text:
## terça-feira, 16 de outubro de 2012

### RSA (algorithm)

RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem. RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman, who first publicly described it in 1977. Clifford Cocks, an English mathematician, had developed an equivalent system in 1973, but it wasn't classified until 1997. A user of RSA creates and then publishes the product of two large prime numbers, along with an auxiliary value, as their public key. The prime factors must be kept secret. Anyone can use the public key to encrypt a message, but with currently published methods, if the public key is large enough, only someone with knowledge of the prime factors can feasibly decode the message.[1] Whether breaking RSA encryption is as hard as factoring is an open question known as the RSA problem.

The RSA algorithm involves three steps: key generation, encryption and decryption.

A working example

Here is an example of RSA encryption and decryption. The parameters used here are artificially small, but one can also use OpenSSL to generate and examine a real keypair.
1. Choose two distinct prime numbers, such as
$p = 61$ and $q = 53$.
2. Compute $n = p q$ giving
$n = 61 \times 53 = 3233$.
3. Compute the totient of the product as $\phi(n) = (p-1)(q-1)$ giving
$\phi(3233) = (61 - 1)(53 - 1) = 3120$.
4. Choose any number $1 < e < 3120$ that is coprime to 3120. Choosing a prime number for $e$ leaves us only to check that $e$ is not a divisor of 3120.
Let $e = 17$.
5. Compute $d$, the modular multiplicative inverse of $e\text{ (mod }\phi(n)\text{)}$ yielding
$d = 2753$.
The public key is ($n = 3233$, $e = 17$). For a padded plaintext message $m$, the encryption function is $m^{17}\text{ (mod }3233\text{)}$.
The private key is ($n = 3233$, $d = 2753$). For an encrypted ciphertext $c$, the decryption function is $c^{2753}\text{ (mod }3233\text{)}$.
For instance, in order to encrypt $m = 65$, we calculate
$c = 65^{17}\text{ (mod }3233\text{)} = 2790$.
To decrypt $c = 2790$, we calculate
$m = 2790^{2753}\text{ (mod }3233\text{)} = 65$.

Source: http://en.wikipedia.org/wiki/RSA_(algorithm) access in 16-october 2012

public class RSACSPSample

{

public static void Main()

{

try

{

//Create a UnicodeEncoder to convert between byte array and string.

UnicodeEncoding ByteConverter = new UnicodeEncoding();

//Create byte arrays to hold original, encrypted, and decrypted data.

byte[] dataToEncrypt = ByteConverter.GetBytes("Data to Encrypt");

byte[] encryptedData;

byte[] decryptedData;

//Create a new instance of RSACryptoServiceProvider to generate

//public and private key data.

using (RSACryptoServiceProvider RSA = new RSACryptoServiceProvider())

{

//Pass the data to ENCRYPT, the public key information

//(using RSACryptoServiceProvider.ExportParameters(false),

//and a boolean flag specifying no OAEP padding.

encryptedData = RSAEncrypt(dataToEncrypt, RSA.ExportParameters(
false), false);

//Pass the data to DECRYPT, the private key information

//(using RSACryptoServiceProvider.ExportParameters(true),

//and a boolean flag specifying no OAEP padding.

true), false);

//Display the decrypted plaintext to the console.

Console.WriteLine("Decrypted plaintext: {0}", ByteConverter.GetString(decryptedData));

}

}

catch (ArgumentNullException)

{

//Catch this exception in case the encryption did

//not succeed.

Console.WriteLine("Encryption failed.");

}

}

static public byte[] RSAEncrypt(byte[] DataToEncrypt, RSAParameters RSAKeyInfo, bool DoOAEPPadding)

{

try

{

byte[] encryptedData;

//Create a new instance of RSACryptoServiceProvider.

using (RSACryptoServiceProvider RSA = new RSACryptoServiceProvider())

{

//Import the RSA Key information. This only needs

//toinclude the public key information.

RSA.ImportParameters(RSAKeyInfo);

//Encrypt the passed byte array and specify OAEP padding.

//OAEP padding is only available on Microsoft Windows XP or

//later.

