text:
# Triangle wave

A bandlimited triangle wave pictured in the time domain (top) and frequency domain (bottom). The fundamental is at 220 Hz (A3).

A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.

Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse).

## Definitions

Sine, square, triangle, and sawtooth waveforms

### Definition

A triangle wave of period p that spans the range [0,1] is defined as:

${\displaystyle x(t)=2\left|{t \over p}-\left\lfloor {t \over p}+{1 \over 2}\right\rfloor \right|}$

where ${\displaystyle \lfloor \,\ \rfloor }$ is the floor function. This can be seen to be the absolute value of a shifted sawtooth wave.

For a triangle wave spanning the range [-1,1] the expression becomes:

${\displaystyle x(t)=2\left|2\left({t \over p}-\left\lfloor {t \over p}+{1 \over 2}\right\rfloor \right)\right|-1.}$

A more general equation for a triangle wave with amplitude ${\displaystyle a}$ and period ${\displaystyle p}$ using the modulo operation and absolute value is:

Triangle wave with amplitude=5, period=4
${\displaystyle y(x)={\frac {4a}{p}}\left|\left(\left(x-{\frac {p}{4}}\right){\bmod {p}}\right)-{\frac {p}{2}}\right|-a.}$

E.g., for a triangle wave with amplitude 5 and period 4:

${\displaystyle y(x)=5{\bigl |}\left((x-1){\bmod {4}}\right)-2{\bigr |}-5.}$

A phase shift can be obtained by altering the value of the ${\displaystyle -p/4}$ term, and the vertical offset can be adjusted by altering the value of the ${\displaystyle -a}$ term.

As this only uses the modulo operation and absolute value, it can be used to simply implement a triangle wave on hardware electronics.

Note that in many programming languages, the % operator is a remainder operator (with result the same sign as the dividend), not a modulo operator; the modulo operation can be obtained by using ((x % p) + p) % p in place of x % p. In e.g. JavaScript, this results in an equation of the form 4*a/p * Math.abs((((x-p/4)%p)+p)%p - p/2) - a.

### Relation to Square Wave

The triangle wave can also be expressed as the integral of the square wave:

${\displaystyle x(t)=\int _{0}^{t}\operatorname {sgn} \left(\sin {\frac {u}{p}}\right)\,du.}$

### Expression in Trigonometric functions

A triangle wave with period p and amplitude a can be expressed in terms of sine and arcsine (whose value ranges from −π/2 to π/2):

${\displaystyle y(x)={\frac {2a}{\pi }}\arcsin \left(\sin \left({\frac {2\pi }{p}}x\right)\right).}$

The identity ${\textstyle \cos {x}=\sin \left({\frac {p}{4}}-x\right)}$ can be used to convert from a triangle "sine" wave to a triangular "cosine" wave. This phase-shifted triangle wave can also be expressed with cosine and arccosine:

${\displaystyle y(x)=a-{\frac {2a}{\pi }}\arccos \left(\cos \left({\frac {2\pi }{p}}x\right)\right).}$

### Expressed as Alternating Linear Functions

Another definition of the triangle wave, with range from −1 to 1 and period p, is:

${\displaystyle x(t)={\frac {4}{p}}\left(t-{\frac {p}{2}}\left\lfloor {\frac {2t}{p}}+{\frac {1}{2}}\right\rfloor \right)(-1)^{\left\lfloor {\frac {2t}{p}}+{\frac {1}{2}}\right\rfloor }}$

### Harmonics

Animation of the additive synthesis of a triangle wave with an increasing number of harmonics. See Fourier Analysis for a mathematical description.

It is possible to approximate a triangle wave with additive synthesis by summing odd harmonics of the fundamental while multiplying every other odd harmonic by −1 (or, equivalently, changing its phase by π) and multiplying the amplitude of the harmonics by one over the square of their mode number, n (which is equivalent to one over the square of their relative frequency to the fundamental).

The above can be summarised mathematically as follows:

{\displaystyle {\begin{aligned}x_{\mathrm {triangle} }(t)&{}={\frac {8}{\pi ^{2}}}\sum _{i=0}^{N-1}(-1)^{i}n^{-2}\sin \left(2\pi f_{0}nt\right)\end{aligned}}}

where N is the number of harmonics to include in the approximation, t is the independent variable (e.g. time for sound waves), ${\displaystyle f_{0}}$ is the fundamental frequency, and i is the harmonic label which is related to its mode number by ${\displaystyle n=2i+1}$.

This infinite Fourier series converges quickly to the triangle wave as N tends to infinity, as shown in the animation.

## Arc length

The arc length per period for a triangle wave, denoted by s, is given in terms of the amplitude a and period length p by

${\displaystyle s={\sqrt {(4a)^{2}+p^{2}}}.}$


text:
Journal article Open Access

Detecting African hoofed animals in aerial imagery using convolutional neural network

Yunfei Fang; Shengzhi Du; Larbi Boubchir; Karim Djouani

Citation Style Language JSON Export

{
"DOI": "10.11591/ijra.v10i2.pp133-143",
"container_title": "IAES International Journal of Robotics and Automation (IJRA)",
"title": "Detecting African hoofed animals in aerial imagery using  convolutional neural network",
"issued": {
"date-parts": [
[
2021,
6,
1
]
]
},
"abstract": "
Small unmanned aerial vehicles applications had erupted in many fields including conservation management. Automatic object detection methods for such aerial imagery were in high demand to facilitate more efficient and economical wildlife management and research. This paper aimed to detect hoofed animals in aerial images taken from a quad-rotor in Southern Africa. Objects captured in this way were small both in absolute pixels and from an object-to-image ratio point of view, which were not perfectly suit for general purposed object detectors. We proposed a method based on the iconic Faster region-based convolutional neural networks (R-CNN) framework with atrous convolution layers in order to retain the spatial resolution of the feature map to detect small objects. A good choice of anchors was of prime importance in detecting small objects. The performance of the proposed Faster R-CNN with atrous convolutional filters in the backbone network was proven to be outstanding in our scenario by comparing to other object detection architectures.
",
"author": [
{
"family": "Yunfei Fang"
},
{
"family": "Shengzhi Du"
},
{
"family": "Larbi Boubchir"
},
{
"family": "Karim Djouani"
}
],
"page": "133-143",
"volume": "10",
"type": "article-journal",
"issue": "2",
"id": "5787947"
}
27
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format: plain


text:
Why did recombination make the universe transparent?

It is commonly said that after the universe cooled enough for ionized Hydrogen to settle down into neutral Hydrogen, i.e. recombination, the universe became transparent. A reason I have heard for this is that most photons don’t have the right energy to be absorbed by H atoms.

But the free electrons before recombination weren’t absorbing the photons either, they were scattering them. Doesn’t light still scatter off bound electrons? For instance, my understanding is that Compton’s original experiment on Compton scattering used graphite as the source of electrons. Certainly then, photons were scattering off the electrons bound in carbon atoms?

I suspect the answer has something to do with the scattering cross section of bound electrons in neutral Hydrogen being much less than that of free electrons, but then why is that the case?

• Are you asking why neutral hydrogen is transparent to visible light? Feb 16 '19 at 22:25
• Yes, that is what I’m asking. Feb 16 '19 at 22:39
• Similar discussion- physics.stackexchange.com/questions/25447/… Feb 17 '19 at 7:11
• Related, yes, but still doesn’t answer my question above. Most answers in that post simply state that neutral hydrogen is transparent without addressing the issue I raise above, about light still being able to scatter off bound electrons. Feb 20 '19 at 22:43

The scattering cross-section for free electrons is known as the Thomson scattering cross-section $$\sigma_T$$.

It is relatively easy to show that once the electrons are bound, the cross-section can be treated like that of a damped harmonic oscillator. If the oscillator is driven at frequencies below the resonant frequency $$\omega_r$$, then the (Rayleigh) scattering cross-section goes as $$\sigma_T (\omega/\omega_r)^4$$.

After recombination most of the hydrogen atoms are in the ground state, so the lowest energy resonance corresponds to Lyman alpha absorption in the UV. But most photons have frequencies in the infrared, much lower than the resonant frequency, so $$\omega \ll \omega_r$$. Hence the scattering cross-section is orders of magnitude lower than $$\sigma_T$$.

When a photon with insufficient energy to move an electron from one energy level to a higher energy level (including to complete ionization) the photon may change direction, but not energy. During a period of time, say e.g. one second, about the same same number of photons move towards the observer, just as if there were no atoms in the way. That is, for each photon that was heading for the observer, and gets deflected to a different direction, there will (on the average) be another photon not heading towards the observer, but after hitting an electron it gets deflected to move exactly towards the observer.

Only a very small fraction of photons emitted from the last ionized atoms will move the energy of an electron high enough so that photons of a different energy are subsequently emitted.

I hope you find this answer to be acceptable.


text:
# 3.1 Complex fourier series

Definition of the complex Fourier series.

In an earlier module , we showed that a square wave could be expressed as a superposition of pulses. As useful asthis decomposition was in this example, it does not generalize well to other periodic signals:How can a superposition of pulses equal a smooth signal like a sinusoid?Because of the importance of sinusoids to linear systems, you might wonder whether they could be added together to represent alarge number of periodic signals. You would be right and in good company as well. Euler and Gauss in particular worried about this problem, and Jean Baptiste Fourier got the credit even though tough mathematical issues were notsettled until later. They worked on what is now known as the Fourier series : representing any periodic signal as a superposition of sinusoids.

But the Fourier series goes well beyond being another signal decomposition method.Rather, the Fourier series begins our journey to appreciate how a signal can be described in either the time-domain or the frequency-domain with no compromise. Let $s(t)$ be a periodic signal with period $T$ . We want to show that periodic signals, even those that haveconstant-valued segments like a square wave, can be expressed as sum of harmonically related sine waves: sinusoids having frequencies that are integer multiples of the fundamental frequency . Because the signal has period $T$ , the fundamental frequency is $\frac{1}{T}$ . The complex Fourier series expresses the signal as a superposition ofcomplex exponentials having frequencies $\frac{k}{T}$ , $k=\{\text{…}, -1, 0, 1, \text{…}\}$ .

$s(t)=\sum_{k=()}$ c k 2 k t T
with ${c}_{k}=\frac{1}{2}({a}_{k}-i{b}_{k})$ . The real and imaginary parts of the Fourier coefficients ${c}_{k}$ are written in this unusual way for convenience in defining the classic Fourier series.The zeroth coefficient equals the signal's average value and is real- valued for real-valued signals: ${c}_{0}={a}_{0}$ . The family of functions $\{e^{i\frac{2\pi kt}{T}}\}$ are called basis functions and form the foundation of the Fourier series. No matter what theperiodic signal might be, these functions are always present and form the representation's building blocks. They depend on thesignal period $T$ , and are indexed by $k$ .
Assuming we know the period, knowing the Fourier coefficientsis equivalent to knowing the signal. Thus, it makes no difference if we have a time-domain or a frequency-domain characterization of the signal.

What is the complex Fourier series for a sinusoid?

Because of Euler's relation,

$\sin (2\pi ft)=\frac{1}{2i}e^{i\times 2\pi ft}-\frac{1}{2i}e^{-(i\times 2\pi ft)}$
Thus, ${c}_{1}=\frac{1}{2i}$ , ${c}_{-1}=-\left(\frac{1}{2i}\right)$ , and the other coefficients are zero.

