Related papers: Formal construction of some exchangeable structure…
Multisets are like sets, except that they can contain multiple copies of their elements. If there are $n_i$ copies of $i$, $1\leq i\leq t$, in multiset $M_t$, then there are $\binom{n_1+\cdots+n_t}{n_1,\ldots, n_t}$ possible permutations of…
Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
Covering space theory is used to construct new examples of buildings.
In the present paper I shall clarify the Babylonian method by which many large tables of reciprocals could be constructed.
We develop a simple method of constructing topological spaces from countable posets with finite levels, one which applies to all second countable T_1 compacta. This results in a duality amenable to building such spaces from finite building…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…
Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra $\mathfrak{sl}(2,\mathbb{R})$ admit solvable structures. These solvable structures can be constructed by using the basis elements…
We consider an urn model leading to a random walk that can be solved explicitly in terms of the well known Jacobi polynomials.
In this paper, we mainly study structure of multiplicative simple Hom-Jordan algebras. We talk about equivalent conditions for multiplicative Hom-Jordan algebras being solvable, simple and semi-simple. As an application, we give a theorem…
Yang-Baxter operators from algebra structures appeared for the first time in [16], [17] and [8]. Later, Yang-Baxter systems from entwining structures were constructed in [5]. In this paper we show that an algebra factorisation can be…
We discuss several constructions of swap polynomials, that is 2--tensor valued matrix polynomials which are multiples of the swap or switch operator.
We provide partial implementations of von Neumann's universal constructor and universal copier, starting out with three types of simple building blocks using minimal assumptions. Using the same principles, we also construct Turing machines.…
We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative…
Semi-entwining structures are proposed as concepts simpler than entwining structures, yet they are shown to have interesting applications in constructing intertwining operators and braided algebras, lifting functors, finding solutions for…
We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent…