Apr 11 '11 at 17:33
@Jason, this is just a result of the intersection pairing, correct? –  confusedmath Apr 12 '11 at 2:34
Yes, I think so. –  Jason DeVito Apr 12 '11 at 3:08

Stillwell's book "Classical topology and combinatorial group theory" gives a proof, with pictures, starting on page 206. It is possible to summarize the proof (use "curve straightening") but I thnk that Stillwell will be a good (or best) place to start.

By the way, the mapping class group is $GL(2,Z)$ if you allow orientation reversing homeomorphisms in the definition.

-


text:
## Chen, Gui-Qiang G.

Compute Distance To:
 Author ID: chen.gui-qiang-g Published as: Chen, Gui-Qiang; Chen, Gui-Qiang G.; Chen, Guiqiang; Chen, G.-Q.; Chen, Gui-qiang; Chen, Guiqiang G.; Chen, Gui Qiang more...less External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef
 Documents Indexed: 220 Publications since 1982, including 1 Book 9 Contributions as Editor Co-Authors: 104 Co-Authors with 195 Joint Publications 3,128 Co-Co-Authors
all top 5

### Co-Authors

 26 single-authored 25 Wang, Dehua 22 Feldman, Mikhail 13 Frid, Hermano 13 Slemrod, Marshall 10 Xiang, Wei 8 Zhang, Yongqian 7 Torres, Monica 6 Chen, Jun 6 LeFloch, Philippe Gerard 5 Glimm, James G. 5 Jerome, Joseph W. 5 Li, Siran 5 Su, Bo 5 Trivisa, Konstantina 4 Ding, Xia-xi 4 Hoff, David 4 Karlsen, Kenneth Hvistendahl 4 Lu, Yunguang 4 Luo, Peizhu 4 Yuan, Hairong 4 Zhu, Xiping 3 Cao, Daomin 3 Christoforou, Cleopatra C. 3 Dafermos, Constantine M. 3 Huang, Feimin 3 Kan, Pui Tak 3 Li, Tianhong 3 Li, Yachun 3 Perepelitsa, Misha 3 Perthame, Benoît 3 Wang, Tianyi 2 Bae, Myoungjean 2 Chang, Tung 2 Deng, Xuemei 2 DiBenedetto, Emmanuele 2 Even, Nadine 2 Fang, Beixiang 2 Klingenberg, Christian 2 Kuang, Jie 2 Kukreja, Vaibhav 2 Li, Banghe 2 Li, YanYan 2 Liu, Hailiang 2 Liu, Tai-Ping 2 Majumdar, Apala 2 Pang, Peter H. C. 2 Qian, Zhongmin M. 2 Rascle, Michel 2 Schrecker, Matthew R. I. 2 Secchi, Paolo 2 Wagner, David Hobson 2 Wang, Tao 2 Yang, Shuli 2 Zhang, Bo 2 Zhang, Rongfang 2 Zhu, Dianwen 2 Ziemer, William Paul 1 Acharya, Amit 1 Al-saedi, Ahmed Eid Salem 1 Ball, John MacLeod 1 Bressan, Alberto 1 Chang, Tong 1 Chen, Anna L. 1 Chen, Geng 1 Chen, Shuxing 1 Clelland, Jeanne Nielsen 1 Comi, Giovanni E. 1 Dan, Osborne 1 Ding, Qian 1 Du, Qiang 1 Fang, Chao 1 Freeman, Randy A. 1 Gasper, George Jun 1 Holden, Helge 1 Hong, Jiaxing 1 Hsu, Elton P. 1 Hsu, T. R. 1 Hu, Jingchen 1 Junca, Stéphane 1 Knops, Robin J. 1 Kratka, Milan 1 Levermore, C. David 1 Lewicka, Marta 1 Li, Dening 1 Li, QinFeng 1 Li, Tatsien 1 Li, Yanyan 1 Liu, Jianguo 1 Liu, Jian Guo 1 Maa, Jerome P.-Y. 1 Pinsky, Mark Allan 1 Rigby, Matthew 1 Ruan, Weihua 1 Russell, David L. 1 Rustichini, Aldo 1 Shu, Chi-Wang 1 Song, Kyungwoo 1 Tadmor, Eitan 1 Tan, Dechun 1 Toro, Eleuterio F. ...and 10 more Co-Authors
all top 5

### Serials

 27 Archive for Rational Mechanics and Analysis 13 Journal of Differential Equations 11 SIAM Journal on Mathematical Analysis 10 Communications in Mathematical Physics 10 Acta Mathematica Scientia 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Discrete and Continuous Dynamical Systems 7 Communications on Pure and Applied Mathematics 6 Acta Mathematica Scientia. Series B. (English Edition) 5 Proceedings of the American Mathematical Society 4 Chinese Annals of Mathematics. Series B 4 Communications in Partial Differential Equations 3 Mathematics of Computation 3 Indiana University Mathematics Journal 3 Quarterly of Applied Mathematics 3 Transactions of the American Mathematical Society 3 Physica D 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Communications in Nonlinear Science and Numerical Simulation 3 Communications on Pure and Applied Analysis 3 Contemporary Mathematics 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Advances in Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Notices of the American Mathematical Society 2 Methods and Applications of Analysis 2 Matemática Contemporânea 2 Journal of Hyperbolic Differential Equations 2 Springer Proceedings in Mathematics & Statistics 1 Acta Mechanica 1 Journal of Mathematical Physics 1 Nonlinearity 1 Transport Theory and Statistical Physics 1 International Journal for Numerical Methods in Engineering 1 Inventiones Mathematicae 1 Journal of Functional Analysis 1 SIAM Journal on Control and Optimization 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of the American Mathematical Society 1 The Journal of Geometric Analysis 1 Acta Mathematica Universitatis Comenianae. New Series 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Partial Differential Equations 1 Chinese Science Bulletin 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 The Asian Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Interfaces and Free Boundaries 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Pure and Applied Mathematics Quarterly 1 Annals of Mathematics Studies 1 The IMA Volumes in Mathematics and its Applications 1 Series in Contemporary Applied Mathematics CAM 1 Science China. Mathematics 1 Bulletin of Mathematical Sciences 1 Discontinuity, Nonlinearity, and Complexity 1 Nonlinear Analysis. Theory, Methods & Applications 1 Annals of PDE 1 Philosophical Transactions A. Royal Society of London
all top 5

### Fields

 207 Partial differential equations (35-XX) 139 Fluid mechanics (76-XX) 19 Numerical analysis (65-XX) 16 Differential geometry (53-XX) 10 Mechanics of deformable solids (74-XX) 9 General and overarching topics; collections (00-XX) 8 Real functions (26-XX) 8 Measure and integration (28-XX) 6 Probability theory and stochastic processes (60-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Biology and other natural sciences (92-XX) 4 History and biography (01-XX) 4 Manifolds and cell complexes (57-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Optics, electromagnetic theory (78-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Relativity and gravitational theory (83-XX) 3 Functional analysis (46-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Ordinary differential equations (34-XX) 1 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Mechanics of particles and systems (70-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

