dual nationality – Can I still get a South African passport if I haven’t lived there since I was a child?

You are still a South African citizen.

The South African Citizenship Act 1995 sets out the rules for loss of citizenship in Chapter 3, Section 6:

6.(1) Subject to the provisions of sub-section (2), A South African shall cease to be a South African citizen if —

(a) he or she, whilst not being a minor, by some voluntary and formal
act other than marriage, acquires the citizenship or nationality of a
country other than the Republic (b) …

You would have lost your citizenship once you had acquired British citizenship, but as you were a minor this section does not apply.

Note that even as an adult it is possible to retain South African citizenship, but one must apply for permission to do so before acquiring a second nationality.

partitioning – Windows 10 Ubuntu 16.04 Dual boot file permission read only in shared parition

I have a dual boot set up with Windows 10 and Ubuntu 16.04. I created a shared partition that can be accessed from both. My problem occurs when I try to access a file I saved on Ubuntu while I’m on Windows or vice versa.

If I’m on Windows, opening a file I saved while I was on Ubuntu, it’s read only and I can save the edited version.

If I’m on Ubuntu, opening a file I saved while I was on Windows, (I forget what happens. I’m currently on Ubuntu right now, but it also doesn’t work)

I’ve tried the common fixes you see online like making sure fast boot is off. This is what the last two lines of my /etc/fstab looks like

UUID=D6CE4D79CE4D52C3 /media/DualStorage ntfs-3g auto,user,permissions,rw,exec 0 0
UUID=0C7435547435422E /media/Windows  ntfs  defaults,umask=222  0 0

How can I fix this permissions issue?

dual boot – Cannot open ubuntu 20.06 which is in downloads on my hp pavilion with xp. dualboot

Step 1- Get a pen drive / HDD with enough space (above 5–6gb is more than enough).

Step 2- Format it by right clicking on the drive and clicking format.

Step 3- Download UNetbootin. This software allows you to create a bootable HDD/pendrive. Do not forget to download the Ubuntu ISO file.

Step 4- if you want to keep Windows XP and Ubuntu, partition your drive. Refer to YouTube tutorials for this because I’m not experienced enough to share this. If you want to kill Windows XP forever, ignore this.

Step 5- Shut down your PC, connect your pen drive and select boot from USB. To do this step successfully, you need to know your motherboard model and company as it varies from company to company. Once again, refer to YouTube for this step.

Step 6- Follow the steps and install just like any other windows program.

Step 7- Post installation, enjoy Linux life.

ct.category theory – What, precisely, do we mean when we say that a f.d. vector space is canonically isomorphic to its double dual?

I’ve been reading the Xena Project blog, which has been loads of fun. In the linked post Kevin gives the natural isomorphism $V to V^{ast ast}$ from a f.d. vector space to its dual as an example of a “canonical isomorphism”:

People say that the obvious map from a vector space to its double dual is “canonical” but they could instead say that it is a natural transformation.

I think this is not a complete description. When we say that $V$ is canonically isomorphic to its double dual we don’t just mean that there exists some natural isomorphism from the identity functor to the double dual functor – what we mean, and what we use in practice, is that a particularly canonical natural transformation $V to V^{ast ast}$ is an isomorphism. We can multiply any such natural isomorphism by a scalar $c neq 0, 1$ in the ground field $k$ and obtain a different natural isomorphism between these two functors, and these are not canonical!

But reading the linked post showed me I don’t know precisely what I mean by “canonical” in the paragraph above. So:

Question: What, precisely, do we mean by “canonical” when we say that the usual natural transformation $V to V^{ast ast}$ is the “canonical” one we want? What other “canonical” maps are canonical in the same way?

What follows are some off-the-cuff thoughts about this.