To find the Fourier coefficients, we note the orthogonality property

$\int_{0}^{T} e^{i\frac{2\pi kt}{T}}e^{-i\frac{2\pi lt}{T}}\,d t=\begin{cases}T & \text{if k=l}\\ 0 & \text{if k\neq l}\end{cases}$
Assuming for the moment that the complex Fourier series "works," we can find a signal's complex Fourier coefficients, its spectrum , by exploiting the orthogonality properties of harmonically related complexexponentials. Simply multiply each side of [link] by $e^{-(i\times 2\pi lt)}$ and integrate over the interval $\left[0,T\right]$ .
$\begin{array}{l}{c}_{k}=\frac{1}{T}\int_{0}^{T} s(t)e^{-(i\frac{2\pi kt}{T})}\,d t\\ {c}_{0}=\frac{1}{T}\int_{0}^{T} s(t)\,d t\end{array}$

Finding the Fourier series coefficients for the square wave ${\mathrm{sq}}_{T}(t)$ is very simple. Mathematically, this signal can be expressed as ${\mathrm{sq}}_{T}(t)=\begin{cases}1 & \text{if 0< t< \frac{T}{2}}\\ -1 & \text{if \frac{T}{2}< t< T}\end{cases}$ The expression for the Fourier coefficients has the form

${c}_{k}=\frac{1}{T}\int_{0}^{\frac{T}{2}} e^{-(i\frac{2\pi kt}{T})}\,d t-\frac{1}{T}\int_{\frac{T}{2}}^{T} e^{-(i\frac{2\pi kt}{T})}\,d t$
When integrating an expression containing $i$ , treat it just like any other constant.
The two integrals are very similar, one equaling the negative of theother. The final expression becomes
${c}_{k}=\frac{-2}{i\times 2\pi k}(-1^{k}-1)=\begin{cases}\frac{2}{i\pi k} & \text{if k\text{odd}}\\ 0 & \text{if k\text{even}}\end{cases}$
$\mathrm{sq}(t)=\sum_{k\in \{\dots , -3, -1, 1, 3, \dots \}} \frac{2}{i\pi k}e^{(i)\frac{2\pi kt}{T}}$
Consequently, the square wave equals a sum of complex exponentials, but only those having frequencies equal to odd multiples of thefundamental frequency $\frac{1}{T}$ . The coefficients decay slowly as the frequency index $k$ increases. This index corresponds to the $k$ -th harmonic of the signal's period.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
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Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
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Rafiq
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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write examples of Nano molecule?
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The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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# NuTeV

Other Web pages: INSPIRE

(Note: The process can take some time.)

## References

#### 1 - Neutrino Oscillations

[1-1]
A search for $\nu_\mu\to\nu_e$ and $\bar\nu_\mu\to\bar\nu_e$ oscillations at NuTeV, S. Avvakumov et al. (NuTeV), Phys. Rev. Lett. 89 (2002) 011804, arXiv:hep-ex/0203018.
[Avvakumov:2002jj]

#### 2 - Physics

[2-1]
On the Effect of Asymmetric Strange Seas and Isospin-Violating Parton Distribution Functions on $\sin^2\theta_W$ Measured in the NuTeV Experiment, G. P. Zeller et al. (NuTeV), Phys. Rev. D65 (2002) 111103, arXiv:hep-ex/0203004.
[Zeller:2002du]
[2-2]
A precise determination of electroweak parameters in neutrino nucleon scattering, G. P. Zeller et al. (NuTeV), Phys. Rev. Lett. 88 (2002) 091802, arXiv:hep-ex/0110059.
From the abstract: The NuTeV collaboration has extracted the electroweak parameter sin2θW from the measurement of the ratios of neutral current to charged current neutrino and anti-neutrino cross-sections. Our value, sin2θW(on-shell)=0.2277±0.0013(stat)±0.0009(syst), is three standard deviations above the standard model prediction.
[Zeller:2001hh]
[2-3]
Extraction of R = sigma(L)/sigma(T) from CCFR $\nu_\mu$ Fe and $\bar\nu_\mu$ Fe differential cross sections, Un-Ki Yang et al. (CCFR/NuTeV), Phys. Rev. Lett. 87 (2001) 251802, arXiv:hep-ex/0104040.
[Yang:2001xc]
[2-4]
Observation of an anomalous number of dimuon events in a high energy neutrino beam, T. Adams et al. (NuTeV), Phys. Rev. Lett. 87 (2001) 041801, arXiv:hep-ex/0104037.
[2-5]
Search for the lepton number violating process $\bar\nu_\mu e^- \to \mu^- \bar\nu_e$, J. A. Formaggio et al. (NuTeV), Phys. Rev. Lett. 87 (2001) 071803, arXiv:hep-ex/0104029.
[Formaggio:2001jz]
[2-6]
Precise measurement of dimuon production cross-sections in $\nu_\mu$ Fe and $\bar\nu_\mu$ Fe deep inelastic scattering at the Tevatron, M. Goncharov et al. (NuTeV), Phys. Rev. D64 (2001) 112006, arXiv:hep-ex/0102049.
[Goncharov:2001qe]
[2-7]
A first measurement of low $x$ low $Q^2$ structure functions in neutrino scattering, B. T. Fleming et al. (CCFR), Phys. Rev. Lett. 86 (2001) 5430-5433, arXiv:hep-ex/0011094.
[Fleming:2000bg]
[2-8]
New measurements of nucleon structure functions from CCRF/NuTeV, A. Bodek et al. (CCRF/NuTeV), Int. J. Mod. Phys. A16 (2001) 202-204, arXiv:hep-ex/0009061.
[Bodek:2000pj]
[2-9]
Measurements of F2 and xF3(nu) - xF3(anti-nu) from CCFR $\nu_\mu$ Fe and $\bar\nu_\mu$ Fe data in a physics model independent way, Un-Ki Yang et al. (CCFR/NuTeV), Phys. Rev. Lett. 86 (2001) 2742-2745, arXiv:hep-ex/0009041.
[Yang:2000ju]
[2-10]
Observation of anomalous dimuon events in the NuTeV decay detector, T. Adams et al. (NuTeV), Int. J. Mod. Phys. A16 (2001) 761-763, arXiv:hep-ex/0009007.
[2-11]
Observation of neutral current charm production in $\nu_\mu$ Fe scattering at the Tevatron, A. Alton et al. (NuTeV), Phys. Rev. D64 (2001) 012002, arXiv:hep-ex/0008068.
[Alton:2000ze]
[2-12]
Search for light-to-heavy quark flavor changing neutral currents in $\nu_\mu$ N and $\bar\nu_\mu$ N scattering at the Tevatron, A. Alton et al. (NuTeV), Phys. Rev. D63 (2001) 012001, arXiv:hep-ex/0007059.
[Alton:2000vv]
[2-13]
Search for a 33.9-MeV/c**2 neutral particle in pion decay, J. A. Formaggio et al. (NuTeV), Phys. Rev. Lett. 84 (2000) 4043-4046, arXiv:hep-ex/9912062.
[Formaggio:1999ne]
[2-14]
Evidence for diffractive charm production in $\nu_\mu$ Fe and $\bar\nu_\mu$ Fe scattering at the Tevatron, T. Adams et al. (NuTeV), Phys. Rev. D61 (2000) 092001, arXiv:hep-ex/9909041.
[2-15]
Search for neutral heavy leptons in a high-energy neutrino beam, A. Vaitaitis et al. (NuTeV), Phys. Rev. Lett. 83 (1999) 4943-4946, arXiv:hep-ex/9908011.
[Vaitaitis:1999wq]

#### 3 - Physics - Conference Proceedings

[3-1]
NuTeV Structure Function Measurement, M. Tzanov, NuTeV (NuTeV), Aip Conf. Proc. 792 (2005) 241, arXiv:hep-ex/0507040. XIII international workshop on Deep Inelastic Scattering DIS 2005.
[Tzanov:2005fu]
[3-2]
New Strange Asymmetry Results from NuTeV, D. Mason (NuTeV), arXiv:hep-ex/0405037, 2004. XXXIXth Rencontres de Moriond, QCD and high energy hadronic interactions, 2004.
[Mason:2004yf]
[3-3]
Implication of the NuTeV result on intrinsic properties of neutrinos, Michael H. Shaevitz, 2004. Nobel Symposium on Neutrino Physics, August 19-24, 2004, Haga Slott, Enkping, Sweden. http://www.physics.kth.se/nobel2004/talks/M_Shaevitz-Implication_of_the_NuTeV_result_on_intrinsic_properties_of_neutrinos.pdf.
[Shaevitz:NOBEL2004]
[3-4]
Conventional Physics Explanations for the NuTeV $sin^2\theta_W$, Kevin S. McFarland, Sven-Olaf Moch, arXiv:hep-ph/0306052, 2003. Electroweak Precision Data and the Higgs Mass, DESY-Zeuthen 28 February 2003.
From the article: The dominant source of electron neutrinos in the NuTeV beams are $K^\pm_{e3}$ decays. An interesting recent development comes from the BNL-E865 experiment which has recently measured a branching ratio for $K^\pm_{e3}$that is $6\%$ larger than the value used by NuTeV. If this result is correct, it is interesting to note that it would not disrupt the agreement between the direct and Monte Carlo measurements of the $\nu_e$ rate at NuTeV and that it would in fact {\em increase} the discrepancy of the NuTeV $\sin2\theta_W$ with the prediction by slightly less than one standard deviation.
[McFarland:2003jw]

#### 4 - Detector

[4-1]
Precision calibration of the NuTeV calorimeter, D. A. Harris et al. (NuTeV), Nucl. Instrum. Meth. A447 (2000) 377-415, arXiv:hep-ex/9908056.
[Harris:1999uv]

