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Sulfuric acid and zinc react to produce hydrogen gas and a zinc salt. This is a synthesis reaction. Solution for When 6.8 g al Aluminum reacts with excess oxygen according to the following balanced equation and 9.0 g of Al2O3 are actually produced, what is the… Example 4 - Aluminum reacts with oxygen gas according to the balanced chemical equation. A synthesis reaction. Aluminum reacts with oxygen to produce solid aluminum oxide. (a) Balanced Molecular equation (please write the answer on your paper) (b) Identify the limiting reactant when 35.5 g of Aluminum reacts with 35.5 g of Oxygen. For each of the following, generate a chemical equation. 1mol Al 27.0g Al . My balanced equation is: a) 2C8H18(g) + 25O2(g) -> 16CO2(g) + 18H2O(g) b) 0.290 mol of octane is allowed to react with 0.670mol of oxygen. X 1mol Al2O3 2mol Al X 102.0g Al2O3 1mol Al2O3 = 47.2g Al2O3 Answer _____ Write the balanced formula unit equation for the reaction. this is because aluminum has a valency of 3 and oxygen … Getting a balanced equation. Relevance. The unbalanced reaction between magnesium and oxygen is: {eq}Mg + O_2 \to MgO {/eq} From the equation, the number of oxygen atoms is not balanced. Aluminum burns in oxygen with a white flame to form the trioxide aluminum (III) oxide, says WebElements. Click to see full answer Consequently, what is the balanced equation when aluminum reacts with copper II sulfate? Aluminum reacts with sulfur gas to form aluminum sulfide. Chemistry 101. From the balanced reaction equation, every 4 moles of aluminum reacted in excess oxygen will produce 2 moles of aluminum oxide. 4Na (s) + O 2(g) 2Na 2 … to produce aluminum oxide ("Al"_2"O"_3). Aluminum sulfate reacts with calcium hydroxide (from lime) to form aluminum hydroxide and calcium sulfate. Al+O - ALO AL+- AL2O3 2AL + 302 - Al2O3 4A1 + … 25.0g Al X . Aluminium–air batteries (Al–air batteries) produce electricity from the reaction of oxygen in the air with aluminium.They have one of the highest energy densities of all batteries, but they are not widely used because of problems with high anode cost and byproduct removal when using traditional electrolytes. Indicate the type of reaction on the line to the left of the equation by classifying each reaction as single replacement (SR), double replacement (DR), decomposition (D), synthesis (S), or combustion (C). 5. What is the word equation and chemical equation of aluminium and oxygen and why? This was covered in 5.09. (please type the answer in the solution box) Look at the Activity Series to answer this question. Atomic Structure. This thin layer protects the underlying metal from corrosion caused by oxygen, water or other chemicals. The equation for Aluminum: a = 2c. Answer to: Which shows a balanced chemical equation for the decomposition of aluminum oxide? The balanced equation is written as: 2Al + 3CuSO4 --> Al2(So4)3 + 3Cu An oxidation-reduction reaction occurs where there is a transfer of elections from Aluminum … Write the balanced equation for the following: a. a. Write balanced equations for the following reactions. Problem #2: Determine the number of grams of NH3 produced by the … Example 5 - Consider the unbalanced chemical e P 4 O 10(s) + H 2 O (l) → H 3 PO 4(aq) Balancing Chemical Reactions For each of the following, generate a chemical equation. 0 0. To create a balanced equation when aluminium reacts with copper (II) sulphate, provide the correct coefficient for each compound. gcsescience.com 22 gcsescience.com. Write the balanced equation . (((Which I found Oxygen to be the limiting reactant.))) Which is the limiting reactant? 9 years ago. Find an answer to your question “Aluminum + oxygen yields aluminum oxide Write a balanced equation for this chemical reaction.A) Al + O → AlO B) Al + O → Al2O3 C) 2Al + ...” in Chemistry if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions. To convert the mass of aluminum … Below are more examples of balanced chemical equations showing state symbols. Al (s) + O 2(g) → Al 2 O 3(s) Phosphoric acid is produced through the reaction of tetraphosphorous decoxide and water. Anonymous. Error: equation Aluminum+O2=AluminumOxygen is an impossible reaction Instructions and examples below may help to solve this problem You can always ask for help in the forum Instructions on balancing chemical equations: Enter an equation of a chemical reaction and click 'Balance'. 1. The balanced chemical equation for this reaction is ul(4"Al"(s) + 3"O"_2(g) rarr 2"Al"_2"O"_3(s) A reaction in which two or more reactants combine to form only one product is called a synthesis reaction. Aluminum + oxygen yields aluminum oxide Write a balanced equation for this chemical reaction. Calculate the number of grams of aluminum oxide produced . Let's look at cobalt (III) oxide. Just use the molar ratio from the balanced equation. Although bright and shiny, aluminum objects are covered with a tight, invisible coating of aluminum oxide, (Al 2 O 3) that forms when freshly exposed aluminum (Al) reacts with oxygen. When 2-propanol burns in oxygen gas, carbon dioxide and water are produced. 4. ____ 12. aluminum sulfate + calcium phosphate ( _____ 24) Aluminum and oxygen react according to the following equation: 4 Al (s) + 3 O2 (g) → 2 Al2O3 (s) b. Balanced symbol equations show what happens to the different atoms in reactions. The balanced equation will appear above. aAl + bO 2 → cAl 2 O 3. Cobalt (III) means its cobalt ion with valency of 3 and since metals form positive ions, this is Co3+ ion. 4 Al + 3 O2---> 2 Al2O3. 1. 23) Aluminum and oxygen react according to the following equation: 4 Al (s) + 3 O2 (g) → 2 Al2O3 (s) In a certain experiment, 4.6 g Al was reacted with excess oxygen and 6.8 g of product was obtained. I . Algebraic Method. 3. A page showing Balanced Chemical Equations for The reactions between Sodium and Oxygen, Aluminium and Chlorine, Aluminium and Oxygen, Calcium and Chlorine, Magnesium and Bromine . These are half equations for some reactions at the anode: 2Cl-→ Cl 2 + 2e-2O 2-→ O 2 + 4e-Example. The balanced chemical equation is 2Al + 3CuSO4 --> Al2(So4)3 + 3Cu When Aluminum is added to Copper Sulfate, it displaces Copper, and it reacts with Sulfate to for Aluminum Sulfate because Aluminum is more reactive than copper. Aluminum reacts with oxygen to produce a compound. (please write the answer on your paper) (c) Calculate the actual yield in grams if the percent yield is 29.80%. For example, copper and oxygen react together to make copper oxide. Magnesium ribbon burns in air to produce a white powder. This has restricted their use to mainly military applications. Mass is not involved. Al3+ + 02- --> Al203. To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. Solution for 2. Write the balanced equation for the formation of table salt, NaCl (sodium chloride), from sodium (Na), and gaseous chlorine (Cl 2). Aluminium + Oxygen --> Aluminium Oxide. Aluminum reacts with oxygen gas to form aluminum oxide according to the equation: $\ce{Al} \left( s \right) + \ce{O_2} \left( g \right) \rightarrow \ce{Al_2O_3} \left( s \right)$ Since there are two oxygen atoms on the reactant side and 3 oxygen atoms on the product side, no single whole-number coefficient will balance the oxygen atoms. Thank you :D. Answer Save. If 13.5 g of aluminum reacts with 12.0 g of oxygen gas the theoretical yield of aluminum oxide is 25.5 g. When the reaction is carried out in the lab, only 23.2 g of aluminum oxide is formed. Then below the word equation, write the balanced chemical equation. Example 5 - Consider the unbalanced chemical e Write a balanced half equation for the formation of oxygen from hydoxide ions. To balance … 4Al + 3O2 = 2Al2O3. chemistry. 2] How many grams of aluminum oxide are formed when 25.0 grams of Aluminum are reacted with oxygen gas? b. Aluminum… What was the percent yield of the reaction? Problem #1: Aluminum oxide is formed from the reaction of metallic aluminum with oxygen gas. Oxide ion = O2- Thus cobalt (III) oxide should have the chemical formula Co2O3 (swop the valencies to get the formula of the compound formed) Balanced chemical equation: 4Co + 3O2 --> 2Co2O3 Hope this helps. Chemists write the chemical reaction between aluminum and oxygen … Use uppercase for the first character in the element and lowercase for the second character. Aluminum reacts with oxygen to form a layer of aluminum oxide on the outside of the metal, according to HowStuffWorks. 2 Answers. Since each element is balanced, the balanced chemical equation is found to be 4Al + 3O 2 → 2Al 2 O 3. 5. Hydrochloric acid and magnesium react to produce hydrogen gas and a magnesium salt. Example 4 - Aluminum reacts with oxygen gas according to the balanced chemical equation. Favorite Answer. Al+O - ALO AL+- AL2O3 2AL + 302… brysonlee brysonlee 10/11/2019 Physics Middle School Aluminum + oxygen yields aluminum oxide es Write a balanced equation for this chemical reaction. 2. If 13.5 g of aluminum reacts with 12.0 g of oxygen gas the theoretical yield of aluminum oxide is 25.5 g. When the reaction is carried out in the lab, only 23.2 g of aluminum oxide is formed. How many moles of Aluminum are needed to form 3.4 moles of Aluminum oxide? We're given that aluminum ("Al") can react with oxygen gas ("O"_2; don't forget it's diatomic!) Be sure to count all atoms on each side of the chemical equation.Of all the options above only option listed above, only option B is correct. Using the algebraic method of balancing chemical equations, the following variables can be assigned to the unbalanced equation. Replace immutable groups in compounds to avoid ambiguity. Examples: Fe, Au, Co, Br, C, O, N, F. Ionic charges are not yet supported and will be ignored. What is the percent yield of this reaction? Aluminium oxide is a chemical compound of aluminium and oxygen with the chemical formula Al 2 O 3.It is the most commonly occurring of several aluminium oxides, and specifically identified as aluminium(III) oxide.It is commonly called alumina and may also be called aloxide, aloxite, or alundum depending on particular forms or applications. - aluminum reacts with oxygen to be the limiting reactant. ) )! Zinc salt - Consider the unbalanced chemical e write balanced equations for the second character grams of aluminum?! E write balanced equations for some reactions at the anode: 2Cl-→ Cl 2 + 4e-Example O 3 this reaction!, enter an equation of aluminium and oxygen and why flame to form the trioxide (! Character in the element and lowercase for the first character in the element and lowercase for the.. O 3 showing state symbols find an answer to: Which shows a balanced for. Valency of 3 and since metals form positive ions, this is Co3+ ion many moles aluminum! 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## 12.2 – Composite and Inverse Functions

### Learning Objectives

• (12.2.1) – Define a composite function
• (12.2.2) – Define an inverse function
• Use compositions of functions to verify inverses algebraically

# (12.2.1) – Define a composite function

Suppose we want to calculate how much it costs to heat a house on a particular day of the year. The cost to heat a house will depend on the average daily temperature, and in turn, the average daily temperature depends on the particular day of the year. Notice how we have just defined two relationships: The cost depends on the temperature, and the temperature depends on the day.

