Related papers: Remarks on relative categoricity
Constellations are partial algebras that are one-sided generalisations of categories. It has previously been shown that the category of inductive constellations is isomorphic to the category of left restriction semigroups. Here we consider…
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
This paper achieves, among other things, the following: 1)It frees the main result of [BFKM] from the hypothesis of determinant class and extends this result from unitary to arbitrary representations. 2)It extends (and at the same times…
Let G be a connected reductive group defined over a non-archimedean local field of characteristic 0. We assume G is quasi-split, adjoint and absolutly simple. Let g be the Lie algebra of G. We consider the space of the invariant…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Let L contain only the equality symbol and let L^+ be an arbitrary finite symmetric relational language containing L . Suppose probabilities are defined on finite L^+ structures with ''edge probability'' n^{- alpha}. By T^alpha, the almost…
Inspired by recent results of unusual properties of loop processes in relative locality, we introduce a way to classify loops in the case of kappa-Poincare momentum space. We show that the notion of orientability is deeply connected to a…
We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which $\hbar$ and $G_N$ may…
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into…
In this paper, we introduce the concept of a relative Heffter space which simultaneously generalizes those of relative Heffter arrays and Heffter spaces. Given a subgroup $J$ of an abelian group $G$, a relative Heffter space is a resolvable…
Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or…
We extend the inflationary fixed-point logic, IFP, with a new kind of second-order quantifiers which have (poly-)logarithmic bounds. We prove that on ordered structures the new logic $\exists^{\log^{\omega}}\text{IFP}$ captures the limited…
We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…
We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…
We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.
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…
In the paper we look for an elegant proof of the characterization of relatively compact families in $L^p-$spaces. At first glance, the suggested approach may seem convoluted and lengthy, but we spare no effort to argue that our proof is in…
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…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…
Both relativistic mechanics and Newtonian mechanics are based on principles that have ontological implications. We propose a series of formalisms that rigorously define the ontology underlying mechanical theories, in order to clarify and…