#### 5 - Conference Proceedings

[5-1]
NuTeV Cross Section and Structure Function Measurements, D. Naples, NuTeV (NuTeV), arXiv:hep-ex/0307005, 2003. DIS03, St. Petersburg, Russia, April 2003.
[Naples:2003ne]
[5-2]
New QCD Results from NuTeV, M. Tzanov, NuTeV (NuTeV), arXiv:hep-ex/0306035, 2003. Rencontres de Moriond, QCD and Hadronic interactions, March 2003.
[Tzanov:2003gq]
[5-3]
NuTeV Status, K. S. McFarland (NuTeV), 2003. 19th International Workshop on Weak Interactions and Neutrinos, WIN2003, October 6-11, Lake Geneva, Wisconsin, USA. http://conferences.fnal.gov/win03/Talks/Kevin%20McFarland.pdf.
[McFarland:WIN2003]
[5-4]
Standard Model Explanations for the NuTeV Electroweak Measurements, R.H. Bernstein (NuTeV), J. Phys. G29 (2003) 1919, arXiv:hep-ex/0210061. NuFact '02.
[Bernstein:2002sa]
[5-5]
Off the Mass Shell: Electroweak Physics at NuTeV, K. S. McFarland et al. (NUTEV), eConf C020620 (2002) SABT01, arXiv:hep-ex/0210010. XXII Physics in Collision Conference.
[McFarland:2002iy]
[5-6]
Electroweak Results from NuTeV, G.P. Zeller (NuTeV), arXiv:hep-ex/0207037, 2002. 37th Recontres de Moriond on Electroweak Interactions and Unified Theories, March 2002.
[Zeller:2002dx]
[5-7]
A departure from prediction: Electroweak physics at NuTeV, K. S. McFarland et al. (NuTeV), arXiv:hep-ex/0205080, 2002. Rencontres de la Vallee d'Aoste, March 2002.
[McFarland:2002rk]
[5-8]
Electroweak physics results from NuTeV, Tim Bolton (NuTeV), arXiv:hep-ex/0205079, 2002. 'QCD and High Energy Interactions', 2002 Recontres de Moriond.
[Bolton:2002rj]
[5-9]
A Departure from Prediction: Electroweak Measurements from NuTeV, M. Shaevitz et al. (NuTeV), 2002. http://www.nevis.columbia.edu/~shaevitz/talks/NuTeV_WMA_Oxford_RAL.ppt.
[Shaevitz:win02]
[5-10]
A Departure from Prediction: Measurement of Precision Electroweak Parameters at NuTeV, S. Zeller (NUTEV), 2002. The American Physical Society's 2002 Meeting of The Division Particles and Fields - DPF02 - May 24-28, 2002, Williamsburg, Virginia, U.S. http://dpf2002.velopers.net/talks/plenary/sam_zeller_talk.pdf.
[Zeller-talk:2002a]
[5-11]
New results from NuTeV, r. Bernstein (NUTEV), 2002. Fourth NuFact '02 Workshop on Neutrino Factories based on Muon Storage Rings, Imperial College, London, 1-6 July 2002. http://www.hep.ph.ic.ac.uk/NuFact02/Scientific-programme/files/Wednesday/wg3/C01_bernstein.pdf.
[Bernstein-talk:2002c]
[5-12]
Precision Electroweak Measurements from NuTeV, Tim Bolton, 2002. The American Physical Society's 2002 Meeting of The Division Particles and Fields - DPF02 - May 24-28, 2002, Williamsburg, Virginia, U.S. http://dpf2002.velopers.net/talks_pdf/536talk.pdf.
[Bolton-DPF02]
[5-13]
Departure from Prediction: Elettroweak Physics at NuTeV, K. S. McFarland (NuTeV), 2002. Les Rencontres de Physique de la Vallee d'Aoste, La Thuile, Aosta Valley, Italy, March 3-9, 2002. http://www.pi.infn.it/lathuile/2002/talks/mcfarland.pdf.
Comment: Contains information on the Energy Range of NuTeV direct measurement of the electron neutrino flux : $80 < E_{\nu} < 180 \, GeV$. It would take a 20% mistake in $\nu_e$ to move $\sin^2 \theta_W$ to SM value.
[McFarland:LaThuile2002]
[5-14]
Results from NUTEV, D. Naples (NUTEV), 2002. XXth International Conference on Neutrino Physics and Astrophysics May 25 - 30, 2002, Munich, Germany. http://neutrino2002.ph.tum.de/pages/transparencies/naples.
[Naples-talk:2002a]
[5-15]
Preliminary measurement of the differential cross section from neutrino nucleon deeply inelastic scattering at NuTeV, J. McDonald et al. (NuTeV), arXiv:hep-ex/0107082, 2001.
[McDonald:2001vv]
[5-16]
Extraction of R = sigma(L)/sigma(T) from CCFR $\nu_\mu$ Fe and $\bar\nu_\mu$ Fe differential cross sections, Arie Bodek et al. (CCFR/NuTeV), Sci.Cult.Ser.-Phys. 21 (2002) 380-383, arXiv:hep-ex/0105067.
[Bodek:2001hy]
[5-17]
A Departure from Prediction: Elettroweak Physics at NuTeV, K. McFarland (NuTeV), 2001. FNAL, October 26, 2001. http://www.pas.rochester.edu/~ksmcf/NuTeV/seminar-only-fnaloct26.pdf.
Comment: Contains information on the NuTeV direct measurement of the electron neutrino flux: $N(\nu_e^{\mathrm{obs}}/\nu_e^{\mathrm{pred}})=1.05\pm0.03$, $N(\bar\nu_e^{\mathrm{obs}}/\bar\nu_e^{\mathrm{pred}})=1.01\pm0.04$.
[McFarland:FNAL-26Oct2001]
[5-18]
Electroweak physics at NuTeV, G. P. Zeller (NuTeV), AIP Conf. Proc. 549 (2000) 809-813, arXiv:hep-ex/0010007.
[Zeller:2000wd]
[5-19]
Recent structure function results from neutrino scattering at Fermilab, Un-Ki Yang et al. (CCFR / NuTeV), arXiv:hep-ex/0010001, 2000.
[Yang:2000uc]
[5-20]
New measurements of nucleon structure functions from the CCFR/NuTeV Collaboration, A. Bodek et al. (CCFR / NuTeV), AIP Conf. Proc. 549 (2000) 509-513, arXiv:hep-ex/0008003.
[Bodek:2000bz]
[5-21]
Measurements of F2, xF3(nu) - xF3(anti-nu) from CCFR $\nu_\mu$ Fe and $\bar\nu_\mu$ Fe data in a model independent way, A. Bodek et al. (CCFR/NuTe), arXiv:hep-ex/0005021, 2000.
[Bodek:2000yr]
[5-22]
Performance of the NuTeV Fe-scintillator sampling calorimeter and implications for thin calorimeters, S. Avvakumov et al. (CCFR/NuTeV), Nucl. Phys. Proc. Suppl. 78 (1999) 232-237, arXiv:hep-ex/0001047.
[Avvakumov:1998nw]
[5-23]
Searches for new physics at NuTeV, J. Conrad (NuTeV), 2000. Prepared for 2nd Tropical Workshop on Particle Physics and Cosmology: Neutrino and Flavor Physics, San Juan, Puerto Rico, 1-6 May 2000.
[5-24]
Recent QCD results from NuTeV / CCFR Collaboration, T. Adams et al. (NuTeV/CCFR), Nucl. Phys. Proc. Suppl. 86 (2000) 93-101.
[5-25]
Recent electroweak results from nu N scattering at NuTeV, Jaehoon Yu (NuTeV), 2000. 30th International Conference on High-Energy Physics (ICHEP 2000), Osaka, Japan, 27 Jul - 2 Aug 2000.
[Yu:2000fy]
[5-26]
A measurement of xF3(nu)-xF3(anti-nu) and R with the CCFR detector, Un-Ki Yang et al. (CCFR-NuTeV), Nucl. Phys. Proc. Suppl. 79 (1999) 89-92, arXiv:hep-ex/9906042.
[Yang:1999yz]
[5-27]
Strange content of the nucleon (NuTeV), T. Adams et al. (NuTeV), arXiv:hep-ex/9906038, 1999.
[5-28]
Charm production at NuTeV, T. Adams et al. (NuTeV), arXiv:hep-ex/9906037, 1999.
[5-29]
A measurement of sin**2(Theta(W)) in nu N scattering from NuTeV, G. P. Zeller et al. (NuTeV), arXiv:hep-ex/9906024, 1999.
[Zeller:1999ts]
[5-30]
Measurement of sin**2(Theta(W)) in nu N scattering from NuTeV, R. A. Johnson et al. (NuTeV), arXiv:hep-ex/9904028, 1999.
[Johnson:1999uk]
[5-31]
Determination of sin**2 theta(w) in neutrino-nucleon scattering at the NuTeV, R. H. Bernstein, T. Adams, A. Alton, S. Avvakumov (The NuTeV), Nucl. Phys. Proc. Suppl. 77 (1999) 265-270.
[Bernstein:1999rg]
[5-32]
Searches for neutrino mass in the NuTeV experiment, M. H. Shaevitz et al. (NuTeV), 1999. In 'Cape Town 1999, Weak interactions and neutrinos' 400- 404.
[Shaevitz:1999xy]
[5-33]
Search for neutral heavy leptons in the NuTeV experiment at Fermilab, R. B. Drucker et al. (NuTeV), arXiv:hep-ex/9811036, 1998.
[Drucker:1998uq]
[5-34]
Neutrino trident production from NuTeV, T. Adams et al. (NuTeV), arXiv:hep-ex/9811012, 1998.
[5-35]
Measurement of sin**2(Theta(W)) from neutrino nucleon scattering at NuTeV, K. S. McFarland et al. (NuTeV), arXiv:hep-ex/9806013, 1998.
[McFarland:1998gg]
[5-36]
Searches for evidence of neutrino mass in the NuTeV experiment at Fermilab, T. Adams et al. (NuTeV), 1998. Prepared for 29th International Conference on High-Energy Physics (ICHEP 98), Vancouver, British Columbia, Canada, 23-29 Jul 1998.
[5-37]
Direct and indirect measurements of the W boson mass at Fermilab, Eric Flattum (CDF, D0 and NuTeV), 1998. To be published in the proceedings of 33rd Rencontres de Moriond: QCD and High Energy Hadronic Interactions, Les Arcs, France, 21-28 Mar 1998.
[Flattum:1998cp]
[5-38]
Electroweak results from NuTeV, R. B. Drucker (NuTeV), 1998. Prepared for 26th SLAC Summer Institute on Particle Physics: Gravity - From the Hubble Length to the Planck Length (SSI 98), Stanford, California, 3-14 Aug 1998.
[Drucker:1998ud]
[5-39]
Measurement of sin**2(Theta(W)) in nu N scattering at the Tevatron, T. Adams et al. (NuTeV), 1998. Prepared for 29th International Conference on High-Energy Physics (ICHEP 98), Vancouver, British Columbia, Canada, 23-29 Jul 1998.
[5-40]
Determination of alpha(s) and measurements of R(L), kappa, and |V(cs)| from nu N DIS at CCFR, J. Yu et al. (CCFR/NuTeV), 1998. To be published in the proceedings of 29th International Conference on High-Energy Physics (ICHEP 98), Vancouver, Canada, 23-29 Jul 1998.
[Yu:1998ir]
[5-41]
Electroweak measurements in nu N deeply inelastic scattering in the CCFR detector, R. B. Drucker (CCFR and NuTeV), 1996. Prepared for 9th Annual Divisional Meeting (DPF 96) of the Division of Particles and Fields of the American Physical Society, Minneapolis, Minnesota, 11-15 Aug 1996.
[Drucker:1996ue]
[5-42]
A Measurement of R = sigma-L / sigma-T in deep inelastic neutrino - nucleon scattering at the Tevatron, A. Bodek et al. (CCFR/NuTeV), J. Phys. G22 (1996) 775-780. Durham Workshop on Hera Physics: Proton, Photon and Pomeron Structure Proceedings, Bristol, England, IOP Publishing., 17-23 Sep 1995, Durham, England.
[Yang:1995wm]

#### Cross search NU

It is possible to perform a cross search between the various pages of Neutrino Unbound.
This is useful if you want to show the common elements that appear in the listings of two (or more) different topics or experiments.

[Go to ...]

## Neutrino Unbound Home

[empty]
Authors:
Stefano Gariazzo / gariazzo@to.infn.it
Carlo Giunti / giunti@to.infn.it
Marco Laveder / marco.laveder@pd.infn.it
Last Update: Wed 20 Sep 2017, 09:48:58 UTC


text:
Time Limit: 1000MS Memory Limit: 32768KB 64bit IO Format: %I64d & %I64u

Description

Angel was caught by the MOLIGPY! He was put in prison by Moligpy. The prison is described as a N * M (N, M <= 200) matrix. There are WALLs, ROADs, and GUARDs in the prison.

Angel’s friends want to save Angel. Their task is: approach Angel. We assume that “approach Angel” is to get to the position where Angel stays. When there’s a guard in the grid, we must kill him (or her?) to move into the grid. We assume that we moving up, down, right, left takes us 1 unit time, and killing a guard takes 1 unit time, too. And we are strong enough to kill all the guards.

You have to calculate the minimal time to approach Angel. (We can move only UP, DOWN, LEFT and RIGHT, to the neighbor grid within bound, of course.)

Input

First line contains two integers stand for N and M.

Then N lines follows, every line has M characters. “.” stands for road, “a” stands for Angel, and “r” stands for each of Angel’s friend.

Process to the end of the file.

Output

For each test case, your program should output a single integer, standing for the minimal time needed. If such a number does no exist, you should output a line containing “Poor ANGEL has to stay in the prison all his life.”

Sample Input

7 8

#.#####.

#.a#..r.

#..#x…

..#..#.#

#…##..

.#……

……..

