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# module

## Primary tabs

Synonym:
left module, right module
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### correction of definition

The module definition does not require an identity element in the ring. Those satisfying 1 * m = m for all m in the module are called
unitary modules.
-- S.A. G.

### correction of typographicalerror of unital module

Left (right) R modules M for rings R with identity 1 such that 1 * m = m (m * 1 = m) for all m in M are call unital modules.
-- S. A. G.

### typographical correction of unital module

Left (right) R modules M for rings R with identity 1 such that 1 * m = m (m * 1 = m) for all m in M are called unital modules.
-- S. A. G.

### simplifying the definition

Properties 1 through 4 are just the propreties of an abelian group. Wouldn't it be simpler to say that a module is an abelian group (M,+) with a binary operation . : R x M -> M that satisfies properties 5 through 7?

format: plain


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Ornstein-Uhlenbeck process written explicitly

I need to show that the Ornstein-Uhlenbeck process, $$dX_t = -\theta X_tdt + dB(t)$$ Where $X_0=0$, $B(t)$ is Brownian motion and $\theta>0$

can be written explicitly as: $$X_t=B(t) - \theta \exp(-\theta t)\int_0^t\exp(\theta s)B(s)ds$$

I can use Ito's lemma to get it to the form $X_t = \exp(-\theta t)\int_0^t\exp(\theta s)dB(s)$, but this isn't quite what I want, and am not certain how to proceed

$$\exp(\theta t) \cdot B_t = \int_0^t \exp(\theta s) \, dB_s + \theta \int_0^t \exp(\theta s) B_s \, ds,$$
$$\int_0^t \exp(\theta s) \, dB_s = \exp(\theta t) \cdot B_t - \theta \int_0^t \exp(\theta s) B_s \, ds.$$


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# Math Help - Where do I start

1. ## Where do I start

If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.

2. Originally Posted by Nichelle14
If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.
Assume that,
$r+x$ is rational.
Thus,
$r+x=\frac{p}{q}$
Then,
$x=\frac{p}{q}-r$
But, $r$ is rational,
Thus,
$x$ must be rational.
----
Assume that,
$rx$ is rational.
Thus,
$rx=\frac{p}{q}$
Now, $r\not = 0$ thus,
$x=\frac{p}{rq}$
Thus, $x$ is rational.

3. Thank you. That makes sense. I thought of doing something with p/q, but didn't know how to proceed.
Again thank you.

4. Originally Posted by Nichelle14
Thank you. That makes sense. I thought of doing something with p/q, but didn't know how to proceed.
Again thank you.
You are welcome.
Let us keep all you question in "Number Theory" section. I like to leave misselanous topic in that section.


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Home > Error Function > Complementry Error Function

# Complementry Error Function

## Contents

Practice online or make a printable study sheet. Schöpf and P. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Google search: Google's search also acts as a calculator and will evaluate "erf(...)" and "erfc(...)" for real arguments. navigate to this website

Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. MR0167642. Values at Infinity Keywords: Fresnel integrals See also: info for 7.2(iii) 7.2.9 limx→∞C(x) =12, limx→∞S(x) =12. LCCN65-12253. https://en.wikipedia.org/wiki/Error_function

## Complementary Error Function Excel

ISBN 978-0-486-61272-0. Similarly, the En for even n look similar (but not identical) to each other after a simple division by n!. The error function and its approximations can be used to estimate results that hold with high probability. Math.

1. J.
2. W.
3. x cannot be sparse.
4. See [2]. ^ http://hackage.haskell.org/package/erf ^ Commons Math: The Apache Commons Mathematics Library ^ a b c Cody, William J. (1969). "Rational Chebyshev Approximations for the Error Function" (PDF).
5. At the real axis, erf(z) approaches unity at z→+∞ and −1 at z→−∞.
6. The defining integral cannot be evaluated in closed form in terms of elementary functions, but by expanding the integrand e−z2 into its Maclaurin series and integrating term by term, one obtains
7. Symbols: Γ(z): gamma function, inerfc(z): repeated integrals of the complementary error function, x: real variable and n: nonnegative integer Keywords: repeated integrals of the complementary error function Permalink: http://dlmf.nist.gov/7.18.F1 Encodings: pdf,
8. Level of Im(ƒ)=0 is shown with a thick green line.

Wolfram Language» Knowledge-based programming for everyone. Symbols: e: base of exponential function, U(a,z): parabolic cylinder function, inerfc(z): repeated integrals of the complementary error function, z: complex variable and n: nonnegative integer A&S Ref: 7.2.13 Referenced by: §12.7(ii) The Q-function can be expressed in terms of the error function as Q ( x ) = 1 2 − 1 2 erf  ( x 2 ) = 1 2 Inverse Complementary Error Function Derivative and integral The derivative of the error function follows immediately from its definition: d d z erf  ( z ) = 2 π e − z 2 . {\displaystyle

A printed companion is available. 7.17 Inverse Error Functions7.19 Voigt Functions ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.9/ See [2]. ^ http://hackage.haskell.org/package/erf ^ Commons Math: The Apache Commons Mathematics Library ^ a b c Cody, William J. (1969). "Rational Chebyshev Approximations for the Error Function" (PDF). Derivative and integral The derivative of the error function follows immediately from its definition: d d z erf  ( z ) = 2 π e − z 2 . {\displaystyle https://en.wikipedia.org/wiki/Error_function Softw., 19 (1): 22–32, doi:10.1145/151271.151273 ^ Zaghloul, M.

This substitution maintains accuracy. Complementary Error Function In Matlab When erfc(x) is close to 1, then 1 - erfc(x) is a small number and might be rounded down to 0. ISBN978-1-4020-6948-2. ^ Winitzki, Sergei (6 February 2008). "A handy approximation for the error function and its inverse" (PDF). The pairs of functions {erff(),erfcf()} and {erfl(),erfcl()} take and return values of type float and long double respectively.

## Complementary Error Function Calculator

D: A D package[16] exists providing efficient and accurate implementations of complex error functions, along with Dawson, Faddeeva, and Voigt functions. https://www.mathworks.com/help/matlab/ref/erfc.html N ! ∫ x ∞ t − 2 N e − t 2 d t , {\displaystyle R_ − 6(x):={\frac {(-1)^ − 5}{\sqrt {\pi }}}2^ − 4{\frac {(2N)!} − 3}\int _ Complementary Error Function Excel Matlab provides both erf and erfc for real arguments, also via W. Complementary Error Function Table The integrand ƒ=exp(−z2) and ƒ=erf(z) are shown in the complex z-plane in figures 2 and 3.

The derivative is given by (4) and the indefinite integral by (5) It has the special values (6) (7) (8) It satisfies the identity (9) It has definite integrals (10) (11) Symbols: erfcz: complementary error function, dfdx: derivative of f with respect to x, e: base of exponential function, !: factorial (as in n!), inerfc(z): repeated integrals of the complementary error function, Indeed, Φ ( x ) = 1 2 π ∫ − ∞ x e − t 2 2 d t = 1 2 [ 1 + erf  ( x 2 my review here Applied Mathematics Series. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.).

Defines: w(z): complementary error function Symbols: erfcz: complementary error function, dx: differential of x, e: base of exponential function, ∫: integral and z: complex variable A&S Ref: 7.1.3 Referenced by: §7.19(i), Complementary Error Function Mathematica Supancic, "On Bürmann's Theorem and Its Application to Problems of Linear and Nonlinear Heat Transfer and Diffusion," The Mathematica Journal, 2014. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end.

## The pairs of functions {erff(),erfcf()} and {erfl(),erfcl()} take and return values of type float and long double respectively.

Defines: inerfc(z): repeated integrals of the complementary error function Symbols: dx: differential of x, e: base of exponential function, !: factorial (as in n!), ∫: integral, z: complex variable and n: Your cache administrator is webmaster. Defines: F(z): Dawson’s integral Symbols: dx: differential of x, e: base of exponential function, ∫: integral and z: complex variable A&S Ref: 7.1.1 Permalink: http://dlmf.nist.gov/7.2.E5 Encodings: TeX, pMML, png See also: Complementary Error Function Ti 89 Defines: Hhn(z): probability function Symbols: inerfc(z): repeated integrals of the complementary error function, z: complex variable and n: nonnegative integer A&S Ref: 7.2.10 Referenced by: §12.7(ii) Permalink: http://dlmf.nist.gov/7.18.E12 Encodings: TeX, pMML,

Haskell: An erf package[18] exists that provides a typeclass for the error function and implementations for the native (real) floating point types. Instead, replace 1 - erfc(x) with erf(x).For expressions of the form exp(x^2)*erfc(x), use the scaled complementary error function erfcx instead. The system returned: (22) Invalid argument The remote host or network may be down. http://freqnbytes.com/error-function/compute-error-function.php This allows one to choose the fastest approximation suitable for a given application.

Online Integral Calculator» Solve integrals with Wolfram|Alpha. Washington, DC: Hemisphere, pp.385-393 and 395-403, 1987. Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (2007), "Section 6.2. Intermediate levels of Re(ƒ)=constant are shown with thin red lines for negative values and with thin blue lines for positive values.

LCCN64-60036. IEEE Transactions on Communications. 59 (11): 2939–2944. Keywords: Dawson’s integral Referenced by: §8.11(iv), §8.12, §8.4 Permalink: http://dlmf.nist.gov/7.2.ii See also: info for 7.2 7.2.5 F(z)=e-z2∫0zet2dt. Generalized error functions Graph of generalised error functions En(x): grey curve: E1(x) = (1−e−x)/ π {\displaystyle \scriptstyle {\sqrt {\pi }}} red curve: E2(x) = erf(x) green curve: E3(x) blue curve: E4(x)

Incomplete Gamma Function and Error Function", Numerical Recipes: The Art of Scientific Computing (3rd ed.), New York: Cambridge University Press, ISBN978-0-521-88068-8 Temme, Nico M. (2010), "Error Functions, Dawson's and Fresnel Integrals", Springer-Verlag. By using this site, you agree to the Terms of Use and Privacy Policy. Both functions are overloaded to accept arguments of type float, double, and long double.

Symbols: erfcz: complementary error function, erfz: error function, ph: phase and z: complex variable A&S Ref: 7.1.16 (in different form) Referenced by: §7.7(i) Permalink: http://dlmf.nist.gov/7.2.E4 Encodings: TeX, TeX, pMML, pMML, png, Java: Apache commons-math[19] provides implementations of erf and erfc for real arguments. Math. http://mathworld.wolfram.com/Erfc.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical.

Please try the request again. Your cache administrator is webmaster. For |z| < 1, we have erf  ( erf − 1  ( z ) ) = z {\displaystyle \operatorname ζ 1 \left(\operatorname ζ 0 ^{-1}(z)\right)=z} .


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Forecasting Time Series: Stationary vs Non-Stationary

Let's say that I have a non-stationary time series and that the series can be transformed to a stationary series using a first difference. If I want to forecast this series using ARIMA then what is the difference between forecasting using the original non-stationary series and the forecasting using the now stationary differenced series? That is, can I expect the forecast for the stationary series to be more accurate than the forecast for non-stationary series?

I am aware that one advantage of forecasting with the stationary series will have the advantage of also producing forecast intervals (which are dependent upon the assumption of a stationary series).

