text:
# Procedure name with small caps in algorithm2e

I know that procedure in algorithm2e only allows captions like \caption{ProcedureName()}.

However, I'd like my procedure to appear in small caps:

\documentclass[12pt,a4paper]{article}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{enumerate}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage[algosection, boxruled, linesnumbered]{algorithm2e}

\begin{document}
\begin{procedure}

\SetKwInOut{Input}{input}
\SetKwInOut{Output}{output}
\Input{Graph $G = (V,E)$}
\Output{}
\ForEach{node $v \in V$}
{
\lIf{$v$ is marked}{remove $v$}
}

\caption{\textsc{removemarked()}}
\label{alg:removemarked}

\end{procedure}
\end{document}

Which of course gives error

Paragraph ended before \algocf@captname was complete

Instead of procedure, if I use \begin{algorithm} ... \end{algorithm}, then it forks fine. Is there a way to make it work in procedure as well?

It's not really well documented in algorithm2e manual, but to achieve what you want, you have to issue the command

\SetProcNameSty{textsc}

The argument of \caption when using the procedure environment can only contain something like name(arg).

In the following MWE I've also added

\SetProcArgSty{textsc}

just in case you are using procedure captions with arguments:

\documentclass[12pt,a4paper]{article}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{enumerate}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage[algosection, boxruled, linesnumbered]{algorithm2e}

\SetProcNameSty{textsc}
\SetProcArgSty{textsc}

\begin{document}
\begin{procedure}

\SetKwInOut{Input}{input}
\SetKwInOut{Output}{output}
\Input{Graph $G = (V,E)$}
\Output{}
\ForEach{node $v \in V$}
{
\lIf{$v$ is marked}{remove $v$}
}

\caption{removemarked()}
\label{alg:removemarked}

\end{procedure}
\end{document}

Output


text:
# \resizebox shifts tikzpicture up when in a subfloat environment

Why when I try to re-scale a tikz figure using \resizebox the baseline is shifted up (regardless of how small the scale factor is), and two horizontal floats are not aligned properly.

\documentclass[twocolumn]{article}

\usepackage{tikz}
\usepackage{graphicx}
\usepackage{subfig}

\pagestyle{empty}

\begin{document}
\begin{figure}
\centering
\begin{tabular}{cc}%
\subfloat[]{%
\fbox{
\resizebox{0.5\linewidth}{!}{%
\begin{tikzpicture}
\node {a};%
\end{tikzpicture}%
}%end resize
}%fbox
}&%end subfloat
\subfloat[]{%
\begin{tabular}{c|cccc}%
& 0 & 1 & \dots & n\\\hline
a & & & &\\
b & & & &\\
c & & & &\\
\dots & & & &\\
d & & & &\\
\end{tabular}%
}%end subfloat
\end{tabular}%
\caption{Why resizebox shifts the baseline up?}
\end{figure}
\end{document}

-
I think you want to avoid the spurious space after \fbox{ by adding % there as well. Note that with the adjustbox package you can simply write \adjustbox{width=0.5\linewidth,fbox}{..} or \begin{adjustbox}{width=0.5\linewidth,fbox} .. \end{adjustbox} and easily add more modifiers. – Martin Scharrer Jan 3 '13 at 9:33

The problem is not the baseline of the \resizebox but the baseline of the tabular which is on its center by default. So changing the baseline of the tabular with [b] solves this issue:

\documentclass[twocolumn]{article}

\usepackage{tikz}
\usepackage{graphicx}
\usepackage{subfig}

\pagestyle{empty}

\begin{document}
\begin{figure}
\centering
\begin{tabular}{cc}%
\subfloat[]{%
\fbox{
\resizebox{0.5\linewidth}{!}{%
\begin{tikzpicture}
\node {a};%
\end{tikzpicture}%
}%end resize
}%fbox
}&%end subfloat
\subfloat[]{%
\begin{tabular}[b]{c|cccc}% === [b] added here ===
& 0 & 1 & \dots & n\\\hline
a & & & &\\
b & & & &\\
c & & & &\\
\dots & & & &\\
d & & & &\\
\end{tabular}%
}%end subfloat
\end{tabular}%
\caption{Why resizebox shifts the baseline up?}
\end{figure}
\end{document}

Addendum 2013-01-04: As user adn has found out, the captions are still not perfectly aligned. (See comments below.) A possible solution would be switching to the subcaption package resp. its \subcaptionbox command:

\documentclass[twocolumn]{article}

\usepackage{tikz}
\usepackage{graphicx}
\usepackage{subcaption}

\pagestyle{empty}

\begin{document}
\begin{figure}
\centering
\begin{tabular}{cc}%
\subcaptionbox{}{%
\fbox{
\resizebox{0.5\linewidth}{!}{%
\begin{tikzpicture}
\node {a};%
\end{tikzpicture}%
}%end resize
}%fbox
}&%end subcaptionbox
\subcaptionbox{}{%
\begin{tabular}{c|cccc}%
& 0 & 1 & \dots & n\\\hline
a & & & &\\
b & & & &\\
c & & & &\\
\dots & & & &\\
d & & & &\\
\end{tabular}%
}%end \subcaptionbox
\end{tabular}%
\caption{Why resizebox shifts the baseline up?}
\end{figure}
\end{document}

Please note that changing the baseline of the inner tabular (with [b]) is not necessary here since a \subcaptionbox always has its baseline between content and caption, and therefore the two \subcaptionboxes are already aligned by default.

-
Thanks, I didn't know that... :) – adn Jan 3 '13 at 9:29
Quick question, is it me or the table is a little bit shifted down in comparison to the tikzpicture? – adn Jan 4 '13 at 1:35
Can't confirm that. Even if I use the magnifying lens of TeXworks the bottom rule of the picture is exactly on a horizontal line with the pixel at the bottom of the tabular. – Axel Sommerfeldt Jan 4 '13 at 4:59
I was talking about the captions (a) and (b), maybe it is just a visual effect. – adn Jan 4 '13 at 5:27
When using my subcaption package instead of subfig (and replacing \subfloat with \subcaptionbox) the effect has gone. So I assume it's a bug in subfig!? Shall I add the subcaption code to my answer? – Axel Sommerfeldt Jan 4 '13 at 7:07

format: plain


text:
# QMMM_Surface: Ziegler-Natta catalysis¶

This is an example of a Ziegler-Natta type catalytic system: a TiCl complex embedded in a MgCl surface with two organic substrates also attached to the surface. To make the computation faster, the QM/MM approach is applied. The QM part includes only the active site and a piece of the MgCl surface.

The computation is formally a geometry optimization, but to keep the sample doable in a reasonable time the sample performs only one geometry update step. In the optimization, all of the MgCl surface atoms are frozen.

The standard force field has been modified to accommodate this calculation. The modified force field file is part of the sample run script. In this modified file, bonds are defined between Mg-Cl atoms in the MM connection table. This results in some torsions where the atoms are collinear. To rectify this problem, the torsional potentials for these atoms are set to potential type ‘0’ (no potential).

There are no capping atoms mediating the bonds between the QM and MM regions because the boundary goes through the MgCl surface, which is ionically bound.

cat << eor > champ_de_force.ff
YBYL/TRIPOS FORCE FIELD FILE FOR ADF QM/MM
MODIFIED WITH UFF1.01 FOR Si Mg Ti Cl
L. Petitjean 15.11.1999
*************************************************************************

(Most of the contents of the modified force field file is omitted here. You quickly get the difference with the standard sybyl force field file in the ADF database by running a UNIX diff on the two files.

====================================
eor

Title  ADF-QMMM in a surface study
NoPrint SFO, Frag, Functions

! keywords for calculation methods and optimization
XC
GGA    BLYP
End

Geometry
Optim          Cartesian Selected
Iterations     1
HessUpd        BFGS
END

The ‘Iterations 1’ subkey specification in the Geometry block specifies that only one step in the optimization is carried out.

BeckeGrid
Quality Basic
End

SCF
Iterations  250
Converge    1E-6 1E-6
Mixing      0.2
DIIS        N=10 OK=0.5 cyc=5 CX=5.0 BFAC=0
End

! keywords for molecule specification
Charge 0 0

Atoms Cartesian
1 Mg    x1   y1   z1

(all other atoms in the Atoms block omitted here)

End

GeoVar
x1=.00000 F
y1=.00000 F
z1=.00000 F
x2=.00000 F
y2=1.72129 F
z2=1.82068 F
x3=.00000 F
y3=.00000 F
z3=-3.64100 F
x4=.00000 F
y4=-1.72130 F
z4=-1.82068 F
x5=.00000 F
y5=1.72130 F
z5=-1.82032 F
x6=.00000 F
y6=1.72130 F
z6=-5.46132 F
x7=2.53903
y7=.03004
z7=-3.50645
x8=2.50628
y8=-.07048
z8=-.10022
x9=2.63009
y9=3.50093
z9=-3.02634
...

Many of the coordinates have a ‘F’ after their initial value specification under Geovar, indicating that these coordinates will be kept frozen during optimization.

The remaining initial value specifications are omitted here.

END
QMMM
OPTIMIZE
MAX_STEPS 3000
METHOD BFGS
PRINT_CYCLES 100
SUBEND

FORCE_FIELD_FILE champ_de_force.ff

The local file ‘champ_de_force.ff’ is used as force field file. Of course, this is the file we’ve just set up in the run script.