}

return encryptedData;

}

//Catch and display a CryptographicException

//to the console.

catch (CryptographicException e)

{

Console.WriteLine(e.Message);

return null;

}

}

{

try

{

byte[] decryptedData;

//Create a new instance of RSACryptoServiceProvider.

using (RSACryptoServiceProvider RSA = new RSACryptoServiceProvider())

{

//Import the RSA Key information. This needs

//to include the private key information.

RSA.ImportParameters(RSAKeyInfo);

//Decrypt the passed byte array and specify OAEP padding.

//OAEP padding is only available on Microsoft Windows XP or

//later.

}

return decryptedData;

}

//Catch and display a CryptographicException

//to the console.

catch (CryptographicException e)

{

Console.WriteLine(e.ToString());

return null;

Postar um comentário


text:
# Is it possible for me to derive Avogadro's number?

To my understanding the mole is the unit used to translate between mass on the atomic level and mass in the macro level, defined as the number of atoms in $12$ grams of Carbon-$12$, which apparently turns out to be $\pu{6.0221409e23}$ atoms, and this was defined as Avogadro's Number.

How was this number derived? Is it something I can derive myself? If I had $12$ grams of Carbon-$12$, how would I be able to deduce that it had $\pu{6.0221409e23}$ atoms?

• It would be hard, very hard. I'll point out that there is a gigantic different in stating that $N_A \approx 6.022 \times 10^{23}$ and stating that $N_A = 6.0221409\times 10^{23}$. Determining a value to eight significant figures requires extremely good experimental technique.
– MaxW
Jul 13 '18 at 3:29
• @MaxW How did Avogadro do it in his time, to whatever degree of precision that he did? Jul 13 '18 at 3:48
• This information is readily available on the web in sources such as Wikipedia. en.wikipedia.org/wiki/Avogadro_constant, "By dividing the charge on a mole of electrons by the charge on a single electron..." Look up Millikan oild rop experiment for charge of e-, Faraday and electrolysis for atomic mass/charge ratio etc. Jul 13 '18 at 4:36
• @DrMoishePippik What is interesting to me is that apparently the oil drop experiment gave an answer that was technically wrong / inaccurate, but we still used it anyway to derive all these other numbers? Jul 13 '18 at 4:43
• It's been refined over time. As @MaxW states, original values had a very large margin of error. It's like Galileo using a chandelier as a clock... instrumentation has improved since then. Jul 13 '18 at 5:09

To determine Avogadro's number you have to measure the same unit at the atomic and macroscopic scales.

This was first achieved by Millikan who measured the charge of an electron. The charge of one mole of electrons was already known and is a Faraday. Dividing both, you get Avogadro's number.

Before that, Josef Loschmidt was the first one to calculate the number of particles in a cubic meter of gas, using the kinetic theory of gases. This is, of course, also related to Avogadro's number. Avogadro himself did not give any number. He just stated that equal volumes of different gases at the same pressure and temperature have equal amount of particles.

A more modern way of doing it is determining the density of an ultra pure element and then determine the number of atoms and their distances in a unit cell with X-ray diffraction.

So yes, you could, in principle, derive Avogadro's number with pure monocrystalline carbon 12. You will, however, need very good instrumentation.

As per the answer to this question on Chemistry SE it might become the other way round. The Avogadro number will be absolute (defined, with 0 error) and then the kilogram will be redefined as a function of the number of atoms in a monocrystalline perfect $\ce{^{28}Si}$ sphere.

format: plain


text:
# What Collider should I use for my Player object?

I am making a 3rd person game with a simple orbit cam and it works fine most of the time, but since I have a box collider and I walk across an uneven surface, the player tends to tip over. How should I set it up so the player would not tip over anymore?

You should use a capsule collider, because it doesn't have edges and works great and also you could apply some constraints in the Rigidbody. It's common to apply.


text:
Purest Vantage D Mannose: Cranberry & Dandelion Extract For UTI?

on

D Mannose by Purest Vantage is a supplement that consumers can use to help them eliminate toxins and other impurities in their body for a healthier liver and urinary function. The remedy is available as a one-time purchase, but consumers can order multiple bottles at once or enroll in a subscription to save some money.

What Is Purest Vantage D Mannose?