Figure 1

Using descriptive variables, we can notate these two functions. The function $C\left(T\right)$ gives the cost $C$ of heating a house for a given average daily temperature in $T$ degrees Celsius. The function $T\left(d\right)$ gives the average daily temperature on day $d$ of the year. For any given day, $\text{Cost}=C\left(T\left(d\right)\right)$ means that the cost depends on the temperature, which in turns depends on the day of the year. Thus, we can evaluate the cost function at the temperature $T\left(d\right)$. For example, we could evaluate $T\left(5\right)$ to determine the average daily temperature on the 5th day of the year. Then, we could evaluate the cost function at that temperature. We would write $C\left(T\left(5\right)\right)$. By combining these two relationships into one function, we have performed function composition.

We read the left-hand side as $f$ composed with $g$ at $x,''$ and the right-hand side as $f$ of $g$ of $x.''$ The two sides of the equation have the same mathematical meaning and are equal. The open circle symbol $\circ$ is called the composition operator.

It is also important to understand the order of operations in evaluating a composite function. We follow the usual convention with parentheses by starting with the innermost parentheses first, and then working to the outside.

### Example

Using the functions provided, find $f\left(g\left(x\right)\right)$ and $g\left(f\left(x\right)\right)$.

$f\left(x\right)=2x+1$

$g\left(x\right)=3-x$

In the following video you will see another example of how to find the composition of two functions.

# (12.2.2) – Define an inverse function

An inverse function is a function for which the input of the original function becomes the output of the inverse function. This naturally leads to the output of the original function becoming the input of the inverse function. The reason we want to introduce inverse functions is because exponential and logarithmic functions are inverses of each other, and understanding this quality helps to make understanding logarithmic functions easier. And the reason we introduced composite functions is because you can verify, algebraically, whether two functions are inverses of each other by using a composition.

Given a function $f\left(x\right)$, we represent its inverse as ${f}^{-1}\left(x\right)$, read as $f$ inverse of $x.''$ The raised $-1$ is part of the notation. It is not an exponent; it does not imply a power of $-1$ . In other words, ${f}^{-1}\left(x\right)$ does not mean $\displaystyle \frac{1}{f\left(x\right)}$ because $\displaystyle \frac{1}{f\left(x\right)}$ is the reciprocal of $f$ and not the inverse.

Just as zero does not have a reciprocal, some functions do not have inverses.

### Inverse Function

For any function $f\left(x\right)$, a function ${f}^{-1}\left(x\right)$ is an inverse function if $f$ if $(f \circ {f}^{-1})(x) = x$ and $(f^{-1} \circ f)(x) = x$

The notation ${f}^{-1}$ is read $\text{}f$ inverse.” Like any other function, we can use any variable name as the input for ${f}^{-1}$, so we will often write ${f}^{-1}\left(x\right)$, which we read as $f$ inverse of $x.''$
Keep in mind that

$\displaystyle {f}^{-1}\left(x\right)\ne \frac{1}{f\left(x\right)}$

and not all functions have inverses.

In our first example we will identify an inverse function from ordered pairs.

### Example

If for a particular function, which has an inverse, $f\left(2\right)=4$ and $f\left(5\right)=12$, what are the corresponding input and output values for the inverse function?

In the following video we show an example of finding corresponding input and output values given two ordered pairs from functions that are inverses.

### How To: Given two functions $f\left(x\right)$ and $g\left(x\right)$, test whether the functions are inverses of each other.

1. Substitute $g(x)$ into $f(x)$. The result must be $x$. $f\left(g(x)\right)=x$
2. Substitute $f(x)$ into $g(x)$. The result must be $x$. $g\left(f(x)\right)=x$

If $f(x)$ and  $g(x)$ are inverses, then  $f(x)=g^{-1}(x)$ and $g(x)=f^{-1}(x)$

In our next example we will test inverse relationships algebraically.

### Example

If $f\left(x\right)=x^2-3$, for $x\ge0$ and $g\left(x\right)=\sqrt{x+3}$, are $g$ and $f$ inverses of each other?

In the following video we use algebra to determine if two functions are inverses.

We will show another example of how to verify whether you have an inverse algebraically.

### Example

If $\displaystyle f\left(x\right)=\frac{1}{x+2}$ and $\displaystyle g\left(x\right)=\frac{1}{x}-2$, are $g$ and $f$ inverses of each other?

We will show one more example of how to use algebra to determine whether two functions are inverses of each other.

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#### Important 1 Mark Book Back Questions (New Syllabus) 2020

12th Standard EM

Reg.No. :
•
•
•
•
•
•

Physics

Time : 00:20:00 Hrs
Total Marks : 20

Part A

24 x 1 = 24
1. Which charge configuration produces a uniform electric field?

(a)

point Charge

(b)

infinite uniform line charge

(c)

uniformly charged infinite plane

(d)

uniformly charged spherical shell

2. Two identical conducting balls having positive charges q1 and q2 are separated by a center to center distance r. If they are made to touch each other and then separated to the same distance, the force between them will be

(a)

less than before

(b)

same as before

(c)

more than before

(d)

zero

3. A toaster operating at 240 V has a resistance of 120 Ω. Th e power is

(a)

400 W

(b)

2 W

(c)

480 W

(d)

240 W

4. What is the value of resistance of the following resistor?

(a)

100 k Ω

(b)

10 k Ω

(c)

1k Ω

(d)

1000 k Ω

5. In a large building, there are 15 bulbs of 40W, 5 bulbs of 100W, 5 fans of 80W and 1 heater of 1kW are connected. The voltage of electric mains is 220V. The minimum capacity of the main fuse of the building will be

(a)

14 A

(b)

8 A

(c)

10 A

(d)

12 A

6. A circular coil of radius 5 cm and 50 turns carries a current of 3 ampere. The magnetic dipole moment of the coil is

(a)

1.0 amp – m2

(b)

1.2 amp – m2

(c)

0.5 amp – m2

(d)

0.8 amp – m2

7. Th ree wires of equal lengths are bent in the form of loops. One of the loops is circle, another is a semi-circle and the third one is a square. Th ey are placed in a uniform magnetic fi eld and same electric current is passed through them. Which of the following loop confi guration will experience greater torque ?

(a)

circle

(b)

semi-circle

(c)

square

(d)

all of them

8. A thin semi-circular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic fi eld B, as shown in the fi gure.

The potential diff erence developed across the ring when its speed v, is

(a)

Zero

(b)

$\frac { { Bv\pi { r }^{ 2 } } }{ 2 }$and P is at higher potential

(c)

πrBv and R is at higher potential

(d)

2rBvand R is at higher potential

9. A circular coil with a cross-sectional area of 4 cm2 has 10 turns. It is placed at the centre of a long solenoid that has 15 turns/cm and a cross-sectional area of 10 cm2. The axis of the coil coincides with the axis of the solenoid. What is their mutual inductance?

(a)

7.54 μH

(b)

8.54 μH

(c)

9.54 μH

(d)

10.54 μH

10. Which of the following are false for electromagnetic waves

(a)

transverse

(b)

mechanical waves

(c)

longitudinal

(d)

produced by accelerating charges

11. Let E = Eo sin[106 x -ωt] be the electric field of plane electromagnetic wave, the value of ω is

(a)

(b)

(c)

(d)

12. Which of the following is NOT true for electromagnetic waves?

(a)

it transport energy

(b)

it transport momentum

(c)

it transport angular momentum

(d)

in vacuum, it travels with different speeds which depend on their frequency

13. If the velocity and wavelength of light in air is Va and λa and that in water is Vw and λw, then the refractive index of water is,

(a)

$\frac{V_W}{V_a}$

(b)

$\frac{V_a}{V_W}$

(c)

$\frac{\lambda_W}{\lambda_a}$

(d)

$\frac{{V_a}\lambda_W}{{V_W}\lambda_a}$

14. A ray of light strikes a glass plate at an angle 60o. If the reflected and refracted rays are perpendicular to each other, the refractive index of the glass is,

(a)

$\sqrt3$

(b)

$\frac{3}{2}$

(c)

$\sqrt{\frac{3}{2}}$

(d)

2

15. A particle of mass 3 × 10–6 g has the same wavelength as an electron moving with a velocity 6 10 × 6m s−1. The velocity of the particle is

(a)

1.82x10-18ms-1

(b)

9x10-2ms-1

(c)

3x10-15ms-1

(d)

1.82x10-15ms-1

16. If a light of wavelength 330 nm is incident on a metal with work function 3.55 eV, the electrons are emitted. Then the wavelength of the emitted electron is (Take h = 6.6 × 10–34 Js)

(a)

<2.75×10−9m

(b)

≥2.75×10−9m

(c)

≤2.75×10−12m

(d)

<2.5×10−10m

17. The charge of cathode rays is

(a)

Positive

(b)

negative

(c)

neutral

(d)

not defined

18. If a half –wave rectifi ed voltage is fed to a load resistor, which part of a cycle the load current will flow?

(a)

00–900

(b)

900–1800

(c)

00–1800

(d)

00–3600

19. The internationally accepted frequency deviation for the purpose of FM broadcasts

(a)

75 kHz

(b)

68 kHz

(c)

80 kHz

(d)

70 kHz

20. Which of the following is an example of breadcast made of communication?

(a)

(b)

Television

(c)

Mobile

(d)

both (a) & (b)

21. For base station to mobile communication, the required frequency band is

(a)

540 - 1600 KHz

(b)

200 - 32 MHz

(c)

840 - 935 MHz

(d)

5.9 - 6.42 GHz

22. The made of propagation used by short wave broadcast services is

(a)

space wave

(b)

skywave

(c)

ground wave

(d)

both (a) & (c)

23. The materials used in Robotics are

(a)

Aluminium and silver

(b)

Silver and gold

(c)

Copper and gold

(d)

Steel and aluminum

24. Nanoscience is the science of object with typical sizes of ___________

(a)

1 - 100 μ

(b)

1 - 100 nm

(c)

1 - 100 cm

(d)

1- 100 m


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# Quiz 5

What is the skinny QR factorization of a vector $\vv$?

