text:
## |cp4space| = 100

This is the 100th article on cp4space, and is inspired by a discussion last night with Gabriel Gendler.

### Triangle centres with complex numbers

Suppose we have a triangle in the Euclidean plane $\mathbb{R}^2$. We can identify the Euclidean plane with the complex plane, and represent the triangle by a set of three complex numbers (one for each vertex). I’ll call these complex numbers x, y and z (corresponding to vertices A, B and C, respectively). We’ll now consider a few interesting points in the plane of the triangle:

The centroid, G, is the easiest triangle centre to express. It’s simply $G(x,y,z) = \frac{1}{3}(x+y+z)$, which is the arithmetic mean of the three vertices. Here, we consider triangle centres to be functions from $\mathbb{C}^3$ to $\mathbb{C}$, which takes the three vertices and returns that triangle centre.

The circumcentre, O, is somewhat more difficult to find. It’s the intersection of the three perpendicular bisectors (shown in red in the diagram above), and we can solve simultaneous linear equations to obtain an expression for the circumcentre.

The orthocentre, H, and the nine-point centre, T, are expressible as simple linear combinations of O and G. For instance, $H(x,y,z) = 3G(x,y,z) - 2O(x,y,z)$ and $T(x,y,z) = \frac{1}{2}(H(x,y,z) + O(x,y,z))$. These points lie on the Euler line, as you can see in the diagram.

Finally, we can also get a simple expression for the symmedian point (either by considering areal coordinates or harmonic quadrilaterals, both of which are explained in MODA).

### Algebraically indistinguishable triangle centres

Consider the Steiner inellipse. This is the largest ellipse that can be contained within a triangle, or (equivalently) the image of the incircle of an equilateral triangle after it has been hit with an affine transformation to become the triangle of interest. Probably the easiest way to explain is with a diagram:

Steiner inellipse — diagram courtesy of Claudio Rocchini

The diagram shows the two foci of the ellipse, f_1 and f_2. It is a remarkable fact that the quadratic polynomial with f_1 and f_2 as roots is the derivative of the cubic polynomial with x,y,z as roots. This gives us the following expression:

Of course, we can now solve this quadratic:

This is a multi-valued function, which gives both foci. It is impossible to create an algebraic expression that gives one focus but not the other; they are roots of the same minimal polynomial with coefficients in $\mathbb{Z}[x][y][z][x^{\star}][y^{\star}][z^{\star}]$. Points with this property (for general fields) are known as Galois conjugates.

The two foci in the previous expression are the same when the radicand (thing being square-rooted) is equal to zero, i.e. when $x^2 + y^2 + z^2 = xy + yz + zx$. This is equivalent to the triangle being equilateral.

### Tritangential circles

The foci of the Steiner inellipse constitute a pair of Galois conjugates. There are other interesting points that belong to larger sets of Galois conjugates. Consider the four circles that are tangent to all three sides of the triangle:

The centres of these circles, $I, I_A, I_B, I_C$, are all roots of the same minimal polynomial, namely this horrible quartic in w:

Here, I’ve used Σ_alt to indicate the alternating sum over permutations of (x, y, z). This is like the symmetric sum, but where the sign of each term is determined by the permutation of the parity. For example, the circumcentre is given by alt[x y y*]/alt[x y*].

### Transcendental triangle centres

The triangle centres (and other points) we’ve explored so far can be given as the roots of polynomials with coefficients in $\mathbb{Z}[x][y][z][x^{\star}][y^{\star}][z^{\star}]$. Some triangle centres, however, have no such expressions. One particularly interesting example is the Hofstadter point, X_360. Let the Cevian AX_360 intersect the line BC at D; this splits it in the ratio $BD : DC = \angle ABC : \angle BCA$. You can immediately spot that this is really bizarre, since a ratio between lengths is identified with a ratio between angles.


text:
# How to Describe an Enlargement with a Negative Scale Factor

## Describing an Enlargement with a Negative Scale Factor

A shape can be enlarged with a negative scale factor.

To describe an enlargement, we need to describe the center of enlargement and the scale factor.

### The Center of Enlargement

The center of enlargement is the point about which a shape is enlarged.

When there is a negative scale factor, the center of enlargement is between the original shape and the enlarged shape.

The center of enlargement can be described using Cartesian coordinates.

### The Scale Factor

The scale factor describes how much larger (or smaller) the enlarged shape is compared to the original shape.

The scale factor is found by dividing a length of a side of the enlarged shape to the length of the corresponding side of the original shape.

When there is a negative scale factor, the enlarged shape is turned upside down. Care needs to be taken when finding the corresponding lengths.

## How to Describe an Enlargement with a Negative Scale Factor

Describing an enlargement with a negative scale factor is easy.

### Question

Describe the enlargement of the light blue shape to the dark blue shape below.

# 1

Find a point on the shape.

We will choose point A on the shape.

# 2

Find where the corresponding point on the enlarged shape will be.

When there is a negative scale factor, the enlarged shape looks like it has been turned upside down. In fact, the shape turned a half turn (rotated 180°).

Imagine turning the original shape a half turn.

The corresponding point will be at the bottom right corner of the triangle.

# 3

Draw the corresponding point on the enlarged shape.

The corresponding point is the bottom right corner of the triangle.

Point A' is the corresponding point on the enlarged shape.

# 4

Join the pair of corresponding points with a line.

# 5

Find another point on the shape.

We will choose point B on the shape.

# 6

Find where the corresponding point on the enlarged shape will be.

When there is a negative scale factor, the enlarged shape looks like it has been turned upside down. In fact, the shape turned a half turn (rotated 180°).

Imagine turning the original shape a half turn.

The corresponding point will be at the bottom left corner of the triangle.

# 7

Draw the corresponding point on the enlarged shape.

The corresponding point is the bottom left corner of the triangle.

Point B' is the corresponding point on the enlarged shape.

# 8

Join the pair of corresponding points with a line.

# 9

Draw the center of enlargement where the two lines meet.

# 10

Describe the center of enlargement in Cartesian coordinates.

In our example, the Cartesian coordinates of the center of enlargement is (3, 2).

We have found the center of enlargement.

We can find the scale factor.

# 11

Find the length of a side on the enlarged shape.

The length of the side A'B' is 4.

# 12

Find the length of the corresponding side on the original shape.

The length of the side AB is 2.

# 13

Divide the length on the enlarged shape (4) by the length on the original shape (2).

$$\frac{A'B'}{AB} = \frac{4}{2}$$ $$\:\:\:\:\:\:\:\:\:\:\:\: = 2$$

# 14

Find the negative of this number (2) to find the scale factor.

$$Scale factor = -2$$

format: plain


text:
Classic Neyman-Pearson approach demo

It notes here that N-P approach does not utilize the information in the accurate p value. Actually, at the time N-P approach was firstly devised, the accurate p value was not available usually. Now almost all statistic softwares provide accurate p values and the N-P approach becomes obsolete. Wilkinson & APA TFSI (1999) recommended to report the accurate p value rather than just significance/insignificance, unless p is smaller than any meaningful precision.

--

Wilkinson, L. & APA TFSI (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594-604.

Different corr(s) of different IV scopes with same regression coef

$Y=\alpha+\beta X+\varepsilon,\;\varepsilon\sim N\left(0,\sigma^{2}\right)$

With $\alpha,\beta, \sigma$ known in the linear relationship, can the correlation in the scatter plot of Y against X be estimated from the linear formula?

You may recall in Hierarchical Linear Model class, the scopes of the W dramatically impact the regression coefficients of F~W in the following R demo (hlm.jpg). While this time the regression coefficient has been fixed to a known $\beta$. So the scopes of X would never impact the regression coefficient. However, it proved that the correlation r could range from zero to unit (or -1) according to the variance of X in the final close form $r=\frac{\beta\mbox{Var}\left(X\right)}{\mbox{Std}\left(Y\right)\mbox{Std}\left(X\right)}=\beta\frac{\mbox{Std}\left(X\right)}{\sqrt{\beta^{2}\mbox{Var}\left(X\right)+\sigma^{2}}}$.

Let me quote as the final words from Cohen (1994; p.1001; Where the role of IV is replaced by that of DV within typical contexts like ANOVA) --

... standardized effect size measures, such as d and f, developed in power analysis (Cohen, 1988) are, like correlations, also dependent on population variability of the dependent variable and are properly used only when that fact is kept in mind.

--

Cohen, J. (1994). The earth is round (p<.05). American Psychologist, 49, 997-1003.

--

Compare to the following case: different corr(s) of different IV scopes with hierarchical regression coefficients --

“Effect Size” — same data, different interpretations

Just a short R-script note to embody the 3-page-paper of Rosenthal & Rubin (1982).

Table 1. (p. 167) listed a simple set-up. There was a between-subject treatment. Control group includes 34 alive cases and 66 dead cases. Treatment group includes 66 alive cases and 34 dead cases. The question is what is the percentage of the variance explained by the nominal IV indicating the group?

The authors pointed out that one may interpret the data result as death rate was reduced by 32% while the other may interpret the same as 10.24% variance was explained. Let's demo it more dramatically to imagine just 4% explained variance would reduce death rate by 20%.

--

Rosenthal, R. & Rubin, D. B. (1982). A simple, general purpose display of magnitude of experimental effect. Journal of Educational Psychology, 74, 166-169.

Anscombe’s 4 Regressions — A Trivially Updated Demo

##---------- ## This is a trivially updated version based on the R document "?anscombe". require(stats); require(graphics) anscombe

##-- now some "magic" to do the 4 regressions in a loop:##< - ff = y ~ x for(i in 1:4) { ff[2:3] = lapply(paste(c("y","x"), i, sep=""), as.name) assign(paste("lm.",i,sep=""), lmi <- lm(ff, data= anscombe)) }

 ## See how close they are (numerically!) sapply(objects(pattern="lm\\.[1-4]$"), function(n) coef(get(n))) lapply(objects(pattern="lm\\.[1-4]$"), function(n) coef(summary(get(n)))) ## Now, do what you should have done in the first place: PLOTS op <- par(mfrow=c(4,3),mar=.1+c(4,4,1,1), oma= c(0,0,2,0)) for(i in 1:4) { ff[2:3] <- lapply(paste(c("y","x"), i, sep=""), as.name) plot(ff, data =anscombe, col="red", pch=21, bg = "orange", cex = 1.2, xlim=c(3,19), ylim=c(3,13)) abline(get(paste("lm.",i,sep="")), col="blue") plot(lm(ff, data =anscombe),which=1,col="red", pch=21, bg = "orange", cex = 1.2 ,sub.caption="",caption="" ) plot(lm(ff, data =anscombe),which=2,col="red", pch=21, bg = "orange", cex = 1.2 ,sub.caption="",caption="" ) } mtext("Anscombe's 4 Regression data sets", outer = TRUE, cex=1.5) par(op) ##

## Anscombe, F. J. (1973). Graphs in statistical analysis. American Statistician, 27, 17–21.

读汪丁丁《为中国股民找一个理由》所想到与读到

...当代中国人生活在千年未有之变局之内，经历着三重转型同时发生的阶段，所以，每一中国人的未来，充满着奈特意义上的不确定性。这种不确定性是不可预期且不可重复的，当代实验经济学家称之为“ambiguity”，以区分于“risk(风险)”。

...

