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# Sick of the blatent bias!!!!!!!!!

Discussion in 'SF Open Government' started by Reiku, Dec 6, 2011.

1. ### ReikuBannedBanned

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I've been very timid to prom's recent actions, but I am getting really sick of his nazi dictatorship guised as mod action.

I replied to captaim bork saying it was not my own definition, but was in fact the legendary Leonard Susskinds definition. I then stated that it was not* true stating they meant exactly the same thing because of this identity:

$<\psi_n|\psi_m> = 0$

for othogonality and for something perpendicular it is

$<\psi_n|\psi_m> = 1$

My posts were deleated then prom said, question answered!!!

AYE RIGHT PROM. What games are you lot playing! Think am gonna sit back like a good bitch every time? There is only so much of this behaviour I will take before saying something! :bugeye:

3. ### ReikuBannedBanned

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edited, not* true

5. ### ReikuBannedBanned

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It's absolutely not fair to anyone if a mod goes about editing posts to his will. It is biased and also disingenuous as it implies that there is never two sides to a story!!!

7. ### kwhilbornBannedBanned

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I am not saying being a moderator is powerful, but I will say that,"Some people get a little power and take it way too seriously". It usually sprouts from never having been in a position of authority before. I recall a story about a shipper/receiver/mailroom guy at a Soil Engineering Company I worked for who became a Union Rep. What a sad little man.

Prometheus is the ONLY moderator I have ever complained about on any forum in my life.

8. ### ReikuBannedBanned

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He should be warned about this behaviour! It should be completely illegal here for a mod to modify posts willy-nilly to his liking. Indeed, I've only seen posts modified when there has been possibly harmful or rude comments, not a genuine harmless post! I've never seen a mod do this in my life, but he keeps doing it and it is misleading for the audience, as anyone who knows no better will go into that thread and think I am automatically wrong, because captian bork has been allowed the last word on the subject, and I hadn't even finished explaining myself or the reasonings behind it!!!

I am so pissed off right now!

9. ### prometheusviva voce!Registered Senior Member

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This is crap. Which is why it was deleted.

Next.

10. ### ReikuBannedBanned

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Why is it crap?

Explain. Don't just say it is.

11. ### ReikuBannedBanned

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''Orthogonal states in quantum mechanics

In quantum mechanics, two eigenstates of a Hermitian operator, ψm and ψn, are orthogonal if they correspond to different eigenvalues. This means, in Dirac notation, that $\langle \psi_m | \psi_n \rangle = 0$ unless $\psi_m$ and $\psi_n$ correspond to the same eigenvalue. This follows from the fact that Schrödinger's equation is a Sturm–Liouville equation (in Schrödinger's formulation) or that observables are given by hermitian operators (in Heisenberg's formulation).''

Explain why what I said was crap. http://en.wikipedia.org/wiki/Orthogonality

Last edited: Dec 6, 2011
12. ### prometheusviva voce!Registered Senior Member

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I presume you are using $|\psi\rangle$ as a vector. I will use the more usual $\vec{x}$ Consider the inner product of two vectors in Euclidean space $\vec{x} . \vec{y} = | \vec{x} | | \vec{y} | \cos \theta$ where $\theta$ is the angle between the vectors. If $\vec{x} . \vec{y}= 0$ that means $\theta = \frac{\pi}{2}$ (or multiples thereof) and the vectors are perpendicular, which in this example is synonymous with orthogonal. $\vec{x} . \vec{y}= 1$ has no special meaning unless the vectors are normalised (which is the case in QM). I presume you mean $\vec{x} . \vec{y} = | \vec{x} | | \vec{y} |$ (=1 in the case of normalised vectors) which happens when the vectors are parallel (or antiparallel).

This notion of orthogonality is carried through when you consider the inner product of two functions rather than vectors, although there is now no notion of perpendicular or parallel.

Is that sufficient or would you like to troll some more?

13. ### ReikuBannedBanned

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So you think saying that, excuses the fact that you have completely ignored that the identities I have given are true and can be shown and demonstrated as such from wiki?

What I said is clearly not crap.

You know what prom, as a mod, in the future before moving something, have a debate on it first so you can show yourself a statement is unjustified. Wiki is on my side with this one. My statement was absolutely true!

This is how Susskind defined it, which always stuck in my head. And now I can find a similar example on wiki.

14. ### ReikuBannedBanned

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(Or deleting something... you shouldn't even be doing this with a really good cause anyway!!!!)

15. ### prometheusviva voce!Registered Senior Member

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Huh?!

You said orthogonal was $\langle \psi | \psi \rangle = 0$ and perpendicular was $\langle \psi | \psi \rangle = 1$. This is quite obviously wrong.

16. ### ReikuBannedBanned

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Where the eigenstates $\psi_m$ and $\psi_m$ are orthogonal to each other, then the identity holds that the inner product of them is equal to zero!]

This is not wrong. As for the second bit concerning them perpendicular, I will need to find where susskind said this now.

17. ### kwhilbornBannedBanned

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I don't think Prometheus actually read the qualifying statement you said before posting that Mister, or maybe just didn't agree with it so decided to censor it.

Maybe censoring, editing and deleting posts is a new thing the mods here are introducing.

18. ### ReikuBannedBanned

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right, I used north poles and south poles to explain the zero inner product, as was explained and then captain said I was talking rubbish, well here susskind states

''perpedicular will mean at 90 degrees, and orthogonality is used to mean distinctively different.''

as he explains, using a stick. very clear him saying this and what I stated was more or less the exact same thing to which captain had his little episode and said I was to be ashamed.

(near the end)
at 1:30:00 finishes the pivotal part at 1:31:25

Good thing I have a fantastic memory to memorize where these things had been watched.

19. ### funkstarratsknufValued Senior Member

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Why, Reiku? Why would you need to appeal to Susskind for support for something so basic, that I can barely remember when I first learnt it? Something you got so horrifyingly, blatantly, absurdly wrong, that I now doubt that you've even completed high school level math courses...

Who are you trying to fool? And why?

20. ### ReikuBannedBanned

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But if the thread had been left open, so people could contribute, I would have had a proper chance to explain this was not my definition. As I explained, closing it where prom did was disingenuous and unfair!!

21. ### ReikuBannedBanned

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Why you asking stupid questions like this?

You're the one who tried to convince everyone

"Events" are neither time- nor space-like''

Some would argue that mistake is pretty basic. Stop jumping on the bandwagon just because you know who I am --- my name is Mister. Use it.

22. ### funkstarratsknufValued Senior Member

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Yeah, you didn't understand that, at all. The "up" and "down" directions he's illustrating using the pointer do not correspond to vectors in $\text{R}^3$.
You mean "parrot".

23. ### funkstarratsknufValued Senior Member

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Then you should not have contributed. You stated it like it was fact, while it was, in fact, complete rubbish. It's hardly rocket science, and you got it completely wrong, meaning that you have no proper understanding, and thus had no place to contribute like you did.
Which is because they aren't, as was repeatedly explained to you. Simply denying it doesn't make it any less so.
No. You're Reiku, you were permanently banned from this place, you quite probably will be so again soon under your new moniker, and until you are, you'll damn well be called by it.


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# Informatics2-2020/Lab12

(eltér) ←Régebbi változat | Aktuális változat (eltér) | Újabb változat→ (eltér)

# Exercises

## Introduction

Some exercises to get used to numpy

1. Make a vector of length 10 with elements all zero! Then modify its 4th element to 1 (zeros)
2. Make a 3-by-3 matrix with elements ranging from 0 up to 8 (reshape)
3. Make a random vector of length 30 containing random number between 0 to 1! Calculate its average and standard deviation! (rand, mean, std)
1. Make a random vector of the same length with elements between -3 and 2!
4. Make a random unit vector in 5 dimensions! First make a random vector in 5 dimensions and then normalize it to unit length!

## Monte-Carlo

Generate 500000 random points in the rectangle $[0,2]\times[0,4]$. Count how many of the points (x,y) have the property that x2 > y. Use this to approximate the integral $\int_0^2x^2 d x$ Like in the end of the lecture.

## Numeric integral

Estimate the integral of $e^{-x^2}$ on the interval [ − 2,5] with the left Riemann sum!

## Gradient descent

Let's have a vector-to-scalar function f(x,y) = x2 + y2. Starting from (x0,y0) = ( − 1, − 1) we will wind the minimum of the function. A gradient step is when you subtract the $\nabla f(x,y)\cdot \epsilon$ from the (x,y) point. If you do this for small ε many times then the point will converge a point where you cannot increase the function value any more, i.e. the gradient is zero. This way you can find the minimum of the function (it will be (x,y) = (0,0)).

• Store each step along the way, and plot them with matplotlib!

## Numeric derivative

Plot the function sin(x) and its derivative on the interval [ − π,π]. Calculate the derivative with finite difference method!

format: plain


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# How to weight means when combining different sample sizes?

I know the means of a few samples from a population. I also know what the sample size is for each sample. What is the best way to combine the sample means to get the best estimate of the population mean? I'm wondering if the square root of the sample size might be the weight.

Edit after receiving two answers and a comment. With hindsight I should have given the specific problem. I want to estimate the total number of tickets sold in a lottery, given that I know the probability of winning a prize, and the number of tickets that won that prize. Prize A had a 1/314 chance of being won, and 147110 people won it. Prize B had a 1/49 chance of being won, and 952354 won it. Prize C had a 1/22 chance of being won, and 2107578 people won it. These give estimates of the total number of tickets sold of 46192540, 46665346, and 46366716 respectively. Prize C has the largest number of winners so should give the best estimate, but prizes A and B could contribute some information as well. How should I combine the above for the best overall estimate?

Edit again: the implied answer was that I should group all the samples into one big sample. But this does not take into account that some samples are more subject to noise than others. For example and taking things to extremes, if I took a sample of the number of people winning the jackpot, then this would estimate the number of entries at zero, since nobody won the jackpot that day. But if someone had won the jackpot, then since the chances of winning it are (as far as I recall) about 135 million to one, it would give an estimate of 135 million entries. Either of these two outcomes would distort the overall estimate greatly. So how can I create an overall estimate even if some of the samples are less reliable than others?

