Related papers: Algebraic structure behind Odrzywo{\l}ek's EML ope…
For the unitary ensembles of $N\times N$ Hermitian matrices associated with a weight function $w$ there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two…
It is well-known that an averaging operator on a commutative associative algebra gives rise to a perm algebra. This paper lifts this process to the level of bialgebras. For this purpose, we first give an infinitesimal bialgebra structure…
In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…
Binary Parseval frames share many structural properties with real and complex ones. On the other hand, there are subtle differences, for example that the Gramian of a binary Parseval frame is characterized as a symmetric idempotent whose…
We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…
We describe the structure of bimodules (over finite dimensional algebras) which have the property that the functor of tensoring with such a bimodule sends any module to a projective module. The main result is that all such bimodules are…
In this note we discuss trees similar to the Calkin-Wilf tree, a binary tree that enumerates all positive rational numbers in a simple way. The original construction of Calkin and Wilf is reformulated in a more algebraic language, and an…
In this paper we study in detail algebraic properties of the algebra $\mathcal D(W)$ of differential operators associated to a matrix weight of Gegenbauer type. We prove that two second order operators generate the algebra, indeed $\mathcal…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural…
Binary multirelations form a model of alternating nondeterminism useful for analysing games, interactions of computing systems with their environments or abstract interpretations of probabilistic programs. We investigate this alternating…
We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…
An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an…
The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data…
We consider differential operators acting on densities of arbitrary weights on manifold $M$ identifying pencils of such operators with operators on algebra of densities of all weights. This algebra can be identified with the special…
Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…
The exponential generating functions of {n^(n+m)} for arbitrary integer m are expressed as rational functions of the e.g.f. of {n^(n-1)} [the tree function] and then of the e.g.f. of {n^n} [the endofunction function]. The coefficients in…