179 Publications have been cited 3,723 times in 2,033 Documents Cited by Year
Hyperbolic conservation laws with stiff relaxation terms and entropy. Zbl 0806.35112
Chen, Gui-Qiang; Levermore, C. David; Liu, Tai-Ping
1994
Formation of $$\delta$$-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. Zbl 1038.35035
Chen, Gui-Qiang; Liu, Hailiang
2003
Divergence-measure fields and hyperbolic conservation laws. Zbl 0942.35111
Chen, Gui-Qiang; Frid, Hermano
1999
Global solutions of nonlinear magnetohydrodynamics with large initial data. Zbl 1001.76118
Chen, Gui-Qiang; Wang, Dehua
2002
Existence and continuous dependence of large solutions for the magnetohydrodynamic equations. Zbl 1036.35126
Chen, Gui-Qiang; Wang, Dehua
2003
Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type. Zbl 1015.35075
Chen, Gui-Qiang; Feldman, Mikhail
2003
Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids. Zbl 1098.76603
Chen, Gui-Qiang; Liu, Hailiang
2004
Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics. Zbl 0689.76022
Ding, Xiaxi; Chen, Gui-Qiang; Luo, Peizhu
1989
A mathematical model for linear elastic systems with structural damping. Zbl 0515.73033
Chen, G.; Russell, D. L.
1982
Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations. Zbl 1031.35077
Chen, Gui-Qiang; Perthame, Benoît
2003
Global solutions to the compressible Navier-Stokes equations for a reacting mixture. Zbl 0771.35044
Chen, Gui-Qiang
1992
Vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for compressible fluid flow. Zbl 1205.35188
Chen, Gui-Qiang G.; Perepelitsa, Mikhail
2010
Zero relaxation and dissipation limits for hyperbolic conservation laws. Zbl 0797.35113
Chen, Gui-Qiang; Liu, Tai-Ping
1993
Compressible Euler-Maxwell equations. Zbl 1019.82023
Chen, Gui-Qiang; Jerome, Joseph W.; Wang, Dehua
2000
On two-dimensional sonic-subsonic flow. Zbl 1128.35070
Chen, Gui-Qiang; Dafermos, Constantine M.; Slemrod, Marshall; Wang, Dehua
2007
Global solutions to the compressible Euler equations with geometrical structure. Zbl 0857.76073
Chen, Gui-Qiang; Glimm, James
1996
Global solutions of the compressible Navier-Stokes equations with large discontinuous initial data. Zbl 0977.35104
Chen, Gui-Qiang; Hoff, David; Trivisa, Konstantina
2000
Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics. III. Zbl 0643.76086
Chen, Guiqiang
1986
On nonlinear stochastic balance laws. Zbl 1261.60062
Chen, Gui-Qiang; Ding, Qian; Karlsen, Kenneth H.
2012
Steady transonic shocks and free boundary problems in infinite cylinders for the Euler equations. Zbl 1075.76036
Chen, Gui-Qiang; Feldman, Mikhail
2004
Global solutions of shock reflection by large-angle wedges for potential flow. Zbl 1277.35252
Chen, Gui-Qiang; Feldman, Mikhail
2010
Existence and stability of compressible current-vortex sheets in three-dimensional magnetohydrodynamics. Zbl 1172.76016
Chen, Gui-Qiang; Wang, Yaguang
2008
Extended divergence-measure fields and the Euler equations for gas dynamics. Zbl 1036.35125
Chen, Gui-Qiang; Frid, Hermano
2003
Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics. I. Zbl 0643.76084
Ding, Xiaxi; Chen, Guiqiang; Luo, Peizhu
1985
Stability of Riemann solutions with large oscillation for the relativistic Euler equations. Zbl 1068.35173
Chen, Gui-Qiang; Li, Yachun
2004
Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws. Zbl 1158.35062
Chen, Gui-Qiang; Ziemer, William P.; Torres, Monica
2009
Formation of singularities in compressible Euler-Poisson fluids with heat diffusion and damping relaxation. Zbl 0914.35102
Wang, Dehua; Chen, Gui-Qiang
1998
Global steady subsonic flows through infinitely long nozzles for the full Euler equations. Zbl 1298.35138
Chen, Gui-Qiang G.; Deng, Xuemei; Xiang, Wei
2012
On the 2-D Riemann problem for the compressible Euler equations I: Interaction of shocks and rarefaction waves. Zbl 0874.76031
Chang, Tung; Chen, Gui-Qiang; Yang, Shuli
1995
Existence and stability of supersonic Euler flows past Lipschitz wedges. Zbl 1121.76055
Chen, Gui-Qiang; Zhang, Yongqian; Zhu, Dianwen
2006
Global solutions to a model for exothermically reacting, compressible flows with large discontinuous initial data. Zbl 1022.76056
Chen, Gui-Qiang; Hoff, David; Trivisa, Konstantina
2003
The Cauchy problem for the Euler equations for compressible fluids. Zbl 1230.35096
Chen, Gui-Qiang; Wang, Dehua
2002
Subsonic-sonic limit of approximate solutions to multidimensional steady Euler equations. Zbl 1333.35168
Chen, Gui-Qiang; Huang, Fei-Min; Wang, Tian-Yi
2016
Quasilinear anisotropic degenerate parabolic equations with time-space dependent diffusion coefficients. Zbl 1084.35034
Chen, Gui-Qiang; Karlsen, Kenneth H.
2005
Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles. Zbl 1131.35061
Chen, Gui-Qiang; Chen, Jun; Feldman, Mikhail
2007
Convergence of shock capturing schemes for the compressible Euler-Poisson equations. Zbl 0858.76051
Chen, G.-Q.; Wang, D.
1996
Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics. II. Zbl 0643.76085
Ding, Xiaxi; Chen, Guiqiang; Luo, Peizhu
1985
Existence theory for the isentropic Euler equations. Zbl 1027.76043
Chen, Gui-Qiang; LeFloch, Philippe G.
2003
Uniqueness and stability of Riemann solutions with large oscillation in gas dynamics. Zbl 1029.76045
Chen, Gui-Qiang; Frid, Hermano; Li, Yachun
2002
Compressible Euler equations with general pressure law. Zbl 0970.76082
Chen, Gui-Qiang; LeFloch, Philippe G.
2000
Existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross-sections. Zbl 1190.76158
Chen, Gui-Qiang; Feldman, Mikhail
2007
Spectral viscosity approximations to multidimensional scalar conservation laws. Zbl 0799.35148
Chen, Gui-Qiang; Du, Qiang; Tadmor, Eitan
1993
Decay of entropy solutions of nonlinear conservation laws. Zbl 0942.35031
Chen, Gui-Qiang; Frid, Hermano
1999
Initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws. Zbl 0962.35122
Chen, Gui-Qiang; Rascle, Michel
2000
Global solutions to the Navier-Stokes equations for compressible heat-conducting flow with symmetry and free boundary. Zbl 1072.35141
Chen, Gui-Qiang; Kratka, Milan
2002
Uniqueness and asymptotic stability of Riemann solutions for the compressible Euler equations. Zbl 0958.35094
Chen, Gui-Qiang; Frid, Hermano
2001
Stability of rarefaction waves and vacuum states for the multidimensional Euler equations. Zbl 1168.35312
Chen, Gui-Qiang; Chen, Jun
2007
On the theory of divergence-measure fields and its applications. Zbl 1024.28009
Chen, Gui-Qiang; Frid, Hermano
2001
Global entropy solutions to exothermically reacting, compressible Euler equations. Zbl 1027.35070
Chen, Gui-Qiang; Wagner, David H.
2003
Regularity of solutions to regular shock reflection for potential flow. Zbl 1170.35031
Bae, Myoungjean; Chen, Gui-Qiang; Feldman, Mikhail
2009
Hyperbolic systems of conservation laws with a symmetry. Zbl 0753.35051
Chen, Gui-Qiang
1991
Isometric immersions and compensated compactness. Zbl 1208.53006
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2010
Transonic nozzle flows and free boundary problems for the full Euler equations. Zbl 1142.35510
Chen, Gui-Qiang; Chen, Jun; Song, Kyungwoo
2006
Remarks on spherically symmetric solutions of the compressible Euler equations. Zbl 0877.35100
Chen, Gui-Qiang
1997
Relativistic Euler equations for isentropic fluids: stability of Riemann solutions with large oscillation. Zbl 1068.35099
Chen, Gui-Qiang; Li, Yachun
2004
On the $$2$$-D Riemann problem for the compressible Euler equations. II: Interaction of contact discontinuities. Zbl 1032.76062
Chang, Tung; Chen, Gui-Qiang; Yang, Shuli
2000
Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge. Zbl 1138.35057
Chen, Gui-Qiang; Li, Tian-Hong
2008
Vanishing viscosity method for transonic flow. Zbl 1140.76014
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2008
Stability of entropy solutions to the Cauchy problem for a class of nonlinear hyperbolic-parabolic equations. Zbl 1027.35080
Chen, Gui-Qiang; DiBenedetto, Emmanuele
2001
$$L^1$$-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations. Zbl 1096.35072
Chen, Gui-Qiang; Karlsen, Kenneth H.
2006
Large-time behavior of entropy solutions of conservation laws. Zbl 0926.35085
Chen, Gui-Qiang; Frid, Hermano
1999
The mathematics of shock reflection-diffraction and von Neumann’s conjectures. Zbl 1403.35001
Chen, Gui-Qiang G.; Feldman, Mikhail
2018
Hyperbolic conservation laws with discontinuous fluxes and hydrodynamic limit for particle systems. Zbl 1195.35211
Chen, Gui-Qiang; Even, Nadine; Klingenberg, Christian
2008
Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles. Zbl 1412.35236
Chen, Gui-Qiang G.; Huang, Fei-Min; Wang, Tian-Yi; Xiang, Wei
2019
Euler equations and related hyperbolic conservation laws. Zbl 1092.35062
Chen, Gui-Qiang
2005
A multidimensional Piston problem for the Euler equations for compressible flow. Zbl 1077.35090
Chen, Gui-Qiang; Chen, Shu-Xing; Wang, Dehua; Wang, Zejun
2005
On the Navier-Stokes equations for exothermically reacting compressible fluids. Zbl 1032.76056
Chen, Gui-Qiang; Hoff, David; Trivisa, Konstantina
2002
Vanishing viscosity solutions of the compressible Euler equations with spherical symmetry and large initial data. Zbl 1323.35136
Chen, Gui-Qiang G.; Perepelitsa, Mikhail
2015
Remarks on DiPerna’s Paper “Convergence of the Viscosity Method for Isentropic Gas Dynamics”. Zbl 0888.35066
Chen, Gui-Qiang
1997
Shock diffraction by convex cornered wedges for the nonlinear wave system. Zbl 1286.35204
Chen, Gui-Qiang; Deng, Xuemei; Xiang, Wei
2014
Divergence-measure fields, sets of finite perimeter, and conservation laws. Zbl 1073.35156
Chen, Gui-Qiang; Torres, Monica
2005
The method of quasidecoupling for discontinuous solutions to conservation laws. Zbl 0797.35112
Chen, Gui-Qiang
1992
Well-posedness of transonic characteristic discontinuities in two-dimensional steady compressible Euler flows. Zbl 1286.35160
Chen, Gui-Qiang; Kukreja, Vaibhav; Yuan, Hairong
2013
Stability of compressible vortex sheets in steady supersonic Euler flows over Lipschitz walls. Zbl 1129.35013
Chen, Gui-Qiang; Zhang, Yongqian; Zhu, Dianwen
2007
Large-time behavior of periodic entropy solutions to anisotropic degenerate parabolic-hyperbolic equations. Zbl 1176.35031
Chen, Gui-Qiang; Perthame, Benoît
2009
Compactness methods and nonlinear hyperbolic conservation laws. Zbl 0959.35115
Chen, Gui-Qiang
2000
Solutions for a nonlocal conservation law with fading memory. Zbl 1129.35049
Chen, Gui-Qiang; Christoforou, Cleopatra
2007
Prandtl-Meyer reflection for supersonic flow past a solid ramp. Zbl 1275.35146
Bae, Myoungjean; Chen, Gui-Qiang; Feldman, Mikhail
2013
Potential theory for shock reflection by a large-angle wedge. Zbl 1135.35357
Chen, Gui-Qiang; Feldman, Mikhail
2005
Global entropy solutions in $$L^\infty$$ to the Euler equations and Euler-Poisson equations for isothermal fluids with spherical symmetry. Zbl 1059.35094
Chen, Gui-Qiang; Li, Tian-Hong
2003
The study on application way of the compensated compactness theory. Zbl 0685.35067
Chen, Guiqiang; Lu, Yunguang
1989
Propagation and cancellation of oscillations for hyperbolic systems of conservation laws. Zbl 0727.35085
Chen, Gui-Qiang
1991
Continuous dependence of entropy solutions to the Euler equations on the adiabatic exponent and Mach number. Zbl 1140.76032
Chen, Gui-Qiang; Christoforou, Cleopatra; Zhang, Yongqian
2008
Particle hydrodynamic moment models in biology and microelectronics: Singular relaxation limits. Zbl 0912.92001
Chen, Gui-Qiang; Jerome, Joseph W.; Zhang, Bo
1997
Structure of Riemann solutions for 2-dimensional scalar conservation laws. Zbl 0851.35085
Chen, Gui-Qiang; Li, Dening; Tan, Dechun
1996
Free boundary problems and transonic shocks for the Euler equations in unbounded domains. Zbl 1170.35483
Feldman, Mikhail; Chen, Gui Qiang
2004
Kolmogorov’s theory of turbulence and inviscid limit of the Navier-Stokes equations in $${\mathbb{R}}^3$$. Zbl 1232.35114
Chen, Gui-Qiang; Glimm, James
2012
The Navier-Stokes equations with the kinematic and vorticity boundary conditions on non-flat boundaries. Zbl 1212.35346
Chen, Guiqiang; Dan, Osborne; Qian, Zhongmin
2009
Existence and the singular relaxation limit for the inviscid hydrodynamic energy model. Zbl 0948.76007
Chen, Gui-Qiang; Jerome, Joseph W.; Zhang, Bo
1998
A study of the Navier-Stokes equations with the kinematic and Navier boundary conditions. Zbl 1206.35193
Chen, Gui-Qiang; Qian, Zhongmin
2010
Centered difference schemes for nonlinear hyperbolic equations. Zbl 1063.65076
Chen, Gui-Qiang; Toro, Eleuterio F.
2004
Analysis on models for exothermically reacting, compressible flows with large discontinuous inital data. Zbl 1075.35036
Chen, Gui-qiang; Trivisa, Konstantina
2005
Two-dimensional steady supersonic exothermically reacting Euler flow past Lipschitz bending walls. Zbl 1374.35304
Chen, Gui-Qiang G.; Kuang, Jie; Zhang, Yongqian
2017
The vanishing viscosity method in one-dimensional thermoelasticity. Zbl 0810.35055
Chen, Gui-Qiang; Dafermos, Constantine M.
1995
Weak continuity of the Gauss-Codazzi-Ricci system for isometric embedding. Zbl 1194.53047
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2010
Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone. Zbl 1154.35401
Chen, Gui-Qiang; Fang, Beixiang
2009
Asymptotic stability of Riemann waves for conservation laws. Zbl 0886.35095
Chen, Gui-Qiang; Frid, Hermano
1997
Existence of entropy solutions to two-dimensional steady exothermically reacting Euler equations. Zbl 1313.35217
Chen, Guiqiang; Xiao, Changuo; Zhang, Yongqian
2014
Uniqueness of transonic shock solutions in a duct for steady potential flow. Zbl 1170.35103
Chen, Gui-Qiang; Yuan, Hairong
2009
Characteristic discontinuities and free boundary problems for hyperbolic conservation laws. Zbl 1270.35308
Chen, Gui-Qiang; Wang, Ya-Guang
2012
Stability of attached transonic shocks in steady potential flow past three-dimensional wedges. Zbl 1475.35206
Chen, Gui-Qiang G.; Chen, Jun; Xiang, Wei
2021
Weak continuity of the Cartan structural system and compensated compactness on semi-Riemannian manifolds with lower regularity. Zbl 1468.83007
Chen, Gui-Qiang G.; Li, Siran
2021
