Related papers: Soft Neutrosophic Algebraic Structures and Their G…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough…
Set representations are the foundation of various set-based approaches in state estimation, reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral shadows, a class of nonlinear geometric objects previously…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the…
The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…
Notions of core, support and inversion of a soft set have been defined and studied. Soft approximations are soft sets developed through core and support, and are used for granulating the soft space. Membership structure of a soft set has…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
In this paper we discuss the notion of smoothness in complex algebraic supergeometry and we prove that all affine complex algebraic supergroups are smooth. We then prove the stabilizer theorem in the algebraic context, providing some useful…
We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components. We apply our work to obtain similar…
Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and…
Rough set theory is an important mathematical tool for dealing with uncertain or vague information. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood opera- tors. Moreover, the…
In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and…
In 1987, Yomdin proved a lemma on smooth parametrizations of semialgebraic sets as part of his solution of Shub's entropy conjecture for $C^\infty$ maps. The statement was further refined by Gromov, producing what is now known as the…
Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later…
In this paper, the notion of the interval valued neutrosophic soft sets ($ivn-$soft sets) is defined which is a combination of an interval valued neutrosophic sets \cite{wan-05} and a soft sets \cite{mol-99}. Our $ivn-$soft sets generalizes…
Issai Schur, in his doctoral thesis (1901) introduced the Schur algebra to study the polynomial representation theory of the general linear group. He described a basis of this algebra and structure constants. Later, Miguel Mendez (2001)…