Related papers: Semi-Centennial REDUCE
Using elementary linear algebra, this paper clarifies and proves some concepts about a recently introduced octonion-like associative division algebra over R. This octonion-like algebra is actually the same as the split-biquaternion algebra,…
Reservoir Computing is a relatively new framework created to allow the usage of powerful but complex systems as computational mediums. The basic approach consists in training only a readout layer, exploiting the innate separation and…
In this paper, we describe the possibilities of using a rapid mental computation system in elementary education. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly.…
This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss…
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key…
A novel model of reversible computing, the $\aleph$-calculus, is introduced. It is declarative, reversible-Turing complete, and has a local term-rewriting semantics. Unlike previously demonstrated reversible term-rewriting systems, it does…
The C-Algorithm introduced in [Chouikha2007] is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
In this article, we give an explicit construction of the simple modules for both non-degenerate and degenerate cyclotomic Hecke-Clifford superalgebras over an algebraically closed field of characteristic not equal to $2$ under certain…
We present a 'calculator' for constructing a homogeneous approximation of nonlinear control systems, which is based on the algebraic approach developed by the authors in their previous papers. This approach mainly uses linear algebraic and…
A Rough semiring $(T,\Delta,\nabla)$ is considered to describe a special distributive Rough semiring known as a Rough bi-Heyting algebra. A bi-Heyting algebra is an extension of boolean algebra and it is accomplished by weaker notion of…
A software model of a reversible processor ReveR with the stack is discussed in this paper. An architecture, the minimal set of elementary reversible operations together with an implementation of the basic control flow structures and…
In this thesis, we consider semi-algebraic sets over a real closed field $R$ defined by quadratic polynomials. Semi-algebraic sets of $R^k$ are defined as the smallest family of sets in $R^k$ that contains the algebraic sets as well as the…
Semi-Lagrangian methods are numerical methods designed to find approximate solutions to particular time-dependent partial differential equations (PDEs) that describe the advection process. We propose semi-Lagrangian one-step methods for…
In this article we define the semigroup associated to a substitution. We use it to construct a minimal automaton which generates a substitution sequence u in reverse reading. We show, in the case where the substitution has a coincidence,…
In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the…
Among the unitary reflection groups, the one on the title is singled out by its importance in, for example, coding theory and number theory. In this paper we start with describing the irreducible representations of this group and then…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
Advances in semiconductor technology are contributing to the increasing complexity in the design of embedded systems. Architectures with novel techniques such as evolvable nature and autonomous behavior have engrossed lot of attention. This…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…