Taking care of the needs of the body is primarily done through the user’s diet. In fact, there is a natural way to solve nearly every imbalance that consumers can think of. To strengthen the bones, drink milk. If the throat is sore, drink tea. When it comes to the urinary tract, consumers can even soothe that with the natural benefits from the ingredients in D Mannose.

With D Mannose by Purest Vantage, consumers can improve both the health of the liver and the urinary tract. Read on below to learn about the ingredients that contribute to the change.

How D Mannose Cranberry & Dandelion Extract For UTI Helps

The reason that D Mannose is so helpful to consumers is because of the formula. The main ingredient is obviously D Mannose, which works within the body to balance the needs of the liver and urinary tract. Along with the benefits described above, the following ingredients contribute to the efficacy:

• Cranberry juice powder, which eliminates the toxins from the body and heals consumers with UTIs
• Dandelion extract, to speed up the rate that the liver eradicates toxins from the body

Cranberries are already well known for their potent help with urinary tract infections, but the combined power of D Mannose with cranberry is a defense and solution that every consumer will appreciate.

Using Purest Vantage D Mannose

Consumers will need to take two capsules a day, though they will be split into two different doses throughout the day. These instructions can be changed by a medical professional, if the user feels that they need a more potent dose.

Pricing For Purest Vantage D Mannose

On Amazon.com, consumers can buy 120 capsules of D Mannose for $14.95. However, there are two ways to save big on the purchase – ordering more than one bottle at once or beginning a subscription. When ordering more than one bottle, consumers will get a discount that is based off the number of bottles they order. Choose from: • 10% off 2 items • 15% off 3 items • 20% off 5 items During the subscription, consumers will get a savings of 5% per bottle, bringing down the cost to$14.20. However, if the user decides to subscribe to at least 5 products, they can increase the savings to 15% per supplement.

Contacting The Creators Of Purest Vantage D Mannose

Even though the user purchases the D Mannose remedy through Amazon Prime, the creators of the treatment – Purest Vantage – will be the ones that can answer any questions about the treatment. There is no phone number available, but consumers can send an email to [email protected]

Purest Vantage D Mannose Conclusion

D Mannose is meant for anyone that has issues in the liver, urinary tract, or kidneys, and wants to solve it with a natural remedy. The ingredients are minimal, using the natural benefits of D Mannose and raspberries to help consumers stop suffering from frequent UTIs.

Supplement Policehttps://supplementpolice.com/
Affiliate Disclosure: For full FTC compliance transparency; please assume we may receive a small commission from the sales of certain products & supplements reviewed. In order to operate optimally, our dedicated team & site is supported by advertising revenue and can be compensated from recommended product links.
3,712Fans
119Followers
549Followers
1,120Subscribers

Affiliate Transparency:

With full FTC compliance disclosure, please know our goal is to highlight human health and develop strategic partnerships with a variety of seasoned supplement suppliers affiliate compensation notice and new wellness product creators from around the world. Our intention is to organize optimal outlets for you, we may receive small commissions from providing links and sharing ads. The team has your best interest at hand, we care as much about your health as you do and that’s why you’re reading this. Want to learn more?


text:
# nquad Integration in SciPy

I am trying to self-learn SciPy and evaluate the following quadruple integral using scipy.integrate.nquad:

$$\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \int_{0}^{1-x} (w+y) \:dz \:dy \:dx \:dw$$

I wrote the following code:

from scipy import integrate

def f(z, y, x, w):
return w + y

def bounds(z):
return [0, 1-z]

I = integrate.nquad(f, [bounds, [0,1], [0,1], [0,1]])

print(I)

However, it gives the following error:

bounds() takes 1 positional argument but 3 were given

Any help to solve this quadruple integral is much appreciated.

## 1 Answer

Assuming it is the $$w$$ variable that has the range $$[0,1-x]$$

from  scipy.integrate import nquad

def func(w,x,y,z):
return w+y

def range_z():
return [0,1]

def range_y(z):
return [0,1]

def range_x(y, z):
return [0,1]

def range_w(x, y, z):
return (0,1-x)

res=nquad(func, [range_w, range_x, range_y, range_z])
print(res)

Running it produces 0.41666666666666674 which matches the analytic answer 5/12.