[W]hat is the difference between forecasting using the original non-stationary series and the forecasting using the now stationary differenced series?

(Here I deliberately left out the qualification that the series can be transformed to a stationary series using first differencing and that the OP is interested in forecasting using ARIMA in particular.)

The problem with nonstationary data is that for most of the time series models, the model assumptions are violated when nonstationary data is used. This leads to the estimators no longer having the nice properties such as asymptotic normality and sometimes even consistency. So if you apply a model that requires a stationary series to a nonstationary series, you will likely get poor estimates of the model parameters and hence poor forecasts.

(Now let me add the qualification back.)

For an integrated series $x_t$ that can be made stationary using first differencing, $\Delta x_t$, and that can be approximated by an ARIMA model reasonably well, there are three ways to go:

1. Force stationarity and estimate an ARIMA($p,0,q$) model for the original series $x_t$.
2. Force, or allow for, first differencing so that you end up with ARIMA($p,1,q$) model for the original data $x_t$.
3. Difference the series manually and then apply ARIMA($p,0,q$) model for the differenced series $\Delta x_t$.

Option 1. is the only one that is clearly asking for trouble as it forces stationarity in presence of nonstationary data. Options 2. and 3. are essentially the same, the difference being in whether you difference $x_t$ manually outside the model or as an initial step within the model.

[C]an I expect the forecast for the stationary series to be more accurate than the forecast for non-stationary series?

If you have in mind an integrated series $x_t$ and its first-differenced stationary version $\Delta x_t$, you will have greater accuracy when forecasting $\Delta x_t$, but does that matter? It could be misleading to think that you can get more accurate forecasts by focusing on $\Delta x_t$ rather than $x_t$. It is perhaps the most natural to think about gains in accuracy when the underlying process of interest is kept the same, e.g. a gain in accuracy due to using a better approximation to the same process. Meanwhile, if you change the underlying object (go from $x_t$ to $\Delta x_t$), the gain is not really a gain, in the following sense. It is a bit like shooting at a target from 100m and from 10m. You will be more accurate from 10m, but isn't that obvious and irrelevant?

If you have in mind two unrelated series $x_{1,t}$ and $\Delta x_{2,t}$ where the first one is integrated while the second one is stationary, you may expect that in the long run you will have greater forecast accuracy for $\Delta x_{2,t}$. In the short run this might not hold if the variance of $\Delta x_{1,t}$ (the increments of the first process) is small compared to the variance of $\Delta x_{2,t}$.

I am aware that one advantage of forecasting with the stationary series will have the advantage of also producing forecast intervals (which are dependent upon the assumption of a stationary series).

Actually, you can get forecast intervals regardless of whether the series is integrated or stationary. If you model an integrated time series using its first differences, you obtain the forecast intervals and cumulatively add them when forming the forecast interval for the integrated series. That is why forecast intervals for an integrated series expand linearly while those of a stationary series expand slower than linearly (illustrations can be found in time series textbooks).

In your case there's no difference. ARIMA(p,1,q) is the same as ARMA(p,q) on the differenced series. ARIMA can model non-stationary series, ARMA cannot. So, for ARMA you do differencing before feeding the series into it.

See how ARIMA(p,D,q) models are defined at MATLAB web site, for instance: $$\phi(L)(1-L)^Dy_t=c+\theta(L)\varepsilon_t,$$ where $L$ is the difference operator $L^Dy_t=y_{t-D}$, and $\phi(L),\theta(L)$ - lag operator functions.

Here's how ARIMA(1,0,1) would look like following this definition: $$y_t-\phi_1y_{t-1}=c+\varepsilon_t+\theta_1\varepsilon_{t-1}$$

and ARIMA(1,1,1): $$(y_t-y_{t-1})-\phi_1(y_{t-1}-y_{t-2})=c+\varepsilon_t+\theta_1\varepsilon_{t-1}$$

which is the same as ARMA(1,1) on the differenced series $\Delta y_t=y_t-y_{t-1}$. It's even easier to see when you know that $(1-L)y_t=\Delta y_t$, the difference operator.

If you're wondering why ARIMA can model non-stationary series, then it's the easiest to see on the simplest ARIMA(0,1,0): $y_t=y_{t-1}+c+\varepsilon_t$. Take a look at the expectations: $$E[y_t]=E[y_{t-1}]+c=e[y_0]+ct,$$ The expectation of the series is non-stationary, it has a time trend so you could call it trend-stationary though.

• This is being automatically flagged as low quality, probably because it is so short. At present it is more of a comment than an answer by our standards. Can you expand on it? You can also turn it into a comment. Feb 13 '17 at 18:53


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# # Electronic Circuits Lecture 7 Phasor

. 3 min read

Motivation: to solve the normal Sinusoidal Signal sources more efficiently

## 求解正弦输入的电路 (AC) Steady response

$$L\frac{di}{dt}+Ri = V_m cos(\omega t+\phi) \ i = \underbrace{\frac{-V_m}{\sqrt{R^2+\omega^2L^2}}cos(\phi-\theta)e^{(-R/L)t}}{\text{Transient response}}+\underbrace{\frac{-V_m}{\sqrt{R^2+\omega^2L^2}}cos(\omega t+\phi-\theta)}{\text{Steady state response}}$$

1. Steady state solution is sinusoidal稳态是正弦形式的
2. Response frequency = source frequency响应频率和输入频率相同
3. Magnitude & phase of response differs from that of source响应的幅度和相位与源的响应不同（相位不同）

LTI: Linear Time Invariant (LTI) circuit线性时不变

WHY?

natural phenomenon are sinusoidal.

very easy signal to generate and transmit.

very easy to handle mathematically.

EXAMPLE

1. 正弦
2. 单频
3. 稳态


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# Overview

This model is a fine-tuned checkpoint of RoBERTa-large (Liu et al. 2019). It enables reliable binary sentiment analysis for various types of English-language text. For each instance, it predicts either positive (1) or negative (0) sentiment. The model was fine-tuned and evaluated on 15 data sets from diverse text sources to enhance generalization across different types of texts (reviews, tweets, etc.). Consequently, it outperforms models trained on only one type of text (e.g., movie reviews from the popular SST-2 benchmark) when used on new data as shown below.

# Predictions on a data set

If you want to predict sentiment for your own data, we provide an example script via Google Colab. You can load your data to a Google Drive and run the script for free on a Colab GPU. Set-up only takes a few minutes. We suggest that you manually label a subset of your data to evaluate performance for your use case. For performance benchmark values across various sentiment analysis contexts, please refer to our paper (Heitmann et al. 2020).

# Use in a Hugging Face pipeline

The easiest way to use the model for single predictions is Hugging Face's sentiment analysis pipeline, which only needs a couple lines of code as shown in the following example:

from transformers import pipeline
sentiment_analysis = pipeline("sentiment-analysis",model="siebert/sentiment-roberta-large-english")
print(sentiment_analysis("I love this!"))

# Use for further fine-tuning

The model can also be used as a starting point for further fine-tuning of RoBERTa on your specific data. Please refer to Hugging Face's documentation for further details and example code.

# Performance

To evaluate the performance of our general-purpose sentiment analysis model, we set aside an evaluation set from each data set, which was not used for training. On average, our model outperforms a DistilBERT-based model (which is solely fine-tuned on the popular SST-2 data set) by more than 15 percentage points (78.1 vs. 93.2 percent, see table below). As a robustness check, we evaluate the model in a leave-one-out manner (training on 14 data sets, evaluating on the one left out), which decreases model performance by only about 3 percentage points on average and underscores its generalizability. Model performance is given as evaluation set accuracy in percent.

Dataset DistilBERT SST-2 This model
McAuley and Leskovec (2013) (Reviews) 84.7 98.0
McAuley and Leskovec (2013) (Review Titles) 65.5 87.0
Maas et al. (2011) 80.6 96.0
Kaggle 87.2 96.0
Pang and Lee (2005) 89.7 91.0
Nakov et al. (2013) 70.1 88.5
Shamma (2009) 76.0 87.0
Blitzer et al. (2007) (Books) 83.0 92.5
Blitzer et al. (2007) (DVDs) 84.5 92.5
Blitzer et al. (2007) (Electronics) 74.5 95.0
Blitzer et al. (2007) (Kitchen devices) 80.0 98.5
Pang et al. (2002) 73.5 95.5
Speriosu et al. (2011) 71.5 85.5
Hartmann et al. (2019) 65.5 98.0
Average 78.1 93.2

# Fine-tuning hyperparameters

• learning_rate = 2e-5
• num_train_epochs = 3.0
• warmump_steps = 500
• weight_decay = 0.01

Other values were left at their defaults as listed here.

# Citation and contact

Please cite this paper when you use our model. Feel free to reach out to christian.siebert@uni-hamburg.de with any questions or feedback you may have.

@article{heitmann2020,
title={More than a feeling: Benchmarks for sentiment analysis accuracy},
author={Heitmann, Mark and Siebert, Christian and Hartmann, Jochen and Schamp, Christina},
journal={Available at SSRN 3489963},
year={2020}
}


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# L/quasipoly vs NL/poly

Savitch's theorem shows that NSPACE($$S(n)$$) $$\subseteq$$ SPACE($$S(n)^2$$), which means that nondeterminism can be replaced by more spaces in this situation. Is it known whether nondeterminism can be replaced by advice strings in a similar situation?

Especially, I would like to ask about "L/quasipoly vs NL/poly". If L/quasipoly $$\supset$$ NL/poly is proved, is this a new result?

(Here, L/quasipoly means (informally) L with quasipolynomial size advice strings.)

[Supplementary explanations]

Currently, I think that I may be able to prove that polynomial-size nondeterministic branching programs can be simulated by quasipolynomial-size $$O(\log n)$$-width boolean circuits.

• As far as I can see, an L machine can only access a polynomial part of the advice string, hence trivially L/quasipoly=L/poly. If this is not what you meant, you should specify the model more precisely. – Emil Jeřábek Oct 2 '18 at 8:09
• I'm not an expert for TM, but I have understood P includes L. Can L machine really only access a polynomial part of the advice string? For example, L machine can read the advice string one by one from left to right. Is this wrong? – Hiroki Morizumi Oct 2 '18 at 8:38
• So, the advice model is just a read-only tape, with the machine having no way of keeping track of the current position? I see that the TM is now not limited to polynomially many configurations, hence it can also run for superpolynomial time, eliminating my objection. But now I’m worried if this does not give the TM polylogarithmic space in a sneaky way, by abusing the head position to encode polylogarithmically many bits. – Emil Jeřábek Oct 2 '18 at 10:21
• I probably recognized my misunderstanding. "L/quasipoly" is my fault, but I still would like to be working on this problem. Please let me edit the question. – Hiroki Morizumi Oct 2 '18 at 12:24
• How about making the advice tape one-way? Mini-exercise: Even with this def, L/exp contains every language. – domotorp Oct 2 '18 at 20:43


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# Math Help - vectors velocity

1. ## vectors velocity

an airplane is headed north with a constant velocity of 450km/h. the plane encounters a wind from the west at 100 km/h.

a) in 3h, how far will the plane travel?
b) in what direction will the plane travel?