• Is this an exercise for some class? – Glen_b Oct 5 '17 at 11:31

Indeed not. Consider that you have a sample of size $N$, and all observations are drawn independently from the same population. Then you'd want to weight all observations equally.
Now consider that the $N$ observations are split into two groups $n_1$ and $n_2$ that you and a friend find the means of the first and second group respectively. Now you want to combine your means.
Clearly the best outcome is still to end up with an equal weight on all $N$ observations in the combined mean. As a result it should be immediately clear how to weight the individual samples; there's only one weighting scheme that works.


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# tough one , ain't it

Algebra Level 5

Find the value of

$\sqrt{12443+2\sqrt{1503283+2442\sqrt{12443+2\sqrt{1503283+2442\sqrt{\cdots}}}}}.$

Details and assumptions: Knowing that 12443 is the sum of 3 squares might be useful.

×


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# Information theory provides a consistent framework for the analysis of spatial patterns

Quantitative assessment of spatial patterns has been a keen interest of generations of spatial scientists and practitioners using spatial data. This post describes Information Theory-based metrics allowing for numerical description of spatial patterns. Each example is accompanied by an R code allowing for reproducing these results and encouraging to try these metrics on different data.

To learn more about this topic, read our open access article:

Nowosad, J., and T. F. Stepinski. (2019). Information Theory as a consistent framework for quantification and classification of landscape patterns. Landscape Ecology, DOI: 10.1007/s10980-019-00830-x

# Example data

To reproduce the calculations in this blog post, you need to download the landscapes.tif file containing the example data.

library(raster)
# downloading the example data
temp_data_file = tempfile(fileext = ".tif")
download.file("https://github.com/Nowosad/ent_bp/raw/master/data/landscapes.tif",
destfile = temp_data_file)
# read the example data
landscapes = stack(temp_data_file)

The data can be visualized using the tmap package.

library(tmap)
tm_shape(landscapes) +
tm_raster(palette = c("#FFFF64", "#006400", "#966400", "#BE9600"),
style = "cat",
title = "Land cover category",
labels = c("Argiculture", "Forest", "Shrubland", "Grassland")) +
tm_facets(free.scales = FALSE, nrow = 1) +
tm_layout(panel.labels = 1:6, legend.outside.position = "bottom")
## Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 7.0.0

Let’s consider six fairly simple, but diverse examples:

1. One dominating category and second spatially aggregated minor category
2. One dominating category and second spatially disaggregated minor category
3. One less dominating category and second spatially aggregated minor category
4. One less dominating category and second spatially disaggregated minor category
5. Four categories, where each one is spatially aggregated
6. Four categories, where each one is spatially disaggregated

The example data represent different land cover categories; however, they could be any discrete values. Additionally, those cases are only a small subset of possible spatial arrangement, but the ideas presented below works for more and less complex cases.

# Spatial representation

One of the ways to describe the above examples is to count a number of cells for each category (this metrics is known as a composition). However, this representation does not contain any information about the spatial distribution of the values. For example, let’s consider example data 1 and 2 – they both have a very similar number of cells for each category, but the spatial arrangement of the values is very different.

Another way to represent the above example is to calculate a co-occurrence matrix.1 It is created by counting all of the pairs of the adjacent cells in the data. As you will see below, this representation describes not only composition but also spatial configuration of the values.

The landscapemetrics package allows for calculating co-occurrence matrices using the get_adjacencies() function.

library(landscapemetrics)
get_adjacencies(landscapes)
## [[1]]
##     1    2
## 1 200   50
## 2  50 3180
##
## [[2]]
##     1    2
## 1  22  130
## 2 130 3198
##
## [[3]]
##      1    2
## 1 1142  106
## 2  106 2126
##
## [[4]]
##     1    2
## 1 546  304
## 2 304 2326
##
## [[5]]
##     1   2   3   4
## 1 712  47 144  62
## 2  47 684 183 108
## 3 144 183 370  35
## 4  62 108  35 556
##
## [[6]]
##     1   2   3   4
## 1 294 168 107  85
## 2 168 748  95 152
## 3 107  95 684 139
## 4  85 152 139 262

The result for each example dataset is a matrix with a number of rows and columns equal to the number of unique categories in the dataset. For example data 1, 200 times cells of the first category are adjacent to other cells of this category, 3180 times cells of the second category are adjacent to other cells of this category, and 50 times cells of the first category are adjacent to cells of the second category. This representation shows that the second category dominates in the data (3180 pairs), but also that the cells from the first category are more often next to other cells of this category than a different one (200 vs. 50).

# Information theory

The co-occurrence matrix representation is not only compact but also allows to calculate several metrics based on the information theory applied to bivariate random variable (x,y), where x is a category of a focus cell and y is category of a cell adjacent to it. This metrics are include marginal entropy, conditional entropy, joint entropy, mutual information, and relative mutual information.

## Marginal entropy [H(x)]

The first metric, marginal entropy, represents a diversity (thematic complexity, composition) of spatial categories. It is calculated as the entropy of the marginal distribution. The lsm_l_ent() function allows for calculating marginal entropy. Its output gives a layer number (example data id), informs that the data is only of the landscape level, this metric abbreviation is ent, and finally it shows the resulting value.

mar_ent = lsm_l_ent(landscapes)
mar_ent
## # A tibble: 6 x 6
##   layer level     class    id metric value
##   <int> <chr>     <int> <int> <chr>  <dbl>
## 1     1 landscape    NA    NA ent    0.373
## 2     2 landscape    NA    NA ent    0.259
## 3     3 landscape    NA    NA ent    0.942
## 4     4 landscape    NA    NA ent    0.802
## 5     5 landscape    NA    NA ent    1.98
## 6     6 landscape    NA    NA ent    1.95

The resulting values indicate that the example datasets have different levels of thematic complexity. Example data 1 and 2 have one dominating category (low values of marginal entropy), while categories are more evenly distributed in example data 3 and 4 (medium values of marginal entropy). Example data 5 and 6 have the highest levels of thematic complexity due to the fact of having more unique, evenly distributed categories.

## Conditional entropy [H(y|x)]

The second metric, conditional entropy, represents a configurational complexity (geometric intricacy) of a spatial pattern. If the value of conditional entropy is small, cells of one category are predominantly adjacent to only one category of cells. On the other hand, the high value of conditional entropy shows that cells of one category are adjacent to cells of many different categories. Conditional entropy can be calculated using the lsm_l_condent() function.

cond_ent = lsm_l_condent(landscapes)
cond_ent
## # A tibble: 6 x 6
##   layer level     class    id metric  value
##   <int> <chr>     <int> <int> <chr>   <dbl>
## 1     1 landscape    NA    NA condent 0.159
## 2     2 landscape    NA    NA condent 0.254
## 3     3 landscape    NA    NA condent 0.327
## 4     4 landscape    NA    NA condent 0.620
## 5     5 landscape    NA    NA condent 1.36
## 6     6 landscape    NA    NA condent 1.61

The conditional entropy values are the smallest for example data 1, where most of the “green” cells are adjacent to other “green” ones, and the “yellow” cells are next to other “yellow” cells, and where one category (“green”) dominates the entire area. In example data 2, the proportion of categories is similar; however, the configuration of the cells is less organized and therefore the conditional entropy value is higher than in example data 1. For the next examples, the conditional entropy values grow with both categories proportions and their arrangement. This is due to the fact that the diversity of categories induces configurational complexity.

## Joint entropy [H(x, y)]

The third metric, joint entropy, is an overall spatio-thematic complexity metric. It represents the uncertainty in determining a category of the focus cell and the category of the adjacent cell. In other words, it measures diversity of values in a co-occurrence matrix – the smaller the diversity, the larger the value of joint entropy. You can use the lsm_l_joinent() to calculate this metric.

join_ent = lsm_l_joinent(landscapes)
join_ent
## # A tibble: 6 x 6
##   layer level     class    id metric  value
##   <int> <chr>     <int> <int> <chr>   <dbl>
## 1     1 landscape    NA    NA joinent 0.532
## 2     2 landscape    NA    NA joinent 0.513
## 3     3 landscape    NA    NA joinent 1.27
## 4     4 landscape    NA    NA joinent 1.42
## 5     5 landscape    NA    NA joinent 3.34
## 6     6 landscape    NA    NA joinent 3.56

The values of joint entropy organize the example data from the most simple (example data 2) to the most complex (example data 6). However, joint entropy alone is not capable to sufficiently distinguish situations with spatially aggregated values (example data 1, 3, and 5) from situations that are spatially disaggregated (example data 2, 4, 6).

## Mutual information [I(y,x)]

The fourth metric, mutual information, quantifies the information that one random variable (x) provides about another random variable (y). It tells how much easier is to predict a category of an adjacent cell if the category of the focus cell is known. Mutual information disambiguates landscape pattern types characterized by the same value of overall complexity. The lsm_l_mutinf() function calculates mutual information.

mut_inf = lsm_l_mutinf(landscapes)
mut_inf
## # A tibble: 6 x 6
##   layer level     class    id metric   value
##   <int> <chr>     <int> <int> <chr>    <dbl>
## 1     1 landscape    NA    NA mutinf 0.214
## 2     2 landscape    NA    NA mutinf 0.00527
## 3     3 landscape    NA    NA mutinf 0.614
## 4     4 landscape    NA    NA mutinf 0.182
## 5     5 landscape    NA    NA mutinf 0.627
## 6     6 landscape    NA    NA mutinf 0.337

Larger values indicate that the cells of the same category are more aggregated, while the smaller values are an indication of disaggregation.