Assuming it is the $$z$$ variable that has the range $$[0,1-x]$$,

from  scipy.integrate import nquad

def func(z,y,x,w):
return w+y

def range_w():
return [0,1]

def range_x(w):
return [0,1]

def range_y(x,w):
return [0,1]

def range_z(y,x,w):
return (0,1-x)

res=nquad(func, [range_z, range_y, range_x, range_w])
print(res)

In this case the answer from the code is 0.5 which matches the analytic answer 1/2.

• Actually it is the z variable that has the range [0,1−x], and the analytic solution is 0.5. Based on your answer I figured out how to get this correct value, please consider editing your answer in order to accept it as a correct one. Thank you! – Sha Jan 20 at 20:42
• @Sha Ok, added another script for the case $z \in [0,1-x]$. – Maxim Umansky Jan 20 at 20:57


text:
# Concept of Matrices

Matrix:
Now, we write formal definition of Matrix.
An arrangement of number into m-rows and n-columns is called a Matrix of order $m{\text{x}}n$.
Matrix always denoted by capital letters $A,B,C, \ldots$ whereas their elements or entries by small letters $a,b,c, \ldots$
e.g.

This form of matrix is called matrix in tabular form, matrix can also be written in short form or abbreviated form as

Order of a Matrix:
The number of rows and number of columns in a matrix, is called order of the matrix, denoted by $m{\text{x}}n$ or $(m,n)$. Where $m =$ number of rows, $n =$ number of columns.


text:
# [texhax] [RESOLVED] TeX based presentations -- setting up "print dialog presets"

Suresh Govindachar sgovindachar at yahoo.com
Tue Apr 1 07:00:37 CEST 2014

Good news!: For the situation of a pdf file being generated from TeX,
have figured out how to initialize the "Print Page Range" entry of the
section titled "Print Dialog Presets" in the pdf document's properties
with values that would results in printing just the pages
1,3,6,9,12,16-18,20-22,26,30,32,33:

Essentially, in the TeX file, add code along the lines of:

\immediate\pdfobj
{ [0 0 2 2 5 5 8 8 11 11 15 17 19 21 25 25 29 29 31 31 32 32] }

\xdef\objDLJS{\the\pdflastobj\space 0 R}
\pdfcatalog{
/Type/Catalog/ViewerPreferences<</PrintPageRange \objDLJS>>
}

When the resulting pdf file is opened in a text editor, one will see
something like:

3 0 obj
[0 0 2 2 5 5 8 8 11 11 15 17 19 21 25 25 29 29 31 31 32 32]
endobj

849 0 obj <<
/Type /Catalog
/Pages 839 0 R
/Outlines 840 0 R
/Names 848 0 R
/Type/Catalog/ViewerPreferences<</PrintPageRange 3 0 R>>  /PageMode
/UseOutlines
>> endobj