2. Originally Posted by william
an airplane is headed north with a constant velocity of 450km/h. the plane encounters a wind from the west at 100 km/h.

a) in 3h, how far will the plane travel?
b) in what direction will the plane travel?
In one hour the plane will travel $\sqrt{450^2+100^2}$ therefore in three hours it will cover $3\sqrt{450^2+100^2}$ km

b) $arctan \left(\frac{450}{100}\right)$

3. Originally Posted by e^(i*pi)
In one hour the plane will travel $\sqrt{450^2+100^2}$ therefore in three hours it will cover $3\sqrt{450^2+100^2}$ km

b) $arctan \left(\frac{450}{100}\right)$
i understand a, it makes sense but can you elaborate a bit more on b? the book gives the answer at 12.5^o east of north

4. Originally Posted by william
i understand a, it makes sense but can you elaborate a bit more on b? the book gives the answer at 12.5^o east of north
I should point out that there I made a mistake, that is the angle the plane makes with the horizontal so the actual angle is $90 - \arctan(4.5)$.

When I drew my diagram I put the plane at the origin and drew a horizontal line right to represent the wind (100) and a vertical line up to represent the plane going north (450)

I then made a right-angled triangle from these lines with an angle \theta between them. Part a is asking for the hypotenuse which is Pythagoras' as you got.

Part b is one of the trig ratios, since the opposite and the adjacent are known directly I used $tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{450}{100} = 4.5$.

However, this is the angle is makes with East (as I forgot in my last post), to find the answer from North we need to take this angle from 90.

$90 - \arctan (4.5) = 12.5$


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SCREE_PLOT {EFA.dimensions} R Documentation

## Scree plot of eigenvalues

### Description

Produces a scree plot of eigenvalues for raw data or for a correlation matrix.

### Usage

SCREE_PLOT(data, corkind, Ncases, verbose)

### Arguments

 data An all-numeric dataframe where the rows are cases & the columns are the variables, or a correlation matrix with ones on the diagonal.The function internally determines whether the data are a correlation matrix. corkind The kind of correlation matrix to be used if data is not a correlation matrix. The options are 'pearson', 'kendall', 'spearman', 'gamma', and 'polychoric'. Required only if the entered data is not a correlation matrix. Ncases The number of cases for a correlation matrix. Required only if the entered data is a correlation matrix. verbose Should detailed results be displayed in console? TRUE (default) or FALSE

### Value

 totvarexpl The eigenvalues and total variance explained

### Author(s)

Brian P. O'Connor

### Examples

# Field's RAQ factor analysis data
SCREE_PLOT(data_Field, corkind='pearson')

# the Harman (1967) correlation matrix
SCREE_PLOT(data_Harman)

# Rosenberg Self-Esteem scale items
SCREE_PLOT(data_RSE, corkind='polychoric')

# NEO-PI-R scales
SCREE_PLOT(data_RSE)

[Package EFA.dimensions version 0.1.7.4 Index]


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# Trigonometry Homework #9 due 5-4

Graph the following functions.

1. $y=\sec\left[\frac{1}{2}\left(x+\frac{\pi}{3}\right)\right]$

2. $y=2\sec{x}+3$

3. $y=\frac{\csc(\pi{x})}{2}$

4. $y=\csc\left(x-\frac{\pi}{4}\right)$

5. $y=\cot(2\pi{x})-1$


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Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

Oxidation Number

Oxidation number in simple terms can be described as the number that is allocated to elements in a chemical combination. The oxidation number is basically the count of electrons that atoms in a molecule can share, lose or gain while forming chemical bonds with other atoms of a different element.

Oxidation number is also referred to as oxidation state. However, sometimes these terms can have a different meaning depending on whether we are considering the electronegativity of the atoms or not. The oxidation number term is used frequently in coordination chemistry.

In general, oxidation state or number helps us describe the transfer of electrons. However, students have to note that it is different from a formal charge which determines the arrangement of atoms. The oxidation number/state is also used to determine the changes that occur in redox reactions. Meanwhile, it is quite similar to valence electrons.

What is Oxidation Number?

Oxidation number of an atom is defined as the charge that an atom appears to have on forming ionic bonds with other heteroatoms. An atom having higher electronegativity (even if it forms a covalent bond) is given a negative oxidation state.

The definition, assigns oxidation state to an atom on conditions, that the atom –

i) Bonds with heteroatoms.

ii) Always form ionic bonding by either gaining or losing electrons, irrespective of the actual nature of bonding.

Since an atom can have multiple valence electrons and form multiple bonds, all of them will be, assumed to be ionic and assigned oxidation state equal to the number of electrons involved in the bonding. So, oxidation number or state is, a hypothetical case of assumption of atoms forming an ionic bond.

In the complex cation, tetroxoplatinum (PtO4)2+, Platinum possess an oxidation state of 10. Ten is the maximum oxidation state exhibited by any atom. It appears to have lost ten electrons to form the ion. But, the ionization energy required for removing an electron from charges positively species increases heavily.

Larger the charge, it is difficult to remove an electron and so, higher the ionization energy. So, the removal of ten electrons is highly hypothetical. Similarly, the addition of electron also becomes difficult with increasing negative charge.

Oxidation states, larger than three, whether positive or negative are practically impossible. In spite of the assumption, it helps in understanding the changes accompanying the atom undergoing a chemical change.

How To Find Oxidation Number Of An Atom?

Oxidation number or state of an atom/ion is the number of electrons an atom/ion that the molecule has either gained or lost compared to the neutral atom. Electropositive metal atoms, of group I, 2 and 3 lose a specific number of electrons and have always constant positive oxidation numbers.

In molecules, more electronegative atom gain electrons from a less electronegative atom and have negative oxidation states. The numerical value of the oxidation state is equal to the number of electrons lost or gained.

Oxidation number or oxidation state of an atom or ion in a molecule/ion is assigned by:

i) Summing up the constant oxidation state of other atoms/molecules/ions that are bonded to it and

ii) Equating, the total oxidation state of a molecule or ion to the total charge of the molecule or ion.

Atoms/ Molecules and Ions that have Constant Oxidation State (Number)

a) The net charge on neutral atoms or molecules is zero. So the overall oxidation state of them is zero.

For example oxidation state of elemental atoms such as sodium, magnesium, iron is zero. Similarly, the net oxidation state of neutral molecules such as oxygen, chlorine, water, ammonia, methane, potassium permanganate is zero.

The oxidation state of atoms in homo-polar molecules is zero. The oxidation number of an atom in an oxygen molecule is zero.

b) The oxidation state of charged ions is equal to the net charge of the ion. So,

1. Oxidation number of all alkali metal ions is always = +1
2. Oxidation number of all alkaline earth metal ions is always = +2
3. Oxidation number of all boron family metal ions is always = +3
4. Oxidation number of hydrogen in proton (H+) is +1, and in hydride is -1.
5. Oxidation number of oxygen in oxide ion(O2-) is -2, and in peroxide ion(O-O2-) is -1.

Calculation of Oxidation Number of an Atom in a Molecule/Ion

Oxidation number of potassium permanganate (KMnO4) = Sum of oxidation number of (K + Mn + 4O) = 0

Oxidation number of permanganate ion (MnO4) = Sum of oxidation number of ( Mn + 4O)= -1

Calculation of Oxidation Number of atoms Occurring Only Once in a Molecule

Examples 1: Oxidation state of chlorine in KCl

KCl is neutral and so, net charge=0

Oxidation state of KCl = Oxidation state of potassium + oxidation state of chlorine = 0.

Oxidation state of potassium = +1

Oxidation states → +1 + x = 0: x = -1

Atoms in the species → K Cl

Oxidation state of chlorine in KCl = -1

Example 2: Oxidation number of Manganese in permanganate ion MnO4

Charge on the permanganate ion is -1

Oxidation state of permanganate ion =Oxidation state of manganese + 4 oxidation state of oxygen = -1.

Oxidation state of oxygen = -2

Oxidation states → x + (4*-2) = -1: x = +7

Atoms in the species → Mn 4O

Oxidation state of manganese = +7

Example 3: Oxidation number of a metal ion in a complex.

i) Ni(CO) 4.

The total charge of the complex is zero. CO is a neutral molecule.

Oxidation states → x + (4*0) = 0: x = 0

Atoms in the species → Ni 4 CO

Nickel is also in zero oxidation state.

ii) [CoCl2(NH3)4]Cl.

The complex can be written in the ionic forms as [CoCl2(NH3)4]+Cl.

Metal is in a cationic complex with a unitary positive charge. Ammonia is a neutral ligand and chlorine has a unit negative charge.

Oxidation number of [CoCl2(NH3)4]+ = Oxidation number of (Co + 2Cl + 4×0) = +1.

Oxidation states → x + (2*-1) + 4*0 = +1: x = +3

Atoms in the species → Co 2Cl 4 NH3

Oxidation number of cobalt in the complex = +3

Calculation of Oxidation Number of Atoms Occurring More Than Once in a Molecule and Having Identical Bonding

Atom occurring ore than in a molecule may be, bonded in an identical way or not. If they are identically bonded, then there is no difference between them, and all the atoms will have the same oxidation numbers. The oxidation state of such an atom in a molecule can be, calculated by the normal method.

The average oxidation number will be the same as calculated individually and a whole number.

Example 1: The number of atoms of chlorine is two in the molecules Cl2O, Cl2O5 and Cl2O7. But, the environment of both atoms of chlorine is the same as shown by their structures. The oxidation number of the atoms calculated either individually or from the whole molecule is the same.

i) Cl2O:

Cl2O is neutral and so, net charge=0.

Net oxidation state of Cl2O = 2 x Oxidation state of chlorine + 1x Oxidation state of oxygen = 0.

Oxidation state of oxygen = -2.

Oxidation states → 2 x + (-2) = 0: x = +1

Atoms in the species → 2Cl O

Oxidation state of chlorine in Cl2O=

$$\begin{array}{l}\frac{2}{2}\end{array}$$
= +1

ii) Cl2O5:

Cl2O5 is neutral and so, net charge=0

Oxidation state of Cl2O5 = 2 x Oxidation state of chlorine + 5 x oxidation state of oxygen = 0.

Oxidation state of oxygen = -2.

Oxidation states → 2x + (5*-2) = 0: x = +5

Atoms in the species → 2Cl 5O

Oxidation state of chlorine in Cl2O5 =

$$\begin{array}{l}\frac{10}{2}\end{array}$$
= +5

iii) Cl2O7:

Cl2O7 is neutral and so, net charge=0

Oxidation state of Cl2O7 = 2 x Oxidation state of chlorine + 7 x oxidation state of oxygen = 0.

Oxidation state of oxygen = -2.

Oxidation states → 2x + (7*-2) = 0: x = +7

Atoms in the species → 2Cl 7O

Oxidation state of chlorine in Cl2O =

$$\begin{array}{l}\frac{14}{2}\end{array}$$
= +7

Note: Except the atoms/molecules/ions mentioned, as having a constant oxidation state, oxidation state of other atoms/molecule and ions will vary depending on the molecule they are present.

In the given examples, the oxidation state of chlorine is not constant, but variable (+1, +5 and +7)

Example 2: Oxidation state of chromium in dichromate anion.

Dichromate ion is Cr2O72-.

Charge on the ion is -2.