Stability of conical shocks in the three-dimensional steady supersonic isothermal flows past Lipschitz perturbed cones. Zbl 1467.35220
Chen, Gui-Qiang G.; Kuang, Jie; Zhang, Yongqian
2021
Convexity of self-similar transonic shocks and free boundaries for the Euler equations for potential flow. Zbl 1445.35247
Chen, Gui-Qiang G.; Feldman, Mikhail; Xiang, Wei
2020
Stability of multidimensional thermoelastic contact discontinuities. Zbl 1444.35116
Chen, Gui-Qiang G.; Secchi, Paolo; Wang, Tao
2020
Loss of regularity of solutions of the Lighthill problem for shock diffraction for potential flow. Zbl 1439.35327
Chen, Gui-Qiang; Feldman, Mikhail; Hu, Jingchen; Xiang, Wei
2020
Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles. Zbl 1412.35236
Chen, Gui-Qiang G.; Huang, Fei-Min; Wang, Tian-Yi; Xiang, Wei
2019
Nonlinear stability of relativistic vortex sheets in three-dimensional Minkowski spacetime. Zbl 1420.35206
Chen, Gui-Qiang G.; Secchi, Paolo; Wang, Tao
2019
Cauchy fluxes and Gauss-Green formulas for divergence-measure fields over general open sets. Zbl 1428.26024
Chen, Gui-Qiang G.; Comi, Giovanni E.; Torres, Monica
2019
Kolmogorov-type theory of compressible turbulence and inviscid limit of the Navier-Stokes equations in $$\mathbb{R}^3$$. Zbl 1453.76056
Chen, Gui-Qiang G.; Glimm, James
2019
Invariant measures for nonlinear conservation laws driven by stochastic forcing. Zbl 1439.35055
Chen, Gui-Qiang G.; Pang, Peter H. C.
2019
The mathematics of shock reflection-diffraction and von Neumann’s conjectures. Zbl 1403.35001
Chen, Gui-Qiang G.; Feldman, Mikhail
2018
Global weak rigidity of the Gauss-Codazzi-Ricci equations and isometric immersions of Riemannian manifolds with lower regularity. Zbl 1407.53040
Chen, Gui-Qiang G.; Li, Siran
2018
Vanishing viscosity approach to the compressible Euler equations for transonic nozzle and spherically symmetric flows. Zbl 1406.35245
Chen, Gui-Qiang G.; Schrecker, Matthew R. I.
2018
Global weak solutions for the compressible active liquid crystal system. Zbl 1406.35265
Chen, Gui-Qiang G.; Majumdar, Apala; Wang, Dehua; Zhang, Rongfang
2018
Isometric embedding via strongly symmetric positive systems. Zbl 1391.53017
Chen, Gui-Qiang; Clelland, Jeanne; Slemrod, Marshall; Wang, Dehua; Yang, Deane
2018
Stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. Zbl 1438.35257
Chen, Gui-Qiang G.; Rigby, Matthew
2018
Fluids, geometry, and the onset of Navier-Stokes turbulence in three space dimensions. Zbl 1398.76060
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2018
Two-dimensional steady supersonic exothermically reacting Euler flow past Lipschitz bending walls. Zbl 1374.35304
Chen, Gui-Qiang G.; Kuang, Jie; Zhang, Yongqian
2017
Stability of transonic shocks in steady supersonic flow past multidimensional wedges. Zbl 1372.35036
Chen, Gui-Qiang; Fang, Beixiang
2017
Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations. Zbl 1383.35146
Chen, Gui-Qiang G.; Chen, Jun; Feldman, Mikhail
2017
Global existence and regularity of solutions for active liquid crystals. Zbl 1373.35235
Chen, Gui-Qiang; Majumdar, Apala; Wang, Dehua; Zhang, Rongfang
2017
Fluids, elasticity, geometry, and the existence of wrinkled solutions. Zbl 1382.35203
Acharya, Amit; Chen, Gui-Qiang G.; Li, Siran; Slemrod, Marshall; Wang, Dehua
2017
Supersonic flow onto solid wedges, multidimensional shock waves and free boundary problems. Zbl 1391.35274
Chen, Gui-Qiang
2017
Subsonic-sonic limit of approximate solutions to multidimensional steady Euler equations. Zbl 1333.35168
Chen, Gui-Qiang; Huang, Fei-Min; Wang, Tian-Yi
2016
Transonic flows with shocks past curved wedges for the full Euler equations. Zbl 1339.35224
Feldman, Mikhail; Chen, Jun; Chen, Gui-Qiang
2016
Incompressible limit of solutions of multidimensional steady compressible Euler equations. Zbl 1348.35175
Chen, Gui-Qiang G.; Huang, Feimin; Wang, Tian-Yi; Xiang, Wei
2016
Vanishing viscosity solutions of the compressible Euler equations with spherical symmetry and large initial data. Zbl 1323.35136
Chen, Gui-Qiang G.; Perepelitsa, Mikhail
2015
Weak continuity and compactness for nonlinear partial differential equations. Zbl 1329.35003
Chen, Gui-Qiang G.
2015
Transport in a three-zone wetland: flow velocity profile and environmental dispersion. Zbl 1333.92070
Wang, Ping; Chen, G. Q.; Jiang, C. B.; Alsaedi, A.; Wu, Z.; Zeng, L.
2015
Free boundary problems in shock reflection/diffraction and related transonic flow problems. Zbl 1353.76045
Chen, Gui-Qiang; Feldman, Mikhail
2015
Environmental dispersion in a tidal wetland with sorption by vegetation. Zbl 1331.92158
Wang, Ping; Chen, G. Q.
2015
Shock diffraction by convex cornered wedges for the nonlinear wave system. Zbl 1286.35204
Chen, Gui-Qiang; Deng, Xuemei; Xiang, Wei
2014
Existence of entropy solutions to two-dimensional steady exothermically reacting Euler equations. Zbl 1313.35217
Chen, Guiqiang; Xiao, Changuo; Zhang, Yongqian
2014
Entropy, elasticity, and the isometric embedding problem: $$\mathbb M^3\rightarrow\mathbb R^6$$. Zbl 1293.53006
Chen, Gui-Qiang G.; Slemrod, Marshall; Wang, Dehua
2014
Existence and stability of global solutions of shock diffraction by wedges for potential flow. Zbl 1284.35282
Chen, Gui-Qiang G.; Xiang, Wei
2014
Well-posedness of transonic characteristic discontinuities in two-dimensional steady compressible Euler flows. Zbl 1286.35160
Chen, Gui-Qiang; Kukreja, Vaibhav; Yuan, Hairong
2013
Prandtl-Meyer reflection for supersonic flow past a solid ramp. Zbl 1275.35146
Bae, Myoungjean; Chen, Gui-Qiang; Feldman, Mikhail
2013
Stability of transonic characteristic discontinuities in two-dimensional steady compressible Euler flows. Zbl 1290.76054
Chen, Gui-Qiang; Kukreja, Vaibhav; Yuan, Hairong
2013
Local uniqueness of steady spherical transonic shock-fronts for the three-dimensional full Euler equations. Zbl 1267.35004
Chen, Gui-Qiang G.; Yuan, Hairong
2013
Weakly nonlinear geometric optics for hyperbolic systems of conservation laws. Zbl 1288.35340
Chen, Gui-Qiang; Xiang, Wei; Zhang, Yongqian
2013
Entropy and convexity for nonlinear partial differential equations. Zbl 1292.35121
Ball, John M.; Chen, Gui-Qiang G.
2013
On nonlinear stochastic balance laws. Zbl 1261.60062
Chen, Gui-Qiang; Ding, Qian; Karlsen, Kenneth H.
2012
Global steady subsonic flows through infinitely long nozzles for the full Euler equations. Zbl 1298.35138
Chen, Gui-Qiang G.; Deng, Xuemei; Xiang, Wei
2012
Kolmogorov’s theory of turbulence and inviscid limit of the Navier-Stokes equations in $${\mathbb{R}}^3$$. Zbl 1232.35114
Chen, Gui-Qiang; Glimm, James
2012
Characteristic discontinuities and free boundary problems for hyperbolic conservation laws. Zbl 1270.35308
Chen, Gui-Qiang; Wang, Ya-Guang
2012
Shallow water equations: viscous solutions and inviscid limit. Zbl 1388.35124
Chen, Gui-Qiang; Perepelitsa, Mikhail
2012
Remarks on the contributions of Constantine M. Dafermos to the subject of conservation laws. Zbl 1265.35001
Chen, Guiqiang G.; Tzavaras, Athanasios E.
2012
Comparison principles for self-similar potential flow. Zbl 1235.35056
Chen, Gui-Qiang G.; Feldman, Mikhail
2012
Multidimensional conservation laws: overview, problems, and perspective. Zbl 1257.35122
Chen, Gui-Qiang G.
2011
On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Zbl 1252.35194
Chen, Gui-Qiang; Torres, Monica
2011
Shock reflection-diffraction and nonlinear partial differential equations of mixed type. Zbl 1246.35135
Chen, Gui-Qiang G.; Feldman, Mikhail
2011
Vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for compressible fluid flow. Zbl 1205.35188
Chen, Gui-Qiang G.; Perepelitsa, Mikhail
2010
Global solutions of shock reflection by large-angle wedges for potential flow. Zbl 1277.35252
Chen, Gui-Qiang; Feldman, Mikhail
2010
Isometric immersions and compensated compactness. Zbl 1208.53006
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2010
A study of the Navier-Stokes equations with the kinematic and Navier boundary conditions. Zbl 1206.35193
Chen, Gui-Qiang; Qian, Zhongmin
2010
Weak continuity of the Gauss-Codazzi-Ricci system for isometric embedding. Zbl 1194.53047
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2010
A fluid dynamic formulation of the isometric embedding problem in differential geometry. Zbl 1187.35135
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2010
On degenerate partial differential equations. Zbl 1235.35003
Chen, Gui-Qiang G.
2010
Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws. Zbl 1158.35062
Chen, Gui-Qiang; Ziemer, William P.; Torres, Monica
2009
Regularity of solutions to regular shock reflection for potential flow. Zbl 1170.35031
Bae, Myoungjean; Chen, Gui-Qiang; Feldman, Mikhail
2009
Large-time behavior of periodic entropy solutions to anisotropic degenerate parabolic-hyperbolic equations. Zbl 1176.35031
Chen, Gui-Qiang; Perthame, Benoît
2009
The Navier-Stokes equations with the kinematic and vorticity boundary conditions on non-flat boundaries. Zbl 1212.35346
Chen, Guiqiang; Dan, Osborne; Qian, Zhongmin
2009
Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone. Zbl 1154.35401
Chen, Gui-Qiang; Fang, Beixiang
2009
Uniqueness of transonic shock solutions in a duct for steady potential flow. Zbl 1170.35103
Chen, Gui-Qiang; Yuan, Hairong
2009
Evolution of discontinuity and formation of triple-shock pattern in solutions to a two-dimensional hyperbolic system of conservation laws. Zbl 1183.35227
Chen, Gui-Qiang; Wang, Dehua; Yang, Xiaozhou
2009
Shock reflection-diffraction phenomena and multidimensional conservation laws. Zbl 1196.35002
Chen, Gui-Qiang; Feldman, Mikhail
2009
Foreword. Zbl 1154.01314
Chen, Gui-Qiang; Hong, Jiaxing
2009
Existence and stability of compressible current-vortex sheets in three-dimensional magnetohydrodynamics. Zbl 1172.76016
Chen, Gui-Qiang; Wang, Yaguang
2008
Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge. Zbl 1138.35057
Chen, Gui-Qiang; Li, Tian-Hong
2008
Vanishing viscosity method for transonic flow. Zbl 1140.76014
Chen, Gui-Qiang; Slemrod, Marshall; Wang, Dehua
2008
Hyperbolic conservation laws with discontinuous fluxes and hydrodynamic limit for particle systems. Zbl 1195.35211
Chen, Gui-Qiang; Even, Nadine; Klingenberg, Christian
2008
Continuous dependence of entropy solutions to the Euler equations on the adiabatic exponent and Mach number. Zbl 1140.76032
Chen, Gui-Qiang; Christoforou, Cleopatra; Zhang, Yongqian
2008
On two-dimensional sonic-subsonic flow. Zbl 1128.35070
Chen, Gui-Qiang; Dafermos, Constantine M.; Slemrod, Marshall; Wang, Dehua
2007
Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles. Zbl 1131.35061
Chen, Gui-Qiang; Chen, Jun; Feldman, Mikhail
2007
Existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross-sections. Zbl 1190.76158
Chen, Gui-Qiang; Feldman, Mikhail
2007
Stability of rarefaction waves and vacuum states for the multidimensional Euler equations. Zbl 1168.35312
Chen, Gui-Qiang; Chen, Jun
2007
Stability of compressible vortex sheets in steady supersonic Euler flows over Lipschitz walls. Zbl 1129.35013
Chen, Gui-Qiang; Zhang, Yongqian; Zhu, Dianwen
2007
Solutions for a nonlocal conservation law with fading memory. Zbl 1129.35049
Chen, Gui-Qiang; Christoforou, Cleopatra
2007
Dependence of entropy solutions in the large for the Euler equations on nonlinear flux functions. Zbl 1133.35066
Chen, Gui-Qiang; Christoforou, Cleopatra; Zhang, Yongqian
2007
Measure-theoretic analysis and nonlinear conservation laws. Zbl 1132.35416
Chen, Gui-Qiang; Torres, Monica; Ziemer, William P.
2007
Existence and stability of supersonic Euler flows past Lipschitz wedges. Zbl 1121.76055
Chen, Gui-Qiang; Zhang, Yongqian; Zhu, Dianwen
2006
Transonic nozzle flows and free boundary problems for the full Euler equations. Zbl 1142.35510
Chen, Gui-Qiang; Chen, Jun; Song, Kyungwoo
2006
$$L^1$$-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations. Zbl 1096.35072
Chen, Gui-Qiang; Karlsen, Kenneth H.
2006
Validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws. Zbl 1099.35062
Chen, Gui-Qiang; Junca, Stéphane; Rascle, Michel
2006
Quasilinear anisotropic degenerate parabolic equations with time-space dependent diffusion coefficients. Zbl 1084.35034
Chen, Gui-Qiang; Karlsen, Kenneth H.
2005
Euler equations and related hyperbolic conservation laws. Zbl 1092.35062
Chen, Gui-Qiang
2005
A multidimensional Piston problem for the Euler equations for compressible flow. Zbl 1077.35090
Chen, Gui-Qiang; Chen, Shu-Xing; Wang, Dehua; Wang, Zejun
2005
Divergence-measure fields, sets of finite perimeter, and conservation laws. Zbl 1073.35156
Chen, Gui-Qiang; Torres, Monica
2005
Potential theory for shock reflection by a large-angle wedge. Zbl 1135.35357
Chen, Gui-Qiang; Feldman, Mikhail
2005
Analysis on models for exothermically reacting, compressible flows with large discontinuous inital data. Zbl 1075.35036
Chen, Gui-qiang; Trivisa, Konstantina
2005
Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids. Zbl 1098.76603
Chen, Gui-Qiang; Liu, Hailiang
2004
Steady transonic shocks and free boundary problems in infinite cylinders for the Euler equations. Zbl 1075.76036
Chen, Gui-Qiang; Feldman, Mikhail
2004
Stability of Riemann solutions with large oscillation for the relativistic Euler equations. Zbl 1068.35173
Chen, Gui-Qiang; Li, Yachun
2004
Relativistic Euler equations for isentropic fluids: stability of Riemann solutions with large oscillation. Zbl 1068.35099
Chen, Gui-Qiang; Li, Yachun
2004
Free boundary problems and transonic shocks for the Euler equations in unbounded domains. Zbl 1170.35483
Feldman, Mikhail; Chen, Gui Qiang
2004
Centered difference schemes for nonlinear hyperbolic equations. Zbl 1063.65076
Chen, Gui-Qiang; Toro, Eleuterio F.
2004
Formation of $$\delta$$-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. Zbl 1038.35035
Chen, Gui-Qiang; Liu, Hailiang
2003
Existence and continuous dependence of large solutions for the magnetohydrodynamic equations. Zbl 1036.35126
Chen, Gui-Qiang; Wang, Dehua
2003
Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type. Zbl 1015.35075
Chen, Gui-Qiang; Feldman, Mikhail
2003
...and 79 more Documents
all top 5

