Related papers: Remarks on Fixed Point Assertions in Digital Topol…
On [3, p. 199] one says "We mention parenthetically that the proof of [99, Lemma 41.3] is incorrect, and we do not know whether it, [99, Theorem 41.5] and [99, Theorem 41.6] are true". The previously cited reference [99] is our reference…
An emended and improved version of the present paper has been archived in math-ph/0505057, and a preliminary account of its content has been published in Phys.Rev.Lett. 92, 60601, (2004). Moreover, in order to prove the relevance of…
Distributional fixed points of a Poisson shot noise transform (for nonnegative, nonincreasing response functions bounded by 1) are characterized. The tail behavior of fixed points is described. Typically they have either exponential moments…
We prove some constructive results that on first and maybe even on second glance seem impossible.
In this note the authors have raised the question regarding the validity of the main result in [1] by setting an example.
Some of my previous publications were incomplete in the sense that non trivial zeros belonging to a particular type of fundamental domain have been inadvertently ignored. Due to this fact, I was brought to believe that computations done by…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
In this paper, we present two types of Lefschetz numbers in the topology of digital images. Namely, the simplicial Lefschetz number $L(f)$ and the cubical Lefschetz number $\bar L(f)$. We show that $L(f)$ is a strong homotopy invariant and…
In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
Fixed points for scalar theories in $4-\varepsilon$, $6-\varepsilon$ and $3-\varepsilon$ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…
A few final comments on arXiv:1210.7548 are given to confute incorrect arguments claimed there.
The development of veracious models of the Internet topology has received a lot of attention in the last few years. Many proposed models are based on topologies derived from RouteViews BGP table dumps (BTDs). However, BTDs do not capture…
We add to our knowledge of the approximate fixed point property (AFPP) in digital topology. We show that a digital image that is a tree has the AFPP. Given two digital images (X, \kappa) and (Y, \lambda) that have the approximate fixed…
Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
In this paper we answer several questions of Dikran Dikranjan about algebraically determined topologies on the group of (finitely supported) permutations of a set X.
This paper presents a comprehensive refutation of the so-called "blockchain trilemma," a widely cited but formally ungrounded claim asserting an inherent trade-off between decentralisation, security, and scalability in blockchain protocols.…