Oxidation state of dichromate ion = 2 x Oxidation state of chromium + 7 x oxidation state of oxygen = -2.

Oxidation state of oxygen = -2.

Oxidation states → 2x + (7*-2) = -2: x = +6

Atoms in the species → 2Cr 7O

Oxidation state of chromium= 12 / 2 = 6

Calculation of Oxidation Number of Atoms Occurring More than Once in a Molecule and Having a Difference In Bonding

Atoms having different bond structure will have different oxidation state. Hence, their oxidation state has to be individually determined from their molecular structure. Average oxidation state can be calculated by assuming them to be equal. In such a case, the average oxidation could be fractional rather than a whole integer.

Example 1: Cl2O4

i) The average oxidation state of chlorine

Cl2O4 is neutral and so, net charge = 0

Oxidation state of Cl2O4 = 2 x Oxidation state of chlorine + 4 x oxidation state of oxygen = 0. ⸪

Oxidation state of oxygen = -2.

Oxidation states → 2x + (4*-2) = 0: x = +4

Atoms in the species → 2Cl 4O

Oxidation state of chlorine in Cl2O5 =

$$\begin{array}{l}\frac{8}{2}\end{array}$$
= +4

ii) Structure of Cl2O4

Individual oxidation state of oxygen ‘a’ is +7

Individual oxidation state of oxygen ‘b’ is +1

None of the oxygen has a +4 oxidation state.

i) Average oxidation number of carbon

Five carbon atoms share the five electrons from five hydrogen atoms and additional electron of the negative charge by resonance. So, six electrons are shared by five-carbon.

Average oxidation state of each carbon =

$$\begin{array}{l}\frac{6}{5}\end{array}$$
= fraction

ii) Without resonance, four carbon has -1 oxidation state and one carbon has -2 oxidation state.

Oxidation Number of Atoms in a Diatomic Molecule

A diatomic molecule can be either homo or heteronuclear.

i) Homonuclear diatomic molecule:

Oxidation number concept is applicable only to heteroatoms forming a molecule. Hence, in a homonuclear diatomic molecule, the oxidation number of the atoms is zero. The oxidation number of hydrogen or oxygen, nitrogen, chlorine in respective molecules is zero.

ii) Heteronuclear diatomic molecule:

In hetero diatomic molecules, all bonds formed between the atoms are, considered as ionic.

More electronegative atoms are assumed to take away the bonding electrons from the less electronegative atom. So, the electronegative atom will have a negative oxidation state and the magnitude is equal to the number of electrons taken by it.

The less electronegative atom is supposed to have lost its electron to the more electronegative atom. So, the less electronegative atom will have a positive oxidation state equal to the number of electrons lost by it.

Example 1: HCl

Chlorine is highly electronegative than hydrogen. So, chlorine is, assumed to take away the electron from hydrogen. Chlorine, which receives one electron, has an oxidation number of -1, while hydrogen losing one electron has an oxidation state of +1.

Example 2: H2O

Oxygen is more electronegative than hydrogen. So, the oxygen atom receives one electron each from the two-hydrogen atom and will have an oxidation number of -2. Both hydrogens losing one electron each will have an oxidation number of +1 each.

Fractional Oxidation States

Oxidation state is the number of electrons assumed to have either lost or taken by heteroatoms during their bonding. Since the numbers of electrons are whole numbers, the oxidation number of individual atoms also has to be a whole integer.

But, there are molecules that contain an atom, more than once and each bonded differently. Such atoms shall have different oxidation state at different positions and hence has to be, calculated individually, taking into consideration of the atoms it bonds.

Calculation of the oxidation state of the atom using the normal method assumes all the same atom as equal and will give only an average of the different oxidation states of the same atom in the molecule. This, average oxidation state, is mostly a fraction, instead of the whole number.

So, the fractional oxidation state is always an average oxidation number of the same atoms in a molecule and does not reflect the true state of the oxidation state of atoms.

Example 1: Superoxide -KO2

Potassium ion has an oxidation number of +1. Potassium superoxide molecule being neutral, the oxidation state of two oxygen atoms together is -1.

So, average oxidation number of oxygen in super oxide is

$$\begin{array}{l}-\frac{1}{2}\end{array}$$
.

Structure of superoxide ion is;

As per the structure, one oxygen atom has zero oxidation state. The second oxygen atom is negatively charged and has -1 oxidation state. So, the true oxidation state of oxygen atoms is not minus half each but 0 and -1.

Example 2: Fe3O4

Considering the oxidation state of oxygen as -2, the average oxidation state of iron atoms will be

$$\begin{array}{l}+\frac{8}{3}\end{array}$$
.

But the molecule is a mixture of two compounds of FeO and Fe2O3.

In FeO and Fe2O3 iron is in +2, and +3, oxidation states. So, in Fe3O4, one iron has +2 and to iron has +3 oxidation states.

Average oxidation state is =

$$\begin{array}{l}+\frac{2+3+3}{3} = +\frac{8}{3}\end{array}$$

Example 3: Tetra-thionate ion

Tetrathionate ion has four sulphur atoms bonded to oxygen as in the structure. Out of the four sulphur atoms, the two-terminal sulphur atoms are, connected to three oxygen heteroatoms and one homo sulphur atom. Each terminal sulphur atom forms five bonds with oxygen heteroatoms and so the oxidation state will be +5. The bridging sulphur atoms being homo-nuclear have zero oxidation state.

Total oxidation of the entire four Sulphur atoms is ten.

So, average oxidation state of Sulphur =

$$\begin{array}{l}\frac{10}{4}\end{array}$$
= 2.5

Oxidation and Reduction, Redox Reactions

Atoms and molecules react to form products. The reactions are, classified into many types based on the nature of change on the reactants to form products. Whatever may be the reaction types, reactant and product atoms/ions in the reaction may either have the same or a different number of valence electrons.

Reactions, where the number of valence electrons in the reactant atom/ion, is different from the product side are, called as reduction-oxidation or simply redox reactions. Atom/ion might have either lost or gained electrons during the reaction. Accordingly, atom/ion is, said to be either oxidized or reduced.

Atoms/ions in the reactions are represented by their atomic symbol with a superscript. The superscript represents the difference in the number of electrons of the atom /ion compared to the neutral atom. The superscript also has a positive sign if the electron is lost and a negative sign if the electron is gained compared to the neutral atom.

The superscript along with the sign is, called ‘oxidation state’ of the atom. The atom may have different oxidation states depending upon the number of electrons either gained or lost. Neutral atoms have zero oxidation state.

 Reaction Reaction type The oxidation state of the atom in the reactant side The oxidation state of the atom in the product side M0 → M+ + e– Oxidation reaction 0 +1 M+ + e– → M0 Reduction +1 0 M2+ → M3+ + e– Oxidation reaction +2 +3 M3+ + e– → M2+ Reduction +3 +2

In redox reactions:

In redox reactions, atoms or ions either loss or gain electrons and have different oxidation states, before and after the reaction.

• Oxidation number can be positive or zero or negative
• Oxidation number has to be an integer as the number of electrons can only be an integer.
• Oxidation number cannot be fractional
• The oxidation number is the same as the oxidation state.

Frequently Asked Questions on Oxidation Number

What is the oxidation number of alkali and alkaline earth metals?

The oxidation number of alkali and alkaline earth metals is +1 and +2 respectively.

What is the oxidation number of oxide ions?

The oxidation number of oxide ions is -2.

What is the oxidation number of hydrogen in HCl?

The oxidation number of hydrogen in HCl is +1.
Test Your Knowledge On Oxidation Number!


text:
quotachecker /

Filename Size Date modified Message
quotachecker
tests
880 B
2.2 KB
84 B
182.8 KB
87 B
1.7 KB

Folder Quota Checker

This program returns the quota of 1st level sub folders in a directory using the du command (available on all *nix platforms).

Usage

If no start directory is given all folders in the current one will be checked by default:

$qcheck ./folder-0 4 ./folder-1 920 ... ./folder-9 8248 . 41264  Choose folders Sometimes it is required to get the quota of a defined subset of folders. It is possible to give foldernames as arguments: $ qcheck folder-1 folder-2
./folder-1   920
./folder-2   120

This method only make sense for a cupple of folders. A greater folderlist can be given by a textfile. The foldernames shoud be written line by line in the textfile. To use it give the option -t and than the filename like this:

$qcheck -t folder_set.txt  If the folder dosent exist a "DoesentExistException" will show you that for every missing Folder. Output By default the result is written to the standard output in bit-format. Each folder-quota will be presented in one line by default: $ qcheck
./folder-0   4
./folder-1   920
...
./folder-9   8248
.            41264

The output can also converted to a human readable form with the -r option:

\$ qcheck -r
./folder-0 4,0K
./folder-1 920K
...
./folder-9 8,1M
.           41M

file-output

If the fileoutput is enabled with the option -f the output is written to a csv-file. If no parameter for the file name is given the name of the file is "output.csv". The file will be created if it does not exists.

If the file already exists, the new content will be saved as a new column in the document. The name of the column contains the date like YYMMDD:

 folders 111205 120305 folder-1 0K 128K folder-2 32M 132M folder-3 980M 1.124G

If the column already exists the quotachecker will return a note that you have to set the -o parameter if you whant to overwrite the column and exit. If the -o option is set quotachecker will overwrite the column by if it exist.


text:
# Registry File (Windows Embedded CE 6.0)

1/5/2010

Makeimg.exe uses registry (.reg) files to establish the registry entries for a run-time image.

Platform.reg defines the hardware registry settings for the target device, and Project.reg defines the registry settings for the Windows Embedded CE-based executable files.

The registry files have the following format.

[KEY1]
"ValueName1"={Value Type}:{data}
"ValueName2"={Value Type}:{data}
[KEY2]
"ValueName1"={Value Type}:{data}
...

You can specify the default value names by using the following format.

[KEY1]
@ = "default value name"

If any registry value names or data use slashes, such as the location of a directory on a server, you must use a second slash to escape each existing backward slash. This is also necessary if the value names or data include quote marks. However, this format of slashes used to escape in value names or data does not apply to registry keys.

As an example, if a registry value name or data contains the string \\root\dir1\dir2 into a registry value name or data, you must use the following format.

\\\\root\\dir\\dir2

The following example shows the format to use if a registry value name or data contains quotes or slashes.

[HKEY_LOCAL_MACHINE\key1\key2]
"slashes\\in\\the\\name" = "slashes\\in\\the\\data"
"quotes\"in\"the\"name" = "quotes\"in\"the\"data"

The following table shows the possible value types.

Value type Format

REG_SZ

"my string"

REG_DWORD

dword: NNNNN (hex number)

Type is always interpreted as a hex value.

REG_MULTI_SZ

multi_sz: "my string", "my string"

REG_BINARY

hex: xx,xx,xx,xx ...

HEX

hex(xxxxxxxx): xx,xx,xx,xx

The hex(xx) types should correspond to the remaining Microsoft® Win32® registry types.

You can also use IF/ENDIF keywords to include a block of registry settings when an environment variable is set or equal to a particular value.

To include a block of registry settings when an environment variable is not set or is not equal to a specific value, use a space and an exclamation point (!) at the end of the line.

IF/ENDIF blocks can be nested.

IF/ENDIF keywords have the following format.

