Year: 2020

Modularity theorem

Jovan Stosic January 30, 2020

The modularity theorem (formerly called the Taniyama–Shimura conjecture) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat’s last theorem. Later, Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor extended Wiles’ techniques to prove the full modularity theorem in 2001.

Source: Modularity theorem – Wikipedia

Modularity theorem was last modified: January 30th, 2020 by Jovan Stosic

Andrew Wiles

Jovan Stosic January 30, 2020

Sir Andrew John Wiles KBE FRS (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat’s Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal by the Royal Society. He was appointed Knight Commander of the Order of the British Empire in 2000, and in 2018 was appointed as the first Regius Professor of Mathematics at Oxford. Wiles is also a 1997 MacArthur Fellow.

Source: Andrew Wiles – Wikipedia

Andrew Wiles was last modified: January 30th, 2020 by Jovan Stosic

Virtualbox shared folder mount from fstab fails; works once bootup is complete

Jovan Stosic January 16, 2020

I ran afoul of this problem too. I mount /var/www using VBox shared folders functionality, so this was quite annoying.

The solution I found was to force the vboxsf module to be loaded early, before the mounting of file systems. Just add vboxsf on a line of its own in /etc/modules.

Another solution is to set noauto in /etc/fstab and manually mount drives in /etc/rc.local, but this wasn’t such a good solution for me because by that time Apache has already started and been unable to find anything in /var/www.

https://askubuntu.com/questions/365346/virtualbox-shared-folder-mount-from-fstab-fails-works-once-bootup-is-complete

Virtualbox shared folder mount from fstab fails; works once bootup is complete was last modified: January 16th, 2020 by Jovan Stosic

5 Best Command Line Archive Tools for Linux

Jovan Stosic January 16, 2020

tar is the standard UNIX/Linux archiving application tool. In its early stage it used to be a Tape Archiving Program which gradually is developed into General Purpose archiving package which is capable of handling archive files of every kind. tar accepts a lot of archiving filter with options.

tar options

  1. -A : Append tar files to existing archives.
  2. -c : Create a new archive file.
  3. -d : Compare archive with Specified filesystem.
  4. -j : bzip the archive
  5. -r : append files to existing archives.
  6. -t : list contents of existing archives.
  7. -u : Update archive
  8. -x : Extract file from existing archive.
  9. -z : gzip the archive
  10. –delete : Delete files from existing archive.
tar Examples

Create a tar archive file.

# tar -zcvf name_of_tar.tar.gz /path/to/folder

Decompress an tar archive file.

# tar -zxvf Name_of_tar_file.tar.gz

Source: 5 Best Command Line Archive Tools for Linux – Part 1

5 Best Command Line Archive Tools for Linux was last modified: January 16th, 2020 by Jovan Stosic

64 bit – Does VirtualBox run 64-bit guests on a 32-bit host? – Ask Ubuntu

Jovan Stosic January 15, 2020

VirtualBox supports 64-bit guest operating systems, even on 32-bit host operating systems, provided that the following conditions are met:

  • You need a 64-bit processor with hardware virtualization support (see Section 10.3, “Hardware vs. software virtualization”).
  • You must enable hardware virtualization for the particular VM for which you want 64-bit support; software virtualization is not supported for 64-bit VMs.
  • If you want to use 64-bit guest support on a 32-bit host operating system, you must also select a 64-bit operating system for the particular VM. Since supporting 64 bits on 32-bit hosts incurs additional overhead, VirtualBox only enables this support upon explicit request.
  • On 64-bit hosts (which typically come with hardware virtualization support), 64-bit guest operating systems are always supported regardless of settings, so you can simply install a 64-bit operating system in the guest.
  • Warning

    On any host, you should enable the I/O APIC for virtual machines that you intend to use in 64-bit mode. This is especially true for 64-bit Windows VMs. See Section 3.3.2, “”Advanced” tab”. In addition, for 64-bit Windows guests, you should make sure that the VM uses the Intel networking device, since there is no 64-bit driver support for the AMD PCNet card; see Section 6.1, “Virtual networking hardware”.

Source: 64 bit – Does VirtualBox run 64-bit guests on a 32-bit host? – Ask Ubuntu

64 bit – Does VirtualBox run 64-bit guests on a 32-bit host? – Ask Ubuntu was last modified: January 15th, 2020 by Jovan Stosic