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# Mac Dual Monitor without apple menu bar and Prevent Second monitor to go black while one is fullscreen, is possible?

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I spend long hours working on my macbook and usually use a second monitor on which I put youtube videos (fullscreen) to pass the time while I work.

It has always bothered me that the apple menu bar appears on the second monitor, I have managed to disable the apple menu bar from the Mission Control preferences but when doing fullscreen with youtube, quicktime, etc. the other monitor goes black

Is there a method to remove the apple menu bar on the second monitor and at the same time prevent the other monitor from going black when doing fullscreen?

## there a 1px red line on my monitor screen

it might sound kinda stupid I know, “it’s just a line at the top” but it bothers me because of the toc.

obs: it interacts with what’s behind it, it’s not a simple line. sometimes it looks like it’s turning off and on smoothly about it, it’s not from the browser, although it seems, I used a program that I have that deletes everything, I deleted the browser, and after I restarted the computer limiting it to microsoft applications, the line continued.
(it doesn’t appear on screenshots)

## Calculating L-smoothness constant for logistic regression.

I am trying to find the $$L$$-smoothness constant of the following function (logistic regression cost function) in order to run gradient descent with an appropriate stepsize.

The function is given as $$f(x)=-frac{1}{m} sum_{i=1}^mleft(y_i log left(sleft(a_i^{top} xright)right)+left(1-y_iright) log left(1-sleft(a_i^{top} xright)right)right)+frac{gamma}{2}|x|^2$$ where $$a_i in mathbb{R}^n, y_i in{0,1}$$,$$s(z)=frac{1}{1+exp (-z)}$$ is the sigmoid function.

$$nabla f(x)=frac{1}{m} sum_{i=1}^m a_ileft(sleft(a_i^{top} xright)-y_iright)+gamma x$$.

My ideas was that the smoothness constant $$L$$ has to be bigger than all the eigenvalues of the hermitian of the given function, this follows from the fact that if $$f$$ is $$L$$-smooth, $$g(x)=frac{L}{2} x^T x-f(x)$$ is a convex function and therefore the hessian has to be positive semi-definite.
The second-order partial derivatives of $$f$$ are given as

$$frac{partial^2 }{partial x_k partial x_j}f(x)=frac{1}{m} sum_{i=1}^ms(a_i^{top} x)left(1-s(a_i^{top} x)right)[a_i]_k[a_i]_j+gammadelta_{ij}$$

from the following github post (https://github.com/ymalitsky/adaptive_GD/blob/master/logistic_regression.ipynb) i know that $$L=frac{1}{4} lambda_{max }left(A^{top} Aright)+gamma$$ , where $$lambda_{max }$$ denotes the largest eigenvalue, which seems good since i figured out that $$s(a_i^{top} x)left(1-s(a_i^{top} x)right)leq frac{1}{4}$$ for all $$x$$.

But i am not able to fit everything together. I would appreciate any help.

## GnuCash – Help Buttons Not Working

GnuCash 2.6.15 – Debian Stretch

`gnucash-docs` and `yelp` packages installed.

While in GnuCash, when I activate a sub-window “Help” button (e.g. as seen by clicking Edit -> Find… -> Help), the mouse pointer changes from a pointer icon to the active processing icon for about 15 seconds. It then changes back to a pointer icon without any other action. No help dialog is created.

However, when clicking (on the main toolbar menu) Help -> Tutorial and Concepts Guide, said guide comes up as is should!

I suspect I may be missing a package, but which one?

## Ultrafilters and compactness

A topological space is compact if and only if every ultrafilter is convergent.

While I was reading the proof of the one Side of theorem above, there is something I could not understand. Following is the proof of of the one side of the theorem.