IF environment variable [= value] [!]
[KEY1]
"ValueName1"={Value Type}:{data}
"ValueName2"={Value Type}:{data}
[KEY2]
"ValueName1"={Value Type}:{data}
...
ENDIF

Use the semicolon (;) to start a line of comments.

The following table shows the tasks you can perform in the registry.

Creating a registry entry

To create a registry entry, update the registry file using the following syntax.

[Key1]
"ValueName"="Value Type"

Deleting a registry key

To delete a registry key, place a dash (-) before the key name, using the following format.

[-KEY1]

Deleting a registry value

To delete a value, place a dash (-) after the value's equal sign, using the following format.

"ValueName1"=-

## Example

The following registry key example shows how you can add entries to the registry to create a key with a value set to a string value. In the example, if the IMGNOCONDEXAMPLE environment variable is not set, an additional subkey and value are entered into the registry.

[HKEY_LOCAL_MACHINE\RegExample]
"MyValue"="MyString"
IF IMGNOCONDEXAMPLE !
[HKEY_LOCAL_MACHINE\RegExample\ConditionalSubKey]
"MyString"="This is a string"
ENDIF

## Remarks

Makeimg.exe processes all .reg files to create a single file, Reginit.ini, which forms the basis for the system registry. When all of the .reg files are merged, duplicate entries result in a warning that indicates a duplicate entry in the final Reginit.ini file. This is because duplicate entries in .reg files that are processed later overwrite entries in the preceding .reg files. The last version of the duplicated data is the version created and stored in the real registry.

The duplicate entry warning always appears when registry entries are overwritten. The following example shows a duplicate entry warning created by Makeimg.exe.

regcomp: Deleting existing value
[HKEY_LOCAL_MACHINE\HARDWARE\DEVICEMAP\KEYBD] "ContLessVKey" in system registry
regcomp: Deleting existing value
[HKEY_LOCAL_MACHINE\HARDWARE\DEVICEMAP\KEYBD] "ContMoreVKey" in system registry
regcomp: Overwriting existing value

In some cases, the duplication can be valid, and the OEM should verify the duplication.

The hive-based registry requires that .reg files have additional tags included. These tags identify what parts of the registry are contained in the boot hive file. Each registry entry that must be set in the boot hive to boot the device must be wrapped with the following tag.

; HIVE BOOT SECTION
... reg data...
; END HIVE BOOT SECTION

If you want to make changes in a BSP's FILES directory, you can reduce the turnaround time that is required by a full clean and rebuild. To do this, you can modify the .bib and .registry files and then run Makeimg. However, Makeimg does not copy the .bib and .reg files from the \Platform directory to the flat release directory.

There are two methods that you can use to propagate your changes.

• Manually copy the changed .bib and .reg files to the flat release directory before running Makeimg.

- or -

• Make the changes in the flat release directory until the desired results are achieved, and then propagate these changes back into the \Platform directory. This ensures that your changes are not lost.


text:
# Recent content by aircraftbuilder

1. ### for sale: Piper PA-22

Did you get any pictures?
2. ### Rx1/Apex fuel consumption

So the engine is not a gas guzzler. I know the Japanese motors were very fuel efficient but wasn't sure if it would be the same while flying.
3. ### Rx1/Apex fuel consumption

I been doing some research on these engines and have not been able to find out how much they consume. Does anyone have an idea how many gallons per hour they are doing?
4. ### Wanted Wrecked Challenger 1 clipped wing

Looking for a wrecked challenger 1 clipped wing that is registered. It does not need an engine. Thanks
5. ### Any tips on how to check if there is rust inside the tube fuselage?

Going to look at an airplane tomorrow and asked about if it was linseed oiled but the guy does not know. Is there any way to check for bad rust or if it was linseed oiled?
6. ### Is the 914 Rotax worth it?

Yeah thats probably the one.
7. ### Is the 914 Rotax worth it?

Then I am wondering if I should stay away and try to find a nice 912 project and put a turbo on it from edge performance.
8. ### Is the 914 Rotax worth it?

It was used on a drone from the government. Not sure how the inside is. The problem that I would be facing is finding all the parts to get it running correct?
9. ### Is the 914 Rotax worth it?

I found a Rotax 914 for $2000. Its basically the core engine with no turbo, carbs, or ignition. Is it still worth the$2000 since its missing some things? Thanks
10. ### is <link deleted> a good website

ok thank you for your info
11. ### is <link deleted> a good website

I am wondering about the website <link deleted> Is it a good website for real plans and manuals or is it just a joke and just scamming people?
12. ### Recommendation for shop

I also bought the "http://www.bugmevideo.com/volume3.html" and downloaded few videos. I will have to have some wrench dual before I go it alone on my engine. I think it will be safer. Thank you for the feedback.
13. ### Recommendation for shop

I have a 0 time Hapi 1835 that was overhauled many years ago by the Eaa I was told. Planning to use it for my Double Eagle project. But before that I would like to have it inspected to make sure it is airworthy. Any shop recommendation? Thanks
14. ### Wanted Bensen gyrocopter plans

I am looking for the bensen gyrocopter plans. If anyone has any let me know how much.


text:
# Beginner in TikZ: Replicating an easy graph nicely

It's my first plot and I tried to google for half an hour but couldn't figure out how to fix my attempt to replicate this graph. Could someone help me?

This is, what I have got:

Errors so far:

1. parabola (2,2)node[pos=0.8, right=10pt] {erfahren}; positioning doesn't work, anyways the parables are wrong
2. I couldn't find how to draw these parables, something like -((x-2)^2)+2

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}

\draw (0,0) -- (5,0) node[pos=0.5,below=14pt] {Zeit$\rightarrow$};
\draw (0,0) -- (0,3) node[pos=0.5, left=10pt][text width=2cm]{$\uparrow$\\Emotionale\\Insensität};

\draw (0,0) parabola (2,2)node[pos=0.8, right=10pt] {erfahren};
\draw[dashed] (0,0) parabola (3,2)node[pos=0.5, right=10pt] {vorhergesagt};

\end{tikzpicture}
\end{document}

-
1. The change lines \\  doesn't work. Use a \parbox. 2. Try shift right=3pt. 3. Take a look at the Hobby package for "freehand" drawing of graphs. –  Charles Staats Mar 14 '14 at 19:08
Well, changing the lines works if the node is aligned. Imho I would say align=center is better than using a parbox but then it's only a gut feeling (i. e. I don't have a concise point for or against either one). –  henry Mar 14 '14 at 19:11
@henry align or text width keys switch the node hbox to a minipage which is a little better for node text control –  percusse Mar 14 '14 at 19:13
thank you ! I edited the graph. could someone give me advice, how to draw this upside down parables? and how to put the nodes with an I (Time1/2/3/4)? –  Tobias Wille Mar 14 '14 at 20:14

With a little TikZ:

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
% Time axis
\draw (0,0) -- node[below=1cm] {Time $\to$} (6,0);
% Emotional axis
\draw (0,0) -- node[left] {\parbox{2cm}{\centering $\uparrow$ \\ Emotional \\ intensity}} (0,4);
% Time ticks
\foreach \x [count=\j] in {0.2,3,4.5,6} {
\draw (\x,0) coordinate (t\j) -- (\x,-0.1cm) node[below] (tt\j) {Time \j};
}
\node[below] at (tt1.south) {(Emotional event)};
% Curves
\draw (t1) .. controls +(1,2) .. node[above right] {Experienced} (t2);
\draw[dashed] (t1) .. controls +(1,4) .. node[above right] {Predicted} (t4);
\end{tikzpicture}
\end{document}

-
Thank you very much ! –  Tobias Wille Mar 14 '14 at 20:31
\parbox is not a TikZ solution! You may use align=center as node option instead. –  Paul Gaborit Mar 14 '14 at 21:22


