Results for query "tworks,however,whenrunningtheapplicationandtriggeringthe&"

Where's the link to this game's SWF file?

jpg&mc_negativescore=0&mc_players_site=1&mc_scoreistime=0&mc_lowscore=0&mc_width=800&mc_height=600&mc_lang=en&mc_webmaster=0&mc_playerbutton=0&mc_v2=0&loggedin=0&mc_loggedin=0&mc_uid=0&mc_sessid=5r1ov9fmqmrdm3tob6afvl08e5&mc_shockwave=0&mc_gameUrl=https://static.com/games/strike-force-heroes-2/en/&mc_ua=b7b3178&mc_geo=us-west-2&mc_geoCode=UK&vid=1&vtype=ima&m_vid=0&mc_preroll_check=0&channel=miniclip.

Finding eigenvalues of an 'almost-tridiagonal' circulant matrix

Consider the $2N\times 2N$ matrix

$$A=\begin{pmatrix} a &1 &0&0&0&\ldots&0&1 \\1 &-a&1 & 0 &0 & \ldots & 0&0
\\0 &1&a&1&0 &\cdots &0&0 \\ 0&0&1&-a &1 & \ldots &0&0
\\& & & \cdots \\ 1&0 &0&0&0&\ldots &1&-a\end{pmatrix}$$

Hopefully the structure is clear, but if not I can clarify further.There is a lot of literature exclusively on eigenvalues of tridiagonal matrices and circulant matrices, however $A$ is neither exactly circulant nor is it exactly tridaigonal.

Primitivity of $AA^\top$

Consider $B:=AA^\top$.}}
\left[ \begin{array}[c]{ccc|ccc|ccc|ccc}
\star & \cdots & \star & 0 & \cdots & 0 &\star& \cdots & \star & 0& \cdots & 0 \\
\vdots & \vdots & \vdots & \vdots &\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
\star & \cdots & \star & 0 & \cdots & 0 &\star& \cdots & \star & 0& \cdots & 0 \\
\hline
\star & \cdots & \star & 0 & \cdots & 0 &\star& \cdots & \star & 0& \cdots & 0 \\
\vdots & \vdots & \vdots & \vdots &\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
\star & \cdots & \star & 0 & \cdots & 0 &\star& \cdots & \star & 0& \cdots & 0 \\
\hline
0 & \cdots & 0 & \star & \cdots & \star & 0& \cdots & 0 & \star& \cdots & \star \\
\vdots & \vdots & \vdots & \vdots &\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
0 & \cdots & 0 & \star & \cdots & \star & 0& \cdots & 0 & \star& \cdots & \star \\
\hline
0 & \cdots & 0 & \star & \cdots & \star & 0& \cdots & 0 & \star& \cdots & \star \\
\vdots & \vdots & \vdots & \vdots &\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
0 & \cdots & 0 & \star & \cdots & \star & 0& \cdots & 0 & \star& \cdots & \star \\
\end{array} \right]
&
\begin{array}[c]{@{}[email protected]{\,}l}
\left.

A question about $O(3,1)$

Recall that $O(3,1)$ is the collection of matrices $A\in M_4(\mathbb R)$ such that
$$A\begin{pmatrix}1 &&&\\&1&&\\&&1&\\&&&-1\end{pmatrix}A^T=\begin{pmatrix}1 &&&\\&1&&\\&&1&\\&&&-1\end{pmatrix}.Can we find a $Q\in O(3,1)$ such that
$$Q\psi Q^{-1}=\begin{pmatrix} 0&a&&\\-a&0&&\\&&0&b\\&&b&0\end{pmatrix}$$
for some $a,b\in \mathbb R$?

Mean of a vector

Then $$\mu_n\to(2,2,2,2,2,102,102,102,102,102).The exact rate of convergence will be determined by the second-largest singular value of the matrix
$$M =
\begin{bmatrix}
\tfrac13 & \tfrac13 & \tfrac13 & & & \\
\tfrac13 & \tfrac13 & \tfrac13 & & & \\
\tfrac13 & \tfrac13 & \tfrac13 & & & \\
& & & 1 & & \\
& & & & 1 & \\
& & & & & \ddots
\end{bmatrix}
\begin{bmatrix}
1 & & & & & \\
& \tfrac13 & \tfrac13 & \tfrac13 & & \\
& \tfrac13 & \tfrac13 & \tfrac13 & & \\
& \tfrac13 & \tfrac13 & \tfrac13 & & \\
& & & & 1 & \\
& & & & & \ddots
\end{bmatrix}
\begin{bmatrix}
1 & & & & & \\
& 1 & & & & \\
& & \tfrac13 & \tfrac13 & \tfrac13 & \\
& & \tfrac13 & \tfrac13 & \tfrac13 & \\
& & \tfrac13 & \tfrac13 & \tfrac13 & \\
& & & & & \ddots
\end{bmatrix}
\cdots$$
but I don't know how to compute that.