### Solution

$\mQ = \vv/normof{\vv}$ because $\mQ^T \mQ = 1$, and then $\mR = \normof{\vv}$ because $\vv = \mQ \mR$.


text:
# Proof or citation?

I'm writing an article. I suppose that I'll submit it to a more or less decent journal (in English). I have doubts about the following: I have a lemma (with quite a trivial proof). I don't want to include this lemma with complete proof due to its triviality and because it has been already proved before in my Ph.D. thesis.

So I may either prove the lemma in the article (this certainly will not be very good) or simply include a citation of my dissertation instead of proof. But the thesis is in Ukrainian and it's not even available freely via the Internet. Which of the two alternatives would you choose?

Do there exist other ways to do this well?

-
Just include the proof. If readers find it trivial then they will skip over it. Citing a dissertation in Ukrainian is worse than useless, it will just annoy people. –  Neil Strickland Jul 14 '14 at 13:24
If you wish, you may include the information that the lemma has been proved in your PhD dissertation, in the introduction, or in a line just before stating it. –  Pietro Majer Jul 14 '14 at 13:57
I generally agree with Neil Strickland. However, if you decide to omit the proof of the lemma and only cite your thesis, in my opinion you should mention that the proof is "quite trivial" (if it really is). Why? I believe most of the readers will not look the result up in your thesis. However, knowing that it should be trivial, they will have more motivation to try finding the proof on their own. –  Michał Kukieła Jul 14 '14 at 14:10
"Citing a dissertation in Ukrainian is worse than useless, it will just annoy people": This is funny to compare this remark to comments in the question mathoverflow.net/q/175988/16178. –  Bruno Jul 14 '14 at 14:52
It happened more than once that the same result would get published more than once by the same author in different languages, as long as later publications mention the earlier ones; rumour has it Riesz did that regularly. Some authors published twice because of the contradictory needs for speedy publication for the priority and well-written thoughtful publication for the posterity. I don't think anybody would have a problem with including the proof of your lemma in the 1st English paper that has it. –  Michael Jul 14 '14 at 21:51

A possible solution is writing before your lemma a sentence like the following: "The following result is easy and probably already known, however we include a proof for the convenience of the reader."

-
Using this solution, if the referee really thinks the proof is straightforward she may suggest you don't include the proof: it gives you a second opinion on the matter. –  Benoît Kloeckner Sep 27 '14 at 7:27

One should distinguish between short, trivial and elementary proofs. Trivial proofs can be omitted with no harm. Omission of proof in the other two classes does seldom any good to the reader. In your shoes I would put full proof in the preprint on arXiv. It can be easily edited out in the published version.

-

On my opinion, the main criterion for a reference is that it must be AVAILABLE. Either on Internet or in most university libraries. An unpublished thesis in Ukrainian which is not available on Internet does not satisfy this criterion. Such a reference is meaningless.

So the real options are: a) to leave the proof to the reader or b) to include it. I do not understand why you call the second option "not very good". What's wrong with including a trivial lemma? A reader for whom it is trivial will just skip the proof.

PS. Why don't you scan your thesis and put in on Internet? Even in Ukrainian.

-

I would include the short proof, but also mention that the lemma appeared before.

-

If you use the word "trivial" in its usual meaning, then no proof is needed -- usually, "trivial" means "immediately obvious to any reader". But since you ask, it seems that you use the word in some other meaning -- perhaps in the meaning of "elementary", but this is only a guess. If this is so, then what I would do in this situation depends on the length of the proof, both in terms of pages as well as in terms of percentage of the total length of the paper, as well as on whether the lemma is needed in the proof of some key result of your paper or just in some example, etc.. If the proof does not make the paper significantly longer, or if it is not longer than one or two pages, I would certainly include it.

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Why are people so obsessed with papers as short as possible? Lengthy elementary proofs can be moved to the appendix, which can be omitted in the published version. Of course, boring the reader with obvious and burying the important under tedious is wrong, but please bear in mind that it is usually the case that what seems to be obvious to the author is often impenetrable (at first reading at least) for a reader. –  Vít Tuček Jul 14 '14 at 18:15
@VítTuček: I am talking about published journal articles, and space in printed journals is typically limited. -- Obviously you can provide any additional information you like on your personal homepage or on some preprint server like the arXiv etc. -- I didn't think anyone needs to be told about the latter. –  Stefan Kohl Jul 14 '14 at 20:01
I understand. I just think that the emphasis should be on dissemination of knowledge and not on making publisher happy. ;) –  Vít Tuček Jul 14 '14 at 20:14
@VítTuček Sadly some referees and editors want explanatory material removed... –  Yemon Choi Jul 14 '14 at 21:54


text:
# How to randomly extract some pages of a PDF file, sort their pages, and finally bundle them into a new PDF?

Some books in amazon.com have excerpts (first several pages plus appendixes) from which we can know their contents, layouts, etc roughly prior to purchasing. Statistically I think it will be better if an excerpt is made by extracting some pages (30-50 pages might be enough) of the corresponding book at random, sort their pages in increasing order, and finally bundle them in to a new PDF.

My question is: how to do it in LaTeX?

## Minimal Working Example

% compile with pdflatex -shell-escape
% =============================================================================================
\def\NoticeThatIAmUsingThisPackageToExtractSomePagesFromAnExternalPDFFileInMyComputer{pdfpages}
% =============================================================================================
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents*}{book.tex}
\documentclass{book}
\usepackage{blindtext}
\begin{document}
\Blinddocument
\end{document}
\end{filecontents*}

\immediate\write18{pdflatex book.tex}
\immediate\write18{pdflatex book.tex}

\usepackage{\NoticeThatIAmUsingThisPackageToExtractSomePagesFromAnExternalPDFFileInMyComputer}

\def\NumberOfPagesOfExcerpt{50}

\begin{document}

% do randomization, sorting and bundling here!
% \includepdf[pages=-]{book}
\end{document}

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It seems like pdfpages would be the way to go here. –  Matthew Leingang Apr 2 '13 at 4:05
You could use pdftk pdflabs.com/tools/pdftk-the-pdf-toolkit –  s0rce Apr 2 '13 at 4:31
Karl'sstudents: I think what @MatthewLeingang is saying that with the pdfpages package you can use something like \includepdf[pages={3,12,19,33,5}]{filename.pdf} etc to insert the desired pages from filename.pdf. So all you need is to randomly generate the page numbers and there are several solution on this site for generating random numbers. –  Peter Grill Apr 2 '13 at 5:03
@PeterGrill: That should be obvious if he parsed my MWE. :-) –  kiss my armpit Apr 2 '13 at 5:08
@Karl'sstudents: You should have made this more clear in the question then, not hiding it inside code. –  Martin Scharrer Apr 2 '13 at 9:34

A lualatex solution:

\documentclass{article}
\usepackage{luatextra}
\usepackage{filecontents}

\begin{filecontents*}{book.tex}
\documentclass{book}
\usepackage{blindtext}
\begin{document}
\Blinddocument
\end{document}
\end{filecontents*}

\begin{luacode}
function get_random_pages(randPages,totalPages, randSeed)
--[[--
Constructs a sorted list of randPages random page numbers within a range 1..totalPages
@Parameter: randPages
The number of random pages to extract
@Parameter: totalPages
Total number of pages in a pdf file
@Parameter: randSeed
Random seed
--]]--
local pagesLeft= {}
local pageList = {}
for pageNo=1, totalPages, 1 do
table.insert(pagesLeft,pageNo)
end

math.randomseed (randSeed)

local r
for i=1, randPages do
r=math.random(#pagesLeft)
table.insert(pageList,pagesLeft[r])
table.remove(pagesLeft,r)
end
table.sort(pageList)
local s="\\includepdf[pages={"
s=s..pageList[1]
for i=2, randPages do
s=s..","..pageList[i]
end
s=s.."}]{book}"
tex.print(s)
end
\end{luacode}

\immediate\write18{pdflatex book.tex}
\immediate\write18{pdflatex book.tex}

\usepackage{pdfpages}

\def\NumberOfPagesOfExcerpt{9}
\def\NumberOfPagesInPdf{17}
\def\randomSeed{27449}

\begin{document}

% do randomization, sorting and bundling here!
\directlua{get_random_pages(\NumberOfPagesOfExcerpt,\NumberOfPagesInPdf,\randomSeed)}

\end{document}

Process with lualatex -shell-escape random_pages.tex.

Edit:

• a standard table.concat function used as suggested by @Aditya,

• a command \randomPages defined with an optional random seed parameter,

• the number of pages in pdf is defined by means of pdftex primitives as in here.

random_pages.tex:

\documentclass{article}
\usepackage{luatextra}
\usepackage{filecontents}

\begin{filecontents*}{book.tex}
\documentclass{article}
\usepackage{geometry}
\geometry{
paperwidth=74mm,
paperheight=105mm,
margin=2em,
bottom=9ex,
}
\usepackage{blindtext}
\begin{document}
\Blinddocument
\end{document}
\end{filecontents*}

\begin{luacode}
function get_random_pages(randPages,totalPages, randSeed)
--[[--
Constructs a sorted list of randPages random page numbers within a range 1..totalPages
@Parameter: randPages
The number of random pages to extract
@Parameter: totalPages
Total number of pages in a pdf file
@Parameter: randSeed
Random seed: used only if >0
--]]--
local pagesLeft= {}
local pageList = {}
for pageNo=1, totalPages, 1 do
table.insert(pagesLeft,pageNo)
end
if randSeed>0 then math.randomseed(randSeed) end
local r
for i=1, math.min(randPages,totalPages) do
r=math.random(#pagesLeft)
table.insert(pageList,pagesLeft[r])
table.remove(pagesLeft,r)
end
table.sort(pageList)
local s="\\includepdf[pages={"
s=s..table.concat(pageList,",")
s=s.."}]{book}"
tex.print(s)
end
\end{luacode}

\immediate\write18{pdflatex book.tex}
\immediate\write18{pdflatex book.tex}

\usepackage{pdfpages}

\def\NumberOfPagesOfExcerpt{42}
\def\randomSeed{27449}

\makeatletter
\newcommand\@randomPages[3]{%
\pdfximage{#2}%
\def\NumberOfPagesInPdf{\the\pdflastximagepages}%
\directlua{get_random_pages(#1,\NumberOfPagesInPdf,#3)}%
}
\def\randomPages{%
\@ifnextchar[{\@with}{\@without}}%
\def\@with[#1]#2#3{%
\@randomPages{#2}{#3}{#1}%
}%
\def\@without#1#2{%
\@randomPages{#1}{#2}{0}%
}%
\makeatother

\begin{document}
% do randomization, sorting and bundling here!