Knight原著并不易读。甚至只是翻查《新帕尔格雷夫经济学大辞典》1987版1996中译本的UncertaintyKnight辞条，就已经令人云里雾里。其中Knight辞条执笔者是G. J. Stigler，他对Knight在Uncertainty上的“贡献”略有微词。Knight原著第7章注解1也小心的指出他打算规避认识论/知识论的讨论。这给我的感觉就好比：讨论一个被定义为“本质上不可讨论的对象”的对象。须知Uncertainty在Knight原著中唯一的内涵就是不可测度，于是所有对它的减少(eliminate)都是对它的否定。一旦比较它有多么地“不可测度”，就是在否定“不可测度”的本质。从罗素悖论的经验，我实在怀疑“不可测度性”程度的比较注定要引出悖论。

--

Knight, F. H. (1921). Risk, Uncertainty, and Profit. Boston, MA: Hart, Schaffner & Marx.


text:
+0

# Could someone please check my work?

-1
168
7
+202

Find the number of ways of distributing 4 different balls among 4 identical boxes.

So I was thinking that it would be \(4^4/4\) since you have 4 choices for each ball but there are 4 we since the boxes are identical we're overcounting by a factor of 4. Is this right?

Feb 8, 2020

#1
+109747
+2

Find the number of ways of distributing 4 different balls among 4 identical boxes.

Counting questions are always tricky, but here is my thinking.

 distribution of balls 1,1,1,1 1 way 2,1,1,0 4C2=6 ways 2,2,0,0 4C2/2=3 ways 3,1,0,0 4C3=4 ways 4,0,0,0 1 way Total = 15 ways

So no, I do not think your way makes any sense.

The red is my edit. Impasta found a fault.  Good logic Impasta!

Feb 8, 2020
edited by Melody  Feb 8, 2020
#5
+202
0

So are you implying for 2-1-1-1, for example, that out of the four balls, we choose 2 out of four balls to be put in one box, and we don't need to account for permutations?

Impasta  Feb 8, 2020
#6
+202
+1

Wait, I'm pretty sure doing it that way overcounts some things. For instance, doing \(\binom{4}{2}\) for 2-2-0-0 will count each way twice since you choosing two balls or you choosing the other two will result in the same balls in boxes. But building off of your idea, I think I can get the answer. Thanks!

Impasta  Feb 8, 2020
edited by Impasta  Feb 8, 2020
#7
+109747
+1

Yes you are right. Excellent spotting!

I have edited my answer acordingly.

Melody  Feb 8, 2020
edited by Melody  Feb 8, 2020


text:
# How can you determine the mass flow rate

## Homework Statement

How can you determine the mass flow rate, given that net power output is 100 MW, of the cooling water if it enters the condenser at 20 C and leaves at 35 C.

## The Attempt at a Solution

I thought that mass flow rate is the same all through out. I have the power and the net work but the required is mass flow rate at those given temperature.

The question is from the rankine cycle.

Related Engineering and Comp Sci Homework Help News on Phys.org
How can the problem be solved, the mass flow rate of the cooling water at the condenser?

You have the power lost at 100MW.

The heat lost is absorbed by the water, making it's temperature rise from 20 C to 35 C.

$$\dot{Q}$$ = $$\dot{m}$$$$C_{p}$$$$\left(T - Ti)$$

That's the mass flow-rate you require to achieve the required heat loss.

Q is the Q out at the condenser and the cp is the specific heat at constant pressure of water?

$$\dot{Q}$$ in this case is the flowrate of heat, which is measured in Watts.

$$C_{p}$$ is the specific heat of water flowing through a control volume, which in this case is your condensor. Evaluate the specific heat at the mean temperature $$T_{m}$$, which is simply the average between the outlet and inlet temperatures.

how can i know cp and Q dot?

$$C_{p}$$ can be found from generic steam tables that list the properties of substances at different temperatures.

$$\dot{Q}$$ is already given to you.

so Q dot is the 100MW. In what part of the steam table can I find the cp values?

Here is an example problem:

net power output is 45MW
Turbine inlet pressure and temperature are 7MPa and 500C
Condenser pressure of 10kPa
Cooling water rate of 2000kg/s

Find:

thermal efficiency of the cycle
mass flow rate of steam
temperature rise of cooling water

I got the thermal efficiency, which is 38.9% and
mass flow rate of 35.998 kg/s

I do not know the temperature rise.
What should I do?
I do not know where the cp can be found at the steam table.

What can be mean by this?

The heat transfer to the steam in the boiler occurs at the rate of 400000 kW.
Does this mean that the power input in the boiler is 400000 kW? or
This mean that the net power is 400000 kW?

what do i do next?


text:
Proceedings of the 12th Asia Pacific Physics Conference (APPC12) 2014
DOI: 10.7566/jpscp.1.013094
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## Abstract: The observables of the perturbed Universe, cosmic microwave background (CMB) anisotropy and large scale structures depend on background cosmological parameters, as well as the form of primordial perturbations. Main cosmological parameters are usually constrained using CMB or large scale structure data based on power-law assumption of the primordial power spectrum (PPS). However while there is no any preferred model for the early universe, this assumption raises a concern that current estimated cosmological pa…

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# 3. Managing Packages

There are two ways of adding packages, either using the add command or the dev command. The most frequently used is add and its usage is described first.

In the Pkg REPL, packages can be added with the add command followed by the name of the package, for example:

Installing known registries into ~/
Resolving package versions...
Installed Parsers ─ v2.4.0
Installed JSON ──── v0.21.3
Updating ~/.julia/environments/v1.8/Project.toml
[682c06a0] + JSON v0.21.3
Updating ~/environments/v1.9/Manifest.toml
[682c06a0] + JSON v0.21.3
[69de0a69] + Parsers v2.4.0
[de0858da] + Printf
[4ec0a83e] + Unicode
Precompiling environment...
2 dependencies successfully precompiled in 2 seconds

Here we added the package Example to the current environment (which is the default @v1.8 environment). In this example, we are using a fresh Julia installation, and this is our first time adding a package using Pkg. By default, Pkg installs the General registry and uses this registry to look up packages requested for inclusion in the current environment. The status update shows a short form of the package UUID to the left, then the package name, and the version. Finally, the newly installed packages are "precompiled".

It is possible to add multiple packages in one command as pkg> add A B C.

The status output contains the packages you have added yourself, in this case, JSON:

(@v1.8) pkg> st
Status ~/.julia/environments/v1.8/Project.toml
[682c06a0] JSON v0.21.3

The manifest status shows all the packages in the environment, including recursive dependencies:

(@v1.8) pkg> st -m
Status ~/environments/v1.9/Manifest.toml
[682c06a0] JSON v0.21.3
[69de0a69] Parsers v2.4.0
[de0858da] Printf
[4ec0a83e] Unicode

Since standard libraries (e.g. Dates) are shipped with Julia, they do not have a version.

After a package is added to the project, it can be loaded in Julia:

julia> using JSON

julia> JSON.json(Dict("foo" => [1, "bar"])) |> print
{"foo":[1,"bar"]}
Note

Only packages that have been added with add can be loaded (which are packages that are shown when using st in the Pkg REPL). Packages that are pulled in only as dependencies (for example the Parsers package above) can not be loaded.

A specific version of a package can be installed by appending a version after a @ symbol to the package name:

Resolving package versions...
Updating ~/.julia/environments/v1.8/Project.toml
⌃ [682c06a0] + JSON v0.21.1
Updating ~/environments/v1.9/Manifest.toml
⌃ [682c06a0] + JSON v0.21.1
⌅ [69de0a69] + Parsers v1.1.2
[de0858da] + Printf
[4ec0a83e] + Unicode
Info Packages marked with ⌃ and ⌅ have new versions available, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use status --outdated -m

As seen above, Pkg gives some information when a package is not installed at its latest version.

If not all three numbers are given for the version, for example, 0.21, then the latest registered version of 0.21.x would be installed.

If a branch (or a certain commit) of Example has a hotfix that is not yet included in a registered version, we can explicitly track that branch (or commit) by appending #branchname (or #commitSHA1) to the package name:

Cloning git-repo https://github.com/JuliaLang/Example.jl.git
Resolving package versions...
Updating ~/.julia/environments/v1.8/Project.toml
[7876af07] + Example v0.5.4 https://github.com/JuliaLang/Example.jl.git#master
Updating ~/environments/v1.9/Manifest.toml
[7876af07] + Example v0.5.4 https://github.com/JuliaLang/Example.jl.git#master

The status output now shows that we are tracking the master branch of Example. When updating packages, updates are pulled from that branch.

Note

If we would specify a commit id instead of a branch name, e.g. add Example#025cf7e, then we would effectively "pin" the package to that commit. This is because the commit id always points to the same thing unlike a branch, which may be updated.

To go back to tracking the registry version of Example, the command free is used:

(@v1.8) pkg> free Example
Resolving package versions...
Installed Example ─ v0.5.3
Updating ~/.julia/environments/v1.8/Project.toml
[7876af07] ~ Example v0.5.4 https://github.com/JuliaLang/Example.jl.git#master ⇒ v0.5.3
Updating ~/environments/v1.9/Manifest.toml
[7876af07] ~ Example v0.5.4 https://github.com/JuliaLang/Example.jl.git#master ⇒ v0.5.3

If a package is not in a registry, it can be added by specifying a URL to the Git repository:

Cloning git-repo https://github.com/fredrikekre/ImportMacros.jl
Resolving package versions...
Updating ~/.julia/environments/v1.8/Project.toml
[92a963f6] + ImportMacros v1.0.0 https://github.com/fredrikekre/ImportMacros.jl#master
Updating ~/environments/v1.9/Manifest.toml
[92a963f6] + ImportMacros v1.0.0 https://github.com/fredrikekre/ImportMacros.jl#master

The dependencies of the unregistered package (here MacroTools) got installed. For unregistered packages, we could have given a branch name (or commit SHA1) to track using #, just like for registered packages.

If you want to add a package using the SSH-based git protocol, you have to use quotes because the URL contains a @. For example,

Cloning git-repo git@github.com:fredrikekre/ImportMacros.jl.git
Updating registry at ~/.julia/registries/General
Resolving package versions...
Updating ~/.julia/environments/v1/Project.toml
[92a963f6] + ImportMacros v1.0.0 git@github.com:fredrikekre/ImportMacros.jl.git#master
Updating ~/.julia/environments/v1/Manifest.toml
[92a963f6] + ImportMacros v1.0.0 git@github.com:fredrikekre/ImportMacros.jl.git#master

#### Adding a package in a subdirectory of a repository

If the package you want to add by URL is not in the root of the repository, then you need pass that subdirectory using :. For instance, to add the SnoopCompileCore package in the SnoopCompile repository:

Cloning git-repo https://github.com/timholy/SnoopCompile.jl.git
Resolving package versions...
Updating ~/.julia/environments/v1.8/Project.toml
[e2b509da] + SnoopCompileCore v2.9.0 https://github.com/timholy/SnoopCompile.jl.git:SnoopCompileCore#master
Updating ~/.julia/environments/v1.8/Manifest.toml
[e2b509da] + SnoopCompileCore v2.9.0 https://github.com/timholy/SnoopCompile.jl.git:SnoopCompileCore#master
[9e88b42a] + Serialization

Instead of giving a URL of a git repo to add we could instead have given a local path to a git repo. This works similar to adding a URL. The local repository will be tracked (at some branch) and updates from that local repo are pulled when packages are updated.

