相关论文: Thin Elements and Commutative Shells in Cubical om…
It is shown that the cubical nerve of a strict omega-category is a sequence of sets with cubical face operations and distinguished subclasses of thin elements satisfying certain thin filler conditions. It is also shown that a sequence of…
We investigate models of algebraic theories in the category of cocommutative coalgebras over a field. We establish some of their categorical properties, similar to those of algebraic varieties. We introduce a class of categories of…
The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the…
A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations.…
Correlations between electrons and the effective dimensionality are crucial factors that shape the properties of an interacting electron system. For example, the onsite Coulomb repulsion, U, may inhibit, or completely block the intersite…
We characterize the asymptotic behaviour, in the sense of $\Gamma$-convergence, of a thin magnetoelastic shallow shell. The compactness is achieved up to rigid motions. For deformations, it relies on an approximation by rigid movements,…
The self-gravitating, spherically symmetric thin shells built of orbiting particles are sstudied. Two new features are found. One is the minimal possible value for an angular momentum of particles, above which elleptic orbits become…
A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical omega-category. This also has the structure of connections in the sense of Brown and Higgins,…
We explore element-wise convex combinations of two permutation-aligned neural network parameter vectors $\Theta_A$ and $\Theta_B$ of size $d$. We conduct extensive experiments by examining various distributions of such model combinations…
Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…
It is emphasized that equivalent definitions of connections on modules over commutative rings are not so in noncommutative geometry.
In these notes we describe models of globular weak $(\infty,m)$-categories ($m\in\mathbb{N}$) in the Grothendieck style, i.e for each $m\in\mathbb{N}$ we define a globular coherator $\Theta^{\infty}_{\mathbb{M}^m}$ whose set-models are…
We show that in a weak globular $\omega$-category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a higher-dimensional generalisation of the Eckmann-Hilton…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
A new class of electromagnetic composite particles is proposed. The composites are very small (the Compton scale), potentially long-lived, would have unique interactions with atomic and nuclear systems, and, if they exist, could explain a…
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…
This paper examines various kinds of subspaces of the non-commutative spaces that are modelled on quasi-projective commutative schemes. It is shown how intersections and unions of weakly closed subspaces, closed subspaces, their weakly open…
Answering a question of Junker and Ziegler, we construct a countable first order structure which is not omega-categorical, but does not have any proper non-trivial reducts, in either of two senses (model-theoretic, and group-theoretic). We…
The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…