One thought is that when we write this map down we’re “using as little as possible”; we’re not even really using that we’re working in vector spaces. If we define the dual to be the internal hom $(V, k)$ then ultimately all we’re using is the evaluation map $V otimes (V, k) to k$ together with currying. In other words, one way to make precise what we’re using is the closed monoidal structure on $text{Vect}$. (We don’t even need a closed structure if we define the dual to be the monoidal dual but I expect the internal hom to be more familiar to more mathematicians.)

So, here’s what I think ought to be true: in the free closed monoidal category on an object $V$ (blithely assuming that such a thing exists – maybe I should have used monoidal duals after all, because I’m much more confident that the free monoidal category on a dualizable object exists), there ought to be a literally unique morphism $V to ((V, 1), 1)$ where $1$ denotes the unit object. This is the “walking double dual map” and, by the universal property, reproduces all the other ones, and I think this is a candidate for what we might mean by “canonical map.”

This trick of taking free categories is a really good trick actually, since it also cleanly describes the nonexistence of canonical maps. For example there is no canonical map $V to V otimes V$, and you could use representation theory to show that the only $GL(V)$-equivariant map is zero, but actually it’s just true that in the free monoidal category on $V$ there are no maps $V to V otimes V$ whatsoever. Similarly there is no canonical map $V to V^{ast}$, and similarly you could use representation theory to show that the only $GL(V)$-equivariant map is zero, but actually it’s just true that in the free closed monoidal category on $V$ (if it exists; take the free monoidal category with duals if not) there are no such maps whatsoever.

But I don’t think this sort of reasoning is enough to capture other examples where two functors are naturally isomorphic and there’s a particularly canonical natural isomorphism that we want in practice. For example, it’s also true that de Rham cohomology $H^{bullet}_{dR}(X, mathbb{R})$ on smooth manifolds is canonically isomorphic to singular cohomology $H^{bullet}(X, mathbb{R})$ with real coefficients, and by this we don’t mean just that there exists some natural isomorphism but that the particularly canonical natural transformation given by integrating differential forms over simplices is an isomorphism. We can multiply any such natural isomorphism by $c^n$ in degree $n$ where $c in mathbb{R} setminus { 0, 1 }$ and we’ll get a different one, even one that respects cup products, and again these are not canonical (although I wonder if we could easily distinguish the usual one from the one obtained by setting $c = -1$ – do we have to choose how simplices are oriented or something like that somewhere?) But now I really don’t know what I mean by that! It doesn’t seem like I can pull the same trick of zooming out to a more general categorical picture. de Rham cohomology is a pretty specific functor defined in a pretty specific way. Maybe this one is a genuinely different sense of “canonical,” closer to “preferred,” I don’t know.


Some previous discussion of “canonical” stuff on MO:

dual boot – Problems installing 20.04 desktop on main drive partition along side Windows 10

0/2 trying to install Ubuntu alongside Windows10

So first off let me say I am a noob to Linux. I have built a few PCs before so I believed I had the ability and have researched this thing thoroughly before hand but I have struck out twice trying to install Ubuntu alongside Windows 10.

I have: 1 Tb NVMe (with windows 10), 1TB SSD (windows apps), 2TB HDD (Backups etc)

The first time I tried the “something else” method after making some free space of 200gb on my main windows drive. I used recommended partition sizes but I got a “fatal error” in grub during install and could no longer access Windows after. It was corrupted and I couldn’t get boot to recognize it. Reinstall was probably needed anyway so I formatted the drive and started over.

The second time the “install alongside windows 10” option was not available so I once again tried “something else”. This time I was prepared with a Windows image in case something went wrong again. It did. I had set up my partitions on the free space by only setting root, swap area and small EFI system partition. No other fancy stuff. The same thing happened and I had to reinstall Windows 10. Thank goodness for my restore image.

Now I don’t know if I’m a glutton for punishment or what but I want to try the install alongside windows 10 option to see if that will work but can’t get it to come up.

What am I doing wrong here!?

18.04 – Linux giving severe problems with Windows dual boot

Can someone help me out with this issue? My laptop has been giving me problems since quite a while now. I had a single Ubuntu 18.04 running that was lagging my system so much that I had to clean install it again. However, it again started giving problems such as

ACPI error, 
blk_update_request: I/O error,
Failed to start Network Time Synchronization, etc.

All of these issues really bugged me off because it was tiresome to run a manual fsck everytime I wanted to boot up the system, so I migrated to Linux mint. The first time the installation failed, and I ran a boot repair. The pastebin link can found here.

Can someone look into it and let me know what exactly to do in this case?

looking for 8 cores or dual cpu e5 processor dedicated server on EU

hello i’m looking for a dedicated server with good uptime

ram: 32gb – 64gb better
cpu: 8 cores (16 threads) or dual e5 six cores, most … | Read the rest of https://www.webhostingtalk.com/showthread.php?t=1821219&goto=newpost

mathematical optimization – SemidefiniteProgramming for operator norms: Stuck at the edge of dual feasibility

I’m trying to calculate operator norms of linear transformations over space of matrices. For instance, find norm of $f(A)=XA$ by optimizing following:

$$max_{|A|=1} |XA|$$

This looks like a semidefinite programme, but I’m having trouble solving it with SemidefiniteOptimization. Simplest failing example is to find operator norm of $f(A)=5A$ in 1 dimension. It fails with Stuck at the edge of dual feasibility. Any suggestions?

Constraints
$$
A succ 0\
Isucc A \
x I succ -5 A
$$

Objective

$$
text{min}_{A,x} x
$$

d = 1;
ii = IdentityMatrix(d);
(* Symbolic symmetric d-by-d matrix *)
ClearAll(a);
X = 5*ii;
A = Array(a(Min(#1, #2), Max(#1, #2)) &, {d, d});
vars = DeleteDuplicates(Flatten(A));

cons0 = VectorGreaterEqual({A, 0}, {"SemidefiniteCone", d});
cons1 = VectorGreaterEqual({ii, A}, {"SemidefiniteCone", d});
cons2 = VectorGreaterEqual({x ii, -X.A}, {"SemidefiniteCone", d});
SemidefiniteOptimization(x, cons0 && cons1 && cons2, {x}~Join~vars)
```

Best config for dual fiber uplink on Cisco Nexus 3048TP?

We have a dual fiber uplink in a colo facility and use two Cisco Nexus 3048TP core switches. What would be the best configuration in terms o… | Read the rest of https://www.webhostingtalk.com/showthread.php?t=1820590&goto=newpost

dual boot – Does grub require passphrase when accessing “Ubuntu” and “Advanced options for Ubuntu”

My previous question was

I was looking to install Ubuntu encrypted with LUKS while dual-booting with windows as I would after shrinking Windows partition from Windows follow these instructions – https://askubuntu.com/a/293029 . I have also researched and know about the evil-maid attack and that someone could change the kernel or install keylogger if my /boot is not encrypted. How would I encrypt Ubuntu with LUKS while having /boot directory encrypted too? In addition to this, from the Grub Recovery Mode the User should not be able to access it and the “root shell” option without entering the password. Could you please explain how I could accomplish this? Thanks

Does help.ubuntu.com/community/ManualFullSystemEncryption help (with dual booted windows and ubuntu) encrypting everything in Ubuntu including the boot partition? Secondly, in addition, would setting up and encrypting everything including boot partition using that guide make it so that when I get in the GRUB, in Advanced Ubuntu options –> Recovery Mode also it for “root shell” asks me for my passphrase? Lastly, if I LUKS encrypt entire Ubuntu except /boot would the GRUB ask me for passphrase when booting into Ubuntu or when accessing Advanced Ubuntu Options such as recovery mode? Additionally, this bug https://bugs.launchpad.net/ubuntu/+source/grub2/+bug/1565950 is solved now, right in latest release of Ubuntu?

GRUB