Irreducible representations of $Sp(4,\mathbb{F}_2)$

I'm trying to construct the irreducible representations (over $\mathbb{C}$) of the finite group $Sp(4,\mathbb{F}_2)$.Using GAP, the character table is as follows:

$$
\left(\begin{matrix}
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & 1 & -1 \\
5 & -3 & 1 & 1 & 2 & 0 & -1 & -1 & -1 & 0 & 1 \\
5 & 3 & 1 & -1 & 2 & 0 & -1 & 1 & -1 & 0 & -1 \\
5 & -1 & 1 & 3 & -1 & -1 & 2 & 1 & -1 & 0 & 0 \\
5 & 1 & 1 & -3 & -1 & 1 & 2 & -1 & -1 & 0 & 0 \\
9 & -3 & 1 & -3 & 0 & 0 & 0 & 1 & 1 & -1 & 0 \\
9 & 3 & 1 & 3 & 0 & 0 & 0 & -1 & 1 & -1 & 0 \\
10 & -2 & -2 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & -1 \\
10 & 2 & -2 & -2 & 1 & -1 & 1 & 0 & 0 & 0 & 1 \\
16 & 0 & 0 & 0 & -2 & 0 & -2 & 0 & 0 & 1 & 0 \\
\end{matrix}\right)$$

Here are the representations I understand.

Iterated semi-direct products

5ex\rlap{\scriptstyle#1}}$

$$
\begin{array}{c}
& & 1 & & 1 & & \\
& & \da{} & & \da{} & & \\
& & C & \ra{=} & C\\
& & \da{} & & \da{} & & \\
1 & \ra{} & A & \ra{} & G & \ra{} & B & \ra{} & 1 \\
& & \da{} & & \da{\pi} & & \da{=} \\
1 & \ra{} & D & \ra{} & E & \ra{} & B & \ra{} & 1 \\
& & \da{} & & \da{} & & \\
& & 1 & & 1 & &
\end{array}
$$
in which all rows and columns are exact.Now $A/[C,D]$ is the direct product $C/[C,D] \times D[C,D]/[C,D]$.

Homotopy limit-colimit diagrams in stable model categories

12 of (a newer version of) Mark Hovey's book Model Categories that, in a stable model category, homotopy pullback squares coincide with homotopy pushout squares."In a diagram of the form
$$
\begin{matrix}
W & & \to && X\\
&\searrow & \\
\downarrow &&Y&&\downarrow\\
&&&\searrow\\
Z & &\to && V,
\end{matrix}
$$
$V$ is a homotopy colimit of
$$
\begin{matrix}
W & & \to && X\\
&\searrow & \\
\downarrow &&Y&&\\
&&&\\\
Z & & &&
\end{matrix}
$$
if and only if
$W$ is a homotopy limit of
$$
\begin{matrix}
& & && X\\
& & \\
&&Y&&\downarrow\\
&&&\searrow\\
Z & &\to && V.

Non-“weakly group theoretical” integral fusion categories?