### Cited by 1,647 Authors

 99 Chen, Gui-Qiang G. 34 Wang, Dehua 29 Shao, Zhiqiang 27 Xin, Zhouping 27 Yang, Hanchun 27 Yuan, Hairong 26 Karlsen, Kenneth Hvistendahl 26 Shen, Chun 25 Wang, Shu 25 Xiang, Wei 24 Huang, Feimin 24 Li, Yachun 23 Sun, Meina 23 Zhu, Changjiang 21 Frid, Hermano 21 Sheng, Wancheng 20 Lu, Yunguang 20 Peng, Yuejun 20 Zhang, Yu 18 Hu, Yanbo 18 Slemrod, Marshall 18 Tan, Zhong 17 Feireisl, Eduard 17 Risebro, Nils Henrik 17 Xu, Jiang 16 Chen, Shuxing 16 Ding, Min 16 Du, Lili 16 Feldman, Mikhail 15 Cheng, Hongjun 15 Luo, Tao 15 Panov, Evgeniy Yu. 15 Qin, Yuming 15 Wang, Tao 15 Yang, Jianwei 15 Yang, Tong 15 Yu, Huimin 15 Zhao, Huijiang 14 Liu, Hailiang 14 Yong, Wen-An 13 Kim, Eun Heui 13 Radkevich, Evgeniĭ Vladimirovich 13 Vasseur, Alexis F. 13 Wang, Yi 13 Yin, Gan 13 Zhan, Huashui 13 Zhang, Yanyan 12 Lai, Geng 12 Yao, Zhengan 12 Yuen, Manwai 11 Andreianov, Boris 11 Gess, Benjamin 11 Guo, Lihui 11 Li, Hailiang 11 Li, Yeping 11 Yin, Huicheng 11 Zhang, Yongqian 11 Zheng, Yuxi 10 Coquel, Frédéric 10 Feng, Yuehong 10 Huang, Lan 10 Kawashima, Shuichi 10 Mei, Ming 10 Natalini, Roberto 10 Tadmor, Eitan 10 Wang, Chunpeng 10 Wang, Jinhuan 10 Xie, Chunjing 10 Zhang, Jianwen 10 Zhang, Kaijun 9 Bae, Myoungjean 9 Berthon, Christophe 9 Coclite, Giuseppe Maria 9 Duan, Ben 9 Ducomet, Bernard 9 Fang, Beixiang 9 Hofmanová, Martina 9 Hsiao, Ling 9 Kreml, Ondřej 9 Li, Jiequan 9 Li, Siran 9 Marcati, Pierangelo 9 Pan, Ronghua 9 Qu, Aifang 9 Secchi, Paolo 9 Segura de León, Sergio 9 Shen, Wen 9 Toro, Eleuterio F. 9 Tsuge, Naoki 9 Wang, Qin 9 Wang, Zejun 8 Abreu, Eduardo 8 Berthelin, Florent 8 Chen, Jun 8 Cheng, Jianfeng 8 Christoforou, Cleopatra C. 8 Dafermos, Constantine M. 8 Jiang, Peng 8 Koley, Ujjwal 8 LeFloch, Philippe Gerard ...and 1,547 more Authors
all top 5