OUTPUT_LEVEL=1
WARNING_LEVEL=1
ELSTAT_COUPLING_MODEL=1

MM_CONNECTION_TABLE
1   Mg  QM    2    4    5    8   58   60
...

Contents of the MM_Connection_Table block is omitted.

SUBEND
CHARGES
1    .957
2    -.608
3    1.017
4    -.411
5    -.561
...

Initial charges are specified for (all) the atoms. Whether or not the charges on the QM (and LI) atoms are used depends on the type of electrostatic coupling between the QM and MM system. See the rest of the QM/MM manual for details.

   SUBEND
END

Fragments
Ti t21.Ti
Cl t21.Cl
Mg t21.Mg
C  t21.C
H  t21.H
End

End Input
eor


text:
# Third (music)

Diatonic intervals
Prime
second
third
fourth
fifth
sixth
seventh
octave
none
decime
undezime
duodecime
tredezime
semitone / whole tone
Special intervals
Microinterval
Comma
Diësis
Limma
Apotome
Ditone Tritone
Wolf
fifth
Natural septime
units
Cent
Millioctave
Octave
Savart

Third (from Latin tertia : "the third") describes the interval in music that spans three levels of a diatonic scale .

Example : Scale section from c '' to e '' - major third c '' e '' one after the other - major third c '' e '' at the same time, then with a minor third c '' es ''.

In a narrower sense, the third is also the third level of the respective scale. The more precise term for this is third tone .

As an interval, a minor third comprises a total of three, a major third four semitone steps (diminished and excessive thirds see below). The third is the complementary interval to the sixth .

## variants

The third can appear in four variants.

The major third (4 semitones) and the minor third (3 semitones), which have a frequency ratio of 5: 4 and 6: 5 in the pure tuning , are very common because they are characteristic of the major-minor system .

Major third , called the major third as a pitch :

Minor third , called a minor third as a pitch :

The excessive third (5 semitones) and the diminished third (2 semitones) are rarer. You need pitches from different scales of the circle of
fifths .

Excessive third . In equal tuning, the major third is equal to the fourth . In a pure mood - like here - the difference can be 41 cents :

Diminished third . In equal tuning, the minor third is equal to the major second .

In the following example of the use of the Neapolitan sixth chord , the tone sequence b-g
sharp occurs in the soprano part. The frequency ratio of this diminished third in pure tuning is (16/15) × (16/15) = 1.137. In the cent measure this corresponds to 223.5 cents. In contrast, the major second is 182.4 cents or 203.9 cents in pure tuning (small or large whole tone), and 200 cents in equal tuning. For a good sound of this cadenza , if possible (e.g. with a vocal or string ensemble), the notes B flat and G sharp should be intonated appropriately by ear .

interval Semitones Examples Reversal interval
(a) major third 4 (2 whole tones) C - E , F - A
" Wake up, the rooster crowed"
small sixth
(b) minor third 3 (1 whole step + 1 semitone) C-It , A - C , E - G
"An Vo gel wanted to be married" (up)
"Ku ckuck calls's out of the woods" (down)
major sixth
(c) excessive third 5 (1 whole tone + 1 hiatus ) C - ice , As - Cis , Ces - E diminished sixth
(d) diminished third 2 (2 semitones) Gis-B , Ais-C , C-Eses , cis-It excessive sixth

In connection with the partial tones , e.g. B. in organ registers , the 5th partial is called the third. This third has a frequency ratio of 5: 4 to the next lower octave. The term minor third for the 19th partial tone, which has a frequency ratio of 19:16 to the next lower octave, is rare in this context. (For comparison: equal minor third: 300 cents , pure minor third (6/5): 315 cents, “ minor third ” related to the 19th partial tone (19/16): 298 cents.) The 19th partial tone also plays one more psychologically Role.

## Mood

The exact frequency ratio of the third is decided by the respective musical tuning system . In addition to the above-mentioned thirds, which ignore the tuning system, the following should be mentioned:

Surname Frequency ratio Cent value
Pythagorean third 81 : 64 407.82 cents
Major third of the same order ${\ displaystyle {\ sqrt [{3}] {2}}}$ : 1 400 cents
Pure major third 5 : 4 386.31 cents
Pure minor third 6 : 5 315.64 cents
Equal minor third ${\ displaystyle {\ sqrt [{4}] {2}}}$ : 1 300 cents
19th octave natural tone 19 : 16 297.51 cents

“Equal” thirds mean the thirds in equal tuning .

In equal tuning (e.g. on a piano ), major thirds are always a little too big, minor thirds a little too small compared to the pure intervals according to the table above. These differences are greatest in the thirds - together with the sixths as complementary intervals - of all intervals (see e.g. the table under Equal Tuning ). If the mood of individual tones can be influenced (e.g. in singing or on a string instrument) and if the intervals of a chord are to sound pure, the respective third scale step must be intonated a little lower as the “major third” and a little higher as the “minor third” .

## Individual evidence

1. M. Honegger, G. Massenkeil (Ed.): Das große Lexikon der Musik Volume 8, Freiburg: Herder 1987, ISBN 3-451-22921-8 , page 114
2. ^ Metzler-Sachlexikon Musik , Stuttgart: Metzler 1978. ISBN 3-476-01544-0 , page 1049
3. ^ HJ Moser: Allgemeine Musiklehre , 3rd edition, Verlag de Gruyter 1968, page 42
4. ^ Walter Opp: Handbuch Kirchenmusik , Volume 1, Merseburger 2001, pages 216, 225, 235. ISBN 3-87537-281-6
5. ^ Wolfgang Auhagen, Claudia Bullerjahn, Holger Höge: Musical memory and musical learning . 2009, ISBN 978-3-8409-2242-8 , pp. 107 ( preview in Google Book search).


text:
# Why is the escape velocity equal to the square root of 2 times the orbital velocity?

IsakVern
If you derive the equation for orbital velocity you get

v_{orbit} = \sqrt{\frac{GM}{R}}

and for escape velocity you get

v_{escape} = \sqrt{\frac{2GM}{R}}=\sqrt{2}\,v_{orbit}

I'm wondering if there is a logical/geometrical explanation for why the escape velocity is exactly square root 2 times the orbital velocity, or if this is just an algebraic coincidence?

## Answers and Replies

Science Advisor
Gold Member
2022 Award
To escape to infinity the total energy of the body must at least be ##0##, i.e.,
$$\frac{m}{2} v^2-\frac{G M m}{R} \geq 0,$$
where ##R## is the radius of the Earth, ##M## its mass, and ##G## Newton's gravitational constant; ##v## is the initial velocity which gets
$$v \geq v_{\text{escape}}=\sqrt{\frac{2 G M}{R}}=\sqrt{2gR},$$
where ##g=M G/R^2## is the gravitational acceleration at the surface of the earth.

What you call ##v_{\text{orbit}}## is the velocity of a body in a circular orbit at radius ##\tilde{R}## (I call it ##\tilde{R}## to distinguish it from the radius of the Earth). Then setting the centripetal force equal to the gravitational force indeed gives
$$\frac{m v_{\text{orb}}^2}{\tilde{R}}=\frac{G M}{\tilde{R}^2} \; \Rightarrow\; v_{\text{orb}}=\sqrt{\frac{G M}{\tilde{R}}}.$$

Ibix
Science Advisor
Homework Helper
Gold Member
It's an algebraic necessity, not coincidence, if you want to know the speed required so that an object leaves the Earth's surface and reaches infinity with zero kinetic energy. The total energy for an orbiting satellite is ##E =KE+PE=-\frac{1}{2}PE##. To have escape velocity from the surface you need the total energy to be zero. That means doubling the kinetic energy of the bound orbit. To do that you must double ##v^2## which means multiplying ##v## by ##\sqrt{2}##.

vanhees71 and Ibix
Science Advisor
2022 Award
Just to expand slightly on @vanhees71's maths, remember that both cases involve the same basic values - ##G##, ##M##, ##R## and ##m##, and you are combining them to make a velocity. Dimensional analysis tells you immediately that the results have to be the same to within a numerical factor.

vanhees71 and PeroK
Science Advisor
Homework Helper
Gold Member
2022 Award
I'm wondering if there is a logical/geometrical explanation for why the escape velocity is exactly square root 2 times the orbital velocity, or if this is just an algebraic coincidence?
The algebraic "coincidence" is that when you set the centripetal force equal to the central force, you get something of the form:
$$\frac{v^2}{r} = \frac{k}{r^2}$$
The ##r## cancels on the denominator, which is similar to integrating the force to get the potential. You'll get a factor of ##n -1## for any force of the form ##1/r^n##. In this case ##n = 2##, so the factor is ##1##.

Then, for the escape velocity you are setting ##\frac 1 2 v^2## equal to the potential which is where the factor of ##\sqrt 2## comes in.