%  \randomPages[\randomSeed]{10}{book.pdf} % supposed to produce a fixed set of pages every time
\randomPages{10}{book.pdf}         % supposed to produce a different set of pages every time

\end{document}

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You can use table.concat function to concat the table to a string. –  Aditya Apr 2 '13 at 7:55
@Aditya: You mean table.concat(pageList,",") ? Yes, thanks for the tip. The code just uses basic commands to make it easier to recode in some other language. –  g.kov Apr 2 '13 at 8:13

Here is a solution that written in ConTeXt Lua Documents. Modify the parameter filename and n appropriately (I'll post a version that uses command line parameters later).

Save this as filter.cld (note the extension!), and process using context filter.cld.

local random = math.random
local format = string.format

-- Sample n items out of m without replacement
function reservoirsample (n, m)
local sampledlist = {}
if n == 0 then return sampledlist end
for i = 1, m do
-- Take the first n samples
if i <= n then
sampledlist[i] = i
else
-- Randomly replace one sample
local j = random(i)
if j < n then
sampledlist[j] = i
end
end
end
table.sort(sampledlist)
return sampledlist
end

local filename="fonts-mkiv.pdf"
local n = 20

context.starttext()

-- Example taken from grph-inc.lua
local fig = figures.push { name = filename }
figures.identify()
figures.check()
local nofpages = fig.used.pages
figures.pop()

selected = reservoirsample(n, nofpages)

print(format("::: File %s has %d pages, selecting %d", filename, nofpages, n))
print(format("::: %s", table.concat(selected, ", ")))

for i = 1,#selected do
context.startTEXpage()
context.externalfigure( {filename}, {page=selected[i]} )
context.stopTEXpage()
end

context.stoptext()

-

Here is a solution that only uses the mathy and loopy bits of pgf. It borrows some code Mark Wibrow wrote on the pgf-users mailing list a while back for shuffling a pgfmath list. Lists in pgfmath are implemented with a hash, rather than a single token list.

To get a random list of k elements from the list {1,...,N}, I create the list {1,...,N} and knuth shuffle it. Then I bubble-sort the first k elements. Then for each i from 1 to k I include the i-th page of the PDF.

\documentclass{article}
\usepackage{pgf,pgffor}
\usepackage{pdfpages}

\makeatletter

% declare a list by its elements
% e.g., \pgfmathdeclarelist{mylist}{{foo}{bar}{baz}}
\def\pgfmathdeclarelist#1#2{%
\def\pgfmath@list@name{#1}%
\c@pgfmath@counta=0%
\pgfmath@declarelistlist#2{\pgfmath@stop}%
}%
\def\pgfmath@declarelistlist#1{%
\ifx#1\pgfmath@stop%
\expandafter\edef\csname pgfmath@list@\pgfmath@list@name @length\endcsname{\the\c@pgfmath@counta}%
\else%
\pgfutil@namedef{pgfmath@list@\pgfmath@list@name @\the\c@pgfmath@counta}{#1}%
\expandafter\pgfmath@declarelistlist%
\fi%
}

% get a list item
% \pgfmathgetlistitem{\cs}{mylist}{3} lets \cs be the 3rd item of mylist
\def\pgfmathgetlistitem#1#2#3{%
\expandafter\let\expandafter#1\expandafter=\csname pgfmath@list@#2@#3\endcsname%
}

% set a list item
% \pgfmathsetlistitem{mylist}{3}{foo} defines the 3rd item of mylist to be foo
% caution - you may need the 3rd argument expanded first.
\def\pgfmathsetlistitem#1#2#3{%
\pgfutil@namedef{pgfmath@list@#1@#2}{#3}%
}

% get the length of a list
% \pgfmathgetlistlength{\mylistlength}{mylist} lets \mylistlength be the length of the list.
\def\pgfmathgetlistlength#1#2{%
\expandafter\let\expandafter#1\expandafter=\csname pgfmath@list@#2@length\endcsname%
}

% set the length of a list
% \pgfmathsetlistlength{mylist}{length} defines the length of mylist to be length
\def\pgfmathsetlistlength#1#2{%
\expandafter\edef\csname pgfmath@list@#1@length\endcsname{#2}
}

\def\pgfmathknuthshuffle#1{%
\pgfmathgetlistlength\pgfmath@len{#1}%
\pgfmathloop%
\ifnum\pgfmathcounter>\pgfmath@len%
\else%
\pgfmathrandominteger\pgfmath@temp{1}{\pgfmath@len}%
\pgfmathgetlistitem\pgfmath@@temp{#1}{\pgfmathcounter}%
\pgfmathgetlistitem\pgfmath@@@temp{#1}{\pgfmath@temp}%
\def\pgfmath@marshal{\pgfmathsetlistitem{#1}}%
\expandafter\pgfmath@marshal\expandafter{\expandafter\pgfmath@temp\expandafter}\expandafter{\pgfmath@@temp}%
\expandafter\pgfmath@marshal\expandafter{\expandafter\pgfmathcounter\expandafter}\expandafter{\pgfmath@@@temp}%
\repeatpgfmathloop%
}

\def\NumberOfPagesOfExcerpt{9}
\def\NumberOfPagesInPdf{17}

% Populate page list. Rather than use \pgfmathdeclarelist we allocate the list and assign in a loop.
% sorry for the \global... pgf's \foreach creates a group.
\def\s@pagelist{pagelist} % makes expansion easier
\pgfmathsetlistlength{pagelist}{\NumberOfPagesInPdf}
\foreach \i in {1,...,\NumberOfPagesInPdf}{
\global\expandafter\pgfmathsetlistitem\expandafter\s@pagelist\expandafter\i\expandafter{\i}
}

\pgfmathknuthshuffle{pagelist}

% now a bubble sort on the first \NumberOfPagesOfExcerpt items in the list.
\pgfmathtruncatemacro{\n}{\NumberOfPagesOfExcerpt-1}
\foreach \j in {1,...,\n}{
\pgfmathtruncatemacro{\k}{\NumberOfPagesOfExcerpt-\j}
\foreach \i in {1,...,\k}{
\pgfmathtruncatemacro{\iplusone}{\i+1}
\pgfmathgetlistitem{\pagei}{pagelist}{\i}
\pgfmathgetlistitem{\pageiplusone}{pagelist}{\iplusone}
\ifnum\pagei>\pageiplusone
\global\expandafter\pgfmathsetlistitem\expandafter\s@pagelist\expandafter\i\expandafter{\pageiplusone}
\global\expandafter\pgfmathsetlistitem\expandafter\s@pagelist\expandafter\iplusone\expandafter{\pagei}
\fi
}
}

\makeatother

\begin{document}

\foreach \i in {1,...,\NumberOfPagesOfExcerpt}{
\pgfmathgetlistitem{\pagei}{pagelist}{\i}
\includepdf[pages=\pagei]{book.pdf}
}

\end{document}

As you can see, it's a bit messy, but it doesn't require lua or an external script. IANACS so I don't know how efficient it is, either. But if you wanted efficiency you wouldn't do this job in TeX. :-)

-

Calling an external randomizer named excerpting.exe from within LaTeX.

## LaTeX Code:

% compile with pdflatex -shell-escape
\documentclass{article}
\usepackage{pdfpages}
\def\bookfilename{status-lua}% http://chat.stackexchange.com/transcript/41?m=8712421#8712421
\def\take{30}
\def\seeder{1}
\def\auxiliaryfilename{random.txt}

\pdfximage{\bookfilename.pdf}
\immediate\write18{excerpting \the\pdflastximagepages\space \take\space \seeder\space \auxiliaryfilename}

\begin{document}
\loop
\includepdf[pages=\data]{\bookfilename}
\repeat
\end{document}

## C# (Fisher-Yates Shuffle):

// excerpting.cs
using System;
using System.IO;
using System.Linq;

namespace Excerpting
{
class Program
{
static void Main(string[] args)
{
int total = int.Parse(args[0]);
int take = int.Parse(args[1]);
int seeder = int.Parse(args[2]);
string filename = args[3];

int[] array = Enumerable.Range(1, total).ToArray();

Random random = new Random(seeder);
for (int i = total - 1; i > 0; i--)
{
int j = random.Next(i+1);
int temp = array[i];
array[i] = array[j];
array[j] = temp;
}

File.WriteAllLines(filename, array.Take(take).OrderBy(x => x).Select(x => x.ToString()));
}
}
}

## C# (Random Sort):

Someone claims that Random Sort has uniform distribution but I have not checked it yet.

// excerpting.cs
using System;
using System.IO;
using System.Linq;

namespace Excerpting
{
class Program
{
static void Main(string[] args)
{
int total = int.Parse(args[0]);
int take = int.Parse(args[1]);
int seeder = int.Parse(args[2]);
string filename = args[3];

Random random = new Random(seeder);
string[] array = Enumerable.Range(1, total)
.OrderBy(x => random.Next())
.Take(take)
.OrderBy(x => x)
.Select(x => x.ToString())
.ToArray();

File.WriteAllLines(filename, array);
}
}
}

-


text:
# fitrm

Fit repeated measures model

## Description

example

rm = fitrm(t,modelspec) returns a repeated measures model, specified by modelspec, fitted to the variables in the table or dataset array t.

example

rm = fitrm(t,modelspec,Name,Value) returns a repeated measures model, with additional options specified by one or more Name,Value pair arguments.

For example, you can specify the hypothesis for the within-subject factors.

## Examples

collapse all

The column vector species consists of iris flowers of three different species: setosa, versicolor, and virginica. The double matrix meas consists of four types of measurements on the flowers: the length and width of sepals and petals in centimeters, respectively.