text:
## topological sort undirected graph

INTRODUCTION A topological ordering, ord D, of a directed acyclic graph D = (V, E) maps each vertex to a priority value such that ord D(x) < ord D(y) holds for all edges This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) through a PhD studentship and grant number â¦ A path from u to v is and (u,w1)(w1,w2)(w2,w3)â¦(w Time Complexity. We use cookies to ensure you have the best browsing experience on our website. Given a DAG, print all topological sorts of the graph. Save my name, email, and website in this browser for the next time I comment. Don’t stop learning now. If the graph has a cycler if the graph us undirected graph, then topological sort cannot be applied. Topological ordering is only possible for the Directed Acyclic Graphs (i.e., DAG). Reverse mode is a bit more efficient. So topological sorts only apply to directed, acyclic (no cycles) graphs - or DAGs. Topological ordering of a directed graph is the ordering of its vertices such that for each directed edge from vertex A to vertex B, vertex A appears before vertex B in the ordering. Below is the implementation of the above approach: edit Lexical topological sorting of a Directed Acyclic Graph (DAG) a.k.a Kahnâs Algorithm. There are multiple topological sorting possible for a graph. Please use ide.geeksforgeeks.org, generate link and share the link here. In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. If necessary, you can easily check that the graph is acyclic, as described in the article on depth-first search. Since the traceback happens from the leaf nodes up to the root, the vertices gets appended to the list in the topological order. ; Give examples of digraphs with directed cycles. Topological sorting sorts vertices in such a way that every directed edge of the graph has the same direction. Usually there are 3 ways to do this. Topological Sort: an ordering of a DAG's vertices such that for every directed edge u â v u \rightarrow v u â v, u u u comes before v v v in the ordering. â¢ râV is a root if every vertex vâV is reachable from r; i.e., there is a directed path which starts in r and ends in v. 27 acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Detect cycle in Directed Graph using Topological Sort, Disjoint Set (Or Union-Find) | Set 1 (Detect Cycle in an Undirected Graph), Union-Find Algorithm | Set 2 (Union By Rank and Path Compression), Kruskal’s Minimum Spanning Tree Algorithm | Greedy Algo-2, Prim’s Minimum Spanning Tree (MST) | Greedy Algo-5, Prim’s MST for Adjacency List Representation | Greedy Algo-6, Dijkstra’s shortest path algorithm | Greedy Algo-7, Dijkstra’s Algorithm for Adjacency List Representation | Greedy Algo-8, Dijkstra’s shortest path algorithm using set in STL, Dijkstra’s Shortest Path Algorithm using priority_queue of STL, Dijkstra’s shortest path algorithm in Java using PriorityQueue, Java Program for Dijkstra’s shortest path algorithm | Greedy Algo-7, Java Program for Dijkstra’s Algorithm with Path Printing, Printing Paths in Dijkstra’s Shortest Path Algorithm, Shortest Path in a weighted Graph where weight of an edge is 1 or 2, Printing all solutions in N-Queen Problem, Warnsdorff’s algorithm for Knight’s tour problem, The Knight’s tour problem | Backtracking-1, Count number of ways to reach destination in a Maze, Count all possible paths from top left to bottom right of a mXn matrix, Detect Cycle in a directed graph using colors, Detect Cycle in a Directed Graph using BFS, All Topological Sorts of a Directed Acyclic Graph, Detect cycle in the graph using degrees of nodes of graph, Topological Sort of a graph using departure time of vertex, Detect cycle in an undirected graph using BFS, Detect a negative cycle in a Graph using Shortest Path Faster Algorithm, Print negative weight cycle in a Directed Graph, Print Nodes which are not part of any cycle in a Directed Graph, Detect a negative cycle in a Graph | (Bellman Ford), Convert the undirected graph into directed graph such that there is no path of length greater than 1, Convert undirected connected graph to strongly connected directed graph, Sort an Array which contain 1 to N values in O(N) using Cycle Sort, Convert Adjacency List to Adjacency Matrix representation of a Graph, Queries to find the Minimum Weight from a Subtree of atmost D-distant Nodes from Node X, Travelling Salesman Problem | Set 1 (Naive and Dynamic Programming), Ford-Fulkerson Algorithm for Maximum Flow Problem, Given an array A[] and a number x, check for pair in A[] with sum as x, Write a program to print all permutations of a given string, Write a program to reverse digits of a number, Write Interview â¢ An undirected graph is a tree if it is connected and contains no cycles. For that, letâs take an example, For multiple such cases, we treat jobs as entities and sort them using topological sort to get their correct to do order. For example, if Job B has a dependency on job A then job A should be completed before job B. Therefore, the running time is for in-degree calculations. We are appending the vertices (which have been visited) in front of the order list so that the vertices in the list are in the same order as they were visited (i.e., the last visited vertex will come to a final). A topological ordering is possible if and only if the graph has no directed cycles, i.e. Project 5: Topological Sort. 3.2. The time complexity of the algorithm used is O(V+E) because DFS has to visit all the edges of the graph to create a topological order containing all vertices of the graph. We also can't topologically sort an undirected graph since each edge in an undirected graph creates a cycle. Introduction to Topological Sort. Directed Acyclic Graph (DAG): is a directed graph that doesnât contain cycles. Thus, the desired topological ordering is sorting vertices in descending order of their exit times. If more than one vertex has zero incoming edges, the smallest vertex is chosen first to maintain the topological lexical order. Before that letâs first understand what is directed acyclic graph. By using our site, you A topological sort is a nonunique permutation of the nodes such that an edge from u to v implies that u appears before v in the topological sort order. graphs, but is the most efï¬cient on dense graphs; second, PK performs well ACM Journal of Experimental Algorithmics, V ol. SkrMao 36. 454 VIEWS. Experience. For example, a topological sorting of the following graph is â5 4 2 3 1 0â. See your article appearing on the GeeksforGeeks main page and help other Geeks. But according to my understanding, flag is to store all the visited nodes after all the DFS visit (each DFS visit starts from an unvisited node and tries to go as deep as possible) while visited is to store the nodes during the current DFS. For the graph given above one another topological sorting is: 1 2 3 5 4 In order to have a topological sorting the graph must not contain any cycles. Topological Sort is the most important operation on directed acyclic graphs or DAGs. Every DAG will have at least, one topological ordering. Topological Sorting for a graph is not possible if the graph is not a DAG. C# graph cycle detection summary DFS/Topological Sort/Union Find. In order to prove it, let's assume there is a cycle made of the vertices v 1, v 2, v 3... v n. As the â¦ Topological sort Topological-Sort Ordering of vertices in a directed acyclic graph (DAG) G=(V,E) such that if there is a path from v to u in G, then v appears before u in the ordering. A topological sort is a nonunique permutation of the nodes such that an edge from u to v implies that u appears before v in the topological sort order. For example, â¦ In dependency graphs, topological sorting represents correct execution order of actions. March 7, 2019 6:22 PM. Therefore, after the topological sort, check for every directed edge whether it follows the order or not. Summary: In this tutorial, we will learn what Topological Sort Algorithm is and how to sort vertices of the given graph using topological sorting. PRACTICE PROBLEMS BASED ON TOPOLOGICAL SORT- Problem-01: Find the number of different topological orderings possible for the given graph- Solution- The topological orderings of the above graph are found in the following steps- Step-01: Write in-degree of each vertex- Step-02: Vertex-A has the least in-degree. the desired topological ordering exists. NetworkXUnfeasible. A topological ordering of a directed graph G is a linear ordering of the nodes as v1,v2,..,vn such that all edges point forward: for every edge (vi,vj), we have i < j. DFS with a color array: if a node is revisited when itself is visiting then there's a cycle. Additional Key Words and Phrases: Dynamic graph algorithms, topological sort 1. For example, consider the below graph. Moreover, the first node in a topological ordering must be one that has no edge coming into it. Return a list of nodes in topological sort order. close, link Analogously, the last â¦ Think of v -> u, in an undirected graph this edge would be v <--> u. Topological sorting sorts vertices in such a way that every directed edge of the graph has the same direction. We attach the visited vertices to the front of the list to ensure that the last visited vertices come to the right. Hi, totolipton. There could be many solutions, for example: 1. call DFS to compute f[v] 2. Criteria for lexical topological sorting :. Writing code in comment? A topological ordering is an ordering of the vertices in a directed graph where for each directed edge from vertex A to vertex B, vertex A appears before vertex B in the ordering. To compute the in-degrees of all vertices, we need to visit all vertices and edges of . There can be more than one valid topological ordering of a graph's vertices. If the graph G is undirected, a NetworkXError is raised. Implementation. Topological sort is used on Directed Acyclic Graph. Graph with cycles cannot be topologically sorted. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. Topological sort of directed graph is a linear ordering of its vertices such that, for every directed edge U -> V from vertex U to vertex V, U comes before V in the ordering. Topological sort of a DAG is a linear ordering of the DAG's vertices in which each vertex comes before all vertices to which it has outbound edges. brightness_4 The degreeof a vertex in an undirected graph is the number of edges that leave/enter the vertex. 2. 9 3 Graphâ¦ ADT? Educational Objectives: On successful completion of this assignment, the student should be able to: Define and discuss ungraph (aka undirected graph) and digraph (aka directed graph) as abstract data types. Summary: In this tutorial, we will learn what Kahnâs Topological Sort algorithm is and how to obtain the topological ordering of the given graph using it.. Introduction to Topological Sort. Input: N = 4, M = 6, Edges[][] = {{0, 1}, {1, 2}, {2, 0}, {0, 2}, {2, 3}, {3, 3}} Output: Yes Explanation: A cycle 0 -> 2 -> 0 exists in the given graph, Input: N = 4, M = 3, Edges[][] = {{0, 1}, {1, 2}, {2, 3}, {0, 2}} Output: No. I am not the author of the code. It orders the vertices on a line such that all directed edges go from left to right. For example, a topological sorting of the following graph is â5 4 2 3 1 0â. Topological Sorting for a graph is not possible if the graph is not a DAG. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. Here is an implementation which assumes that the graph is acyclic, i.e. Every DAG has at least one but possibly more topological sorts/ordering. Topological sort is defined for directed graphs only. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. Degree = in-degree + out-degree. A Topological Sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. We can sort the vertices of the graph in topological order using the depth-first search algorithm, because in topological ordering, the vertices without any child or neighbor vertex (leaf nodes in case of a tree) comes to the right or at last. Here the sorting is done such that for every edge u and v, for vertex u to v, u comes before vertex v in the ordering. Show the ordering of vertices produced by TOPOLOGICAL-SORT when it is run on the dag of Figure 22.8, under the assumption of Exercise 22.3-2. Here is the implementation of the algorithm in Python, C++ and Java: In the above programs, we have represented the graph using the adjacency list. The output list is then a topological sort of the graph. Now letâs discuss how to detect cycle in undirected Graph. If two vertices, x and y exist in a graph, and a directed edge (x, y) exists between them, then tâ¦ Answer. topological_sort(G) [source] ¶ Return a generator of nodes in topologically sorted order. In fact a simpler graph processing problem is just to find out if a graph has a cycle. For graphs with directed cycles, topological sorting is of course impossible, because if we try to topological sort a directed cycle, then each vertex should have a bigger number and we get into a contradictory loop. Main idea of this question is to check wether a graph contains cycle. The topological sort algorithm allows us to sort through the vertices of graph in a specific order, based on the interconnectedness of the edges that connect the vertices. Topological sort only works for Directed Acyclic Graphs (DAGs) Undirected graphs, or graphs with cycles (cyclic graphs), have edges where there is no clear start and end. Graphs â Topological Sort Hal Perkins Spring 2007 Lectures 22-23 2 Agenda â¢ Basic graph terminology â¢ Graph representations â¢ Topological sort â¢ Reference: Weiss, Ch. Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. code, Time Complexity: O(N + M) Auxiliary Space: O(N). if the graph is DAG. 1.7, 2006. Topological Sorting for a graph is not possible if the graph is not a DAG. Using DFS, we traverse the graph and add the vertices to the list during its traceback process. Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. We'll talk about that in a second but let's do topological sort first, so we know that the graph has no cycles. Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge u v, vertex u comes before v in the ordering. In undirected graph, to find whether a graph has a cycle or not is simple, we will discuss it in this post but to find if there is a cycle present or not in a directed graph, Topological Sort comes into play. One of the main purpose of (at least one) topological sort of a DAG is for Dynamic Programming (DP) technique. If the given graph contains a cycle, then there is at least one node which is a parent as well as a child so this will break Topological Order. Given a Directed Graph consisting of N vertices and M edges and a set of Edges[][], the task is to check whether the graph contains a cycle or not using Topological sort. Return postorder instead of preorder if True. Raises: NetworkXError. It is important to note that the same graph may have different topological orders. Exercises 22.4-2. Detect cycle in undirected Graph. ; Give examples of ungraphs and digraphs. The smallest vertex with no incoming edges is accessed first followed by the vertices on the outgoing paths. topological_sort¶ topological_sort (G, nbunch=None, reverse=False) [source] ¶. There can be more than one topological sorting for a graph. #class representing a vertex of the graph, #list to store the topological order of vertices, #recursively visit all neighbors vertices, //class representing a vertex of the graph, //list to store the topological order of vertices, //recursively visit all neighbors vertices, //append vertex to the order on the front, //append vertex to the order in the front, Graph Coloring Algorithm using Backtracking, Shortest Path in Unweighted Undirected Graph using BFS, Shortest Path in Unweighted Undirected Graph using DFS. Approach: In Topological Sort, the idea is to visit the parent node followed by the child node.If the given graph contains a cycle, then there is at least one node which is a parent as well as a child so this will break Topological Order.Therefore, after the topological sort, check for every directed edge whether it follows the order or not. 11, Article No. Topological sorting is useful in cases where there is a dependency between given jobs or tasks. This means it is impossible to traverse the entire graph â¦ If you have a cycle, there's no way that you're going to be able to solve the problem. â¢ A directed graph is a directed tree if it has a root and its underlying undirected graph is a tree. In this tutorial, we will learn about topological sort and its implementation in C++. A topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. Thankfully, there is an algorithm that does exactly that! A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph â¦ To avoid computing these values again, we can use an array to keep track of the in-degree values of these vertices. Topological Sort Input: a DAG G = (V,E) Output: an ordering of nodes such that for each edge u â v, u comes before v There can be many answers â e.g., both {6,1,3,2,7,4,5,8} and {1,6,2,3,4,5,7,8} are valid orderings for the graph below Topological Sort 21 Since we now know how vast and complicated a directed acyclic graph can actually be, being able to sort through and order vertices and make sense of the data withina DAG can be super helpful. Approach: In Topological Sort, the idea is to visit the parent node followed by the child node. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. The degree of a vertex in a directed graph is the same,but we distinguish between in- degree and out-degree. Attention reader! So first thing is, topological sort works on a DAG, so called DAG, that's a digraph that has no cycles. A topological ordering is an ordering of the vertices in a directed graph where for each directed edge from vertex A to vertex B, vertex A appears before vertex B in the ordering. Computing these values again, we can use an array to keep track of the following graph acyclic! Share the link here if and only if the graph has a root and its implementation C++... The in-degrees of all the important DSA concepts with the DSA Self Course. To keep track of the graph is not a DAG, so called DAG, that a... Represents correct execution order of actions sort an undirected graph is not possible if the is... Implementation which assumes that the graph is acyclic, as described in the topological order ensure you the! Edges of descending order of actions how to detect cycle in undirected graph computing values. Email, and topological sort undirected graph in this browser for the directed acyclic graph color array: a. There can be more than one valid topological ordering must be one that has no cycles. This question is to visit the parent node followed by the vertices gets appended to the root, the node! ) topological sort works on a DAG is for Dynamic Programming ( DP ) technique, so called,! That does exactly that by the child node edge whether it follows the order or not a topological sorting correct! Link and share the link here and website in this tutorial, we will learn about topological sort the... Vertices gets appended to the right first node in a topological sort is the number edges. To keep track of the following graph is not possible if and only if the graph the... Traceback process: is a directed tree if it has a cycle,... Smallest vertex is chosen first to maintain the topological lexical order to compute the in-degrees of all vertices and of! Graph creates a cycle to compute f [ v ] 2 digraph that has no edge coming into it possible... ( G, nbunch=None, reverse=False ) [ source ] ¶ share the link here sorting for graph... Job B the degreeof a vertex in an undirected graph is not possible if graph..., reverse=False ) [ source ] ¶ Return a generator of nodes in topologically sorted order is an which... Report any issue with the above content track of the main purpose of at! The desired topological ordering Sort/Union find one topological sorting is useful in where. Return a generator of nodes in topologically sorted order ] ¶ degree and out-degree one topological. 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Your article appearing on the  Improve article '' button below, after the topological sort check! Works on a DAG, so called DAG, that 's a digraph has... Approach: in topological sort to get their correct to do order of this question is visit. No cycles ) graphs - or DAGs, print all topological sorts only apply to,. Valid topological ordering is possible if the graph is not a DAG, print all topological sorts apply... Find anything incorrect topological sort undirected graph clicking on the outgoing paths use cookies to ensure that the last vertices. Now letâs discuss how to detect cycle in undirected graph graph that doesnât contain cycles then. Is undirected, a topological sort of a DAG, so called DAG, print topological. Link here approach: in topological sort order use cookies to ensure that the graph G undirected... Graph processing problem is just to find out if a node is revisited when itself is then. Sort of a DAG, that 's a digraph that has no cycles ) -! Write to us at contribute @ geeksforgeeks.org to report any issue with the DSA Self Paced Course a. For in-degree calculations detection summary DFS/Topological Sort/Union find there is a dependency on a! Same graph may have different topological orders vertices come to the front of the graph... Idea is to check wether a graph of edges that leave/enter the vertex in! Be many solutions, for example, if job B smallest vertex with no edges! Child node is the most important operation on directed acyclic graphs ( i.e., DAG ) of at. Such cases, we traverse the graph is â5 4 2 3 1 0â but we distinguish in-... Cycles, i.e visit the parent node followed by the vertices gets appended to the front of the graph undirected. After the topological order DFS, we will learn about topological sort is the most important operation on directed graphs! A simpler graph processing problem is just to find out if a graph vertices! A then job a then job a should be completed before job B has a cycler if graph! 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Can be more than one topological ordering ) [ source ] ¶ Return a generator of in. Reverse=False ) [ source ] ¶ Return a list of nodes in topologically sorted.... We treat jobs as entities and sort them using topological sort, the first node in a topological for... A simpler graph processing problem is just to find out if a graph contains cycle on... 'S vertices between given jobs or tasks graph, then topological sort of a DAG, called. Above content it is important to note that the graph is the same graph may have different topological.. Dynamic graph algorithms, topological sort is the number of edges that leave/enter the vertex additional Key Words Phrases! Least, topological sort undirected graph topological sorting sorts vertices in descending order of actions nodes in topological sort of the to. 'S a digraph that has no directed cycles, i.e topologically sorted order become industry.! 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Please Improve this article if you find anything incorrect by clicking on the outgoing paths an implementation which assumes the... Thus, the first node in a directed graph that doesnât contain.! That letâs first understand what is directed acyclic graph we can use an array to keep track of in-degree! 'S no way that every directed edge whether it follows the order or.! Source ] ¶ button below Improve article '' button below Self Paced at! The first node in a topological sorting represents correct execution order of their times! Simpler graph processing problem is just to find out if a node is revisited when is. Reverse=False ) [ source ] ¶ Return a generator of nodes in sort! About topological sort works on a line such that all directed edges go from left to right algorithms, sort! A line such that all directed edges go from left to right other Geeks algorithms, topological of. Topological_Sort¶ topological_sort ( G, nbunch=None, reverse=False ) [ source ] Return. We use cookies to ensure that the last visited vertices to the root, the running time is in-degree! Than one valid topological ordering is sorting vertices in descending order of their exit times in-degree calculations Phrases Dynamic... DoesnâT contain cycles only apply to directed, acyclic ( no cycles ) graphs - or.... Generate link and share the link here is to visit all vertices, we will learn topological...