You might not see the stuff about Outlines;  I see them because my TeX

--Suresh


text:
# Drawing with Loops¶

drawing_with_loops.py
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 """ Example "Arcade" library code. This example shows how to use functions and loops to draw a scene. It does not assume that the programmer knows how to use classes yet. If Python and Arcade are installed, this example can be run from the command line with: python -m arcade.examples.drawing_with_loops """ # Library imports import arcade import random SCREEN_WIDTH = 800 SCREEN_HEIGHT = 600 def draw_background(): """ This function draws the background. Specifically, the sky and ground. """ # Draw the sky in the top two-thirds arcade.draw_rectangle_filled(SCREEN_WIDTH / 2, SCREEN_HEIGHT * 2 / 3, SCREEN_WIDTH - 1, SCREEN_HEIGHT * 2 / 3, arcade.color.SKY_BLUE) # Draw the ground in the bottom third arcade.draw_rectangle_filled(SCREEN_WIDTH / 2, SCREEN_HEIGHT / 6, SCREEN_WIDTH - 1, SCREEN_HEIGHT / 3, arcade.color.DARK_SPRING_GREEN) def draw_bird(x, y): """ Draw a bird using a couple arcs. """ arcade.draw_arc_outline(x, y, 20, 20, arcade.color.BLACK, 0, 90) arcade.draw_arc_outline(x + 40, y, 20, 20, arcade.color.BLACK, 90, 180) def draw_pine_tree(center_x, center_y): """ This function draws a pine tree at the specified location. Args: :center_x: x position of the tree center. :center_y: y position of the tree trunk center. """ # Draw the trunkcenter_x arcade.draw_rectangle_filled(center_x, center_y, 20, 40, arcade.color.DARK_BROWN) tree_bottom_y = center_y + 20 # Draw the triangle on top of the trunk point_list = ((center_x - 40, tree_bottom_y), (center_x, tree_bottom_y + 100), (center_x + 40, tree_bottom_y)) arcade.draw_polygon_filled(point_list, arcade.color.DARK_GREEN) def main(): """ This is the main program. """ # Open the window arcade.open_window(SCREEN_WIDTH, SCREEN_HEIGHT, "Drawing With Loops") # Start the render process. This must be done before any drawing commands. arcade.start_render() # Call our drawing functions. draw_background() # Loop to draw ten birds in random locations. for bird_count in range(10): # Any random x from 0 to the width of the screen x = random.randrange(0, SCREEN_WIDTH) # Any random y from in the top 2/3 of the screen. # No birds on the ground. y = random.randrange(SCREEN_HEIGHT / 3, SCREEN_HEIGHT - 20) # Draw the bird. draw_bird(x, y) # Draw the top row of trees for x in range(45, SCREEN_WIDTH, 90): draw_pine_tree(x, SCREEN_HEIGHT / 3) # Draw the bottom row of trees for x in range(65, SCREEN_WIDTH, 90): draw_pine_tree(x, (SCREEN_HEIGHT / 3) - 120) # Finish the render. # Nothing will be drawn without this. # Must happen after all draw commands arcade.finish_render() # Keep the window up until someone closes it. arcade.run() if __name__ == "__main__": main()


text:
# 6 Introduction to Instance-level Exploration

Instance-level exploration methods help to understand how does a model yield a prediction for a particular single observation. We can think about the following situations as examples:

• We may want to evaluate effects of explanatory variables on the model’s predictions. For instance, we may be interested in predicting the risk of heart attack based on a person’s age, sex, and smoking habits. A model may be used to construct a score (for instance, a linear combination of the explanatory variables representing age, sex, and smoking habits) that could be used for the purposes of prediction. For a particular patient, we may want to learn how much do the different variables contribute to the score?
• We may want to understand how would the model’s predictions change if values of some of the explanatory variables changed? For instance, what would be the predicted risk of heart attack if the patient cut the number of cigarettes smoked per day by half?
• We may discover that the model is providing incorrect predictions and we may want to find the reason. For instance, a patient with a very low risk-score experienced a heart attack. What has driven the wrong prediction?

In this part of the book, we describe the most popular approaches to instance-level exploration. They can be divided into three classes:

• One approach is to analyze how does the model’s prediction for a particular instance differ from the average prediction and how can the difference be distributed among explanatory variables? This method is often called the “variable attributions” approach. An example is provided in panel A of Figure 6.1. Chapters 7-9 present various methods for implementing this approach.
• Another approach uses the interpretation of the model as a function and investigates the local behaviour of this function around the point (observation) of interest $$\underline{x}_*$$. In particular, we analyze the curvature of the model response (prediction) surface around $$\underline{x}_*$$. In case of a black-box model, we may approximate it with a simpler glass-box model around $$\underline{x}_*$$. An example is provided in panel B of Figure 6.1. Chapter 10 presents the Local Interpretable Model-agnostic Explanations (LIME) method that exploits the concept of a “local model”.
• Yet another approach is to investigate how does the model’s prediction change if the value of a single explanatory variable changes? The approach is useful in the so-called “What-if” analyses. In particular, we can construct plots presenting the change in model-based predictions induced by a change of a single explanatory variable. Such plots are usually called ceteris-paribus (CP) profiles. An example is provided in panel C in Figure 6.1. Chapters 11-13 introduce the CP profiles and methods based on them.

