Related papers: Symmetries and Invariant Differential Pairings
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Multiple testing problems arise naturally in scientific studies because of the need to capture or convey more information with more variables. The literature is enormous, but the emphasis is primarily methodological, providing numerous…
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
This paper proposes a novel perspective on learning, positing it as the pursuit of dynamical invariants -- data combinations that remain constant or exhibit minimal change over time as a system evolves. This concept is underpinned by both…
We lay down the foundations for a systematic study of differentiable and algebraic supervarieties, with a special attention to supergroups.
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
The aim of this paper is to investigate different types of multi-integrals of finite variation and to obtain decomposition results.
This paper investigates the effects that perturbations to an optical system, such as translations or rotations of the optical elements, have on the final location where a light ray strikes a detector. Symmetry arguments are employed to give…
Our purpose in this article is to study anti-invariant statistical submersions from holomorphic statistical manifolds. Firstly we introduce holomorphic statistical submersions satisfying the certain condition, after we give anti-invariant…
We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…
In this paper we analyze the geometric structure and properties of a certain class of subsets of $\Bbb R^d$, known in the literature as 1-multicones, and here simply called multicones, which are quite natural generalizations of the…
We review several algebraic, combinatorial and geometric interpretations of motivic Donaldson-Thomas invariants of symmetric quivers.