Ibix


text:
# Differential phase extraction in an atom gradiometer

@article{Santos2015DifferentialPE,
title={Differential phase extraction in an atom gradiometer},
author={Franck Pereira Dos Santos},
journal={arXiv: Atomic Physics},
year={2015},
pages={063615}
}
We present here a method for the extraction of the differential phase of an atom gradiometer that exploits the correlation of the vibration signal measured by an auxiliary classical sensor, such as a seismometer or an accelerometer. We show that sensitivities close to the quantum projection noise limit can be reached, even when the vibration noise induces phase fluctuations larger than 2$\pi$. This method doesn't require the correlation between the atomic and classical signals to be perfect and…

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## References

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• Phys. 11, 113010
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### Phys

• Rev. Lett. 78, 2046
• 1997


text:
## Thursday, 30 September 2010

### The Shoulders of Giants

Last week NAG held its 34th AGM and prior to the business part of the meeting we had the pleasure of hearing a lecture by Professor Nick Higham of the University of Manchester on the subject How and How Not to Compute the Exponential of a Matrix. The lecture was filmed and can be viewed here. Matrix functions are useful in a number of areas, in particular for describing the solutions of certain types of differential equations. NAG is working with Nick to include his algorithms in future marks of the Library.

One of the things I particularly enjoyed about Nick's talk was the way that he set the subject in its proper historical context, starting with the work of 19th Century mathematicians such as Sylvester and Cayley. Working at the cutting edge of computing technology its easy to forget how much of what we do depends on work that goes back hundreds of years. It wasn't always this way: Fermat, having claimed to have found a proof of what became known as his last theorem, added the waspish comment "and perhaps, posterity will thank me for having shown it that the ancients did not know everything".

A few years ago SIAM interviewed a number of prominent people who had been active in the early days of numerical analysis and scientific computing, including NAG's own Brian Ford. You can find transcripts of the interviews and related material on SIAM's website. Reading these transcripts is illuminating, particularly to a (relative) youngster like me, especially given the number of references to NAG's early history that they contain. I hope that SIAM keeps up this activity, and continues to collect personal reminiscences from prominent people in the field.

## Thursday, 23 September 2010

### A New Version of HTML

As you may have heard, HTML5, a new version of HTML, the main markup language for the web is under development. This is the first version for quite some time, HTML4.01, the current version, was released in December, 1999. There was an XML version, XHTML 1.0, XHTML (Released in January 2000 and revised August 2002), but it did not contain any new features.

Much of the buzz around HTML5 concentrates on new features such as video (as an alternative to using flash plugins etc) and canvas (a JavaScript API for 2 dimensional graphics), but in this article I want to look at the features that impact on the kind of technical, mathematical documents used by NAG.

### SVG and MathML

SVG is an XML format for describing scalar graphics, using a similar graphics model to PostScript or PDF, but using XML syntax and CSS for styling, just as for HTML. It has been around for some years, but HTML5, for the first time, specifies how it works in the context of HTML (rather than XML). In a related move, Internet Explorer 9 will support SVG. (Other common browsers have supported it for some years.)

Many of the function plots in the NAG documentation are generated from gnuplot. Gnuplot can save to SVG as well as the EPS and PNG outputs that we currently use. Also the remaining diagrams are currently stored as EPS (for use in PDF versions of the document) and EPS can usually be converted without any loss of information to SVG.

There are many advantages to using a scalable format for plots, especially documents that are read on smaller devices such as tablets (or phones), but also printing at higher resolution; being able to scale and zoom in as required without the loss of quality inherent in scaling bitmap images is a big win.

The other XML-derived language supported natively by the HTML5 parser is MathML. MathML should be familiar to most NAG users as it has been used in the XHTML version of our documentation for years. However being able to use MathML in HTML should hopefully simplify the installation of this documentation, and also the prominence given to MathML by its inclusion in HTML5 will also hopefully encourage the remaining browser vendors, who do not natively support it, to implement mathematics rendering in their browsers.

### Current State of (Future) Browsers

All the common desktop browsers are moving towards supporting HTML5 in the near future. The following sections list the state of SVG and MathML rendering in some common cases.

#### Internet Explorer 9 Beta

IE 9 finally adds SVG support to Microsoft's Internet Explorer browser. Design Science's MathPlayer may still be used to get very high quality rendering of MathML. There are currently some problems in interfacing MathPlayer and IE 9, and some of the markup that worked in IE 8 no longer works, however this may be fixed before the full product comes out, or a few lines of IE-specific javascript, as used in the example below, may be used to work around the main problems.

Warning: IE 9 Beta, unlike all the other test releases of browsers mentioned here will replace your existing Internet Explorer installation. If you wish to test IE 9 rendering without removing your IE 8 (or earlier) installation make sure that you install the Platform Preview rather than the Beta. The platform preview releases use the IE 9 rendering engine but without all the normal browser menus and facilities, and it does not replace your existing browser.

IE 9 Beta 1 was tested.

#### Firefox 4.0 Beta

Firefox 4 uses the new HTML5 parser which automatically places MathML elements in the MathML namespace and SVG elements in the SVG namespace. The rendering of MathML and SVG in HTML 5 is then essentially exactly as has been available in earlier Firefox releases in XHTML documents, but now also available in HTML.

Firefox 4 Beta 6 was tested.

#### WebKit Nightlies

A Nightly release is a public binary release that is essentially just a snapshot of the current development build. As such it is expected to have bugs and unimplemented features. However these releases, which show the development state of the core rendering engine used by both Chrome and Safari browsers show that it has a reasonably well developed SVG renderer, and that MathML support, while very new, is improving. (These WebKit browsers have very good CSS support so until the native MathML is ready for use it will probably be possible to use a CSS rendering of MathML in these cases, as is done for the current NAG XHTML documentation).

WebKit-r67637, from 16th September was tested.

### An Example

We do not yet have any definite plans or dates to move towards using HTML5, it depends a lot on the timing of the above test releases becoming mainstream (which is likely to be very soon) and how long it takes for use of older browsers to die out. (This can take a long time, many people only change their browser when they get a new machine, Internet Explorer 6 (released in 2001 and replaced by IE 7 in 2006 and IE 8 in 2009) is still in widespread use for example.)

As an experiment we have converted one example routine document into HTML5, using inline MathML and SVG. Note in the example all links to external documents have been made to point back to the test document so that it is self-standing. The document has 207 MathML fragments, which are essentially unchanged from the existing XHTML+MathML version of the document, the two plots shown in the example section, which were previously only available as monochrome scalable images in the PDF version of the document, or a coloured PNG bitmaps in the XHTML version, are provided as scalable SVG which is directly included into the HTML file, not referenced using <img src=....

The document is reported as valid HTML5+SVGMathML by the validator.nu online validator.

The document appears to be perfectly usable in Firefox 4 and IE 9. The MathML support in WebKit is still very new, and there also appear to be some problems with the SVG which get rendered with a black background in the Windows nightly build of 16th September. Note however that, as their name suggests nightly builds are unstable test releases and should not be taken as indicative of the final product. The fact that the SVG was fully rendered apart from some colour problems, and that the MathML was recognized, albeit with some rendering problems, is I think a good sign that WebKit based browsers (Safari, Chrome, and many mobile phone browsers) will support these documents in the near future.

Fortran Library Mark 22 Routine Document (D02AGF)
XHML+PNG+MathML Mark 22 Documentation d02agf.xml
PDF Mark 22 Documentationd02agf.pdf
HTML5+SVG+MathML Experimental d02agf.html

### Conclusions

HTML5 will be mainstream in currently popular browsers very soon, it will take a few years before its use may be assumed, but it promises to be a big improvement for technical documents.

Both MathML and SVG allow the use of scalable formats freeing the web from the use of inappropriate bitmap images. This simplifies document distribution and should improve the quality both for printing and for use on a wider range of devices, including greatly increased accessibility.

## Monday, 13 September 2010

### Do you want ice with your supercomputer?

Would you like ice with your drink?” It’s a common question of course. One that divides people – few will think “I don’t mind” – most have a firm preference one way or the other. There are people who hate ice with their drink and those who freak if there is none. National stereotypes have a role to play – in the USA the question is not always asked – it’s assumed you want ice with everything. In the UK, you often have to ask specifically to get ice.

Yet the role of ice in making our drinks chilled is misleading. I once had a discussion with a leading American member of the international HPC community about this. “No ice”, he was complaining as we headed out of a European country, “they had no ice for the drink”.

I don’t get this obsession with ice”, I chipped in. “What?!” He looked at me as if I were mad. “Why do you like your coke warm?

Ah, but that’s just it”, I replied. “I hate warm drinks – I really like my coke chilled. But surely, in this modern world over a century after the invention of the refrigerator, it’s not unreasonable to expect the fluid to be chilled – without the need to drop lumps of solid water into it?

Ah, fair point”, he conceded.

What has this got to do with supercomputing? Perhaps the common thread is that usually we just accept the habitual choices of ways to do things – and don’t often step back to think – “are those the only choices?

Maybe we should step back a little more often and ask ourselves what we are trying to achieve with HPC – and are the usual choices the only ways forward? Or are there different ways to approach the problem that will deliver simpler, better or cheaper performance?

Perhaps your business/research goals mean you need to conduct more complex modelling or you need faster performance. Maybe the drive of computing technology towards many-core processors rather than faster processors is limiting your ability to achieve this. (I have had several conversations recently, where companies are buying older technology because their software won’t run on multicore).

The “ice or no ice” question might be whether or not to upgrade your HPC with the latest multicore processors. But what about the “just chill the fluid” option? Well, how about upgrading the software instead, or as well?

