## linear algebra – How to find \$ lim limits_ {n to infty} A ^ n \$?

Given $$4 times4$$ matrix,
$$A = begin {bmatrix} 0.4 & 0.3 & 0.2 & 0.1 \ 0.1 & 0.4 & 0.3 & 0.2 \ 0.3 and 0.2 and 0.1 and 0.4 0.2 and 0.1 and 0.4 and 0.3 end {bmatrix} .$$
Can we prove $$lim limits_ {n to infty} A ^ n = begin {bmatrix} 0.25 and 0.25 and 0.25 and 0.25 0.25 and 0.25 and 0.25 and 0.25 0.25 and 0.25 and 0.25 and 0.25 0.25 and 0.25 and 0.25 and 0.25 end {bmatrix}$$
manually? I tried to find $$A ^ 2$$, and $$A ^ 3$$ During a very long time. All the ways to find $$lim limits_ {n to infty} A ^ n$$?

## algorithms – Find all separators in a tree

Let a tree of N colored vertices in one of the colors 1 … N.

Let's call a separator edge if, when this edge is removed from the tree, all the vertices of each color remain connected.

The goal is to find all the separators in a tree in time O (N) and in memory O (N).

My first approach was to use FCB to find the LCA for all the vertices of each color, and then the separator was an edge that was not between an ACV and some vertices if the same color was used for any color , but I can. do not propose ideas to go further.

## Python – Find Recessions in US GDP Data Using PANDAS

For one mission, I identify the first quarter of the 2008 recession in the United States. The Excel data that I use can be downloaded here: gdplev.xls. How can I improve this pandas code to make it more idiomatic or optimized?

``````def get_recession_start ():
& # 39; & # 39; & # 39; Returns the year and the quarter of the hour of the beginning of the recession as
string value in a format such as 2005q3 & # 39; & # 39;
names =["Quarter", "GDP in 2009 dollars"],
parse_cols = "E, G",
skiprows = 7)
GDP_df = GDP_df.query ("Quarter> =" 2000q1 "")
GDP_df["Growth"] = GDP_df["GDP in 2009 dollars"].pct_change ()
GDP_df = GDP_df.reset_index (drop = True)
# recession defined as two consecutive quarters of negative growth
GDP_df["Recession"] = (GDP_df.Growth <0) & (GDP_df.Growth.shift (-1) <0)
returns GDP_df.iloc[GDP_df[GDP_df[GDP_df[GDP_df["Recession"].idxmax ()]["Quarter"]
get_recession_start ()
``````

## 2013 – Help yourself! I accidentally deleted the left navigation so as not to find my pages

Click the gear icon (top right corner) and select Site Content. This will take you to a page where you can see your libraries (including the Pages library).

And to retrieve it in the left nave, go to the library, click on Library Settings in the ribbon, then on "List Name, Description and Navigation" (first link on the settings page). Under Show this document library on Quick Launch, select Yes and save.

## Collision Resolution with a 2D Rectangle: Find a Restore Point

I have a question in 2 parts:

1:
I have 2 rectangles, A and B. B is a wall and A is moving. My simple logic is this: every time A moves, he moves according to an offset (x, y) and then checks whether he has collided with something. If it collides with something, step back in the opposite direction until the collision does not occur anymore.

The problem here is that if A moves in big pieces, he could jump B completely.

The desired behavior is to know where A should be when he touched for the first time one of the faces of B, then return to that point and apply the collision resolution.

2:
And if B moves too?

What I am currently doing to avoid this problem is to create large collision boxes and to ensure moving objects do not exceed the maximum. This approach seems to be limiting in the future.

I suppose there is a mathematical way to solve this problem, but I have found no answer to my research. All tips / suggestions are greatly appreciated.

Thank you!

## calculation – Look for where I was wrong: find the volume of a solid that is in both a cylinder and a sphere

I am currently working on this issue:

Find the volume of the solid that is in both the cylinder $$x ^ 2 + y ^ 2 = 1$$ and the sphere $$x ^ 2 + y ^ 2 + z ^ 2 = 4$$.

I decided to use the polar coordinates for the cylinder equation to become $$r ^ 2 = 1$$ and the sphere becomes $$r ^ 2 + z ^ 2 = 4$$.

Solve for $$z$$, I receive inequality $$– sqrt {4-r ^ 2} leq z leq sqrt {4-r ^ 2}$$. Since I know what $$r ^ 2$$ is, I plug this in to get the inequality where $$z$$ entered $$– sqrt {3}$$ and $$sqrt {3}$$. By combining this to make a triple integral, I receive:

$$int_0 ^ {2 pi} int_0 ^ 1 int _ {- sqrt {3}} ^ sqrt {3} rdzdrd theta$$

However, Slader has a different answer where they do not connect $$sqrt {3}$$ within. Why not connect the value for $$r ^ 2$$ to do the wrong calculation? It's not $$r ^ 2$$ always $$1$$?

## recursion – Find an expression for Sn + 1 in terms of Sn and Sn-1 that holds for all n> = 2

Let Sn be the number of ternary strings of length n in which each 1 is immediately followed by a 2 (these strings can not end with a 1). Find an expression for Sn + 1 in terms of Sn and Sn-1 that holds for all n> = 2.

I do not know how to solve this problem. I have the basic cases S1 = 2 and S2 = 5 but I do not know how to proceed from here

## c – error: 'expected' before 'return', have the same number of closing and opening points and not find the problem

error: 'expected' before 'return'
returns 0

I can not understand why he asks for a "while" before coming back

Tried to nest the code differently and can not find it works.

``````int random;
int userinput;
random = rand ()% 1000 + 1;

make
{
printf ("Can you guess the random number?  n");
scanf ("% d", & userinput);

if (random> = userinput)
{
printf ("The number you entered is too high! Try again!  n");
}

else if (random <= userinput)
{
printf ("The number you entered is too low! Try again!  n");
}

while (random! = userinput)
{
printf ("You guessed it! Correct! The number is:% d  n", random);
}
}
returns 0;
``````

## Find two contrasting colors that can contain white / yellow / red text that works for color blindness

I write a simple user interface using Material Design, and more specifically Material Ui using their Dark theme. I have a simple table to display text; However, I want the table to alternate between two contrasting colors to better indicate which lines belong to a "group". I must also display a warning or error state, which means that the usually white text must be yellow or red accordingly. I need red and yellow to have a strong contrast with the background colors, because the monitoring user interface is usually only viewed by users looking to see if it's in. good condition, non-good condition must be obvious.

I have trouble choosing contrasting colors because of my attempt to keep things functional for color-blind people. In addition to trying to make sure that they can tell the difference between my contrasting colors regardless of colorblindness, I must also choose colors that look right and that contrast appropriately with the white, yellow or red text.

I have indicators other than color to indicate the state and how the rows are grouped in case a color-blind could not tell the difference between my contrasting colors; but i would like to do my best to choose the right colors in order to be as functional as possible.

I finally thought I had a good combination, but when I had recourse to a colorblind person, he could see everything, but the red error text on my background caused such a strong contrast that it was obviously hurting her eyes, a problem I had not had. even thought to worry before.

I'm trying to stay in the color palette of the Matieral interface, but I'm not limited to these if I can find colors that work. I feel as if someone should already have this problem and there should already be a color combination recommended for this type of use case. Can any one give me a good site or a good resource to find good contrasting colors?