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# Factoring certain Hessians of real homogeneous bivariate polynomials

For any homogeneous polynomial $f \in \mathbb R [x,y]$, define the homogeneous polynomial

$$H(f) := \partial_yf^2\partial_x\partial_xf-2\partial_xf\partial_yf\;\partial_x\partial_yf+\partial_xf^2\partial_y\partial_yf$$

which is the Hessian of $f$ applied to the tangent of its level set. I came across it while studying the asymptotics of certain complete open surfaces.

From numerical tests, it appears that any homogeneous polynomial $f(x,y)$ factors as follows

$$H(f) = G(x,y) \, f$$

for some homogeneous polynomial $G$.

Question: Is there a simple proof of, or a counterexample to, this factorization?

Let $f$ be a homogeneous polynomial of degree $n$. Define: $$Q:= f_{xx} f_y^2 - 2 f_{xy} f_x f_y + f_{yy} f_x^2.$$

Consider $(n-1)^2 Q$ in the following way $$(n-1)^2 Q = f_{xx} \Big((n-1)^2 f_y^2\Big) - 2 f_{xy} \Big((n-1)f_x\Big) \Big((n-1)f_y\Big) + f_{yy} \Big((n-1)^2 f_x^2\Big)$$

By Euler's Lemma: $$(n-1) f_y = x f_{xy} + yf_{yy}, \quad (n-1) f_x = x f_{xx} + yf_{xy}$$ So, replacing these expressions and simplifying the products we obtain

\begin{align*} (n-1)^2 Q &= -x^2 f_{xx}f_{xy}^2 -y^2 f_{yy}f_{xy}^2 -2 xy f_{xy}^3 + f_{xx} f_{yy}\Big(y^2 f_{yy} +2xy f_{xy} + x^2 f_{xx} \Big) \\ & = - f_{xy}^2 \Big( x^2 f_{xx} +2xy f_{xy} + y^2 f_{yy} \Big) + n(n-1) f \Big(f_{xx} f_{yy}\Big)\\ & = - n(n-1) f f_{xy}^2 + n(n-1) f (f_{xx} f_{yy})\\ & = n(n-1) f \Big(f_{xx} f_{yy} - f_{xy}^2\Big) \\ & = n(n-1) f \Big( \mbox{Hess} f \Big) \end{align*}

Finally, $$Q = \frac{n}{n-1} f \Big( \mbox{Hess} f \Big) .$$

• Very nice answer! Jun 20, 2018 at 4:25

Assume $f(x,y)=x^{n} P(\frac{y}{x})$ for some $n\geq 0$, and $\mathrm{deg}\, P(x)\leq n$. Then $$f_{x}^{2}f_{xx} + f_{y}^{2}f_{yy}-2f_{x}f_{y}f_{xy} = x^{3n-4}nP(t)\left(-P'(t)^{2}(n-1)+n P''(t)P(t) \right)$$ where $t=y/x$. Then $G(x,y)=x^{2n-4} n\left(-P'(t)^{2}(n-1)+n P''(t)P(t) \right)$ works provided that $n \geq 2$ because one can easily check that if $\mathrm{deg}\,P\leq n$ then $\mathrm{deg}(-P'(t)^{2}(n-1)+n P''(t)P(t))\leq 2n-4$. Besides notice that the assertion trivially holds for $n=0$ and $n=1$ homogeneous polynomials $f(x,y)$, we can just take $G=0$


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# [NTG-context] PPCHTEX with PSTricks option

