## Is a virtual machine efficient for isolating viruses from pop-up ads?

To be more clear, I would like to access movie streaming websites which have lots of (pop-up) ads and I’m fearful that I might deal with viruses.

Would VirtualBox help me isolate this type of viruses? What can I do to prevent this?

## Can I use a virtual machine to connect to a public WIFI securely to use Internet? (isolating the host)

I want to use my laptop to connect to a public WiFi in a library but…

I have strong security in my Windows host machine (comodo firewall using a public network settings and rules, protocols disabled, limited privileges account, GPO rules, services disabled…) and use dnscrypt…. but i think this wound’t be enough to be totally safe or yes?.

I have no VPN right now. Can I use virtual machine to connect an use only Internet securely?. Isolating the host?.

I have a Wifi usb dongle too. So i was thinking in disabling all the network interfaces in the host (including the VM one) and conect the VM (guest) to that dongle.

What do you recommend, there is any guide out there to do this with Virtual Box?

Is only to browse internet and probably download some documents/programs, not to use my user credentials by loging in some web but I want to access my projects and documents in my host HDDs securely isolanting it from the internet.

If I wanted only internet no HDD access.. I would use Tails and run, but…

## Isolating $k$ in $H_k=\frac{c}{k+1}$

I am trying to find an equilibrium point of two algorithms, parametrized by $$k$$. The performance of the two algorithms:

• $$\frac{c}{k+1}$$ (where $$c$$ is some given positive constant)
• $$H_k$$ (the $$k$$-th harmonic number)

I am looking for a value $$k$$ such that $$H_k=\frac{c}{k+1}$$. I was able find a relatively close approximation using product-log (Lambert W function). Set $$k=e^{W(c)}-1$$. This yields (using $$e^{W(x)}=\frac{x}{W(x)}$$):

• $$\frac{c}{k+1}=\frac{c}{e^{W(c)}-1+1}=\frac{c}{e^{W(c)}}=\frac{c}{\frac{c}{W(c)}}=W(c)$$
• $$H_k=H_{e^{W(c)}-1}\approx\ln(e^{W(c)}-1)+ 1\approx W(c) + 1$$

I wonder if there is a way to reach an exact solution, or, to have a solution that minimizes the difference between the two expressions.

## How to rewrite $M_1\otimes M_2$ isolating $M_2$?

Is there a way to rewrite $$M_1\otimes M_2$$ as $$M \cdot M_2$$ ($$M$$ multiplied by $$M_2$$) with the objective of isolating $$M_2$$?

Or $$vec(M_1\otimes M_2)$$ as $$M\cdot vec(M_2)$$?