Related papers: A ternary Relation Algebra of directed lines
We discuss the projective line $\mathbb{P}(R)$ over a finite associative ring with unity. $\mathbb{P}(R)$ is naturally endowed with the symmetric and anti-reflexive relation "distant". We study the graph of this relation on $\mathbb{P}(R)$…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
Relational parametricity was first introduced by Reynolds for System F. Although System F provides a strong model for the type systems at the core of modern functional programming languages, it lacks features of daily programming practice…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
The Djokovi\'{c}-Winkler relation $\Theta$ is a binary relation defined on the edge set of a given graph that is based on the distances of certain vertices and which plays a prominent role in graph theory. In this paper, we explore the…
The Representation Theorem of Lions (RTL) is a version of the Lax--Milgram Theorem where completeness of one of the spaces is not complete. In this paper, RTL is deduced from an operator-theoretical version on normed space. The main point…
An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…
This is the author's 2004 Master's thesis at Iowa State University, done under the supervision of Roger D. Maddux. It provides a background in relation algebras. Three results from the literature are demonstrated in full: (i.) RRA is a…
This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor…
Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is…
Grant-free random access (RA) techniques are suitable for machine-type communication (MTC) networks but they need to be adaptive to the MTC traffic, which is different from the human-type communication. Conventional RA protocols such as…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and…
In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated…
We study unitary multigraded non-associative algebras R generated by an ordered set X over a field K of characteristic 0 such that the mappings d_k: x_l->delta_{kl}, x_k,x_l in X, can be extended to derivations of R. The class of these…
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
We consider a real manifold of dimension 3 or 4 with Minkovsky metric, and with a connection for a trivial GL(n,C) bundle over that manifold. To each light ray on the manifold we assign the data of paralel transport along that light ray. It…
In order to unify the methods which have been applied to various topics such as BRST theory of constraints, Poisson brackets of local functionals, and certain developments in deformation theory, we formulate a new concept which we call the…
Relation extraction (RE) involves identifying the relations between entities from underlying content. RE serves as the foundation for many natural language processing (NLP) and information retrieval applications, such as knowledge graph…
This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming…