There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

We investigate a special sequence of random variables $A(N)$ defined by an exponential power series with independent standard complex Gaussians $(X(k))_{k \geq 1}$. Introduced Hughes, Keating, and O'Connell in the study matrix theory, this relates to Gaussian multiplicative chaos (in particular "holomorphic chaos'' per Najnudel, Paquette, Simm) functions. Soundararajan Zaman recently determined...

We prove a multiplicative version of the equivariant Barratt-Priddy-Quillen theorem, starting from additive proven in [13]. The proof uses elaboration an infinite loop space machine that manufactures orthogonal G-spectra symmetric monoidal G-categories. new produces highly structured associative ring and module appropriate input. It relies on operadic multicategories are considerable independen...

Analytic Hierarchy Process (AHP) is one of the most popular multi-attribute decision aid methods. However, within AHP, there are several competing preference measurement scales and aggregation techniques. In this paper, we compare these possibilities using a decision problem with an inherent trade-off between two criteria. A decision-maker has to choose among three alternatives: two extremes an...

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...