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3 votes

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Difference Equations and displacement operator

answered Aug 27, 2017 at 14:10

2 votes

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Show that $K=\mathbb{Q}(\alpha,\sqrt{-3},\sqrt[3]{10})$ is a splitting field for $f(x)$.

answered Jul 31, 2021 at 19:49

2 votes

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Help with a nonhomogeneous function for a boundary value problem

answered Apr 7, 2013 at 2:12

1 vote

Find the flux of the vector field across the boundary of the cube

answered Apr 21, 2014 at 21:16

1 vote

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Evaluate the DFT of the vectors $(1,1,0,0)$ and $(1,1,1,0,0)$

answered Nov 5, 2014 at 16:42

1 vote

Show that all elements in the conjugacy class of $\sigma$ in $S_n$ are conjugate in $A_n$ if and only if $\sigma$ commutes with an odd permutation.

answered Feb 2, 2018 at 15:37

1 vote

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Given the frame $B=\{(1,1,0),(0,1,1),(1,1,1),(0,0,1),(0,1,-1)\}$, find (if possible) a (i) $(2,1)$ surgery,

answered Oct 27, 2014 at 19:49

1 vote

Calculate the divisor of the differential $dx/y$ on $C$ and use the result to show that $C$ has genus $g$.

answered Apr 17, 2022 at 18:29

1 vote

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Proof of $ \bigcup\limits_{i=1}^n F_i = \bigcup\limits_{i=1}^n E_i $

answered Sep 5, 2022 at 20:46

0 votes

Let $G=(\mathbb{Q}-\{0\},*)$ and $H=\{\frac{a}{b}\mid a,b\text{ are odd integers}\}$. Show $H$ is a normal subgroup of $G$.

answered Nov 4, 2014 at 22:43

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PDE: Determine the region above the $x$-axis for which there is a classical solution.

answered Jan 15, 2018 at 16:20

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$M$ is a maximal subgroup of $G$ then either $N_G(M)=M$ or $N_G(M)=G$.

answered Feb 6, 2021 at 19:37

0 votes

Find a simpler description for each of the following rings.

answered Aug 2, 2021 at 1:46

0 votes

Let $U,V$ be $\mathbb{F}$-vector spaces and $u\in \text{Hom}(U,V)$. Define the transpose of $u$.

answered Oct 14, 2021 at 2:36

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Evaluate the DFT of the vector $(f(x_0),\dots,f(x_{18}),f(x_{19}))$

answered Nov 5, 2014 at 18:12

0 votes

Show that the set $\{c_0,\dots,c_{N-1}\} \subset \mathbb{C}^N$ with vectors is an orthonormal basis of $\mathbb{R}^N$.

answered Nov 8, 2014 at 20:55

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How many coefficients are needed to reconstruct exactly vectors

answered Nov 11, 2014 at 23:14

0 votes

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CHECK: For each of the following permutations $\rho$ in $S(6)$ write $\rho$ as the product of disjoint cycles:

answered Nov 10, 2014 at 21:39

0 votes

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Let $\varphi:G \to K$ be an epimorphism. Let $J \triangleleft K$. Prove there exists a normal subgroup $H$ of $G$ such that $G/H \cong K/J$.

answered Nov 10, 2014 at 21:36

0 votes

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Show that $\{f_{n,m}\}$ is an orthogonal basis of $L^2(T)$.

answered Dec 2, 2014 at 5:37

0 votes

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Prove there is a polynomial $P_0$ with the property that $\mathcal{I}$ consists precisely of the multiples of $P_0$.

answered Oct 11, 2015 at 20:43

0 votes

Isomorphism of simple extensions

answered Oct 19, 2015 at 18:25

0 votes

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Prove that a non-empty subset of the real numbers union its boundary set is a closed set.