Sample Output

13

Source

ZOJ Monthly, October 2003

AC代码：

#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;
int n, m;
char map[210][210];
bool vis[210][210];
const int dx[] = {0, 0, 1, -1},
dy[] = {1, -1, 0, 0};
struct node
{
int x, y, step;
bool operator < (const node b) const
{
return step > b.step;
}
}start;
priority_queue <node> q;
bool input()
{
if (scanf("%d %d\n", &n, &m) == 2)
{
for (int i = 0; i < n; i++)
scanf("%s\n", map[i]);
return 1;
}
return 0;
}
void solve()
{
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
if (map[i][j] == 'a')
start = (node){i, j, 0};
memset(vis, 0, sizeof(vis));
while (!q.empty())
q.pop();
q.push(start);
while (!q.empty())
{
node u = q.top();
q.pop();
if (vis[u.x][u.y])
continue;
vis[u.x][u.y] = 1;
if (map[u.x][u.y] == 'r')
{
printf("%d\n", u.step);
return;
}
node next;
for (int i = 0; i < 4; i++)
{
next.x = u.x + dx[i];
next.y = u.y + dy[i];
if (next.x < 0 || next.x >= n || next.y < 0 || next.y >= m || map[next.x][next.y] == '#' || vis[next.x][next.y])
continue;
if (map[next.x][next.y] == 'x')
next.step = u.step + 2;
else
next.step = u.step + 1;
q.push(next);
}
}
printf("Poor ANGEL has to stay in the prison all his life.\n");
}
int main()
{
while (input())
solve();
return 0;
}


text:
# User:Boris Tsirelson/sandbox

2010 Mathematics Subject Classification: Primary: 62E [MSN][ZBL]

A probability distribution of a random variable $X$ which takes non-negative integer values, defined by the formula $$\label{*} P(X=k)=\frac{ {k+m-1 \choose k}{N-m-k \choose M-m} } { {N \choose M} } \tag{*}$$ where the parameters $$N,M,m$$ are non-negative integers which satisfy the condition $$m\leq M\leq N$$. A negative hypergeometric distribution often arises in a scheme of sampling without replacement. If in the total population of size $$N$$, there are $$M$$ "marked" and $$N-M$$ "unmarked" elements, and if the sampling (without replacement) is performed until the number of "marked" elements reaches a fixed number $$m$$, then the random variable $$X$$ — the number of "unmarked" elements in the sample — has a negative hypergeometric distribution \eqref{*}. The random variable $$X+m$$ — the size of the sample — also has a negative hypergeometric distribution. The distribution \eqref{*} is called a negative hypergeometric distribution by analogy with the negative binomial distribution, which arises in the same way for sampling with replacement.

The mathematical expectation and variance of a negative hypergeometric distribution are, respectively, equal to

$$m\frac{N-M} {M+1}$$

and

$$m\frac{(N+1)(N-M)} {(M+1)(M+2)}\Big(1-\frac{m}{M+1}\Big) \, .$$

When $$N, M, N-M \to \infty$$ such that $$M/N\to p$$, the negative hypergeometric distribution tends to the negative binomial distribution with parameters $$m$$ and $$p$$.

The distribution function $$F(n)$$ of the negative hypergeometric function with parameters $$N,M,m$$ is related to the hypergeometric distribution $$G(m)$$ with parameters $$N,M,n$$ by the relation $$F(n) = 1-G(m-1) \, .$$ This means that in solving problems in mathematical statistics related to negative hypergeometric distributions, tables of hypergeometric distributions can be used. The negative hypergeometric distribution is used, for example, in statistical quality control.

#### References

 [Be] Y.K. Belyaev, "Probability methods of sampling control", Moscow (1975) (In Russian) MR0428663 [BoSm] L.N. Bol'shev, N.V. Smirnov, "Tables of mathematical statistics", Libr. math. tables, 46, Nauka (1983) (In Russian) (Processed by L.S. Bark and E.S. Kedrova) MR0243650 Zbl 0529.62099 [JoKo] N.L. Johnson, S. Kotz, "Distributions in statistics, discrete distributions", Wiley (1969) MR0268996 Zbl 0292.62009 [PaJo] G.P. Patil, S.W. Joshi, "A dictionary and bibliography of discrete distributions", Hafner (1968) MR0282770
How to Cite This Entry:
Boris Tsirelson/sandbox. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox&oldid=41611


text:
# Why don't we have an analogous of range:codomain for _:domain?

According to this site, the range is a subset of the codomain and represents what actually can be the output of a function. Why don't we have a name for the subset of the domain that can actually be the input of a function. Or, why my question makes no sense?

• A function MUST be defined on the entire domain (otherwise it is a lie/"partial" function) – Alec Teal Sep 10 '15 at 21:21

All of the domain is the input of the function. $f: \mathbb{N} \to \mathbb{R}$ means precisely that for every natural number $n$ there is a real $r_n$ which has $f(n) = r_n$. It makes no sense to say that $f$ is from $\mathbb{R} \to \mathbb{R}$, even though $\mathbb{N} \subset \mathbb{R}$, because to say that $f: \mathbb{R} \to \mathbb{R}$ is to say that for each real, $f$ takes a value on that real. In this example, there's just no way to say that $f(1/2)$ even has a value.
You may be looking for the idea of a partial function, which is not necessarily defined on its whole domain. We then say that the "domain of definition" of the partial function is the set consisting of everything on which the function really does take a value. For instance, the partial function $f: \mathbb{R} \to \mathbb{R}$ corresponding to the bona fide function $f: \mathbb{N} \to \mathbb{R}$ would have domain of definition $\mathbb{N}$, and domain $\mathbb{R}$.


text:
# List of Notes - Category: Applications of Derivatives

## Related Rates

Suppose we are given one quantity x that depends on another quantity y. If rate of change of quantity x with respect to time t is given, how do we find rate of change of y with respect to time? We need to do it because in real-worlds problems it is often easier to calculate rate of change of x then rate of change of y.

## Optimization Problems

Perhaps, the most important application of derivatives is solving optimization problems.

With the help of derivatives we can find minimum and maximum values. That's exactly what we need in optimization problems.

## Applications to Economics

Suppose that some factory produces x units of good. Let's denote cost of producing x units of good by C(x).

Cost function C(x) is the cost of producing x units of certain product.

Marginal cost is the rate of change of cost with respect to x. In other words marginal cost function is the derivative of cost function.

## Tangent Line to Parametric Curves

Sometimes function is defined parametrically, but we still need to find equation of tangent line.

So, let parametric curve is defined by equations x=f(t) and y=g(t).

Suppose f and g are differentiable functions and we want to find the tangent line at a point on the curve where y is also a differentiable function of x.

## Tangent Line in Polar Coordinates

Let's see how to derive equation of tangent line when we are given equation of curve r=f(theta) in polar coordinates.

We will proceed in the same fashion as with tangent lines to parametric curves, because polar coordinates in some sense similar to parametric curves.


text:
Representation Theory Seminar

Info

The seminar runs on Thursdays at 3:10pm–4:00pm in Carver Hall 401 at Iowa State University. Talks range from expository given by local speakers, to invited research talks. Themes include

• finite- and infinite-dimensional associative algebras and their modules,
• (quantized) enveloping algebras, Yangians, finite W-algebras, affine Hecke algebras,
• connections to geometry, combinatorics, physics and other fields.

Talks

Nov 16, 2017
Finite complex reflection groups: Invariant and coinvariant rings
Tathagata Basak (ISU)
Let $$G$$ be a group of linear maps on a vector space $$V$$. The invariant ring of $$G$$ is the ring of polynomial functions on V that are invariant under $$G$$ action. We will discuss the invariant rings of finite complex reflection groups. We shall illustrate how properties of the reflection group are encoded in the ring of invariants and co-invariants.
Nov 9, 2017
Galois representations in Galois theory
Shuvra Gupta (ISU)
We will start with a gentle introduction to Galois Representations. We will then discuss how questions in Galois Theory can be answered using techniques from Galois Representations. If there is time, I will discuss a project that I have been pursuing with Yeansu Kim to realise spin groups over $$\mathbb{Q}$$.
October 26, 2017
Combinatorial generation of multi-highest-weight crystals
John Dusel (Mount St. Mary's University)

A crystal is a type of directed graph that encodes essentially all the combinatorial information about of a Lie algebra, its associated quantum group, and their representations. In this talk we will study the structure of a crystal with respect to an automorphism of the underlying Dynkin diagram, via a process known as folding.

The folding procedure introduced here extends a well-known Lie theoretic construction based on fixed-points. The latter was used by Lusztig in his celebrated construction of the canonical basis for a quantized enveloping algebra of multiply-laced type. Folding does not preserve the property of being highest-weight. This leads to a new type of crystal that corresponds to a new type of representation of a quantized enveloping algebra. We call these crystals multi-highest-weight.

In certain cases the multi-highest-weight crystal obtained from folding $$B(\infty)$$ — the crystal for the lower triangular half of a quantized enveloping algebra — can be combinatorially generated using subsets of the Weyl group known as balanced parabolic quotients. I will explain how this generation can be accomplished both intrinsically and using the semigroup structure of Nakashima and Zelevinsky's polyhedral realization.

October 12, 2017
Finite complex reflection groups: Introduction
Tathagata Basak (ISU)
We will introduce the class of finite complex reflection groups and give many examples. We will describe their Coxeter-like diagrams and braid groups and talk about some of the mysteries surrounding them.
October 5, 2017
Maximal subalgebras of finite-dimensional algebras
Alexander Sistko (University of Iowa)
We present classification theorems for maximal subalgebras of finite-dimensional algebras over a field $$k$$. This is done by first classifying maximal subalgebras of semisimple algebras, and then lifting to the  general case. When $$k$$ is nice (ex. algebraically closed), the classification can be understood in terms of the ideal structure of the Jacobson radical. For bound quiver algebras, this gives us nice presentations for subalgebras. Trivial extensions and separable extensions feature prominently in the classification, and allow us to relate representation-theoretic properties of an algebra to those of its subalgebras via induction and restriction. If time permits, we discuss related problems and applications, ex. determining isomorphism classes of subalgebras, and finding minimal generating sets of algebras.
September 28, 2017
Definability in the foundations of Euclidean geometry and the product rule for derivations
Richard Kramer (ISU)
In this talk, we discuss the results of investigations that began with a solution to an open problem posed by Schwabhäuser and Szczerba regarding definability (without parameters) in the three dimensional Euclidean geometry of lines, asking whether intersection was definable from perpendicularity (two lines intersecting at a right angle). It is not. The result is a “new” 3-dimensional geometry of lines, which we call perpendicular geometry, since it can be formalized from perpendicularity. Further investigations produce a rather complete classification of possible geometries arising from elementary Euclidean binary relations between lines in $$\mathbb{R}^3$$, modulo the determination of (metrical) projective geometries formalized by binary relations between points. The classification shows that in a sense made precise, perpendicular geometry is the only new geometry that can arise from binary geometric relations, except for possible new projective plane geometries, which we conjecture do not exist. Generalizing to geometries of s-flats in n-dimensional Euclidean geometry, we state a theorem which provides the essential first step towards a similar classification for the general case. The theorem states that parallel is definable in such a geometry no matter what binary geometric relation that one might chose to formalize geometry (with an enumerated list of trivial exceptions). To what extent this is true for ternary or higher order geometric relations is open, even for lines in $$\mathbb{R}^3$$. We conjecture that it remains true, that is, that parallel is definable from anything “except for the exceptions”. Finally, we note that perpendicular geometry, whose automorphism group is connected with derivations, sheds some rather curious light on the relationship between the product rule for derivations over a ring, and the sum rule. For example, it is a direct consequence of perpendicular geometry that the product rule for the cross product of 3-dimensional vectors implies the sum rule. It is conjectured that this is also true of all finite dimensional semi-simple Lie algebras over the complex numbers.
September 21, 2017
Irreducible components of exotic Springer fibers
Daniele Rosso (Indiana University Northwest)
The Springer resolution is a resolution of singularities of the variety of nilpotent elements in a reductive Lie algebra. It is an important geometric construction in representation theory, but some of its features are not as nice if we are working in Type $$C$$ (Symplectic group). To make the symplectic case look more like the Type $$A$$ case, Kato introduced the exotic nilpotent cone and its resolution, whose fibers are called the exotic Springer fibers. We give a combinatorial description of the irreducible components of these fibers in terms of standard Young bitableaux and obtain an exotic Robinson-Schensted correspondence. This is joint work with Vinoth Nandakumar and Neil Saunders.
September 14, 2017
Canonical Galois orders and maximal commutativity
Jonas Hartwig (ISU)
Galois rings and orders, defined by Futorny and Ovsienko in 2010, form a class of algebras which include many important algebras in representation theory, such as the (quantized) enveloping algebra of $$\mathfrak{gl}_n$$, type $$A$$ restricted Yangians and finite W-algebras. I will present a new criterion for determining when a Galois ring is a Galois order. This can be applied in particular to $$U_q(\mathfrak{gl}_n)$$ which also proves the quantum Gelfand-Zeitlin subalgebra is maximal commutative. This establishes several conjectures including bounds on fibers of irreducible Gelfand-Zeitlin characters. The method in fact applies to all of the mentioned examples and give unified new proofs.
September 7, 2017
Global Weyl modules for non-standard maximal parabolic subalgebras
Matthew Lee (UC Riverside)
In this talk we will discuss the structure of non standard maximal parabolics of twisted affine Lie algebras, global Weyl modules and the associated commutative associative algebras. Since the global Weyl modules associated with the standard maximal parabolics have found many applications the hope is that these non-standard maximal parabolics will lead to different, but equally interesting applications.
August 31, 2017
The current algebra of $$\mathfrak{sl}_2$$ and its representations
Jonas Hartwig (ISU)
An introduction to the current algebra of $$\mathfrak{sl}_2$$ will be given. This Lie algebra is infinite-dimensional and has non-semisimple finite-dimensional modules (i.e. Weyl's theorem fails). Some classes of modules will be discussed, and open problems in the area stated.

