相关论文: On the use of group theory to generalize elements …
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…
Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of…
This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is…
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this…
There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…
We revisit simple and powerful methods for multiple pairwise comparisons that can be used in designs with three groups. We argue that the proper choice of method should be determined by the assessment which of the comparisons are considered…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
Physical properties of matter are tightly related with the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and…
In this paper we prove a sufficient condition for the existence of matchings in arbitrary groups and its linear analogue, which lead to some generalizations of the existing results in the theory of matchings in groups and central extensions…
We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…
We consider the problem of constructing matched groups such that the resulting groups are statistically similar with respect to their average values for multiple covariates. This group-matching problem arises in many cases, including…
This study examines the notion of generators of a pairwise comparisons matrix. Such approach decreases the number of pairwise comparisons from $n\cdot (n-1)$ to $n-1$. An algorithm of reconstructing of the PC matrix from its set of…
We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…
In 2003, Cohn and Umans proposed a group-theoretic approach to bounding the exponent of matrix multiplication. Previous work within this approach ruled out certain families of groups as a route to obtaining $\omega = 2$, while other…
In this work we consider interval metrics on groups; that is, integral invariant metrics whose associated weight functions do not have gaps. We give conditions for a group to have and to have not interval metrics. Then we study Lee metrics…
In this paper we build a set of parametric quotient Lie group structures on the probabilistic simplex that can be extended to real vector space structures. In particular, we rediscover the main mathematical objects generally used when…
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…