Warning

Note that tracking a package through add is distinct from develop (which is described in the next session). When using add on a local git repository, changes to files in the local package repository will not immediately be reflected when loading that package. The changes would have to be committed and the packages updated in order to pull in the changes. In the majority of cases, you want to use develop on a local path, not add.

### Developing packages

By only using add your environment always has a "reproducible state", in other words, as long as the repositories and registries used are still accessible it is possible to retrieve the exact state of all the dependencies in the environment. This has the advantage that you can send your environment (Project.toml and Manifest.toml) to someone else and they can Pkg.instantiate that environment in the same state as you had it locally. However, when you are developing a package, it is more convenient to load packages at their current state at some path. For this reason, the dev command exists.

Let's try to dev a registered package:

(@v1.8) pkg> dev Example
Updating git-repo https://github.com/JuliaLang/Example.jl.git
Resolving package versions...
Updating ~/.julia/environments/v1.8/Project.toml
[7876af07] + Example v0.5.4 ~/.julia/dev/Example
Updating ~/.julia/environments/v1.8/Manifest.toml
[7876af07] + Example v0.5.4 ~/.julia/dev/Example

The dev command fetches a full clone of the package to ~/.julia/dev/ (the path can be changed by setting the environment variable JULIA_PKG_DEVDIR, the default being joinpath(DEPOT_PATH[1],"dev")). When importing Example julia will now import it from ~/.julia/dev/Example and whatever local changes have been made to the files in that path are consequently reflected in the code loaded. When we used add we said that we tracked the package repository; we here say that we track the path itself. Note the package manager will never touch any of the files at a tracked path. It is therefore up to you to pull updates, change branches, etc. If we try to dev a package at some branch that already exists at ~/.julia/dev/ the package manager will simply re-use the existing path. If dev is used on a local path, that path to that package is recorded and used when loading that package. The path will be recorded relative to the project file, unless it is given as an absolute path.

Let's try modify the file at ~/.julia/dev/Example/src/Example.jl and add a simple function:

plusone(x::Int) = x + 1

Now we can go back to the Julia REPL and load the package and run the new function:

julia> import Example
[ Info: Precompiling Example [7876af07-990d-54b4-ab0e-23690620f79a]

julia> Example.plusone(1)
2
Warning

A package can only be loaded once per Julia session. If you have run import Example in the current Julia session, you will have to restart Julia to see the changes to Example. Revise.jl can make this process significantly more pleasant, but setting it up is beyond the scope of this guide.

To stop tracking a path and use the registered version again, use free:

(@v1.8) pkg> free Example
Resolving package versions...
Updating ~/.julia/environments/v1.8/Project.toml
[7876af07] ~ Example v0.5.4 ~/.julia/dev/Example ⇒ v0.5.3
Updating ~/.julia/environments/v1.8/Manifest.toml
[7876af07] ~ Example v0.5.4 ~/.julia/dev/Example ⇒ v0.5.3

It should be pointed out that by using dev your project is now inherently stateful. Its state depends on the current content of the files at the path and the manifest cannot be "instantiated" by someone else without knowing the exact content of all the packages that are tracking a path.

Note that if you add a dependency to a package that tracks a local path, the Manifest (which contains the whole dependency graph) will become out of sync with the actual dependency graph. This means that the package will not be able to load that dependency since it is not recorded in the Manifest. To synchronize the Manifest, use the REPL command resolve.

In addition to absolute paths, add and dev can accept relative paths to packages. In this case, the relative path from the active project to the package is stored. This approach is useful when the relative location of tracked dependencies is more important than their absolute location. For example, the tracked dependencies can be stored inside of the active project directory. The whole directory can be moved and Pkg will still be able to find the dependencies because their path relative to the active project is preserved even though their absolute path has changed.

## Removing packages

Packages can be removed from the current project by using pkg> rm Package. This will only remove packages that exist in the project; to remove a package that only exists as a dependency use pkg> rm --manifest DepPackage. Note that this will remove all packages that (recursively) depend on DepPackage.

## Updating packages

When new versions of packages are released, it is a good idea to update. Simply calling up will try to update all the dependencies of the project to the latest compatible version. Sometimes this is not what you want. You can specify a subset of the dependencies to upgrade by giving them as arguments to up, e.g:

(@v1.8) pkg> up Example

This will only allow Example do upgrade. If you also want to allow dependencies of Example to upgrade (with the exception of packages that are in the project) you can pass the --preserve=direct flag.

(@v1.8) pkg> up --preserve=direct Example

And if you also want to allow dependencies of Example that are also in the project to upgrade, you can use --preserve=none:

(@v1.8) pkg> up --preserve=none Example

## Pinning a package

A pinned package will never be updated. A package can be pinned using pin, for example:

(@v1.8) pkg> pin Example
Resolving package versions...
Updating ~/.julia/environments/v1.8/Project.toml
[7876af07] ~ Example v0.5.3 ⇒ v0.5.3 ⚲
Updating ~/.julia/environments/v1.8/Manifest.toml
[7876af07] ~ Example v0.5.3 ⇒ v0.5.3 ⚲

Note the pin symbol showing that the package is pinned. Removing the pin is done using free

(@v1.8) pkg> free Example
Updating ~/.julia/environments/v1.8/Project.toml
[7876af07] ~ Example v0.5.3 ⚲ ⇒ v0.5.3
Updating ~/.julia/environments/v1.8/Manifest.toml
[7876af07] ~ Example v0.5.3 ⚲ ⇒ v0.5.3

## Testing packages

The tests for a package can be run using test command:

(@v1.8) pkg> test Example
...
Testing Example
Testing Example tests passed

## Building packages

The build step of a package is automatically run when a package is first installed. The output of the build process is directed to a file. To explicitly run the build step for a package, the build command is used:

(@v1.8) pkg> build IJulia
Building Conda ─→ ~/.julia/scratchspaces/44cfe95a-1eb2-52ea-b672-e2afdf69b78f/6e47d11ea2776bc5627421d59cdcc1296c058071/build.log
Building IJulia → ~/.julia/scratchspaces/44cfe95a-1eb2-52ea-b672-e2afdf69b78f/98ab633acb0fe071b671f6c1785c46cd70bb86bd/build.log

[ Info: Installing Julia kernelspec in /home/kc/.local/share/jupyter/kernels/julia-1.8

## Interpreting and resolving version conflicts

An environment consists of a set of mutually-compatible packages. Sometimes, you can find yourself in a situation in which two packages you'd like to use simultaneously have incompatible requirements. In such cases you'll get an "Unsatisfiable requirements" error:

Unsatisfiable requirements detected for package D [756980fe]:
D [756980fe] log:
├─possible versions are: 0.1.0-0.2.1 or uninstalled
├─restricted by compatibility requirements with B [f4259836] to versions: 0.1.0
│ └─B [f4259836] log:
│   ├─possible versions are: 1.0.0 or uninstalled
│   └─restricted to versions * by an explicit requirement, leaving only versions: 1.0.0
└─restricted by compatibility requirements with C [c99a7cb2] to versions: 0.2.0 — no versions left
└─C [c99a7cb2] log:
├─possible versions are: 0.1.0-0.2.0 or uninstalled
└─restricted by compatibility requirements with A [29c70717] to versions: 0.2.0
└─A [29c70717] log:
├─possible versions are: 1.0.0 or uninstalled
└─restricted to versions * by an explicit requirement, leaving only versions: 1.0.0

This message means that a package named D has a version conflict. Even if you have never added D directly, this kind of error can arise if D is required by other packages that you are trying to use.

Note

When tackling these conflicts, first consider that the bigger a project gets, the more likely this is to happen. Using targeted projects for a given task is highly recommended, and removing unused dependencies is a good first step when hitting these issues. For instance, a common pitfall is having more than a few packages in your default (i.e. (@1.8)) environment, and using that as an environment for all tasks you're using julia for. It's better to create a dedicated project for the task you're working on, and keep the dependencies there minimal. To read more see Working with Environments

The error message has a lot of crucial information. It may be easiest to interpret piecewise:

Unsatisfiable requirements detected for package D [756980fe]:
D [756980fe] log:
├─possible versions are: [0.1.0, 0.2.0-0.2.1] or uninstalled

means that D has three released versions, v0.1.0, v0.2.0, and v0.2.1. You also have the option of not having it installed at all. Each of these options might have different implications for the set of other packages that can be installed.

Crucially, notice the stroke characters (vertical and horizontal lines) and their indentation. Together, these connect messages to specific packages. For instance the right stroke of ├─ indicates that the message to its right (possible versions...) is connected to the package pointed to by its vertical stroke (D). This same principle applies to the next line:

├─restricted by compatibility requirements with B [f4259836] to versions: 0.1.0

The vertical stroke here is also aligned under D, and thus this message is in reference to D. Specifically, there's some other package B that depends on version v0.1.0 of D. Notice that this is not the newest version of D.

Next comes some information about B:

│ └─B [f4259836] log:
│   ├─possible versions are: 1.0.0 or uninstalled
│   └─restricted to versions * by an explicit requirement, leaving only versions 1.0.0

The two lines below the first have a vertical stroke that aligns with B, and thus they provide information about B. They tell you that B has just one release, v1.0.0. You've not specified a particular version of B (restricted to versions * means that any version will do), but the explicit requirement means that you've asked for B to be part of your environment, for example by pkg> add B. You might have asked for B previously, and the requirement is still active.

The conflict becomes clear with the line

└─restricted by compatibility requirements with C [c99a7cb2] to versions: 0.2.0 — no versions left

Here again, the vertical stroke aligns with D: this means that D is also required by another package, C. C requires v0.2.0 of D, and this conflicts with B's need for v0.1.0 of D. This explains the conflict.

But wait, you might ask, what is C and why do I need it at all? The next few lines introduce the problem:

└─C [c99a7cb2] log:
├─possible versions are: [0.1.0-0.1.1, 0.2.0] or uninstalled
└─restricted by compatibility requirements with A [29c70717] to versions: 0.2.0

These provide more information about C, revealing that it has 3 released versions: v0.1.0, v0.1.1, and v0.2.0. Moreover, C is required by another package A. Indeed, A's requirements are such that we need v0.2.0 of C. A's origin is revealed on the next lines:

└─A [29c70717] log:
├─possible versions are: 1.0.0 or uninstalled
└─restricted to versions * by an explicit requirement, leaving only versions 1.0.0

So we can see that A was explicitly required, and in this case, it's because we were trying toadd it to our environment.

In summary, we explicitly asked to use A and B, but this gave a conflict for D. The reason was that B and C require conflicting versions of D. Even though C isn't something we asked for explicitly, it was needed by A.

To fix such errors, you have a number of options:

• try updating your packages. It's possible the developers of these packages have recently released new versions that are mutually compatible.
• remove either A or B from your environment. Perhaps B is left over from something you were previously working on, and you don't need it anymore. If you don't need A and B at the same time, this is the easiest way to fix the problem.
• try reporting your conflict. In this case, we were able to deduce that B requires an outdated version of D. You could thus report an issue in the development repository of B.jl asking for an updated version.
• try fixing the problem yourself. This becomes easier once you understand Project.toml files and how they declare their compatibility requirements. We'll return to this example in Fixing conflicts.

