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We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the…
We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to characterize posets in which some of these mappings coincide. We define special mappings determined…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
A poset is representable if it can be embedded in a field of sets in such a way that existing finite meets and joins become intersections and unions respectively (we say finite meets and joins are preserved). More generally, for cardinals…
We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular this allows us to characterize the homotopy colimits of diagrams of…
In this paper we study quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin to the Conway--Schneeberger 15 theorem.
The purpose of this article is to give a short introduction to the concept of quasi-unitary equivalence of quadratic forms and its consequences. In particular, we improve an estimate concerning the transitivity of quasi-unitary equivalence…
Let Q be a non-singular quadratic form with integer coefficients. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q=0. When Q is positive definite we provide improved upper bounds…
Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded…
We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…
Suppose given a commutative quadrangle in a Verdier triangulated category such that there exists an induced isomorphism on the horizontally taken cones. Suppose that the endomorphism ring of the initial or the terminal corner object of this…
For general non-classical systems, we study the different classical representations that fulfill the specific context dependence imposed by the hidden measurement system formalism introduced in quant-ph/0008061. We show that the collection…
In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute…
We offer some elementary characterisations of group and round quadratic forms. These characterisations are applied to establish new (and recover existing) characterisations of Pfister forms. We establish "going-up" results for group and…
We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences of the existence of Hall polynomials, in particular, we are…
This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, arrangements of subspaces, finite simplicial complexes, and…
In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.
We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.
For any finite poset $P$ we have the poset of isotone maps $\text{Hom}(P,\mathbb{N})$, also called $P^{op}$-partitions. To any poset ideal ${\mathcal J}$ in $\text{Hom}(P,\mathbb{N})$, finite or infinite, we associate monomial ideals: the…
Maniplexes are coloured graphs that generalise maps on surfaces and abstract polytopes. Each maniplex uniquely defines a partially ordered set that encodes information about its structure. When this poset is an abstract polytope, we say…