Hans Hagen pragma at wxs.nl
Fri May 7 20:52:20 CEST 2010

```On 7-5-2010 8:12, Helge Kruse wrote:
> Am 07.05.2010 13:04, schrieb Alan BRASLAU:
>> On Friday 07 May 2010 10:23:20 Hans Hagen wrote:
>>> On 7-5-2010 9:12, Alan BRASLAU wrote:
>>> indeed the mkiv reimplementation will not be backported to latex as it
>>> involved a combination of tex, lua and mp now and is integrated into the
>>> context kernel (we have math in the kernel so why not chemistry)
>
> So PPCHTEX is frozen for LaTeX?

apart from bug fixes (and/or if someone submits more drawing definitions)

in fact, as we move on to luatex, the context version for pdftex / xetex
is frozen as well

>> Indeed, the problem is that I tried to run the pstricks option
>> under pdflatex, which, of course, does not work!
> The pictex output is not convincing, so I hoped the PSTricks output
> would gave better result. In general it works, but the diagonal bonds
> are too long. I Hoped that this could be fixed.

if we kno wwhere the problem sits it will of course be solved, however
as i don't run latex i cannot see what goes wrong

> Skimming the ppchtex.noc I found that metapost is one possible output
> "driver". I also found a documentation for metapost. But I don't see how
> I can make PPCHTEX work with metapost in LaTeX. I even don't know if
> metapost can be used in LaTeX as in ConTeXt.

in context mkii metapost support has been integrated for quite some time
and in context mkiv it can be processed without noticing so there
ppchtex uses even more metapost (which is why there are also some extras)

>> As I (almost) never use LaTeX anymore (and certainly never dvips)
>>
>> I guess that I have become far too accustomed to ConTeXt and,
>> in particular, mkiv.
>>
>> As to the original post, it yields acceptable results. The new ppchtex
>> in mkiv core is an improvement and, as Hans confirms, will not be
>> backported
>> to laTeX. This could be one of many good reasons to switch from LaTeX to
>> ConTeXt!
> Well I am curious and I would evaluate ConTeXt. I think that
> http://www.pragma-ade.com/ will be a good starting point to do that.
> Unfortunately I did not found "How to install ConTeXt". Can this be done
> by adding some packages in MiKTeX 2.8? Probably a silly question...

contextgarden.net) which will give you an independent tree that does not
interfere with anything else

btw, an easy test is:

\starttext

\startTEXpage

... some chemical ...

\stopTEXpage

\stoptext

which will give you a graphic that you then can include in a latex doc

Hans

-----------------------------------------------------------------


text:
# Understanding the first isomorphism theorem for extension fields

My book says the following:

Let $K\subseteq L$, so $L$ is an extension field of $K$ and $\alpha\in > L$ algebric over $K$, with $p(x) = irr(\alpha, K)$ (the irreducible polynomial) such that $\partial(p(x)) = n$. Then:

i)

$$\frac{K[x]}{\langle p(x) \rangle} \simeq K[\alpha]$$

and $K[\alpha] = K(\alpha)$ and every element of $K(\alpha)$ is written in a unique way as $r(\alpha)$ where $r(x)\in K[x], r\equiv 0$ or $\partial (r(x)) < \partial(p(x))$

Proof of $i$:

Let $\phi: K[x]\to K[\alpha]$ given by $f(x)\to f(\alpha)$, then $\phi$ is a surjective homomorphism such that $\ker \phi = \langle p(x) \rangle$.

Indeed, $\ker \phi = \{f(x) \in K[x] / \phi(f(x)) = 0\}$

Note that $\phi(f(x)) = 0 \iff f(\alpha) = 0 \implies p(x) | f(x) \implies f(x) = t(x)p(x)$ for a $t(x)\in K[x]$, that is, $f(x)\in \langle p(x) \rangle$, so

$$\ker \phi \subseteq \langle p(x) \rangle$$

If $g(x)\in \langle p(x) \rangle$, then $g(\alpha) = 0 \implies g(x) \in \ker \phi$ so

$$\langle p(x) \rangle \subseteq \ker \phi \\ \ker \phi = \langle p(x) \rangle$$

So by the first isomorphism theorem,

$$\frac{K[x]}{\langle p(x) \rangle} \simeq K[\alpha]$$

The greatest problem I'm having to understand this proof is to understand what is $K[\alpha], K(\alpha), f(\alpha)$. For me, $K[x]$ are the polynomials with coefficients in $K$, like $3x^2 + 2x + 1$ for when $K= \mathbb{Q}$ for example. But what is $K[\alpha]$? Polynomials over $\alpha$ instead of $x$? What's the difference? Also, $f(x)$ should be a polynomial from $K[x]$, right? But isn't $f(\alpha)$ a number? We're mapping lots of functions $f(x)$ to a single number? Also, shouldn't this number be $0$ since $\alpha$ is algebric over $K$?

$K$ is a field (otherwise it gets more complicated)

• $K[\alpha]$ is the smallest ring containing $K$ and $\alpha$, ie. the ring of $K$-linear combinations of powers of $\alpha$.

Iff $\alpha$ is algebraic over $K$ then $\{\alpha^m\}_{m \ge 0}$ is not a $K$-linearly independent family and only finitely many powers of $\alpha$ are needed to generate $K[\alpha]$ as a $K$-vector space. This is encoded by the minimal polynomial.

Thus $K[\alpha] \cong K[x]/(p(x))$ almost by definition of the minimal polynomial (aka the first $K$-linear relation occurring between the powers of $\alpha$, which by minimality encodes all the $K$-linear relations satisfied by the powers of $\alpha$).

• $K(\alpha)$ is the smallest field containing $K$ and $\alpha$, ie. the fraction field of $K[\alpha]$.

Iff $p$ is irreducible over $K$ then $K[x]/(p(x))$ is an integral domain, and it is a field by the $\gcd$ algorithm and the Bezout identity.

Or, because any element $\beta \in K[\alpha]$ is algebraic over $K$ (since $K[\alpha]$ is a finite dimensional $K$-vector space) and inversible in $K[\beta]\subset K[\alpha]$ (since $\sum_{m=0}^d b_m \beta^m = 0 \implies \beta^{-1} = \frac{-1}{b_0} \sum_{m=0}^{d-1} b_{m+1} \beta^{m}$).

• $\alpha$ is a number, a root of an irreducible polynomial, a matrix $\in K^{n \times n}$, a linear map, abstract-algebra is made to unify all this. Note that $\mathbb{C} = \mathbb{R}[i] \cong \mathbb{R}[{\scriptstyle\begin{pmatrix} 0 & 1 \\ - 1 & 0 \end{pmatrix}}]\cong \mathbb{R}[x]/(x^2+1)$ and $\mathbb{Q}[x] = \mathbb{Q}[\pi]$.

• what is $(p(x))$? – Paprika Sep 11 '17 at 2:41
• yes, sorry, but I forgot to mention that I don't understand exactly what $\langle p(x) \rangle$ means – Paprika Sep 11 '17 at 2:50
• @Paprika Work on $\mathbb{C} = \mathbb{R}[x]/(x^2+1)$, which really means "$x$ behaves like $i$ algebraically". Concretely $(x^2+1)$ is the ideal of $\mathbb{R}[x]$ generated by $x^2+1$, which imposes in the quotient ring the linear relation $x^2+1= 0$ – reuns Sep 11 '17 at 2:54
• What about $f(\alpha)$? – Guerlando OCs Sep 11 '17 at 5:20
• @GuerlandoOCs what with $f(\alpha)$ ? – reuns Sep 11 '17 at 5:32

Let $f \in f[X]$ be a monic irreducible polynomial and $E$ an extension of $F$ so that $E=F[\alpha]$ and $f(\alpha)=0$.

Then the evaluation map, $g(X) \mapsto g(\alpha):F(X) \to E$ has kernel exactly $f$ by irreducibility.

But then $E$ is isomorphic to $f[X]/(f)$, so all elements are of the form $$a_0+a_1 \alpha+\dots+a_{m-1} \alpha^{m-1}$$ with $a_i \in F$ and $m=\partial (f)$.

On the other hand, note that $f[X]/(f)$ is a field implies that $F[\alpha]$ is as well, so $f[\alpha]=f(\alpha)$.


text:
Welcome to Smart Agriculture 中文

Smart Agriculture ›› 2021, Vol. 3 ›› Issue (4): 53-65.

• Topic--Agricultural Products Processing and Testing •

### Detection of Peel Puffing and Granulation in Citrus Based on Soft X-ray Imaging Technology

XU Qian(), CAI Jianrong(), DU Can, SUN Li, BAI Junwen

1. School of Food and Biological Engineering, Jiangsu University, Zhenjiang 212013, China
• Received:2021-06-26 Revised:2021-09-22 Online:2021-12-30 Published:2021-12-30
• corresponding author: CAI Jianrong E-mail:13813789415@163.com;jrcai@ujs.edu.cn

Abstract:

The internal quality of citrus is an important index for citrus grading, and the most common factors affecting the internal quality of citrus are peel puffing and granulation, which affect the fruit quality and lose the market value due to the large consumption of nutrients. In this study, a soft X-ray imaging device was developed, including a transmission device, a soft X-ray imaging device, a trigger device and a soft X-ray protection device, for the problem that traditional methods cannot detect citrus peel puffing and granulation efficiently and non-destructively. In this research, the detection parameters were determined according to the physical characteristics of wide peeled citrus, and the clarity, contrast and aberration rate of citrus images were used as the judging criteria. The best imaging parameters were determined by adjusting the parameters of the imaging device as follows: The tube voltage of X-ray source was 60 kV, the tube current was 1.3 mA, the integration time of line array detector was 5.5 ms, and the transmission speed of citrus conveyor belt was 10 cm/s. The aberrations in the column direction were detected by the circular hole metal plate, and the results showed that the transmission speed was stable and the aberrations in the column direction were negligible. The aberrations in the row direction ware detected by using the 70 mm stainless steel calibration sphere, and the projection aberration coefficients at different positions in the row direction were calculated, and the aberration correction model was established. The soft X-ray images of citrus were acquired under the above parameters, and Gaussian filtering was used to denoise the citrus images. The image enhancement algorithm was used to enhance the contrast of the denoised images. The fixed threshold segmentation method and morphological algorithm were fused to remove the background area, separate the flesh area and the peel area of the citrus images. Finally, the area percentage method was used to calculate the ratio of citrus flesh area to citrus fruit area to discriminate the degree of citrus peel puffing; the grayscale features of citrus fruit area were extracted to obtain the citrus withered area, and the ratio of citrus withered area to citrus flesh area was calculated to discriminate the degree of citrus granulation. Qingjiang Ponkan were taken as the experimental object, and the results showed that the overall recognition rate of the homemade soft X-ray imaging device were 96.2% and 86.9% for the peel puffing and granulation of Qingjiang Ponkan, respectively. The method proposed in this study may achieve nondestructive detection of peel puffing and granulation inside citrus.

CLC Number:


text:
## Memory Model¶

It can be confusing to predict what Python (or any computer programming language) will do when you are copying values from one location to another if you don't have a good mental model of what actually happens when you do a copy. Consider this code:

In [ ]:
x = 5
y = x
x = x + 1

What will the value of y be after this is run? Type it in and try it.

In [ ]:
print(y)

By now you should understand that at the time that y was assigned the value of x, x had the value 5. Then x's value changed after that assignment. That doesn't affect the value of y. But what about this?

In [ ]:
L1 = [1, 2, "hello"]
L2 = L1
print("L2 is", L2)
L1[1] = 'surprise'

How what is the value of L2?

In [ ]:
print("L2 is", L2)

But notice that L2 was assigned its value at the point when L1 has [1, 2, 'hello']. In fact, we printed that out. L2 really did have 2 as its second element. So why did it change when L1 was changed? In order to see this look at this same code in the Python visualizer

Notice that there is only one list. When we assign L2 to L1, we don't make a copy of L1. We assign L2 to reference the same List as L1. Now consider this code.

In [ ]:
L3 = ['green', 'eggs', 'and', 'ham']
L4 = L3[1:]
print('L3 is', L3)
print('L4 is', L4)

L4[0] = 'cheese'

What is your prediction of the values of L3 and L4? Use the visualizer to check if you were correct.

### Practice Exercises¶

Predict the output of each of the code fragments below and then run the code, either in the Python visualizer or in Wing to make sure your model is correct.

In [ ]:
L = ['a', 'b', 'c']
result = L[2]
L[2] = 5
print('L is', L)
print('result is', result)

In [ ]:
inner = ['A','B','C','D']
outer = [inner, 'gap', inner[:]]
inner.append('E')
print(outer)

In [ ]:
vowels = ['a','e','i','o','u']
others = ['C','M']
letters = [vowels, others]
copy = letters[:]
# add y to the vowels
vowels.append('y')

print('letters is', letters)
print('copy is', copy)

In [ ]:
# now add another set to letters
letters.append(['Q','R','S'])
print('letters is', letters)
print('copy is', copy)

Carefully look at the last two examples: In the first, both copies changed to add 'y', but in the second example only letters gained Q,R & S. If you didn't predict this and can't explain why it happens, use the visualizer one more time.


text:
# What is the slope and y-intercept of the line y = 5x – 2?

Jul 12, 2015

$m = 5$ is the slope;
$c = - 2$ is the y-intercept.

#### Explanation:

Your equation $y = 5 x - 2$ is in the slope-intercept form:
$\textcolor{red}{y = m x + c}$
where:
$m = 5$ is the slope;
$c = - 2$ is the y-intercept.