Related papers: Continuity in Information Algebras
In this note we compare the a-invariant of a homogeneous algebra B to the a-invariant of a subalgebra A. In particular we show that if $A \subset B$ is a finite homogeneous inclusion of standard graded domains over an algebraically closed…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
The main aim of the present paper is to introduce new classes of functions called $ \alpha $ $^m $ continuous maps and $ \alpha $ $^m $ irresolute maps. We obtain some characterizations of these classes and properties are studied.
In this article, we introduce the notion of a curved absolute $\mathcal{L}_\infty$-algebra, a structure that behaves like a curved $\mathcal{L}_\infty$-algebra where all infinite sums of operations are well-defined by definition. We develop…
We consider abstract Sobolev spaces of Bessel-type associated with an operator. In this work, we pursue the study of algebra properties of such functional spaces through the corresponding semigroup. As a follow-up of [4], we show that under…
We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…
We connect the discrete and continuous Bogomolny equations. There exists one-parameter algebra relating two equations which is the deformation of the extended conformal algebra. This shows that the deformed algebra plays the role of the…
This paper which is part of the New Faculty Highlights Invited Speaker Program of AAAI'23, serves as a comprehensive survey of my research in transfer learning by utilizing embedding spaces. The work reviewed in this paper specifically…
First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will…
In calculus, an indefinite integral of a function $f$ is a differentiable function $F$ whose derivative is equal to $f$. In present paper, we generalize this notion of the indefinite integral from the ring of real functions to any ring. The…
Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…
The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…
The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially $C^{*}$-algebras. Here we document our formalization of the continuous functional calculus in Lean, which…
Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an "almost common knowledge topology" reflecting…
Stable event structures, and their duality with prime algebraic domains arising as partial orders of configurations, are a landmark of concurrency theory, providing a clear characterisation of causality in computations. They have been used…
Human adaptability relies crucially on learning and merging knowledge from both supervised and unsupervised tasks: the parents point out few important concepts, but then the children fill in the gaps on their own. This is particularly…
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these…
This paper explores a new class of incomplete preferences -- termed ``connected preferences'' -- in which maximal domains of comparability are topologically connected. We provide necessary and sufficient conditions for continuous…