Related papers: M\"obius Functions of Some Annular Noncrossing Obj…
Motivated by recent work on mixtures of classical and free probabilities, we introduce and study the notion of $\epsilon$-noncrossing partitions. It is shown that the set of such partitions forms a lattice, which interpolates as a poset…
In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general…
We discuss the multiplicity of the non-trivial zeros of the Riemann zeta-function and the summatory function $M(x)$ of the M\"obius function. The purpose of this paper is to consider two open problems under some conjectures. One is that…
Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.
We consider transcendental meromorphic functions for which the zeros, 1-points and poles are distributed on three distinct rays. We show that such functions exist if and only if the rays are equally spaced. We also obtain a normal family…
We consider nonsymmetric operads with two binary operations satisfying relations in arity 3; hence these operads are quadratic, and so we can investigate Koszul duality. We first consider operations which are nonassociative (not necessarily…
Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type, and discuss their Symmetry…
The rowmotion action on order ideals or on antichains of a finite partially ordered set has been studied (under a variety of names) by many authors. Depending on the poset, one finds unexpectedly interesting orbit structures, instances of…
Given sphere preserving (M\"obius) transformations in $n$-dimensional Euclidean space one can use the Poincar\'e extension to obtain sphere preserving transformations in a half space of $n+1$ dimensions. The Poincar\'e extension is usually…
Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.
We define the class of non-decomposable $N$-ary operations in the mixed tensor algebra $\bigoplus\limits_{i,j=0}^\infty A_i^j$. There are higher Jacobi-like identities for (binary) deformed matrix commutator and a 3-ary operation which is…
We investigate the width complexity of nondeterministic unitary OBDDs (NUOBDDs). Firstly, we present a generic lower bound on their widths based on the size of strong 1-fooling sets. Then, we present classically cheap functions that are…
This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic…
We extend a procedure for construction of the photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a…
In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of…
We establish and explore a relationship between two approaches to moment-cumulant relations in free probability theory: on one side the main approach, due to Speicher, given in terms of M\"obius inversion on the lattice of noncrossing…
M\"obius transformations have been studied over the field of complex numbers. In this paper, we investigate M\"obius transformations over two rings which are not fields: the ring of double numbers and the ring of dual numbers. We give types…
We study the projective derivative as a cocycle of M\"obius transformations over groups of circle diffeomorphisms. By computing precise expressions for this cocycle, we obtain several results about reducibility and almost reducibility to a…
Functional bases of second-order differential invariants of the Euclid, Poincar\'e, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to describe new classes of nonlinear many-dimensional invariant…
The following two assertions are equivalent for an o-minimal expansion of an ordered group $\mathcal M=(M,<,+,0,\ldots)$. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous…