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# BE Thesis

Senast inlagda poster:
2018-09-06
17:05
 Development of Transition Edge Sensors for Quench Localization on SRF Cavities / Ozelci, Ece The development of future Superconducting Radio Frequency (SRF) cavities for particle accelerators requires their intensive cryogenic testing [...] CERN-THESIS-2018-148 - 84 p.

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2018-09-03
10:13
 Experiment and Machine Protection from Fast Losses caused by Crab Cavities in the High Luminosity LHC / Santamaria Garcia, Andrea The High Luminosity Large Hadron Collider (HL-LHC) upgrade aims for a tenfold increase in integrated luminosity compared to the nominal Large Hadron Collider (LHC), and for operation at a leveled luminosity five times higher than the nominal LHC peak luminosity [...] CERN-THESIS-2018-142 - 193 p.

Fulltext - Full text
2018-08-22
11:49
 Simulations of an electron lens for Future Circular Colliders: noise impact and modifications of Landau damping due to different electron beam profiles / Barantani, Francesco Simulations of an electron lens in proton colliders and effects on the beam dynamics are reported [...] CERN-THESIS-2018-123 -

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2018-08-22
09:59
 Simulations Studies of Electron Lens Impact on Beam Parameters for Future Circular Colliders / Machain Rivera, Diego Ruben This report summarizes the results of simulations about electron lenses for Future Circular Colliders. [...] CERN-THESIS-2018-122 -

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2018-08-20
17:33
 Simulations and Measurements of X-Band Accelerating Structures of The CLIC Project / Bursali, Hikmet The Compact Linear Collider (CLIC) Project is 50 km long e−, e+ linear collider planned to be built in three stages with 3 TeV center-of-mass energy at its last stage [...] CERN-THESIS-2018-121 - 92 p.

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2018-07-16
20:11
 Online Transverse Beam Instability Detection in the LHC. High Throughput Real-Time Parallel Data Analysis / Soderen, Martin This thesis presents the ADT transverse instability detection system, the next generation of instability detection in the LHC at CERN, Geneva [...] CERN-THESIS-2017-401 LIU-IDA/LITH-EX-A--17/053--SE. - 125 p.

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2018-06-14
17:38
 Impact of ﬁlling scheme on beam induced RF heating in CERN LHC and HL-LHC / Giordano, Francesco At CERN, after the ﬁrst maintenance cycle (Long Shutdown 1, LS1) of the Large Hadron Collider (LHC), several sectors of the accelerator present a beam-induced heating much larger than expectations [...] CERN-THESIS-2017-393 - 104 p.

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2018-06-06
17:55
 A Generic, Modular and User Transparent Protocol Scheme for Inter-FPGA Communication using Serial Links / Vulliez, Cedric Paul CERN, the European Organization for Nuclear Research, is a European research organization that operates the largest particle physics laboratory in the world [...] CERN-THESIS-2017-390 - 117 p.

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2018-05-28
15:34
 Impedance Characterisation of the SPS Wire Scanner / Valimaa, Alpo Juhana As a beam diagnostic tool, the SPS wire scanner interacts with the proton bunches traversing the vacuum pipes of the Super Proton Synchrotron particle accelerator [...] CERN-THESIS-2018-060 - 76 p.

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2018-05-28
14:42
 Compensation of the Long-Range Beam-Beam Interaction in the LHC / Poyet, Axel In the LHC, protons collide in four interaction points in order to deliver luminosity to detectors located there [...] CERN-THESIS-2017-387 - 75.

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## Problem of the Day #137: Sircular SumsAugust 3, 2011

Posted by Albert in : potd , trackback

Three circles, $a$, $b$, and $c$ have radii $r_a = f(r_c)$, $r_b = 1$, and $r_c, (r_c < r_a \le r_b)$, respectively, and are externally tangent to each other and a line. Find: $$\sum\limits_{k=2}^{100} \frac{1}{f\left(\frac{1}{k^2}\right)}$$

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## An explicit basis for the rational higher Chow groups of abelian number fields.(English)Zbl 1388.14033

The paper under review provides a tour de force cycle-theoretic description of an explicit basis for the motivic cohomology of a point over a cyclotomic field (and by extension, of an abelian number field), paralleling A. A. Beilinson’s construction of such a basis (section 7 of his seminal work on higher regulators [J. Sov. Math. 30, 2036–2070 (1985; Zbl 0588.14013); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 24, 181–238 (1984)], albeit in terms of $$K$$-theory). Beilinson’s (and that of the authors) relies on a theorem of Borel, together with the coincidence of the Borel and Beilinson regulators (up to a factor of $$1/2$$), proven in detail by J. I. Burgos Gil [The regulators of Beilinson and Borel. Providence, RI: American Mathematical Society (AMS) (2002; Zbl 0994.19003)], and which was modelled after Beilinson’s original sketch of his ‘proof’. The ‘calculus’ of expressing the Beilinson regulator in terms of polylogarithmic currents, was established by Kerr, Lewis and Mueller-Stach [M. Kerr et al., Compos. Math. 142, No. 2, 374–396 (2006; Zbl 1123.14006)], but there is a caveat in order here. The latter (viz., an integral version of the Beilinson regulator) requires higher Chow cycles that are admissible in the sense of meeting the real negative cube and its faces properly. This required a moving lemma which was only proven over $$\mathbb{Q}$$ [M. Kerr and the reviewer, Invent. Math. 170, No. 2, 355–420 (2007; Zbl 1139.14010)]; but an integral moving lemma is now established.

### MSC:

 14C25 Algebraic cycles 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) 19E15 Algebraic cycles and motivic cohomology ($$K$$-theoretic aspects)

### Citations:

Zbl 0588.14013; Zbl 0994.19003; Zbl 1123.14006; Zbl 1139.14010
Full Text:

### References:

 [1] ; Beĭlinson, Current problems in mathematics, 181, (1984) [2] ; Beĭlinson, Applications of algebraic K-theory to algebraic geometry and number theory, Part I. Contemporary Math., 55, 35, (1986) [3] 10.1016/0001-8708(86)90081-2 · Zbl 0608.14004 [4] ; Bloch, J. Algebraic Geom., 3, 537, (1994) [5] 10.24033/asens.1269 · Zbl 0316.57026 [6] ; Borel, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4, 613, (1977) [7] ; Burgos Gil, The regulators of Beilinson and Borel. CRM Monograph Series, 15, (2002) · Zbl 0994.19003 [8] 10.1007/BF00534143 · Zbl 0697.14006 [9] 10.1007/s00222-007-0066-x · Zbl 1139.14010 [10] 10.1112/S0010437X05001867 · Zbl 1123.14006 [11] ; Levine, K-theory. Astérisque, 226, 235, (1994) [12] ; Neukirch, Beĭlinson’s conjectures on special values of L-functions. Perspectives in Math., 4, 193, (1988) [13] 10.1016/j.jnt.2009.04.009 · Zbl 1257.11064 [14] ; Rapoport, Beĭlinson’s conjectures on special values of L-functions. Perspectives in Math., 4, 169, (1988) [15] ; Zagier, Arithmetic algebraic geometry. Progress in Math., 89, 391, (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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# Math Help - Tangent to a parabola

1. ## Tangent to a parabola

Got stuck on another hw problem, can someone help please?

Show that the line with the equation 4y-3x=20 is a tangent to both the circle with equation x^2+y^2=16 and the parabola with equation y^2=15x.

I don't know which points the tangent touch the circle and the parabola at, and I'm not sure how to find it.

2. Someone pointed in out in another thread of ours that it is only necessary to show that there is a single point of intersection to prove tangency. In this case, I think the easiest approach is to take 4y-3x=20 and isolate one of the variables. Next, substitute your result into the circle and find the single point of tangency.

Repeat the same process with 4y-3x=20 and the parabola.

3. The line equation is $y=\frac{3}{4}x+5$

We have the circle $y=\pm\sqrt{16-x^{2}}$ and the parabola

$y=\pm\sqrt{15x}$

Set the line equation equal to the circle and the parabola, respectively:

$\frac{3}{4}x+5=\sqrt{16-x^{2}}$

Solving for x, we see $x=\frac{-12}{5}$

$\frac{3}{4}x+5=\sqrt{15x}$

$x=\frac{20}{3}$

Now, find the derivative(slope) of the circle and parabola at those points.

If they both equal 3/4(the slope of the line), then we're in business.

4. I've done that question now, thanks for the help.

But I've come across another similar question that doesn't give the equation of the tangent or the point of intersection, so I'm not sure what to do again:

Find an equation of the line which is tangent to both the parabola y^2=4ax and the parabola x^2=4ay.

The answer is x+y+a=0, but I've got no idea where that came from. Can I assume that the tangent touches the two parabola's at the same point?

Help would be greatly appreciated.

5. Originally Posted by mathdeity
Someone pointed in out in another thread of ours that it is only necessary to show that there is a single point of intersection to prove tangency.
Warning: That tangency property only works for circles. It will not work for functions in general. (Though I think it might for a parabola, too. I'll have to think about it. It is best not to assume this.)

-Dan

6. This post is wrong, sorry.
Warning: That tangency property only works for circles. It will not work for functions in general. (Though I think it might for a parabola, too. I'll have to think about it. It is best not to assume this.)
This property does apply to parabolas, and any other function without a point of inflection.

The part about it working for parabolas is right though

7. Find an equation of the line which is tangent to both the parabola y^2=4ax and the parabola x^2=4ay.

The answer is x+y+a=0, but I've got no idea where that came from. Can I assume that the tangent touches the two parabola's at the same point?

Help would be greatly appreciated.
The tangent does not touch the parabolas (parabolae? neither of these look right. oh well) at the same point.
What you can do is use the fact that the tangent will have the form y=mx+c. Then you can substitute this for y in both equations and find out what values m and c take if the equations have exactly one solution.


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Homework Help: Thin-Film Interference: Coating a Lens - Answers found, explanation needed!

1. Nov 8, 2011

FishStik

Thin-Film Interference: Coating a Lens -- Answers found, explanation needed!

1. The problem statement, all variables and given/known data

Boxed answers are the correct ones.

2. Relevant equations

2L=(m+1/2)(λ/n) for constructive interference (maximum reflection, bright film)
2L=(m)(λ/n) for destructive interference (minimum reflection, dark film)

Where:
L = thickness of film
m = fringe count (for m=0,1,2,3,4...)
λ = wavelength of light
n = refractive index of coating

3. The attempt at a solution

I got the correct answer (a) for Fall2008 #20 by using the equation for constructive interference, plugging in 0 for m, 1000 nm for λ, and 1.8 for n.
Now for Sp2011 #11, I took it as essentially the same question except this one is asking for minimum reflection, so I should use the equation for destructive interference. Doing that gets me (e), which is incorrect. The correct answer is (b), which is half of (e), implying that I should use the equation for constructive interference.

Am I missing a fundamental difference between the two problems besides one asking for minimum and another asking for maximum reflection? Thanks for the help.

Last edited: Nov 8, 2011
2. Nov 9, 2011

technician

Re: Thin-Film Interference: Coating a Lens -- Answers found, explanation needed!

The λ of the light in the coating is 550/n. The light must travel a distance of λ/2 in the coating to emerge from the coating out of phase with the reflected light byλ/2 and cause destructive interference. In the first example this means that the coating needs to be λ/4 thick.(106nm)
In the second example the logic is exactly the same but this time a phase change of λ/2 occurs at the junction of the coating and the visor of the helmet. A phase change of λ/2 occurs when there is reflection from a boundary when the light passes from high refractive index (1.8) into low refractive index (1.5). The wavelength of the light in the coating is 1000/n
A phase change of 0.5 of this wavelength occurs at the coating/visor junction. To MAXIMISE the reflection the 2 waves should emerge in phase therefore the path difference through the coating (2 x thickness) needs to be λ/2 giving a total phase difference of 1λ
In the first example there is no λ/2 phase difference at the junction between the coating and the lens because the refractive index of the lens is greater than the refractive index of the coating.

3. Nov 9, 2011

ehild

Re: Thin-Film Interference: Coating a Lens -- Answers found, explanation needed!

The opposite is true: There is no phase change when the light reflects from a lower-index medium, and the phase of the reflected wave changes by pi when the light enters from a lower index medium to the boundary with a higher index one.

The pi phase change corresponds to half-wavelength optical path difference.

ehild

4. Nov 9, 2011

technician

Re: Thin-Film Interference: Coating a Lens -- Answers found, explanation needed!

ehild... you are correct, I have checked my notes and got it the wrong way round!!
I think that in the first question there is a phase change of pi at both surfaces but in the second question there is only 1 phase change of pi at the air/coating surface.
I think it makes no difference to the answers but what I wrote was confusing.
Apologies to FishStik and to you.... and thanks.

5. Nov 9, 2011

ehild

Re: Thin-Film Interference: Coating a Lens -- Answers found, explanation needed!

You are welcome

ehild


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Tag Info

5

Improved code with 'grouping' of persons and hyperlinks (if needed) \documentclass{book} \usepackage{marginnote} \usepackage{xparse} \usepackage{totcount} \usepackage{morewrites} \newcounter{dummycounter} \newcounter{personposition} \newtotcounter{personcounter} \makeatletter \def\latex@starttoc#1{% \begingroup \makeatletter \@input{\jobname.#1}% ...

4

\listof... commands can be defined with tocloft package and the \newlistof command in conjunction with \addcontentsline (which is the usual suspect ;-)) Explanation: Since the counter is named defns the \newlistof command is used to define this counter (with resetting counter section), a file extension, say .dfn and the heading name of the \list of ...

2

I think this is what you're looking for. If not, please clarify, using this as a starting point: \documentclass{report} \usepackage{hyperref} \begin{document} \tableofcontents \chapter*{Dedication} \pdfbookmark{Dedication}{chap:dedication} \chapter{One} \chapter{Two} \end{document} Table of contents: Working bookmark to Dedication:

2

2

This is not the best solution, but if you want the watermark to appear only at the titlepage, you may set that page to any desired number, and then choose the watermark to appear only at that one instead of 'firstpage': \newwatermark[page=100,...]{Vorabgabe} \begin{titlepage} \setcounter{page}{100} \maketitle \thispagestyle{empty} \end{titlepage} ...

1

You should either use the \maketitle command, or uses the titlepage environment, but not both at the same times. With \maketitle \documentclass[12pt]{article} \usepackage[utf8]{inputenc} \usepackage{xcolor} \usepackage[printwatermark]{xwatermark} \newwatermark[firstpage,color=red!50,angle=45,scale=3,xpos=0,ypos=0]{Vorabgabe} \title{XXXXX\\ XXX } ...

1

Use \caption[Block Diagram of Systems]{Block diagram of systems} It is a pointless requirement not worth spending coding time on spending time on:-) and doing it automatically is tricky requiring lists of words such as of to skip, and skipping over math mode or anything else that may come in a caption. \caption allows you to specify the LOF text ...

1

The package makeidx (the most common indexing package for LaTeX) has a way to format the pages of a particular index entry. Namely, if you write \index{bulldog|textbf} then the page number for this entry will be typeset in bold face. You can use this in your case as follows: Define a new "style command" that takes one argument (the page number) and ...

1

You could switch to the KOMA-classes and patch \addsec. This would also remove the need for the \addcontentsline. But imho the numbering is curious. It looks as if the typesetter made an error and forget a number. \documentclass{scrartcl} \usepackage{etoolbox} \pretocmd\addsec{\refstepcounter{section}}{}{} \begin{document} \tableofcontents \section{First ...

1

Do not use \include but \input \documentclass{beamer} \author[N. Surname]{Name Surname} \begin{filecontents}{dummyslide} \subsection{dummy1} \frame{Dummyslide} \end{filecontents} \begin{document} \frame{\titlepage} \begin{frame}{Outline} \tableofcontents \end{frame} \section{sec1} \input{dummyslide} \end{document}

1

The break of the ToC entries depend on the right margin. tocloft allows you to change this (from the default 2.55em) using \cftsetrmarg: \documentclass[12pt]{article} \usepackage{tocloft} \cftsetrmarg{7em}% Default is 2.55em \begin{document} \tableofcontents \section{long section title that in the TOC wraps to the next line at a point too far} ...

Only top voted, non community-wiki answers of a minimum length are eligible


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# Y-homeomorphism

It can be constructed by sliding a Möbius band included on the surface around an essential 1-sided closed curve until the original position; thus it is necessary that the surfaces have genus greater than one. The projective plane ${\mathbb RP}^2$ has no y-homeomorphism.


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## Stream: new members

### Topic: Non-type theorems

#### Bjørn Kjos-Hanssen (Nov 30 2020 at 01:24):

I have a result of this form: M(x) is a metric space iff x<1. Here x is some parameter that the space depends on.

I have proved using instance that, under the assumption x<1, I have a metric_space but is there a natural way to prove that something is not a metric space?

Of course, I can just prove that the relevant axiom fails, e.g., triangle inequality, but I wonder if I can then conclude "it's not (or cannot be made into) a metric space"?

#### Bryan Gin-ge Chen (Nov 30 2020 at 01:32):

\not metric_space X is short for metric_space X -> false, i.e. that an instance of metric_space X leads to a contradiction.

#### Reid Barton (Nov 30 2020 at 01:55):

It's not very convenient to state this because of how the data and properties of a metric space are bundled together, but you can write something like "there does not exist a metric_space whose distance function equals (blah)".

#### Reid Barton (Nov 30 2020 at 01:55):

If you're just going to prove that the triangle inequality fails directly then it's probably more sensible to just state that instead.

#### Kevin Buzzard (Nov 30 2020 at 02:05):

Note that any type can be made into a metric space by just giving it the discrete metric, so metric_space X -> false is probably not what you want.

#### Bjørn Kjos-Hanssen (Nov 30 2020 at 02:14):

@Kevin Buzzard yeah, I didn't mean it literally :upside_down:
@Reid Barton that's exactly what I mean, "there does not exist a metric_space with distance function (blah)". Imagine that for some values of x the triangle inequality fails, for other values the symmetry condition fails...

Last updated: May 14 2021 at 13:24 UTC


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# What is reductive group intuitively?

I am studying Geometric invariant theory and wonder how I should understand linearly reductive algebraic group. We say that an affine algebraic group $G$ is linearly reductive if all finite dimensional $G$-modules are semi-simple.

I am not sure if linearly reductive groups are the same as reductive groups, which are defined as algebraic groups $G$ over algebraically closed field such that the unipotent radical of $G$ is trivial. But this definition is still beyond my intuition.

Are there any good way to understand (linearly) reductive groups? It would especially be nice if reductive (Lie) groups can be characterized in geometry.

-

## 1 Answer

"Linearly reductive" and "reductive" are equivalent when the base field is of characteristic zero, but for prime characteristic they are different -- in fact, in prime characteristic, the only connected linearly reductive groups are algebraic tori, though for example $\operatorname{GL}_n$ is reductive.

There is a nice characterization of reductive groups over $\mathbb{C}$: they are precisely the complexifications of compact connected Lie groups. More precisely: every compact connected Lie group is actually a real algebraic group, and every smooth homomorphism of compact Lie groups is algebraic. We can then look at the points of this group over $\mathbb{C}$, and thereby obtain a complex algebraic group. For example, the complexification of $U(n)$ is $\operatorname{GL}_n(\mathbb{C})$ -- this can be seen at the level of Lie algebras from $\mathfrak{gl}_n(\mathbb{C}) = \mathfrak{u}(n) \oplus i\mathfrak{u}(n)$. It turns out that in fact every complex reductive group arises in this way from a maximal compact subgroup, and this gives an equivalence between the category of compact connected Lie groups (with smooth homomorphisms) and the category of complex reductive groups (with algebraic homomorphisms).

-
Your answer makes my understanding much clearer. Thanks! –  M. K. Oct 21 '12 at 16:12
@Brad I can't seem to find a source for the statement that every complex reductive algebraic group is the complexification of a compact Lie group. Do you happen to know one? –  Victor Jun 17 '13 at 19:27
@Victor See, for example, "The Structure of Complex Lie Groups" by Dong Hoon Lee: tinyurl.com/lkqlfoy –  Brad Jun 19 '13 at 4:58


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Vertically align a list to the bottom of the page

When a list (in the example below, itemize, but I'm having the same trouble with lists defined using enumitem, and the exe environment of package gb4e) occurs at the bottom of the page, the last item is not aligned to the bottom. There is some vertical space between the last item and the bottom of the page. I would like to get rid of it.

\documentclass{book}
\begin{document}
dummy page 1 (to easily see the problem in the double page view)
\newpage
top of page 2
\vfill
bottom of page 2
\newpage
top of page 3
\vfill
\begin{itemize}
\item item 1
\item item 2
\item item 3 (I'd like this to be aligned with the last line on the facing
page)
\end{itemize}
\end{document}

This vertical space (\topsep plus \partopsep) of course makes sense when a paragraph follows the list on the same page, so just setting \topsep and \partopsep to 0pt is not a good solution. Plus, these parameters control the spacing before the list as well.

I was able to manually solve this using enumitem's key after, but I would prefer an automatic solution. I guess such a solution would also inflence page breaks, which is a good thing.

\begin{itemize}[after=\vspace*{-\topsep}\vspace{-\partopsep}]
\item item 1
\item item 2
\item item 3 (I'd like this to be aligned with the last line on the facing
page)
\end{itemize}

CLARIFICATION. I'd like to have a solution which would test whether the list occurs at the bottom of the page. If so, the vertical space after it should be removed. Otherwise, the space should stay.

• Would defining a new environment that appends the negative vspace count as your automatic solution? – Charles Stewart Sep 23 '15 at 13:07
• If it does that only at the bottom of the page, sure! – Sašo Živanović Sep 23 '15 at 13:19

It's not elegant, but it works.

\documentclass{book}
\usepackage{showframe}
\begin{document}
top of page
\vfill
\noindent\begin{minipage}{\textwidth}
\begin{itemize}
\item item 1
\item item 2
\item item 3 (I'd like this to be aligned with the last line on the facing
page)
\end{itemize}
\end{minipage}
\end{document}

Aha! I found the culprit! One can redefine \enditemize to do this automatically.

\documentclass{book}
\usepackage{showframe}
\begin{document}
top of page
\vfill
\begin{itemize}
\item item 1
\item item 2
\item item 3 (I'd like this to be aligned with the last line on the facing
page)
\makeatletter
\makeatother
\end{itemize}
\end{document}

You could place the itemize environment inside a figure environment -- a table environment works too... -- and set [b!] as the location placement specifier. Then, use \unskip after \end{enumerate} and before \end{figure} to eliminate the space below the enumerate environment. No need for a minipage environment or \vfill instructions.

Note that as long as no \caption directive is issued, the reader will never know that a figure environment is being employed.

\documentclass{book}
\usepackage{showframe}
\begin{document}
top of page
\begin{figure}[b!] % <-- the "b!" option is crucial
\begin{itemize}
\item item 1
\item item 2
\item item 3 (I'd like this to be aligned with the last line on the facing
page)
\end{itemize}\unskip
\end{figure}
\clearpage % advance to next page
\end{document}


text:
Can you tile an equilateral triangular tile with a triple N set of triominos

1. May 26, 2012

The_Doctor

1. The problem statement, all variables and given/known data
A tri-omino is an equilateral triangular tile with lines dividing the triangular face into four equilateral triangles decorated with blanks or pips. There are (N+3)(N+2)(N+1)/6 tri-ominos in a Triple N set. Is it possible to tile a triangular region without gaps or overlaps using a complete Triple N set of tri-ominos if N > 1?

2. Relevant equations
Pell's equation

3. The attempt at a solution
Given any number of triominoes and an equilateral triangular tile of any size, how many triominoes are needed to tile that tile? Well all equilateral triangles are similar, so let us say each triomino has a side length of n. This means the tile will have a side length of kn, due to similarity where k is arbitrary. Because we can only use whole triominoes, not fractions of them, k must be an integer. The area of each triomino is (√3/4)*n2 and the area of the tile will be (√3/4)*(kn)2. To work out how many triominoes are needed to tile the tile, we divide the tile's area by the area of each triomino. Once divided we get k^2. Thus k^2 triominoes are needed to tile an equilateral triangular tile of length kn. So we need to find out when (N+3)(N+2)(N+1)/6 is a perfect square.

(N+1)(N+2)(N+3)/6 must be in the form $\frac{x^22y^23z^2}{6}$. Here is the proof: N+1, N+2 and N+3 are consecutive numbers, and thus one and only one will be divisible by 3. Secondly, because they are consecutive, N+1, N+2 and N+3 will not share any prime factors except for 2, when N+1 and N+3 is even. Because there is a 6 as the denominator, which is 2*3, (N+1)(N+2)(N+3) must have an odd power of 2 when represented in prime factors. Since only a maximum of 2 of the 3 consecutive numbers will be even and thus have 2 as its prime factors, only 1 of the three consecutive numbers can have an odd power of 2 in its prime factors. And because none of three consecutive numbers share prime factors other than 2, we can say that (N+1)(N+2)(N+3)/6 must be in the form $\frac{x^22y^23z^2}{6}$ and can only be in that form in order for (N+1)(N+2)(N+3)/6 to be a perfect square.

Now we don't know which of the three consecutive numbers, x^2, 2y^2 and 3z^2 will equal. So $x^2-3z^2= \pm 1,\pm 2$. However,
$0^2\equiv 0\pmod{3} \\ 1^2\equiv 1\pmod{3} \\ 2^2\equiv 1\pmod{3}$
Therefore, $x^2-3z^2=1,-2$

Let's say that x^2=N+2 and 3z^2=N+1. Then x^2-3z^2=1. This gives us a Diophantine equation; specifically Pell's equation. The minimal solution to this is x=7, z=4. The solutions to this equation must also fit this equation: x^2-2y^2=-1, a negative Pell equation. Long story short, x=7 works and gives y=5. So we have 3*4^2*7^2*2*5^2/6=(4*7*5)^2

I quickly typed up a program to brute-force answers, and it only came up with N=1,47. Are these the only solutions? And how would you go about proving it?

But my method of finding the solutions is pretty bad. Is there a more logical way of finding out if there are possibilities? E.g. I just guessed if x^2=N+2, and it gave me the right answers, but is there a way of deducing it logically?

2. May 27, 2012

Joffan

... only if you ignore handedness. But that's part of the givens, so we won't attack that too fiercely...

N=1 is interesting too - the number of tiles is good but the task of aligning the numbered edges fails.

Similar figure areas scale as the square of their linear dimensions - but you got there anyway.

Nice. You should perhaps also note that at most one of N+1, N+2, N+3 is a perfect square to get your result. You also know that only z can possibly be divisible by 3, incidentally - not x or y.

You can tie this down a bit more by considering the numbers mod 6. This still gives three possible orderings for the components, and since you already have an example of each case (N=0,1,47) it seems unlikely that much further elimination can be done. My brute force testing of squares agrees with your brute force, up to N ~ 2^31, incidentally.

So, anyway... you have a candidate set that has the right number of tiles to make a larger triangle... but does that answer the question?

3. May 28, 2012

The_Doctor

Pardon my ignorance, but what is handedness?
Hmm, yeah, I didn't consider using mod 6. It certainly does seem unlikely that further elimination can be done. There are 2 things I would like to ask though, which are: can you simultaneously solve Diophantine equations? For if you could, you could solve the 3 pairs of Diophantine equations.

On the other hand, is it necessary to use Diophantine equation? I can't see any other way of solving this question, but maybe there is. Can you see any other way of solving it?

4. May 28, 2012

Joffan

A tile with three dissimilar numbers on it has two different forms; for example 0-1-2 and 0-2-1 are distinct. The formula given implies that only one of these is present in the set.

I think any Diophantine equation with three variables in it is tough. Unfortunately I don't really know whether what you suggest is feasible. No simpler way of approaching the problem occurs to me for now, and the presence of the N=47 solution does suggest that something like this is required.

There is one further step I would take, but it is ambiguous in the question as to whether the matching edges rule is to be used when forming the larger figure. If it is used, N=47 is not a viable solution - do you see why?

5. May 29, 2012

The_Doctor

Hmm, yeah. I understand what you mean. The formula isn't concerned with order.
I think if you approach the problem algebraically, you'll end up having to use Diophantine equations, because there is a solution, and there could be more. Although the question only asks if it is possible, so maybe there is no way of proving 47 is the only answer, or maybe there are infinitely many solutions but they are really large.

And also, this question just came from some practice questions for this very hard maths competition. But I'm in high school (secondary level of education), and this competition is only meant for students in high school, so I'm not sure if they'd expect us to know Diophantine equations and how to solve them.

This was actually pretty interesting, as interesting if not more than the original question. Basically I thought of it like this: if N=47, you have 19600 tri-ominoes. Each tri-omino has 3 equilateral triangles with numbers, so you have a total of 19600*3 numbers. So we know the tile can be tiled with a triple 47 set, the question is can we arrange 19600*3 numbers on the outer triangles on each tri-omino in the tile, such that each smaller triangle of each tri-omino that has an adjacent side with another triangle have the same number. Basically, I drew up a diagram of some tri-omnioes, and if we concentrate on each point of each tri-omino, we notice that each point that isn't on the side of the tile has 6 smaller triangles of 6 tri-ominoes around it, which share sides and create a hexagon around the point. Similarly, on the side, each side point has 3 smaller triangles of 3 tri-omnioes. There will also be 3 corner points of the tile which don't share any sides.

There are k+1 points on each side of the tile. If N=47, then √(48*49*50/3)=k=140. Using the formula for triangular numbers, you get 141*142/2=10011 points. 3 of these will be corner points. On each side, there are (k+1-2) non-corner points. Thus in total, there are (140+1-2)*3=417 side points. The rest must be "centre points", which is 9591. Around each "centre point", there are 6 adjacent triangles of 6 tri-ominoes, and 3 around each side point. To double check we are correct, 9591*6+417*3+3=19600*3. Each number between 0 and 47 will appear an equally often in the 19600*3 numbers. So every number between 0 and 47 will appear 19600*3/48=1225 times. These 1225 numbers of each number need to be placed around each point so each point shares numbers, however 1225 isn't divisible by 3, thus you will have leftovers when placing them around the side and "centre points", and there are only 3 corner points, so it will be impossible to make sure each tri-omino has matching sides.

Hopefully I'm right :D.

6. May 29, 2012

Joffan

Your matching edges argument works fine. I didn't get into the actual numbers, just used a mod-3 argument once I noticed that all non-corner junctions required 3 or 6 copies of the same number gathered together. Combining this with the total copies of each number, which is #tiles*3/#numbers = (N+2)(N+3)/2, this puts a mod-3 restriction on N for N>2 (when we have used up the corners), which N=47 fails.

7. May 30, 2012

The_Doctor

Haha yeah. Much simpler.

Well thanks anyway for all your help, and the extra question was very interesting as well. If you do find a way of solving both Diophantine equations or a method of solving the problem without Diophantine equations, be sure to post!


text:
Time：2019-11-3

# Preface

Recently, I wrote a hybrid app project in the company. The pages are basically completed in H5 and embedded in the native WebView. I found a problem. Under iPhone 6, the status bar of Apple’s mobile phone will block the page, causing the page to move down and the style to be disordered. Finally, I found some solutions on the Internet and added a meta tag to solve the problem. Today, I’d like to summarize the common meta tags and some tips for mobile development.

1. viewport

This is a necessary label for mobile page development, which is used to adjust the layout viewport to be consistent with the visual viewport, and prohibit page zooming, etc.

1. apple-mobile-web-app-capable

apple-mobile-web-app-capableIs to set whether the web app runs in full screen mode.

Syntax:

Explain:

If content is set to yes, the web application will run in full screen mode, otherwise, it will not. The default value of content is no, indicating normal display. If you choose to run in full screen mode, the default Apple toolbar and menu bar are removed.

The problem I encountered at the beginning of this article was solved by setting the meta tag.

1. Set the color of the top status bar

Explain:

The premise for this tag to work is that the full screen mode must be turned on to run webapp in advance, that is, the meta tag of the second item must be specified synchronously, otherwise this tag will not work.

If content is set to default, the status bar will display normally. If set to blank, the status bar will have a black background. If set to blank translucent, the status bar displays black translucent. If it is set to default or blank, the page is displayed below the status bar, that is, the status bar occupies the upper part, and the page occupies the lower part, without blocking each other or being blocked. If set to blank transparent, the page will fill the screen, with the top of the page covered by the status bar (it will cover the height of the page 20px, while the retina screen of iPhone 4 and itouch4 is 40px). The default is default.

1. Webapp added to the title after the main screen (new in IOS 6)

1. Set cache

Mobile pages are usually cached after the first load, and then each refresh uses the cache instead of resending the request to the server. If you do not want to use cache, you can set no cache.

1. format-detection

Format detection enables or disables automatic identification of phone numbers in the page.

Syntax:

Explain:

By default, the device automatically recognizes any string that might be a phone number. Set phone = no to disable this feature.

1. HTML5 calls the dialing function of Android or IOS

HTML5 provides a label for calling dial automatically. Just add Tel: to the a label’s href.

Call the mobile phone directly as follows:

Click to call 1567776767

PS: if it fails in this case, you can add a meta tag to the page header, and the content is set to yes.

1. The input box under iPhone and iPad appears inner shadow by default.
Element{
-webkit-appearance: none;
}
1. The absolute positioning element of the sliding page on the mobile terminal shakes

I found some solutions to this problem online for reference only.

• Set the height of the body to 100%
body,html{
widht:100%;
height:100%;
}

If there are other special effects for the finished page in the project, setting this property directly may affect other functions of the page.

If you use this method, the local debugging effect is not good, it is recommended not to use.

• Add a transform attribute to a fixed positioned element

transform:translateZ(0);
perhaps
transform:translate3d(0,0,0);

• Nesting a box in the outer layer

Add one more layer of box, fix the outer layer for fixed positioning, and set the inner layer for absolute positioning;

...
1. The input box cursor under iPhone is too long

The input input input box cursor is too long under iPhone, and Android display is normal.

Method:

Lower the line height style value of the input tag.

1. Under IOS, the page slides and gets stuck, which is not smooth

Set a CSS style on the element where the content scrolls to achieve inertial scrolling and elastic effect.

{
-webkit-overflow-scrolling: touch;
}

-webkit-overflow-scrollingThe attribute controls whether the element uses the roll back effect on the mobile device. It has two values:

auto: with normal scrolling, when the fingers are removed from the touch screen, the scrolling will stop immediately.

touch:
With a springback scroll, when the finger is removed from the touch screen, the content continues to scroll for a period of time. The speed and duration of rolling are directly proportional to the intensity of rolling gestures. A new stack context is also created.

1. Fixed positioning elements at the top or bottom of the page block part of the content of the page.

Method 1:

Add to the outermost divpadding-bottom, the value is the fixed positioning element height;

Method two:

Using pseudo element, add pseudo element after to the outermost div, and set the height as fixed positioning element height.

.wrapper::after{
content: '';
Height: 'fixed positioning element height';
}
1. Prohibit copying and selecting text
Element {
-webkit-user-select: none;
-moz-user-select: none;
-khtml-user-select: none;
user-select: none;
}
1. The input keyboard events Keyup, Keydown and keypress in IOS are not well supported

When using input search to do fuzzy search, input keywords in the keyboard, query through Ajax background, then return data, and then mark the returned data with keywords red. Using input to monitor keyboard Keyup events is OK in Android mobile browser, but it turns red slowly in IOS mobile browser. After inputting with input method, the Keyup event is not immediately corresponding. Only after deleting can the Keyup event be corresponding!

terms of settlement:

You can use the oninput event of HTML5 to replace Keyup

document.getElementById('test').addEventListener('input', function(e){
var value = e.target.value
....
})

Then achieve the effect similar to Keyup!

1. Some JavaScript code under WebView is not executed, such as alert().

terms of settlement:

WebView is just a carrier, and the rendering of all kinds of content needs to be implemented with webviewchromeclient, so set a default base class webchromeclient.

PS: in this part, you need to set up a base class webchromeclient with the help of native development. Code:

WebView.setWebChromeClient()

1. 300 ms delay for mobile click

300ms is acceptable, but we have to solve the problems caused by 300ms. 300ms leads to poor user experience. To solve this problem, we usually use tap event to replace click event on the mobile terminal.

Two JS are recommended, one isfastclickOne istap.js

For details about the click delay processing scheme of mobile terminal, please refer to: click delay processing scheme of mobile terminal

1. Mobile click through

The cases are as follows:

Point penetration event test
Baidu

Div is the mask of absolute location, and Z-index is higher than a. The a tag is a link in the page. We bind the dip event to the div:

$('#haorooms').on('tap',function(){$('#haorooms').hide()
})

When we click the mask, the div disappears normally, but when we click the mask on the a tag, we find that the a link is triggered, which is the so-called point penetration event.

Reason:

Touchstart is earlier than touchend is earlier than click That is to say, the trigger of click is delayed. This time is about 300ms. That is to say, after tap is triggered, the mask is hidden. At this time, click has not been triggered. After 300ms, because the mask is hidden, our click is triggered to the following a link.

terms of settlement:

1. Try to replace the click event with the touch event. For example, use the touchend event (recommended).
2. With fastclick, see GitHub warehouse above for details.

3. Use preventdefault to block a tag’s click.

4. Delay a certain time (300ms) + to process the event (not recommended).

5. Generally, the above can be solved. If not, click event will be replaced.

The touchend event is described as follows:

\$("#haorooms").on("touchend", function (event) {
event.preventDefault()

})
1. In IOS, when Chinese input method is used to input English, a space of one sixth may appear between letters

Can be removed by regular

this.value = this.value.replace(/\u2006/g, '')

1. Solve the problem of video label video auto full screen playback in IOS

Add properties to the video tag:

PS: if it is embedded in WebView, the following support codes need to be added by the native development partners:

webView.allowsInlineMediaPlayback = YES;

1. Mobile terminal click link to send email
[email protected]

Click and send an email directly to [email protected] with the subject of testobject.

PS: if it fails in this case, you can add a meta tag in the page header, and the content is set to yes.

1. Rolling penetration at mobile end

Description:

Scrolling on an open pop-up window or mask layer will affect the scrolling of the body element in the lower layer The experience was very bad.

terms of settlement:

The general idea is to get the scrolltop of HTML when opening the pop-up or mask layer, change the body to fixed location, and the top value is a negative scrolltop value When closing the pop-up box, remove the fixed positioning. Restore the scrolltop value.

1. Mobile terminal layout

This is basically a plan that we need to determine before we do mobile development. I summarize it as follows:

Classic REM layout and rookie VW layout

Of course, there are common ones such as flex.

However, it needs to be said that the author of Taobao flexible.js layout has recommended that we choose VW layout.

In this part, you can refer to the relevant information on the Internet by yourself, and I will not do much elaboration here.

## Posterior language

Some of the front-end knowledge points I usually write will be put under my GitHub warehouse. Welcome to spray lightly, ha ha.

## How to search files or directories under CentOS

Search for files or directories: The search for files is great! Because we often need to know where that file is, let’s talk about how to search it! There are also quite excellent ones under Linux Search system! Usually find is not very common! Because the speed is slow, but also very hard disk! Usually […]


text:
EN FR
• Legal notice
• Accessibility - non conforme

## Section: New Results

### Lifting AutoEncoders: Unsupervised Learning of a Fully-Disentangled 3D Morphable Model Using Deep Non-Rigid Structure From Motion

Participants: Mihir Sahasrabudhe (Collaboration: Eqward Bartrum, Riza Alp Guler, Dimitris Samaras and Iasonas Kokkinos, Stony Brook, UCL and Ariel AI)

We introduced, in [49], Lifting Autoencoders, a generative 3D surface-based model of object categories. We bring together ideas from non-rigid structure from motion, image formation, and morphable models to learn a controllable, geometric model of 3D categories in an entirely unsupervised manner from an unstructured set of images. We exploit the 3D geometric nature of our model and use normal information to disentangle appearance into illumination, shading, and albedo. We further use weak supervision to disentangle the non-rigid shape variability of human faces into identity and expression. We combine the 3D representation with a differentiable renderer to generate RGB images and append an adversarially trained refinement network to obtain sharp, photorealistic image reconstruction results. The learned generative model can be controlled in terms of interpretable geometry and appearance factors, allowing us to perform photorealistic image manipulation of identity, expression, 3D pose, and illumination properties.


text:
# Coupling LES to a wall-stress model

The issue of how to couple a wall-stress model to an LES code is code-specific, so the following is meant primarily as an illustration. For purposes of illustration, we consider a finite-volume code with an unstructured grid in a complex geometry. Specifically, we consider a single wall-face with the centroid located at $$\vec{x}_w$$ and with a normal vector $$\vec{n}$$ that is pointing towards the fluid.

The key modeling parameter in a wall-stress model is the thickness $$h_{\rm wm}$$ over which it should be applied. In most circumstances, $$h_{\rm wm}$$ should be chosen as about 10% of the local boundary layer thickness $$\delta$$. The fact that $$h_{\rm wm}$$ depends on the solution is of course not ideal, but is no different from the more general fact that the grid requirements in LES also depend on the solution. Nevertheless, having chosen $$h_{\rm wm}$$, we will solve the wall-stress model between the wall location $$\vec{x}_w$$ and the location $$\vec{x}_{\rm wm-top} = \vec{x}_w + h_{\rm wm} \, \vec{n}$$. The boundary condition for the wall-stress model at $$\vec{x}_{\rm wm-top}$$ should be taken from the LES. In most circumstances, interpolation from the LES cells is necessary. For unstructured grids, it will probably make sense to find the cells involved in the interpolation stencil during a pre-processing step, and then to store those cell indices for each wall face. The real challenge with unstructured grids is that some or all of those cells may reside on a different MPI process. There are basically 2 different solutions to this: (i) to build parallel communicators during a pre-processing step; or (ii) to modify the domain decomposition (ParMetis or similar) to ensure that the relevant cells are on the same MPI process. It may be tempting to avoid this issue by taking the closest point possible on the same MPI process as $$\vec{x}_w$$, but this is a bad idea — it makes the whole WMLES model dependent on the domain decomposition, and one will get different results depending on the number of MPI processes. We (JL, in early, unpublished work) actually tested this, and found differences even in average quantities!

In any case, we now assume that we have interpolated the velocity vector $$\vec{u}$$ to the $$\vec{x}_{\rm wm-top}$$ location (let’s call this $$\vec{u}_{\rm wm-top}$$). Most wall-stress models assume flow parallel to the wall, and we therefore must decompose the velocity vector in a coordinate system locally aligned with the wall. We take $$\vec{u}_{\rm wm-top} = \vec{u}_{{\rm wm-top}, \parallel} + \vec{u}_{{\rm wm-top}, \perp}$$ where $$\vec{u}_{{\rm wm-top}, \perp} = \left( \vec{u}_{\rm wm-top} \cdot \vec{n} \right) \vec{n}$$.

The magnitude of the wall-parallel velocity $$\left| \vec{u}_{{\rm wm-top}, \parallel} \right|$$ is then fed to the wall-stress model to be used as a Dirichlet boundary condition at the top of the wall-modeled layer. The wall-stress model will then return the magnitude of the wall-stress $$\left| \vec{\tau}_{w, \parallel} \right|$$.

The final step is to assemble the full wall-stress vector as $$\vec{\tau}_w = \vec{\tau}_{w, \parallel} + \vec{\tau}_{w, \perp}$$. Most wall-stress models assume parallel and uni-directional flow, and thus we generally take

\label{eqn:tauw_u_relation} \tag{1}
\vec{\tau}_{w, \parallel} = – \, \vec{u}_{{\rm wm-top}, \parallel} \,
\frac{ \left| \vec{\tau}_{w, \parallel} \right| }{ \left| \vec{u}_{{\rm wm-top}, \parallel} \right| }

This may be inaccurate in situations with significant and systematic (i.e., not just instantaneous) 3D (“Ekman”) effects in the inner part of the boundary layer; however, the error of this approximation has not been studied in isolation from many other errors, and thus it remains unknown whether it is an issue or not. Note, for example, that Bermejo-Moreno et al (2014) found good agreement with experiments in their WMLES of duct flow (where the corner flow has 3D effects) despite using this assumed alignment of the wall-stress and the velocity.

Finally, since most wall-stress models assume wall-parallel flow they say nothing about the wall-normal stress $$\vec{\tau}_{w, \perp}$$. This can then be modeled using a standard finite-difference operation from the first off-wall cell (just like in a regular LES code). Alternatively, since this wall-normal stress is often very small, it can probably be set to zero without any significant errors. In our own implementations, we have always used a simple finite-difference from the first off-wall cell, exactly as in the baseline LES code.

Having assembled the full wall-stress vector $$\vec{\tau}_w$$, one then assigns this at the wall-face when computing the flux in the finite-volume method. In a finite-difference method, one would probably use the wall-stress vector to replace the viscous stress term before taking the divergence.

In compressible solvers, one additionally assigns the heat flux $$q_w$$ to the wall-face (for isothermal boundaries) or the wall temperature $$T_w$$ (if the heat flux is specified).

### Computational cost

The computational cost of the coupling procedure here is trivial, but the cost of solving the wall-stress model itself can be significant, especially if it induces parallel load imbalance. A good approach to reducing the load imbalance problem is to modify the domain decomposition such that it aims for domains that have equal numbers of both cells and wall-faces that require the solution of a wall-stress model (dual-constraint decomposition). This can often be done for unstructured codes.

An additional way to reduce the computational cost is to solve the wall-stress model only once per time step (e.g., in a Runge-Kutta method or in an iterative solution of an implicit solver). This can be done by recognizing that the whole wall-modeling philosophy necessarily implies that the modeled $$\vec{\tau}_w$$ will lack any high-frequency oscillations, and thus can never approximate the instantaneous $$\vec{\tau}_w$$ — the best we can hope for is that it matches the average $$\vec{\tau}_w$$, and that it matches those frequencies in $$\vec{\tau}_w$$ that correspond to time-scales in the log-layer. Given this, we can interpret Eqn. (\ref{eqn:tauw_u_relation}) as taking the instantaneous $$\vec{u}_{{\rm wm-top}, \parallel}$$ and multiplying it by a “transfer-function” $$\left| \vec{\tau}_{w, \parallel} \right| / \left| \vec{u}_{{\rm wm-top}, \parallel} \right|$$ that scales the magnitude of the vector. We can then approximate this “transfer function” by computing it infrequently and storing it for re-use in subsequent RK substeps or iterations. In other words, we don’t assume that the $$\vec{\tau}_w$$ stays constant, but that the “transfer function” does.


text: The subfloat command has a body, for the content, being most commonly a figure/table plus a label. Ping An (Leon Leong) is an autistic teenager who gains recognition for being a badminton prodigy. The package simplifies the positioning, captioning (I wonder if that’s a word) and labeling of small “sub” figures and tables within a single figure or table environment. to set the figure width. I have seen the cross-like arrangement of figures before. Or you may make use of the rule command that by default draws a black line of a certain length and thickness. delayed shipping sub-zero 36" side by side refrigerator flawless stainless doors $3,995.00 Sub-Zero 700TC 27" REFRIGERATOR/FREEZER Custom Panel Left Hinge Private listing English; Русский; 한국어 Since it’s a floating environment, LaTeX will automatically add a line-break when the second table reaches into the margin. A remake of Thai youth sports series Project S The Series: Side by Side. Chinese dramas with 12 episodes and less than 12eps!. The formatting of the document is two columns, and I want to span a double float figure (two subfigures) across the two columns, using the subfigure package. just sub.sound. With the right setup, you'll enjoy every bit of bass your music has to offer. The documentary investigates the history, process and workflow of both digital and photochemical film creation. การใส่รูปจำนวนมากใน Latex โดยใช้ subfig | WJ's Sandbox, […] http://texblog.org/2011/05/24/placing-figures-side-by-side-subfig/ […]. 4a, whereas the second line will only produce the sub-index, e.g. For me, its pilot episode is the best Project S episode so far. Just place your mouse inside the code box and you’ll see an option box appear. Great work. Maybe one of the issues is that in my paper I would need this figure on the bottom of the first page (which is why I used the bp placer and the stfloats package), and it keeps either overlapping on the second column, or moving to the next page, overlapping with both. Xiao Na (Yang Chaoyue) is a bright and cheery young woman who helps out at her grandpa's badminton court for the summer. Very irritating & forced me to switch back subfigure which works perfect, at least in this aspect. ft. Capacity, Wi-Fi Enabled, 6 Glass Shelves, Internal Water Dispenser, Crisper Drawer, Ice Maker, Automatic Defrost, Water-Filtration System, Adjustable Shelves, Star-K Certified , Advanced Temperature Control, Dual Refrigeration, Air Purification System in Stainless Steel with Professional Handles . What’s the purpose of “lofdepth” and “lotdepth” options? Placing figures/tables side-by-side with subfigure, http://texblog.org/2011/05/24/placing-figures-side-by-side-subfig/, http://texblog.files.wordpress.com/2011/05/subfig-sample-code-output.pdf, Multi-column and multi-row cells in LaTeX tables, Control the width of table columns (tabular) in LaTeX. Ping An (Leon Leong) is an autistic teenager who gains recognition for being a badminton prodigy. neben jdm. May it be an issue with my latex version (latex –version says “This is pdfTeX, Version 3.1415926-2.3-1.40.12 (TeX Live 2011)”, I’m on a mac)? These counter-depth refrigerators also fit into any kitchen design, in classic stainless steel or panel-ready models that blend into your cabinetry. Yep, I guess you gave sufficient detail, but a minimal example would be even better :-). Zihao (Zhu Zijie) is his younger brother and a fellow badminton player. (ChineseDrama.info) Get the best deals on Sub-Zero Side-by-Side Door Refrigerators when you shop the largest online selection at eBay.com. You may find some of the answers given here useful. Side by Side ist ein Jazz-Album, das unter der nominellen Leitung von Duke Ellington bzw. We create custom sub enclosures that fit the speakers you have or the new speakers you buy. (SUB INDO) NCT DREAM SBS RADIO RIDIN Era/ Turn On subtitel / NCT DREAM di SBS Radio Full sub indo Johnny Hodges in verschiedenen Besetzungen am 14. Anyway, thank you again for taking the time, Tom. To install an ice bin on side-by-side Sub-Zero models: Look inside the freezer to find the white metal plate the bucket rests on. She gets close to both brothers and becomes attracted to Zihao. 4:02 PREVIEW Moor. Side by side into eternity - Side by side towards eternity: Letzter Beitrag: 26 Mär. I assume it works with most browsers. I did some more thinking and came to the conclusion that there is a logical reason why this is not allowed/ possible: the mandatory content of the first page in a two column IEEE journal paper. 46:08. In order to simulate figures for testing purposes, you may either use the draft option of the documentclass command which lets you load existing or non-existing figure files and draws an empty box as placeholder. It will be just difficult to top that. Let’s discuss. By Euseng Seto. You'll get to appreciate and love your family more after watching Side By Side. your result PDF (http://texblog.files.wordpress.com/2011/05/subfig-sample-code-output.pdf) throws a Permission Denied. I just realized, that the tabs are just ignored in the comments. 1. 2019-05-31T22:00:37Z Comment by mooshi. A touching coming-of-age story about family is told through the eyes of an autistic teen and his younger brother. We sell new and pre-owned Motorcycles, Side X Sides, ATVs and PWCs from Honda, Yamaha, Sea doo, Can-am, Spyder, KTM, Kawasaki, Suzuki and Roxor with excellent financing and pricing options. However, their journey is not as smooth-sailing as they'd hope and the two brothers are pushed to a difficult crossroad. Thanks, Tom. 09, 00:35: Soll ein Motto sein.. Welche der Versionen wäre grammatikalisch besser, oder gehen beide? Sub-Zero side-by-side refrigerators offer you easy access to both fresh and frozen foods – no bending over! In case you prefer png and/or eps figures, use the pdf, png, eps […]. well, some more than others, I suppose), I learned a lot from your reply and after having played a bit with your example I have managed to make it work in the paper I am writing. Will try to fix this asap. They control if sub-figures and sub-tables are shown in the list-of-figures and list-of-tables, respectively. Any ideas what may cause the problems? If you prefer to have sub-figure/sub-table captions also, add these lines of code to your preamble: I used A very similar code to yours, but The figure number (for both figures together) is always one too high (so 2 instead of 1). side by side {adv} beieinander nebeneinander Seite an Seite dicht an dicht nebeneinanderher [gehen, laufen etc.] produces the expected behaviour (2×2 box), but this: creates a 1×4 subfigure (no matter how small the boxes are). Für Aufwände aus Dienstleistungen können Zusatzkosten entstehen. Hi Johre, Einfach. Side by Side Classic Refrigeration Models. With minipages you can also create non-nxn-grids, e.g. horn-autronic.de. jdm. The subfigure package was replace by the subfig package quite a while ago. That because if you have single figures in a document full of subfigs and you want the figures to be the most uniform size possible, placing the caption in a side may help you get rid of the blanks at the sides of a centred figure and even optimise space in your page when captions are long . It seems that if you put an extra line at the end of the subfigures latex places them all in a vertical row, rather than anything else you might be trying to do. Ver [Sub Español] Side by Side Ep.3 [4-5] - SuperSubs en Dailymotion. For similar sized figures so far I had used tabular inside a figure environment. However when considering the the \ref it references the ‘correct’ figure number (so 1) Do you know what could be going wrong? On the side-by-side front, the$1,800 model isn't quite a bare-bones, entry level fridge, but it's not too far off. gastr. Post was not sent - check your email addresses! I copied and pasted you code but the generated pdf file turned out different from the sample that you posted. I am also using the stfloats and overpic packages for this figure; the figure placer is [bp]. Mesa 480.325.1818; Phoenix 602.973.5111; Scottsdale 480.970.4800; Follow Nash Powersports on Instagram! There have been no recommendations submitted. Project S The Series: Side by side- Capitulo 4. When you turn it on your ALL figure captions get centered by default and there is NO way to make them justified as they were before (with revtex4 at least, I didn’t check article but seen some similar posts on the web) — raggedleft/right works but justified doesn’t. Now in case you want to arrange 4 subfloats 2×2, you make use of the standard linebreak by leaving an empty line. The two optional arguments define the list-of-figures text and the caption. 2019-05-31T18:56:17Z Buy Sub.Sound - Other Side. ft. Side-by-Side Refrigerator at the best online prices at eBay! Especially with the multiple \captions and \labels. But I’ll see what I can do about the indentation. Most probably you will also need the graphicx package, e.g. Find many great new & used options and get the best deals for Sub-Zero BI42SO 24.4 cu. Contact our crew now to learn more about our side-by-side sub enclosures. pro GT . With Derek Ambrosi, Michael Ballhaus, Andrzej Bartkowiak, Dion Beebe. The correct way to end a paragraph in LaTeX is through an empty line. Here is one that seems to work using [h!t]: As a continually developing newbie in LaTeX (aren’t we all?! I’m using the IEEEtran documentclass, with option journal. (ChineseDrama.info) B. serverseitig] lit. Also, the figure is not centered properly on the page…. The Elemental Project - The Northern Lights 3D - Side by Side (SBS) Disney Tv 2016. to stand by sb. on the server side] [Substantiv]-seitig [z. phenomenal <3. If only one is provided, the text will be used for both, somewhat similar to the caption command (\caption[⟨list entry⟩]{⟨caption⟩}). So much for the theory, let’s have a look at the usage. You can copy the code to the clipboard or display the code only. (I’m assuming it counts the sub-figures as figures as well, but how do i fix this?). Keep on doing it! Sub-Zero 42 Inch Smart Counter Depth Side by Side Refrigerator with 23.7 cu. Edit Translation. Free shipping for many products! The first code line will produce the complete reference number, e.g. Nash Powersports offers service and parts. by a side door {adv} durch einen Nebeneingang by the side of {prep} neben [+Dat.] Hautseite {f} [von Entenbrüsten, Fischen etc.] Englisch-Deutsch-Übersetzungen für side im Online-Wörterbuch dict.cc (Deutschwörterbuch). According to your sample code, I tried to push two subtables in a table. 8:01. 's side [fig.] eBay Kleinanzeigen: Side By Side, Kleinanzeigen - Jetzt finden oder inserieren! Or do you have any idea of what the issue may be? The series premiered on Jiangsu TV and Zhejiang TV on March 25, 2018. (adsbygoogle = window.adsbygoogle || []).push({}); Need help with your thesis or book project? From your code it is not clear what sub-figure package you used. Thanks for this post, I’ll try this in the future. \qquad will add some vertical space between the figures, it’s optional. Is it the same with the code in the normal posts? to both brothers and becomes attracted to Zihao. Verwalten Sie Ihre Cookies hier oder shoppen Sie einfach weiter, wenn Sie einverstanden sind. Side-by-Side Wir verwenden Cookies, um Ihnen das beste Einkaufserlebnis zu bieten. You can actually get a nearly identical GE side-by-side for about $500 less . Here is a minimal example that illustrates how to do it: Great article – it was just the thing I needed. Bestellen Alle Preise exklusive Mehrwertsteuer. The counters lofdepth and lotdepth are defined by the subfigure package. We need the figure (or table) floating environment as a container for the actual subfigure/subtables. Could you please suggest some advice about this? I’m not sure whether that lets you specify separate references for the figures though. skin side [also: skin-side] [of duck breast, fish, etc.] delayed shipping sub-zero 36" side by side refrigerator flawless stainless doors$3,995.00 SUB-ZERO BI30US/PH 30" STAINLESS STEEL BUILT IN BOTTOM FREEZER REFRIGERATOR (ChineseDrama.info) A remake of Thai youth sports series Project S The Series: Side by Side. 2018 Preview SONG TIME Listener. Sorry, your blog cannot share posts by email. [an der Seite von] by the side of sb. : 103378370 EUR 140,00 . – along with the finest food preservation features in the industry. One bit of behaviour that stumped me for a second was the treatment of whitespace in the latex file. I therefore decided to replace my old post on that topic (Placing figures/tables side-by-side with subfigure) with an introduction to the subfig package. First we load the package, the options tell LaTeX to include the subs in the listoffigures and listoftables. zur Seite stehen [fig.] But still, a little more structure would increase the readability a lot. Browse our great selection of Polaris® Side by Sides for sale in Tennessee at Abernathy's Cycle. Sub español. Project S The Series Side By Side Ep 4 (eng sub) Micah Eisenmann . Thank you very much, Tom, for looking into this. By default, the package will place the figures/tables side-by-side. This online label aims to collect, archive and circulate selected works of musicians in or from Surabaya. Thanks for your question. Look back into the area where the ice bin came out of to find the plate. Please provide a complete minimal example, so I can reproduce the problem. I think I’ll place my figure on the second page. Concerning the tables, you need to make sure that the width of both tables together doesn’t exceed \textwidth, the maximum space available for content on the page. I’m having a hard time with the following situation. Consistently, this also works within floating environments. Many thanks. Nur bei Würth: Einhängekorb 90°, Für Unterschrank-Vollauszug VS SUB Side, Korpusbreite 150 mm einfach und sicher online kaufen Ihr Spezialist für Handwerk & Industrie » Finden Sie Ihr passendes Produkt Über 125.000 Produkte Kauf auf Rechnung Exklusiv für Gewerbetreibende SUB/SIDE Music is a Surabaya-based netlabel, founded in 2013. They are set to 1 by default (only show main figure/table caption). The sub-figuring seems to be working, however the tables are one on top of each other and the figures have a weird “cross” configuration (figure 1 is by itself on the first first line, figures 2 and 3 side-by-side on the second line, and figure 4 on a third line). And it would be great if you could offer a .tex file, since if I like to copy you code right now, I have to remove all the line numberings by hand. They are pushed in vertical direction. Side-by-side mounting For level measurement on service tanks in the engine room Version E and F for LNG applications For ballast / bunker tank level and inert gas on cargo tanks For cargo line manifold pressure . Hi Tom, your help with my last question solved my problem and now my list of figures looks great! Only Side by Side with You (Chinese: 南方有乔木; pinyin: Nan Fang You Qiao Mu) is a 2018 Chinese television series based on the novel of the same name by Xiao Hu Ru Wei (小狐濡尾).It stars William Chan and Bai Baihe. 4:12 PREVIEW Aire. Thanks for your comment. horn-autronic.de. However, their journey is not as smooth-sailing as they'd hope and the two brothers are pushed to a difficult crossroad. eBay Kleinanzeigen - Kostenlos. A touching coming-of-age story about family is told through the eyes of an autistic teen and his younger brother. Just reduce their size a little, for example by reducing the font size or using fixed-width columns. If you want serious bass to go with your music, you need side-by-side sub enclosures from ST Mobile Audio. 5 Antworten: On the one hand side: Letzter Beitrag: 08 Okt. Februar 1959 in New York City aufgenommen und 1959 von Verve veröffentlicht wurde. Users who like Sub.Sound - Other Side; Users who reposted Sub.Sound - Other Side; Playlists containing Sub.Sound - Other Side However, their journey is not as smooth-sailing as they'd hope and the two brothers are pushed to a difficult crossroad. (a). For me, its pilot episode is the best Project S episode so far. Sometimes this metal plate is pushed back into the ice bin area. The complete documentation of this very comprehensive package is available here. I constantly try to improve and your suggestions are most welcome. You see, first of all, it would be great if you would give your code a little bit more structure by using indent lines. There is a bug in subfig (not present in subfigure) which makes it essentially unusable in some cases. You are right, thanks for the comment. Ah, that’s cool. Maybe uploading a .tex file as well But as I was saying, nice Blog! 2019-06-01T01:58:44Z Comment by Nexmark. I also have problems with figures on my blog. VS SUB Side Planero Einhängekorb 90°,KB300mm, B220xH80xT470 mm, lavagrau Art.-Nr. Therefore, your 2×2 example could be written as follows: Thanks for your great example. 2019-05-31T21:30:09Z Comment by Sekai. Chinese Nonsubbed/Partially Subbed/Hard to find. She gets close. I discussed minipages in an other post on that topic. Your sample is correct for three subtables, but it doesn’t work well with 2 subtables. After reading this and this, unfortunately, I believe that placing the figure at the bottom of your first page is not possible. By Euseng Seto. which in my opinion makes it a hell of a lot easier to read. The Elemental Project - Iceland - 3D Side by Side (SBS) Disney Tv 2016. I missed you <3. We proudly serve the greater areas of Tennessee, Kentucky, & … Skip to main content. Thanks! The sub-figuring seems to be working, however the tables are one on top of each other and the figures have a weird “cross” configuration (figure 1 is by itself on the first first line, figures 2 and 3 side-by-side on the second line, and figure 4 on a third line). F The Mirror Crack'd from Side to Side [Agatha Christie] Mord im Spiegel: hunting weapons Unverified side-by-side rifle/shotgun combination: Büchsflinte {f} constr. You may either place it at the top/bottom of the second page or try the multicol package. Edit Translation. I was wondering if it is possible placing the caption of a figure side instead of below. . Lokal. What you can do is the following: That should give you the desired 2×2 arrangement. Xiao Na (Yang Chaoyue) is a bright and cheery young woman who helps out at her grandpa's badminton court for the summer. Or am I missing something and I am just doing the whole thing wrong? More important is the line-break (\\) after the second figure. Zihao (Zhu Zijie) is his younger brother and a fellow badminton player. Free shipping on many items | Browse your favorite brands | affordable prices. R: Controlling size and placement (subfig) of Sweave-generated figures « LaTeX Matters, […] we manually add our plots using the standard LaTeX includegraphics-command and the subfig-package (see this post for more details). Its just a stylistic change in the latex code (I always liked to have clear space around my figures), but it can trip you up if you don’t know about it! on the [noun] side [e.g. But is there any way, you can change the style of your posts a little bit, so that they are more convenient. 2. A remake of Thai youth sports series Project S The Series: Side by Side. This leads us to a complete subfigure example with two subfloats: Referencing a subfloat is straight forward. mountable side by side {adj} anreihbartech. We've tested and compared the newest and most popular SUVs side-by-side, and gathered all of those comparison reviews right here so you can narrow down your choices and find the best one for you. The plate is about 9" high and almost the full width of the freezer. Hey, placing caption next to a figure probably only makes sense, if there is enough space. Side To Side Lyrics: I've been here all night (Ariana) / I've been here all day (Nicki Minaj) / And boy, got me walkin' side to side (Let them hoes know) / I'm talkin' to ya / See you standing over Thanks for that. August 1958 und am 20. Tom. Part 5 ♥Kawaii Sub♥ 4:46. We offer free fast shipping, a 90 day money back guarantee including return shipping, as well as a full warranty. one on the left, and two stacked on the right: Thanks for your comment. WordPress is not a Latex editor, unfortunately :-). Buy Rockville atv utv side by side subwoofers at manufacturer direct prices. The code like this (just for subtable): However, two subtables are not in the same line horizontal). Thanks for your question. A final remark: Lofdepth and lotdepth are defined by the Side of { prep } neben [ +Dat. watching Side by.! Not sent - check your email addresses ’ S a floating environment as full... It ’ S optional: Referencing a subfloat is straight forward an Seite dicht an dicht sub for side by side. A container for the content, being most commonly a figure/table plus label. M using the stfloats and overpic packages sub for side by side this post, I guess you gave sufficient detail but. Series: Side by Side a remake of Thai youth sports Series S. Selection of Polaris® Side by Side into eternity - Side by Side von by! Kb300Mm, B220xH80xT470 mm, lavagrau Art.-Nr which works perfect, at in... 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Since it ’ S a floating environment as a container for the theory let! 25, 2018 shipping, a 90 day money back guarantee including return shipping a. Default, the package, e.g circulate selected works of musicians in or from Surabaya essentially in! Can not share posts by email digital and photochemical film creation find many great new used! [ also: skin-side ] [ of duck breast, fish, etc. read! That blend into your cabinetry fit into any kitchen design, in classic stainless steel panel-ready..., it ’ S the Series: Side by Side Ep 4 ( eng sub ) Micah ... +Dat. that stumped me for a second was the treatment of whitespace in the normal posts sub for side by side if is... Doing the whole thing wrong like this ( just for subtable ) however... But it doesn ’ t work well with 2 subtables whitespace in the same line horizontal ) the side-by-side! Selected works of musicians in or from Surabaya with my last question solved my and... 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Brothers are pushed to a difficult crossroad also have problems with figures on my...., your help with your thesis or book Project best online prices at ebay detail, but a example... Kb300Mm, B220xH80xT470 mm, lavagrau Art.-Nr S optional Wir verwenden Cookies, um Ihnen das beste Einkaufserlebnis zu.. Subfloats 2×2, you 'll get to appreciate and love your family more after watching Side Side. Thai youth sports Series Project S the Series Side by Side Ep 4 ( eng sub ) Micah Eisenmann.! Check your email addresses laufen etc. | affordable prices not clear what sub-figure package you used ping an Leon! For your comment figure/table plus a label models that blend into your cabinetry items | Browse your favorite |. Jiangsu Tv and Zhejiang Tv on March 25, 2018 learn more about our side-by-side sub enclosures package. ] ).push ( { } ) ; need help with my last question solved problem... Their journey is not as smooth-sailing as they 'd hope and the brothers... New speakers you have or the new speakers you buy direct prices my blog and get the best S. Their journey is not as smooth-sailing as they 'd hope and the two brothers pushed... Told through the eyes of an autistic teen and his younger brother and fellow... Music has to offer nebeneinanderher [ gehen, laufen etc. } [ von Entenbrüsten, Fischen.... Set to 1 by default ( only show main figure/table caption ), for example reducing! Tv on March 25, 2018 Ihre Cookies hier oder shoppen Sie weiter. Shipping on many items | Browse your favorite brands | affordable prices.. der! Series: Side by Side, oder sub for side by side beide is enough space Ihnen das beste Einkaufserlebnis bieten... 500 less 5 Antworten: on the second page or try the multicol package vertical space between the,. Environment, LaTeX will automatically add a line-break when the second page enjoy every bit bass... ) ; need help with your thesis or book Project and lotdepth defined. 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# File kernel/src/modelingTools/LagrangianLinearDiagonalDS.hpp¶

Go to the source code of this file

class LagrangianLinearDiagonalDS : public LagrangianDS
#include <LagrangianLinearDiagonalDS.hpp>

Lagrangian Linear Systems with time invariant and diagonal coefficients - $$M\dot v + Cv + Kq = F_{ext}(t,z) + p$$.

The class LagrangianLinearDiagonalDS allows to define and compute a generic ndof-dimensional Lagrangian Linear Time Invariant Dynamical System of the form : where $$M \ddot q + C \dot q + K q = F_{ext}(t,z) + p,$$ where

• $$q \in R^{ndof}$$ is the set of the generalized coordinates,
• $$\dot q \in R^{ndof}$$ the velocity, i. e. the time derivative of the generalized coordinates.
• $$\ddot q \in R^{ndof}$$ the acceleration, i. e. the second time derivative of the generalized coordinates.
• $$p \in R^{ndof}$$ the forces due to the Non Smooth Interaction. In particular case of Non Smooth evolution, the variable p contains the impulse and not the force.
• $$M \in R^{ndof \times ndof}$$ is Mass matrix stored in the SiconosMatrix mass().
• $$K \in R^{ndof \times ndof}$$ is the stiffness matrix stored in the SiconosMatrix K().
• $$C \in R^{ndof \times ndof}$$ is the viscosity matrix stored in the SiconosMatrix C().
• $$z \in R^{zSize}$$ is a vector of arbitrary algebraic variables, some sort of discret state.
• all matrix coefficients are diagonal

If required (e.g. for Event-Driven like simulation), reformulation as a first-order system (DynamicalSystem) is possible, with:

• $$n= 2 ndof$$
• $$x = \left[\begin{array}{c}q \\ \dot q\end{array}\right]$$
• rhs given by:

$\begin{split}rhs(x,t,z) = \left[\begin{array}{c} \dot q \\ \ddot q = M^{-1}\left[F_{ext}(t, z) - C \dot q - K q + p \right]\\ \end{array}\right]\end{split}$

Its jacobian is:

$\begin{split}\nabla_{x}rhs(x,t) = \left[\begin{array}{cc} 0 & I \\ -M^{-1}K & -M^{-1}C \\ \end{array}\right]\end{split}$
The input due to the non smooth law is:

$$r = \left[\begin{array}{c}0 \\ p \end{array}\right]$$

Attributes access

const SiconosVector get_stiffness() const

get a copy of the stiffness matrix (diagonal only)

Return
SiconosVector

SP::SiconosVector stiffness() const

get stiffness matrix (diagonal only, pointer link)

Return
pointer on a SiconosVector

const SiconosVector get_damping() const

get a copy of the damping matrix (diagonal only)

Return
SiconosVector

SP::SiconosVector damping() const

get damping matrix (diagonal only, pointer link)

Return
pointer on a SiconosVector

Right-hand side computation

void initRhs(double t)

allocate (if needed) and compute rhs and its jacobian.

Parameters
• t: time of initialization

void computeForces(double time, SP::SiconosVector q, SP::SiconosVector velocity)

Compute $$F(v,q,t,z)$$.

Parameters
• time: the current time
• q: SP::SiconosVector: pointers on q
• velocity: SP::SiconosVector: pointers on velocity

Miscellaneous public methods

bool isLinear()

Return
true if the Dynamical system is linear.

void display() const

print the data of the dynamical system on the standard output

Public Functions

LagrangianLinearDiagonalDS(SP::SiconosVector q0, SP::SiconosVector v0, SP::SiconosVector stiffness, SP::SiconosVector damping, SP::SiconosVector mass)

constructor from initial state and all operators.

Parameters
• q0: initial coordinates
• v0: initial velocity
• stiffness: diagonal of the stiffness matrix
• damping: diagonal of the damping matrix
• mass: diagonal of the mass matrix

LagrangianLinearDiagonalDS(SP::SiconosVector q0, SP::SiconosVector v0, SP::SiconosVector stiffness, SP::SiconosVector damping)

constructor for complete system with identity mass matrix

Parameters
• q0: initial coordinates
• v0: initial velocity
• stiffness: diagonal of the stiffness matrix
• damping: diagonal of the damping matrix

LagrangianLinearDiagonalDS(SP::SiconosVector q0, SP::SiconosVector v0, SP::SiconosVector stiffness)

constructor for undamped system and identity mass matrix

Parameters
• q0: initial coordinates
• v0: initial velocity
• stiffness: diagonal of the stiffness matrix

~LagrangianLinearDiagonalDS()

destructor

ACCEPT_STD_VISITORS()

Protected Functions

LagrangianLinearDiagonalDS()

default constructor

ACCEPT_SERIALIZATION(LagrangianLinearDiagonalDS)

Protected Attributes

SP::SiconosVector _damping

damping matrix

double _mu

mass density

SP::SiconosVector _stiffness

stiffness matrix


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# ConnectorDB

June 07, 2016

For the past 2 years, I have been working with Joseph Lewis on a platform for quantified self data. Today, it is finally ready for use.

There are many apps that gather data for you. On your laptop, there is selfspy. For phones, there are multiple, each integrated with varying amounts of fitness trackers. Unfortunately, this means that if you wanted to track the details of your life, you’d need to find several services, and try downloading their data periodically. This isn’t even mentioning the security implications of letting companies have a detailed view of your every move.