Books:

Archive

04/28/17 Adnan Abdulwahid (ISU) Nakayama Functor and Quiver Representations Abstract
04/07/17 Miodrag Iovanov (UI) On Incidence Algebras and their Representations Abstract
03/24/17 JH Tensor products of representations
03/10/17 JH Weight modules over noncommutative Kleinian fiber products Notes Paper1 Paper2
03/03/17 JH Unitarizable representations Notes
02/24/17 Ben Sheller (ISU) Lie group actions and stratified spaces Notes
02/10/17 JH Gelfand-Tsetlin Bases Notes
02/03/17 JH Parabolic induction Fernando
01/27/17 JH Simple weight modules over Lie algebras Mathieu
01/20/17 Mark Hunacek (ISU) Modular Lie algebras Benkart Rumynin
12/02/16 Animesh Biswas (ISU) The Heisenberg group and its representations
11/18/16 Tathagata Basak (ISU) Reflection groups II
11/11/16 Tathagata Basak (ISU) Reflection groups I Notes
11/04/16 JH What about $$E_9$$? Kac-Moody algebras. Notes
10/31/16 JH [Comb/Alg Sem] Lie superalgebras and super-differential operators II
10/24/16 JH [Comb/Alg Sem] Lie superalgebras and super-differential operators I Notes Kac Serganova
10/21/16 JH Classification of simple Lie algebras Notes
10/14/16 JH Root space decomposition for $$\mathfrak{sl}(3)$$
09/30/16 JH Lie algebras and homomorphisms;
Examples; Classification problem
Notes


text:
Integrate the functions in Exercises 1 to 9.    Q2.    $\sqrt{1 - 4x^2}$

D Divya Prakash Singh

Given function to integrate $\sqrt{1 - 4x^2}$

Now we can rewrite as

$= \int \sqrt{1 - (2x)^2}dx$

As we know the integration of this form is $\left [ \because \int \sqrt{a^2-x^2}dx =\frac{x}{2}\sqrt{a^2-x^2} +\frac{a^2}{2}\sin^{-1}\frac{x}{a} \right ]$

$= \frac{(\frac{2x}{2})\sqrt{1^2-(2x)^2}+\frac{1^2}{2}\sin^{-1}\frac{2x}{1}}{2\rightarrow Coefficient\ of\ x\ in\ 2x} +C$

$= \frac{1}{2}\left [ x\sqrt{1-4x^2}+\frac{1}{2}\sin^{-1}2x \right ]+C$

$= \frac{x}{2}\sqrt{1-4x^2}+\frac{1}{4}\sin^{-1}2x+C$

Exams
Articles
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text:
## anonymous 3 years ago Show that

1. anonymous

Show that: $|cosz|^{2}= \cos^{2}x+\sinh^{2}x$ Hint: using $\cos z = \frac{ e^{iz} + e^{-iz}}{ 2 }$ $\sin z = \frac{ e^{iz} - e ^{-iz} }{ 2i }$ $\cosh z = \frac{ e^{z}+e^{-iz} }{ 2 }$ $\sinh z = \frac{ e^{z} - e^{-z} }{ 2 }$

2. anonymous

Sorry I MEAN, show that $|\cos z|^{2} = \cos^{2} x + \sinh^{2}y$

3. anonymous

would you kindly help me again @niksva ??

4. anonymous

Take LHS first (cosz)^2 replace z with x +iy cos(x+iy) = cos(x)cos(iy) - sin(x)sin(iy)

5. anonymous

as cos(iy) = coshy and sin(iy) =i sinhy therefore cosz = cos(x)cos(hy)-i sin(x)sin(hy)

6. anonymous

@gerryliyana after squaring and applying (a-b)^2 formula , the equation become difficult to solve

7. anonymous

i've tried.., but didn't match,

8. anonymous

how did u approach the problem?

9. anonymous

using hint above..., i tried, one by one.., hbu?? it's make sense ?

10. anonymous

how can u apply above hint in RHS?

11. anonymous

what the next ??

12. anonymous

my ques is as z = x + iy where x is real number and y is imaginary number can we write cosx= (e^ix+ e^-ix)/2 ???????/ according to me, we cannot write this as x is a real number

13. anonymous

@UnkleRhaukus help?

14. anonymous

$\Large{ \cos z={e^{-iz}+e^{iz}\over2}\\ LHS=|\cos z|^2={1\over4}\left(e^{-2iz}+2e^{-iz+iz}+e^{2iz}\right)\\ \quad={1\over2}+{1\over4}\left[e^{-2i(x+iy)}+e^{2i(x+iy)}\right]\\ \quad=\color{red}{{1\over4}\left(2+e^{2y}+e^{-2y}\right)+{1\over4}\left(e^{-i2x}+e^{i2x}\right)}\\ RHS=\cos^2x+\sinh^2y\\ \quad={1\over4}\left(e^{-i2x}+e^{i2x}+2\right)-{1\over4}\left(e^{2y}-2+e^{-2y}\right)\\ }$ They do not seem to match!!

15. anonymous

have idea ???

16. anonymous

yes. you can prove it thus way: 1) get LHS = "a" 2) if you can show RHS = "a", then LHS=RHS="a" and QED. but following this, the two sides probably have an issue with the "signs"

17. anonymous

no wait.. my bad.. I took "sin y" instead of "sinh y" $\Large{ \cos z={e^{-iz}+e^{iz}\over2}\\ LHS=|\cos z|^2={1\over4}\left(e^{-2iz}+2e^{-iz+iz}+e^{2iz}\right)\\ \quad={1\over2}+{1\over4}\left[e^{-2i(x+iy)}+e^{2i(x+iy)}\right]\\ \quad=\color{red}{{1\over4}\left(2+e^{2y}+e^{-2y}\right)+{1\over4}\left(e^{-i2x}+e^{i2x}\right)}\\ RHS=\cos^2x+\sinh^2y\\ \quad={1\over4}\left(e^{-i2x}+e^{i2x}+2\right)+{1\over4}\left(e^{2y}-2+e^{-2y}\right)\\ \quad=\color{red}{{1\over4}\left(e^{2y}+e^{-2y}\right)+{1\over4}\left(e^{-i2x}+e^{i2x}\right)}\\ {\rm SO,}\\ \color{green}{\boxed{|\cos z|^2={1\over2}+\cos^2x+\sinh^2y}} }$

18. anonymous

19. anonymous

as you see, the LHS and the RHS differ by $$1\over2$$.

20. anonymous

yes., i see, did you know why ???


text:
## Project description

pygnurl is a dynamic GNU Readline interface. It provides:

• A Pythonic interface similar to rl for ease of use

• An interface to custom bindable functions

• A readline compatibility layer for existing code

You should use pygnurl if you specifically want to use GNU Readline from your Python program. If you are just looking for tools to help you build a command line interface, you may prefer prompt_toolkit.

## Requirements

Linux users should already have Readline as part of the standard library. pygnurl uses this version by default.

Windows users can get a pre-built 32-bit Readline DLL from gnuwin32.

## Quick Start Guide

Install pygnurl using pip install pygnurl.

Set the PYGNURL_LIB environment variable to the filename of your Readline library. This will be loaded using the shared library search order rules of your system. (Linux users can skip this step to use the system version).

If your version of Python already has a readline module, you will need to do one of the following things to let pygnurl override it:

2. Install using easy_install instead of pip

If you are using Python 3.4 or later, completion and history will be set up for you automatically. If you are using an older version, you will need to set this up yourself.

>>> import rlcompleter
>>> r<tab><tab>

## Examples

pygnurl/examples/startup.py - An example startup file suitable for everyday use. Point the PYTHONSTARTUP environment variable at this file to automatically get tab completion and saved history in your interpreter. (If you are using Python 3.4 or later, you do not need to use this example.)

pygnurl/examples/functions.py - An example startup file demostrating a custom bindable command. You must also use this with the PYTHONSTARTUP environment variable. Run help(pygnurl.examples.functions) for more information.

pygnurl/examples/mycmd.py - A simple command line showing tab completion capabilities. The argument to cat is completed based on your local filesystem.

## Motivation

pygnurl aims to provide full GNU Readline support across all platforms with no compilation overhead. Any pre-built Readline library should be able to be dropped in with no code modifications. If necessary, version- or platform-specific compatibility fixes can be implemented in Python, not C.

## Development

For source code, questions and bug reports, visit the GitHub repository:

https://github.com/evanunderscore/pygnurl

## Alternatives

readline - Part of the standard library. Python on Mac OS X may implement this using libedit instead of GNU Readline and must be configured accordingly.

rl - Alternative Python bindings for GNU Readline.

prompt_toolkit - Library for building powerful interactive command lines in Python.

Platforms

Library

Interface

pygnurl

Any

Dynamic

Extended

Unix-like

Static

Basic

Windows

Pure Python

Basic

Unix-like

Static

Basic

rl

Unix-like

Static

Extended

prompt_toolkit

Any

Pure Python

Alternative

## Known Bugs

• ANSI color codes in the IPython terminal are not able to be printed. As a workaround, the codes are stripped and a plain prompt is displayed instead.

• libreadline6 from MinGW lags behind one keystroke when using the arrow keys. This appears to be related to the Readline callback interface.

## Project details

Uploaded source
Uploaded 2 7


text:
How to build two lines aligned maps

I would like to write a map between two objects, with a map below which specify where any single object is sent. To be more precise. I want to write $A \rightarrow B$, and right below it $\alpha \mapsto \beta$. I tried with the command $\underset$ but the maps below gets too smaller, and it's not aligned to the map above. What is the right command?

I apologize if this question has been already asked. To me it looks elementary, nevertheless I couldn't find it nor here nor googling around. Thank you very much for your time!