NAG has plenty of case studies to show where enhancements to software have achieved huge gains in performance or capability (e.g., www.hector.ac.uk/cse/reports).

Sometimes buying more compute power is the right answer. Sometimes, extracting more efficient performance from what you have is the answer. Bringing them together - a balance of hardware upgrades and software innovations might well give you the best chance of optimising cost efficiency, performance and sustainability of performance.

## Wednesday, 8 September 2010

### Working on the ADVISE project

For the past three and a half years, my colleagues and I have been working on ADVISE, a TSB-funded collaborative research project which has been developing a new toolkit for visualization and analysis. Besides NAG, the partners in the project were VSNi and the University of Leeds. VSNi have expertise in statistics, as implemented in their GenStat product, while Leeds have an international reputation for their work in visualization research. As for NAG, we've had some success with IRIS Explorer, a popular visualization toolkit which allows users to construct applications by connecting modules together via a visual programming interface.

We retained that interface in ADVISE (see Figure 1) because it has proved to be a rather intuitive way to create, modify and interact with applications. Thus, in this figure, the user selects modules from the repository on the right and connects them together in the area on the left. The widgets for controlling one of the modules are in the pane on the right at the bottom, whilst messages from the system are displayed in the area at top right.

In a similar spirit of re-use, the visualization and analysis functionality encapsulated within the ADVISE modules has come from porting just about all of the modules from IRIS Explorer into the new environment, and creating new modules that generate and process scripts of GenStat commands. We've used ADVISE to visualize and analyze a variety of data - see, for example, Figure 2, which is a display of some of the results from Christoper Goodyer's simulations of diffusion through skin.

So much for the re-use of old technology, but what's new in ADVISE? Well, its architecture makes use of recent technology developments in web services and distributed computing. This has several advantages, including the fact that it's easier to integrate applications built using ADVISE with the web (for example, running inside a browser), and that it's possible to connect ADVISE applications to other services (which could, for example, act as data sources).

To illustrate this ease of integration, Figure 3 shows a web-based application that's been created in ADVISE for the visualization of air-quality data. The window at the back shows the interface for selecting the location and duration of the data to be visualized, the next window shows that data displayed as a coloured elevated surface and the window in front shows the same data displayed as a 3D histogram. Widgets in the web page (linked to ADVISE modules) give the user a simple interface to the application - for example, allowing control over the type of display (surface or histogram), other parameters associated with the visualization, and selection of the next dataset to be displayed.

If you want to know more about the ADVISE project, or the system we produced, head over to our web page, which contains more pictures of visualizations created with the toolkit together with papers, posters and talk slides from throughout the life of the project. One picture you won't find over there, however, is the one below, which shows the whole ADVISE team (with the exception of Jungwook Seo and Colin Myers from Leeds) in all their glory at the end of the final project review meeting last month. There were (a lot of) other pictures taken at the same event, but this is the only one in which the project members aren't holding glasses.


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# Hell Is Other Resources

I hate Mondays. Let's leave it at that, shall we?

Interesting stuff on the Net I've left out so far:

I've also got quite a backlog in terms of reading - I've yet to start on a couple of books (and e-books) I've come across, and since those seem far more harmless at this point I think I'll get started now.


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# Exterior cone condition for $\mathrm{supp}\, u$ and Lebesgue points of $u$

Let $$u:\mathbb{R}^n \to \mathbb{R}$$ be an $$L^1$$ function with compact support. Let $$\bar x \in \partial \mathrm{supp}\, u$$ and assume that $$\mathrm{supp} \, u$$ satisfies the exterior cone condition at $$\bar x$$. Does this imply that $$\bar x$$ is a Lebesgue point for $$u$$?

• @PiotrHajlasz Yes. Thanks. – user124345 Jan 6 '19 at 17:58

Let $$f(x)=\begin{cases} \sin (1/x), & 0 Then $$f\in L^1(\mathbb{R})$$ has compact support equal $$[0,1]$$ and $$0$$ is not a Lebesgue point of $$f$$. However, $$\frac{1}{t}\int_0^t f(t)\, dt \to 0 \quad \text{as t\to 0^+.}$$ This is because of high oscillations of $$f$$ which cause a lot of cancellation. When you look at the definition of the Lebesgue point, then you have to take the absolute value and there is no cancellation phenomena and the integrals $$\frac{1}{t}\int_0^t |f(t)|\, dt = \frac{1}{t}\int_0^t |f(t)-f(0)|\, dt$$ do not converge to zero as $$t\to 0^+$$.


text:
Bundschuh, P., Väänänen, K. (2018) Hypertranscendence and algebraic independence of certain infinite products. Acta Arithmetica, 184 (1), 51-66. doi:10.4064/aa170528-16-12

### Hypertranscendence and algebraic independence of certain infinite products

Saved in:
Author: Bundschuh, Peter1; Väänänen , Keijo2
Organizations: 1Mathematisches Institut, Universität zu Köln, Weyerta, 86-90, 50931 Köln, Germany
2Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Language: English
Published: Polish Academy of Sciences, Institute of Mathematics, 2018
Publish Date: 2019-03-28
Description:

# Abstract

We study infinite products $$F(z)=\prod_{j\ge0}p(z^{d^j})$$, where $$d\ge2$$ is an integer and $$p\in\mathbb{C}[z]$$ with $$p(0)=1$$ has at least one zero not lying on the unit circle. In that case, $$F$$ is a transcendental function and we are mainly interested in conditions for its hypertranscendence. Moreover, we investigate finite sets of infinite products of type $$F$$ and show that, under certain natural assumptios, these functions and their first derivatives are algebraically independent over $$\mathbb{C}(z)$$.

see all

Series: Acta arithmetica
ISSN: 0065-1036
ISSN-E: 1730-6264
ISSN-L: 0065-1036
Volume: 184
Issue: 1
Pages: 51 - 66
DOI: 10.4064/aa170528-16-12


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# [Tex/LaTex] Left and right aligned minipages, with table layout

minipagetablesvertical alignment

I am trying to create a layout with two "columns," where the right-hand column itself has two columns, which are right and left aligned, respectively. For instance:

This is some text in the first                Label  Foo
column.                               Another Label  Foo Bar Baz

I am familiar with the technique to create left and righ aligned text on the same line via minipage environments, so extending that idea I've setup the right-hand column to contain a tabular to line up its labels and text. Here's what I have:

\documentclass[letterpaper,12pt]{report}
\usepackage[margin=1in]{geometry}
\begin{document}

\noindent
\begin{minipage}[t]{.49\textwidth}
\flushleft
Some long testing text to illustrate the alignment problem.
\end{minipage}
%
\hfill
%
\noindent
\begin{minipage}[t]{.49\textwidth}
\flushright
\begin{tabular}{r l}
\textbf{Some Long Label} & Bar \\
\textbf{Another Long Label} & Foo Bar Baz \\
\end{tabular}
\end{minipage}

\end{document}

This compiles and mostly works, except for one problem: the top of the text in the table appears somewhat higher than the top of the text in the left minipage. I believe this is due to the fact that tabular's naturally have some extra vertical space before and after them, but I do not know how to fix the problem.

My question is either, how can I fix my code to have the lines of text in each minipage line up vertically or, alternatively, is there some cleaner way of creating this layout without using tabular?

You forgot to use [t] also in the tabular:

\documentclass[letterpaper,12pt]{report}
\usepackage[margin=1in]{geometry}
\begin{document}

\noindent
\begin{minipage}[t]{.49\textwidth}
\raggedright
Some long testing text to illustrate the alignment problem.
\end{minipage}% <-- Don't forget this one
%
\hfill
%
\begin{minipage}[t]{.49\textwidth}
\raggedleft
\begin{tabular}[t]{@{} r l @{}}% <-- Don't forget @{}!
\textbf{Some Long Label} & Bar \\
\textbf{Another Long Label} & Foo Bar Baz \\
\end{tabular}
\end{minipage}

\end{document}

Never use \flushleft and \flushright as commands: they exist only because there are the environments flushleft and flushright. The commands to use are \raggedright and \raggedleft.

An easier approach is with tabular*:

\documentclass[letterpaper,12pt]{report}
\usepackage[margin=1in,showframe]{geometry}
\begin{document}

\noindent
\begin{tabular*}{\textwidth}{@{}p{.45\textwidth}@{\extracolsep{\fill}}r@{}}
\raggedright
Some long testing text to illustrate the alignment problem.
&
\begin{tabular}[t]{@{}r l@{}}
\textbf{Some Long Label} & Bar \\
\textbf{Another Long Label} & Foo Bar Baz \\
\end{tabular}
\end{tabular*}

\end{document}

I added showframe just to show the margins.


text:
# Mass is a _____ quantity. (a) scalar (b) vector (c) tensor (d) None of these

Correct option: (a) scalar

Mass is a scalar quantity. The mass of a body is a scalar quantity. The mass has only magnitude, not direction. If we consider the weight, it is the force experienced by the object due to its mass. Hence, weight has both magnitude and direction.

### Scalar quantity

A scalar quantity is defined as the physical quantity with magnitude and no direction.  In other terms, a scalar is a measure of quantity. For example, if I say that the height of a tower is 15 meters, then the tower’s height is a scalar quantity as it needs only the magnitude of height to define itself.


text:
## 3.20 Wighted AM vs Weighted HM

Suppose, a bus travels 10 km at 10 kph, another 15 km at 20 kph, and another 20 km at 25 kph. What is the average speed.