Let $$X$$ be compact and assume that $$mathcal{F}$$ is the ultrafilter on $$X$$ without a limit point. Then for each $$xin X$$, there exists an open neighborhood $$U_{x}$$ of it such that each $$U_{x}$$ does not contain any member of $$mathcal{F}$$. Since $$mathcal{U}={U_{x} : xin X}$$ is an open cover of $$X$$, there exists a finite subfamily $${U_{x_{i}}: i=1,2,…,n}$$ of $$mathcal{U}$$ such that $$X=bigcup_{i=1}^{n} U_{x_{i}}$$. Let $$Ainmathcal{F}$$ be fixed. Then $$A=(Acap U_{x_{1}})cap (Acap U_{x_{2}})…(Acap U_{x_{n}})inmathcal{F}$$ and thus there exists an $$iin{1,2,…,n}$$ such that the subset $$Acap U_{x_{i}}$$ is in $$mathcal{F}$$ which is a contradiction.

The thing that I could not understand, why there exists $$iin{1,2,…,n}$$ such that $$Acap U_{x_{i}}$$ must be in $$mathcal{F}$$? If you clarify this, it would highly be appreciated. Thank you.

## Representing \$G=text{GL}^+(2,mathbf R)\$ as the matrix product \$G=TH\$. If \$H=text{SO}(2)\$, what is \$T\$?

In this paper (Equation 2.6 and 2.7) the author seems to suggest that one can represent the $$text{GL}^+(4,mathbf R)$$ group using the product of two exponentials: $$exp (epsilon cdot T) exp (u cdot J)$$, where $$T$$ are the generators of shears and dilation, and $$J$$ are the generators of Lorentz transformations.

My take on the subject is that since $$T$$ and $$J$$ do not commute, one cannot write $$G$$ as a product of these two exponentials. One must instead write $$G=exp ( epsilon cdot T + u cdot J )$$. It appears to me the author is wrong.

Is the author correct, or am I?

How can I represent $$text{GL}^+(2,mathbf R)$$ as the matrix product $$G=TH$$ where $$H=text{SO}(2)$$?

## Pushout in the category of commutative unital \$C^{ast}\$-algebras

What is the pushout in the category of commutative unital $$C^{ast}$$-algebras? Is it the tensor product? Is it the same as in the category of noncommutative unital $$C^{ast}$$-algebras?

## Bounds on the maximum real root of a polynomial with coefficients \$-1,0,1\$

Suppose I have a polynomial that is given a form
$$f(x)=x^n – a_{n-1}x^{n-1} – ldots – a_1x – 1$$

where each $$a_k$$ can be either $$0,1$$.

I’ve tried a bunch of examples and found that the maximum real root seems to be between $$1,2$$, but as for specifics of a polynomial of this structure I am not aware.

Using IVT, we can see pretty simply that $$f(1)leq0$$ and $$f(2)> 0$$ so there has to be a root on this interval, but thats a pretty wide range was wondering if this was previously studied

## What are active deformable particles?

Could anyone please clarify to me what active particles, in particular active deformable particles are? I have never heard of them, and I am quite curious

## Autoequivalences of \$operatorname{Coh}(X)\$

Let $$X$$ be a smooth projective variety over an algebraically closed field $$k$$ of characteristic zero.

Is there a description of $$operatorname{Aut}(operatorname{Coh}(X))$$, i.e. the autoequivalences of the category $$operatorname{Coh}(X)$$?

Clearly it contains $$operatorname{Aut}(X)ltimesoperatorname{Pic}(X)$$ as a subgroup.

## What exactly does the Remainder Estimate for Integral Test actually mean? \$R_n le int_{n}^{infty}f(x)dx\$

$$int_{n+1}^{infty}f(x)dx le R_n le int_{n}^{infty}f(x)dx$$

What does this actually mean?

Let’s use n=5.

The $$R_5$$ is the error of the partial sum $$S_5$$

That error is less than the sum of the remaining terms from 5 to $$infty$$ ?

Why is that?

Also, why is it greater than sum of the remaining terms from 6 to $$infty$$ ?

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