• Welcome to TeX.SX. A tip: If you indent lines by 4 spaces, then they're marked as a code sample. You can also highlight the code and click the "code" button ({}). Jan 23 '13 at 16:54
• @ClaudioFiandrino, Thank you for your suggestion, I'll stick to it for future questions! Jan 23 '13 at 16:55

Something like this or variants like aligned if you want it to be part of a larger expression.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align*}
A&\rightarrow B\\
a&\mapsto b
\end{align*}

\end{document}

• rats, ya beat me. but you might want to mention commutative diagram packages like xypic or tikz for more complicated diagrams. Jan 23 '13 at 17:02
• @barbarabeeton and not forgetting amscd ? Jan 23 '13 at 17:05
• amscd is intentionally limited. it only handles strictly horizontal or vertical arrows, so if anything slanted is needed, forget it. better to start with something more functional. Jan 23 '13 at 17:12

amsmath and mathtools offers extensible arrows. (If I get the question correctly)

\documentclass{article}
\usepackage{mathtools}

\begin{document}
$A \xrightarrow[\alpha \mapsto \beta]{} B$
\end{document}


text:
# Net worth tracking

Posted on 2015-03-02

I like to keep a close track on my spending and income and to optimize both using historical data. I used to have a large spreadsheet for this purpose, but I was lucky to find the excellent HomeBank instead of keeping it. Unfortunately, HomeBank alone eventually wasn’t enough to track all my assets.

I have a custom setup which collects the values of my assets. Most of the code is at github.com/MichalPokorny/scripts (with horrible undocumented dependencies on btckit, worthy and maybe a few others). In this post, I give a high-level overview of how it works at the moment.

## The problem

The system needs to keep track of various assets which aren’t straightforward to appraise:

• I own a few Bitcoins (which were a large portion of my wealth back in the last bubble at the end of 2014).
• I have some money in conservative investment funds backed mostly by government bonds.

• As I am writing this, I have a separate French bank account in euros. At the time when I needed to track it, HomeBank did have a limited form of multicurrency support, but if I remember correctly, I had a good reason for not using that (the feature may not have been usable in my particular case).

• In 2014, I started dabbling in stocks.
• And I also have some cash.

The original problem was keeping track of my fiat money and of my Bitcoins. I wanted to have something stupidly hacky and working. Net worth tracking may have better solutions today (even for the weird structure of my assets), but I guess I’m going to keep using this solution until I’m bored enough to find a replacement :)

## Collecting and storing the data

I have a Ruby script that figures the value of my assets using various sources and then saves the data. The script is in ~prvak/bin/net-worth-keeper and it’s run as a cronjob every hour or so:

# crontab
SHELL=/bin/bash
PATH=/bin:/usr/bin:/usr/local/bin:/home/prvak/bin:/home/prvak/.gem/ruby/2.0.0/bin:/home/prvak/bin/gobin
HOME=/home/prvak
0 */1 * * * net-worth-keeper --log --quiet

Cron has the added benefit of sending me a mail when the script fails.

I keep all the data in a simple CSV file at ~prvak/misc/net-worth.csv. CSVs are simple and readable by everything (think OpenOffice Calc, Gnuplot, Ruby, Octave, etc.). They are also human-readable and writeable.

The beginning of the CSV file looks like this (data obviously scrambled):

2013-09-28 21:00:05,1380394805,11013579.15,123456.7,890123.45,9999999,0.0,0.0
2013-09-28 21:16:15,1380395775,11015200.366,125000.7,890200.666,9999999,0.0,0.0
...
• The first column (2013-09-28 21:00:05) is the date and time the data was collected, in a human-readable format.
• The second column (1380394805) is also the date and time, but in machine-readable format (Unix time = number of seconds since the Epoch).
• Every remaining field contains the value of an asset in CZK (Czech koruna).

Note the zeroes at the end - for example, I didn’t have any stocks at first. When I needed to start tracking them, I just wrote the tracking code and ran a complicated NoSQL CSV migration (i.e. I added “,0.0” at the end of each line).

New entries are always appended at the end of the file.

## The sources of asset values

The original net-worth-keeper just fired a bunch of other programs using the parallel gem. Every program’s responsibility was to get the price of one asset (e.g. my Bitcoins) and output it in CZK. net-worth-keeper waited until those programs crashed or gave a valid output, parsed the output and appended it to the CSV file.

Those binaries shared a lot of common code or common libraries (like currency conversion) and they fired a lot of expensive Ruby interpreters. I eventually moved shared code into one directory. Now net-worth-keeper calls a library function (Prvak::Finance::NetWorth.load_assets), which returns a breakdown of asset values as a Ruby Hash (like {'Money' => 12345, ...}).

The breakdown is still done in parallel, but now most of the “workers” are actually just Ruby functions (like Prvak::Finance::IKSPortfolio.load.value or Prvak::Finance::Homebank::Accounting.load.total_value). I can still use separate executables where needed. Every data source just returns a single number (of CZK) or crashes and burns.

I have the following data sources:

• Prvak::Finance::Homebank::Accounting loads a static HomeBank .xhb file, which has a simple XML format. It uses the wonderful nokogiri gem to parse it and crudely adds up all transactions. There are a few small gotchas regarding “hidden accounts”, internal transfers, and so on.

• Prvak::Finance::IKSPortfolio understands investment funds provided by the company I invest through (IKS). Basically, you buy a number of “investment certificates” for price X and hope price eventually befomes >X. I have “investment certificates” for several funds (they differ in their asset allocation).

I store the relevant data in ~prvak/.iks-portfolio.yml:

---
invested: 9900000
assets:
KB Konzervativní profil: 500317
Amundi Funds Equity Global Resources (CZK): 23144
...

invested stores the amount of CZK invested into investment funds. The assets hash is keyed by the name of a fund and values are numbers of investment certificates you hold. I then use a small gem of mine (iks-scrape) to get the value of those.

iks_scrape can’t use any API to get the price, but luckily there is a constant URL (http://www.iks-kb.cz/web/fondy_denni_hodnoty.html) where you can find the data. The incredibly useful mechanize gem parses the HTML like a piece of cake.

• I use BtcKit::BtcPrice to get the pitiful state of my Bitcoin hoard. There’s again a file in my home which stores how many BTC do I have. I simply pull some recent CZK trades from the LocalBitcoins JSON API and compute an average. I tried various other providers for the data with varying success. LocalBitcoins is good enough for now.

• Stocks used to be handled by Prvak::Finance::Stocks. This is now a thin wrapper around worthy (the Ruby implementation broke one day and I decided I want to learn a bit of Go instead :).

Worthy loads a JSON file from my ~ that describes what stocks and foreign currencies do I own on my broker account:

{"stocks": {"MSFT": 123, "AAPL": 456, ...}, "currencies": {"USD": 666, ...}}

The yahoo_stock_api module sends one batch request to the Yahoo finance API. The request format could use some readability improvements and it would be cool if the API decided on one error value instead of randomly using N/A, 1.0 or 0.0, but if you use just the basic stuff, it’s solid.

I only ask for the last closing price and for the tickers (to ensure the order of stocks is in sync).

After we know how much money is the broker account worth, we just need to convert the various currencies to CZK and we are done. I use the very useful freecurrencyconverterapi.com - the API is dead simple and does everything I need. This Go module calls what I need.

• Finally, there’s the euro account. It’s again stored in a file, and I convert to CZK again using freecurrencyconverterapi.com.

## Using the data

The net-worth-keeper binary by default runs in an “interactive mode”, which asks the the terminal-table gem to print a summary of asset values (remember, I track each asset separately, not just the sum of everything). In addition to this, I also have a small Gnuplot file in ~prvak/misc/plot-net-worth.gnuplot, which plots a stacked plot of asset values:

set datafile separator ','
set xdata time
set format x "%d.%m"
set timefmt "%Y-%m-%d %H:%M:%S"
set key vert out center left
set autoscale xfixmin

plot \
"net-worth.csv" u 1:($6+$5+$4+$7+$8) w filledcurves x1 title 'EUR účet', \ "" u 1:($6+$5+$4+$7) w filledcurves x1 title 'Akcie', \ "" u 1:($6+$5+$4) w filledcurves x1 title 'KB účty', \
"" u 1:($6+$5) w filledcurves x1 title 'IKS fondy', \
"" u 1:6 w filledcurves x1 title 'Bitcoiny', \
\
"" u 1:6 w lines title 'Bitcoiny', \
"" u 1:5 w lines title 'IKS fondy', \
"" u 1:4 w lines title 'KB účty', \
"" u 1:7 w lines title 'Akcie', \
"" u 1:8 w lines title 'EUR účet', \

I run it using in an interactive Gnuplot session. Sorry for not including the output - I’m not comfortable with giving it to everyone on the internet. If you squint just right, you can actually see some trends where they should be :)

## Final notes

I have recently started rewriting parts of the code to Go. There are many things I like about Go - like the syntax, the blazing speed of tools, the One True Formatting (gofmt), or the package management (imports + go get). On the other hand, it is much less annoying to write quick JSON/YAML parsers in Ruby than in Go, but I hope this is just a temporary rough edge. The language is also less mature, so some libraries don’t quite exist yet (like Mechanize). However, I have high hopes for Go.

It would be nice to extend this system one day to track my “savings ratio”. The “savings ratio” is exactly what it says on the tin - how much money you save divided by how much money you earn (not including investment income). I hope to write one day about why I think tracking this value would be useful.

This system has problems when I’m moving larger amounts of money through “asset boundaries” - for example, it takes some time for money to travel between bank accounts. One needs to remember to put the transaction in both places once it finishes. A similar problem arises when I expect to be reimbursed for an expense by an employer - I don’t want to record that as a wedge in my nice graphs, but I also don’t want to have large disagreements between my records and the real state of my accounts. I don’t think I can have both.


text:
This will create active bindings amongst the synonyms. To minimize copying, the first one that exists in the character vector will become the "canonical" object. All others named in the character vector will be activeBindings to that canonical one. This synonym list will be assigned to the envir, as an object named objectSynonyms. That object will have an attribute called, bindings indicating which one is the canonical one and which is/are the activeBindings. EXPERIMENTAL: If the objects are removed during a spades call by, say, a module, then at the end of the event, the spades call will replace the bindings. In other words, if a module deletes the object, it will "come back". This may not always be desired.

objectSynonyms(envir, synonyms)

## Arguments

envir

An environment, which in the context of SpaDES.core is usually a simList to find and/or place the objectSynonyms object.

synonyms

A list of synonym character vectors, such as list(c("age", "ageMap", "age2"), c("veg", "vegMap"))

## Value

Active bindings in the envir so that all synonyms point to the same canonical object, e.g., they would be at envir[[synonym[[1]][1]]] and envir[[synonym[[1]][2]]], if a list of length one is passed into synonyms, with a character vector of length two. See examples.

## Details

This is very experimental and only has minimal tests. Please report if this is not working, and under what circumstances (e.g., please submit a reproducible example to our issues tracker)

This function will append any new objectSynonym to any pre-existing objectSynonym in the envir. Similarly, this function assumes transitivity, i.e., if age and ageMap are synonyms, and ageMap and timeSinceFire are synonyms, then age and timeSinceFire must be synonyms.

