State initialization (quantum computing) Updated 2025-07-16
Switzerland Updated 2025-07-16
Heat equation Updated 2025-07-16
Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.
Some interesting properties:
- TODO confirm: for a fixed boundary condition that does not depend on time, the solutions always approaches one specific equilibrium function.This is in contrast notably with the wave equation, which can oscillate forever.
- TODO: for a given point, can the temperature go down and then up, or is it always monotonic with time?
- information propagates instantly to infinitely far. Again in contrast to the wave equation, where information propagates at wave speed.
Sample numerical solutions:
One-to-one (data-model) Updated 2025-07-16
Subtitle editor Updated 2025-07-16
ELF Hello World Tutorial Section header table Updated 2025-07-16
Array of
Elf64_Shdr structs.Each entry contains metadata about a given section.
e_shoff of the ELF header gives the starting position, 0x40 here.So the table takes bytes from 0x40 to
0x40 + 7 + 0x40 - 1 = 0x1FF.Some section names are reserved for certain section types: www.sco.com/developers/gabi/2003-12-17/ch4.sheader.html#special_sections e.g.
.text requires a SHT_PROGBITS type and SHF_ALLOC + SHF_EXECINSTRRunning:outputs:
readelf -S hello_world.oThere are 7 section headers, starting at offset 0x40:
Section Headers:
[Nr] Name Type Address Offset
Size EntSize Flags Link Info Align
[ 0] NULL 0000000000000000 00000000
0000000000000000 0000000000000000 0 0 0
[ 1] .data PROGBITS 0000000000000000 00000200
000000000000000d 0000000000000000 WA 0 0 4
[ 2] .text PROGBITS 0000000000000000 00000210
0000000000000027 0000000000000000 AX 0 0 16
[ 3] .shstrtab STRTAB 0000000000000000 00000240
0000000000000032 0000000000000000 0 0 1
[ 4] .symtab SYMTAB 0000000000000000 00000280
00000000000000a8 0000000000000018 5 6 4
[ 5] .strtab STRTAB 0000000000000000 00000330
0000000000000034 0000000000000000 0 0 1
[ 6] .rela.text RELA 0000000000000000 00000370
0000000000000018 0000000000000018 4 2 4
Key to Flags:
W (write), A (alloc), X (execute), M (merge), S (strings), l (large)
I (info), L (link order), G (group), T (TLS), E (exclude), x (unknown)
O (extra OS processing required) o (OS specific), p (processor specific)The
struct represented by each entry is:typedef struct {
Elf64_Word sh_name;
Elf64_Word sh_type;
Elf64_Xword sh_flags;
Elf64_Addr sh_addr;
Elf64_Off sh_offset;
Elf64_Xword sh_size;
Elf64_Word sh_link;
Elf64_Word sh_info;
Elf64_Xword sh_addralign;
Elf64_Xword sh_entsize;
} Elf64_Shdr; Political correctness Updated 2025-07-16
Ciro Santilli believes it generally hurts more than it helps.
Especially when you can't even mention censored things to criticize them. You have to pretend they never existed. So people will forget about them, and do them again in the future.
Quartz clock Updated 2025-07-16
Adjoint operator Updated 2025-07-16
Given a linear operator over a space that has a inner product defined, we define the adjoint operator (the symbol is called "dagger") as the unique operator that satisfies:
Taylor expansion definition of the exponential function Updated 2025-07-16
The Taylor series expansion is the most direct definition of the expontial as it obviously satisfies the exponential function differential equation:
pyenv Updated 2025-07-16
Python
abc Updated 2025-07-16 Python scientific library Updated 2025-07-16
Python web framework Updated 2025-07-16
virtualenv Updated 2025-07-16
python3 -m pip install --user virtualenv
virtualenv .venv
. .venv/bin/activate
pip install -r requirements.txt Before Present Updated 2025-07-16
Hermite polynomials Updated 2025-07-16
Show up in the solution of the quantum harmonic oscillator after separation of variables leading into the time-independent Schrödinger equation, much like solving partial differential equations with the Fourier series.
I.e.: they are both:
- solutions to the time-independent Schrödinger equation for the quantum harmonic oscillator
- a complete basis of that space
Problem Book in Quantum Field Theory by Voja Radovanovic (2008) Updated 2025-07-16
QuTech Academy Updated 2025-07-16
One of their learning sites: www.qutube.nl/
The educational/outreach branch of QuTech.
Renormalization group Updated 2025-07-16
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