Related papers: Normal forms and representable functions in Moisil…

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

We investigate the algebra generated by the operators $x$ and $\mathrm{I} = \int_0^x$, which satisfy the commutation relation \[ [\mathrm{I},x] = \mathrm{I}x - x\mathrm{I} = - \mathrm{I}^2. \] We develop a combinatorial framework for the…

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…

In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…

We develop the viewpoint that the opposite of the category of W*-algebras and unital normal *-homomorphisms is analogous to the category of sets and functions. For each pair of W*-algebras, we construct their free exponential, which in the…

The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U(N_+,N_-) are provided. They generalize the Virasoro and W_\infty algebras to higher dimensions. The…

In this paper we study left and right n-regular functions that originally were introduced in [FL4]. When n=1, these functions are the usual quaternionic left and right regular functions. We show that n-regular functions satisfy most of the…

Here we initiate an investigation into the class mLMn{\times}m of monadic n{\times}m-valued Lukasiewicz-Moisil algebras (or mLMn{\times}m-algebras), namely n{\times}m-valued Lukasiewicz-Moisil algebras endowed with a unary operation called…

For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…

Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…

In a noncommutative algebra there is no canonical way to express elements in univalent way, which is often called "ordering problem". In this note we give product formula of the Weyl algebra in generic ordered expression. In particular, the…

We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to…

In this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in…

The norm closure of the algebra generated by the set $\{n\mapsto {\lambda}^{n^k}:$ $\lambda\in{\mathbb {T}}$ and $k\in{\mathbb{N}}\}$ of functions on $({\mathbb {Z}}, +)$ was studied in \cite{S} (and was named as the Weyl algebra). In this…

We introduce a general theory of twisting algebraic structures based on actions of a bialgebra. These twists are closely related to algebraic deformations and also to the theory of quasi-triangular bialgebras. In particular, a deformation…

We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models and, hence, the results apply to a wide class of modal logics including, for example,…

We propose a doxastic \L ukasiewicz logic \textbf{B\L} that is sound and complete with respect to the class of Kripke-based models in which atomic propositions and accessibility relations are both infinitely valued in the standard…

A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is presented. A natural approach to building coherent states associated to deformed algebras is then deduced.

Normal and composition series of modules enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is discussed.

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…