This simply connected is called the universal covering group.
FeathersJS Heroku deployment Updated 2025-07-16
Got it working as mentioned at: github.com/cirosantilli/feathers-chat/tree/sequelize-pg
Bibliography:
There's also a
heroku branch at: github.com/feathersjs/feathers-chat/tree/heroku, but it also seems to use NeDB? So you can have a filesystem in Heroku? Doesn't seem so: stackoverflow.com/questions/42775418/heroku-local-persistent-storage Exam as a service Updated 2025-07-16
This is Ciro Santilli's name for the idea that we should not have structured degrees at university that require entry exams, only tests that anybondy could take, likely for free, and then they would just have proof that they know the stuff for e.g. teachers that care about a subject while selecting students to work with them in research.
We just need control rooms where someone can watch students for cheating. Multiple different exams can be taken in the same room of course, students just have to sign up in advance. The exams should happen regularly depending on demand. E.g. extremelly common subjects should happen every month, and highly specialized ones every 6 months or 1 year.
Questions should be always taken from an open question pool which also contains answers, thus allowing anyone to effectively study for it.
We then make an API available, so that students can grant access to specific results to anyone they choose, or even make the results public for anyone to see. This way the people that care about the exams can just machine learn what exams correlate with their desired performance.
Bibliography:
Exceptional object Updated 2025-07-16
Oh, and the dude who created the en.wikipedia.org/wiki/Exceptional_object Wikipedia page won an Oscar: www.youtube.com/watch?v=oF_FLN-TmCY, Dan Piponi, aka
@sigfpe. Cool dude.Cool examples:
Excessive encapsulation is the root of much evil Updated 2025-07-16
Some anecdotes.
Ciro Santilli never splits up functions unless there is more than one calling point. If you split early, the chances that the interface will be wrong are huge, and a much larger refactoring follows.
int cross_block_var;
// First step.
{
int myvar;
}
// Second step.
{
int myvar;
}Ciro has seen and had to deal with in his lifetime with two projects that had like 3 to 10 git separate Git repositories, all created and maintained by the same small group of developers of the same organization, even though one could not build without the other. Keeping everything in sync was Hell! Why not just have three directories inside a single repository with a single source of truth?
Another important case: Linux should have at least a C standard library, init system, and shell in-tree, like BSD Operating Systems, as mentioned at: Section "Linux".
Existence and uniqueness of solutions of partial differential equations Updated 2025-07-16
Unlike for ordinary differential equations which have the Picard–Lindelöf theorem, the existence and uniqueness of solution is not well solved for PDEs.
For example, Navier-Stokes existence and smoothness was one of the Millennium Prize Problems.
Existence of the matrix logarithm Updated 2025-07-16
en.wikipedia.org/wiki/Logarithm_of_a_matrix#Existence mentions it always exists for all invertible complex matrices. But the real condition is more complicated. Notable counter example: -1 cannot be reached by any real .
The Lie algebra exponential covering problem can be seen as a generalized version of this problem, because
- Lie algebra of is just the entire
- we can immediately exclude non-invertible matrices from being the result of the exponential, because has inverse , so we already know that non-invertible matrices are not reachable
Existential risk of AGI Updated 2025-07-16
www.cam.ac.uk/research/news/the-best-or-worst-thing-to-happen-to-humanity-stephen-hawking-launches-centre-for-the-future-of
The rise of powerful AI will either be the best or the worst thing ever to happen to humanity. We do not yet know which.
Exotic sphere Updated 2025-07-16
Expectation value Updated 2025-07-16
Experimental physics Updated 2025-07-16
Experiment and theory are like the yin and yang: opposites, but one cannot exist without the other.
Feces Updated 2025-07-16
Federal University of São Carlos Updated 2025-07-16
Female Updated 2025-07-16
ExpertRank Updated 2025-07-16
Was adopted by AskJeeves in 2001.
The Google Story Chapter 11. "The Google Economy" comments:
As they saw it, generation one was AltaVista, generation two was Google, and generation three was Teoma, or what Ask Jeeves came to refer to as Expert Rank. Teoma's technology involved mathematical formulas and calculations that went beyond Google's PageRank system, which was based on popularity. In fact, the concept had been cited in the original Stanford University paper written by Sergey Brin and Larry Page as one of the methods that could be used to rank indexed Web sites in response to search requests. "They called their method global popularity and they called this method local popularity, meaning you look more granularly at the Web and see who the authoritative sources are," Lanzone said. He said Brin an Page had concluded that local popularity would be exceedingly difficult to execute well, because either it would require too much processing power to do it in real time or it would take too long.
googlesystem.blogspot.com/2006/03/expertrank-authoritative-search.html mentionsand:
ExpertRank is an evolution of IBM's CLEVER project, a search engine that never made it to public.
The difference between PageRank and ExpertRank is that for ExpertRank the quality of the page is important and that quality is not absolute, but it's relative to a subject.
There are other more recent algorithms with similar names, and are prehaps related:
- www.researchgate.net/publication/257015904_ExpertRank_A_topic-aware_expert_finding_algorithm_for_online_knowledge_communities ExpertRank: A topic-aware expert finding algorithm for online knowledge communities (2013)
- ieeexplore.ieee.org/document/5260966 ExpertRank: An Expert User Ranking Algorithm in Online Communities
Explicit scalar form of the Maxwell's equations Updated 2025-07-16
For numerical algorithms and to get a more low level understanding of the equations, we can expand all terms to the simpler and more explicit form:
Exponential map Updated 2025-07-16
Most commonly refers to: exponential map.
Exponential map (Lie theory) Updated 2025-07-16
Like everything else in Lie group theory, you should first look at the matrix version of this operation: the matrix exponential.
The exponential map links small transformations around the origin (infinitely small) back to larger finite transformations, and small transformations around the origin are something we can deal with a Lie algebra, so this map links the two worlds.
The idea is that we can decompose a finite transformation into infinitely arbitrarily small around the origin, and proceed just like the product definition of the exponential function.
The definition of the exponential map is simply the same as that of the regular exponential function as given at Taylor expansion definition of the exponential function, except that the argument can now be an operator instead of just a number.
Exponentiation Updated 2025-07-16
Exponentiation functional equation Updated 2025-07-16
We define this as the functional equation:It is a bit like cauchy's functional equation but with multiplication instead of addition.
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