Store the data in a table array.

t = table(species,meas(:,1),meas(:,2),meas(:,3),meas(:,4),...
'VariableNames',{'species','meas1','meas2','meas3','meas4'});
Meas = table([1 2 3 4]','VariableNames',{'Measurements'});

Fit a repeated measures model, where the measurements are the responses and the species is the predictor variable.

rm = fitrm(t,'meas1-meas4~species','WithinDesign',Meas)
rm =
RepeatedMeasuresModel with properties:

Between Subjects:
BetweenDesign: [150x5 table]
ResponseNames: {'meas1'  'meas2'  'meas3'  'meas4'}
BetweenFactorNames: {'species'}
BetweenModel: '1 + species'

Within Subjects:
WithinDesign: [4x1 table]
WithinFactorNames: {'Measurements'}
WithinModel: 'separatemeans'

Estimates:
Coefficients: [3x4 table]
Covariance: [4x4 table]

Display the coefficients.

rm.Coefficients
ans=3×4 table
meas1       meas2      meas3      meas4
________    ________    ______    ________

(Intercept)             5.8433      3.0573     3.758      1.1993
species_setosa        -0.83733     0.37067    -2.296    -0.95333
species_versicolor    0.092667    -0.28733     0.502     0.12667

fitrm uses the 'effects' contrasts which means that the coefficients sum to 0. The rm.DesignMatrix has one column of 1s for the intercept, and two other columns species_setosa and species_versicolor, which are as follows:

$\begin{array}{c}species_setosa=\left\{\begin{array}{ll}1& if\phantom{\rule{0.2777777777777778em}{0ex}}setosa\\ 0& if\phantom{\rule{0.2777777777777778em}{0ex}}versicolor\\ -1& if\phantom{\rule{0.2777777777777778em}{0ex}}virginica\end{array}\phantom{\rule{0.5em}{0ex}}\phantom{\rule{0.5em}{0ex}}and\phantom{\rule{0.5em}{0ex}}\phantom{\rule{0.5em}{0ex}}species_versicolor=\left\{\begin{array}{ll}0& if\phantom{\rule{0.2777777777777778em}{0ex}}setosa\\ 1& if\phantom{\rule{0.2777777777777778em}{0ex}}versicolor\\ -1& if\phantom{\rule{0.2777777777777778em}{0ex}}virginica\end{array}\end{array}$

Display the covariance matrix.

rm.Covariance
ans=4×4 table
meas1       meas2       meas3       meas4
________    ________    ________    ________

meas1     0.26501    0.092721     0.16751    0.038401
meas2    0.092721     0.11539    0.055244     0.03271
meas3     0.16751    0.055244     0.18519    0.042665
meas4    0.038401     0.03271    0.042665    0.041882

The matrix Y contains response data for 16 individuals. The response is the blood level of a drug measured at five time points (time = 0, 2, 4, 6, and 8). Each row of Y corresponds to an individual, and each column corresponds to a time point. The first eight subjects are female, and the second eight subjects are male. This is simulated data.

Define a variable that stores gender information.

Gender = ['F' 'F' 'F' 'F' 'F' 'F' 'F' 'F' 'M' 'M' 'M' 'M' 'M' 'M' 'M' 'M']';

Store the data in a proper table array format to conduct repeated measures analysis.

t = table(Gender,Y(:,1),Y(:,2),Y(:,3),Y(:,4),Y(:,5),...
'VariableNames',{'Gender','t0','t2','t4','t6','t8'});

Define the within-subjects variable.

Time = [0 2 4 6 8]';

Fit a repeated measures model, where blood levels are the responses and gender is the predictor variable. Also define the hypothesis for within-subject factors.

rm = fitrm(t,'t0-t8 ~ Gender','WithinDesign',Time,'WithinModel','orthogonalcontrasts')
rm =
RepeatedMeasuresModel with properties:

Between Subjects:
BetweenDesign: [16x6 table]
ResponseNames: {'t0'  't2'  't4'  't6'  't8'}
BetweenFactorNames: {'Gender'}
BetweenModel: '1 + Gender'

Within Subjects:
WithinDesign: [5x1 table]
WithinFactorNames: {'Time'}
WithinModel: 'orthogonalcontrasts'

Estimates:
Coefficients: [2x5 table]
Covariance: [5x5 table]

The table between includes the eight repeated measurements, y1 through y8, as responses and the between-subject factors Group, Gender, IQ, and Age. IQ and Age as continuous variables. The table within includes the within-subject factors w1 and w2.

Fit a repeated measures model, where age, IQ, group, and gender are the predictor variables, and the model includes the interaction effect of group and gender. Also define the within-subject factors.

rm = fitrm(between,'y1-y8 ~ Group*Gender+Age+IQ','WithinDesign',within)
rm =
RepeatedMeasuresModel with properties:

Between Subjects:
BetweenDesign: [30x12 table]
ResponseNames: {'y1'  'y2'  'y3'  'y4'  'y5'  'y6'  'y7'  'y8'}
BetweenFactorNames: {'Age'  'IQ'  'Group'  'Gender'}
BetweenModel: '1 + Age + IQ + Group*Gender'

Within Subjects:
WithinDesign: [8x2 table]
WithinFactorNames: {'w1'  'w2'}
WithinModel: 'separatemeans'

Estimates:
Coefficients: [8x8 table]
Covariance: [8x8 table]

Display the coefficients.

rm.Coefficients
ans=8×8 table
y1         y2         y3         y4          y5           y6         y7          y8
________    _______    _______    _______    _________    ________    _______    ________

(Intercept)                141.38     195.25     9.8663    -49.154       157.77     0.23762    -42.462      76.111
Age                       0.32042    -4.7672    -1.2748     0.6216      -1.0621     0.89927     1.2569    -0.38328
IQ                        -1.2671    -1.1653    0.05862     0.4288      -1.4518    -0.25501    0.22867    -0.72548
Group_A                   -1.2195    -9.6186     22.532     15.303       12.602      12.886     10.911      11.487
Group_B                    2.5186      1.417    -2.2501    0.50181       8.0907      3.1957     11.591      9.9188
Gender_Female              5.3957    -3.9719     8.5225     9.3403       6.0909       1.642    -2.1212      4.8063
Group_A:Gender_Female      4.1046     10.064    -7.3053    -3.3085       4.6751      2.4907     -4.325     -4.6057
Group_B:Gender_Female    -0.48486    -2.9202     1.1222    0.69715    -0.065945    0.079468     3.1832      6.5733

The display shows the coefficients for fitting the repeated measures as a function of the terms in the between-subjects model.

## Input Arguments

collapse all

Input data, which includes the values of the response variables and the between-subject factors to use as predictors in the repeated measures model, specified as a table.

The variable names in t must be valid MATLAB® identifiers. You can verify the variable names by using the isvarname function. If the variable names are not valid, then you can convert them by using the matlab.lang.makeValidName function.

Data Types: table

Formula for model specification, specified as a character vector or string scalar of the form 'y1-yk ~ terms'. The responses and terms are specified using Wilkinson notation. fitrm treats the variables used in model terms as categorical if they are categorical (nominal or ordinal), logical, character arrays, string arrays, or cell arrays of character vectors.

For example, if you have four repeated measures as responses and the factors x1, x2, and x3 as the predictor variables, then you can define a repeated measures model as follows.

Example: 'y1-y4 ~ x1 + x2 * x3'

### Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'WithinDesign','W','WithinModel','w1+w2' specifies the matrix w as the design matrix for within-subject factors, and the model for within-subject factors w1 and w2 is 'w1+w2'.

Design for within-subject factors, specified as the comma-separated pair consisting of 'WithinDesign' and one of the following:

• Numeric vector of length r, where r is the number of repeated measures.

In this case, fitrm treats the values in the vector as continuous, and these are typically time values.

• r-by-k numeric matrix of the values of the k within-subject factors, w1, w2, ..., wk.

In this case,fitrm treats all k variables as continuous.

• r-by-k table that contains the values of the k within-subject factors.

In this case, fitrm treats all numeric variables as continuous, and all categorical variables as categorical.

For example, if the table weeks contains the values of the within-subject factors, then you can define the design table as follows.

Example: 'WithinDesign',weeks

Data Types: single | double | table

Model specifying the within-subject hypothesis test, specified as the comma-separated pair consisting of 'WithinModel' and one of the following:

• 'separatemeans' — Compute a separate mean for each group.

• 'orthogonalcontrasts' — This is valid only when the within-subject model has a single numeric factor T. Responses are the average, the slope of centered T, and, in general, all orthogonal contrasts for a polynomial up to T^(p – 1), where p is the number if rows in the within-subject model.

• A character vector or string scalar that defines a model specification in the within-subject factors. You can define the model based on the rules for the terms in modelspec.

For example, if there are three within-subject factors w1, w2, and w3, then you can specify a model for the within-subject factors as follows.

Example: 'WithinModel','w1+w2+w2*w3'

Data Types: char | string

## Output Arguments

collapse all

Repeated measures model, returned as a RepeatedMeasuresModel object.

For properties and methods of this object, see RepeatedMeasuresModel.

collapse all

### Model Specification Using Wilkinson Notation

Wilkinson notation describes the factors present in models. It does not describe the multipliers (coefficients) of those factors.

The following rules specify the responses in modelspec.

Wilkinson NotationMeaning
Y1,Y2,Y3Specific list of variables
Y1-Y5All table variables from Y1 through Y5

The following rules specify terms in modelspec.

Wilkinson notationFactors in Standard Notation
1Constant (intercept) term
X^k, where k is a positive integerX, X2, ..., Xk
X1 + X2X1, X2
X1*X2X1, X2, X1*X2
X1:X2X1*X2 only
-X2Do not include X2
X1*X2 + X3X1, X2, X3, X1*X2
X1 + X2 + X3 + X1:X2X1, X2, X3, X1*X2
X1*X2*X3 - X1:X2:X3X1, X2, X3, X1*X2, X1*X3, X2*X3
X1*(X2 + X3)X1, X2, X3, X1*X2, X1*X3

Statistics and Machine Learning Toolbox™ notation always includes a constant term unless you explicitly remove the term using -1.


text:
Geometry And Topology

Download A survey of the spherical space form problem by J. F. Davis PDF

By J. F. Davis

ISBN-10: 3718602504

ISBN-13: 9783718602506

Similar geometry and topology books

Differential Topology: Proceedings of the Second Topology Symposium, held in Siegen, FRG, Jul. 27–Aug. 1, 1987

The most topics of the Siegen Topology Symposium are mirrored during this number of sixteen learn and expository papers. They focus on differential topology and, extra in particular, round linking phenomena in three, four and better dimensions, tangent fields, immersions and different vector package morphisms.

