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Classifying irreducible finite-dimensional representations of the $q$-Weyl algebra

I have that $A = \langle x, y : yx = qxy \rangle$ is the $q$-Weyl algebra, with basis $x^iy^j$, $i, j \in \mathbb{Z}$. The base field is $\mathbb{C}$. I need to classify the irreducible finite-dimensional representations. Assuming $V$ is such a module, I have shown that $\{v, xv, \dots, x^{m-1}v\}$ is a basis, where […]

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Let $G=\{-1,1,i,-i\}$ be the fourth roots of unity. Prove $G$ is a group under multiplication and $G$ is isomorphic to $\Bbb{Z}_4$..

A) Prove that $G=\{(-1,1,i,-i)\}$ is a group under multiplication. a.1) First I need to show that G is indeed closed under the operation * we have $1*1=1$ where $1 \in G$ we have $-1*-1 = 1$ where $1 \in G$ we have $1*-1 = -1$ where $-1 \in G$ and $-1 * 1 =-1 \in […]

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Linux Mastering Development Ubuntu

nvme(kingston a2000) sometimes stops giving response in ubuntu 18.04(dell Inspiron 15 5580)

I installed new nvme in my Inspiron 15 5580. The laptop boots fine with my nvme but the problem is that sometimes it stops responding (not able to read anything). Most of the time it happens at the time of power off and everything hangs so i tried pressing ctrl + alt + prtScr + […]

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Mastering Development

Graham Scan for calculating the convex hull of a given set of points in R

I need to code the Graham scan algorithm to find convex hull of a given set of points. I have been trying a lot and, I do not achieve a solution. I have the following code for graham function grahamScanConvexHull<-function(points){ vertices <- data.frame(x=double(), y=double()) flag <- T # Get the most left down_point and leave […]

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Linux Mastering Development Ubuntu

nvme(kingston a2000) sometimes stops giving response in ubuntu 18.04(dell Inspiron 15 5580)

I installed new nvme in my Inspiron 15 5580. The laptop boots fine with my nvme but the problem is that sometimes it stops responding (not able to read anything). Most of the time it happens at the time of power off and everything hangs so i tried pressing ctrl + alt + prtScr + […]

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Linux Mastering Development Ubuntu

nvme(kingston a2000) sometimes stops giving response in ubuntu 18.04(dell Inspiron 15 5580)

I installed new nvme in my Inspiron 15 5580. The laptop boots fine with my nvme but the problem is that sometimes it stops responding (not able to read anything). Most of the time it happens at the time of power off and everything hangs so i tried pressing ctrl + alt + prtScr + […]

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Ask Mathematics

Proving linearity of the differential operator $a_n(x)D^n+a_{n-1}(x)D^{n-1}+\ldots+a_1(x)D+a_0(x)$.

I am taking a first course on ordinary differential equations(with background in linear algebra). I would like to know, if the proof to the below claim is correct (and that I am not using advanced facts to prove basic facts). Prove that every expression of the form: $$a_n(x)D^n+a_{n-1}(x)D^{n-1}+\ldots+a_1(x)D+a_0(x)$$ defines a linear transformation from $C^n[a,b]$ to […]

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Mastering Development

How to determine the recurrence relation described by the efficiency of this code

I´m new to algorithm analysis. I found this code online boolean p (ints,intt,intn){ if (n==1) { if e(s,t) return true; else return false; } else { for(i=1;i<=n;i++) { if (p(s,i,n/2) and p(i,t,n/2)) return true; } } return false; } How can I determine the recurrence relation described by the efficiency of this code? Supposing that […]

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$(0,1] \cup \left(\frac{1}{2}+\frac{1}{2^2},\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}\right] \cup \cdots$ is not in $\mathbf{A}$

I have a little problem with understanding following example. If I want to explain this to someone so I should be sure of my understanding. (sorry for not native English) I know (i) since we can choose a partition (with finite member) on $(0,1]$ like $$\left(0,\frac{1}{2}\right]\cup \left(\frac{1}{2},1\right]$$. Am i right? (1) For part (ii) if […]

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$(0,1] \cup \left(\frac{1}{2}+\frac{1}{2^2},\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}\right] \cup \cdots$ is not in $\mathbf{A}$

I have a little problem with understanding following example. If I want to explain this to someone so I should be sure of my understanding. (sorry for not native English) I know (i) since we can choose a partition (with finite member) on $(0,1]$ like $$\left(0,\frac{1}{2}\right]\cup \left(\frac{1}{2},1\right]$$. Am i right? (1) For part (ii) if […]