1,746 research outputs found
3D MODELING OF PROCESSES OF CROSS SEPARATION OF VARIABLE PROFILES ON SCISSORS
Investigation of the process of separation of variable profiles
Mathematics discovered, invented, and inherited
The classical platonist/formalist dilemma in philosophy of mathematics can be
expressed in lay terms as a deceptively naive question: is new mathematics
discovered or invented?
Using an example from my own mathematical life, I argue that there is also a
third way: new mathematics can also be inherited -- and in the process briefly
discuss a remarkable paper by W. Burnside of 1900.Comment: Version 2: A few references have been added
http://www.borovik.net/selecta
Black Box White Arrow
The present paper proposes a new and systematic approach to the so-called
black box group methods in computational group theory. Instead of a single
black box, we consider categories of black boxes and their morphisms. This
makes new classes of black box problems accessible. For example, we can enrich
black box groups by actions of outer automorphisms.
As an example of application of this technique, we construct Frobenius maps
on black box groups of untwisted Lie type in odd characteristic (Section 6) and
inverse-transpose automorphisms on black box groups encrypting .
One of the advantages of our approach is that it allows us to work in black
box groups over finite fields of big characteristic. Another advantage is
explanatory power of our methods; as an example, we explain Kantor's and
Kassabov's construction of an involution in black box groups encrypting .
Due to the nature of our work we also have to discuss a few methodological
issues of the black box group theory.
The paper is further development of our text "Fifty shades of black"
[arXiv:1308.2487], and repeats parts of it, but under a weaker axioms for black
box groups.Comment: arXiv admin note: substantial text overlap with arXiv:1308.248
Construction of Curtis-Phan-Tits system in black box classical groups
We present a polynomial time Monte-Carlo algorithm for finite simple black
box classical groups of odd characteristic which constructs all root
-subgroups associated with the nodes of the extended Dynkin
diagram of the corresponding algebraic group.Comment: 35 page
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