Each method has its own merits and limitations. They are briefly discussed in the corresponding chapters. Chapter 14 offers a comparison of the methods.


text:
## The smallest degree of a factor of a cyclotomic polynomial mod a prime

Let $\ell$ be a prime and let $\Phi_\ell(x) = \dfrac{x^\ell-1}{x-1} \in \mathbb{Z}[x]$ be the $\ell$th cyclotomic polynomial. In this exercise, we will determine the smallest degree of a factor of $\Phi_\ell$ mod $p$, and in particular determine when $\Phi_\ell$ is irreducible mod $p$. (Recall that $\Phi_\ell$ is irreducible over $\mathbb{Q}$ by Eisenstein’s criterion.)

1. Show that if $p = \ell$ then $\Phi_\ell$ is divisible by $x-1$ in $\mathbb{F}_\ell[x]$.
2. Suppose $p \neq \ell$ and let $f$ denote the order of $p$ in $\mathbb{F}_\ell^\times$ (that is, $f$ is minimal such that $p^f \equiv 1$ mod \ell\$). Show that $f$ is minimal such that $\mathsf{GL}_f(\mathbb{F}_p)$ contains an element $A$ of order $\ell$.
3. Show that $\Phi_\ell$ is not divisible by any polynomial of degree smaller than $f$ in $\mathbb{F}_p[x]$. Let $m_A(x) \in \mathbb{F}_p[x]$ denote the minimal polynomial for a matrix $A$ as in (2) and conclude that $m_A(x)$ is irreducible of degree $f$ and divides $\Phi_\ell(x)$ in $\mathbb{F}_p[x]$.
4. Prove that $\Phi_\ell(x)$ is irreducible mod $p$ if and only if $\ell-1$ is the smallest power of $p$ which is congruent to 1 mod $\ell$; that is, $p$ is a primitive root mod $\ell$.

1. As we showed in this previous exercise, $(x-1)^\ell = x^\ell - 1$ in $\mathbb{F}_\ell[x]$. So we have $\Phi_\ell(x) = (x-1)^{\ell-1}$.
2. Suppose $f$ is the order of $p$ mod $\ell$. Recall that $|\mathsf{GL}_f(\mathbb{F}_p)| = \prod_{i=1}^f (p^f - p^{f-i})$. In particular, $|\mathsf{GL}_f(\mathbb{F}_p)| \equiv 0$ mod $\ell$ since $p^f - 1 \equiv 0$. By Cauchy’s Theorem, there exists an element $A$ of order $\ell$ in $\mathsf{GL}_f(\mathbb{F}_p)$.

Now suppose $\mathsf{GL}_m(\mathbb{F}_p)$ has an element $A$ of order $\ell$. Then we have $\prod_{i=1}^m (p^m - p^{m-i}) \equiv 0$ mod $\ell$, and so $p^m - p^{m-i} \equiv 0$ mod $\ell$ for some $i$. Then $p^i \equiv 0$ mod $\ell$. If $m < f$, we have a contradiction, since $f$ is minimal such that $p^f \equiv 1$ mod $\ell$.

3. Suppose $\Phi_\ell(x)$ is divisible by a polynomial $q(x)$ of degree $m < f$ over $\mathbb{F}_p$. Then the companion matrix of $q$ has dimension $m < f$ and satisfies $x^\ell - 1 = 0$. This contradicts (2), which showed that $f$ is minimal such that $\mathsf{GL}_f(\mathbb{F}_p)$ contains an element of order $\ell$.

Now let $m_A(x)$ be the minimal polynomial of the matrix $A$ of order $\ell$ in $\mathsf{GL}_f(\mathbb{F}_p)$. The degree of $m_A$ is at least $f$, by the first paragraph of (3). Moreover the degree of $m_A$ is at most $f$, since the characteristic polynomial of $A$ has degree $f$. So the degree of $m_A$ is exactly $f$. Moreover, $m_A$ must be irreducible, since any proper divisor of $m_A$ also divides $\Phi_\ell(x)$ over $\mathbb{F}_p$ and has degree less than $f$.