## Examples

sim <- simInit()
#> Setting:
#>   options(
#>     reproducible.cachePath = '/tmp/RtmppEYNhs/myProject/cache'
#>   )

sim$age <- 1:10; sim <- objectSynonyms(sim, list(c("age", "ageMap"))) identical(sim$ageMap, sim$age) #> [1] TRUE sim$age <- 4
identical(sim$ageMap, sim$age)
#> [1] TRUE
sim$ageMap <- 2:5 sim$ageMap[3] <- 11
identical(sim$ageMap, sim$age)
#> [1] TRUE

# Also works to pass it in as an object
objectSynonyms <- list(c("age", "ageMap"))
sim <- simInit(objects = list(objectSynonyms = objectSynonyms))
#> Setting:
#>   options(
#>     reproducible.cachePath = '/tmp/RtmppEYNhs/myProject/cache'
#>   )
identical(sim$ageMap, sim$age) # they are NULL at this point
#> [1] TRUE
sim$age <- 1:10 identical(sim$ageMap, sim$age) # they are not NULL at this point #> [1] TRUE ## More complicated, with 'updating' i.e., you can add new synonyms to previous sim <- simInit() #> Setting: #> options( #> reproducible.cachePath = '/tmp/RtmppEYNhs/myProject/cache' #> spades.inputPath = '/tmp/RtmppEYNhs/myProject/inputs' #> spades.outputPath = '/tmp/RtmppEYNhs/myProject/outputs' #> spades.modulePath = '/tmp/RtmppEYNhs/myProject/modules' #> spades.scratchPath = '/tmp/RtmppEYNhs/SpaDES/scratch' #> ) #> Using setDTthreads(1). To change: 'options(spades.DTthreads = X)'. os <- list(c("age", "ageMap"), c("vegMap", "veg"), c("studyArea", "studyArea2")) os2 <- list(c("ageMap", "timeSinceFire", "tsf"), c("systime", "systime2"), c("vegMap", "veg")) sim <- objectSynonyms(sim, os) sim <- objectSynonyms(sim, os2) #> age, ageMap already exist; using the first one, age #> vegMap, veg already exist; using the first one, vegMap # check sim$objectSynonyms
#> [[1]]
#> [1] "studyArea"  "studyArea2"
#>
#> [[2]]
#> [1] "age"           "ageMap"        "timeSinceFire" "tsf"
#>
#> [[3]]
#> [1] "systime"  "systime2"
#>
#> [[4]]
#> [1] "vegMap" "veg"
#>
#> attr(,"bindings")
#> attr(,"bindings")[[1]]
#> attr(,"bindings")[[1]]$canonicalVersion #> [1] "studyArea" #> #> attr(,"bindings")[[1]]$activeBindingObjects
#> [1] "studyArea2"
#>
#>
#> attr(,"bindings")[[2]]
#> attr(,"bindings")[[2]]$canonicalVersion #> [1] "age" #> #> attr(,"bindings")[[2]]$activeBindingObjects
#> [1] "ageMap"        "timeSinceFire" "tsf"
#>
#>
#> attr(,"bindings")[[3]]
#> attr(,"bindings")[[3]]$canonicalVersion #> [1] "systime" #> #> attr(,"bindings")[[3]]$activeBindingObjects
#> [1] "systime2"
#>
#>
#> attr(,"bindings")[[4]]
#> attr(,"bindings")[[4]]$canonicalVersion #> [1] "vegMap" #> #> attr(,"bindings")[[4]]$activeBindingObjects
#> [1] "veg"
#>
#>


text:
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### AuthorTopic: North Korea 1:1 public beta  (Read 16488 times)

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#### Triad773

• member
• Offline
• Posts: 478
##### Re: North Korea 1:1 public beta
« Reply #36 on: January 04, 2010, 10:00:19 AM »

PD- have you tried turning off Clamp (to Allow) in your nVidia 3D settings by chance?

From the error message it looked like that was erroring out.

Just a thought- I had a somewhat similar issue recent;y with another map. Hope it helps, good luck.

Triad
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#### Checkyersix

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• Dr. Frankenplane
##### Re: North Korea 1:1 public beta
« Reply #37 on: January 04, 2010, 10:08:53 AM »

Sorry PD, I think we got our wires crossed. I meant this static.ini checker:

http://www.allaircraftarcade.com/forum/viewtopic.php?t=20224&highlight=static+checker

Use the search...missing objects function. It should return a list of missing objects, if there are any.

Thanks,

CY6.
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#### pilotsden

• member
• Offline
• Posts: 187
##### Re: North Korea 1:1 public beta
« Reply #38 on: January 04, 2010, 10:26:43 AM »

it has a list of three,but this is not what we need....
shows the two folders CY6_North-k
_TEX
all.ini
nothing else shows...
has also shown i have a list of double entries......
PS
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#### pilotsden

• member
• Offline
• Posts: 187
##### Re: North Korea 1:1 public beta
« Reply #39 on: January 04, 2010, 10:42:29 AM »

I may have found our problem......there are two static ini's....which one should i delete please
the second one also has double entries...but only three......
Double object (174) => (1022): buildings.House$FurnitureSandbag_Wall2 Double object (175) => (1023): buildings.House$FurnitureSandbags_Round2
Double object (1511) => (1652): buildings.House\$ladder
PD
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#### pilotsden

• member
• Offline
• Posts: 187
##### Re: North Korea 1:1 public beta
« Reply #40 on: January 04, 2010, 09:39:14 PM »

On behalf of ''The Boy's of 60 Squadron'' a special thank-you to CY6.he went many an extra mile to solve our online join problem.....it was 100% operational with 12 guys in total able to join and fly uninterupted for two hrs and 15 min this evening with not one glitch or setback.....Fantastic support and so very much appreciated......now to build the mission for Bridges of toko ri....
Also,thanks to all for your input on this thread...
PD
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#### Checkyersix

• Modder
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• Posts: 1194
• Dr. Frankenplane
##### Re: North Korea 1:1 public beta
« Reply #41 on: January 05, 2010, 02:37:20 AM »

*Updated*

Posted the beta 3 version with the actors.static fix that worked for pilotsden & co.

CY6.
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#### Cracken

• FMB addict
• member
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• Posts: 285
##### Re: North Korea 1:1 public beta
« Reply #42 on: January 08, 2010, 03:20:58 PM »

Hi, I love this map and am building a campaign for it! I have respect for 3BG map, but this one is better:-) (3BG boys even forgot the famous mig base at An-tung). The next thing is I see no use for Japan in KTO scenarios. So, THX for your work! Even if you claim it is a beta map, I think it deserves a campaign:-))
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#### Checkyersix

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• Posts: 1194
• Dr. Frankenplane
##### Re: North Korea 1:1 public beta
« Reply #43 on: January 08, 2010, 03:42:21 PM »

Thanks for building a campaign and I look forward to playing it. What period / aircraft are you using?

I like Dixiecapt's map - it's a lot of fun and they managed to squeeze in a lot of detail in much less space. I'd probably put part of Japan on my map too, but I don't think the game could handle it.
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#### Rock

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• Posts: 533
• Aviator modding
##### Re: North Korea 1:1 public beta
« Reply #44 on: January 08, 2010, 03:43:18 PM »

Gonna have to download this when i get back home. Looks like a winner though mate. Well done!
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#### Cracken

• FMB addict
• member
• Offline
• Posts: 285
##### Re: North Korea 1:1 public beta
« Reply #45 on: January 09, 2010, 06:20:41 AM »

I like Dixie's map too. However, I am not patient to wait minutes for the map to load. I would be glad if your map remained as it is. I like it is another option for people with not-so-advanced PCs. And we really do not need Tokyo when shooting migs overt the Yalu.

I hope Cirx will soon give a new FM to F-86, the current one is no match for the Mig.

And my campaign - I will not announce anything but the finished thing. (The reason is simple, I usually change a campaign I work on. I do not want to dissapoint anybody who could be eagerly waiting for it:-) Hope you understand. I hope we all will be soon involved in this great strory. (Will add a link to my campaign here as well.)
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#### SAS~vampire_pilot

• SAS Team
• member
• Online
• Posts: 6918
• a million fixes
##### Re: North Korea 1:1 public beta
« Reply #46 on: January 11, 2010, 10:30:58 PM »

I like Dixie's map too. However, I am not patient to wait minutes for the map to load. I would be glad if your map remained as it is. I like it is another option for people with not-so-advanced PCs. And we really do not need Tokyo when shooting migs overt the Yalu.

that may be right but maybe a s a second map?

there exists a need for a well populated central japan map!!
Tokyo area and down to Kyushu with Kobe and so on is so missing.

#### Cracken

• FMB addict
• member
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##### Re: North Korea 1:1 public beta
« Reply #47 on: January 24, 2010, 01:18:50 AM »

Found this south of Soul...

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# A certain ellipse is tangent to both the -axis and the -axis, and its foci are at and  Find the length of the major axis.

+1
86
3
+109

A certain ellipse is tangent to both the $$x$$-axis and the $$y$$-axis, and its foci are at $$(2, -3 + \sqrt{5})$$ and $$(2, -3 - \sqrt{5})$$ Find the length of the major axis.

May 7, 2019

#1
+101872
+1

The major axis will lie parallel to the y axis

So we have this form   :  (y - k)^2   +  (x - h)^2

_______       _______   =    1

a^2                b^2

The center of the ellipse  is  (2, - 3)  = (h, k)

Since the ellipse is tangent to the y axis and (2, -3) is the center.....then the minor axis must be 4 units in length

So  b = 4/2  = 2   and b^2  = 2

And we can find "a" thusly :   a^2 - b^2  = c^2

a^2  = ???

b^2 = 4

c^2 = (√5)^2  = 5

So

a^2 - 4 = 5

a^2  = 9

a = 3

And the major axis  = 2a  = 2(3)  = 6

Here's a graph : https://www.desmos.com/calculator/iagepa6zop

May 7, 2019
#3
+109
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Thanks only thing what "thusly" is that a math term I should know or is it just like a therefore. I know it is a dumb question I should know the answer to.

May 13, 2019


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The incomplete exponential \boldmath{$_pR_q(\alpha,\beta;z)$} function with some applications
• +1
• Ankit Pal,
• R. Jana,
• Ghazi Khammash,
• AJAY SHUKLA
Ankit Pal
Sardar Vallabhbhai National Institute of Technology
Author Profile
R. Jana
Sardar Vallabhbhai National Institute of Technology
Author Profile
Ghazi Khammash
Al Aqsa University
Author Profile
AJAY SHUKLA
Sardar Vallabhbhai National Institute of Technology
Author Profile

Abstract

In this paper, we are motivated to establish a generalization of $_pR_q(\alpha,\beta;z)$ function in terms of incomplete exponential functions and obtain some properties of the incomplete exponential $_pR_q(\alpha,\beta;z)$ function. Further we give generating relations for incomplete exponential $_pR_q(\alpha,\beta;z)$ function. Some applications related to ground water pumping (Hydrology) modelling and probability theory have also been discussed.


text:
# [R-sig-Geo] Analytical covariance expression of backtransformed Box-Cox data

Ole F. Christensen olefc at daimi.au.dk
Thu Jan 6 10:04:21 CET 2005

```Dear Anders

As far as I know, an exact expression is not available in any nice form.
However you can create an approximation using a first order Taylor
expansion of f around y_0=E[Y_i], assuming a constant mean,

f(y) \approx f(y_0)+ (y-y_0) f`(y_0)

and then use the approximation to calculate the covariance.

It may not be accurate, and you can improve on it by using a higher

Do you actually need the covaraince cov(X_i,X_j) ? or do you only want
mean and varinnce ?

Ole

Anders Malmberg wrote:

>
> I have a question not related to R itself. It is of a theoretical
> nature. I hope this
> is ok.
>
> I am facing the problem where some spatial data follows the Gaussian
> distribution
> after a Box-Cox transformation. I am using geoR and I understand that
> for lambda \neq 0 or 0.5 calculates the mean and variance through
> simulation
> (using backtransform.moments()).
>
> If X is original data and Y is Box-Cox transformed data for which I have
> estimates of the parameters in exponential covariance function, then
> it should be that (mean=0),
>
> cov(X_i,X_j)=E(X_i X_j) = E(f(Y_i) f(Y_j))
>
> where "f" is the inverse of the Box-Cox transform. But this turns out
> to be quite messy.
> Is it possible to find an analytical expression for any lambda?
>
>
> Anders
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo at stat.math.ethz.ch
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
>

--
Ole F. Christensen
BiRC - Bioinformatics Research Center
University of Aarhus

```


text:
# k-partite design

Is the following true? For every $$n \geq 1, k\geq 2$$, there is a set $$S \subseteq [n]^k$$ of size $$|S| = n^2$$ such that every two $$k$$-tuples in $$S$$ have at most one common entry.