### Cited in 240 Serials

 236 Journal of Differential Equations 123 Journal of Mathematical Analysis and Applications 121 Archive for Rational Mechanics and Analysis 75 ZAMP. Zeitschrift für angewandte Mathematik und Physik 70 Journal of Hyperbolic Differential Equations 63 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 58 SIAM Journal on Mathematical Analysis 58 Nonlinear Analysis. Real World Applications 54 Journal of Mathematical Physics 42 Journal of Computational Physics 40 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 34 Communications in Mathematical Physics 28 Mathematics of Computation 25 Nonlinearity 24 Chinese Annals of Mathematics. Series B 24 Acta Mathematica Scientia. Series B. (English Edition) 24 Communications on Pure and Applied Analysis 22 Applicable Analysis 22 Quarterly of Applied Mathematics 22 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 21 Mathematical Methods in the Applied Sciences 21 Communications in Partial Differential Equations 20 Journal of Mathematical Fluid Mechanics 19 Discrete and Continuous Dynamical Systems 18 Transactions of the American Mathematical Society 18 Applied Mathematics Letters 18 Boundary Value Problems 17 Journal of Functional Analysis 16 Acta Applicandae Mathematicae 16 Physica D 16 Acta Mathematicae Applicatae Sinica. English Series 15 Advances in Mathematics 15 Journal de Mathématiques Pures et Appliquées. Neuvième Série 14 Journal of Scientific Computing 14 Science China. Mathematics 13 Proceedings of the American Mathematical Society 12 Calculus of Variations and Partial Differential Equations 12 Journal of Mathematical Sciences (New York) 11 Numerische Mathematik 11 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 11 NoDEA. Nonlinear Differential Equations and Applications 11 Kinetic and Related Models 11 Advances in Mathematical Physics 10 Computers & Mathematics with Applications 10 Journal of Computational and Applied Mathematics 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Communications on Pure and Applied Mathematics 9 Applied Numerical Mathematics 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Applied Mathematics and Computation 8 SIAM Journal on Scientific Computing 8 Acta Mathematica Sinica. English Series 8 Bulletin of the Brazilian Mathematical Society. New Series 8 Networks and Heterogeneous Media 7 Computers and Fluids 7 SIAM Journal on Applied Mathematics 7 European Journal of Mechanics. B. Fluids 7 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 7 Stochastic and Partial Differential Equations. Analysis and Computations 6 Computer Methods in Applied Mechanics and Engineering 6 Journal of Statistical Physics 6 Abstract and Applied Analysis 6 Journal of Evolution Equations 5 Transport Theory and Statistical Physics 5 Inventiones Mathematicae 5 Japan Journal of Industrial and Applied Mathematics 5 Advances in Difference Equations 5 Nonlinear Analysis. Theory, Methods & Applications 4 BIT 4 Indiana University Mathematics Journal 4 Mathematische Annalen 4 Monatshefte für Mathematik 4 SIAM Journal on Numerical Analysis 4 Asymptotic Analysis 4 The Journal of Geometric Analysis 4 Stochastic Processes and their Applications 4 Bulletin of the American Mathematical Society. New Series 4 Journal of Dynamics and Differential Equations 4 Boletim da Sociedade Brasileira de Matemática. Nova Série 4 Mathematics and Mechanics of Solids 4 Journal of the European Mathematical Society (JEMS) 4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Applied Mathematics 4 Multiscale Modeling & Simulation 4 Communications in Computational Physics 4 Advances in Nonlinear Analysis 4 Annals of PDE 4 Electronic Research Archive 3 Indian Journal of Pure & Applied Mathematics 3 Journal of Engineering Mathematics 3 Physics Letters. A 3 The Annals of Probability 3 Rendiconti del Seminario Matematico della Università di Padova 3 Ricerche di Matematica 3 SIAM Journal on Control and Optimization 3 Studies in Applied Mathematics 3 Zeitschrift für Analysis und ihre Anwendungen 3 Revista Matemática Iberoamericana ...and 140 more Serials
all top 5

### Cited in 43 Fields

 1,803 Partial differential equations (35-XX) 1,178 Fluid mechanics (76-XX) 233 Numerical analysis (65-XX) 108 Statistical mechanics, structure of matter (82-XX) 72 Probability theory and stochastic processes (60-XX) 62 Mechanics of deformable solids (74-XX) 53 Classical thermodynamics, heat transfer (80-XX) 33 Differential geometry (53-XX) 32 Calculus of variations and optimal control; optimization (49-XX) 31 Optics, electromagnetic theory (78-XX) 26 Operations research, mathematical programming (90-XX) 25 Real functions (26-XX) 25 Astronomy and astrophysics (85-XX) 22 Measure and integration (28-XX) 22 Functional analysis (46-XX) 22 Biology and other natural sciences (92-XX) 21 Relativity and gravitational theory (83-XX) 20 Dynamical systems and ergodic theory (37-XX) 20 Global analysis, analysis on manifolds (58-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 13 Operator theory (47-XX) 13 Systems theory; control (93-XX) 12 Ordinary differential equations (34-XX) 8 Integral equations (45-XX) 7 Functions of a complex variable (30-XX) 6 Geophysics (86-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Approximations and expansions (41-XX) 5 General topology (54-XX) 5 Manifolds and cell complexes (57-XX) 5 Mechanics of particles and systems (70-XX) 5 Quantum theory (81-XX) 4 General and overarching topics; collections (00-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Information and communication theory, circuits (94-XX) 3 Potential theory (31-XX) 2 History and biography (01-XX) 2 Integral transforms, operational calculus (44-XX) 2 Statistics (62-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX)

### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.


text:
# 2022 Australian National University|EMET3007/8012 Assignment 2

0

## Instructions:

This assignment is worth either 20% or 25% of the final grade, and is worth a total of 75 points. All working must be shown for all questions. For questions which ask you to write a program, you must provide the code you used. If you have found code and then modified it, then the original source must be cited. The assignment is due by 5pm Friday 1st of October (Friday of Week 8), using Turnitin on Wattle. Late submissions will only be accepted with prior written approval. Good luck.

[10 marks] In this exercise we will consider four different specifications for forecasting monthly Australian total employed persons. The dataset (available on Wattle) AUSEmp 1oy 2022. csv contains three columns; the first column contains the date; the second contains the sales figures for that month (FRED data series LFEMTTTTAUM647N), and the third contains Australian GDP for that month.1] The data runs from January 1995 to January $2022 .$

Let $M_{i t}$ be a dummy variable that denotes the month of the year. Let $D_{i t}$ be a dummy variable which denotes the quarter of the year. The four specifications we consider are
\begin{aligned} &S_1: y_t=a_0+a_1 t+\alpha_4 D_{4 t}+\epsilon_t \ &S_2: y_t=a_1 t+\sum_{i=1}^4 \alpha_i D_{i t}+\epsilon_t \ &S_3: y_t=a_0+a_1 t+\beta_{12} M_{12, t}+\epsilon_t \ &S_4: y_t=a_1 t+\sum_{i=1}^{12} \beta_i M_{i t}+\epsilon_t \end{aligned}
where $\mathbb{E} \epsilon_t=0$ for all $t$.

a) For each specification, describe this specification in words.
b) For each specification, estimate the values of the parameters, and compute the MSE, $\mathrm{AIC}$, and BIC. If you make any changes to the csv file, please describe the changes you make. As always, you must include your code.
c) For each specification, compute the MSFE for the 1-step and 5-step ahead forecasts, with the out-of-sample forecasting exercise beginning at $T_0=50$.
d) For each specification, plot the out-of-sample forecasts and comment on the results.

[10 marks] Now add to Question 1 the additional assumption that $\epsilon_t \sim \mathcal{N}\left(0, \sigma^2\right)$. One estimator ${ }^2$ for $\sigma^2$ is
$$\hat{\sigma}^2=\frac{1}{T-k} \sum_{t=1}^T\left(y_t-\hat{y}_t\right)^2$$
where $\hat{y}_t$ is the estimated value of $y_t$ in the model and $k$ is the number of regressors in the specification.
a) For each specification $\left(S_1, \ldots, S_4\right)$, compute $\hat{\sigma}^2$.
b) For each specification, make a $95 \%$ probability forecast for the sales in June $2021 .$
c) For each specification, compute the probability that the total employed persons in June 2022 will be greater than $13.5$ million. According to the FRED series LFEMTTTTAUM647N, what was the actual employment level for that month.
d) Do you think the assumption that $\epsilon_t$ is iid is a reasonable assumption for this data series.

[10 marks] Here we investigate whether adding GDP $\mathrm{Gs}^3$ as a predictor can improve our forecasts. Consider the following modified specifications:
\begin{aligned} &S_1^{\prime}: y_t=a_0+a_1 t+\alpha_4 D_{4 t}+\gamma x_{t-h}+\epsilon_t \ &S_2^{\prime}: y_t=a_1 t+\sum_{i=1}^4 \alpha_i D_{i t}+\gamma x_{t-h}+\epsilon_t \ &S_3^{\prime}: y_t=a_0+a_1 t+\beta_{12} M_{12, t}+\gamma x_{t-h}+\epsilon_t \ &S_4^{\prime}: y_t=a_1 t+\sum_{i=1}^{12} \beta_i M_{i t}+\gamma x_{t-h}+\epsilon_t \end{aligned}
where $\mathbb{E} \epsilon_t=0$ for all $t$, and $x_{t-h}$ is GDP at time $t-h$. For each specification, compute the MSFE for the 1-step ahead, and the 5-step ahead forecasts, with the out-of-sample forecasting exercise beginning at $T_0=50$. For each specification, plot the out-of-sample forecasts and comment on the results.

[15 marks] Here we investigate whether Holt-Winters smoothing can improve our forecasts. Use a Holt-Winters smoothing method with seasonality, to produce 1-step ahead and 5-step ahead forecasts and compute the MSFE for these forecasts. You should use smoothing parameters $\alpha=\beta=\gamma=0.3$ and start the out-of-sample forecasting exercise at $T_0=50$. Plot these out-of-sample forecasts and comment on the results.
Additionally, estimate the values for $\alpha, \beta$, and $\gamma$ which minimise the MSFE. Find the MSFE for these parameter vales and compare it to the baseline $\alpha=\beta=\gamma=0.3$.

[5 marks] Questions 1, 3 and 4 each provided alternative models for forecasting Australian Total Employment. Compare the efficacy of these forecasts. Your comparison should include discussions of MSFE, but must also make qualitative observations (typically based on your graphs).

[10 marks] Develop another model, either based on material from class or otherwise, to forecast Australian Total Employment. Your new model should perform better (have a lower MSFE or MAFE) than all models from Questions 1,3, and 4. As part of your response to this question you must provide:
a) a brief written explanation of what your model is doing,
b) a brief statement on why you think your new model will perform better,
c) any relevant equations or mathematics/statistics to describe the model,
d) the code to run the model, and
e) the MSFE and/or MAFE error found by your model, and a brief discussion of how this compares to previous cases.

