Related papers: Functorial maps and weak parities
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
This note has an experimental nature and contains no new theorems. We introduce certain moves for classical knot diagrams that for all the very many examples we have tested them on give a monotonic complete simplification. A complete…
In this paper, we introduce the concept of weak fuzzy linear topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this topology consists of all weakly lower semi-continuous fuzzy sets on a…
We prove that for some knot-like objects one can easily recognize non-equivalence w.r.t. all Reidemeister moves by studying some equivalence classes modulo only 2nd Reidemeister moves. There are applications to virtual knots, graph-links…
We define counting and cocycle enhancement invariants of virtual knots using parity biquandles. These invariants are determined by pairs consisting of a biquandle 2-cocycle \phi^0 and a map \phi^1 with certain compatibility conditions…
In the present note we focus on conic line arrangements in the plane with quasihomogeneous ordinary singularities from the perspective of weak Ziegler pairs. The foundations of this article come from an active area of research devoted to…
Weak unit disk contact graphs are graphs that admit representing nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. In this work we focus on graphs without…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
A sequence of $F$-polynomials $\{ F^n_K (t, \ell)\}_{n=1}^{\infty}$ of virtual knots $K$ was defined by Kaur, Prabhakar, and Vesnin in 2018. These polynomials have been expressed in terms of index value of crossing and $n$-writhe of $K$. By…
Given a group endowed with a Z/2-valued morphism we associate a Gauss diagram theory, and show that for a particular choice of the group these diagrams encode faithfully virtual knots on a given arbitrary surface. This theory contains all…
Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…
Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.
The algebraic path problem provides a general setting for shortest path algorithms in optimization and computer science. This work extends the algebraic path problem to networks equipped with input and output boundaries. We show that the…
We connect the weak measurements framework to the path integral formulation of quantum mechanics. We show how Feynman propagators can in principle be experimentally inferred from weak value measurements. We also obtain expressions for weak…
In this paper, we study the relation between geodesic and harmonic mappings. Harmonic mappings are defined between Riemannian manifolds as critical points of the energy functional, on the other hand, geodesic mappings are defined in a more…
Every second flat Reidemeister move of knot projections can be decomposed into two types thorough an inverse or direct self-tangency modification, respectively called strong or weak, when orientations of the knot projections are arbitrarily…
The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.
Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results.…
Tannaka Duality describes the relationship between algebraic objects in a given category and their representations; an important case is that of Hopf algebras and their categories of representations; these have strong monoidal forgetful…
We construct a denotational model of linear logic, whose objects are all the locally convex and separated topological vector spaces endowed with their weak topology. The negation is interpreted as the dual, linear proofs are interpreted as…