Homotopy theory of diagrams

During this paper we improve homotopy theoretical equipment for learning diagrams. specifically we clarify how one can build homotopy colimits and boundaries in an arbitrary version type. the foremost proposal we introduce is that of a version approximation. A version approximation of a class $\mathcal{C}$ with a given classification of vulnerable equivalences is a version class $\mathcal{M}$ including a couple of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which fulfill sure homes.

Additional info for A survey of the spherical space form problem

Sample text

To adequately sample all the features of a model, we employ a parametrization distortion metric based on stretch minimisation. We minimise this nonlinear metric each time a new vertex is introduced, by locally optimising its location and those of its immediate neighbours. 5, we also perform a global pass, optimising all vertices introduced so far. When optimising any vertex, we constrain it to the kernel of its neighbourhood, to prevent ﬂips. Degenerate triangles are prevented naturally by the stretch metric, which becomes inﬁnite in that case.

Embedded Image Coding Using Zerotrees of Wavelet Coeﬃcients. IEEE Transactions on Signal Processing, 41(12):3445–3462, 1993. 56. D. Shikhare, S. P. Mudur. Compression of Large 3D Engineering Models using Automatic Discovery of Repeating Geometric Features. In proceedings of 6th International Fall Workshop on Vision, Modeling and Visualization, 2001. 57. O. Sorkine, D. Cohen-Or, and S. Toldeo. High-Pass Quantization for Mesh Encoding. In Proc. of Eurographics Symposium on Geometry Processing, 2003.

Cowsar, and D. Dobkin. MAPS: Multiresolution adaptive parameterization of surfaces. Computer Graphics, 32(Annual Conference Series):95–104, August 1998. 26 Pierre Alliez and Craig Gotsman 45. E. Lee and H. Ko. Vertex Data Compression For Triangular Meshes. In Proc. Paciﬁc Graphics, pages 225–234, 2000. 46. H. Lee, P. Alliez, and M. Desbrun. Angle-Analyzer: A Triangle-Quad Mesh Codec. In Eurographics Conference Proceedings, pages 383–392, 2002. 47. M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D.


text:
# help prove Theorem 1.8 page 133 S.Burris H.P Sankappanavar

Printable View

• November 5th 2005, 06:58 AM
Mauroit
help prove Theorem 1.8 page 133 S.Burris H.P Sankappanavar
I need some help with the proof of Theorem 1.8 on page 133 of Stanley Burris and H.P. Sankappanavar: A Course in Universal Algebra.
• November 11th 2005, 05:25 PM
hpe
Quote:

Originally Posted by Mauroit
I need some help with the proof of Theorem 1.8 on page 133 of Stanley Burris and H.P. Sankappanavar: A Course in Universal Algebra.

Use the facts that $b \in B|a, \, c \in B|a'$.


text:
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Archived threads in /sci/ - Science & Math - 116. page
Images are sometimes not shown due to bandwidth/network issues. Refreshing the page usually helps.

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Is it a realistic solution of the fermi paradox to assume that all intelligent species develop life like virtual reality earlier than viable interstellar travel and therefor just stay on their home planet for ever playing the Gods in their comfortable computer simulations?
Because that seems the most plausible to me
>>
Is there some kind of quota being enforced that /sci/ needs at least 6 Fermi paradox threads per day?
>>
no that's fucking dumb

the actual explanation is that the universe is really really big and the chance of intelligent being near enough to contact us is very remote

even if they had light speed travel they wouldn't be able to reach us
>>
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>>8418827
>realistic solution of the fermi paradox

Attenuation is a fucking bitch.

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What is the thinking mans sport /sci/?

[You must have an IQ of 170 or greater to post in this thread.]
>>
videogames
>>
>>8418726
Bowls
>>
>>8418726
Me and my friends (Chemistry, engineering, and pure math) play tennis shittily

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What does /sci/ think about Mechanical Engineering?
>>
>>8418694
It is really wide.
You should specialize.
>>
>>8418694
Makes me feel hardcore.
>>
>>8418694

solidworks gets tiring after a while.

t. designer of turrets and enclosures for industrial artificial intelligences.

PS. Switched to CS. Considering switching to biz.

PPS. ME and EE was more interesting than CS IMO.

How much Trig is in Calc I? Do I need a Trig class beforehand? How much Calc is in Physics I? Will I need a Calc class beforehand? Sorry if this is a dumb question, my schools advisors have not helpful.
>>
>>8418663
If you know what a sine and a cosine is, you should be pretty much set. Why do Americans need an entire university class on trigonometry anyway? Shouldn't you be doing that in school?
>>
>>8418663
>How much Trig is in Calc I?
Not a whole bunch. So long as you have taken a pre-calc course you should be fine. Calc 2 on the other hand has a lot of trig, generally speaking.

If you're completely oblivious to calculus and your alegebra is so-so you it might serve you better to take calc 1 first, albeit the calc isnt that rigorous. But if your algebra is on point you could get by taking the two together.
>>
>>8418663
>Why do Americans need an entire university class on trigonometry anyway?

I have never heard of a school offering Trig as a seperate course in my school district in the US but i have heard about it before. I think it was originally a secondary track for those not able to do pre-calc and calc. Algebra 2 covers trig very briefly and in pre-calc you really get the full trig treatment. So, for those not taking pre-calc learning trig is really helpful for real world application.

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I tried to read the original article by Witten about the Witten effect. I realize that I had to pay 30 dollars for the article.
>Fuckthisshit.jpg
Find out about Sci Hub (arxiv has been my friend for too long!)
Find out about the "controversy" regarding the legitimacy of Sci Hub.
Some guy wrote "to steal is to steal."
Go to my article published on PRD. I realize I have to pay 25 dollars. Use Sci Hub to get my own article (it is on the arxiv, but I just wanted to see the "published" version.)

Am...
>>
>>8418660
Scientific journals should have been demonopolized long ago via the internet. Steal from those fuckers indiscriminately as much as you can!
>>
It's lining some middleman's pockets for sure. Same problem as academia.

You forget that people need houses and cars and lattes and caribbean vacations. That def costs 25 per article.
>>
>>8418665

>You forget that people need houses and cars and lattes and caribbean vacations. That def costs 25 per article.

>People that are not the scientist!

It will be amazing to see if Witten get's 10% from each of those 25. He might be rich without us knowing it!

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How do I know if the book that the professor requires is actually a good book for the subject and level of the course?
>>
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>>
>>8418422
Is that you?
>>
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>>8418425

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Is Pharmacy a meme? What do Pharmacists even do?
>>
>>8418403
afaik they pull prescriptions off of shelves and hand them to customers
>>
>>8418403
If you can, get an MD, do all the shit pharmacist do, but with more value. I'm mainly talking about general practitioner MDs.
>>
>>8418419
OP here. That's what I plan to do.

I was just wondering because...well, why do Pharmacists need as much training as a Doctor?

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https://arxiv.org/abs/1603.01482

>yfw the greatest leap in applied physics has gotten almost zero attention
>yfw this guy is going to revolutionize technology from computing to nuclear fusion and become a billionaire, but no one currently knows about him

Talk about keeping a low profile! The fuck is he waiting for? a public demonstration of these materials would make him into a living god. how hard is it to get your patents and trademarks straight? Could he be lying? but why?
>>
>>8418306
I want my flying car.
>>
>>8418306
He's either delusional or lying for attention.
>>
>>8418306
my EE prof mentioned this last week. very casually.

apparently the breakthrough research was basically inevitable, just a matter of time. no one is excited because everyone saw it coming.

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What made you pick your field? For example, I genuinely never understood people who study geography. What's the appeal of it?
>>
>>8418291

>geography

I dont know why i like it. I remember as a kid i could memorize all the countries, rivers, oceans, islands and cities. It helped me win 4th in the state geography bee in 6th grade. I still don't understand how i could this and yet be a utter failure at all other subjects (SS i do well in, Chemistry as well). I was diagnosed with Autism a few years ago and the psych told me autistic people are naturally drawn to memorizing random things. For some its numbers or...
>>
>>8418327
Fix yourself dumbass.
>>
>>8418327
>Geography and history students are autists
Well, that settles it.

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According to the multiverse theory, there are infinite amount of parallel universes with infinite amount of possible outcomes and variatons. I deduce from this that there should be an universe, that at this exact moment of time, would open a wormhole to ours' and destroy all of existence. If the theory truly is true, then why isn't this happening.
>>
>>8418275
>moment of time
>i deduce
>wormhole

paging highschool principal, one of your students is posting on 4chan from a school computer again
>>
>>8418282
prome me wrong
>>
Maybe it is indeed happening, but there would also be another universe where that is not happening, which is the one we will continue to exist in, according to the anthropic principle.

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What do you study and where are you in those studies?

>Age
>Field(s) of Interest
>Years in field/Relevant Degrees
>Notable Accomplishments
>>
21
Electrical Engineering
3, working on B.S.
>Nothing notable
>>
>>8418270
34
Around 27 years now
>>
>>8418270
>18
>Computational Mathematics in general, inspired by Wildberger. Specifically algebra.
>1
>Got perfect As in my first semester and I got a job as a programmer before even turning 18.

T-that is notable right?

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>it took andrew wiles 7 years to prove fermat's last theorem
>fermat did it in one sitting

top kek
>>
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where's the proof kiddo?
>>
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>>8418201
Rekt OP.
You must be analblasted now.
>>
>I would write the proof of they're was enough space
Fermat shitposting before it was kewl xDd

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If evolution is real, then why do suicidal people exist?

If they kill themselves, they are less likely to pass the suicidal genes into further generations.
>>
>>8418180
>suicidal genes
I hope you kill yourself so you don't pass on your mental retardation genes.
>>
If evolution is real, then why do weaboos exist?

If they are permavirgins, they are less likely to pass the weaboo genes into further generations.
>>
>>8418180

one can exhibit the will to survive through fierce adversity wouldn't you agree? It is rather logical/instinctive.
There's a flip side to that coin that will always be there I believe, even if you don't want to see it.

