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pro vyhledávání: '"NISHIMURA, Hirokazu"'
Autor:
Nishimura, Hirokazu
Topos theory is a category-theoretic axiomatization of set theory. Model categories are a category-theoretical framework for abstract homotopy theory. They are complete and cocomplete categories endowed with three classes of morphisms (called fibrati
Externí odkaz:
http://arxiv.org/abs/1702.05769
Autor:
Nishimura, Hirokazu
It was shown by the author [International Journal of Theoretical Physics 36 (1997), 1099-1131] in synthetic differential geometry that what is called the general Jacobi identity obtaining in microcubes underlies the Jacobi identity of vector fields.
Externí odkaz:
http://arxiv.org/abs/1608.02486
Autor:
Nishimura, Hirokazu
This paper gives a first step towards developing synthetic differential geometry within homotopy type theory. Its model theory will be discussed in a subsequent paper.
Externí odkaz:
http://arxiv.org/abs/1606.06540
We have studied the infinitesimal Baker-Campbell-Hausdorff formula up to n=4 (Math. Appl. 2 (2013), 61-91). In this note we correct some errors in our calculation for n=4 and presents the calculation for n=5 by using Mathematica.
Externí odkaz:
http://arxiv.org/abs/1507.01453
Autor:
Nishimura, Hirokazu
Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.
Externí odkaz:
http://arxiv.org/abs/1406.0075
Autor:
Nishimura, Hirokazu
It is well known in classical electrodynamics that the magnetic field given by a current loop and the electric field caused by the corresponding dipoles in sheets are very similar, as far as we are far away from the loop, which enables us to deduce A
Externí odkaz:
http://arxiv.org/abs/1401.1561
Autor:
Nishimura, Hirokazu
Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of infinite-dimensional Lie groups how to construct a Lie group with a given Lie algebra as its Lie algebra or whether there exists such a Lie group at all. We
Externí odkaz:
http://arxiv.org/abs/1307.5520
Autor:
Nishimura, Hirokazu
After the torch of Anders Kock [Taylor series calculus for ring objects of line type, Journal of Pure and Applied Algebra, 12 (1978), 271-293], we will establish the Baker-Campbell-Hausdorff formula as well as the Zassenhaus formula in the theory of
Externí odkaz:
http://arxiv.org/abs/1304.4667
Autor:
Nishimura, Hirokazu
In our previous paper (Axiomatic Differential Geometry II-3) we have discussed the general Jacobi identity, from which the Jacobi identity of vector fields follows readily. In this paper we derive Jacobi-like identities of tangent-vector-valued forms
Externí odkaz:
http://arxiv.org/abs/1211.5271
Autor:
Nishimura, Hirokazu
The principal objective in this paer is to study the relationship between the old kingdom of differential geometry (the category of smooth manifolds) and its new kingdom (the category of functors on the category of Weil algebras to some smooth catego
Externí odkaz:
http://arxiv.org/abs/1210.3422