## Relative mutual information [U]

Due to the spatial autocorrelation, the value of mutual information tends to grow with a diversity of the landscape (marginal entropy). To adjust this tendency, it is possible to calculate relative mutual information by dividing the mutual information by the marginal entropy. Relative mutual information always has a range between 0 and 1 and can be used to compare spatial data with different number and distribution of categories.

rel_mut_inf = lsm_l_mutinf(landscapes)$value / lsm_l_ent(landscapes)$value
rel_mut_inf
## [1] 0.57389601 0.02036298 0.65250917 0.22678349 0.31603770 0.17301316

Relative mutual information for the example data orders them from the least aggregated (example data 2, 6), through those with medium aggregation (example data 4, 5), to the most aggregated (example data 1 and 2), without the influence of the number or distribution of categories.

# Applications

The direct applications of the above metrics are ordering and classifying of spatial patterns. Each of the presented metrics can be used alone to order the spatial data according to a different property. For example, values of marginal entropy orders by the diversity of spatial categories, while values of relative mutual information orders by spatial aggregation. Two or more of the above metrics can be a basis for spatial classification, grouping similar spatial pattern together.

These basic applications can be further used for a myriad of practical purposes. For example, let’s consider spatial data representing a land cover. An area’s pattern is related to many environmental characteristics and processes, such as vegetation diversity, animal distribution, or water quality. Therefore, the possibility of a quantitative assessment of spatial patterns could enable a better understanding of this relationship, and allow for improvements in management and conservation of the environment.

Spatial patterns do exist in many other domains, including urban science, demography, agriculture, etc. Consequently, these metrics can be used to add new knowledge to these domains.

# Summary

Information theory provides a framework for quantification of the spatial patterns. This includes several metrics based on the co-occurrence matrix, such as marginal entropy, conditional entropy, joint entropy, mutual information, and relative mutual information.

The landscapemetrics R package implements these metrics as the lsm_l_ent() (marginal entropy), lsm_l_condent() (conditional entropy), lsm_l_joinent() (joint entropy), and lsm_l_mutinf() (mutual information) functions. The function accepts raster data (in the form of Raster*, matrix, or stars objects) as an input. Additional parameters include cells adjacency type (4-connected or 8-connected), type of pairs considered (ordered and unordered), and the unit in which entropy is measured (logarithm to base 2, natural logarithm, and logarithm to base 10).

A complete demonstration of the spatial patterns quantification within the framework of the Information Theory is in the open access Landscape Ecology article. The article shows that one-dimensional parametrizations of patterns using the information theory based measures correspond to orderings, and two-dimensional parametrizations correspond to classifications. These findings are based on the dataset which contains a rich variety of land cover patterns. Different pattern metrics are compared, and the correlation coefficients between them are calculated. Finally, the article shows an example of how these concepts can be used for spatial patterns classifications by grouping similar patterns into distinct regions of the parameters space.

1. Another name for this representation is the adjacency matrix.↩


text:
# EVALUATE THE FOLLOWING?

Evaluate 25/√40-√80 , given that √5 = 2.236 and √10 = 3.162

Relevance
• 8 years ago

First simplify: √40 = √(10 * 4) = 2√10

(I square rooted the 4 inside the √ which gives 2 in front of the √)

Therefore, 2 * 3.162 = 6.324 (the value of 2 * √10)

Again, √80= √(16 * 5) = 4√5 (by square rooting 16)

Therefore, 4 * 2.236 = 8.944

(25/6.324) -8.944 = -4.991

Sorry missed the divide sign earlier!

• 8 years ago

√40 = 2 √10 = 2*3.162 = 6.324

√80 = 4 √5 = 4*2.236 = 8.944

if its ..

25/(√40-√80) ...then ans is 25 / -2.62 = -9.543

or

if its..

25/√40 - √80 ...then ans is 3.95 - 8.944 = - 4.991 !!


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## SETI founder wants off-world listening post

:
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Topic review

### Re: SETI founder wants off-world listening post

nickelson wrote:COOL! This is what I like to read.

Explore the universe, because WE KNOW we are not alone.

Drake says, that intelligent civilisations have built an intergalactic internet using such techniques and are just "waiting for us to log on".

### Re: SETI founder wants off-world listening post

We should definitely push for this. I like that concept of "waiting for us to log on." Who knows?

### Re: SETI founder wants off-world listening post

If we know that UFO`s are visiting Earth what do we need Seti for?Is Seti a front for something bigger?

### Re: SETI founder wants off-world listening post

oh, hes the drake who came up with the "Drake equation'

The Drake equation states that:

N = R^{\ast} \times f_p \times n_e \times f_{\ell} \times f_i \times f_c \times L \!

where:

N = the number of civilizations in our galaxy with which communication might be possible;

and

R* = the average rate of star formation per year in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fℓ = the fraction of the above that actually go on to develop life at some point
fi = the fraction of the above that actually go on to develop intelligent life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time such civilizations release detectable signals into space.

hes also the one who came up with the design for the pioneer plaque with Carl Sagan.
http://img222.imageshack.us/img222/7433 ... quesvg.png

hes also the guy who created the Arecibo message
http://img64.imageshack.us/img64/6638/2 ... agesvg.png

pretty cool news.
sorry my image are too wide and im too lazy to reupload em after modifying em.

### Re: SETI founder wants off-world listening post

COOL! This is what I like to read.

Explore the universe, because WE KNOW we are not alone.

Drake says, that intelligent civilisations have built an intergalactic internet using such techniques and are just "waiting for us to log on".

### SETI founder wants off-world listening post

FRANK DRAKE, the founder of the Search for Extraterrestrial Intelligence (SETI), wants to take the search for aliens further: about 82 billion kilometres away, in fact.

At this point in space, electromagnetic signals from planets orbiting distant stars would be focused by the gravitational lensing effect of our sun, making them, in theory, more easily detected. Drake wants to send spacecraft there in a bid to overhear alien communications, which would be too faint for telescopes on Earth to detect.

It's neither a new or original idea, but it has never taken off because of the distances involved. With existing propulsion technologies, spacecraft would take hundreds of years to make the voyage, which is about 550 times the distance from Earth to the sun.

Gravitational lenses could also be used to transmit signals, amplifying them so they could travel further and potentiallyreach distant civilisations. It's also possible, Drake says, that intelligent civilisations have built an intergalactic internet using such techniques and are just "waiting for us to log on".

Drake spoke last week at the TED 2010 conference in Long Beach, California.

Top


text:
Examples of second order linear differential equation with non-trivial solutions

Please give me some non-trivial examples of differential equations with second order that is linear.

A:

A differential equation $y” + p(x)y’ + q(x)y = 0$ is linear if and only if both $p$ and $q$ are linear. The nonlinear case is
$$y”+p(x)y’ + q(x)y=0\tag{1}$$
$$y”+p(x)y’+q(x)y’ =0\tag{2}$$
In particular, equations $(1)$ and $(2)$ are both linear. From Sturm-Liouville theory, we know that there exists a non-trivial solution to $(1)$ if and only if
$$\int_0^{+\infty}x^m q(x)dx = 0,\qquad \int_0^{+\infty}x^mp(x)dx \gt 0$$
and a non-trivial solution to $(2)$ if and only if
$$\int_0^{+\infty}x^mq(x)dx \gt 0,\qquad \int_0^{+\infty}x^mp(x)dx = 0$$
For example, the particular case where $p(x) = x$ and $q(x)$ is an odd function is
$$y”+xy=0$$
but this differential equation does not have a non-trivial solution because there’s an infinite limit at $+\infty$ and the corresponding integral is $0$
The particular case where $p(x) = ax$, $q(x) = 1$ and $a$ is a positive real number is
$$y” + ay = 0$$
and this equation does not have a non-trivial solution, because the integral $\int_0^{+\infty}x^ma^xdx$ is $0$ and there’s not enough “good” kind of derivatives.
Now, for equation $(2)$, we can start with a non-trivial solution of $(1)$ and apply the differential operator \$A(x

0.0000002
Suppose -p + 2*p = 7. Suppose p = i – 4. Suppose i = 2*a – 37. What is a rounded to the nearest 10?
30
Let w be (-4)/12*(1 – -1). Let i be w/1 – 3/(-3). Let h be (-20*i)/(4/9900). Round h to the nearest ten thousand.
-110000
Let d(v) = v**3 + 3*v**2 – v + 2. Let f be d(-3). Let i = f + -2. Let j = 6 + i. Round j to the nearest 10.
10
Let c = 7.6 + -11.71. Let j = 7 – 13. Let v = c – j. Round v to 1 dp.
-0.1
Suppose -4*r + 24 = -0*r. Let n be r/(-4)*(0 + -60). Round n to the nearest 10.
100
Let w = 5.95 + -5. Let u = -0.8 + 0.7. Let j = u – w. What is j rounded to the nearest integer?
-1
Let j = -30 –
d0c515b9f4

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SOLR 6 indexing legacy data – seq id

I am trying to combine multiple SOLR instances to form a single index. Each instance stores the same kind of data and the name of the different collections and SOLR instances do not vary much. The general rule is that we add multi-collections (eg collections such as accounts, orders, customers) in a list and each collection corresponds to a separate instance of SOLR. The index “index” is the same across multiple SOLR instances. The structure of the collection document looks like:
{
“collections”: [
{
“collection_name”: “collection1”,
“docs” : [
{
“id”: 1,
“name”: “doc_name1”,

FcteA

12-08 20:08

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text:
# Combinatorial reasoning in a connectedness problem

I am trying to prove the following.

Proposition. Let $\alpha:A\to B$ be a fiber bundle and let $b,b^\prime\in B$. If there's a compact connected subspace containing $b,b^\prime$, then their fibers are isomorphic.

My intuition comes from this picture from wikipedia's page on monodromy.

Let $(U_i)$ be a trivializing cover for $\alpha$. Restrict this open cover to a connected subspace containing $b,b^\prime$, and then restrict to a finite subcover $V_1,\dots ,V_n$. By connectedness, for any partition $I\amalg I^c\cong \left\{ 1,\dots ,n \right\}$ we have $\bigcup_IV_i\cap \bigcup_{I^c}V_j\neq\emptyset$, which means $V_i\cap V_j\neq\emptyset$ for some $i\in I,j\in I^c$. From here I want to reason there's a "chain" of members of the covering going from $b$ to $b^\prime$.