[15 marks] Consider the ARX(1) model
$$y_t=\mu+a t+\rho y_{t-1}+\epsilon_t$$
where the errors follow an $\mathrm{AR}(2)$ process
$$\epsilon_t=\phi_1 \epsilon_{t-1}+\phi_2 \epsilon_{t-2}+u_t, \quad \mathbf{u} \sim \mathcal{N}\left(0, \sigma^2 I\right)$$
for $t=1, \ldots, T$ and $e_{-1}=e_0=0$. Suppose $\phi_1, \phi_2$ are known. Find (analytically) the maximum likelihood estimators for $\mu, a, \rho$, and $\sigma^2$.

Hint: First write $y$ and $\epsilon$ in vector/matrix form. You may wish to use different looking forms for each. Find the distribution of $\epsilon$ and $y$. Then apply some appropriate calculus. You may want to let $H=I-\phi_1 L-\phi_2 L^2$, where $I$ is the $T \times T$ identity matrix, and $L$ is the lag matrix.

# 2022 Australian National University|EMET3007/8012 Assignment 2

0

## Instructions:

This assignment is worth either $20 \%$ or $25 \%$ of the final grade, and is worth a total of 75 points. All working must be shown for all questions. For questions which ask you to write a program, you must provide the code you used. If you have found code and then modified it, then the original source must be cited. The assignment is due by $5 \mathrm{pm}$ Friday 1st of October (Friday of Week 8), using Turnitin on Wattle. Late submissions will only be accepted with prior written approval. Good luck.

[10 marks] In this exercise we will consider four different specifications for forecasting monthly Australian total employed persons. The dataset (available on Wattle) AUSEmp 1oy 2022. csv contains three columns; the first column contains the date; the second contains the sales figures for that month (FRED data series LFEMTTTTAUM647N), and the third contains Australian GDP for that month.1] The data runs from January 1995 to January $2022 .$

Let $M_{i t}$ be a dummy variable that denotes the month of the year. Let $D_{i t}$ be a dummy variable which denotes the quarter of the year. The four specifications we consider are
\begin{aligned} &S_1: y_t=a_0+a_1 t+\alpha_4 D_{4 t}+\epsilon_t \ &S_2: y_t=a_1 t+\sum_{i=1}^4 \alpha_i D_{i t}+\epsilon_t \ &S_3: y_t=a_0+a_1 t+\beta_{12} M_{12, t}+\epsilon_t \ &S_4: y_t=a_1 t+\sum_{i=1}^{12} \beta_i M_{i t}+\epsilon_t \end{aligned}
where $\mathbb{E} \epsilon_t=0$ for all $t$.

a) For each specification, describe this specification in words.
b) For each specification, estimate the values of the parameters, and compute the MSE, $\mathrm{AIC}$, and BIC. If you make any changes to the csv file, please describe the changes you make. As always, you must include your code.
c) For each specification, compute the MSFE for the 1-step and 5-step ahead forecasts, with the out-of-sample forecasting exercise beginning at $T_0=50$.
d) For each specification, plot the out-of-sample forecasts and comment on the results.

[10 marks] Now add to Question 1 the additional assumption that $\epsilon_t \sim \mathcal{N}\left(0, \sigma^2\right)$. One estimator ${ }^2$ for $\sigma^2$ is
$$\hat{\sigma}^2=\frac{1}{T-k} \sum_{t=1}^T\left(y_t-\hat{y}_t\right)^2$$
where $\hat{y}_t$ is the estimated value of $y_t$ in the model and $k$ is the number of regressors in the specification.
a) For each specification $\left(S_1, \ldots, S_4\right)$, compute $\hat{\sigma}^2$.
b) For each specification, make a $95 \%$ probability forecast for the sales in June $2021 .$
c) For each specification, compute the probability that the total employed persons in June 2022 will be greater than $13.5$ million. According to the FRED series LFEMTTTTAUM647N, what was the actual employment level for that month.
d) Do you think the assumption that $\epsilon_t$ is iid is a reasonable assumption for this data series.

[10 marks] Here we investigate whether adding GDP $\mathrm{Gs}^3$ as a predictor can improve our forecasts. Consider the following modified specifications:
\begin{aligned} &S_1^{\prime}: y_t=a_0+a_1 t+\alpha_4 D_{4 t}+\gamma x_{t-h}+\epsilon_t \ &S_2^{\prime}: y_t=a_1 t+\sum_{i=1}^4 \alpha_i D_{i t}+\gamma x_{t-h}+\epsilon_t \ &S_3^{\prime}: y_t=a_0+a_1 t+\beta_{12} M_{12, t}+\gamma x_{t-h}+\epsilon_t \ &S_4^{\prime}: y_t=a_1 t+\sum_{i=1}^{12} \beta_i M_{i t}+\gamma x_{t-h}+\epsilon_t \end{aligned}
where $\mathbb{E} \epsilon_t=0$ for all $t$, and $x_{t-h}$ is GDP at time $t-h$. For each specification, compute the MSFE for the 1-step ahead, and the 5-step ahead forecasts, with the out-of-sample forecasting exercise beginning at $T_0=50$. For each specification, plot the out-of-sample forecasts and comment on the results.

[15 marks] Here we investigate whether Holt-Winters smoothing can improve our forecasts. Use a Holt-Winters smoothing method with seasonality, to produce 1-step ahead and 5-step ahead forecasts and compute the MSFE for these forecasts. You should use smoothing parameters $\alpha=\beta=\gamma=0.3$ and start the out-of-sample forecasting exercise at $T_0=50$. Plot these out-of-sample forecasts and comment on the results.
Additionally, estimate the values for $\alpha, \beta$, and $\gamma$ which minimise the MSFE. Find the MSFE for these parameter vales and compare it to the baseline $\alpha=\beta=\gamma=0.3$.

[5 marks] Questions 1, 3 and 4 each provided alternative models for forecasting Australian Total Employment. Compare the efficacy of these forecasts. Your comparison should include discussions of MSFE, but must also make qualitative observations (typically based on your graphs).

[10 marks] Develop another model, either based on material from class or otherwise, to forecast Australian Total Employment. Your new model should perform better (have a lower MSFE or MAFE) than all models from Questions 1,3, and 4. As part of your response to this question you must provide:
a) a brief written explanation of what your model is doing,
b) a brief statement on why you think your new model will perform better,
c) any relevant equations or mathematics/statistics to describe the model,
d) the code to run the model, and
e) the MSFE and/or MAFE error found by your model, and a brief discussion of how this compares to previous cases.

[15 marks] Consider the ARX(1) model
$$y_t=\mu+a t+\rho y_{t-1}+\epsilon_t$$
where the errors follow an $\mathrm{AR}(2)$ process
$$\epsilon_t=\phi_1 \epsilon_{t-1}+\phi_2 \epsilon_{t-2}+u_t, \quad \mathbf{u} \sim \mathcal{N}\left(0, \sigma^2 I\right)$$
for $t=1, \ldots, T$ and $e_{-1}=e_0=0$. Suppose $\phi_1, \phi_2$ are known. Find (analytically) the maximum likelihood estimators for $\mu, a, \rho$, and $\sigma^2$.

Hint: First write $y$ and $\epsilon$ in vector/matrix form. You may wish to use different looking forms for each. Find the distribution of $\epsilon$ and $y$. Then apply some appropriate calculus. You may want to let $H=I-\phi_1 L-\phi_2 L^2$, where $I$ is the $T \times T$ identity matrix, and $L$ is the lag matrix.

# matlab作业代写matlab代考

0

MATLAB（”MATrix LABoratory “的缩写）是由MathWorks公司开发的一种专有的多范式编程语言和数字计算环境。MATLAB允许进行矩阵操作、绘制函数和数据、实现算法、创建用户界面以及与用其他语言编写的程序对接。

## 代写matlab作业代做matlab

matlab包含几个不同的主题，列举如下：

• 强弱型化Strong and weak typing
• 单位矩阵Identity matrix
• 共轭转置Conjugate transpose
• λ演算 Lambda calculus

## matlab的历史

Some especially large changes to the software were made with version 8 in 2012.The user interface was reworked[citation needed] and Simulink’s functionality was expanded.By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live Editor notebook, and other features.

## 微积分课后作业代写

(define eqv?
(lambda (x y)
(cond
((eq? x y))
((number? x)
(and (number? y)
(if (exact? x)
(and (exact? y) (= x y))
(and (inexact? y) (= x y)))))
((char? x) (and (char? y) (char=? x y)))
(else #f))))
(eqv? 'a 3) #f
(eqv? #t 't) #f
(eqv? "abc" 'abc) #f

## matlab课后作业代写的应用代写

MATLAB可以调用用C或Fortran编程语言编写的函数和子程序。创建的包装函数允许MATLAB数据类型被传递和返回。MEX文件（MATLAB可执行文件）是通过编译此类函数而创建的可动态加载的对象文件。自2014年以来，正在增加与Python的双向对接。


text:
# Why do we plot distributions (histograms, etc) per logarithmic interval (i.e. per “dec”/“dex”)?

I was trying to explain why we plot distributions (for example the Luminosity distribution function attached) per logarithmic interval (another example would be spectral energy distributions per logarithmic frequency interval), when I realized I have absolutely no idea myself.

In this image the AGN luminosity function, $$\phi(L) \equiv \frac{d \Phi}{d \log L},$$ is plotted in units of per-cubic-Mpc, per-log-L. $\Phi$ has perfectly intuitive meaning: the number-density of AGN, but why use the (differential) luminosity function $\phi$ instead?

Edit: to clarify a little, what we're confused about is not the log-log nature of it, but the units. Lets say I have a distribution of L values, I can then compute the histogram over some bins, $n(L)$, then plot $\log n$ vs. $\log L$ --- that's fine. But here, the distribution is not just $\log n$ vs. $\log L$, it's $(\log n / \log L)$ vs. $\log L$.

i.e. I didn't mean to ask, "Why is log-log plotting useful?"

Let's say I'm looking at the histogram of people's height in the World, but then I plot the logarithm of the number of people with a given height divided by the width of their height bin (e.g. 6 in)... why?

• $f(x)\sim x^{\alpha}\Rightarrow$ linear plot on log-log with slope $\alpha$ is one reason. – Kyle Kanos May 23 '17 at 18:38
• @KyleKanos please see edit – DilithiumMatrix May 23 '17 at 20:11

This is something that is fairly obvious if you learned data analysis in the days before computers were easy, because then you would understand that a plotting $y$ versus $x$ on log-log paper is equivalent to plotting $\log y$ against $\log x$ on ordinary linear graph paper.

You are literally saying "I want to plot $\phi$ against $L$" $$\phi = \phi\left(L\right) \,,$$ but "I have to show a huge range" or "I want to expose a power law" (or a change in the power law as above), so I will plot $$\log \left(\frac{\phi(L)}{\phi(L_\odot)}\right)$$ versus $$\log\left(\frac{L}{L_\odot}\right) \;.$$ instead.

Then you just look at the units of what you are plotting.

