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We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…
Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient…
Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this article, we will consider the types of partitions with restrictions on consecutive parts. We will show that such partitions are…
A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…
On the affine space containing the space $\mathcal{S}$ of quantum states of finite-dimensional systems there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding relevant…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
We show that hereditarily indecomposable spaces can be characterized by a special instance of the Intermediate Value Theorem in their rings of continuous functions.
The partitioning of space by hyperplanes in the context of discrete classification problem is considered. We obtain some relations for the number of partitions and establish a recurrence relation for the maximal number of partitions of R^n…
We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with…
We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula and explicit formula. We find a connection between multidimensional permutations…
The Fibonacci numbers are the prototypical example of a recursive sequence, but grow too quickly to enumerate sets of integer partitions. The same is true for the other classical sequences $a(n)$ defined by Fibonacci-like recursions: the…
We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…
Indecomposable but reducible representations of several Lie algebras of local scale-transformations, including the Schr\"odinger and conformal Galilean algebras, and some of their applications in physical ageing are reviewed. The physical…
We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…
We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes…
It was shown in \cite{sc12} that for a certain class of structures $\I$, $\I$-indexed indiscernible sets have the modeling property just in case the age of $\I$ is a Ramsey class. We expand this known class of structures from ordered…
Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary relations and maps preserving them. In this paper we…
We study the structure of the category of integrable level zero representations with finite dimensional weight spaces of affine Lie algebras. We show that this category possesses a weaker version of the finite length property, namely that…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…