4. By part (3), the smallest degree of a (nonunit) divisor of $\Phi_\ell(x)$ over $\mathbb{F}_p$ is precisely the order of $p$ mod $\ell$. So $\Phi_\ell$ is irreducible over $\mathbb{F}_p$ if and only if the order of $p$ mod $\ell$ is $\ell-1$; that is, if $p$ is a generator of $\mathbb{F}_\ell$ or a primitive $\ell$th root of 1.


text:
3.1 Qml 1.0 tutorial  (Page 3/5)

 Page 3 / 5

It also has an optional id attribute. If you are using more than one resource for a particular item and need to keep trackof which resource is which, you will want to include an id tag.

The resource tag is an empty tag, which means you must include a slash at the end of the tag.

Example

<resource uri="http://cnx.rice.edu/datasets/dataset1.csv" id="resource1" />

How you construct the answer tag, including whether you include an answer tag at all, depends on your item-type. However, in allcases where you have an answer tag, the ID of the answer tag must not contain any commas, as the key tag refers to the answerIDs separated by commas.

Single-response, multiple-response, and ordered-response

To write answer tags for single-response, multiple-response, and ordered-response items:

You will want one answer tag for each response option. Each answer tag has an id, which is referenced by the key tag,below. Preferably, the id tags should have an obvious relation to the response option. For example, if yourresponse options are "London, England;" "Washington, DC;" and "Paris, France" your id attributes could be london,washington, and paris.

Each of your answer tags should contain a response tag and may contain a feedback tag if you wish to provide feedbackspecific to that response (general feedback goes in another tag). The response tag contains the response option, in textor markup, and has no attributes. Be aware that the stylesheets for the Connexions project currently only allowplain text and CNXML (with or without MathML) within response tags. If you use CNXML (with or without MathML) within a QMLtag, the first tag must be a section tag, which may contain any of the tags a CNXML section tag is allowed to contain.

The feedback tag contains feedback to be displayed to the user upon selection of that response option. The feedback may betext or markup. The feedback tag does not have attributes for single-response, multiple-response, or ordered-response items.

Example for a single-response question

<item id="item1" type="single-response"><question>Are bananas a fruit or a vegetable?</question><resource uri="http://bananas.com/banana_dataset1.csv" /><answer id="fruit"><response>A fruit.</response><feedback>Correct!</feedback></answer><answer id="vegetable"><response>A vegetable.</response><feedback>Incorrect.</feedback></answer><hint>Bananas grow on trees.</hint><feedback>Bananas are a fruit.</feedback><key answer="fruit" /></item>

Text-response items

To write answer tags for text-response items: Because text-response items do not have response options, you willhave either have no answer tag (if you are not providing response feedback) or only one answer tag which may containtwo response-specific feedback tags: one for a correct response, one for an incorrect response.

The feedback tag containing the correct feedback should have the attribute correct="yes", and the other should have theattribute correct="no". You may also include a general feedback tag; this is recommended as Connexions does not haveplans to provide response processing for text-response items and at the present time only shows the general feedback forthe user to compare his/her answer with. The content of the feedback tags may be text or markup; be aware that thestylesheets for the Connexions project currently only allow plain text and CNXML (with or without MathML) within questiontags. If you use CNXML (with or without MathML) within a QML tag, the first tag must be a section tag, which may contain any of the tags a CNXML section tag is allowed to contain.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!


text:
# Math Help - Help!!! Distributive property with exponents

1. ## Help!!! Distributive property with exponents

use the distributive property to expand these expressions. leave ur answer in exponential form.

7^7(7^9 +7^4) = __________

6k^2(3k^4 - 9k^8) = _________

these are 2 of like 100 i have, i just want to make sure im doing them right so i dont have to redo them later, and well fail the assignment.

2. Remember the product of powers property of exponents: $a^{m} \cdot a^{n} = a^{m+n}$.

I'll do the first one.

1)

$7^{7}\left(7^{9}+7^{4}\right) = 7^{7} \cdot 7^{9} + 7^{7} \cdot 7^{4} = 7^{7+9} + 7^{7+4} = 7^{16} + 7^{11}$.


text:
Remark 63.18.7. Since a $\mathbf{Z}_\ell$-sheaf is only defined on a Noetherian scheme, it is torsion if and only if its stalks are torsion.

There are also:

• 2 comment(s) on Section 63.18: On l-adic sheaves

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).