Now, there is a subtlety that relates to the fact that this is a histogram. In a naive view, histograms just count how many of something are associates with particular ranges of the independent variable, and that has the odd property of making the vertical axis of the graph depend inversely on the size of the binning. To facilitate comparisons between hisotgrams with different binning—even if they both use equal sized bins—you have to divide the vertical axis by the bin size. So that historgrams in my fields often have units of "events per 50 MeV" or similar.

In principle you can neglect that if you don't want to compare to another histogram unless you have bins of different sizes: then even comparing from bin to bin requires that kind of normalization. And log-scales are of little use unless you let the bin size vary.

• Either I'm not understanding, or perhaps I didn't explain the question well: I'm happy with plotting log-log. But the subtlety I don't understand is the units of the ordinate being not just $\log \phi$, but $\log \phi$ per logarithmic interval. I've tried to edit the question to clarify a bit. – DilithiumMatrix May 23 '17 at 19:38
• @DilithiumMatrix Ah. So this is really about why histograms are scaled by bin-size in the first place. I've explained that context as well. – dmckee --- ex-moderator kitten May 23 '17 at 20:11

I don't know in this specific case, but in most instances where we plot something in logarithmic space, it is because the data spans many orders of magnitude and there are important features to be identified at both large and small scales.

If you were to plot your luminosity in linear space, it would basically just go from 1e-3 to 0 almost instantly and then just appear to stay there. You would miss the fact there it looks like there are two regions that are linear (in log space) with a blending function in between. You would also miss the differences between the lines -- in linear space, they would all collapse together and look like a blob of a line headed to zero.

In almost all instances, log spacing is used because the data spans a huge number of values and this helps highlight the differences that would ordinarily be hidden at large and small scales.

• In signal processing/analysis log-space is extremely important for that reason. You want to see how something behaves over many frequency ranges (for example the difference between interaction at the Hz range and GHz range). – JMac May 23 '17 at 18:43


text:
# How does in-order traversal in Binary search tree works (recursion)

I visit some question but their implementations are slightly different and my doubt is not like theirs. I have this code in Javascript.

The code is typical BST implementation with methods to support in-order traversal. The code that is the most relavant for this question is the the inOrderTraverse and inOrderTraverseNode. I cannot understand how this code work.

function BinarySearchTree() {

var Node = function (key) {
this.key = key;
this.left = null;
this.right = null;
};

var root = null;

this.inOrderTraverse = function (callback) {

inOrderTraverseNode(root, callback);
}

this.insert = function (key) {

var newNode = new Node(key);

if (root === null) {
root = newNode;
}
else {
insertNode(root, newNode);
}

}

var insertNode = function (node, newNode) {

if (newNode.key < node.key) {
if (node.left === null) {
node.left = newNode;
} else {
insertNode(node.left, newNode);
}
} else {
if (node.right === null) {
node.right = newNode;
} else {
insertNode(node.right, newNode);
}
}

};

var inOrderTraverseNode = function (node, callback) {

if (node !== null) {
inOrderTraverseNode(node.left, callback);
callback(node.key);
inOrderTraverseNode(node.right, callback);
}
}
}

The code that will use the BinarySearchTree "class".

function printNode(value) {
document.writeln(value);
}

var tree = new BinarySearchTree();

tree.insert(11);
tree.insert(7);
tree.insert(15);
tree.insert(5);
tree.insert(3);
tree.insert(9);
tree.insert(8);
tree.insert(10);
tree.insert(13);
tree.insert(12);
tree.insert(14);
tree.insert(20);
tree.insert(18);
tree.insert(25);
tree.insert(6);

tree.inOrderTraverse(printNode);

This will generate a BST like this:

taken from the book Learning Javascript Data Structure and Algorithms by Loiane Grone

I will explain how I think the in-order functionality works.

    var inOrderTraverseNode = function (node, callback) {

if (node !== null) {     //checks if the node is null, 11 is not null so it continues
inOrderTraverseNode(node.left, callback);     //keep executing this code until it finds a node with left null
callback(node.key);      //3, the node with left null is printed
inOrderTraverseNode(node.right, callback);     // checks if the 3 node has a right node, it doesn't have, so the execution finishes
}

}

11 the root node is passed to the inOrderTraverseNode, it checks to see if the left is a null, if it is not it continues passing the left node until the left node is null. When a left null node is found Then it prints the value, callback(node.key) will execute as callback(3), so the 3 will be the first item printed on the screen. The execution then continues to inOrderTraverseNode(node.right, callback), 3 don't have a right child so execution will go on and that's that.

in my mind the output would be 3 only.

How do the in-order traversal get from 3 to the 5?

• Questions about code are off-topic, here. Is there a conceptual question about traversals that you can ask without all the code? May 15, 2018 at 10:23

The important part is to consider the entire call stack.

When you're calling inOrderTraverseNode on the root, what happens first is it calls it on its left child, and so on.

So at the point that we call it on 3, the call stack above us looks like

inOrderTraverseNode(Node(11), callback)
inOrderTraverseNode(Node(7), callback)
inOrderTraverseNode(Node(5), callback)
inOrderTraverseNode(Node(3), callback)

Eventually, the inOrderTraverseNode on the node with value 3 returns (after calling it on the null children).

At this point, the current point in code execution is at:

  if (node !== null) {     //checks if the node is null, 11 is not null so it continues
inOrderTraverseNode(node.left, callback);     //keep executing this code until it finds a node with left null
> callback(node.key);      //3, the node with left null is printed
inOrderTraverseNode(node.right, callback);     // checks if the 3 node has a right node, it doesn't have, so the execution finishes
}

But now the node in question is 5, we've returned back up a level, so the stack is:

inOrderTraverseNode(Node(11), callback)
inOrderTraverseNode(Node(7), callback)
inOrderTraverseNode(Node(5), callback)

So the callback is called on 5, and now we continue execution, recursively traversing the right subtree. After that, that code returns, and eventually we have the stack:

inOrderTraverseNode(Node(11), callback)
inOrderTraverseNode(Node(7), callback)

And now we're finished with the left subtree, so we call the callback with 7.

And so on. So imagine the stack growing every time you call it on a subtree. Then you go back up, process that node, then head back down to the other subtree (growing the stack again), and processing that.

So what you're neglecting from your explanation is that after execution finishes, it goes back to the code that called it. So although it makes it down to 3, and processes fully there, that code was called from the call at 5, so it has to finish processing that call. Likewise for each further call up. This is the same process that brings you back to where you were after you call it.

• Let me see if I understood. inOrderTraverseNode(node.left, callback) executes until it gets to 3, when it gets to 3 the left child is null so the execution continues to callback(3) , then it checks for a right child on node 3 that doesn't exist so the execution stack goes up with 5 and then callback(5) is executed. then it checks for a right child on the 5 node, it doesn't exist, so execution continues up with 7, callback(7) is executed then it checks for a right child on 7, it does exist, it's 9. The 9 is checked to see if it has a left child .... May 14, 2018 at 19:52
• Yeah, you've got it exactly! May 15, 2018 at 15:25

Consider indorder as a command in military. Let the binary tree be the hierarchy among the soldiers.

The general shouts "inorder!" and that means, when a subordinate receives the order, he tells it to his "left" subordinates. If he has no subordinates on the left side, then he yells out his name, and only then he commands his right subordinate to execute the order.

Inorder! command means "tell your first subordinate, do it yourself, and then tell your right subordinate. Afther you are finished, report to your superior."

The general is the root of the binary tree. He shouts out "inorder!"

That means his left subordinate gets the order, and shouts out "inorder!" himself. This process goes on until the order reaches to a soldier who has no left subordinate. Then, he yells out his name and gives the order to his right subordinate.

After all his right subordinates are done, he reports back to his immediate superior. The superior, like him, yells out his name and gives the order to his right subordinate.

When all the left side is done, the general (root of the binary tree) yells out his name and gives the order to his right side.

Now, consider this tree
(taken from https://www.geeksforgeeks.org/tree-traversals-inorder-preorder-and-postorder/):

The general is 1. He shouts "inorder!"

2 recieves the order, and he shouts "inorder!"

4 receives the order. He has no left child, and thus shouts his name: 4

He has also no right child, and thus reports to 2.

Left side of 2 is done, and this 2 shouts his name: 2, and then gives the order to the right side.

This process goes on, until the root is notified a second time.


text:
# The guy wires are used to support the telephone pole

The guy wires are used to support the telephone pole. Represent the force in each wire in Cartesian vector form. Neglect the diameter of the pole.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### Solution:

We will first write the locations of point A, B, C, and D in Cartesian vector form.

Using the diagram, the locations of the points are:

$A:(0i+0j+4k)$ m

$B:(0i+0j+5.5k)$ m

$C:(-1i+4j+0k)$ m

$D:(2i-3j+0k)$ m

We will now write position vectors for points from A to C and B to D.

$r_{AC}\,=\,\left\{(-1-0)i+(4-0)j+(0-4)k\right\}$

$r_{AC}\,=\,\left\{-1i+4j-4k\right\}$ m

$r_{BD}\,=\,\left\{(2-0)i+(-3-0)j+(0-5.5)k\right\}$

$r_{BD}\,=\,\left\{2i-3j-5.5k\right\}$ m

A position vector, denoted $\mathbf{r}$ is a vector beginning from one point and extending to another point. It is calculated by subtracting the corresponding vector coordinates of one point from the other. If the coordinates of point A was $(x_A,y_A,z_A)$ and the coordinates of point B was$(x_B,y_B,z_B)$, then $r_{AB}\,=\,(x_B-x_A)i+(y_B-y_A)j+(z_B-z_A)k$

Let us now find the magnitude of each position vector.

magnitude of $r_{AC}\,=\,\sqrt{(-1)^2+(4)^2+(-4)^2}$

magnitude of $r_{AC}\,=\,5.74$ m

magnitude of $r_{BD}\,=\,\sqrt{(2)^2+(-3)^2+(-5.5)^2}$

magnitude of $r_{BD}\,=\,6.58$ m

The magnitude is equal to the square root of the sum of the squares of the vector. If the position vector was $r\,=\,ai+bj+ck$, then the magnitude would be, $r_{magnitude}\,=\,\sqrt{(a^2)+(b^2)+(c^2)}$. In the simplest sense, you take each term of a vector, square it, add it together, and then take the square root of that value.

We can now write the unit vectors for $r_{AC}$ and $r_{BD}$.

$u_{AB}\,=\,\left(-\dfrac{1}{5.74}i\,+\,\dfrac{4}{5.74}j\,-\,\dfrac{4}{5.74}k\right)$

$u_{BD}\,=\,\left(\dfrac{2}{6.58}i\,-\,\dfrac{3}{6.58}j\,-\,\dfrac{5.5}{6.58}k\right)$

The unit vector is each corresponding unit of the position vector divided by the magnitude of the position vector. If the position vector was $r\,=\,ai+bj+ck$, then unit vector, $u\,=\,\dfrac{a}{\sqrt{(a^2)+(b^2)+(c^2)}}+\dfrac{b}{\sqrt{(a^2)+(b^2)+(c^2)}}+\dfrac{c}{\sqrt{(a^2)+(b^2)+(c^2)}}$

Now, we will write each force in Cartesian vector form by multiplying the force by each corresponding unit vector.

