## Distribution of the linear transformation of the distributed Dirichlet random vector

Now I come across the same problem with you. Do you understand the distribution of the linear transformation of the distributed Dirichlet random vector?

## Separation vector on dense subalgebra

Accept $$M$$ be a vN algebra and $$U$$ Let be a S.O.T dense, self-conjugated subalgebra of $$M$$ has separation vector, does $$M$$ to have? If not, please give counterexample.

## c ++ – New values ​​for the vector of const char * do not get push_back ()

I have a vector of cons char *. Which is actually a timestamp. Each time, I get the last value and convert it to an integer, increasing by 40. And then back to vector as const char *. My problem is that new values ​​do not get push_back (). Vector already contains a value.

I tried to create instances instead of doing it directly

``````string is = to_string (y);
some_vector.push_back (is.c_str ());
``````

I do

``````string is = to_string (y);
const char * temp = is.c_str ();
some_vector.push_back (is.c_str ());
``````

My complete code is

``````vector Time restriction;
for (int i = 1; i <= 10; i ++)
{
const char * tx = TimeConstraint.back ();

int y;
string stream strval;

strval << tx;
strval >> y;

y = y + 40;

string is = to_string (y);
const char * temp_pointer = is.c_str ();
TimeConstraint.push_back (temp_pointer);

}
``````

New values ​​are not added to the TimeConstraint vector

Each time, I must press the incremented value of the last element of the push_back () vector. Please help me

## export – Issue when exporting vector graphics (PDF) to Mathematica notebook front-end with remote kernel on Linux

I can not export vector graphic images (especially PDF) to a Mathematica notebook frontend in Windows 8.1 with a remote kernel on a Linux server.

However, I can easily export raster image formats.

Interestingly enough, when accessing the server directly from the ssh command line, the Mathematica kernel starts and runs `export` Command, it works fine.

Mathematica 11.3 is the version used on both computers.

Example of a Mathematica notebook:

``````Set directory["/home/results"]

plt = plot[x, {x, 0, 1}]

export["test.gif", plt]  (*Works well*)

export["test.jpg", plt]  (*Works well*)

export["test.png", plt]  (*Works well*)

export["test.pdf", plt]  (*It does not work*)

export["test.eps", plt]  (*It does not work*)
``````

## Differential Geometry – Can we always find a curve on the manifold whose tangent vector always belongs to a linear subspace?

Suppose we have a smooth manifold $$M$$ and the tangential space of each point $$x in M ​​$$ has a non-empty intersection with a given linear subspace. Could we find a curve? $$M$$ so that the tangent vector of the point on that curve always belongs to this linear subspace?

$$textbf {my try:}$$ If the dimension for the linear subspace is one or two, I think I can find the curve. But I do not know if the dimension is larger than two?

## Fourier transform the size of a vector

How would you perform the Fourier transform of the size of the x-vector (ie sqrt (x ^ 2 + y ^ 2 + z ^ 2), where x, y, z are the components of the vector x)? Is it similar to the one-dimensional case? I was not able to extrapolate the logic from the 1d case to the general vector.

## Vector analysis – Define the path integral if the scalar \$ f \$ and the curve \$ mathbf {c} \$ are in * curvilinear * coordinates

I'm currently doing a multivariable calculus course. I have seen path integrals in the Cartesian coordinate system as the following definition:

Definition.
The path integral of $$f (x, y, z)$$ along the curve $$C$$ is

$$int_C f ds = int_a ^ bf ( mathbf {x} (u)) || mathbf {x} & # 39; (u) || you$$

from where $$mathbf {x}:[a,b] to mathbb R ^ 3$$ is the parametric representation of $$C$$, The definition did not refer to the coordinate system.

Question.
Suppose that $$(x, y, z) = mathbf Phi ( xi_1, xi_2, xi_3)$$ where the
transformation $$mathbf Phi: U to V$$ is sufficiently differentiable and has one
inverse $$mathbf { Phi ^ {- 1}}: V to U$$ from where $$U, V$$ are open subsets of $$mathbb R ^ 3$$,

What would be the definition of a path all over $$C$$ when $$f$$ is a function of curvilinear
Coordinates ($$xi_1, xi_2, xi_3$$) and the curve has been parameterized
curvilinear coordinates as $$mathbf { xi} = mathbf { xi} (u)$$ to the $$a le > u le b$$?

Is the definition consistent with a regular "Cartesian" path? If so, can you derive from the above definition for Cartesian how you would obtain a path integral for a function in curvilinear coordinates?