HM $$\rightarrow$$ consider distances as weights

AM $$\rightarrow$$ consider times as weights

Time, $$t=\frac d v=$$ 1, 0.75, 0.8

• $$WHM = \frac{10+15+20}{\frac{10}{10}+\frac{15}{20}+\frac{20}{25}}$$=17.65
• $$WAM = \frac{1\times 10 + 0.75 \times 20 + 0.80 \times 25}{1+0.75+0.80}$$ = 17.65
• True mean, $$\bar v=\frac{\sum d}{\sum t}=\frac{45}{2.55}=$$ 17.65


text:
# Ito's formula and Brownian motion

Let $a \in R$,$B=(B^1,B^2)$ a brownian motion. $$X_t=e^{B_t^1}\left(\int_0^te^{-B_s^1}dB_s^2+a\int_0^te^{-B_s^1}ds\right)$$

Show there is a brownian motion $\beta$ such that $$X_t=\int_0^t \sqrt{1+X_s^2}d\beta_s+\int_0^t(a+X_s/2)ds$$

For the moment: $$U_t=e^{B_t^1}$$

By the Ito's formula: $$U_t=1+\int_0^tU_sdB_s^1+(1/2)\int_0^tU_sds\\ dU_t=U_tdB_t^1+(1/2)U_tdt\\ dX_t=dB_t^2+X_tdB_t^1+(a+(1/2)X_t)dt$$ But how to show $$dB_t^2+X_tdB_t^1=\sqrt{1+X_t^2}d\beta_t?$$

Thank you

Define \begin{align*} \beta_t = \int_0^t \frac{dB_t^2 + X_t dB_t^1}{\sqrt{1+X_t^2}}. \end{align*} Then \begin{align*} \langle\beta, \beta\rangle_t = t. \end{align*} By Levy's characterization, $\{\beta_t \mid t \ge 0\}$ is a Brownian motion.


text:
## Essential University Physics: Volume 1 (3rd Edition)

We know that the power is: $\frac{Btu}{h}=\frac{1054J}{3600s}=0.292W$


text:
# determine density of oxygen gas using modified ideal gas equation

I am trying to determine the density of a gas (oxygen). As the gas is a compressible fluid a modified version of the ideal gas equation is required. I have been given the following equation and I am struggling to interpret it. I would like advice on the unit conversions and whether this is the correct equation at all.

$$\rho=\frac{(P+1.01325).10^5.MW}{z.8314.(T+273)}$$

where:

$\rho$ = density (Kg/m3)

P = pressure (bar(g))

MW = molecular weight (in kg/kmol)

z = compressibility factor (dimensionless)

T = temperature (deg. C)

I think that the 1.01325 converts the bar.g. to bar.a. then to pascals using the 100,000 multiplier?

Has the universal gas constant $8.314 J/(k.mol)$ been converted to $J/(K.kmol)$ ?

• I can't see why you bother with it. It's simply pV=zRT transformed so you could easily calculate density with data given. – Mithoron Feb 4 '16 at 17:21
• Z been compressibility in your equation? Apparently I need to consider compressibility. Something to do with pressure drop over pipe lengths. I will comment further soon – LiamH Feb 4 '16 at 17:27
• This has nothing to do with flow in pipes. The z in this equation is the compressibility (correction) factor for real gases compared to ideal gases (not the distance along a pipe). You need to determine the reduced temperature and pressure of oxygen, scaling by the critical properties. You have a graph that gives z as a function of reduced temperature and pressure. Once you know z, you can calculate the density. Isn't this being covered in your course? – Chet Miller Feb 4 '16 at 22:29
• I am not on a course, unfortunately, and I am having to learn this as I go. My intention was to use this equation to obtain the density, which is used in the Darcy equation to calculate pressure drop per unit length of straight pipe. – LiamH Feb 5 '16 at 7:51
• See any Thermodynamics book, but the best one that I am aware of is Fundamentals of Engineering Thermodynamics by Moran et al. To get an extended treatment of chemical thermodynamics (chemical reactions and phase equilibrium), I suggest Introduction to Chemical Engineering Thermodynamics by Smith and Van Ness. – Chet Miller Feb 5 '16 at 13:02

## 1 Answer

What an awkward, ugly equation that is! Mithoron is correct about the traditional, elegant and understandable form.

Yes, (P+1.01325)*10^5 converts gauge pressure in atmospheres to absolute pressure in Pascals.

z is compressibility - look up the Nelson-Obert generalized compressibility charts.

As for the 8314, the units here should be Pa*m^3/kmol-K. Dividing it by the molecular weight in kg/kmol will give you the specific gas constant for oxygen in Pa-m^3/kg-K. That's already been done in this equation.

Look up compressibility factor on wikipedia then find the Nelson Obert charts online, also critical data for oxygen, and use them to determine whether your oxygen is ideal in the P, T range you are dealing with (z factor between 1.01 and 0.99). The specific volume of the gas depends on z as well as on P and T, but you can neglect the z correction if it's within a percent or two of the ideal value of 1.

Responding to your subsequent comment:

P, T and z determine the gas's specific volume in m^3/kg, which along with mass flow rate (kg/s) and pipe cross-sectional area (m^2) determine flow velocity (m/s), which along with pipe roughness will determine friction factor, which along with gas viscosity, pipe length and the presence of fittings like elbows and open valves, will determine pressure drop.


text:
# Tag Info

The canonical baseband version of BPSK is that we wish to transmit a sequence $\{a_k\}$ of bits ($0$ or $1$) at a rate of $1$ bit every $T$ seconds using a pulse $g(t)$ of duration $T$ and so the transmitted baseband signal is $$s_{\text{baseband}}(t) = \sum_{k=-\infty}^\infty (-1)^{a_k}g(t-kT).$$ This is a sequence of nonoverlapping pulses of the form $\pm ... 0 According to Wikipedia: The forward transformation is: $$F(x) = \newcommand{\sgn}{\operatorname{sgn}} \sgn(x)\frac{\ln(1+\mu |x|)}{\ln(1+\mu)}$$ Where$F(x)$and$x$both lie between -1 and 1. After this conversion is it necessary to quantize$F(x)$appropriately. The reverse transformation is given by: $$F^{-1}(y) = \sgn(y)\frac{(1+\mu)^{|y|}-1}{\mu}$$ ... 2 In the context of wireless communications, the channel impulse response (CIR) is often estimated indirectly via the time-varying transfer function (TVTF)$H(t, f)$, defined by: $$H(t, f) = \mathcal F_\tau [ h(t, \tau)]$$ where$\mathcal F_\tau [ \cdot ]$denotes the Fourier transform with respect to the$\tau$(lag) variable. For example, the air interface ... 0 I finally derive a solution for my problem. I believe that this explanation is consistent. Let$\mathbf{a} = [a_0,a_1,...,a_N]$is the uncoded bit vector. Without loss of generality, let us assume that the convolutional encoder is of rate$R=1/n$. Therefore, each$a_k$will be encoded to a$\mathbf{c}_k = [c_{0,k},c_{1,k},\dots,c_{n-1,k}]$. Here, the overall ... 3 What you have studied doesn't seem to include a definition of Average Power. For deterministic signal$x(t)$, the instantaneous power delivered at time$t$is$x^2(t){\big (}$yeh, yeh, nitpickers should choose$R=1$in their beloved formula$\dfrac{V^2}R\big )$which varies from instant to instant. Thus, the average power delivered by$x(t)$can be ... 2 is there any difference between DC power and average power Yes. DC power is the square the of the mean of the signal . Average power is the mean of the square of the signal. It looks your teacher is using poor terminology. In this case "average power" and "total power" are the same. Neither one is a great term. 3 IEEE ICASSP is probably still the largest international conference on communications and signal processing. IEEE Transactions on Signal Processing and Communications are well-regarded journals. 1 Your questions are quite broad and hence difficult to answer. If the communication system can afford the bandwidth for a pilot signal, then a pilot can be used. Yes, channel estimation would be needed. Typically, SNRs would be calculated in the digital domain. However, these answers won't help you and you'll need to delve into the theory more deeply. If you ... 2 A DC offset in the frequency domain will be an impulse at$f=0$. The interpretation of this is a single tone interference: "DC" is no different spectrally than any other frequency when viewed as the Fourier Transform of a complex signal with positive and negative frequencies as the baseband spectrum centered about$f=0$is identical to that ... 2 I think you misunderstand what the book is saying. There is nothing like a "unit-energy" that you can compute. There is, however, a "unit-energy [...] pulse", which is a pulse with energy equal to$1$. So if you have some pulse$p(t)$with energy $$E_p=\int_{-\infty}^{\infty}|p(t)|^2dt\tag{1}$$ and you want to normalize it such that its ... 1 Each IFFT complex result bin represents an amplitude and a phase for some frequency. You can use the sum of the a sine and a cosine in the appropriate ratios to produce a sinusoid of any phase (see trig identity). The IQ inphase and quadrature modulators produce the sine and cosine in the appropriate ratios to produce the transmit phase as needed. This ... 1 Because the output of the IFFT operation is a vector of complex numbers. An RF signal is a real thing, so you can't just multiply a sine wave by a complex number and get something sensible. However, you can map a complex number onto an RF carrier by multiplying the real part by$\cos \omega t$, and the imaginary part by$\sin \omega t$. This is I/Q ... 0 I can also not really understand what your question is exactly. In terms of I and Q component, you can simply think of a complex receive symbol, where the real part corresponds to the I and the imaginary part corresponds to the Q value. However, if you want to demodulate a signal (e.g. 4QAM) you have to use a defined mapping from the modulator to demodulate ... 0 The script below is my solution for my case. I hope that it could be useful for anyone facing the same issue. The code can be directly pasted in a "Embedded Python Block". I wrote some comments to explain the mechanism. I hope you find well. Any kind of improvement is welcome! import numpy as np from gnuradio import gr import pmt class ... 2$E_s$would be the energy of the channel symbols at the output of the matched filter as scaled by the path loss between transmitter and receiver as long as all timing and carrier offsets have been corrected for and channel equalization completed - consider how after matched filtering with carrier and timing offsets removed we use just one sample per symbol ... 2 Did Dialup Modem use closed or open loop power/volume control? Yes. How did they determine Tx level? "Dialup Modem" is a very big term that spans > 50 years of technological development. Early modems for landline telephone very pretty plain binary FSK. So, there wasn't much use for any fine-grained volume control. V.90 modems sense the ... 1 Q1: no, not in general. If the sum of multiple sequences is one of the sequences that are in your codebook$x^i\$ (or a multiple), then this will become impossible to resolve. The sequences need to be mutually orthogonal, or the channels will "crosstalk". Look up DSSS, this is exactly what you're doing. Q2: because OOK doesn't use the channel half ...