## Garbage collecting old, unused packages

As packages are updated and projects are deleted, installed package versions and artifacts that were once used will inevitably become old and not used from any existing project. Pkg keeps a log of all projects used so it can go through the log and see exactly which projects still exist and what packages/artifacts those projects used. If a package or artifact is not marked as used by any project, it is added to a list of orphaned packages. Packages and artifacts that are in the orphan list for 30 days without being used again are deleted from the system on the next garbage collection. This timing is configurable via the collect_delay keyword argument to Pkg.gc(). A value of 0 will cause anything currently not in use to be collected immediately, skipping the orphans list entirely; If you are short on disk space and want to clean out as many unused packages and artifacts as possible, you may want to try this, but if you need these versions again, you will have to download them again. To run a typical garbage collection with default arguments, simply use the gc command at the pkg> REPL:

(@v1.8) pkg> gc
Active manifests at:
~/BinaryProvider/Manifest.toml
...
~/Compat.jl/Manifest.toml
Active artifacts:
~/src/MyProject/Artifacts.toml

Deleted ~/.julia/packages/BenchmarkTools/1cAj: 146.302 KiB
Deleted ~/.julia/packages/Cassette/BXVB: 795.557 KiB
...
Deleted ~/.julia/artifacts/e44cdf2579a92ad5cbacd1cddb7414c8b9d2e24e (152.253 KiB)
Deleted ~/.julia/artifacts/f2df5266567842bbb8a06acca56bcabf813cd73f` (21.536 MiB)

Deleted 36 package installations (113.205 MiB)
Deleted 15 artifact installations (20.759 GiB)

Note that only packages in ~/.julia/packages are deleted.

## Offline Mode

In offline mode, Pkg tries to do as much as possible without connecting to internet. For example, when adding a package Pkg only considers versions that are already downloaded in version resolution.

To work in offline mode use import Pkg; Pkg.offline(true) or set the environment variable JULIA_PKG_OFFLINE to "true".

## Pkg client/server

When you add a new registered package, usually three things would happen:

1. update registries,

The General registry and most packages in it are developed on GitHub, while the artifacts data are hosted on various platforms. When the network connection to GitHub and AWS S3 is not stable, it is usually not a good experience to install or update packages. Fortunately, the pkg client/server feature improves the experience in the sense that:

1. If set, the pkg client would first try to download data from the pkg server,

By default, the client makes upto 8 concurrent requests to the server. This can set by the environment variable JULIA_PKG_CONCURRENT_DOWNLOADS.

Since Julia 1.5, https://pkg.julialang.org provided by the JuliaLang organization is used as the default pkg server. In most cases, this should be transparent, but users can still set/unset a pkg server upstream via the environment variable JULIA_PKG_SERVER.

# manually set it to some pkg server
julia> ENV["JULIA_PKG_SERVER"] = "pkg.julialang.org"
"pkg.julialang.org"

julia> ENV["JULIA_PKG_SERVER"] = ""
""

For clarification, some sources are not provided by Pkg server

• packages/registries fetched via git


text:
We have moved to a new Sailfish OS Forum. Please start new discussions there.

# SIM Hijack attack

Is Sailfish vulnerable? https://thehackernews.com/2019/09/simjacker-mobile-hacking.html

edit retag close delete

1

Oh yes

and can be exploited regardless of which handsets victims are using.

And oh, oh: not completely regardless. My N900 would be safe as it does not have this S@T technology :)

( 2019-09-13 00:58:13 +0300 )edit
3

@peterleinchen, an N900 is just as vulnerable (or safe) as any other device! This attack is completely independent of the operating system, as no code needs to be run on the main CPU.
The attack solely uses the resources of the SIM card, all of which are JavaCards by specification, plus information provided by the cellular modem (location, IMEI etc.).
So ultimately it all depends on your SIM card providing a S@T implementation (or not).
Please use the force and read the source! Feel free to point out misunderstandings by me, accompanied by a pointer to a contradictory statement there.

( 2019-09-13 01:48:23 +0300 )edit
1

I was under the impression that as the N900/Maemo does not have an Implementation of this SIM kit application and this part of source

Once this information is retrieved, the Simjacker code running on the UICC then collates it and sends the combined information to a recipient number via another SMS (we call this the ‘Data Message’), again by triggering logic on the handset.

I may be wrong...

( 2019-09-13 08:22:19 +0300 )edit

"One important note is that for some specific attacks handset types do matter. Some, such as setting up a call, require user interaction to confirm, but this is not guaranteed and older phones or devices with no keypad or screens (such as IoT device) may not even ask for this." On some CDMA oriented (but GSM compatible) android phones S@T browser is missing too.

( 2019-09-13 17:03:19 +0300 )edit
2

@peterleinchen, well AFAICS the terms "device" and "handset" are used interchangeably in both of the documents (the high-level one [1] and the bit more detailed one [2]) and addresses the whole device, including cellular modem etc.
The used language is remarkably imprecise, but that "triggering logic on the handset" IMO means nothing more than "let the modem send out the exfiltrated data per SMS", just as the modem was used before that to collect information e.g. location data.

@Linuxovod, S@T is clearly described as a software component deployed with and running on the UICC (i.e. any modern SIM card).

( 2019-09-13 17:48:13 +0300 )edit

Sort by » oldest newest most voted

No, SailfishOS is not vulnerable, just as all other operating systems are not. But your SIM card might.

more

1

( 2019-09-13 07:38:41 +0300 )edit
1

@olf they say: "One important note is that for some specific attacks handset types do matter. Some, such as setting up a call, require user interaction to confirm, but this is not guaranteed and older phones or devices with no keypad or screens (such as IoT device) may not even ask for this." My question meant what will Sailfish do in this case.

( 2019-09-13 17:00:12 +0300 )edit
1

Question reopened. The attack needs handset support. Does SF support STK? If yes, possible to disable?

( 2019-09-13 18:12:47 +0300 )edit
1

Well that aspect seem to be quite clear: Modern phones will ask the user for confirmation on specific actions initiated by the SIM card and carried out by the modem, such as making a call.
Those actions mentioned for the specific attack example (receiving and sending SMS, retrieving IMEI and location data) are not among those "special actions" (for reasons). Hence the OS is not informed (i.e. asked to obtain a confirmation by the user), thus does not and cannot "do" anything.

( 2019-09-13 18:17:40 +0300 )edit
2

@Stefanix, can you please provide a pointer, why you believe that this "attack needs handset support".
S@T definitely needs no OS support.

IMO it is rather the opposite: Some classes of devices ("handset types") may ask user for a confirmation, if triggered to do so by the UICC (= SIM card), while others either do not (unimplemented, e.g. on old dumb-phones) or cannot (lack of screen and keypads; e.g. (IoT devices etc.).

( 2019-09-13 18:27:46 +0300 )edit

The attack is dependent on two conditions. 1) UICC SIM, meaning, GSM network 2) The precense of STK application, which is an application that lives on the UICC SIM card, but is not necessarily present for all carrier SIMs, for example, it is not present on my carrier (Denmark) The STK application on SIM card, communicates with the phone, and is communicating via the application present in ofono. This can be disabled, and your phone would not be vulnerable.

more

As I understand the vulnerability, disabling SIM-Toolkit should be a workaround...

more

Ist the STK supported at all? If yes, can it be deactivated?

( 2019-09-13 20:06:15 +0300 )edit
2

https://together.jolla.com/question/182073/sim-card-removed-issue-with-sailfishx/

There you can find how-to disable STK...

( 2019-09-13 20:17:11 +0300 )edit
1

Thanks, neo, for that link! So I would conclude that SF together with STK enabled SIMs has this vulnerability. Disabling the STK as suggested by jovirkku should prevent the described attacks. @Linuxovod: This should answer your question.

( 2019-09-13 20:29:52 +0300 )edit
1

@Neo: +1

So I would conclude that SF together with STK enabled SIMs has this vulnerability.

Yes and no, because it is OS independent: "STK enabled SIMs" is the point.

Disabling the STK as suggested by jovirkku should prevent the described attacks.

I am afraid "disabling" the STK for the rild (which configures and serves the cellular modem) just suppresses triggers from the STK to cause actions on the main CPU (e.g. installing icons for starting Java applications on the UICC / SIM card or asking for user confirmations).

( 2019-09-13 21:14:48 +0300 )edit
1

@olf: Actually I am not familiar with the ME SW architectures, But what you write is not consistent. You confirm that it is possible to configure the cellular modem's STK functions (if they exist), i.e triggers. I would call that a OS function. On the other hand you write that the modem function of forwarding SM on STK request is independent of the OS and not changeable. If we can disable triggers, we could also disable the whole STK support. Of course this is implementation dependent. The STK spec require to support all functions of a class ("However, any ME claiming to supportSIM Application Toolkit need not support all toolkit functions, but shall support all functions within a classas given in the table below:"), So a partial support of STK functions would not be compliant. If there is a function to disable the STK (and some MS have that on the UI), the whole STK support would have to be disabled.

( 2019-09-13 22:01:16 +0300 )edit

I would be nice to have some kind of script or approach to pen test the SIM card that is in the Jolla phone. Even on the site which reported this error, there were no approaches on how to actually check and test the SIM card, which is somewhat annoying. On a forthcoming event a larger amount of information about this issue will (?) be revealed, but it would be nice to see whether one is vulnerable to this kind of attack or not.

https://simjacker.com/ That is all a bit pointless.

more


text:
It’s a shame! Rsync is an old, stable, field-tested, nice, quick and versatile tool for backups. And if you had bad luck, like I did, and just cut and pasted the first best example found on the Internet, and that example didn’t behave the way I thought it supposed to, you are lost, because all the solution I found at Google at the first page, sound more like voodoo, rather than a real and reasonable explanation.  And because I write this Blog in order not run ever into same issues again, I decided to write this little solution for my rsync problem, so I can easily look it up one fine day I need it again. And I really hope, this little article will be higher rated at Google, at least higher than the other solutions. This would definitely save ppls time. Here we go. There are at least two known reasons for the “cannot delete non-empty directory” problem:

### The Backup Problem

You’ve got two directories. One is called SOURCE and the other is called BACKUP. Now you want to sync these to directories, e.g. via a cron-job. This cron-job is the bad one, which I used the first time:

# m h dom mon dow command
0 2 * * * /usr/bin/rsync -avb --delete /SOURCE/ /BACKUP >/dev/null 2>&1

The first day, this cron-job was running, all was fine, and I didn’t saw anything suspicious. On the other day I’ve deleted a few files in SOURCE, but to my surprise, the files haven’t been deleted inBACKUP. Instead the deleted files have been renamed simply by adding a suffix to the filename. This suffix was a dash (“~“). So since these directories weren’t empty, they couldn’t be deleted, no matter what switch I’ve tried with rsync. Using the “--dry-run” switch, I could see, which directories couldn’t be deleted:

/usr/bin/rsync -avb --delete /SOURCE/ /BACKUP --dry-run

I’ve got a bunch of

cannot delete non-empty directory

The problem is the “-b” or the “--backup” switch. If you specify the backup option, you tell rsync not to delete the files, but to back them up. This is done by the previously mentioned suffix, the dash. And this whole matter is done in the directory, where you deleted your files. There are two solutions actually. The first one is not to use the backup switch at all. You can even specify the “--prune-empty-dirs“, or short “-m” switch, to ensure empty folder are being deleted also.

/usr/bin/rsync -avm --delete /SOURCE/ /BACKUP --dry-run

Or you really intend to use the --backup switch, but then please also specify a backup directory for it, where all these deleted files are moved into. This switch is called: “--backup-dir=“. If you don’t specify it, don’t expect rsync to delete empy directories, because rsync cannot delete empty directories, and it really doesn’t matter whether you additionally specify “--force“, or not. In combination with “--delete” it’s even double senseless.

### The Exclude Problem

The second problem wasn’t figured out by myself, but this Blog article referring to this article here. It describes a deadlock between the switches listed right below, even without using the notorious backup switch (-b) at all:

• --delete

• --exclude <exclude pattern>

• --ignore-existing

Also here the --force switch is without effect. Here the writer points out, an additional

• --delete-excluded


text:
# Multiset

893pages on
this wiki

A multiset is a collection of unordered objects.

Unlike sets, elements of multisets need not be distinct.

## Multiset coefficientEdit

The number of multisets of size k taken from a set of cardinality n is denoted by the multiset coefficient, denoted by $\scriptstyle\left(\!\!{n\choose k}\!\!\right)$, and is equal to:

$\left(\!\!{n\choose k}\!\!\right) = {n + k - 1 \choose k}={n+k-1 \choose n-1}$.


text:
# Closest Vector in a Inner Product Space

Let $V$ = $\mathbb{R}^n$

Note that $\langle -,-\rangle$ defines the Inner Product on $\mathbb{R}^n$

$$\|v\| = \sqrt{\langle v,v \rangle}$$

Consider the standard Distance Function $$d(x,y) = \|x-y\|$$

Let $W$ $\subset V$ be a Subspace of Dimension $n-1$ defined by the equation

$W = {(x_1,......,x_n)} : {x_1+x_2+.....x_n=0}$

Show that the vector in $W$ closest to the vector $(x_1,.....,x_n)$ is the vector $$(x-\lambda,.....,x_n-\lambda)$$

where $\lambda = \frac{x_1+....+x_n}{n}$

How do I go about this? I'm a little confused since I've been taught almost like an algorithim that the orthogonal projection via gram schmidt is the closest vector but I'm not able to use it here properly. Is there a proper way to approach such problems?

Hint: Because $W$ is a hyperplane defined by a single linear equation, its orthogonal complement $W^{\perp}$ can be read off its defining equation: $$W^{\perp} = \operatorname{Span}\{\mathbf{1}\} = \operatorname{Span}\{(1, 1, \dots, 1)\}.$$ Now decompose an arbitrary vector $x$ as \begin{align*} x &= \operatorname{proj}_{W}(x) + \operatorname{proj}_{W^{\perp}}(x) \\ &= \bigl(x - \operatorname{proj}_{\mathbf{1}}(x)\bigr) + \operatorname{proj}_{\mathbf{1}}(x). \end{align*}


text:
# Structural and compositional analysis of $InBi_xAs_ySb_{(1-x-y)}$ films grown on GaAs(0 0 1) substrates by liquid phase epitaxy

Dixit, VK and Keerthi, KS and Bhat, HL and Bera, Parthasarathi and Hegde, MS (2003) Structural and compositional analysis of $InBi_xAs_ySb_{(1-x-y)}$ films grown on GaAs(0 0 1) substrates by liquid phase epitaxy. In: Applied Surface Science, 220 (1-4). pp. 321-326.

 PDF Structural_and_compositional.pdf Restricted to Registered users only Download (351Kb) | Request a copy

## Abstract

The growth of epitaxial $InBi_xAs_ySb_{(1-x-y)}$ layers on highly lattice mis-matched semi-insulating GaAs substrates has been successfully achieved via the traditional liquid phase epitaxy. Orientation and single crystalline nature of the film have been confirmed by X-ray diffraction. Scanning electron micrograph shows abrupt interface at micrometer resolution. Surface composition of Bi(x) and As(y) in the $InBixAsySb_{(1-x-y)}$ film was measured using energy dispersive X-ray analysis and found to be 2.5 and 10.5 at.%, respectively, and was further confirmed with X-ray photoelectron spectroscopy. Variation of the composition with depth of the film was studied by removing the layers with low current (20 μA) $Ar^+$ etching. It was observed that with successive Ar+ etching, In/Sb ratio remained the same, while the As/Sb and Bi/Sb ratios changed slightly with etching time. However after about 5 min etching the As/Sb and Bi/Sb ratios reached constant values. The room temperature band gap of $InBi_{0.025}As_{0.105}Sb_{0.870}$ was found to be in the range of 0.113–0.120 eV. The measured values of mobility and carrier density at room temperature are $3.1 \times 10^4 cm^2 V^{-1} s^{-1}$ and $8.07 \times 10^{16} cm^{-3}$, respectively.

Item Type: Journal Article The Copyright belongs to Elsevier. X-ray diffraction;Liquid phase epitaxy;Antimonides;Semiconducting III–V materials Division of Chemical Sciences > Solid State & Structural Chemistry UnitDivision of Physical & Mathematical Sciences > Physics 05 May 2006 19 Sep 2010 04:26 http://eprints.iisc.ernet.in/id/eprint/6563


text:
# Open $\sigma$-compact sets with finite measure

Let $X$ be locally compact Hausdorff space and let $\mu$ be positive Borel measure, finite on compacts, outer regular with respect to open subsets, for each Borel set, and inner regular with respect to compact subsets, for each open set and for each Borel with finite measure. Is it true that for every compact $F$ there exists an open $\sigma$-compact $G$ such $F\subset G$ and $G$ has finite measure.

Thanks.

-

-


text:
# Revision history [back]

Your computation asks for a square roots of $275$ modulo $625$ (since $-84100 = 275\mod 625$). There exist many such square roots (amongst which $30$ and $280$), as shown by the following computation:

sage: Zmod(625)(275).sqrt(all=True)
[30, 95, 155, 220, 280, 345, 405, 470, 530, 595]

Thus, the functions sqrt in Magma and SageMath both give sensible results. They simply do not make the same choice when they choose one of the possible square roots.

Note : There exist two implementations in SageMath for the computation of square roots in $\mathbb Z/n\mathbb Z$. One is specific for small values of $n$ (32 bits) and the other for larger values of $n$. It happens that they do not to make the same choice for a square root. In your case, sqrt is the method for small values of $n$. But one can specifically call the other implementation using square_root.

The method for small values return the smallest (using the natural order on integers) square root, that is $30$ in your case, using a brute force algorithm. The algorithm used for large values is based on Newton method.

Important remark: My explanation are specific to the value $625$ which is a prime power, different from $3$ modulo $4$.

Questions for knowledgeable SageMath developers:

1. The alias square_root = sqrt is defined in IntegerMod_abstract but not in IntegerMod_int, whence the different answers. Should it be defined also in IntegerMod_int for consistency?
2. Is there a satisfactory way to define a preferred square root in $\mathbb Z/625\mathbb Z$, to ensure consistency between implementations, and to satisfy the principle of least surprise?


text:
Article Contents
Article Contents

# Dynamical behavior for a Lotka-Volterra weak competition system in advective homogeneous environment

• * Corresponding author

The author is supported by NSF grant 11801089, Postdoctoral Science Foundation of China(N0.2018M643281)

• We consider a two-species Lotka-Volterra weak competition model in a one-dimensional advective homogeneous environment, where individuals are exposed to unidirectional flow. It is assumed that two species have the same population dynamics but different diffusion rates, advection rates and intensities of competition. We study the following useful scenarios: (1) if one species disperses by random diffusion only and the other assumes both random and unidirectional movements, two species will coexist; (2) if two species are drifting along the different direction, two species will coexist; (3) if the intensities of inter-specific competition are small enough, two species will coexist; (4) if the intensities of inter-specific competition are close to 1, the competitive exclusion principle holds. These results provide a new mechanism for the coexistence of competing species. Finally, we apply a perturbation argument to illustrate that two species will converge to the unique coexistence steady state.

Mathematics Subject Classification: Primary: 35K57, 35B32; Secondary: 92D25.

 Citation:


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Back to Coding Theory
Back to notes

# Reed-Solomon Code

In this note, we introduce some basic properties of Reed-Solomon code and present a simple decoding algorithm.

## Definition and basic facts

Let $n$ denote the block length, prime power $q$ denote the alphabet size, $k$ denote the message length, and $d$ denote the minimum distance. Define the Reed-Solomon code as follows.

For integer $1\leq k<n\leq q$ and a set $S={\alpha_1,\dots,\alpha_n}\subseteq\mathbb{F}_q$, we define the Reed-Solomon code

$\text{RS}_{q,S}[n,k] := \{(p(\alpha_1),\dots,p(\alpha_n)):\ p\text{ is a polynomial of degree at most }k-1 \}.$

Intuitively, we think of the code of Reed-Solomon code as a low degree ($k-1$) polynomial and the codeword is the evaluation of the polynomial on set $S$ of size $n$. Thus, we have the following facts directly from the definition and the properties of polynomials.

• The rate is $1-k/n$.
• The minimum distance is $n-k+1$.
• This follows from the fact (“Degree Mantra”) that two distinct univariate degree $d$ polynomial intersect on at most $d$ points.

The good thing about Reed-Solomon code is that its rate achieves the Singleton bound, i.e., Reed-Solomon code has optimal rate. However, the alphabet size required is pretty large: $q>n$. Thus, many people have been worked hard to reduce the alphabet size of the Reed-Solomon code while preserving the optimality of code rate.

### Linear code characterization

Recall that there are three important issues in linear code: the generator matrix, the parity checking matrix, and the dual code. In the following, we consider a special case of Reed-Solomon code where $n=q$ and $S={0,1,2,\dots,q-1}$.

• The generator matrix of Reed-Solomon code

The generating matrix of Reed-Solomon code is simply the sumatrix of Vandermonde matrix of $S$ up to degree $k-1$. We denote the code as $\text{RS}_q[n,k]$.

• The parity checking matrix of Reed-Solomon code

From the generator matrix characterization of Reed-Solomon code, one can see that every codeword lie in the row space of $G$. Thus, to find the parity checking matrix, it is equivalent to find the perp of the row space of $G$. Thus, we need some properties from the Vandermonde matrix as follows. (Note that these properties hold when $n=q$)

Let $V_i$ denote the $i$th row of the Vandermonde matrix, then for any $i,j\in[n]$,

$% $

From the above lemma, we know that the first $n-k$ row of the Vandermonde matrix is perpendicular to $\text{RS}_q[n,k]$. As the dimension of $\text{RS}_q[n,k]$ is $k$ and the dimension of the universe is $n$, we conclude that the parity checking matrix of $\text{RS}_q[n,k]$ is

• The dual code of Reed-Solomon code

By the property of linear code, we know that the generator matrix of the dual code of $\text{RS}_q[n,k]$ is the transpose of the parity checking matrix of $\text{RS}_q[n,k]$. That is, the dual code of $\text{RS}_q[n,k]$ is $\text{RS}_q[n,n-k+1]$.

## Nice resources

• Book chapter by Madu Sudan, Venkatesan Guruswami, and Atri Rudra.
• Background in polynomials and finite fields.
• A very comprehensive introduction to Reed-Solomon code.
• A property of MDS codes.
• Nice exercises cover many useful properties of Reed-Solomon code and some variants.
• Lecture notes of an IT course at University of Wyoming.
• Short and self-contained.


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Electric Potential Sample Problem

Given electric potential equation $V = x^3yz+2y^2z+xz^4$, find:

a. The corresponding electric field equation for this potential

Using the identity

b. The charge density of the field at $(2,-3)$

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To all math majors: "Mathematics is a wonderfully rich subject."

Dr. Paul Garrett


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1. ## Linearly Independent Vectors

Problem:
Consider the vectors $\vec{v_{1}},\vec{v_{2}},...,\vec{v_{m}}$ in $\mathbb{R}^{n}}$, with $\vec{v_{m}} = \vec{0}$. Are these vectors linearly independent?

My solution:
No, they are not. Since $\vec{v_{m}} = \vec{0}$, $rank[\vec{v_{1}} ... \vec{v_{m}}]$ will fail to equal m. There will not be a pivot in every column, which is a requirement for a set of linearly independent vectors.

Am I on the right track? Any input appreciated!

2. Originally Posted by tangibleLime
Consider the vectors $\vec{v_{1}},\vec{v_{2}},...,\vec{v_{m}}$ in $\mathbb{R}^{n}}$, with $\vec{v_{m}} = \vec{0}$. Are these vectors linearly independent?
No, they are not. Since $\vec{v_{m}} = \vec{0}$, $rank[\vec{v_{1}} ... \vec{v_{m}}]$ will fail to equal m. There will not be a pivot in every column, which is a requirement for a set of linearly independent vectors.
I mean, if you want to do it in terms of matrices you're correct, but isn't it just simpler to note that $0v_1+\cdots+v_m=0$?


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# Can I prove that $\sqrt n\log{\sqrt n}=\Theta(n)$?

I'd like to prove that $\sqrt n\log{\sqrt n}=\Theta(n)$ but I'm not sure how to do it.

This is my attempt: $$\lim_{n \to \infty}\frac{\log{\sqrt n}}{\sqrt n}=0 \Rightarrow \log{\sqrt n}=o(\sqrt n) \text{(Little o)}$$

Therefore: $$\sqrt n\log{\sqrt n}=o(\sqrt n\cdot \sqrt n)=o(n)$$ But this is too much as I need theta.

• You can't prove it since it's not true. Jun 7 '17 at 18:15
• "I calculated 1+1=2, but that's too much as I need 1" -- see the problem here?
– Raphael
Jun 7 '17 at 21:43

$$\lim_{n\to\infty} \frac{\sqrt n \log\sqrt n}{n} = 0$$

Since this $\Theta(\sqrt n \log \sqrt n) = o(n) < \Theta(n)$.

Two functions $f(x), g(x)$ are asymptotically equal iff

$$\lim_{x\to\infty} \frac{f(x)}{g(x)} = c,\ c \in \mathbb{R},\ c > 0$$

• but this is exactly what I wrote in my question
– Yos
Jun 7 '17 at 18:22
• @Yos, no, you have divided $\log \sqrt n$ instead of $\sqrt n \log \sqrt n$. Jun 7 '17 at 18:23
• but you're getting the same result I got, what does you answer contribute?
– Yos
Jun 7 '17 at 18:25
• @Yos, yes, result is the same, because the statement itself is wrong. It would be correct if limit would be finite non-zero. Jun 7 '17 at 18:27
• So you should say this explicitly in your answer. Otherwise you're just providing an almost identical calculation and identical result.
– Yos
Jun 7 '17 at 18:28


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The presence of the hydroxide is demonstrated by the addition of a few drops of phenolphthalein indicator, which turns the solution pink, indicating that the solution is basic. Hydrogen Gas Reacts With Copper(II) Oxide To Form Copper Metal And Water Vapor According To The Reaction: CuP + H2 ---- Cu + H2O. What Is The Formula For Iron (III) Oxide? What Is The Symbol Equation For Iron + Oxygen = Iron Oxide? so yeah, I'm not too great with stoichiometry and i was wondering if anyone could solve these problems so I can get a template for the rest of the problems :p After a second or so, the calcium metal begins to bubble vigorously as it reacts with the water, producing hydrogen gas, and a cloudy white precipitate of calcium hydroxide. What Is The Balanced Equation For Sodium Oxide Combines With Water To Form Sodium Hydroxide? c . what type of reaction is Na2B4O7.10H2O + 2HCl -> 2NaCl(aq) + 5H2O + 4B(OH)3. the final balanced equation should look like: it is important to never forget the … When calcium oxide (chemical formula: CaO) reacts with water (chemical formula: H2O), the following reaction takes place: `CaO + H_2O -> Ca(OH… This is a highly exothermic reaction. 0 0. calcium oxide water balanced equation is important information accompanied by photo and HD pictures sourced from all websites in the world. Calcium oxide reacts with water to form calcium hydroxide. It can be produced by direct reaction of the elements: 3 Ca + N 2 → Ca 3 N 2. This is a highly exothermic reaction. (d) Calcium hydride reacts with water to generate hydrogen gas. chemistry. As there are not equal number of atoms on both reactant and product side. (a) Write the net ionic equation of the reaction. Favourite answer. 4Fe + 3O    -> 2Fe    O What Is The Balanced Equation For Sodium Sulfate And Calcium Nitrate? 3. The reaction between quick lime and water is … Consider the reaction between calcium chloride, CaCl2, and sodium carbonate, Na2CO3.