Is there an integral fusion category of rank $7$, FPdim $210$ and type $[[1,1],[5,3],[6,1],[7,2]]$, with the following fusion rules?$\small{\begin{smallmatrix}
1 & 0 & 0 & 0& 0& 0& 0 \\
0 & 1 & 0 & 0& 0& 0& 0 \\
0 & 0 & 1 & 0& 0& 0& 0 \\
0 & 0 & 0 & 1& 0& 0& 0 \\
0 & 0 & 0 & 0& 1& 0& 0 \\
0 & 0 & 0 & 0& 0& 1& 0 \\
0 & 0 & 0 & 0& 0& 0& 1
\end{smallmatrix} ,
\begin{smallmatrix}
0 & 1 & 0 & 0& 0& 0& 0 \\
1 & 1 & 0 & 1& 0& 1& 1 \\
0 & 0 & 1 & 0& 1& 1& 1 \\
0 & 1 & 0 & 0& 1& 1& 1 \\
0 & 0 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1
\end{smallmatrix} ,
\begin{smallmatrix}
0 & 0 & 1 & 0& 0& 0& 0 \\
0 & 0 & 1 & 0& 1& 1& 1 \\
1 & 1 & 1 & 0& 0& 1& 1 \\
0 & 0 & 0 & 1& 1& 1& 1 \\
0 & 1 & 0 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1
\end{smallmatrix} ,
\begin{smallmatrix}
0 & 0 & 0 & 1& 0& 0& 0 \\
0 & 1 & 0 & 0& 1& 1& 1 \\
0 & 0 & 0 & 1& 1& 1& 1 \\
1 & 0 & 1 & 1& 0& 1& 1 \\
0 & 1 & 1 & 0& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1
\end{smallmatrix} ,
\begin{smallmatrix}
0 & 0 & 0 & 0& 1& 0& 0 \\
0 & 0 & 1 & 1& 1& 1& 1 \\
0 & 1 & 0 & 1& 1& 1& 1 \\
0 & 1 & 1 & 0& 1& 1& 1 \\
1 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 2& 1 \\
0 & 1 & 1 & 1& 1& 1& 2
\end{smallmatrix} ,
\begin{smallmatrix}
0 & 0 & 0 & 0& 0& 1& 0 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 2& 1 \\
1 & 1 & 1 & 1& 2& \color{purple}{1}& \color{purple}{2} \\
0 & 1 & 1 & 1& 1& \color{purple}{2}& \color{purple}{2}
\end{smallmatrix} ,
\begin{smallmatrix}
0 & 0 & 0 & 0& 0& 0& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 1 \\
0 & 1 & 1 & 1& 1& 1& 2 \\
0 & 1 & 1 & 1& 1& \color{purple}{2}& \color{purple}{2} \\
1 & 1 & 1 & 1& 2& \color{purple}{2}& \color{purple}{1}
\end{smallmatrix}}$

or also the same rules with a little $\color{purple}{\text{variation}}$ for the 7-dim.

A double grading of catalan numbers

I will think of the vertices of tree as members of an asexually reproducing species, and therefore use language like "sibling", "cousin", "child", "parent", "generation" etc.For example, in the tree
$$\begin{matrix}
& & a & & \\
& & \downarrow & & \\
& & b & & \\
& \swarrow & \downarrow & \searrow \\
c & & d & & e \\
& & \downarrow & & \downarrow \\
& & f & & g \\
& & \downarrow & \searrow & \\
& & h & & i \\
& & & & \downarrow \\
& & & & j \\
\end{matrix}$$
the crucial elements are $a$, $b$ and $i$.

Verifying the correctness of a Sudoku solution

We are thus looking for a solution of the following grid:
$$\begin{array}{|ccc|ccc|ccc|ccc|ccc|}
\hline
1&&&2&&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\hline
&&&1&&&2&&&&&&&&&\\
&&&&&&&&&&&&&&\cdots&\\
&&&&&&&&\ddots&&&&&&&\\
\hline
2&&&&&&&&&1&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\hline
\strut&&&&&&&&&&&&&&&\\
\strut&&&&\vdots&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\hline
\end{array}$$
where the upper part is a $q'\times q'$ subgrid, $q'=q/2$.$S$ is not included in the complement of a Sudoku permutation of one of the following sets:

a) $\{r_1,r_2\}$

b) $\{r_1,c_1,b_1\}$

c) $\{b_1,b_2,b_4,b_5\}$

d) $\{r_1,r_4,b_1,b_4\}$

e) $\{r_1,c_1,b_2,b_4,b_5\}$

f) $\{b_2,b_3,b_4,b_6,b_7,b_8\}$

g) $\{r_1,r_4,b_1,b_5,b_7,b_8\}$

h) $\{r_1,c_1,b_3,b_5,b_6,b_7,b_8\}$

Maximal incomplete sets http://math.

Is the operadic butterfly symmetric?

The operadic butterfly is a diagram in the category of operads in vector spaces.$$\begin{array}{ccccc}
& Dend & & & & Dias & \newline
\nearrow & &\searrow & &\nearrow & &\searrow\newline
Zinb & & &Ass & & & \quad Leib \newline
\searrow & &\nearrow & &\searrow & &\nearrow\newline
& Comm & & & & Lie & \newline
\end{array}$$

Here is a paper by Loday in which some discussion can be found.