text:
#### Approach #1: Simulation [Accepted]

Intuition

We can simulate the position of the robot after each command.

Algorithm

Initially, the robot is at (x, y) = (0, 0). If the move is 'U', the robot goes to (x, y-1); if the move is 'R', the robot goes to (x, y) = (x+1, y), and so on.

Complexity Analysis

• Time Complexity: , where is the length of moves. We iterate through the string.

• Space Complexity: . In Java, our character array is .

Analysis written by: @awice.


text:
Uniqueness of local Langlands correspondence for connected reductive groups over real/complex field. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T16:21:44Z http://mathoverflow.net/feeds/question/31172 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/31172/uniqueness-of-local-langlands-correspondence-for-connected-reductive-groups-over Uniqueness of local Langlands correspondence for connected reductive groups over real/complex field. Kevin Buzzard 2010-07-09T11:17:40Z 2011-11-30T07:10:29Z
In Langlands' notes "On the classification of irreducible representations of real algebraic groups", available at the Langlands Digital Archive page here, Langlands gives a construction which is now referred to as "the local Langlands correspondence for real/complex groups".

What Langlands does in practice in this paper is the following. Let $K$ denote either the real numbers or a finite field extension of the real numbers (for example the complex numbers, or a field isomorphic to the complex numbers but with no preferred isomorphism). Let $G$ be a connected reductive group over $K$. Langlands defines two sets $\Pi(G)$ (infinitesimal equivalence classes of irreducible admissible representations of $G(K)$) and $\Phi(G)$ ("admissible" homomorphisms from the Weil group of $K$ into the $L$-group of $G$, modulo inner automorphisms). He then writes down a surjection from $\Pi(G)$ to $\Phi(G)$ with finite fibres, which he constructs in what is arguably a "completely canonical" way (I am not making a precise assertion here). Langlands proves that his surjection, or correspondence as it would now be called, satisfies a whole bunch of natural properties (see for example p44 of "Automorphic $L$-functions" by Borel, available here), although there are other properties that the correspondence has which are not listed there---for example I know a statement explaining the relationship between the Galois representation attached to a $\pi$ and the one attached to its contragredient, which Borel doesn't mention, but which Jeff Adams tells me is true, and there is another statement about how infinitesimal characters work which I've not seen in the literature either.

So this raises the following question: is it possible to write down a list of "natural properties" that one would expect the correspondence to have, and then, crucially, to check that Langlands' correspondence is the unique map with these properties? Uniqueness is the crucial thing---that's my question.

Note that the analogous question for $GL_n$ over a non-arch local field has been solved, the crucial buzz-word being "epsilon factors of pairs". It was hard work proving that at most one local Langlands correspondence had all the properties required of it---these properties are listed on page 2 of Harris-Taylor's book and it's a theorem of Henniart that they suffice. The Harris-Taylor theorem is that at least one map has the required properties, and the conclusion is that exactly one map does. My question is whether there is an analogue of Henniart's theorem for an arbitrary connected reductive group in the real/complex case.
 http://mathoverflow.net/questions/31172/uniqueness-of-local-langlands-correspondence-for-connected-reductive-groups-over/31946#31946 Answer by Emerton for Uniqueness of local Langlands correspondence for connected reductive groups over real/complex field. Emerton 2010-07-15T03:04:44Z 2011-11-30T07:10:29Z
Dear Kevin,

Here are some things that you know.

(1) Every non-tempered representation is a Langlands quotient of an induction of a non-tempered twist of a tempered rep'n on some Levi, and this description is canonical.

(2) Every tempered rep'n is a summand of the induction of a discrete series on some Levi.

(3) The discrete series for all groups were classified by Harish-Chandra.

Now Langlands's correspondence is (as you wrote) completely canonical: discrete series with fixed inf. char. lie in a single packet, and the parameter is determined from the inf. char. in a precise way.

All the summands of an induction of a discrete series rep'n are also declared to lie in a single packet. So all packet structure comes from steps (1) and (2).

The correspondence is compatible in a standard way with twisting, and with parabolic induction.

So:

If we give ourselves the axioms that discrete series correspond to irred. parameters, that the correspondence is compatible with twisting, that the correspondence is compatible with parabolic induction, and that the correspondence is compatible with formation of inf. chars., then putting it all together, it seems that we can determine step 1, then 2, then 3.

I don't know if this is what you would like, but it seems reasonable to me.

Why no need for epsilon-factor style complications: because there are no supercuspidals, so everything reduces to discrete series, which from the point of view of packets are described by their inf. chars. In the p-adic world this is just false: all the supercuspidals are disc. series, they have nothing analogous (at least in any simple way) to an inf. char., and one has to somehow identify them --- hence epsilon factors to the rescue.

[Added: A colleague pointed out to me that the claim above (and also discussed below in the exchange of comments with Victor Protsak) that the inf. char. serves to determine a discrete series L-packet is not true in general. It is true if the group $G$ is semi-simple, or if the fundamental Cartan subgroups (those which are compact mod their centre) are connected. But in general one also needs a compatible choice of central character to determine the $L$-packet. In Langlands's general description of a discrete series parameter, their are two pieces of data: $\mu$ and $\lambda_0$. The former is giving the inf. char., and the latter the central char.]
 http://mathoverflow.net/questions/31172/uniqueness-of-local-langlands-correspondence-for-connected-reductive-groups-over/64491#64491 Answer by Jeffrey Adams for Uniqueness of local Langlands correspondence for connected reductive groups over real/complex field. Jeffrey Adams 2011-05-10T11:42:10Z 2011-05-10T11:42:10Z
Here is a slight refinement of Emerton's answer.

Any L-homomorphism $\phi:W_\mathbb R\rightarrow \phantom{}^LG$ defines an infinitesimal character $\lambda$ and a central character $\chi$. If $\phi(W_\mathbb R)$ is not contained in a proper Levi this defines an L-packet: the set of relative discrete series with this infinitesimal and central character (relative = discrete series modulo center). Every relative discrete series L-packet arises this way.

Now compatibility with parabolic induction determines all L-packets as follows. If $\phi(W_\mathbb R)$ is contained in a proper Levi subgroup $\phantom{}^LM$, the preceding construction defines a relative discrete series L-packet for $M$. The L-packet for $G$ is defined to be the irreducible summands of $Ind_{MN}^G(\pi_M)$ as $\pi_M$ runs over the L-packet of $M$ (for the correct choice of $N$). This induction can be done in stages: a tempered step, which is completely reducible, followed by an induction which gives unique irreducible summands. (This incorporates the "twisting" mentioned above).

As Emerton says this is canonical since we don't need L or epsilon factors to define relative discrete series L-packets. I'd like to know if anything like this, however speculative, might hold for general p-adic groups; in particular whether epsilon factors really do come to the rescue outside of GL(n) and perhaps classical groups. See http://mathoverflow.net/questions/24376.


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# Solar Luminosity

In Astrophysical, the solar luminosity is the unit of Luminosité conventionally used to express the luminosity of the star S. It is equal to that of the Sun.

Its symbol and its value are:

$L_ \left\{\ odot\right\} = 3,826 \ times 10^ \left\{26\right\} \; \left\{\ rm W\right\}$.

In the System cgs, the numerical value of the solar luminosity is multiplied by 10 7 since the Watt (or Joule by second) is replaced by the Erg by second. The solar luminosity becomes, in approached value,

$L_ \left\{\ odot\right\} \ simeq 4 \ times 10^ \left\{33\right\} \; \left\{\ rm erg\right\} \ cdot \left\{\ rm S\right\} ^ \left\{- 1\right\}$.
The solar unit of Masse is, it, of approximately 2× 10 33   G. Also, in these units, the numerical value of the solar luminosity is it in these units about the double of that of the solar mass. In other words L   /  M   ~  2.