When you predict the products and write a balanced equation the coefficient of phosphoric acid is a.1 b.2 c.3 d.6 e.4, write the chemical equations for the following sentences a) Aluminum reacts with oxygen to produce aluminum oxide I put Al + O2 ----------> 2Al2O3 b) Phosphoric acid, H3PO4, is produced through the reaction between tetraphosphorous decoxide and water … Iron reacts with water vapours to form iron (III) oxide. This is a neutralization reaction, which is a type of double replacement reaction. When i put calcium in water it dissolved and made the liquid that was left in the beaker murky and was no longer colourless. 4. Calcium oxide reacts with water in a combination reaction to produce calcium hydroxide: A 2.00-g sample of is reacted with 1.93 g of . The equation for the reaction with CO2 is : Ca(OH)2(aq) + CO2(g) → CaCO3(s) + H2O(l) 0 0. What Is The Difference Between The Boy Scouts And Congress/parliament? Balanced word equation: Two moles of ethanoic acid (acetic acid) react with one mole of calcium hydroxide to produce one mole of calcium acetate and two moles of water. When calcium oxide reacts with water calcium hydroxide is formed. d. What Is Its Formula? CaO (s) + 2HNO3 (aq) → Ca(NO3)2 (aq) + H2O(l) 0.4262 g of calcium oxide is reacted with 0.1250 L of 0.06000 M nitric acid. A chemical equation is a description of the proportion of reactants than combine to yield a specific chemical product. c. Ammonia reacts with water to form ammonium hydroxide. Copper metal reacts with sulfuric acid and water to produce copper sulfate pentahydrate and sulfur dioxide. Our channel. chemistry. The equation would be: So the two others are just wrong, there is no HCl, I've done this my self in the lab, and if CaCl2 made HCl, it would make it useless in many instances. How many grams of calcium oxide, CaO, can be produced from 4.20 g of calcium metal and 1.60 g of oxygen gas? In symbols please. A. Write a balanced chemical equation for the reaction. (iii).Sodium + Water –> Sodium hydroxide + Hydrogen. What Is The Total Ionic Equation For Nitric Acid And Barium Carbonate? Calcium + Phosphorous to produce Calcium Phosphide is an ionic synthesis reaction. (a O + H₂O -> CaCOH)2 2 B. What Is The Equation For Calcium Oxide And Water? I know that a gas was formed (hydrogen) from a flaming splint test. $\ce{CaO} \left( s \right) + \ce{H_2O} \left( l \right) \rightarrow \ce{Ca(OH)_2} \left( aq \right)$ Sulfur trioxide gas reacts with water to form sulfuric acid. When calcium oxide reacts with water calcium hydroxide is formed. (ii) Write the balanced chemical equation of this reaction. 72. calcium oxide + sulfur dioxide → calcium sulfite CaO + SO 2 → CaSO 3 73. carbon dioxide + magnesium hydroxide → magnesium carbonate + water CO 2 + Mg(OH) 2 → MgCO 3 + H 2O 74. calcium oxide + hydrochloric acid → calcium chloride + water CaO + 2HCl → CaCl 2 + H 2O 75. calcium carbonate + silicon dioxide → calcium … How many grams of water are needed to react completely with 25.0 grams of calcium oxide? The chemical equation is … Sodium oxide is a simple strongly basic oxide. b. 18156 views Step 2. b. Calcium oxide reacts with water to form calcium hydroxide. The equation is calcium oxide + water -> calcium hydroxide. How many grams of calcium hydroxide are produced when 87.95 grams of water are used? 102.80g tho. My guess is that the word equation is: Calcium+Water--> Hydrogen +CalciumOxide. Chemistry Introductory Chemistry: An Active Learning Approach Sulfur dioxide, oxygen, and calcium oxide react to form calcium sulfate. We say, for example, “chemically combined together”. How many grams of calcium hydroxide are produced when 87.95 grams of water are used? Problem 89 Write a balanced equation for each of the following reactions: (a) Heating phosphorous acid yields phosphoric acid and phosphine $\left(\mathrm{PH}_{3}\right) .$ (b) Lithium carbide reacts with hydrochloric acid to give lithium chloride and methane. Get answers by asking now. The correct word is “mix”. Balanced word equation: Two moles of ethanoic acid (acetic acid) react with one mole of calcium hydroxide to produce one mole of calcium acetate and two moles of water. Solid calcium oxide reacts with liquid water to produce calcium hydroxide. Which of the following equations represents the balanced equation for the reaction of iron and oxygen? Solid copper reacts with solid sulfur to form solid copper(I) sulfide. 0.0714 1.29 0.00 1.04 0.00396 . Write a balanced equation for the reaction. Download this image for free in High-Definition resolution the choice "download button" below. 2NH4Cl + CaO -> 2NH3 + H2O + CaCl2. The combustion of pamoic acid (C 23 H 16 O 4). 001. Formation of Calcium Hydroxide:Reaction between quick lime (Calcium oxide, CaO) and water is a combination reaction. Calcium metal reacts with phosphorus to produce calcium phosphide. Ans. Do you think that pornograhic videos can be bad for your sex life? ... when heated reacts to form calcium oxide, CaO, and … (a) Write a balanced thermochemical equation for the reaction. When calcium is chemically combining with oxygen then it results into the formation of chemical compound called calcium oxide. Balanced Equation Of lime water react with carbon dioxide gas to form solid calcium carbonate and water? c . MgSO4 + BaCl2 ---> MgCl2 + BaSO4 A metathesis (double replacement) reaction forming Magnesium Chloride and Barium Sulphate. (b) Write balanced chemical equation with state symbols for the following reaction : Sodium hydroxide solution reacts with hydrochloric acid solution to produce sodium chloride solution and water. In general: #"acid + metal hydroxide"# #rarr# #"salt + water… Calcium hydroxide is also called slaked lime or hydrated lime. Could someone please tell me what the balanced chemical equation is? When the equation is written and balanced, the coefficient of carbon is 34) A) 4. A very common example is the reactions of oxides with water. Davy B. Lv 6. (a O + H₂O -> CaCOH)2 2 B. C) 1. All you have to is write the equation and then notice that you have 2 Na on... What Is The Equation For Calcium Oxide And Nitric Acid? It is calcium hydroxide. oxide, the principal ore of tin, with carbon. When 11.0 g of calcium metal is reacted with water, 5.00 g of calcium hydroxide is produced. Relevance. Using the following balanced equation, calculate the percent yield for the reaction? It is calcium hydroxide. Calcium oxide is also called quick lime. (b) Calculate the moles of calcium oxide and nitric acid. The equation is calcium oxide + water -> calcium hydroxide. Using the following balanced equation, calculate the percent yield for the reaction? For example, when sodium and chlorine combine, they form sodium chloride which can be written Na + Cl --> NaCl The balanced chemical reaction is: C a C 2 + 2 H 2 O → C a ( O H ) 2 + C 2 H 2 (b) Using Table 8.3, calculate ΔH f ° for calcium … Calcium is a chemical compound and its molecular formula is CaO. © 2003-2020 Chegg Inc. All rights reserved. Silver nitrate reacts with sulfiric acid to If the names of substances are simply replaced by their symbols and, , most chemical equations are not correct. Therefore, the balanced equation will be as follows. D) 2. Sodium Oxide. then write a balanced equation for each of the following reactions. What is the balanced equation for calcium carbonate--->calcium oxide+carbon dioxide? 0.0714 1.29 0.00 1.04 0.00396 . The numbers are subscript. A. 4 Answers. calcium hydroxide + carbon dioxide = calcium carbonate + water; sulfur + ozone = sulfur dioxide Examples of the chemical equations reagents (a complete equation will be suggested): H 2 SO 4 + K 4 Fe(CN) 6 + KMnO 4; Ca(OH) 2 + H 3 PO 4; Na 2 S 2 O 3 + I 2; C 8 H 18 + O 2; hydrogen + oxygen; propane + oxygen calcium oxide with water balanced equation is important information accompanied by photo and HD pictures sourced from all websites in the world. If you do not find the exact resolution you are looking for, then go for a native or higher resolution. Source(s): balanced equation calcium carbonate gt calcium oxide carbon dioxide: https://shortly.im/ilkMk. 0000019958 00000 n 3CaCl2 + 2Al = 3Ca + 2AlCl3 (600-700° C). Check whether the equation is balanced by counting the atoms of each element. The balanced equation... What Happens When You Mix Water And Calcium Oxide? In general: #"acid + metal hydroxide"# #rarr# #"salt + water"# Calcium oxide is also called quick lime. The ionic equation for sodium sulfate and calcium nitrate is: SO42-+Ca2+=CaSO4... Calcium Oxide Is Used To Make Soil Less Acidic. … How many grams of water remain after the reaction is complete? Find another reaction. 2Na + 2H 2 O –> 2NaOH + H 2. Privacy Solid calcium oxide was taken in a container and water was added slowly to it. How many grams of water remain after the reaction is complete? Calcium hydroxide, CA(OH)2, also known as slaked lime, is formed. Calcium oxide reacts with water in a combination reaction to produce calcium hydroxide: CaO (s) + H2O (l) → Ca(OH)2 (s) In a particular experiment, a 5.50-g sample of CaO is reacted with excess water and 6.77 g of Ca(OH)2 is recovered. Calcium hydride reacts with water to form calcium hydroxide and hydrogen gas. chemistry   2   2     3... What Is The Balanced Equation Of Ammonium Sulfate And Calcium Hydroxide? A. It is basic because it contains the oxide ion, O 2-, which is a very strong base with a high tendency to combine with hydrogen ions.. CaO(s) + H2O(l) → Ca(OH)2(s) Calcium hydroxide in a solid form is used to neutralise acidity on farm land and in lakes affected by acid rain. Solid Calcium Oxide Reacts With Liquid Water To Produce Calcium Hydroxide. In this reaction, quick lime reacts with water to form slaked lime (calcium hydroxide, Ca(OH)2). What Mass Of Copper Is Produced If 255 L Of Hydrogen At STP Are Used Up In This Reaction? Sodium reacts with water to produce sodium hydroxide and hydrogen gas. You should not have used the word “combine” in your question. How many grams of water are needed to react completely with 25.0 grams of calcium oxide? a. The broadly used term "lime" connotes calcium-containing inorganic materials, in which carbonates, oxides and hydroxides of calcium, silicon, … Reaction with water: Sodium oxide reacts exothermically with cold water to produce sodium hydroxide solution.A concentrated solution of sodium oxide in water … Calcium oxide (CaO), commonly known as quicklime or burnt lime, is a widely used chemical compound.It is a white, caustic, alkaline, crystalline solid at room temperature. Write a balanced chemical equation on with state symbols for the following reactions. Calcium hydride (CaH2) reacts with water to produce calcium hydroxide (Ca(OH)2) and hydrogen gas. (Na)2 O + H2O--> 2NaOH. When 11.0 g of calcium metal is reacted with water, 5.00 g of calcium hydroxide is produced. The combustion of decane. CaCO3 = CaO + CO2 ?? When calcium oxide reacts vigorously with water to produce calcium hydroxide a large amount of heat is evolved and thus temperature of the system increases hence it confirms that a chemical reaction has been taken place. How many grams of calcium oxide, CaO, can be produced from 4.20 g of calcium metal and 1.60 g of oxygen gas? (a O + H₂O -> CaCOH)2 2 B. [ Check the balance ] Calcium oxide react with nitric acid to produce calcium nitrate and water. d. Calcium oxide reacts with water in a combination reaction to produce calcium hydroxide: CaO (s) + H2O (l) → Ca (OH) 2 (s) In a particular experiment, a 5.50-g sample of CaO is reacted with excess water and 6.77 g of Ca (OH) 2 is recovered. Write a balanced chemical equation for each reaction. Identify all of the phases in your answer. Solid calcium oxide reacts with liquid water to produce calcium hydroxide. Solid calcium oxide reacts with liquid water to produce calcium hydroxide. (3 points) Write a balanced equation, without including states, for each step in the process: a. Calcium carbonate (from limestone) is heated and decomposes into calcium oxide and carbon dioxide. Do You Allow Your Pet To Sleep In The Bed With You? What Is The Balanced Equation For Nitric Acid Reacting With Strontium Hydroxide? 8 years ago. You are asking for the following equation to be written out and balanced: calcium hydroxide plus carbon dioxide yields calcium carbonate plus water. Does Copper (II) Oxide Dissolve In Water? Identify all of the phases in your answer. | Calcium hydroxide and hydrogen gas are generated when calcium reacts with water. Ask a Question. Observations: The mixture produces a hissing sound. Calcium oxide reacts with nitric acid (HNO3) to form aqueous calcium nitrate and water. How To Find The Weight In Grams Of 1 Mole Of Calcium Oxide? & Calcium hydride reacts with water to form calcium hydroxide and hydrogen gas. Word equation: ammonium chloride + calcium oxide -> ammonia + water +calcium chloride. A dilute aqueous solution of calcium hydroxide is known as limewater and is used the laboratory to test for carbon dioxide gas. Answer Save. Calcium Oxide Is Used To Make Soil Less Acidic. c. Sulfur dioxide gas reacts with oxygen gas to form sulfur trioxide gas. Calcium Carbide CaC2 reacts with Water to form Acetylene; balanced equation: CaC2+2H2O=C2H2+Ca(OH)2? The aqueous product of this reaction can be heated to evaporate the water, leaving a white solid, Ca (OH) 2 (s).Ca (s) + H2O (l) = = > Ca (OH) 2 (aq) + H2 (g)Compare the … How Do You Feel About Parents Who Cannot Pay For Their Children's School Books? Net Chemical Equation For The Production Of Acrylic Acid From Calcium Carbide, Water And Carbon Dioxide? why only these? (i) Solution of barium chloride and Sodium sulphate in water react to give insoluble barium sulphate and the solution of sodium chloride. Sodium sulfate reacts with calcium nitrate to form sodium nitrate and calcium sulfate. Im 14 turning 15 and i want a belly piercing how do i tell my parents i want one? When calcium carbide reacts with water it produces calcium hydroxide and acetylene gas. The balanced chemical equation for the reaction is; CaO + H2O ------> Ca (OH)2. Trevor H. Lv 7. Lime water is a solution of calcium hydroxide in water . Write the balanced equation for this reaction. Symbol equation: 2NH4Cl + CaO -> 2NH3 + H2O + CaCl2 Word equation: ammonium chloride + calcium oxide -> ammonia + water + calcium chloride This reaction is represented by the balanced equation below. Write the balanced equation for this reaction. This is a neutralization reaction, which is a type of double replacement reaction. The products of this reaction are tin and carbon dioxide. (i) State two observations made in the experiment. Download this image for free in High-Definition resolution the choice "download button" below. 102.80g tho Answer: (i) Solid calcium oxide was taken in a container and water was added to it. Write a balanced equation for the reaction. When one mole of calcium carbonate reacts with ammonia, solid calcium cyanamide, CaCN 2, and liquid water are formed. 4. Write a balanced chemical equation for the reaction in which sulfuric acid (H2S04) reacts with potassium hydrx»dde to … This is a single displacement reaction. balenced equation for barium oxide (BaO) reacts with water … The reaction absorbs 90.1 kJ of heat. The equation is: Ca + 2H 2 O.... See full answer below. Write a balanced equation for the reaction. what type of reaction is Na2B4O7.10H2O + 2HCl -> 2NaCl(aq) + 5H2O + 4B(OH)3. the final balanced equation should look like: it is important to never forget the parenthesis. The balanced chemical equation for the reaction is. Calcium reacts with water. Calcium carbonate reacts with hydrochloric acid to produce calcium chloride, water and carbon dioxide gas. Solid iron(III) oxide reacts with hydrogen gas to form solid iron and liquid water. In chemistry the word “combine” has a special meaning. 0 0. Calcium oxide reacts with nitric acid (HNO 3 3) to form aqueous calcium nitrate and water. Calcium is a chemical compound and its molecular formula is CaO. Terms How To Find The Weight In Grams Of 1 Mole Of Calcium Oxide? 18156 views Step 2. The chemical reaction equation for this reaction is as follows. A. View desktop site, 4. State symbols are not required. Calcium oxide reacts with water in a combination reaction to produce calcium hydroxide: CaO (s) + H 2 O (I) → Ca(OH) 2 (s) In a particular experiment, a 1.50-g sample of CaO is reacted with excess water and 1.48 g of Ca(OH) 2 is recovered. B) 3. When copper(ll) carbonate is heated, it forms copper(ll) oxide and carbon dioxide Copper combines with sulfur to form copper(l) sulfide. 2. Bismuth (III) oxide and zinc metal react to produce zinc (II) oxide and bismuth metal. Calcium oxide reacts with water in a combination reaction to produce calcium hydroxide: A 2.00-g sample of is reacted with 1.93 g of . When calcium carbonate is heated it decomposes into calcium oxide and carbon dioxide. Still have questions? Calcium oxide reacts readily with water to produce an aqueous solution of calcium hydroxide. Thermodynamic properties of substances The solubility of the substances Periodic … Here are some related questions which you might be interested in reading. 8 years ago. calcium oxide + water → calcium hydroxide. Didn't find the answer you were looking for? chemistry Calcium oxide reacts with water to form calcium hydroxide. It reacts with water or even the moisture in air to give ammonia and calcium hydroxide: Ca 3 N 2 + 6 H 2 O → 3 Ca(OH) 2 + 2 NH 3 Calcium nitride is formed along with the oxide, CaO, when calcium burns in air. If you do not find the exact resolution you are looking for, then go for a native or higher resolution. Q3. (ii) Gas evolution. What Is Its Formula? This page looks at the reactions of the Group 2 elements - beryllium, magnesium, calcium, strontium and barium - with water (or steam). (NH4)2SO4 + Ca(OH)2 ------> 2NH4OH + CaSO4... What is the Ionic equation for sodium sulfate and calcium nitrate? CaO + H2O = CA(OH)2... What Is The Balance Equation For Diphosphorus Pentoxide And Water?
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/ Lattice arXiv:0910.4682