We like to talk about heroes and leaders, which are prime example of survival instincts taken to the extreme.
This would make no sense without the other end of the line. Each segment in time/space has two ends, humans are no exception

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When you see it..
>>
>>8417957
Shit brix
>>
>>8417957
>that dick on Bezos' chest
More like Blow Orifice amirite
>>
>>8417962
Yeah

I understand rockets are all vaguely phallic

But they literally drew a fucking dildo on their logo instead of a spaceship

What the fuck?

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If you're doing scientific computing, post which programming languages you know and the type of work you do.

I want to learn a language for scientific computing. So far, my computational experience has been with computational packages and I want to move on to making my own programs. I've had experience working with FORTRAN for simple Newtonian modeling and I know how to use Matlab (which isn't really useful for fast number crunching iirc).

I'm already familiar with Linux and computing clusters. Just the language.
>>
There's this one programming language but i forgot what it is...it's like snake or something
>>
>>8418599
>computing clusters
Python? ;)
>>
>>8418599
Cobra? Anaconda? Adder? No idea what you're on about I don't think there's any language with a snake.

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I don't understand many worlds

Lets say you have a universe consisting of 2 binary bits, the binary bits, a split based on whether or not a bit changes, and in this universe, it always happens in the order from left to right. There's a 3rd binary l/r that simply represents if it is the left or the right bit's turn to change

So the base universe
00 l

splits into
10 r
00 r

splits into
11 l
10 l
-
01 l
00 l

Splits into
11 r
10 r
-
01 r
00 r
--
01 r
00 r
-
11 r
10 r

Is...
>>
>multiverse
>>>/x/
>>
>>8417818
t. brainlet
>>
>>8417815
I'm confused, how does 00 l become 00 r if the left bit hasn't changed?

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Trying to wrap my head around the Wang's carpets and the theory of neutron mouths being wormholes.

Also can someone explain spin to me?
>A fermion needed two full rotations, 720 degrees to come back into phase.
Having trouble visualizing this.
>>
By the first rotation, it wasn't a fermion anymore, by the second rotation it turned back into one. How about throwing a knife, what are the chances the pointy end will hit the wall?

I don't know about that second part though, but it makes me think about somewhere i read all electrons are the same, single electron, being bounced around at a crazy speed.
>>
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>>8417731
>A fermion needed two full rotations, 720 degrees to come back into phase.
Think of fermions as being connected to the world with thin invisible ribbons that cant pass thru each other. rotating the fermion 360deg will give those ribbons a twist. This twist cant be undone unless you rotate the fermion back. Now rotate the fermion 720deg, the double twists in the ribbons can now be undone without any rotations.

Follow this gif and you can see how it goes back to its original state...
>>
>>8417742
>>8417750

Thank you. But what do the twisting ribbons represent in the real world?

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Is Kurzgesagt a good youtube channel or is it popsci bullshit? I want your opinions.
>>
Leave.
>>
>>8417703
Watch potholer54 videos.
You will never need to ask anyone if something is scientifically reliable enough ever again.
>>
>>8417758
>>>/pol/

298 KB,
>it's a "draw loads of tedious graphs by hand" assignment
>>
Same here senpai lmao ecks dee
>>
>>8417704
>>8417681
ahahah hahaha hahahha hah hahah hahahahhaha ha hahahah hahahah hahahahahahhah hahahahah hahah I llive for this hahahah ah ahahah ahaa
>>
>it's a "evaluate 250 limits but don't use L'Hopitals rule" assignment

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Hmmmm
>>
>>8417551
Look at Africa
>>
>>8417551
africa+genocide
>>
>>8417551
Just because some of a particular organism evolved doesn't mean that all of them have to evolve aswell.

For instance, look at bacteria. Bacteria exposed to antibiotics multiple times usually become resistant while bacteria of the same species in areas that don't commonly use antibiotics don't have the resistance.

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What are the most intelligent/mentally challenging trades in the military? I want to join, but don't want to have a muscle for a brain.
>>
IT maybe.
>>
fields that take only brass
>core of engineers
>medical corps
>public health service
>>
A friend of a friend of mine was a technician or whatever it's called on a nuclear submarine (not an engineer with an engineering degree.) Basically he was the guy who was in charge of making sure the reactor didn't blow up.

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What's the point in science when Ivy league frat bros will always shit on you and benefit off the fruits of your labor?

The guy who invented lipitor made billions for pfizer then got FIRED.

The MBA middle manager fucks take your research and knowledge then make fortunes off it. Even if you become a tenured professor you're probably making your university millions and millions while seeing 200k tops, while the football coach of the university is getting paid 10 million a year.

Being a scientist is basically "work like a dog for next to nothing...
>>
>>8417321
>What's the point in science when you don't make money?
Figuring things out. If you think this is about money then you're suffering from a very serious misconception. Money is not the same thing as value. Most rich people, like most people, are hollow idiots. Money has very little to do with "value". If you want to be Kim Kardashian then you should definitely not pursue science or math.
>>
Oh, you sweet summer child...

Your main concern shouldn't be getting milked by Chad. You'll be lucky to even make it that far. You should be worried about even getting your foot in the door without being backstabbed by dozens of other highly qualified scientists who will try to steal your work.
>>
>>8417321
>while seeing 200k tops
>only 200k
if you did science to get rich you are retarded, regardless beyond like 85-90k happiness from money plateaus

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Calculus would be an obvious example. What else?
>>
Statistics, linear algebra, differential equations for sure
>>
>>8417292
algebraic topology so that you can understand phase transitions in exotic states of matter
you're not a real physicist without it
>>
>>8417292
Linear algebra/functional analysis are kind of "in disguise" in intro QM/Q-chem
Those also use some basic results from group theory to simplify calculations
Relativity requires an acquaintance with manifolds and tensor analysis

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Any mathematicians starting to wonder if math is better left as a hobby and not as a career?

I mean the rabbit hole has gone so deep that most people publishing "new" mathematics don't really have any idea why its useful, what it means or why we should even care.

I'm facing this dilemma as I decide on graduate school, I have done "graduate" real analysis and its cool, same with topology - I read them for fun and I like it a lot but once you start reading research papers it sort of feels like a game without a goal and to be stuck doing...
>>
>>8417140

You're pretty much right. I'd advise against pure math graduate school unless you live, breathe, and shit $(\infty,1)$ TFQT topoi (or whatever esoteric object of study is relevant to your interests). Consider applied math or statistics if you want to go to grad school.
>>
>>8417200

applied math is shit. 'look at these graphs for 5 hours and tell me what to do"

great for easy money if you're good at that type of thing, but if you have any kind of passion for math besides some autistic need for number crunching then that kind of job seems kind of boring.
>>
>>8417200
Physics is cool too.

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Can we ban it already? Infinities do not exist in nature and it leads to completely preposterous results like the Riemann rearrangement theorem. It's a goddamn mess.
>>
Infinity does not apply to our real universe so it can't apply in everyday applications but we need it in order to prove mathematical theorems. Ya feel?
>>
>>8427639
Not op but yes that exactly right!
>>
>>8427639
this

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How can we fix this?
>>
>>8417099
Stop over analyzing things
>>
>>8417099
This video has to be faked somehow, but it does show how retarded these word problems are in common core. Students just look for keywords and translate the problem back into a simple math question. Rarely are they given a vague problem with multiple avenues of attack.
>>
>>8417099
I figure a big part of it is conditioning from being attacked when they say they don't know or understand something. Politicians have this issue all the time where they think they have to be omniscient and if they don't know something they should just fill in the gaps with made up evidence. The stigma on not knowing things has to stop and people need to know that it's okay to ask questions when they don't understand something. For example instead of saying global warming is a hoax by the Chinese...

File: reeeewe.jpg (249 KB, 735x1306) Image search: [iqdb] [SauceNao] [Google]
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post pic of what you are currently doing and guess the specific topic of others
>>
File: IMG_6623.jpg (1 MB, 3264x2448) Image search: [iqdb] [SauceNao] [Google]
1 MB, 3264x2448
>>8416947

Looks like electromagnetics

My turn. This should be easy
>>
>>8417014
analog circuits; transistor stuff?
>>
Working on a lab report for my biochem lab, lowkey fucked up and didn't have a chance to really work on it until tonight. Probably going to be around 20ish pages.

My TA didn't post a picture of one of my gels like she was supposed to and I emailed her days ago about it and she never responded back to me or posted it on our course site... I'm going to be pissed if they take off points for not having it. Probably just going to use someone else's picture to be safe and just site it and mention somewhere that it was never posted.

File: imgres.jpg (5 KB, 321x157) Image search: [iqdb] [SauceNao] [Google]
5 KB,
1. The Government Lies (Remember the Dress incident? With the gooey stuff?)

It's well known that the government lies, murders and steals in order to keep in control of the population. It doesn't take a rocket scientist to know that JFK's head did not explode backwards caused by a bullet coming from the book depository. So if the government would murder the president and cover it up... why wouldn't they lie about other stuff?
2. NASA has been caught manipulating images and evidence before

http://www.spaceref.com/news/viewpr.html?pid=30000

http://www.news.com.au/technology/conspiracy-theorists-confident-photoshopped-nasa-image-is-a-cover-up/story-e6frfro0-1225936084529

Once...
>>
File: pepeclever.jpg (6 KB, 186x272) Image search: [iqdb] [SauceNao] [Google]
6 KB, 186x272
>>8416620
Finally someone who brings fourth a clever discussion on the big debate on "Flath Eath Theory"! People like you who make their own research and questions this mad society we live in a too few.
>>
Finally someone with good points! critical thinking is the way to go, wake up sheeple
>>
>>8416620
Bump for the burn, I want to see /sci/ unleash its power level.

File: Pepe Asian.jpg (177 KB, 800x820) Image search: [iqdb] [SauceNao] [Google]
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Unless you've taken post-graduate mathematics you are a brainlet.

Prove me wrong.

>protip: you cant.
>>
In my university "theory of computation" is a post-graduate course for mathematicians. I'm a CS guy so I obviously completed an equivalent course for my bachelor's degree. So I've taken "post-graduate mathematics".

>>
aim sorri foor distoorbing u dis fine mornink becoose aim a brainlett
>>
So that's what this board's all about?