## ag.algebraic geometry – Each holomorphic vector bundle over a compact Riemann surface can be defined by only one transition function.

It is known that any holomorphic bundle of any order over a non-compact Riemann surface is trivial. A proof can be found in Forster's "Lectures on Riemann Surfaces," section 30.

To let $$E$$ be a holomorphic vector bundle over a compact Riemann surface $$X$$ with measuring device group $$G$$, One consequence of the above sentence is the limitation $$E | _ {X – {p }}$$ for every point $$p in X$$ is a trivial bundle. Thus $$E$$ can be restored by specifying the transition function $$g: D cap (X – {p }) rightarrow G$$ from where $$D$$ is a small disk with $$p$$,

Is that correct? If not, could you give a counterexample? I am mainly interested in the modulo space of holomorphic bundles $$X$$ in a concrete way, e.g. Use transition functions.

## How can the presence of each element of a vector be checked line by line in an array in R?

Assuming I have a vector in the range of 1 to 10, I would like to check the binary shape for each element of the vector if it exists in the array row, where 0 is for non-presence and 1 for presence, regardless of that Element that I repeat I would count only 1, for example in the first line of the array I have that[1,]= c (1,5,2,2,1), I would have 0 for elements 3,4,6,7,8,9,10 and 1 for elements 1,2,5

## Plotting – The gradient method in the vector field on the surface table does not work, the module is slow

For teaching purposes, I would like to create a vector field on a surface and visualize the path of the gradient method.

The surface and the gradient are generated with

``````f[x_, y_] : = Sin[x] cos[y];
GR[x_, y_] : = D[f[xx, yy], {{xx, yy}, 1}]/. {xx -> x, yy -> y};
a = 5;
xmin = -a; xmax = a;
ymin = -a; ymax = a;
nmax = 10;
mmax = 10;
dx = (xmax - xmin) / nmax;
dy = (ymax-ymin) / mmax;
grf = table[xi = xmin + i*dx; yj = ymin + j*dy;
v = {xi, yj};
w = v + Evaluate@gr[xi, yj];
arrow[{v, w}],
{i, 0, nmax}, {j, 0, mmax}];
pp = plot3D[f[x, y], {x, xmin, xmax}, {y, ymin, ymax}, Mesh -> None,
PlotStyle -> {Orange, Opacity[0.75]}]graphic[grf]
``````

The gradient field is also converted into a tangent vector field

``````pp = plot3D[f[x, y], {x, xmin, xmax}, {y, ymin, ymax}, Mesh -> None,
PlotStyle -> {Orange, Opacity[0.75]}];
grfplt = table[xi = xmin + i*dx; yj = ymin + j*dy;
v = {xi, yj, f[xi, yj]};
gg = gr[xi, yj];
w = v + {gg[[1]]gg[[2]]f[Xi+gg[Xi+gg[xi+gg[xi+gg[[1]], yy + gg[[2]]]};
{i, 0, nmax}, {j, 0, mmax}];
show[pp,grfplt]
``````

The paths of the gradient method should be generated with

``````gradmeth[f_, x0_, y0_] : =
table[xa = x0; ya = y0; gg = gr[xa, ya]; xb = xa + gg[[1]];
yb = ya + gg[[2]]; v = {xa, ya, f[xa, ya]};
w = {xb, yb, f[xb, yb]};
xa = xb; ya = yb;
{i, 0, 15}
];
show[pp, grfplt, gr1, gr2]
``````

But obviously the statement xa = xb; ya = yb; overwrite w every time.

That's why I used a module

``````gradmeth[f_, x0_, y0_, col_] : = Module[{xa, xb, ya, yb, gg, v, w, ll}
xa = x0; ya = y0; ll = {};
To the[i = 0, i <= 10, i ++,
gg = gr[xa, ya]; xb = xa + gg[[1]]; yb = ya + gg[[2]];
v = {xa, ya, f[xa, ya]};
w = {xb, yb, f[xb, yb]};
w}]}]]; *)
attach[ll, {col, Thick, Arrowheads[.05], Arrow[{v, w}]}];
xa = xb; ya = yb;
];
ll
]gr1 = Graphics3D[gradmeth[f, 2, 2, Red]];
gr2 = Graphics3D[gradmeth[f, -2, -1, Blue]];
show[pp, grfplt, gr1, gr2]
``````

This is very slow!

Can I repair the table approach?

Can I speed up the module approach?