Numerical study of chiral magnetic effect in quenched SU(2) lattice gauge theory

Buividovich, P.V. (Moscow, ITEP) ; Chernodub, M.N. (Moscow, ITEP) ; Luschevskaya, E.V. (Moscow, ITEP) ; Polikarpov, M.I. (Moscow, ITEP)

Published in: PoS LAT2009
Pages: 7

Abstract: A possible experimental observation of the chiral magnetic effect in heavy ion collisions at RHIC was recently reported by the STAR Collaboration. We study signatures of this effect in SU(2) lattice gluodynamics with the chirally invariant Dirac operator. We find that at zero temperature the local fluctuations of an electric current of quarks and chirality fluctuations increase with external Abelian magnetic field. The external magnetic field leads to spatial separation of the quark's electric charges. The separation increases with the strength of the magnetic field. As temperature gets higher the dependence of these quantities on the strength of the magnetic field becomes weaker. In the deconfinement phase the local fluctuations of the chiral density and of the spatial components of the quarks electric current are large and are almost independent on the external magnetic field. The local fluctuations of the electric charge density decrease with the strength of the magnetic field in this phase.

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Numbers of unique views: 355


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### dtalamas24's blog

By dtalamas24, 7 years ago,

Motivating problem: You have an array of size N with N different numbers; calculate the sum of the numbers in the interval of a to b.

What is the proof that a Segment Tree performs those queries in log(n) time? Or where can I find the proof? Thanks.

• -4

 » 7 years ago, # |   +13 The segment tree has O(log(n)) levels. The algorithm visits at most O(1) nodes per level during the query, because of this:Let [L, R) be the interval covered by current vertex. Let denote # number covered by [a, b) and . the other nodes. Only these situations can occur: if R<=a || b<=L, we dont care about this node, situation looks like .......... if a<=L && b<=R, whole node is in interval [a,b), situation looks like ########## L==a or b==R, #######... or .......### none of the previous options ...#####.. The situations 1 and 2 cost O(1) time.The situation 3 divides the interval into two smallers ones. At most one of children will have type 3, the others will be 1 or 2. ...####### -> ...## + ##### (3 -> 3, 2) .......### -> ..... + ..### (3 -> 1, 3) .....##### -> ..... + ##### (3 -> 1, 2) The situation 4 can divide into: ....#####.. -> ...## + ###.. (4 -> 3, 3) ......##... -> ..... + .##.. (4 -> 1, 4) .....###... -> ..... + ###.. (4 -> 1, 3) So there will be only one child of type 4 or there will be at most two children of type 3.At the beginning of query we have one of the stituations 1, 2, 3, 4 on top level. It is easy to see that there can be at most 1 node of type 4 per level and if there is no type 4 there can be at most two nodes of type 3 per level. So there can be only 4 = O(1) nodes visited in each level (at most two of type {3,4})That means O(log(n)) visited nodes. Inside each node we spent O(1) time.
•  » » 10 months ago, # ^ |   -8 I think Case 2 and 3 are interchangeably drawn.
•  » » 6 months ago, # ^ |   0 Shouldn't case 2 be a <= L && R <= b? Because you said the whole interval[L, R) is in interval [a, b). Anyway, this is by far the best time complexity analysis of segment tree that I have came across. Thanks :)
 » 7 years ago, # |   +8 Well, firstly, you have to build the tree in O(nlogn). Every vertex has: interval covered, sum-to-be-added and overall-sum. So when you go deeper if the interval searched is bigger than the covered you just get the sum. So in the worst case you will have query (a = n/2, b=n/2+1) for which you will go to 2 different leaves of the tree. This means 2*logn operations at most in one query. The sum-to-be-added value is used if you have updates for an interval for the same reason. When you reach a fully covered interval you update that value, so that you can use it in the queries by adding that value times the length of the answer to the result. PS: The update trick with sum-to-be added is called lazy propagation, so you can look for it on the net.
 » 7 years ago, # |   0 A short idea of lazy propagation:Let's take the same type you propose, where queries are for sum of interval.Imagine that you want to increase all the numbers in the interval corresponding to node n by x. You don't need to update the whole subtree; instead, just mark in n "for this subtree, each element is actually plus x". Now, you don't traverse deeper into the subtree anymore.Now, what happens if you need to traverse some of the nodes of this subtree later? You must pass through n. And at that point, you can update the sons of n — if all elements in the interval of n are larger by x, then so will be all the elements in the intervals of the sons of n (since those 2 together make the interval of n). So, you just copy the information "for this subtree, each element is actually plus x" into the sons of n.Now, you must make sure you won't repeat that again for the same information. In node n, you remember the sum of its interval [z,k). Increase that sum by x * (k - z) (all the k - z elements are increased by x). And set x = 0. If there are more queries which end at node n, x can be further modified.The details of how the updates are done differ slightly between different types of trees, but the overall idea stays the same: if you know that an operation is applied to a subtree, store it at the root.
 » 7 years ago, # |   +3 It´s because a segment tree have log(n) levels, and in every step, if your querry is outside the interval of the node that you are you can discard this node, if all your querry is inside the interval of your node you return this sum, else you need to go to the next level. but if you see this, you will do this maximum 2 times for level, then your complexity will be 2(log(n)). :)


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My Math Forum Sandwich Theorem Trig Funcs.

 Calculus Calculus Math Forum

 July 8th, 2019, 05:44 AM #1 Senior Member   Joined: Oct 2015 From: Greece Posts: 137 Thanks: 8 Sandwich Theorem Trig Funcs. For some reason I struggle using the sandwich theorem in solving trigonometric function limits. Example 1.png Solution 2.png But I can not understand how he does that. My try using $\displaystyle -|θ| < sinθ < |θ|$ : $\displaystyle -|2x| < sin2x < |2x| \Leftrightarrow \frac{-|2x|}{x} < \frac{sin2x}{x} < \frac{|2x|}{x}$ what now? how does the books reaches this: $\displaystyle \frac{-1}{x} < \frac{sin2x}{x} < \frac{1}{x}$ ???? How does he also get rid of the absolute value? I solved this with words $\displaystyle \lim_{x \to \infty} \frac{sin2x}{x}$, $\displaystyle \lim_{x \to \infty} sin2x = a \epsilon R$, so $\displaystyle \frac{a}{\lim_{x \to \infty}x}=0$ Last edited by babaliaris; July 8th, 2019 at 05:50 AM.
 July 8th, 2019, 06:13 AM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 2,980 Thanks: 1573 the value of sin(any angle) is inclusively between -1 and 1, i.e $-1 \le \sin(2x) \le 1$ since $x \to \infty$, $x$ is a positive, non-zero number and one can divide each term in the above inequality by $x$ $\dfrac{-1}{x} \le \dfrac{\sin(2x)}{x} \le \dfrac{1}{x}$ as $x \to \infty$, both $-\dfrac{1}{x}$ and $\dfrac{1}{x}$ tend to zero ... Thanks from babaliaris
July 8th, 2019, 06:18 AM   #3
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Joined: Oct 2015
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Quote:
 Originally Posted by skeeter the value of sin(any angle) is inclusively between -1 and 1, i.e $-1 \le \sin(2x) \le 1$ since $x \to \infty$, $x$ is a positive, non-zero number and one can divide each term in the above inequality by $x$ $\dfrac{-1}{x} \le \dfrac{\sin(2x)}{x} \le \dfrac{1}{x}$ as $x \to \infty$, both $-\dfrac{1}{x}$ and $\dfrac{1}{x}$ tend to zero ...
When can this inequality $\displaystyle -|θ| < sinθ < |θ|$ be useful?

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American Institute of Mathematical Sciences

July  2020, 40(7): 4179-4196. doi: 10.3934/dcds.2020177

A new type of non-landing exponential rays

 1 Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China 2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

* Corresponding author: Song Zhang

Received  April 2019 Revised  January 2020 Published  April 2020

Fund Project: This work is supported by the Fundamental Research Funds for the Central Universities (Grant No. 2019kfyXJJS135) and the National Natural Science Foundation of China (Grant No. 11901219)

In this paper, we will construct a new type of non-landing exponential rays, each of whose accumulation sets is bounded, disjoint from the ray and homeomorphic to the closed topologist's sine curve.

Citation: Jianxun Fu, Song Zhang. A new type of non-landing exponential rays. Discrete & Continuous Dynamical Systems - A, 2020, 40 (7) : 4179-4196. doi: 10.3934/dcds.2020177
References:

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References:
The folding process of $\gamma_{6}^0$ by $g_{1}^- \circ g_{2}^+ \circ \cdots\circ g_{5}^-\circ g_{6}^+$ for the above choice of $\xi_i$ with $i = 0,1,\cdots,5$
Here is the sketch of $\gamma_0^{-12}$. The black polylines with different-sized bold show the idea of how the limit curve $\eta$ is produced in the accumulation set of $\gamma_0$
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# Fanography

A tool to visually study the geography of Fano 3-folds.

Identification
##### Fano variety 4-7

blowup of 2-32 in the disjoint union of a curve of degree $(0,1)$ and a curve of degree $(1,0)$

Picard rank
4 (others)
$-\mathrm{K}_X^3$
36
$\mathrm{h}^{1,2}(X)$
0
Hodge diamond
1
0 0
0 4 0
0 0 0 0
0 4 0
0 0
1
1
0 4
0 0 14
0 0 0 21
0 0 0
0 0
0
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
21
$-\mathrm{K}_X$ very ample?
yes
$-\mathrm{K}_X$ basepoint free?
yes
hyperelliptic
no
trigonal
no
Birational geometry

This variety is rational.

This variety is the blowup of

• 3-24, in a curve of genus 0
• 3-28, in a curve of genus 0
Deformation theory
number of moduli
0

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$\mathrm{GL}_2$ 4 0
Period sequence

The following period sequences are associated to this Fano 3-fold:

GRDB
#57
Fanosearch
#69
Extremal contractions
Semiorthogonal decompositions

A full exceptional collection can be constructed using Orlov's blowup formula.

Structure of quantum cohomology
Zero section description

Fano 3-folds from homogeneous vector bundles over Grassmannians gives the following description(s):

variety
$(\mathbb{P}^1)^2 \times (\mathbb{P}^2)^2$
bundle
$\mathcal{O}(0,0,1,1) \oplus \mathcal{O}(1,0,1,0) \oplus \mathcal{O}(0,1,0,1)$

variety
$(\mathbb{P}^1)^2 \times \operatorname{Fl}(1,2,3)$
bundle
$\mathcal{O}(1,0; 1,0) \oplus \mathcal{O}(0,1;0,1)$