Does anyone know if this is true? Is there a reference?

• please explicitly define "one common entry" since you talk about tuples not sets Jan 25, 2022 at 21:21
• If it means "tuples match in at most one coordinate", it would be false already for $n=2$, $k=4$. If one of the tuples is (w.l.o.g.) 1111, each of the other three tuples must have three 2's, so any two of them will have two matching 2's. So is there some other meaning of "one common entry"? Jan 26, 2022 at 1:20
• Thanks, Jukka. I missed this simple example.. Jan 26, 2022 at 12:23
• So this "tuples match in at most one coordinate" is the intended meaning? In that case we have an answer to the question. Jan 26, 2022 at 13:06

Assuming that "at most common entry" means that any two tuples $$(x_1,\ldots,x_k)$$ and $$(y_1,\ldots,y_k)$$ match in at most one position, that is, there is at most one $$i$$ such that $$x_i=y_i$$.
The claim is false for $$n=2$$ and any $$k \ge 4$$. We would need $$n^2=4$$ tuples $$x,y,z,w$$. Then each of $$y$$ and $$z$$ must differ from $$x$$ in at least $$k-1$$ positions, which implies that $$y$$ and $$z$$ match in at least $$k-2 \ge 2$$ positions.
(If the meaning was that any two tuples contain at most one common value, regardless of position, the claim would fail already with $$n=2$$, $$k=2$$, because there are only four different tuples $$(1,1),(1,2),(2,1),(2,2)$$, and $$(1,2),(2,1)$$ have two common values $$1$$ and $$2$$.)


text:
### Tony Phillips' Take Blog on Math Blogs

 Mail to a friend · Print this article · Previous Columns Tony Phillips' Take on Math in the Media A monthly survey of math news

# This month's topics:

## Moiré patterns, rational numbers and quantum fractals

Back in 1976 Douglas Hofstadter was a physics graduate student. His thesis addressed the problem of Bloch electrons in magnetic fields, which comes up in the analysis of the Hall effect. This effect, known since 1879, happens when a conductor in the $(x,y)$-plane is placed in a magnetic field oriented along the $z$-axis. Then a current flowing in the $x$-direction creates a voltage difference in the $y$-direction. The dependance of this Hall voltage $V_H$ on the voltage $V_x$ in the $x$-direction becomes intricate for high magnetic fields and low temperatures, due to quantization.

Bloch electrons are electrons in a periodic potential, for example in a crystalline lattice. If the conductor in the Hall effect has such a structure then, as Hofstadter writes in the published version of his thesis (Phys. Rev. B 14 2239-2249), the analysis is "a very peculiar problem, because it is one of the very few places in physics where the difference between rational numbers and irrational numbers makes itself felt." More specifically, a fundamental parameter in the problem is the ratio between two characteristic periods. One is the period of the motion of an electron in a potential with periodic spacing $a$. This period is proportional to $a^2$. The other is the orbital period of the "cyclotron" motion of electrons in a strong magnetic field of magnitude $B$; that one is proportional to $1/B$. When $B$ is extremely large (Hofstadter's estimate was 100,000 teslas for a typically scaled crystal) the two periods become comparable. Then the variation of $V_H$ with $V_x$ depends critically on whether the two periods are rationally related or not.

Hofstadter worked out the behavior completely, and explained how the graph of the energy spectrum "has some very unusual properties. The large gaps form a very striking pattern somewhat resembling a butterfly; perhaps equally striking are the delicacy and beauty of the fine-grained structure. These are due to a very intricate scheme, by which bands cluster themselves into groups, which themselves may cluster into larger groups, and so on." This pattern, which became known as the Hofstadter butterfly (it was discovered and published well before the concept "fractal" became commonplace), seemed destined to an only theoretical existence, because of the huge magnetic fields involved.

Nevertheless this spring three reports were published with experimental confirmation of features of the butterfly:

All three teams relied on building a new kind of material by depositing one or more layers of graphene (a compound formed of carbon atoms arrayed in a hexagonal lattice) on top of a crystal of boron nitride whose surface has the same tiling, only 1.8% larger. If the two lattice axes are perfectly aligned, a "moiré superlattice" is formed which has some of the physical properties of a 2-dimensional crystal, but with cells about 50 times larger than those in graphene. If the axes have a slight angular offset, the cell size gets smaller, but is still large enough to make an experiment possible with currently available magnets.

Superimposing two hexagonal lattices with slightly different sizes creates a moiré pattern that is again a hexagonal lattice; here for legibility the two are shown with an angular offset of $5^{\circ}$.

Here are sample figures from the articles.

From Kim et al. Height is proportional to the magnetic field $B$, which varies from 0 to 30T; color indicates absolute value of Hall resistivity (proportional to Hall voltage). Traces of the Hofstadter Butterfly appear as "anomalous quantum Hall states" (yellow and red lines, starting around $B = 15$T). Image used courtesy of P. Kim.

From Hunt et al.. Height is proportional to the magnetic field $B$ which with their magnet could reach 45T. The lower diagram compares the experimental results with Gregory Wannier's 1978 predictions that the energy gaps in the Hofstadter spectrum would lie along linear trajectories with rational slope. Larger image. Images courtesy of Ben Hunt.

## The differential geometry of the Endoplasmic Reticulum

John Farrell, who covers science and technology for the Forbes website, posted "Scientists Explore The Pure Geometry Inside Our Cells" on July 24, 2013. He was picking up a research article in the then current Cell, with the title: Stacked Endoplasmic Reticulum Sheets Are Connected by Helicoidal Membrane Motifs. The authors are Mark Terasaki (UConn), Tom A. Rapoport (HHMI, Harvard) and 10 collaborators. The endoplasmic reticulum (ER) is a structure of hollow sheets and tubules inside cells that serves as a locus for synthesis and modification of cellular materials, as well as a highway network for transporting them throughout the cell. The article treats the stacked configuration of the ER, which has been known for about 60 years, and occurs in "cells that secrete most of their synthesized proteins ..., such as pancreatic and salivary gland cells." Mathematically the most striking finding is the one Farrell alludes to: the sheets in the stacks are layers of a local helicoidal structure. As the authors put it: "The overall structure resembles a parking garage."

A stack of parallel slices from a small region of a cell in the salivary gland of a mouse, made with a scanning electron microscope, and showing sheets of the ER. Slice dimensions: $800\times 950\times 40$nm (total volume surveyed here is about $\frac{1}{5}$ of a cubic micron). In these slices, the sheets of the ER appear in cross-section. The authors identify individual sheets, labeled $A,B,C,D,E$ here, and follow them through the sequence of slices. During the sequence, sheets separate and reattach: the analysis shows that the slices in this stack happened to be very nearly parallel with the axis of a local helicoidal structure, so that this combinatorial pattern is the same, overall, as the pattern of intersections of a mathematical helicoid with a moving plane parallel to its axis. (Compare with the schematic diagram on right, and with the MAPLE-generated helicoid in the next image). SEMicrographs courtesy of Mark Terasaki et al..

A plane parallel to the axis of a helicoid and sweeping left to right generates the same overall pattern of intersections as the parallel slices of the ER sample sectioned above.

Why helicoids? Now differential geometry comes into the picture. The authors' hypothesis is that "the observed sheet stack structure corresponds to a minimum of elastic energy of sheet edges and surfaces." An ER sheet is in fact hollow: it consists of two planar membranes connected by an edge membrane (this structure is visible in the SEmicrograph cross-sections above). They consider three contributions to the energy: bending at the edges, bending of surfaces and a component which results from spatial confinement. [Away from the edges the surface is rather flat, so one can expect the bending at the edges to be dominant in the calculation.] Considering a single connection between sheets, the authors note that "the energy of the edge line is minimal if the line curvature is constant and equal to the negative spontaneous curvature."

A double-layer sheet boundary has negative Gaussian curvature when the boundary is concave (curves away from the surface). The bending energy is minimized when the boundary follows a constant-pitch spiral, with pitch determined by the layer separation and other physical parameters.

Finally, the authors observe that that in a given volume of stacked ER there will be many connections. Since a right-handed helicoidal connection block can fit together smoothly with a left-handed one, the authors hypothesize connections with the two helicities fitting together checkerboard-style in a locally planar array. They remark that "the predicted one-to-one relationship between left- and right-handed helicoidal connections is in reasonable agreement with the 3D reconstructions of the experimental data."

In a "Preview" in the same issue, Wallace Marshall (UCSF) refers to D'Arcy Thompson. A century ago, he "proposed that physical principles such as surface tension could dictate biological form. But then the genome happened, and with it came the desire to explain away questions of cellular structure by telling ourselves that geometry is encoded in the genome." Marshall points to this paper as breathing "new life into the old dream of mathematical biology," and ends: "Maybe ER stack connectors are special cases in that simple math and physics won't explain all or even most cellular structure. The jury is still out. The fact that Terasaki et al. .... needed advanced microscopy methods to visualize their structure suggests that we might not see recognizable mathematical forms because we don't yet know how to look for them."

Tony Phillips
Stony Brook University
tony at math.sunysb.edu


text:
Problem with Dot and FortranForm

I am trying to convert some set of equations to a form that will be easy for Python to evaluate numerically, hence I am using Mathematica's FortranForm

My problem is that

FortranForm[np.diag]

gives

Dot(np,diag)

whereas I want

np.diag

I do not want

FortranForm["np.diag"]

which results in

"np.diag"

What I want is to be able to cast the DiagonalMatrix[equations] part of my expressions to the equivalent in Python - np.diag(equations), where I have imported numpy as np

Solution, but not the desired one

I found a way round my problem, though it is not what I want, but I will post it for people that my just care about the end result.

Use FortranForm["np.diag"] and then export the result to a text file. Then in Python one can read the file and rewrite it line by line, while stripping all the quotes using this piece of code

def fromMathematica(func):
"""" string -> string

Imports a file, created by Mathematica and reads it, so that it can be evaluated for specific values
"""
file = open('path' + func + .txt' , 'r+')
file.seek(0)
file.truncate()
for line in lines:
line = line.replace('"', '').strip()
file.write(line)
file.seek(0)
return m

• You have to do some transformations manually. In this case, you might want to use StringReplace. – Sumit Dec 15 '16 at 10:34
• I am not sure I see your point. My problem is that if it is a string, FortranForm will return it surrounded by quotes, which is what I want to avoid – ThunderBiggi Dec 15 '16 at 11:58
• I think you are taking an ill-concieved approach trying to use mathematics dot product function to produce a name-scoping construct in python. Suggest name the function something like npdotdiag in mathematica and do a stringreplace on the result. (You should not need to do anything by hand! ) – george2079 Dec 15 '16 at 12:58

Probably I don't understand your problem correctly, still giving it a try ..

ff = FortranForm[p + DiagonalMatrix[a + b]]

p + DiagonalMatrix(a + b)

StringReplace[ToString[ff], "DiagonalMatrix" -> "np.diag"]

p + np.diag(a + b)

• This exactly solves my problem for the moment. I didn't think of replacing stuff after using FortranForm. I will see what happens when I try that approach on my pages long equations :) – ThunderBiggi Dec 15 '16 at 14:15

I would give DiagonalMatrix a custom FortranForm:

Unprotect[DiagonalMatrix];
Format[DiagonalMatrix,FortranForm]=Format["np.diag", OutputForm];
Protect[DiagonalMatrix];

Then:

ToString[p + DiagonalMatrix[a + b], FortranForm]

"p + np.diag(a + b)"