Related papers: Continuity in Information Algebras
As shape analysis of the form presented in Srivastava and Klassen's textbook 'Functional and Shape Data Analysis' is intricately related to Lebesgue integration and absolute continuity, it is advantageous to have a good grasp of the latter…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on some classes of associative algebras, including unital algebras, the semigroup algebras of rectangular bands, algebras with enough…
We expand the toolbox of (co)homological methods in computational topology by applying the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine topological information with algebraic information, they allow for…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…
We study the existence of automatic presentations for various algebraic structures. An automatic presentation of a structure is a description of the universe of the structure by a regular set of words, and the interpretation of the…
The subject considered in this paper has, at least, three points of interest. Suppose that we have a sequence of one-dimensional analytic varieties in a domain in $\Bbb C^n$. The cluster of this sequence consists from all points in the…
Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the…
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
For appropriate parameters $k,p,q$, we introduce and systematically study the class of $(k,p,q)$-differential subalgebras. This is a vast class of Banach $^*$-algebras defined by their relation with their $C^*$-envelopes. Some examples are…
The interpretation of the P-value and its monotone transform s=-log2(p), or S-value, remains debated despite decades of dedicated literature. Within the neo-Fisherian framework, these values are often described as indices of…
In various domains and cases, we observe the creation and usage of information elements which are unnamed. Such elements do not have a name, or may have a name that is not externally referable (usually meaningless and not persistent over…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
Continual learning is a process that involves training learning agents to sequentially master a stream of tasks or classes without revisiting past data. The challenge lies in leveraging previously acquired knowledge to learn new tasks…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
We extend in this article the classical Sobolev inequalities for the module of continuity for the functions belonging to the integer order Sobolev's space on the Sobolev-Bilateral Grand Lebesgue spaces. As a consequence, we deduce the…
The paper introduces a (universal) C*-algebra of continuous functions vanishing at infinity on the n-dimensional quantum complex space. To this end, the well-behaved Hilbert space representations of the defining relations are classified.…