## See too

 Random links: MenuetOS | Terciario | Giordano saver | Championship of Switzerland of football 1975-1976 | 1935 in Canada | Brian P. Schmidt | Liste_d'aéroports_par_code_de_l'A.I.T.A_:_B


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# Thrifty numbers Part 4

Logic Level 2

$\large{ \square \, + \, \square \, = \, \square \\ \square \, - \, \square \, = \, \square \\ \square \, \times \, \square \, = \, \square \\ \square \, \div \, \square \, = \, \square \\ }$

Given that the integers $$0,1,2,\ldots,9$$ are to be filled in all the twelve square boxes above such that all four equations above are satisfied.

What is the maximum possible distinct number of integers used?

Details and Assumptions

• You can use the same integer more than once.

• You are not required to use all nine integers.

• Each square box can only fill in exactly one digit.

×


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# How to debug framerate drops with VBOs, OpenGL

I'm working on an experimental app to test how VBOs perform when rendering a minecraft-like world. If the performance is better than what I use now I'll update my actual game. Based on what everyone says, VBOs should totally be the right direction, but it's really hard making that become a reality.

I've finally gotten to a point where I've replicated culling block faces, I'm properly using the buffer IDs to render and not building the VBO every frame - there's no a ton of performance tweaking left aside from:

• Using an indexed system so I can send fewer vertices
• Using a ByteBuffer for my color/texture values instead of floats (I need to find a good way, right now everything is interleaved)
• I could take block face culling a little further because in the test app, they don't check across chunks for solid blocks.

My primary issue is that for some reason, when I render 15x16 chunks (16x16x16 blocks per chunk in my test app) the performance and rendering is great. Movement is fluid, 60fps.

At 16x16 chunks, performance drops to like 5fps. I've run profiling like VisualVM and see no unusual differences in the speeds/memory of the code between the two states. It's odd how the addition of one extra row of chunks can take performance down so much - there must be some specific threshold I cross.

How can I better debug what's happening? Where should I be looking? There are no console errors.

This test app is open source so you can look at the code:

Update I've updated my actual game with the VBO work I've been doing in this test app and the performance of the 10x10 grid of chunks (16x16x128) was so horrid that my system took minutes to allow me to kill the app. I'll certainly spend some time adjusting things and making sure that it's performance-tuned for my app, but wow - still not seeing how VBOs are all they're cracked up to be.

• are you using VBO per chunk? or per block? – concept3d Dec 9 '13 at 9:09
• The buffer is per chunk – BotskoNet Dec 9 '13 at 17:16

For the actual problem (slow rendering of VBO), you might try to use instancing. That only helps if you have hundreds or thousands of objects to render.

You can debug the problem several ways. AMD Perfstudio and Nvidia Nsight are tools for getting debug data from the GPU. You could use those to try to find out the problem.

Another way to debug the problem is to measure the time each operation takes. Timing a certain operation looks like this:

glFinish(); // Make sure there is no work queued in the GPU
double timeBefore = getCurrentTime(); // milliseconds
theGlDrawCallOrBufferUpdateEtc(); // the GL function you want to measure
glFinish(); // Finish that
double timeAfter = getCurrentTime();

double timeTheFunctionTook = timeAfter - timeBefore;

This might give you a hint of which GL calls are causing the lag. You can use the same thing to measure any other parts of the code too. if there are no GL calls, just drop the glFinish() calls as they are not required then.

• I looked into instancing quite a but but people advised that it's not useful when each block only has certain faces visible. – BotskoNet Dec 11 '13 at 16:01


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# If $G$ is a group and $g\in G$, then for all $n,m\in\mathbb{Z}$, we have the following properties.

Proof attempt:

(a) $$g^ng^m=g^{n+m}$$

(b) $$(g^n)^{-1}=g^{-n}$$

Proof(informal rough draft).

(a) Since $$g\in G$$, we can rewrite $$g^n=gg...g$$ for n-factors of $$g$$ and $$g^m=gg...g$$ for m-factors of $$g$$, since rules of exponents still hold for groups(given definition in the book). If $$G$$ is under a group under addition, we can add the exponents to obtain $$g^ng^m=g^{n+m}$$.

Have not yet began (b).

Thoughts? This is an intro to group theory/proof class so instructor said it should be simple yet very direct.

• If the basis of your proof is "rules of exponents still hold for groups," then you're just assuming exactly what you're trying to prove... so I think you're oversimplifying it. A better way is to do a quick induction argument. – user296602 Feb 1 at 2:54
• You are writing the group multiplicatively, not additively. You are adding integers $m$ and $n$. – J. W. Tanner Feb 1 at 2:57
• How does your book define $g^n$ for $n \in \mathbb{Z}$? – Theo Bendit Feb 1 at 2:57
• For (b), it suffices to show $(g^n)(g^{-n})$ is the identity element. – angryavian Feb 1 at 3:01
• @Ryan Ugh. I much prefer a recursive definition, as it's more precise and easier to work with in proofs. But, also importantly, how do they define $g^{-n}$ for $n > 0$? Is it just $(g^{-1})^n$? – Theo Bendit Feb 1 at 3:05

Your proof of part (a) is, as mentioned in the comments, not a proof; you are assuming that which you wish to show. Furthermore, writing "If $$G$$ is under a group [sic] under addition, we can add the exponents to obtain $$g^n g^m = g^{n+m}$$ is not just assuming that which you want to show, but also is misleading: this identity holds in any group, and the question asks you to show that it indeed holds for any group, not just a group with addition as its operation.
For part (a), you say that the definition of $$g^n$$ that you were given is as the product of $$n$$ copies of $$g$$. What happens if you multiply $$n$$ copies of $$g$$, and then multiply this by $$m$$ copies of $$g$$? How do you write this product in your group, before and after you carry out the multiplication?
For part (b), as stated in the comments, it suffices to show that $$g^n g^{-n}$$ is the identity element. As (presumably, analogous to the definition in (a)) the definition of $$g^{-n}$$ given is the product of $$n$$ copies of $$g^{-1}$$, what would you get if you first multiply $$n$$ copies of $$g$$, followed by $$n$$ copies of $$g^{-1}$$? How would you write either product in $$G$$?


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# Convexity of the set of gradients of a convex function

If $\vec{y}_1$ and $\vec{y}_2$ are the gradients of a differentiable convex function $f(x)$ at points $\vec{x}_1$ and $\vec{x}_2$ does there exist a $\nabla f^{-1}( \alpha \vec{y}_1 + (1-\alpha)\vec{y}_2)$ in the domain of $f.$

The forward image of the domain mapped by the gradient is the domain of the Legendre conjugate so I think the above is true. If you could point me to a proof that will be very helpful.

I can see that the Legendre conjugate is convex because it is a supremum of affine functions, but am looking for a more direct intuition / construction for the forward image of the domain mapped by the gradient. What is bothering me is what happens when the supremum that is used to define the conjugate is not achieved. The value of the conjugate is set to $\infty$ but is there a way to show that the set over which the supremum is achieved is convex (even if $f$ is unbounded below).

-


text:
# zbMATH — the first resource for mathematics

Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor. (English) Zbl 1294.53006
The authors introduce the notion of biconservative surfaces. They first find the PDE that satisfies the mean curvature function of a biconservative surface in a three dimensional space form. Then, the paper is devoted to the local classification of biconservative surfaces in three dimensional space forms. This is done in three sections in which they examine separately the cases of surfaces in the Euclidean space, in the sphere and in the hyperbolic space.