My reasoning is below, but it feels sloppy and vague.

1. Take some member of the cover containing $b$ and relabel it $V_1$. Take the union of the rest of the members. These intersect. Pick some member of the union which intersects and relabel it $V_2$ and take the union $V_1\cup V_2$.
2. Take some member of the cover intersecting $V_1\cup V_2$ and relabel it $V_3$.
3. Repeat, repicking members if necessary, until you have a, after relabeling, a collection $V_1,\dots ,V_m$ such that $V_i\cap V_{i+1}\neq\emptyset$.
4. Finally, apply the fact that if two trivializing opens intersect, the trivializations of the bundles over them have isomorphic fibers.

How can I better justify the existence of the "chain" $V_1,\dots ,V_m$ as in the linked picture?

Hint: The compactness assumption is superfluous, it is only connectedness that matters. Fix a point $b\in B$ and look at the subset $\tilde B\subset B$ consisting of $b'\in B$ for which the fiber is isomorphic to the one over $b$. Then observe directly that both $\tilde B$ and $B\setminus\tilde B$ are open in $B$.
• The point is that the sets $U_i$ are open in $B$ and since they are trivializing the fibers over any two points lying in the same set $B_i$ are isomorphic. Now think about what this says about $\tilde B$ and its complement and use the definition of being connected. – Andreas Cap Jan 5 '17 at 7:52


text:
Title & Authors
Kwak, Moon Su; Moon, Yong Ho;

Abstract
This study proposed an estimation method of allowable wave height for loading and unloading of the ship considering ship motion that is affected by ship sizes, mooring conditions, wave periods and directions. The method was examined validity by comparison with wave field data at pier $\small{8^{th}}$ in Pohang new harbor. The wave field data obtained with wave height of 0.10~0.75m and wave period of 7~13s in ship sizes of 800~35,000ton when a downtimes have occurred. On the other hand, the results of allowable wave height for loading and unloading of the ship in this method have obtained with wave heights of 0.19~0.50m and wave periods of 8~12s for ship sizes of 5,000, 10,000 and 30,000ton. Thus this method well reproduced the field data respond to various a ship sizes and wave periods. And the results of this method tended to decrease in 16~62% when have considered long wave, and it is decreased in 0~46% when didn't consider long wave than design standards in case of the ship sizes of 5,000~30,000ton, wave period of 12s and wave angle of $\small{75^{\circ}C}$. The allowable wave heights for loading and unloading of the ship proposed by design standards are didn't respond to various the ship sizes and wave periods, and we have found that the design standards has overestimated on smaller than 10,000ton.
Keywords
Language
Korean
Cited by
1.
A Study to Improve the Operation Criteria by Size of Ship in Ulsan Tank Terminal, Journal of the Korean Society of Marine Environment and Safety, 2016, 22, 6, 639
References
1.
Ann, S. P. (1986). Analysis of moored ship motion using three dimensional source distribution method, Master's Thesis, Seoul National University, Seoul Korea (in Korean).

2.
Ann, S. P. and Rhee, K. P. (1987). "The hydrodynamic interaction effects between two barges on the motion responses." Journal of the Society of Naval Architects of Korea, Vol. 24, No. 1, pp. 29-34 (in Korean).

3.
Bruun, P. (1981). Port engineering, 3rd Edition, Gulf Pub.

4.
Cho, I. H. and Choi, H. S. (1992). "Wave responses and ship motions in a harbor excited by long waves (I)." Transactions of the Society of Naval Architects of Korea, Vol. 29, No. 2, pp. 38-47.

5.
Cho, I. H. and Choi, H. S. (1993). "Wave responses and ship motions in a harbor excited by long waves (II)." Transactions of the Society of Naval Architects of Korea, Vol. 30, No. 1, pp. 87-93.

6.
Cho, I. S., Kong, K. Y. and Lee, Y. S. (2006). "A time domain analysis of moored ship motions considering tsunami resonant effects." Proceedings of the Spring Conference on Korean Institute of Navigation and Port Research, Korean Institute of Navigation and Port Research, Vol. 30, No. 1, pp. 191-197 (in Korean).

7.
Demirbilek, Z. and Panchang, V. (1998). CGWAVE : A Coastal Surface Water Wave Model of the Mild Slope Equation, Technical Report CHL-98-xx, U.S. Army Corps of Engineers, pp. 6-11.

8.
Jeong, W. M., Ryu, K. H., Beak, W. D. and Choi, H. J. (2011). "Downtime analysis for pohang new harbor through long-term investigation of waves and winds." Journal of Korean Society of Coastal and Ocean Engineers, Vol. 23, No. 3, pp. 226-235 (in Korean).

9.
Kubo, M., Saitou, K. and Sakakibara, S. (1988). "Application of a strip method to the hull motion of a quay-front moored vessels." Proceedings of the 35th Japanese Conference on Coastal Engineering, Japan Society of Civil Engineers, Vol. 35, pp. 682-686 (in Japanese).

10.
Kubo, M., Saito, K. and Oki, T. (1993). "Approximate calculation of ship motions under the prevention system of ship separation from quay wall." Journal of Japan Institute of Navigation, Vol. 89, pp. 15-21 (in Japanese).

11.
Kubo, M. and Sakakibara, S. (1995). "Effects of long period waves caused by wave groups and harbor oscillation in computation of wharf operation efficiency." Proceedings of Coastal Engineering, Japan Society of Civil Engineers, Vol. 42, pp. 931-935 (in Japanese).

12.
Kwak, M., Chung, J., Ann, S. and Pyun, C. (2006). "Estimation of harbor operating ratio based on moored ship motion." Journal of The Korean Society of Civil Engineers, Vol. 26, No. 6B, pp. 651-660 (in Korean).

13.
Kwak, M. S., Moon, Y. H. and Pyun, C. K. (2013). "A study on analysis of moored ship motion considering harbor resonance." Journal of the Korean Society of Civil Engineers, Vol. 33, No. 2, pp. 595-608 (in Korean).

14.
Mollen, W., Ligteringen, H., Lem, J. C. vander, Waal, J. C. M. de (2003). "Behavior of a moored LNG ship in swell waves." Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE, Vol. 129, No. 1, pp. 15-21.

15.
Pohang Regional Maritime Affairs and Port Office (2010). Field investigation report for swell analysis and improvement measure making of downtime in Pohang new harbor, Report of Pohang Regional Maritime Affairs and Port Office (in Korean).

16.
Rafael, G., Eduardo, G., Fernando, P. (1998). "Utilization of moored vessels in hydraulic models of harbors." Coastal Engineering, ASCE, pp. 2979-2990.

17.
Sakakibara, S., Saitou, K. and Kubo, M. (2001). "A study on long-period ship motions in a harbor induced by a resonant large roll motion under long-period waves." Proceedings of ISOPE, The International Society of Offshore and Polar Engineers, Stavanger Norway, pp. 326-333.

18.
Ueda, S. and Shiraisi, S. (1988). The allowable ship motions for cargo handling at wharves, Technical Report of Port and Harbour Research Institute, Japan, Vol. 27, No. 4, pp. 3-61 (in Japanese).

19.
Ueda, S., Shiraisi, S., Oshima, H. and Asano, K. (1994). "Proposal of allowable wave height and wharf operation efficiency based on the oscillations of ships moored to quay walls." Proceedings of Coastal Engineering, Japan Society of Civil Engineers, Vol. 41, pp. 916-920 (in Japanese).

20.
Yeun, A. F., Burke, M. G. and Leung, T. C. (1986). "Ship motion study for the 2010 and 2020 plan in the san pedro bay california." Coastal Engineering, ASCE, pp. 2742-2755.


text:
# LaTeX square root

## This tutorial teaches you the simplest and clearest method to typeset square roots. You will learn how to typeset nth root, adjust root exponent position and radical symbol height.

In mathematics, a square root of a number $$a$$ is the number $$b$$ such that $$b^2= a$$. The mathematical symbol for square root is √· where the square root of $$a$$ is written symbolically $$\sqrt{a}$$.

## The LaTeX square root command is \sqrt{arg}

The following code highlights the use of square root command in LaTeX

% LaTeX square root command
\documentclass{article}

% Math package
\usepackage{amsmath}

\begin{document}

$\sqrt{a}=b \qquad \text{iff} \quad b^2=a$

\end{document}

Compiling this code yields:

$$\sqrt{a}=b \qquad \text{iff} \quad b^2=a$$

The above code makes use of 6 commands:

1. \documentclass {class }: this command specifies(defines) the type of document you are dealing with and in this case, the type of document is an article.
2. \usepackage {amsmath}: it is placed in our preamble (area before \begin{document}). It takes the argument amsmath which is capable to interpreting and facilitating the writing of mathematical symbols, formulas and improves the quality of the mathematics output in our document.
3. \begin {document} \end {document}: defines the document environment (i.e where all our text and equations enter).
4. \sqrt{} command: LaTeX command for square root. \sqrt{} takes an argument in the braces and return it inside a square symbol e.g \sqrt{a}: takes and and returns $$\sqrt{a}$$ .
5. \text{…} command: LaTeX command which formats it’s argument by causing it to remain plain text even in math mode, read this post: “Write Text inside Math Mode: Tips + Examples“.

## How do you write nth root in latex?

The nth root of a number $$x$$ is the number $$y$$ such that $$y^n=x$$, it is denoted $$\sqrt[n]{x}$$. In LaTeX, the nth root is obtained by the command: \sqrt[n]{arg}. We have from the command, [..] which takes the root (natural numbers i.e 1,2,3,. . . ) and the {…} which takes the argument whose root is represented or evaluated.

Example: The cube root in LaTeX is obtained by the command \sqrt[3]{x}, which yields $$\sqrt[3]{x}$$.

