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An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…

We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…

In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…

We prove that the Newton product of efficient polynomial projectors is still efficient. Various polynomial approximation theorems are established involving Newton product projectors on spaces of holomorphic functions on a neighborhood of a…

We consider the Poisson algebra S(M) of smooth functions on T^*M which are fiberwise polynomial. In the case where M is locally projectively (resp. conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp.…

We study the recurrence of the product of n functions, each of which satisfies the same recurrence relation.

We prove a connectedness result for products of weighted projective spaces.

We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.

In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…

We study the class of those linear relations that can be factorized as products of idempotent relations. We provide several characterizations of this class, extending known factorization results for operators to the more general setting of…

We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.

Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential…

The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…

This is a review paper about symmetric products of spaces $SP^n(X):= X^n/S_n$. We focus our attention on the symmetric products of 2-manifolds and make a journey through selected topics of algebraic topology, algebraic geometry,…

A concept of multiplicator of symmetric function space concerning to projective tensor product is introduced and studied. This allows to obtain some concrete results. In particular, the well-known theorem of R. O'Neil about the boundedness…

We establish a linearization criterion for skew products of contractions in any dimension. We prove their smooth or holomorphic parameter dependence. In the smooth setting, we use the language of tame Fr\'echet spaces. We apply our result…

We derive an explicit expression for an associative *-product on fuzzy complex projective spaces. This generalises previous results for the fuzzy 2-sphere and gives a discrete non-commutative algebra of functions on fuzzy complex projective…

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the…

We construct a weighted version of polyhedral products and compute its cohomology in special cases. This is applied to resolve Steenrod's cohomology realization problem in a case related to products of spheres.

We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…