# The import java.util.Collections cannot be resolved

A

#### Aish97

##### Guest
Aish97 Asks: The import java.util.Collections cannot be resolved
Code:
package Collection_1;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Iterator;
import java.util.List;

public class ArrayListMethods {

public static void main(String[] args)
{

List<Integer> intList = new ArrayList<Integer>();
Collections.sort(intList);

}

}

This code is giving the error The import java.util.Collections cannot be resolved while importing import java.util.Collections. I'm using sort method from Collections class. I'm using eclipse IDE for writing the code. If anyone has any idea please try to answer.

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#### Continuous morphism in function fields with extra conditions

joaopa Asks: Continuous morphism in function fields with extra conditions
Let $\Omega$ be the completion of $\overline{\mathbb F_q\left(\left(\frac1T\right)\right)}$ for the topology induced by the valuation $-\deg$ on $\mathbb F_q\left(\left(\frac1T\right)\right)$. Consider $s$ distinct non zero elements $\alpha_1,\cdots,\alpha_s$ of $\overline{\mathbb F_q(T)}$. One assumes that $\deg(\alpha_1)\le\cdots\le\deg(\alpha_s)$. Does there exist a non zero morphism $\sigma$ of $\Omega$ such that $\sigma\left(\overline{\mathbb F_q(T)}\right)\subset\overline{\mathbb F_q(T)}$ and $\deg(\sigma(\alpha_i))<\deg(\sigma(\alpha_{i+1}))$ for any $i\in[1,s-1]$

Be careful for the sign. In the third line, it is $\le$ and the fourth one $<$.

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#### Modifying a matrix equation

C.Koca Asks: Modifying a matrix equation
I have a matrix equation of the form

$$Q=SBS+SBA+HSBZ+ABS+ABA+ABZ+ZBS+ZBA+ZBZ.$$

If it weren't for the $H$ matrix in the third term, the whole thing would be

$$Q^\prime=(S+A+Z)B(S+A+Z).$$

As it is, I was able to reduce it to

$$Q=(S+A+Z)B(S+A+Z)+(H-I)SBZ,$$ but I want to eliminate the addition, if possible. In other words, I am looking for an expression like

$$Q=f(S,A,H,Z)Bg(S,A,H,Z),$$ where $f(.)$ and $g(.)$ are matrix functions.

All matrices are square and real. $S$ is symmetric and $H$ is a diagonal, i.e., they commute.

I am looking for some $f(.)$ and $g(.)$. I will be calculating $$Q^{}=f^n(S,A,H,Z) B g^n(S,A,H,Z),$$ and I will be using SVD to proceed. Thus eliminating the addition helps me a lot.

Thanks!

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#### Invert transform of a generating function

Seth Asks: Invert transform of a generating function
A055887's generating function is given as a transform of another generating function $\frac{1}{1-P(x)}$. It's clear from the definition that this is $\sum_{n=0}^{\infty} \left [ \sum_{i+j+k+...=n} P(i)P(j)P(k)... \right ] x^n$ but I'm struggling to derive this.

I've seen $x$ in $\frac{1}{1-x} = 1+x+x^2+x^3$ be replaced $x$ with $a x$, $x^2$, $x^m$, $-x$ but I only proved these by working backwards. Starting with the result and showing $S - Sx = 1$ then concluding $S = \frac{1}{1-x}$.

This was called "invert transform" in A067687 but that term doesn't seem to be defined or commonly used outside of OEIS.

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#### Shouldn’t vacuous truths be false since they imply false information?

copepod Asks: Shouldn’t vacuous truths be false since they imply false information?
Example: “All the lions I own are healthy”.

In real-world situations, such as court hearings, this sentence will be regarded as a lie if I don’t actually have any lions. Makes sense: what i really say is “I have lions and they’re all healthy”. It’s false, and because it’s synonymous with the original, the original is also false. Logic does agree that the rewording is false, but it doesn’t view it as a synonym with the original, which it treats as a vacuous truth. Why?

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#### Mathematically prove that a Beta prior distribution is conjugate to a Geometric likelihood function

Shivam Dave Asks: Mathematically prove that a Beta prior distribution is conjugate to a Geometric likelihood function
I have to prove with a simple example and a plot how prior beta distribution is conjugate to the geometric likelihood function. I know the basic definition as

'In Bayesian probability theory, a class of distribution of prior distribution $\theta$ is said to be the conjugate to a class of likelihood function $f(x|\theta)$ if the resulting posterior distribution is of the same class as of $f(\theta)$.'

But I don't know how to prove it mathematically.

P.S. - It would really nice of you guys to provide some good material on bayesian statistic and probability theory.

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#### Maximal compact subgroup of $GL_n(\mathbb C_p)$

boxdot Asks: Maximal compact subgroup of $GL_n(\mathbb C_p)$
It is known that the general linear group $GL_n(\mathbb Q_p)$ over the $p$-adic numbers has $GL_n(\mathbb Z_p)$ as a maximal compact subgroup and every other maximal compact subgroup of $GL_n(\mathbb Q_p)$ is conjugated to this one. (Unfortunately, I don't have any reference for this fact and so I don't know any proof.)

Q: Is this also true for $GL_n(\mathbb C_p)$ and $GL_n(\mathcal O)$, where $\mathcal O \subset \mathbb C_p$ is the integer ring?

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#### Value of Product Based on Bitcoins

• Chuck
• Finance
• Replies: 0
Chuck Asks: Value of Product Based on Bitcoins
If I chose to accept Bitcoin as a payment for my product, and the price of the bitcoin goes up or down, then technically I am not getting as much for my product in the long run correct? Because the exchange is based on the dollar as one of the currencies. So If my product cost's 100.00 and that is a certain percentage of a bitcoin then if the bitcoin say its worth 7100.00 that would be .014 bitcoins. But if the bitcoin decreased in price say to 5100.00 then that same product would cost .019 bitcoins. Correct? How dos the fluctuation in price affect the value of my product in dollars?

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