answered Sep 30, 2014 at 15:24

0 votes

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Prove that any non empty set G with a binary operation $\bullet$ satisfying the following requirements is a group

answered Oct 11, 2014 at 21:16

0 votes

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Find a tight frame in $\mathbb{R}^2$ with 10 elements of lengths $\{ \mathscr{L}_1,\dots,\mathscr{L}_{10} \}$, with

answered Oct 19, 2014 at 23:41

0 votes

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Find couples of frames $B\neq B_1$ with 5 elements in $\mathbb{R}^3$ which are (i) PRR equivalent, (ii) similar, and (iii) unitary equivalent

answered Oct 23, 2014 at 17:29

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Show that B is a tight frame if and only iff $\sum_{j=1}^N \|v_j\|^2e^{2i\theta_j}=0$

answered Oct 23, 2014 at 17:32

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Find a compression of the frames over the subspaces

answered Oct 27, 2014 at 19:54

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28 Answers

Difference Equations and displacement operator

Show that $K=\mathbb{Q}(\alpha,\sqrt{-3},\sqrt[3]{10})$ is a splitting field for $f(x)$.

Help with a nonhomogeneous function for a boundary value problem

Find the flux of the vector field across the boundary of the cube

Evaluate the DFT of the vectors $(1,1,0,0)$ and $(1,1,1,0,0)$

Show that all elements in the conjugacy class of $\sigma$ in $S_n$ are conjugate in $A_n$ if and only if $\sigma$ commutes with an odd permutation.

Given the frame $B=\{(1,1,0),(0,1,1),(1,1,1),(0,0,1),(0,1,-1)\}$, find (if possible) a (i) $(2,1)$ surgery,

Calculate the divisor of the differential $dx/y$ on $C$ and use the result to show that $C$ has genus $g$.

Proof of $ \bigcup\limits_{i=1}^n F_i = \bigcup\limits_{i=1}^n E_i $

Let $G=(\mathbb{Q}-\{0\},*)$ and $H=\{\frac{a}{b}\mid a,b\text{ are odd integers}\}$. Show $H$ is a normal subgroup of $G$.

PDE: Determine the region above the $x$-axis for which there is a classical solution.

$M$ is a maximal subgroup of $G$ then either $N_G(M)=M$ or $N_G(M)=G$.

Find a simpler description for each of the following rings.

Let $U,V$ be $\mathbb{F}$-vector spaces and $u\in \text{Hom}(U,V)$. Define the transpose of $u$.

Evaluate the DFT of the vector $(f(x_0),\dots,f(x_{18}),f(x_{19}))$

Show that the set $\{c_0,\dots,c_{N-1}\} \subset \mathbb{C}^N$ with vectors is an orthonormal basis of $\mathbb{R}^N$.

How many coefficients are needed to reconstruct exactly vectors

CHECK: For each of the following permutations $\rho$ in $S(6)$ write $\rho$ as the product of disjoint cycles:

Let $\varphi:G \to K$ be an epimorphism. Let $J \triangleleft K$. Prove there exists a normal subgroup $H$ of $G$ such that $G/H \cong K/J$.

Show that $\{f_{n,m}\}$ is an orthogonal basis of $L^2(T)$.

Prove there is a polynomial $P_0$ with the property that $\mathcal{I}$ consists precisely of the multiples of $P_0$.

Isomorphism of simple extensions

Prove that a non-empty subset of the real numbers union its boundary set is a closed set.

Prove that any non empty set G with a binary operation $\bullet$ satisfying the following requirements is a group

Find a tight frame in $\mathbb{R}^2$ with 10 elements of lengths $\{ \mathscr{L}_1,\dots,\mathscr{L}_{10} \}$, with

Find couples of frames $B\neq B_1$ with 5 elements in $\mathbb{R}^3$ which are (i) PRR equivalent, (ii) similar, and (iii) unitary equivalent

Show that B is a tight frame if and only iff $\sum_{j=1}^N \|v_j\|^2e^{2i\theta_j}=0$

Find a compression of the frames over the subspaces