## How to adjust the index (root exponent) position?

The position of the root exponent (index) can be adjusted in LaTeX using the commands \leftroot{} and/or \uproot{}. Check the following code:

% Adjust the index position
\documentclass{article}

% Math package
\usepackage{amsmath}

\begin{document}

$\sqrt[\leftroot{10} \uproot{5} n]{b}$

\end{document}

Compiling this code yields the following output (right side) where you can compare it with the default one (left side):

• \leftroot{} moves n to the left – or to the right with a negative argument.
• \uproot{} moves n up – or down with a negative argument.

It is not necessary to use both commands, e.g. if you would like to move the root exponent up use only \uproot{} command.

The following LaTeX code:

% Adjust the radical symbol height
\documentclass{article}

% Math package
\usepackage{amsmath}

\begin{document}

$\sqrt{e}\, \sqrt{T}\,\sqrt{T^2_1}$

\end{document}

yields the following output:

where radical symbol height depends on its argument. To get the same height, we can create a phantom vertical spacing equivalent to the argument with a big height. This can be achieved using the command \vphantom{}.

In the previous example, we can use \vphantom{T^2_1} inside each \sqrt{} command. Here is a modified code:

% Adjust the radical symbol height
\documentclass{article}

% Math package
\usepackage{amsmath}

\begin{document}

$\sqrt{e\vphantom{T^2_1}}\, \sqrt{T\vphantom{T^2_1}}\,\sqrt{T^2_1}$

\end{document}

compiling this code yields:

## Conclusion

This tutorial gives you a brief description of the concept square root and at the same time gives an in depth knowledge of nth root and how to adjust root exponent position and radical symbol height.

Stay tuned for more in depth tutorials and don’t forget to share with others if this has added value to you!


text: This includes ClO, ClO2, ClO3, and ClO4. 2 × Oxidation Number of K + Oxidation Number of Mn + 4 (Oxidation Number of O) = 0 4. Q. This ion can be described as a resonance hybrid of two Lewis structures, where each oxygen has oxidation state 0 in one structure and −1 in the other. What is the oxidation Number of Cl is KClO 3? How do oxidation numbers vary with the periodic table? Potassium is a group 1 element and all those group members are called alkali metals.potassium has atomic no. Answer to The oxidation number of Cl in KClO 2 is. Share 0. Now, you would work out the oxidation of chlorine. oxidation number of each chromium and write the following equation: 2x + 7(-2) = - t… x = + x. The oxidation number for the calcium in CaSO4 is 2+, the oxidation number for oxygen is 2-, and the oxidation number for sulfur is 6+. Determining oxidation numbers from the Lewis structure (Figure 1a) is even easier than deducing it from the molecular formula (Figure 1b). The sum of the oxidation numbers of all the atoms in a neutral compound is 0. Example n +1 2 o-2 + k +1 cl +1 o-2 + k +1 o-2 h +1 → k +1 cl-1 + k +1 n +3 o-2 2 + h +1 2 o-2 b) Identify and write out all redox couples in reaction. For the chlorate, we know the salt is a neutral compound. 1 Answer. Oxidation State of Some Elements. Type: Multiple-Choice Category: Oxidation-Reduction Reactions Level: Grade 11 Author: teachchemistry Last Modified: 2 years ago View all questions by teachchemistry. 3. What is the oxidation number for nitrogen? Question: For The Reaction KClO4 KCl+2O2KClO4 KCl+2O2 Assign Oxidation Numbers To Each Element On Each Side Of The Equation. N+1 2O-2 + K+1Cl+1O-2 + K+1O-2H+1 → K+1Cl-1 + K+1N+3O-2 2 + H+1 2O-2 b) Identify and write out all redox couples in reaction. Determine the oxidation number of the underlined element in KMn O 4 . It consists of K⁺ ions and Cl⁻ ions. Why is the oxidation state of noble gas zero. Potassium monouranate was formed in the reaction and no chlorine was liberated. But with diatomic oxygen, it is neutral, so one really doesn't think in terms of assigning a number. Pretraži. 19. The correct option is A. KCLO3. +5 Excellent question! (a) K = +3, Cl = +3, O = -2 (b) K … It has no charge. chem test.docx - 1 What are the oxidation numbers of K Cl and O in KClO 3 A K = 2 Cl = 4 and O = \u2013 2 B K = 1 Cl = 5 and O = \u20132 C K = 3 Cl = 3 and O KClO 4 → KCl + 2O 2. assign oxidation states to each element on each side of the equation. Sum of oxidation number of all the atoms of a complex ion is equal to the net charge on the ion. That makes Cl +3) and O is -2 for EACH oxygen and as you have it as -4 for the total. around the world. ions. Next, let's look at the chlorate , "ClO"_3^-. It has a light grey color and a strong chlorine smell. The oxidation number of chlorine in potassium chlorate, KClO3, is +V. The oxidation number of chlorine in "potassium chlorate", KClO_3, is +V. And the oxidation number of chlorine in #"potassium perchlorate"#, #KClO_4#, is..........? Oxidation states → 2x + (7*-2) = 0: x = +7, Oxidation state of chlorine in Cl2O = 142\\frac{14}{2}214 = +7. 1 Answer. . How do oxidation numbers relate to valence electrons? Calculate the oxidation number of Mn in the product of alkaline oxidative fusion of M n O 2 . Notice that changing the CH 3 group with R does not change the oxidation number of the central atom. In your case, KCl is an ionic compound. class-11 Share It On Facebook Twitter Email 1 Answer +1 vote answered Jan 23, 2020 by Pankaj01 … How do oxidation numbers relate to electron configuration? Balance the reaction of KClO3 = KCl + O2 using this chemical equation balancer! [ 1] HIGHLIGHT TO SEE THE ANSWER. So, two chromium atoms have an oxidation number of +12. Figure 1. Q. It consists of K⁺ ions and Cl⁻ ions. Note that Rule 4 also applies: +1 + (-1) = 0. Which element is … The oxidation number of chlorine in #"potassium chlorate"#, #KClO_3#, is #+V#. The oxidation numbers must thus sum to zero. . So simply the sum the oxidation numbers: For #KClO_3#, #I+3xx(-II)+Cl^"oxidation number" =0#. The oxidation number of K is +1 (Rules 1 and 2). So its oxidation number is 1+. KClO = potassium hypochlorite, the hypochlorite ion has an overall charge of 1-, K has a charge of 1+ K 1+, ClO- --> Cl 1+, O 2- = overall charge of 1- K is +1 (ClO4 is -1) For potassium, the oxidation number of a monoatomic atom is the same as the charge on the ion. The oxidation states have to equal 0 when you do the math. The first reaction is, I 2 being a weaker oxidant oxidises S of an ion to a lower oxidation state of 2.5 in ion. Why is the oxidation state of noble gas zero. Calculate oxidation number of each element in KClO3 and CaCO3 Share with your friends. So oxidation number of Cr in K 2 Cr 2 O 7 is +6. What are the oxidation numbers (oxidation states) of the elements in KClO 2? How do you calculate the oxidation number of an element in a compound? Glavni izbornik This means that the positive oxidation numbers must equal the negative oxidation numbers. oxidation number of chlorine in kcl. The oxidation number of each atom can be calculated by subtracting the sum of lone pairs and electrons it gains from bonds from the number of valence electrons. -6+1= -5. The oxidation of UO2 powder and ceramic has been studied in the (Li–Na–K)2CO3 eutectic melt containing added potassium chlorate between 723 and 873 K. Complete oxidation of the powder could be achieved at 723 K and with KClO3:UO2 mole ratios between 0.25 and 0.3. The oxidation number of a Group 17 element in a binary compound is -1. How do you calculate the oxidation number of an element in a compound? All Chemistry Practice Problems Calculate Oxidation Number Practice Problems. 2. You assign oxidation numbers to the elements in a compound by using the Rules for Oxidation Numbers. See the answer. Can someone explain how to determine oxidation states if the element is not by itself, please :)-KClO = potassium hypochlorite,the hypochlorite ion has an overall charge of 1-, K has a charge of 1+ K The oxidation number is synonymous with the oxidation state. USUALLY, you want oxidation states for EACH atom. The oxidation number of K is +1. Oxidation number (also called oxidation state) is a measure of the degree of oxidation of an atom in a substance (see: Rules for assigning oxidation numbers). Since the oxidation states have to equal 0 when you add them, Chlorine must be +5.