# All Questions

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### About counting the terms of the expression $x^{m-1} + x^{m-2} +\ldots+ x^0$ given that $x=1$

I want to understand how I can count the terms of the expression $x^{m-1} + x^{m-2} +\ldots+ x^0$ when $x=1$. The result is $m$, I dont know how to count them formally, any advice would be helpful. ...
55 views

### King, Queen, 2 rooks, 2 bishops and 2 knights in 1 line -basic combinatorics [duplicate]

This is also a basic combinatorics question, but I don't understand part of its solution. We have a King, a Queen, 2 rooks, 2 bishops and 2 knights (each of the last three pieces are identical, i.e. ...
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### Different ways to write $n$

What is a general formula $n(n)$ for this? We know that starting from below, we can see how many numbers a certain $n$ generates by counting the number of numbers contained in the column $n$ is in, ...
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### Recursion with generating function.

Using generating function determine $u_n$ $$u_{n+2} -6u_{n+1} + 9u_n = 2^n + n$$ I am asking for you to give me some advices. Thanks in advance.
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### (Geometric algebra) Acceleration of a particle with constant speed as a bivector-vector inner product

I've been working on (self-studying) Geometric Algebra for Physicists which, sadly, has no solutions manual. This is not a problem in general, but I feel like one of my solutions for a question asked ...
52 views

### linear programming slater condition

I am wondering if anyone could help to come up with a such example: ...
104 views

### Understanding a “matrix representation”

Consider an abstract linear transformation; $$f: V \rightarrow V$$ $V$is a polynomial vector space of degree less than or equal to 2. Thus, it has a basis $1,x,x^2$. Now, what does it mean to say ...
187 views

### Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$

Conjecture: There does not exist a non-integer $x$ such that $$2^x=a$$ $$3^x=b$$ $$5^x=c$$ where $a,b,c$ are all integers. I'm aware that the similar question There does not ...
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### Help explain this “atom” and what this $G$ is.

Following are some slides from a lecture that you can watch here (starting at 20:40). It is explaining the Hierarchical Dirichlet Process. https://www.youtube.com/watch?v=PxgW3lOrj60 In the first ...
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### If $T \models \phi$ then there is a finite subtheory $T' \subset T$ such that $T' \models \phi$

Use the Compactness Theorem to show: if $T \models \varphi$ then there is a finite subtheory $T' \subset T$ such that $T' \models \varphi$. I don't see how I can use the compactness theorem here. ...
261 views

### Compute the wedge product

This is my first time computing the wedge product, I am not sure if I have done it correctly as I do not have solutions, if I have gotten the answer right or am doing the right method please say. ...
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### Find the ring of homomorphisms $\mathbb{Z} \to \mathbb{Z}$ [duplicate]

Show, which well-known ring is isomorphic to ring $End(\mathbf{Z})(+,ͦ,-,0,id)$ of homomorphisms $\mathbf{Z}$ -> $\mathbf{Z}$, where $\mathbf{Z}$ is commutative group $\mathbf{Z}(+)$ and 0 constant ...
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### What is the inverse function of the Log Gamma function?

What is the inverse function of the Log Gamma function? $\log\Gamma(x)$ http://mathworld.wolfram.com/LogGammaFunction.html Can it be inverted, and why not, if not?
113 views

### Is there a transitive permutation group satisfying these properties?

Let $G \subset S_n$ be a transitive permutation group and let $H=G_1:=\{ g \in G \ \vert \ g(1)=1 \}$. Let $(K_i)_{i \in I}$ be the sequence of minimal overgroups of $H$ in $G$. Note that if $G$ is ...
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### $R$ noetherian, $I$ injective $R$-module $\Rightarrow$ $S^{-1}I$ is injective over $S^{-1}R$
I am trying to prove that if $R$ is a noetherian ring, $S$ a multiplicative part and $I$ an injective $R$-module, then $S^{-1}I$ is an injective $S^{-1}R$-module. So far I thought: I reduce to check ...