File: _20161014_212642.jpg (61 KB, 553x351) Image search: [iqdb] [SauceNao] [Google]
61 KB,
Why do dogs look more human than chimps?

their eyes, faces, expressions are so human-like
>>
It's not dogs that look like humans. It's you that looks like a dog.
>>
>>8416411
Because dogs are the most philosophical animal. A dog doesn't like what it doesn't know and likes what it knows. So it he likes and dislikes by the test of knowledge and ignorance, which is the definition of a philosopher. Philosophers are humans of course, so dogs are more like humans than they are like chimps.
>>
>>8416417
I bet you look like curious george :^)

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text:
Back to all tutorials

# Marine Propeller - CFD Simulation SimFlow Tutorial

## 1. Create Case

We will start the simulation by creating a new case named propeller

1. Go to panel

2. Provide name propeller

3. Click

## 2. Import Geometry - Propeller

1. Click

2. Select geometry file propeller.stl.gz

3. Click

## 3. Imported Geometry Units

The STL format does not contain the unit information which are defined during the geometry export. If we do not know the exported unit, we can estimate it based on the total size of the model. It is displayed next to Geometry size label. In our case, the default unit meter is correct.

1. To confirm default unit meter, press

## 4. Propeller Geometry

After importing geometry, it will appear in the 3D window.

1. Click to zoom the geometry

## 5. Domain Boundary

We need to create a cylindrical boundary for the domain. For this purpose, we will create a cylindrical geometry for later use in the meshing process.

1. Click Create Cylinder

2. Rename cylinder_1 to external
(double click on the name to rename it, press enter to apply)

3. Click Properties button if properties panel is not displayed

4. Set origin, axis, and length of the cylinder accordingly
Origin $${\sf [m]}$$-1e-0300
Axis $${\sf [-]}$$100
Length $${\sf [m]}$$1.502

## 6. Refinement Area (I)

To better resolve the flow near the propeller, we will create an area with a higher mesh resolution. To do this, we will create a new geometry by copying settings from external geometry.

1. Click Options of the external geometry

2. Select Duplicate option

## 7. Refinement Area (II)

1. Click Properties if they are not displayed

2. Rename external_1 to refine

3. Set radius of the refinement geometry

Radius $${\sf [m]}$$0.3

## 8. Display Geometries

In order to see all geometries, we will decrease the opacity of the external and refine.

1. Select external

2. Click Display Properties

4. Adjust opacity to 50% for refine geometry by repeating previous steps

## 9. Meshing Parameters - External

1. Go to Hex Meshing panel

2. Enable Mesh Geometry on external geometry

## 10. Meshing Parameters - Propeller

1. Select propeller geometry

2. Enable Mesh Geometry

3. Enable Create Boundary Layer Mesh

4. Set Refinement to Min 3 Max 4

## 11. Meshing Parameters - Refine

We want to create refinement in the area along the propeller induced flow.

1. Select refine geometry

2. Enable Mesh Geometry

3. Set refinement Level to 2

## 12. Base Mesh

We want to create a mesh of only one blade of the propeller. For this purpose, we will create a base mesh covering only one-fourth of the geometry.

1. Go to the Base tab

2. Define base mesh minimum and maximum extend
Min $${\sf [m]}$$000
Max $${\sf [m]}$$1.511

3. Define Division along each axis
Division302020

## 13. Base Mesh Boundaries

1. 2 Define boundary names accordingly
X- inlet
X+ outlet
Y- right

_Z-_ _left_

## 14. Material Point

Now we will define material point outside the propeller geometry.

1. Go to Point tab

2. Set location of the material point
Material Point0.50.50.5

## 15. Start Meshing Process

1. Go to Mesh tab

2. Start the meshing process with button

## 16. Mesh

After a few minutes of meshing the following mesh should appear.

## 17. Boundary Types

After creating the mesh, we have to set proper boundary types.

1. Go to Mesh panel

2. Change the boundary type of the external geometry to patch

3. Make sure you have appropriate boundary types selected

## 18. Boundary Interface (I)

As we will be simulating only one blade of the propeller we have to create a boundary interface to make the model periodic.

1. Hold CTRL key and select left and right boundary

2. Click Create Arbitrary Interface between left and right boundary

## 19. Boundary Interface (II)

1. Expand the interface properties

2. Change Transform type to Rotational

3. Define Rotation Axis
Rotation Axis100

## 20. Select Solver - SIMPLE

For the simulation of a marine propeller, we will use a steady-state incompressible simpleFoam solver.

1. Go to Setup panel

2. Enable filter

3. Enable flow filter

4. Pick SIMPLE (simpleFoam) solver

5. Click button to choose the solver

## 21. Turbulence Model

For the purpose of this tutorial we will simulate the turbulence phenomenon using $$Realizable \; k{-} \varepsilon$$ model.

1. Go to Turbulence panel

2. Select RANS modeling

3. Select $$Realizable \; k{-} \varepsilon$$ turbulence model

## 22. Water Properties

1. Go to Transport Properties panel

2. Define kinematic viscosity of water

$$\nu$$ $${\sf [m^2/s]}$$1e-06

Note that you do not have to define density. The equations that describe single phase incompressible flow operates on a kinematic pressure(pressure divided by reference density). Therefore, the density property does not explicitly appear and you have to remember to multiply resulting pressure and forces by the density value to obtain a physical results.

## 23. Cell Zones for MRF (I)

To be able to model propeller rotation, we will take advantage of a rotating reference frame. This technique will allow modeling the propeller rotation without a need to rotate the mesh. The rotating reference frame can only be applied to a sub-region of the mesh defined by a cell zone object (a list of mesh cells). Therefore, we will first create a cell zone.

1. Go to Mesh panel

2. Expand list of options form the default region

## 24. Cell Zones for MRF (II)

For the purpose of this tutorial we will use the whole mesh as the rotating zone. To do this we need to create the cell zone inside the external geometry.

1. Select external geometry

2. Click

## 25. Rotating Reference Frame

1. Go to Cell Zones panel

2. Enable Rotating Reference Frame for external zone

3. Define Axis of the propeller
Axis-100

4. Select boundaries that will not be defined in the rotating frame of reference
Static Boundaries:
external
inlet
left
outlet
right

## 26. Boundary Conditions - External (Turbulence)

1. Go to Boundary Conditions panel

2. Select external boundary

3. Select Turbulence tab

4. Set Turbulence Intensity to 1e-02

## 27. Boundary Conditions - Inlet

We will use the same boundary conditions for inlet and external boundaries, to achieve this we can copy settings from the external boundary to inlet.

1. Make sure you have selected the external boundary

2. Click Copy Boundary Conditions

3. Select inlet boundary

4. Click

## 28. Boundary Conditions - Outlet

1. Change outlet character to Outflow

## 29. Monitor Forces

We want to monitor solution progress by observing force coefficients.

1. Go to Monitors panel

2. Select Forces tab

3. Expand Monitored Boundaries list

4. Select propeller boundary

## 30. Run - Time Control

1. Go to Run panel

2. Set Number of Iterations to 1000

## 31. Run - CPU

To speed up the calculation process increase the number of CPUs basing on your PC capability. The free version allows you to use only 2 processors in parallel mode. To get the full version, you can use the contact form to Request 30-day Trial

Estimated computation time for 2 processors: 10 minutes

1. Switch to CPU tab

2. Use parallel mode

3. Increase the Number of processors

4. Click button

## 32. Monitor Solution - Force

Check if solution converges by observing stabilization of forces on the propeller boundary.

1. Click on Forces tab to display Force Monitor

When a simulation is finished, we want to calculate additional solution field to be used in postprocessing.

1. Go to Calculate panel

2. Select Q Criterion field

3. the field

Please Note: After clicking the Calculate button, SimFlow will calculate the new flow variable, which will be stored in your project folder and will be accessible in the ParaView.

## 34. Start Postprocessing with ParaView

1. Go to Postprocessing panel

2. Run ParaView

## 35. ParaView - Load Results

1. Click Last Frame to select the last result set

2. Click to load results into ParaView

3. After loading results they will be shown in the 3D graphic window

## 36. ParaView - Display Q Contour (I)

To show the propeller we will create now a contour.

1. Make sure you have your case selected

2. Click Contour

## 37. ParaView - Display Q Contour (II)

1. Set Contour by to Q

2. Set contour range to  500  and click enter
(double click to edit visible value)

3. Click to create new contour

4. After applying changes the contour will be shown in the 3D window

## 38. ParaView - Show Full Propeller (I)

As you can see there is only a quarter of the propeller visible and we would like to show the full geometry. In order to do that we have to duplicate and transform a partial propeller.

1. Make sure you have Contour1 selected

2. From the Sources Menu select Search option to open a search window

3. Start typing the word transform

4. Select Transform option

5. Make sure you have Transform1 selected

6. Define 90 degree rotation about the X axis and click enter

7. Click 2 times to create transformation

## 39. ParaView - Show Full Propeller (II)

We have to repeat the previous step to make another transformation - Transorm1 → Transform2

1. Make sure you have Transform1 selected

2. From the Sources Menu select Search option to open a search window

3. Start typing the word transform

4. Select Transform option

5. Make sure you have Transform2 selected

6. Define 90 degree rotation about the X axis and click enter

7. Click 2 times to create transformation

## 40. ParaView - Show Full Propeller (III)

We have to repeat the previous step to make another transformation - Transorm2 → Transform3

1. Make sure you have Transform2 selected

2. From the Sources Menu select Search option to open a search window

3. Start typing the word transform

4. Select Transform option

5. Make sure you have Transform3 selected

6. Define 90 degree rotation about the X axis and click enter

7. Click 2 times to create transformation

## 41. Display Full Propeller

To make the full geometry visible, we have to change the visibility of all geometries

1. Make sure the contour and all its transformations are visible

2. Select Contour1

3. Choose pressure p from the coloring list

4. Click Toggle Color Legend Visibility and choose Blue to Red Rainbow

## 42. Final Results

In the 3D view the contour of full propeller should appear


text:
Thursday
August 21, 2014

# Homework Help: Pre-calculus

Posted by Anonymous on Sunday, May 12, 2013 at 8:55pm.

Given that alpha=(14pi/3) what is the least positive angle coterminal with alpha?

• Pre-calculus - Reiny, Sunday, May 12, 2013 at 10:38pm

14π/3 = 4π + 2π/3

So it would be 2π/3

( you have 2 complete rotations + 2π/3)

 First Name: School Subject: Answer:

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