$F_A\,=\,250\left(-\dfrac{1}{5.74}i\,+\,\dfrac{4}{5.74}j\,-\,\dfrac{4}{5.74}k\right)$

$F_A\,=\,\left\{-43.5i+174j-174k\right\}$ N

$F_B\,=\,175\left(\dfrac{2}{6.58}i\,-\,\dfrac{3}{6.58}j\,-\,\dfrac{5.5}{6.58}k\right)$

$F_B\,=\,\left\{53.2i-79.8j-146k\right\}$ N

$F_A\,=\,\left\{-43.5i+174j-174k\right\}$ N
$F_B\,=\,\left\{53.2i-79.8j-146k\right\}$ N


text:
MITEX

## NOTE: THIS SERVICE IS STILL IN DEVELOPMENT. USE AT YOUR OWN RISK.

This is MITeX, an online LaTeX composer. You can use a graphical interface, or edit the source of the preamble and body.


text:
### Multiplicative Masking for AES in Hardware

Lauren De Meyer, Oscar Reparaz, and Begül Bilgin

##### Abstract

Hardware masked AES designs usually rely on Boolean masking and perform the computation of the S-box using the tower-field decomposition. On the other hand, splitting sensitive variables in a multiplicative way is more amenable for the computation of the AES S-box, as noted by Akkar and Giraud. However, multiplicative masking needs to be implemented carefully not to be vulnerable to first-order DPA with a zero-value power model. Up to now, sound higher-order multiplicative masking schemes have been implemented only in software. In this work, we demonstrate the first hardware implementation of AES using multiplicative masks. The method is tailored to be secure even if the underlying gates are not ideal and glitches occur in the circuit. We detail the design process of first- and second-order secure AES-128 cores, which result in the smallest die area to date among previous state-of-the-art masked AES implementations with comparable randomness cost and latency. The first- and second-order masked implementations improve resp. 29% and 18% over these designs. We deploy our construction on a Spartan-6 FPGA and perform a side-channel evaluation. No leakage is detected with up to 50 million traces for both our first- and second-order implementation. For the latter, this holds both for univariate and bivariate analysis.

Available format(s)
Category
Implementation
Publication info
A minor revision of an IACR publication in TCHES 2018
Keywords
Contact author(s)
lauren demeyer @ esat kuleuven be
History
Short URL
https://ia.cr/2018/865

CC BY

BibTeX

@misc{cryptoeprint:2018/865,
author = {Lauren De Meyer and Oscar Reparaz and Begül Bilgin},
title = {Multiplicative Masking for AES in Hardware},
howpublished = {Cryptology ePrint Archive, Paper 2018/865},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/865}},
url = {https://eprint.iacr.org/2018/865}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
# performance - Word ladder leetcode

I am working on Word Ladder - LeetCode

Given two words (beginWord and endWord), and a dictionary's word list, find the length of shortest transformation sequence from beginWord to endWord, such that:

1. Only one letter can be changed at a time.
2. Each transformed word must exist in the word list. Note that beginWord is not a transformed word.

Note:

• Return 0 if there is no such transformation sequence.
• All words have the same length.
• All words contain only lowercase alphabetic characters.
• You may assume no duplicates in the word list.
• You may assume beginWord and endWord are non-empty and are not the same.

Example 1:

Input:
beginWord = "hit",
endWord = "cog",
wordList = ["hot","dot","dog","lot","log","cog"]

Output: 5

Explanation: As one shortest transformation is "hit" -> "hot" -> "dot" -> "dog" -> "cog",
return its length 5.

Example 2:

Input:
beginWord = "hit"
endWord = "cog"
wordList = ["hot","dot","dog","lot","log"]

Output: 0

Explanation: The endWord "cog" is not in wordList, therefore no possible transformation.

My Approach:

1. Create a graph with word distances
2. Calculate the distance to the endWord using BFS

Code:

class Solution:
def ladderLength(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
if endWord not in wordList:
return 0

graph = {}
wordList = [beginWord] + wordList if beginWord not in wordList else wordList
for i in range(len(wordList)):
wordU = wordList[i]
# Compute distances and prepare a graph when the distance is equal to one
for j in range(i+1, len(wordList)):
wordV = wordList[j]

if wordU not in graph.keys():
graph[wordU] = []
if wordV not in graph.keys():
graph[wordV] = []

if self.word_difference(wordU, wordV) == 1:
graph[wordU].append(wordV)
graph[wordV].append(wordU)

visited = set()
queue = [beginWord]
distances = {w:1 for w in queue} # since the first word is 1 we are putting 2 here for the root
return self.BFS(graph, endWord, visited, queue, distances)

def word_difference(self, word1, word2):
# Compute the difference in words
distance = 0
for c1, c2 in zip(word1, word2):
if c1 != c2:
distance += 1
return distance

def BFS(self, graph, endNode, visited, queue, distances):
while queue:
node = queue.pop(0)
if node not in visited:
if node == endNode:
return distances[node]
for neighbour in graph[node]:
if neighbour not in visited:
distances[neighbour] = distances[node] + 1
queue.append(neighbour)
return 0

The problem is that the above code is failing on a test case with large word list.

The discussions forum had a solution which took a similar approach but is clearing all the test cases. How can I optimize my solution?

Measure first. If you have a performance problem, make sure you know where it is. A simple, low-tech way to do this is to start throwing time markers into the code and printing the elapsed time for different phases of the work. In your case, the graph-building is the costly part of the process, so there's no need to waste time thinking about how to optimize the BFS code.

from time import time

t1 = time()
...              # Do some work.
t2 = time()
...              # Do some other work
t3 = time()

print('Phase 1', t2 - t1)
print('Phase 2', t3 - t2)

Your algorithm and the one from the discussion forum are quite different. Yes, they both build a graph and then use BFS on it. But, as noted, the performance problem lies in the graph building. Your algorithm is O(N*N): nested loops over wordList. But the other solution is effectively O(N) because the inner loop is over the positions in the current word, not the entire word list.

# Your approach: O(N*N).
for i in range(len(wordList)):
...
for j in range(i+1, len(wordList)):
...

# Discussion forum: O(N*m), where m is tiny, effectively a constant.
for word in word_list:
for i in range(len(word)):
...

Too much computation: word difference is not relevant. A clue that your algorithm is inefficient comes from realizing that we don't actually care about word distances. Our goal is to build a graph linking immediate neighbors (those having a difference of exactly 1), but your algorithm does the work of actually computing all pairwise differences.

Invert the strategy: create linking keys. Suppose you realize that you don't need the word differences. The problem becomes, how do we find immediate neighbors (those having a difference of exactly 1) without actually computing any differences? That's not an easy question to answer, of course, and to some extent it requires a leap of insight. Nonetheless, there is still a general lesson to be learned. The wildcard-based strategy in the discussion forum achieves that goal by figuring out a way to map each word to some linking-keys, such that immediate neighbors will share a common key. The way to do that is to convert each word (a sequence of characters) into other sequences of characters where each character gets replaced by a generic value.

# The word
dog


text:
1. ## Probability of receiving a reply

Letters are sent by post and the probability that they are delivered in days are:
days: 1 2 3
1st class: 0.9 0.1 0
2nd class: 0.1 0.6 0.3
A secretary sends 4 letters and the receivers reply to them immediately on the same class mail. find the probability of receiving at least two replies within three days using second class post?
P(reply in 3 days)= $0.1\times 0.1+2\times 0.1\times 0.6=0.13$
P(1 reply in 3 days)= $0.13\times (0.87)^{3}=0.0856$
P(no replies in 3 days)= $0.87^4=0.573$
P(at least 2 replies)= $1-(0.0856+0.573)=0.341$
What have i done wrong? I have spent quite some time over it and can't see where i have missed anything
Thanks

2. Originally Posted by arze
Letters are sent by post and the probability that they are delivered in days are:
days: 1 2 3
1st class: 0.9 0.1 0
2nd class: 0.1 0.6 0.3
A secretary sends 4 letters and the receivers reply to them immediately on the same class mail. find the probability of receiving at least two replies within three days using second class post?
P(reply in 3 days)= $0.1\times 0.1+2\times 0/1\times 0.6=0.13$ <= did you mean 2*0.1*0.6?
P(1 reply in 3 days)= $0.13\times (0.87)^{3}=0.0856$
P(no replies in 3 days)= $0.87^4=0.573$
P(at least 2 replies)= $1-(0.0856+0.573)=0.341$
What have i done wrong? I have spent quite some time over it and can't see where i have missed anything
Thanks
What does that mean?

3. sorry typing error, i have edited it

4. Originally Posted by arze
Letters are sent by post and the probability that they are delivered in days are:
days: 1 2 3
1st class: 0.9 0.1 0
2nd class: 0.1 0.6 0.3
A secretary sends 4 letters and the receivers reply to them immediately on the same class mail. find the probability of receiving at least two replies within three days using second class post?
P(reply in 3 days)= $0.1\times 0.1+2\times 0.1\times 0.6=0.13$
P(1 reply in 3 days)= $0.13\times (0.87)^{3}=0.0856$ this is the probability of a reply to only one specific letter
P(no replies in 3 days)= $0.87^4=0.573$
P(at least 2 replies)= $1-(0.0856+0.573)=0.341$
What have i done wrong? I have spent quite some time over it and can't see where i have missed anything
Thanks
P(reply to 1st letter)= $(0.13)0.87^3$

P(reply to 2nd letter)= $(0.13)0.87^3$

P(reply to 3rd letter)= $(0.13)0.87^3$

P(reply to 4th letter)= $(0.13)0.87^3$

P(no replies)= $0.87^4$

P(at most 1 reply)= $4[(0.13)0.87^3]+0.87^4=0.573+0.342=0.915$

P(at least 2 replies)= $1-0.915=0.085$


text:
, 12.11.2019 11:31, ILOVEAARON39821

# Aline is drawn through (–7, 11) and (8, –9). the equation y – 11 = (x + 7) is written to represent the line. which equations also represent the line? check all that apply.

### Other questions on the subject: Mathematics

Mathematics, 21.06.2019 21:00, dijaflame67
Negative x over 2+3/2 is greater than five over to what’s the given in quality
Mathematics, 21.06.2019 21:30, gungamer720
Aladder that is 20ft long is leaning against the side of a building. if the angle formed between the ladder and the ground is 75 degrees how far is the bottom of the from the base of the building?
Mathematics, 21.06.2019 22:30, puffley
Tan198=asin164=? how to solve this? ?