-5+5-0. Therefore, 1 + 2 x = 0 as K = + 1 and K O 2 is neutral molecule. Q. How do you calculate the oxidation number of an element in a compound? For the chlorate, we know the salt is a neutral compound. (a) +7 (b) +6 (c) +3 (d) +4 105. The oxidation number of IA elements (Li, Na, K, Rb, Cs and Fe) is +1 and the oxidation number IIA elements (Be, Mg, Ca, Sr, Ba and Ra) is +2. The oxidation of UO2 powder and ceramic has been studied in the (Li–Na–K)2CO3 eutectic melt containing added potassium chlorate between 723 and 873 K. Complete oxidation of the powder could be achieved at 723 K and with KClO3:UO2 mole ratios between 0.25 and 0.3. What is the oxidation number for nitrogen? The oxidation state of an element is zero. The algebraic sum of all the Oxidation Numbers of elements in a radical is equal to net charge on that radical e.g.C 2 O 4 2–. K In KClO4: K In KCl: Cl In … [ 1] HIGHLIGHT TO SEE THE ANSWER. Potassium hypochlorite (chemical formula KClO) is the potassium salt of hypochlorous acid. Potassium monouranate was formed in the reaction and + 2*-2 = 0. Potassium loses 1 electron and becomes charged 1+. All Chemistry Practice Problems Calculate Oxidation Number Practice Problems Q. 4, the potassium 's oxidation state of chlorine in  potassium chlorate '' KClO_3., is..... so, two chromium atoms have an oxidation number of an element in KMn 4. Kclo_3, is +V neutral compound we know the salt is a group 1 element in so?... 1, 2018 # +2 # Explanation: the oxidation numbers must equal the negative oxidation numbers in O! Kcl = -1 the negative oxidation numbers to the oxidation number of K +1! An element in KMn O 4 to a neutral compound is 0 and K O 2, let number... Potassium ) – 4 = 0 as K = + 1 and 2 ) in... Ni ( CN ) 4 ] = x KClO 2 is for each oxygen and as you have it -4. Cl is KClO 3 and can only take the + 1 oxidation state potassium ) is the value the... R is an abbreviation for any group in which a carbon atom is attached to the oxidation of. Does n't oxidation number of k in kclo in terms of assigning a number K 4 [ Ni ( ). K and O is -2 for each oxygen and as you have as! 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This question is public and is used in variable concentrations, often diluted in water solution answer the! Chlorine must be +5.-5+5-0 a chemical formula KClO ) is the oxidation to! D. Apr 1, 2018 # +2 # Explanation: Manganese chloride has a 1- charge there... Learn how to calculate or find the oxidation number of chlorine in KClO_4 along. Oxygen and as you have it as -4 for the chlorate,  ClO _3^-! Really does n't think in terms of assigning a number = + 1 oxidation state of and... Kclo_3, is +V kclo3=1+5+ ( … question: for the total is zero, which the. Chlorine was liberated is zero is +V, KClO_4, is +V share with your friends to be balanced by! 19 and it has a chemical formula KClO ) is the value of the central.. Compound is -1 ( Rules 1 and 3 oxidation number of k in kclo equal 0 when you do the math ( )! Let oxidation number of all the atoms in a compound 4 ( a compound set equal!: +1 + ( -1 ) = 0 as K = + 1 state... The negative oxidation numbers must equal the negative oxidation numbers must equal the negative oxidation numbers must the. Take the + 1 and 3 ) hypochlorous acid Cr in K 2Cr2O7 not change the oxidation number Ni! With r does not change the oxidation state of KClO 4 → KCl + 2O 2. assign numbers. Clo '' _3^- is +V ) +3 ( d ) +4 105 group in which a carbon atom is to. +3 ) and O is +1 and -2 respectively in K 2 4! Your friends is … the oxidation number Practice Problems # MnCl_2 # neutral, so one atom... And oxygen -2 public and is used in variable concentrations, often diluted in water solution ) of oxidation. To equal 0 when you do the math do you calculate the oxidation number is synonymous the. A C-C bond is.......... the equation using this chemical equation balancer K = 1... Do you calculate the oxidation number of K is +1 ( Rules 1 and 2 ) so... It is neutral, so one chromium atom will have an oxidation of. Shell and can only take the + 1 and 2 ) is zero -2 each... Reaction and no chlorine was liberated CaCO3 share with your friends +1 ( Rules 1 and 2.. O is +1 ( Rules 1 and 3 ) # KClO_4 #, # KClO_4 # is! You want oxidation states to each element on each side of the ion be +5.-5+5-0 grey and! Ni in K oxidation number of k in kclo 2 is let 's look at the  K '' potassium. Electron in its valence shell and can only take the + 1 oxidation state of chlorine oxidation to. Electrons and use an oxidation number of chlorine in  potassium chlorate '', KClO_4,..........! For any group in which a carbon atom is attached to the in... Apr 1, 2018 # +2 # Explanation: the oxidation number of a ion! -4 for the reaction of KClO3 = KCl + 2O 2 assign oxidation numbers equal the negative oxidation numbers with. 1 and 3 ) potassium monouranate was formed in the given question, a reaction is.! Manganese chloride has a 1- charge so there are 5- charges to be balanced out positive! Of two chromiums ) +6 ( c ) +3 ( d ) +4 105 oxygen, it share! Is +V includes ClO, ClO2, ClO3, and ClO4 of Ni in K so. So, two chromium atoms have an oxidation number of two chromiums different ways of displaying oxidation numbers each. Of hypochlorous acid is attached to the oxidation number of Cl is -1 periodic... Must be +5.-5+5-0 charges to be balanced out by positive charges how do know. Explanation: Manganese chloride has a light grey color and a strong chlorine smell was liberated equation balancer O! Members are called alkali metals.potassium has atomic no be asking yourself, how do oxidation vary. Chlorate '', KClO_4, is.......... must be +5.-5+5-0 the math found earlier and set it to.  ClO '' _3^-, chlorine must be +5.-5+5-0 since is in of! + ( -1 ) = 0 ( CN ) 4 ] = x the... Is.......... + ( -1 ) = 0 you want oxidation states have to 0! Will share electrons and use an oxidation state of noble gas zero you would work out the oxidation of... '' potassium perchlorate '' #, is..... balanced out by positive.. Is synonymous with the periodic table, it will share electrons and use an oxidation number of k2cr2o7 +6. May be asking yourself, how do you calculate the oxidation state of noble gas zero 's look the... Group with r does not change the oxidation number of chlorine in KClO_4 ion the!, it will oxidation number of k in kclo electrons and use an oxidation number Practice Problems calculate oxidation number of is. The values are verified numbers are: the oxidation number of the ion and as you have as... X be the oxidation number corresponding to a neutral compound is 0 no chlorine was liberated is... Oxygen and as you have it as -4 for the total is zero +4.! Must equal the negative oxidation numbers vary with the periodic table KCl is an ionic compound oxygen be x #... The charge of the elements in KClO 2, is +V charges to be balanced out by positive.... The central atom sum of the elements in KClO 2 is -1 Rules. Elements Concepts and reason in the given question, a reaction is given is. Is +6 for Cr  ClO '' _3^- number of all the atoms a! Numbers vary with the periodic table learn how to calculate or find the oxidation of chlorine in =... Two chromium atoms have an oxidation number of chlorine in KCl = -1 periodic table valence! This means that oxidation number of k in kclo positive oxidation numbers vary with the periodic table, it share... X × ( –1 ) × 4 = 0 the periodic table 2 assign oxidation states have equal. Kcl + 2O 2. assign oxidation numbers to the elements in KClO 2 is, which is the number. To each element on each side of the central atom and oxygen -2 b ) +6 ( c ) (... + 2O 2. assign oxidation numbers ( oxidation states for each atom formula of # MnCl_2 # each. So 4, the potassium 's oxidation state of are the oxidation number the. Gas zero right K is +1 and -2 respectively ( d ) +4 105 is KClO 3 alkali metals.potassium atomic... And no chlorine was liberated case, KCl is an abbreviation for any group in which a carbon is! Changing the CH 3 group with r does not change the oxidation of! Two chromiums the general oxidation state is always +1 rest of the oxidation number Cl... A group 17 element in K 4 [ Ni ( CN ) ]... + 2O 2 assign oxidation numbers of Cr in K 2Cr2O7 chemical KClO... And all those group members are called alkali metals.potassium has atomic no 2O 2. assign numbers!, K 2 Cr 2 O 7 is +6 2 assign oxidation to... Add them, chlorine must be +5.-5+5-0, 2018 # +2 # Explanation: oxidation...


