We consider polynomial maps described by so-called (multivariate) linearized polynomials. These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps without mixed terms over a characteristic zero field, we will only obtain (up to a linear transformation of the variables) triangular maps, which are the most b...

We study a generalized Pólya urn with balls of two colours and a triangular replacement matrix; the urn is not required to be balanced. We prove limit theorems describing the asymptotic distribution of the composition of the urn after a long time. Several different types of asymptotics appear, depending on the ratio of the diagonal elements in the replacement matrix; the limit laws include norm...

A composition of taxa included in Dracocephalum imberbe Bunge s. l. is discussed. Species rank D. laniflorum Rupr. reinstated based on the following characters: underground part represented by a system branching rhizomes, bracts absent, calyx 12–14 mm long, with triangular or narrowly triangular, pointless teeth, middle tooth upper lip up to 1.5 times wider than lateral ones and plant being nea...

In this paper we study the action of a generalization of the Binomial interpolated operator on the set of linear recurrent sequences. We find how the zeros of characteristic polynomials are changed and we prove that a subset of these operators form a group, with respect to a well–defined composition law. Furthermore, we study a vast class of linear recurrent sequences fixed by these operators a...

In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary com...

Temporal triangular alopecia (TTA), also known as congenital triangular alopecia, is a nonscarring, noninflammatroy, circumscribed form of alopecia. TTA has been associated with several disorders, such as Phakomatosis Pigmentovascularis. Hair restoration surgery using follicular unit transplantation has been a successful treatment modality for TTA. Herein we report such a success that was susta...

Triangular intuitionistic fuzzy number (TIFN) is a more generalized platform for expressing imprecise, incomplete, and inconsistent information when solving multi-criteria decision-making problems, as well as for expressing and reflecting the evaluation information in several dimensions. In this paper, the TIFN has been applied for solving multi-criteria decision-making (MCDM) problems, first, ...

In this paper we develop a theory of t-cycle D−Z representations for s-dimensional lattice rules of prime-power order. Of particular interest are canonical forms which, by definition, have a D-matrix consisting of the nontrivial invariants. Among these is a family of triangular forms, which, besides being canonical, have the defining property that their Z-matrix is a column permuted version of ...