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安裝中文字典英文字典辭典工具!
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- (Are there) subtleties in the definition of biproduct
The correct definition of a biproduct is discussed extensively in this blog post The conditions you write down are morally wrong because they don't guarantee uniqueness up to unique isomorphism, which is something you'd like any universal thing to satisfy
- How to find fundamental set of solutions of complementary equation of a . . .
This time that does not appear to work I checked Paul Dawkins' website as you recommended and formed y2=v*y1 and applied the reduction of order I am supposed to do this as a byproduct of finding the general solution It does not appear to be a byproduct! This is a long problem $\endgroup$ –
- linear algebra - Why does cross product give a vector which is . . .
It was a byproduct of the more general concept of product of quaternions Because of its properties, the cross product became popular when it was shown to be useful to solve physics problem However, I accidentally found a motivation for the cross product by consideration of the linear combination of two vectors in 3D space
- What does a half derivative mean? - Mathematics Stack Exchange
Here's why, lets ask the question not what 1 2 means in therms of children but how it came along It came along because we wanted to generalize the set of numbers to include stuff in between the integers It came along for applications besides counting children and is in fact most specifically an "accidental-byproduct" of the existence of division
- calculus - Are discontinuous functions integrable? And integral of . . .
Yes! In fact, this is a byproduct of what's commonly known as the second fundamental theorem of calculus
- Connection between cross product and determinant
There certainly is a connection! Other answers have shown that, of course, but it goes a little deeper than that: determinants and cross products are both based on antisymmetric linear combinations of permutations
- differential geometry - Why are we interested in Einstein metrics . . .
Perelman solved Thurston's Geometrization conjecture that completely classified compact 3-manifolds (and as a byproduct, this solved the famous Poincaré conjecture) The proof relies on the so called Ricci flow , which (very, very) coarsely allows one to obtain Einstein metrics as limits of solutions to the analogue of the heat equation in the
- Why have we chosen our number system to be decimal (base 10)?
I think the answer here might be, that the guys who thought base 10 was a good idea had the largest sticks If one trusts the wikipedia, the Babylonians had a base 60 system, which can still be felt today with this "60 minutes in an hour" nonsense, and a (related) base 12 system was widely in use too
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