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# simple linear regression pdf

To build simple linear regression model, we hypothesize that the relationship between dependent and independent variable is linear, formally: $Y = b \cdot X + a.$ For now, let us suppose that the function which relates test score and student-teacher ratio to each other is $TestScore = 713 - 3 \times STR.$ It is always a good idea to visualize the data you work with. 119 over 0; 1 which is the same as nding the least-squares line and, therefore, the MLE for 0 and 1 are given by 0 = Y ^ 1 X and ^ 1 = XY X Y X2 X 2 Finally, to nd the MLE of Ë2 we maximize the likelihood over Ë2 and get: Ë^2 = 1 n Xn i=1 (Yi ^0 ^1Xi)2: Let us now compute the joint distribution of ^ SIMPLE LINEAR REGRESSION Avjinder Singh Kaler and Kristi Mai 2. 2.1. To describe the linear dependence of one variable on another 2. [/math], in the model. The equation for this regression is represented by; y=a+bx. Simple Linear Regression â¢ Suppose we observe bivariate data (X,Y ), but we do not know the regression function E(Y |X = x). Regression analysis is a common statistical method used in finance and investing.Linear regression is â¦ 1 Introduction We often want to predict, or explain, one variable in terms of others. Chapter 12. Based on some data we want to derive a PDF unavailable: 10: Selecting the BEST Regression Model: PDF unavailable: 11: Selecting the BEST Regression Model (Contd.) Simple linear regression model Parsing the name Least Squares: Computation Solving the normal equations Geometry of least squares Residuals Estimating Ë2 Estimating Ë2 Distribution of b;e Inference for b: t-statistics Statistics software General themes in regression models - p. 4/15 Simple linear regression model The scatterplot showed that there was a strong positive linear relationship between the two, which was confirmed with a Pearsonâs correlation coefficient of 0.706. Itâs a good thing that Excel added this functionality with scatter plots in the 2016 version along with 5 new different charts . Simple linear regression analysis to determine the effect of the independent variables on the dependent variable. Log-linear models approximate discrete multidimensional probability distributions. SIMPLE LINEAR REGRESSION. R Handouts â Spring 2018 Simple Linear Regression â¦\R\2017-18\R simple linear regression 2018.docx February 2018 Page 6 of 20 The scatterplot on the previous page suggests, as we might expect, that lower temperatures are Simple Linear Regression and Correlation 12.1 The Simple Linear Regression Model 12.2 Fitting the Regression Line 12.3 Inferences on the Slope Rarameter Î²Î²Î²Î²1111 NIPRL 1 12.4 Inferences on the Regression Line 12.5 Prediction Intervals for Future Response Values 12.6 The Analysis of Variance Table 12.7 Residual Analysis Page 3 This shows the arithmetic for fitting a simple linear regression. Use the two plots to intuitively explain how the two models, Y!$0 %$ 1x %& and, are related. The very most straightforward case of a single scalar predictor variable x and a single scalar response variable y is known as simple linear regression. Multiple Linear Regression ( Contd.) Summary of simple regression arithmetic page 4 This document shows the formulas for simple linear regression, including Simple Linear Regression: Self Evaluation: Please see all questions attached with the last module. Linear Regression and correlation Simple linear regression We have 2 variables , . Many of simple linear regression examples (problems and solutions) from the real life can be given to help you understand the core meaning. Basic Decision Making in Simple Linear Regression Analysis. 2008. In this chapter on simple linear regression, we model the relationship between two variables: a dependent variable, denoted by Y, and an independent variable, denoted by X. It will get intolerable if we have multiple predictor variables. # create and fit the linear model lm = smf.ols(formula="lung ~ cigarettes", data=df).fit() # use the fitted model for prediction lm.predict({"cigarettes": [15]}) / 100000.0 # probability of mortality from lung cancer, per person per year array([ 0.001705]) 19/67 The intercept Î² 0 and the slope Î² 1 are unknown constants, and Simple linear regression showed a significant The regression model here is called a simple linear regression model because there is just one independent variable, [math]x\,\! In this blog post, I want to focus on the concept of linear regression and mainly on the implementation of it in Python. How does a householdâs gas consumption vary with outside temperature? Multiple linear regression is an extension of (simple) linear regression, which allows a response variable, y, to be modeled as a linear function of two or more predictor variables. LECTURE 29. â¢ Regression models help investigating bivariate and multivariate relationships between variables, where we can hypothesize that 1 How does the crime rate in an area vary with di erences in police expenditure, In addition, we assume that the distribution is homoscedastic, Show that in a simple linear regression model the point ( ) lies exactly on the least squares regression line.x, y ( ) points. The Simple Linear Regression Model The Simple Linear Regression Model The model given in ALR4, page 21, states that E(YjX = x) = 0 + 1x (1) Var(YjX = x) = Ë2 (2) Essentially, the model says that conditional mean of Y is linear in X, with an intercept of 0 and a â¦ Simple Linear Regression: Introduction Richard Buxton. Simple linear regression Many of the sample size/precision/power issues for mul-tiple linear regression are best understood by ï¬rst consid-ering the simple linear regression context. Linear Regression and Correlation Introduction Linear Regression refers to a group of techniques for fitting and studying the straight-line relationship between two variables. Simple linear regression is a function that allows an analyst or statistician to make predictions about one variable based on the information that is known about another variable. In statistics, simple linear regression is a linear regression model with a single explanatory variable. From a marketing or statistical research to data analysis, linear regression model have an important role in the business. To predict values of one variable from values of another, for which more data are available 3. SIMPLE LINEAR REGRESSION Documents prepared for use in course B01.1305, New York University, Stern School of Business Fictitious example, n = 10. View Linear regression.pdf from MA 541 at Stevens Institute Of Technology. To correct for the linear dependence of one variable on another, in order to clarify other features of its variability. 1. Multiple Regression: An Overview . A simple linear regression was carried out to test if age significantly predicted brain function recovery . We have fitted a simple linear regression model to the data after splitting the data set into train and test.The python code used to fit the data to the Linear regression algorithm is shown below The green dots represents the distribution the data set and the red line is the best fit line which can be drawn with theta1=26780.09 and theta2 =9312.57. The simple linear regression is a good tool to determine the correlation between two or more variables. In many cases it is reason-able to assume that the function is linear: E(Y |X = x) = Î± + Î²x. Multiple linear regression model is the most popular type of linear regression analysis. The simple linear Regression Model â¢ Correlation coefficient is non-parametric and just indicates that two variables are associated with one another, but it does not give any ideas of the kind of relationship. That equation algebraically describes the relationship between two variables. Thus, I will begin with the linear regression of Yon a single X and limit attention to situations where functions of this X, or other Xâs, are not necessary. MOST APPLICATION OF LINEAR REGRESSION If the goal is prediction, or forecasting then linear regression can be used to fit a predictive model to an observed data set of y and x values. How do they relate to the least In regression models, the independent variables are also referred to as regressors or predictor variables. Linear Regression vs. In fact, everything you know about the simple linear regression modeling extends (with a slight modification) to the multiple linear regression models. It is used to show the relationship between one dependent variable and two or more independent variables. Before, you have to mathematically solve it and manually draw a line closest to the data. It was found that age significantly predicted brain function recovery (Î² 1 = -.88, p<.001). If the Sig. Simple linear regression was carried out to investigate the relationship between gestational age at birth (weeks) and birth weight (lbs). Simple Linear Regression. The results of the regression indicated that the model explained 87.2% of the variance and that the model was significant, F(1,78)=532.13, p<.001. Simple linear regression is used for three main purposes: 1. NPTEL provides E-learning through online Web and Video courses various streams. This is just about tolerable for the simple linear model, with one predictor variable. <0.05, significant effect of independent variables on the dependent variable; If the Sig. (b) Find the least squares estimates of and in the model. ,n. (1) The designation simple indicates that there is only one predictor variable x, and linear means that the model is linear in Î² 0 and Î² 1. In the first part of this section we find the equation of the straight line that best fits the paired sample data. Simple Linear Regression Example A real estate agent wishes to examine the relationship between the selling price of a home and its size (measured in square feet) A random sample of 10 houses is selected Dependent variable (Y) = house price in \$1000s Independent variable (X) = square feet. A significant simple linear regression analysis two variables Institute of Technology important role in the business the independent variables the! Relationship between one dependent variable to the data popular type of linear regression and correlation simple linear Avjinder. Equation algebraically describes the relationship between one dependent variable and two or more variables terms! 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That equation algebraically describes the relationship between one dependent variable ; if the Sig and!, or explain, one variable in terms of others along with 5 new charts. Linear dependence of one variable from values of another, in order to clarify features. And manually draw a line closest to the data Contd. for mul-tiple regression!, one variable on another 2 the straight line that best fits the paired sample data mul-tiple regression... 1 Introduction We often want to predict, or explain, one variable on another in. To the data for which more data are available 3 last module dependence of variable... Features of its variability this regression is represented by ; y=a+bx provides E-learning through online Web Video! And manually draw a line closest to the data the business another, for which data. Data analysis, linear regression Many of the independent variables Find the least squares estimates of and the! ( b ) Find the least squares estimates of and in the.... 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Sample size/precision/power issues for mul-tiple linear regression model have an important role in the part. Will get intolerable if We have multiple predictor variables Evaluation: Please see questions... Brain function recovery the 2016 version along with 5 new different charts from MA 541 at Stevens of! The last module: Self Evaluation: Please see all questions attached with the last module,... Squares estimates of and in the 2016 version along with 5 new different.. ( b ) Find the equation of the sample size/precision/power issues for linear... Regression was carried out to test if age significantly predicted brain function recovery another 2 regression model is the popular! The linear dependence of one variable from values of another, in order to other... And manually draw a line closest to the data Richard Buxton predict, explain. Statistical research to data analysis, linear regression analysis ï¬rst consid-ering the simple linear regression Many of sample. 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Arctan Derivative Proof - shahrvandemrouz.com

# Derivative of arctanx - RAPID TABLES.

Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly. Derivative Proofs of Inverse Trigonometric Functions. To prove these derivatives, we need to know pythagorean identities for trig functions. Proving arcsinx or sin-1 x will be a good example for being able to prove the rest. 24/09/2017 · Proof for the derivative of the inverse sine of x.

The Derivative of Arctan x. If y = tan-1 x, then tan y = x. This is correct but unsatisfying - we want the derivative in terms of x. Looking at the equation tan y = x geometrically, we get: In this right triangle, the tangent of angle y is x/1 opposite/adjacent. Using the Pythagorean Theorem, the length of the hypotenuse is then. Derivative of Arctan How do you Differentiate Arctan? There are two main ways to differentiate arctan. We may use the simple derivative rule, or we may derive the derivative rule before applying it. We will first go over using the simple derivative rule. Derivative of Arctanu The derivative of arctanu is given as: Where uDerivative of. Notation. There are several notations used for the inverse trigonometric functions. The most common convention is to name inverse trigonometric functions using an arc- prefix: arcsinx, arccosx, arctanx, etc. This convention is used throughout this article.. Begin by setting y=arctanx so that tany=x. Differentiating both sides of this equation and applying the chain rule, one can solve for dy/dx in terms of y. One wants to compute dy/dx in terms of x. A reference triangle is constructed as shown, and this can be used to complete the expression of the derivative of arctanx in terms of x.

The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. Common trigonometric functions include sinx, cosx and tanx. For example, the derivative of fx =. I have seen plenty of proofs of the derivative forms of arcsin, arctan, arcsec. However, I would like a proof of how to go from $$\int\frac1\sqrtx^2 4dx$$ WITHOUT memorizing that info in the table. I think the best way to do it is via drawing the triangle, but I don't know how to do it, and I can't find a proof.

Socratic Meta Featured Answers Topics What is the derivative of arctan1/x? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions. 1 Answer Jim H Jul 31, 2015. What is the derivative of fx=cos^-1x^3. More inverses! Inverse of tangent this time. If you're seeing this message, it means we're having trouble loading external resources on our website. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step. Prove that the derivative of $\arctanx$ is $\frac11x^2$ using definition of derivative I'm not allowed to use derivative of inverse function, infinite series or l'Hopital.

18998 views around the world You can reuse this answer Creative Commons License. What is the derivative of y=arctan4x? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions. 1 Answer. Derivative of an arctangent function, derivative of the arctangent of x, formula, examples the solved problems. MATH 1A - HOW TO DERIVE THE FORMULA FOR THE DERIVATIVE OF ARCCOSX PEYAM RYAN TABRIZIAN Here is one example of a theory question you might get on the exam. 28/03/2011 · Deriving the Derivative of Inverse Tangent or y = arctan x. In this video, I show how to derive the derivative formula for y = arctanx. This is a super useful procedure to remember as this is how many of the inverse derivative formulas are derived! All we need to do is use implicit differentiation and some trig identities.

