Related papers: A note on positive partial transpose blocks
A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence…
This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…
This article surveys recent advances and future challenges in the $2$-representation theory of finitary $2$-categories with a particular emphasis on problems related to classification of various classes of $2$-representations.
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
In recent years considerable progress has been made towards developing a general theory of quantum entanglement. In particular, criteria to decide whether a given quantum state is entangled are of high theoretical and practical interest.…
The subject of this paper is a simulation to that in [1] but here we consider substitutions corresponding to transpositions instead of replacements.
The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild…
In this expository note, I present some of the key features of the lattice of torsion classes of a finite-dimensional algebra, focussing in particular on its complete semidistributivity and consequences thereof. This is intended to serve as…
In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of…
We consider the action of the modular group $\Gamma (2)$ on the set of positive rational fractions. From this, we derive a model for a classification of fractional (as well as integer) Hall states which can be visualized on two…
Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded…
This thesis is about the study of Lie groupoids endowed with a compatible (multiplicative) differential 1-form. The motivation and scope of the present work is to study the geometry of PDEs using the formalism of Lie groupoids and…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
This semi-expository paper surveys results concerning three classes of orthogonal polynomials: in one non-hermitian variable, in several isometric non-commuting variables, and in several hermitian non-commuting variables. The emphasis is on…
The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its continuity or discontinuity depending on the cluster weight…