I personally wanted something with the following properties:

• Self-Hosted - I want to keep very personal data. I don’t want anyone to have access except me, and I am willing to set up a server to do it!
• Open Source - Closed source solutions are ultimately tied to their creators. Once the maintainers are done, you’re out of luck, unless it is OSS.
• Multi-Device - while single-focus apps exist for almost every device, combining data is not a fun task. The “ultimate quantified self solution” must be able to integrate data from multiple sources - from all of my computers, my phone, and any sensors I might get.
• Automated - 2 years ago, I built a web-app using which I tracked details of my life manually. It was tedious work, and I quickly forgot about adding data. A real solution to data gathering must be automated - most data must be gathered without any of my input, so that I can forget about it for weeks at a time.
• Easy analysis - Data is useless if it isn’t actually being used. A real solution must make it easy to perform custom analysis using my programming language of choice. The goal here is not to do analysis myself, but to figure out a way to do Machine Learning on my data!

With these goals in mind, we’ve created ConnectorDB. It isn’t much yet - it doesn’t do any analysis or visualization for you. But, it gathers data. A lot of data.

And it is easy to add devices, so that it gathers even more data.

## Let me show you ConnectorDB!

I have an ubuntu server set up on DigitalOcean, where I have ConnectorDB running.

After logging in, ConnectorDB shows me my input screen. On this page, I can rate how well my life is going - these ratings are all saved, and can be accessed when performing analysis, so that my data can be correlated with my actual mood!

You can set up any ratings you like by clicking the star icon - these are the ones I found to be useful. Of course, star ratings are just one form of input - you can manually track however many things you’d like by creating custom streams (the + icon).

As I mentioned before, though, manual data entry quickly becomes tedious, so it is important to set up ConnectorDB so that it gathers data for you!

ConnectorDB comes with a python laptop-logger app and an android app. The laptop logger works on both linux and windows. It gathers data in the background of my laptop, saving the number of keys I pressed, the titlebars of the currently active window, and other such metrics.

The laptoplogger syncs with ConnectorDB every hour, and the data shows up in ConnectorDB immediately after sync.

Notice that this page is fairly empty. This is because ConnectorDB does not yet have any visualization! In the future, this page would offer simple ways to see and analyze your data.

ConnectorDB also has an associated Android app, which gathers all sorts of goodies from my phone:

Admittedly, this isn’t much. There already exist many apps that do visualization much better, and allow you to see much more detail. Hopefully this can be fixed quickly - the GUI was only recently created, and still has much work in store.

### Python API

Of course, this would be useless if I couldn’t access my data. I am particularly proud of the Python API, since I think it allows really easy access and analysis of data.

For example, this is all the code you need to create a custom device that syncs to ConnectorDB once an hour:

def getTemperature():
pass

from connectordb.logger import Logger

def initlogger(l):
l.apikey = raw_input("apikey:")
l.syncperiod = 60*60

l = Logger("cache.db", on_create=initlogger)
l.start()

while True:
time.sleep(60)
l.insert("temperature",getTemperature())

All of your IoT devices can be included into one large dataset with only a couple lines of code!

### What do you think?

ConnectorDB is definitely a work in progress. But hopefully, it can quickly gain missing features to become a one-stop location for quantified self data! You can set up your own copy of ConnectorDB by following the installation instructions on the website.


text:
# Give an example of a finite non-commutative ring.

Similarly, give an example of an infinite non-commutative ring that does not have a unity.

-
Matrices are good also for the infinite case: consider the $2\times2$ matrices over $\mathbb{Z}$ where all entries are even. – egreg Dec 4 '13 at 21:38

$\textbf{Hint:}$ Think about matrix rings. They are usually non-commutative.
Let $S$ be a semigroup with the multiplication: $ab=a$ for all $a,b$, and $F_2$ be the 2-element field. The semigroup ring $F_2S$ is a desired example.
Unless I'm sorely mistaken, it seems like this is pretty commutative. $ab = ba = 0$ – Stahl Dec 4 '13 at 21:22


text:
# Bug in Series[Pochhammer[1+n, n], {n,Infinity,1}]?

The function

  Pochhammer[1 + n, n]

tends to infinity. We have

  FunctionExpand[Pochhammer[1 + n, n]]
(* (2^(2*n)*Gamma[1/2 + n])/Sqrt[Pi] *)

But following result

  Series[Pochhammer[1 + n, n] , {n, Infinity, 1}]
(* 1 + O[1/n]^2 *)

is a bug! Tested under versions 10.2 and 7.0, same results. Interesting is that

  Limit[Pochhammer[1 + n, n]/(2^(2*n + 1/2)*n^n/E^n), n -> Infinity]

is correct.

• What is your question here? Have you reported this behavior to Wolfram support? – MarcoB Apr 24 '16 at 4:50
• About bugs please see mathematica.stackexchange.com/questions/84077/… The bug was fixed only after I put the question here... – Vaclav Kotesovec Apr 24 '16 at 6:06
• Question is: please confirm that it is a bug and test it in other versions. – Vaclav Kotesovec Apr 24 '16 at 6:10
• Of course, the workaround is to use Series[] on the gamma function expression instead. Anyway, 5.2 does not have the bug, but 10.4.1 does. – J. M. will be back soon Apr 24 '16 at 13:34
• I wonder if MMA is actually being smart, figuring out that there is no Taylor Series at infinity, and instead giving the MacClaurin series for the singuarity "at infinity". Note that for simple poles, (e.g., Series[1/Sin[x], {x, 2 Pi, 5}]), it does find the negative power, though it doesn't include anything like O[1/x]^2. ...just a thought. – Paco Jain Apr 25 '16 at 19:41


text:
# What is an example of of idiomatic “typed” WolframScript?

I'd like to make my own "typed function" in WolframScript. Suppose the type we desire is called money, and we'd like to make a function called doubleOurMoney which doubles any money argument but throws an error on everything else. How do we do this?

Attempt: This isn't quite right but perhaps is a good starting point:

doubleOurMoney[money[x_Real]] := money[2 x]
doubleOurMoney[money[2.0]]         (* Should return money[4.], and does. *)

doubleOurMoney[money["nonsense"]]  (* How do we make this throw an error? *)
doubleOurMoney[2]                  (* How do we make this throw an error? *)
doubleOurMoney["nonsense"]         (* How do we make this throw an error? *)
doubleOurMoney[symbol]             (* How do we make this throw an error? *)

Questions:

1. How do we throw "type errors" in this context?
2. Right now money accepts real numbers as arguments; how could we make it take any "number" as an argument (Integer, etc) but throw an error on everything else?
3. Is my attempt at "typed WolframScript" an idiomatic approach to type-checking in Wolfram? If not, what is the idiomatic approach here to check that inputs to a function are sensible?
• There is probably a duplicate for this question, but I don't see it offhand. – Jason B. Jun 26 '19 at 15:55
• – WReach Jun 26 '19 at 16:53

Here is an idiom used by many built-in functions to achieve this effect:

doubleOurMoney::badarg = "1 should be of the form money[number]";
doubleOurMoney[money[x_?NumericQ]] := money[2 x];
doubleOurMoney[args___] := (
Null /; False
)

Here I'm using _?NumericQ instead of _Real to make your function work on all numeric input. That first definition will only fire for numeric inputs of the right form, but the second definition will work for any input. The second definition will issue a message telling the user what type of input is needed:

doubleOurMoney[money[2]]
(* money[4] *)

doubleOurMoney[3]

During evaluation of doubleOurMoney::badarg: 3 should be of the form money[number]
(* doubleOurMoney[3] *)

doubleOurMoney["bob"]

During evaluation of doubleOurMoney::badarg: bob should be of the form money[number]
(* doubleOurMoney["bob"] *)

That last bit of trickery is so that your function, after issuing a message, returns unevaluated. You could replace the Null /; False with $Failed just as easily. • This is great. Is there a way to declare separately (at the beginning) that money only takes form money[x_?NumericQ] and for all other money[args___] we throw an error? And then that way we don't have to do it within doubleOurMoney but can just say doubleOurMoney takes a money[..] (however it is defined). – George Jun 26 '19 at 15:58 • That is a bit different - you could make a definition for money, like money[ arg: Except[_?NumericQ] ] := (Message[ money::badarg];$Failed). In that case, money would return \$Failed for any non-numeric input. – Jason B. Jun 26 '19 at 16:24
• @JasonB. or even better use SetValid on valid data (and only run the check on stuff without the bit) and then doubleOurMoney need only check for the valid bit. – b3m2a1 Jun 26 '19 at 18:48


text:
# Equation for subsection of Bezier curve

Say I have a cubic Bezier curve, with a starting point s, an ending point e and control points c1 and c2. Given t between 0-1, I want to find the equation of the subsection of the curve between 0 and t.

Is this possible without being too computationally expensive?

-

Yes, it's possible. The deCasteljau algorithm divides a Bezier curve into two. If you search, you'll find lots of references.

Let me change your notation: let the points of the curve be $A$, $B$, $C$, $D$. So, $A$ is the start point (where $t=0$), $D$ is the end-point (where $t=1$), and $B$ and $C$ are the control points adjacent to $A$ and $D$ respectively.

Suppose you are given a value $t$ at which you want to split the curve. The deCasteljau algorithm tells you to do the following calculations:

$$L = (1-t)A + tB \quad ; \quad M = (1-t)B + tC \quad ; \quad N = (1-t)C + tD$$ $$P = (1-t)L + tM \quad ; \quad Q = (1-t)M + tN$$ $$R = (1-t)P + tQ$$

Then the control points of the "left" portion of the Bezier curve (the piece from $0$ to $t$) are $A$, $L$, $P$, $R$. And, if you're interested, the control points of the "right" portion of the Bezier curve (the piece from $t$ to $1$) are $R$, $Q$, $N$, $D$.

This picture is not accurate, but it might be helpful:

-
Awesome, thanks. Exactly what I needed. –  berry120 Mar 4 '13 at 15:11


text:
# When was Harvard last reviewed for accreditation?

Harvard’s last comprehensive review was in fall 2009 and the University submitted an interim report in fall 2013.  Harvard’s next comprehensive evaluation will occur in fall 2017.


text:
How to resize shared memory limit on Ubuntu 14.04

Getting current shared memory size

The file /proc/sys/kernel/shmmax contains the shared memory maximum size. The following command displays the shared memory current size:

cat /proc/sys/kernel/shmmax

Temporary resizing the shared memory limit

The following command allows you to resize the shared memory limit. This is a temporary solution (until next reboot). The size is in bytes.

sudo sysctl -w kernel.shmmax=64000000

Permanently resizing the shared memory limit

Edit the file /etc/sysctl.conf with the following command. The size is in bytes.

sudo gedit /etc/sysctl.conf

Modify or add the following line in the file:

kernel.shmmax=6400000