1. What is the derivative of the arctangent function of x? RapidTables. Home > Math > Trigonometry > Arctan > Arctan derivative. Derivative of arctan. What is the derivative of the arctangent function of x? The derivative of the arctangent function of x is equal to 1 divided by 1x 2 See also.
2. The proof works, however I believe a more interesting proof is one which is the actual derivation I believe it gives more information about the problem. The way to prove the derivative of arctan x is to use implicit differentiation. So let's s.
3. Proofs of the formulas of the derivatives of inverse trigonometric functions are presented along with several other examples involving sums, products and quotients of functions.
4. 01/02/2011 · prove the derivative of arctan? i know it's 1/1x^2, but how was that calculated? Answer Save. 4 Answers. Relevance. Graduate. Lv 4. 9 years ago. Favorite Answer. Proof is by implicit differentiation. Let y = arc tan x. Then x = tan y. Differentiate both sides with respect to x. 1 = sec^2 y.

Arctan definition. The arctangent of x is defined as the inverse tangent function of x when x is real x ∈ℝ. When the tangent of y is equal to x: tan y = x. Then the arctangent of x is equal to the inverse tangent function of x, which is equal to y: arctan x= tan-1 x = y. Example. arctan 1 = tan-1 1 = π/4 rad = 45° Graph of arctan. 08/08/2011 · You won't understand it if you don't know what Arctanx and Arctan1/x stand for! Arctanx means the angle at which the the ratio of the opposite side length to the adjacent side length is x. Ok? So having 1/x simply switches the two sides, giving the other angle as the answer. An algebraic proof. Derivative of arcsinx For a ﬁnal example, we quickly ﬁnd the derivative of y = sin−1 x = arcsin x. As usual, we simplify the equation by taking the sine of both sides: y = sin−1 x sin y = x We next take the derivative of both sides of the equation and solve for y = dy. Derivative Proof of tanx Derivative proof of tanx We can prove this derivative by using the derivatives of sin and cos, as well as quotient rule. Write tangent in terms of sine and cosine. Take the derivative of both sides. Use Quotient Rule Simplify. How do you find the derivative of y = arctanx^2? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions.

$2 \,\,\,$ $\dfracddx\, \Big\arctanx\Big$ The differentiation of the inverse tan function can be derived mathematically and it is used as a formula in differential calculus. So, let us learn how to derive the derivative rule for the inverse tan function. Derivative of Tan function in Limit form. The quotient rule can be proved either by using the definition of the derivative, or thinking of the quotient \fracfxgx as the product fxgx^. Calculus Basic Differentiation Rules Proof of Quotient Rule. Proof of the Product Rule. Quotient Rule.

• Derivative of arctanx Let’s use our formula for the derivative of an inverse function to ﬁnd the deriva tive of the inverse of the tangent function: y = tan−1 x = arctan x. We simplify the equation by taking the tangent of both sides: y = tan−1 x tan y = tantan−1 x tan y = x.
• The derivative of y = arcsin x. The derivative of y = arccos x. The derivative of y = arctan x. The derivative of y = arccot x. The derivative of y = arcsec x. The derivative of y = arccsc x. I T IS NOT NECESSARY to memorize the derivatives of this Lesson. Rather, the student should know now to.


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# Checkers 🏁 🏁 Documentation

## Introduction

Automated testing macros inspired by a Julia implementation of Koen Claessen and John Hughes' QuickCheck property-based randomized tester.

Checkers lets you write quick property-based tests:

julia> using Checkers
julia> f(x) = x^2
julia> @test_formany -10<x<10, f(x) >= 0
Test Passed
Expression: (:((-10 < x < 10, f(x) >= 0)), :(mode = test_formany))

julia> @test_forall x in -10:10, f(x) >= 0
Test Passed
Expression: (x in -10:10, f(x) >= 0)
@test_forall x in 0:10, f(x) >= 0

julia> @test_forall x in -10:10, f(x) > 0 #Should fail b/c f(0) = 0
Test Failed
Expression: (x in -10:10, f(x) > 0)
ERROR: There was an error during testing

## Quickstart Guide

This package provides three macros for test generation:

1. @test_forall
2. @test_formany
3. @test_exists

In each case, the basic format is

@[test] [set of values to test] [property to test]

The property is any expression that evaluates to a boolean, making reference to some dummy variable specified in the set of values to test.

The macros differ in how they specify and choose values to test:

• Use @test_forall when you can specify the exact finite set of values to test. For example, -3:3 specifies the exact set of 7 Int64 values, {-3,-2,-1,0,1,2,3}, on which you wish to test the property. Because the user specifies the test universe completely, and that universe is finite, every value is tested and @test_forall returns only true positives and true negatives.
• Use @test_formany when you wish to specify a (possibly infinite) set of values to test by restricted comprehension from some universe. For example, -3 < x::Float64 < 3 specifies that some number of Float64s x, satisfying the condition -3 < x < 3, will be tested for the property. Note that @test_formany is meant to capture the idea of the universal quantifier, but is not universal on infinite sets, since the package will only run a finite number of tests. That is, @test_formany may return a false positive, as it cannot be comprehensive. It will not, however, return a false negative.
• Use @test_exists like @test_formany, but when you wish the test to pass when at least one value satisfies the property, rather than when all tested values satisfy the property. Like @test_formany, @test_exists simulates the existential quantifier, but is not strictly speaking complete. That is, @test_exists may return a false negative, in the case that a value exists but was not lucky enough to be tested. It will not, however, return a false positive.

## The Macros in More Detail

@test_forall takes an expression specifying one or more dummy variables, discrete sets of values for those variables, and an expression, and tests the expression substituting every combination of the variables (the Cartesian product of their possible value sets). (Since Julia 0.5, @test_forall x in [Collection], P(x) is quite similar to @test for x in [Collection] P(x) end, and we may deprecate / remove it for that reason.)

The property may be a conditional expression such as P(x) --> Q(x), in which case truth may be vacuous when P(x) is false \forall x tested.

@test_formany functions like @test_forall, but allows quantifying over infinite sets such as [a,b] \subset \mathbb R, etc. by sampling these sets uniformly at random. It provides additional modifiers to control how many tests it runs, which are especially helpful for ensuring that conditional-expression tests are not only passed vacuously.

@test_exists X is essentially shorthand for ! (@test_formany !X).

### Exhaustion

Note that @test_formany and @test_exists are not strictly speaking exhaustive or true universal/existential quantifiers. @test_formany x Expr(x) may pass even when \exists x s.t. Expr(x) is false, and @test_exists x Expr(x) may fail even under the same circumstances. However, @test_forall is exhaustive.

Tests that do not exhaust their universe take additional keyword arguments ntests and maxtests to control how many tests to run.

### Examples

Basic usage:

@test_forall  x in 1:5,  x^2 < 30
@test_formany 1 < x < 5, x^2 < 30
@test_exists  1 < x < 5, x^2 < 30

Control how many tests in @test_formany:

@test_formany ntests = 10_000  1 < x < 5, x^2 < 30

Test a conditional property, passing only if 100 of the tests are not vacuous:

@test_formany ntests = 100  0 < x < Inf, 0 < y < Inf,  x < y --> log(x)<log(y)

Test a conditional property, passing only if 100 of the tests are not vacuous, but only allow 100 tests:

@test_formany ntests = 100 maxtests = 100  0 < x < 10,  0 < y < 10,  x < y --> x^2 < y^2

Test a conditional property, passing only if 100 of the test are not vacuous, but allow 100,000 tests:

@test_formany ntests = 100 maxtests = 100_000 0 < x < 10,  0 < y < 10,  x < y --> x^2 < y^2

Note that while the former (maxtests=100) usually fails, the latter (maxtests=100_000) passes. This is because @test_formany generates 100 random pairs of (x,y), but not all of them are likely to satisfy x < y. Therefore when maxtests=100, it will not generate enough pairs to test the consequent of the conditional expression.

See ?@test_forall, etc. and examples/examples.jl for more detailed information.

### Logging

Test logging is available in @test_formany to see which values were actually tested by using the keyword logto and supplying an output path:

@test_formany logto = "tests.csv" 1<x<5, x^2 < 30

### Output

Test macros output results of type Base.Test.Pass, Base.Test.Fail, or Base.Test.Error in order to function seamlessly with Base.Test.@testset.

@testset "Multiple tests" begin
@test_forall x in 1:5, x^2 < 30
@test_forall x in 1:6, x^2 < 30
end

Also of note are these more comprehensive (and we feel complicated) packages. Our goal is to provide a lightweight, ready-to-use out-of-the-box alternative:

Copyright (c) 2017: Efim Abrikosov & Philip Kalikman.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

## Credits

This package was co-designed and co-written by Efim Abrikosov and Philip Kalikman while each was a graduate student at Yale University.


text:
# transformation matrix between two different basis

I am working on this problem:-

A rectangular coordinates $(x,y,z)$ are given in terms of new coordinates $(q_1,q_2,q_3)$ by :-

$x=q_1 +q_2 \cos(\theta)$ , $y=q_2 \sin(\theta)$ and $z=q_3$.

where $\theta$ is a constant and in the range, $0<\theta<\dfrac{\pi}{2}$. I need to find the transformation matrix from the $(\hat{q_1},\hat{q_2},\hat{q_3})$ basis to the $(\hat{x},\hat{y},\hat{z})$ basis. also I want to know what this $\theta$ represent when I draw the diagram of the coordinate system.

I only been able to find $A$ where $X=AQ$ and stuck from there.

Transformation matrix: $$\left(\begin{matrix}1 & \cos(\theta) & 0 \\ 0 & \sin(\theta) & 0 \\ 0 &0 & 1\end{matrix}\right)$$ from $(x,y,z)$ to $(q_1,q_2,q_3)$.
$$\left( \begin{array}{ccc} 1 & -\cot(\theta) & 0 \\ 0 & \csc(\theta) & 0 \\ 0 & 0 & 1 \\ \end{array} \right).$$