##### MSC:
 53A05 Surfaces in Euclidean and related spaces 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 49Q10 Optimization of shapes other than minimal surfaces
Full Text:
##### References:
 [1] Balmuş, A., Montaldo, S., Oniciuc, C.: Biharmonic PNMC submanifolds in spheres. Ark. Mat. (to appear) · Zbl 1282.53047 [2] Balmuş, A.; Montaldo, S.; Oniciuc, C., Properties of biharmonic submanifolds in spheres, J. Geom. Symmetry Phys., 17, 87-102 (2010) · Zbl 1195.53080 [3] Balmuş, A.; Montaldo, S.; Oniciuc, C., Biharmonic hypersurfaces in 4-dimensional space forms, Math. Nachrichten, 283, 1696-1705 (2010) · Zbl 1210.58013 [4] Balmuş, A.; Montaldo, S.; Oniciuc, C., Classification results for biharmonic submanifolds in spheres, Israel J. Math., 168, 201-220 (2008) · Zbl 1172.58004 [5] Baird, P., Eells, J.: A conservation law for harmonic maps. In: Geometry Symposium, Utrecht 1980, pp. 1-25, Lecture Notes in Mathematics, 894. Springer, Berlin (1981) · Zbl 0485.58008 [6] Caddeo, R.; Montaldo, S.; Oniciuc, C., Biharmonic submanifolds in spheres, Israel J. Math., 130, 109-123 (2002) · Zbl 1038.58011 [7] Chen, B-Y, Total Mean Curvature and Submanifolds of Finite Type. Series in Pure Mathematics 1 (1984), Singapore: World Scientific, Singapore [8] Chen, B-Y, Some open problems and conjectures on submanifolds of finite type, Soochow J. Math., 17, 169-188 (1991) · Zbl 0749.53037 [9] Chen, B-Y; Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces, Mem. Fac. Sci. Kyushu Univ. Ser. A, 45, 323-347 (1991) · Zbl 0757.53009 [10] Do Carmo, M.; Dajczer, M., Rotation hypersurfaces in spaces of constant curvature, Trans. Am. Math. Soc., 277, 685-709 (1983) · Zbl 0518.53059 [11] Eells, J.; Sampson, Jh, Harmonic mappings of Riemannian manifolds, Am. J. Math., 86, 109-160 (1964) · Zbl 0122.40102 [12] Eells, J., Lemaire, L.: Selected topics in harmonic maps. In: CBMS Regional Conference Series in Mathematics, 50. American Mathematical Society, Providence (1983) · Zbl 0515.58011 [13] Hasanis, Th; Vlachos, Th, Hypersurfaces in $$\mathbb{E}^4$$ with harmonic mean curvature vector field, Math. Nachrichten, 172, 145-169 (1995) · Zbl 0839.53007 [14] Hilbert, D., Die grundlagen der physik, Math. Ann., 92, 1-32 (1924) [15] Jiang, Gy, The conservation law for 2-harmonic maps between Riemannian manifolds, Acta Math. Sin., 30, 220-225 (1987) · Zbl 0631.58007 [16] Loubeau, E.; Montaldo, S., Biminimal immersions, Proc. Edinb. Math. Soc., 51, 421-437 (2008) · Zbl 1144.58010 [17] Loubeau, E.; Montaldo, S.; Oniciuc, C., The stress-energy tensor for biharmonic maps, Math. Z., 259, 503-524 (2008) · Zbl 1139.58010 [18] Oniciuc, C., Biharmonic maps between Riemannian manifolds, An. Ştiinţ. Univ. Al. I. Cuza. Iaşi. Mat. (N.S.), 48, 237-248 (2002) · Zbl 1061.58015 [19] Ou, Y-L, Biharmonic hypersurfaces in Riemannian manifolds, Pac. J. Math., 248, 217-232 (2010) · Zbl 1205.53066 [20] Ou, Y.-L.; Wang, Z.-P., Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries, J. Geom. Phys., 61, 1845-1853 (2011) · Zbl 1227.58004 [21] Sanini, A., Applicazioni tra varietà riemanniane con energia critica rispetto a deformazioni di metriche, Rend. Mat., 3, 53-63 (1983) · Zbl 0514.53037 [22] Sasahara, T.: Surfaces in Euclidean 3-space whose normal bundles are tangentially biharmonic. Arch. Math. (Basel), to appear · Zbl 1253.53007
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.


text:
# First European Physical Society Conference on Gravitation

19-21 February 2019
"Sapienza" University, Phys. Dept. Marconi
Europe/Rome timezone

## MICROSCOPE: while waiting for the final results

21 Feb 2019, 09:35
35m
Aula Amaldi ("Sapienza" University, Phys. Dept. Marconi)

### Aula Amaldi

#### "Sapienza" University, Phys. Dept. Marconi

Rome
talk Gravity: Experiments

### Speaker

Prof. Joel Bergé (ONERA / Paris Saclay University)

### Description

MICROSCOPE is a CNES-ESA-DLR-ONERA-CNRS-OCA-ZARM space mission that aimed to test the Weak Equivalence Principle (WEP) at the $10^{-15}$ level, i.e. two orders of magnitude better than the best "pre-MICROSCOPE" on-ground tests. The WEP is the cornerstone of General Relativity, the postulate that led Einstein to establish his theory: it states that all bodies fall at the same rate, independently of their mass and composition. Alternative theories of gravity, like those developed to overcome such conundrums as dark energy or the unification of gravity with the forces of the standard model of particle physics, generically predict a small violation of the WEP. As a consequence, not only does MICROSCOPE test the very foundation of General Relativity, but it also provides new constraints on theories beyond Einstein's.

Launched on April 25, 2016, the MICROSCOPE satellite and its scientific instruments provided high-quality data during the entire mission, which came to its end on October 16, 2018. The first results, based on 7% of the total data, ruled out a violation of the WEP greater than $2\times10^{-14}$. Since then, more data have been taken and additional analyses have been conducted to better constrain the level of systematic errors. While the remaining data is still being analysed, the final MICROSCOPE results should come closer to the $10^{-15}$ precision; they should be published at the end of 2019.

In this talk, I will first introduce the MICROSCOPE mission, in particular its scientific goals and measurement principles. Then, I will discuss its first results and mention what constraints MICROSCOPE can bring on some modified gravity models.

### Primary author

Prof. Joel Bergé (ONERA / Paris Saclay University)


text:
• October 18, 2021, 02:41:19 AM
• Welcome, Guest

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AuthorTopic: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!  (Read 78046 times)

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kaxII

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #36 on: October 16, 2012, 02:38:57 PM »

I would like to ask is it me or is the stall speed extremely high and why is there no aileron trim? As if I do a tight turn even at 320km/h I will stall, also the roll to the right is extremely big to not have aileron trim. I can also not trim it through the rudder as it just makes it less controllable and males it yaw to the left.
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LuseKofte

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #37 on: October 16, 2012, 02:49:30 PM »

Stall is not always a speed related thing, the typhoon was a big disappointment for RAF until they discovered its ability as a weapon plattform . RAF modern fighters (WWII) the Spitfire was really a bad weapon platform.  There are many articles about its bad handling character around. a FM discussion is deemed to fail since getting the right performance in this game means something else is wrong. In this game you need to focus on the performance the planewas known to have and face the consequences  in other aspect
Correcting every tiny bit will make all planes a P 51, if you know what I mean.
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crazyflak

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #38 on: October 16, 2012, 02:59:20 PM »

Unfortunately, we don't have FM experts anymore, so the FMs cannot truly be fine-tuned.

I have to say, though, that Birdman did his best to correct some shortcomings of my initial rough FM that departed from Tempest (all previous Typhoons simply took Tempest FM, which is very obviously unnatural, as its design is entirely different) and adopted Hurricane as base (wings and control surfaces from typhoon are of same design than Hurricane).

About aileron trim, you're right, I just checked and indeed the FM has it set to 0 (=none) which might be an overlook, but I doubt, as most aileron trims could not be adjusted in flight. I have to go check my typhoon book just to be sure before amending the possible mistake. Thank you for noticing it out.
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LuseKofte

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #39 on: October 16, 2012, 03:16:47 PM »

Oh I never use the ailerontrim
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karo

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #40 on: October 17, 2012, 03:08:42 PM »

Kaxii, Typhoon or Tempest?

I would like to ask is it me or is the stall speed extremely high

The laminar flow wing - that should explain everything
and why is there no aileron trim?

There was not aileron trim on the real plane too. (I'm 90% sure about it, but I will check my books again)
I would like to ask is it me or is the stall speed extremely high and why is there no aileron trim? As if I do a tight turn even at 320km/h I will stall, also the roll to the right is extremely big to not have aileron trim.
320km/h? .... You have to fly it faster, much faster or to use combat flaps.

Tempest is one of my favorite planes in the game
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CWMV

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #41 on: October 17, 2012, 07:36:56 PM »

320kph??? What are you doing so slowin a tempest?
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andylamb1

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #42 on: October 19, 2012, 04:08:44 AM »

I'm lost after many hours of head scratching as to how to get the listed set of weapons playable for the Tiffi (25Lb anti ship and anti personelle rockets). Don't know if i'm missing another mod or something, but it's making me cry  .

Anyhoo, what fantastic addition to this now class act of a sim (and getting greater all the time, thanks to the whole community).

Many thanks to  Ranwers, Josse, Flakiten, et al for all your hard work.

andy

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osakaboy

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #43 on: October 20, 2012, 03:54:32 AM »

Just a quick note incase the original poster was refering to the Sea Fury, indeed the Sea fury did have aileron trim BUT it could only be adjusted on the ground before or after flight. So our model is correct in having no inflight aileron trim.
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kaxII

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #44 on: October 20, 2012, 04:02:39 AM »

320kph??? What are you doing so slowin a tempest?

i dunno it just doesn't go faster than 400km for me although my new joystick has marginally helped but i think my tempest is lazy and hates me because im not treting properly
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GilB57

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #45 on: October 31, 2012, 06:57:14 AM »

Hi everybody !

I found some skin bug on new Typhie when viewed from inside cockpit (look on the right):

I wondered what was the problem and finally solved it (on the left): it seems that the part of the skin used to "paint" fuselage in front of cockpit remains unherited from Tempest skin.
Fortunately, despite this part is already used for the canopy frame, it's possible to fix this awfull black patches & lines.

Are you interested in corrected skins and default skins ?
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kaxII

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #46 on: October 31, 2012, 07:19:01 AM »

Post a link of the updates and try will probably put it into the pack, also I have a glitch on the sea tempest where I can not see the small dot in the reticule when viewing from the normal FOV.
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GilB57

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Re: Typhoon & Tempest (+Seafury) family upgrade (Beta) V2c update!
« Reply #47 on: October 31, 2012, 08:38:08 AM »

In order to do this update, I need to know one little thing : the name of the fuselage part BEHING cockpit (were the little antenna is attached) is it CF_D0 or CF_D1 or another ?

(because I think I didn't gave the good parent in hier.him file:

The antenna still there    )
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