Related papers: Weak Hadamard Star Configurations and Apolarity
Bocci, Carlini, and Kileel have shown that the square-free Hadamard product of a finite set of points $Z$ that all lie on a line $\ell$ in $\mathbb{P}^n$ produces a star configuration of codimension $n$. In this paper we introduce a…
We describe properties of Hadamard products of algebraic varieties. We show any Hadamard power of a line is a linear space, and we construct star configurations from products of collinear points. Tropical geometry is used to find the degree…
We investigate if an existing notion of weak sequential convergence in a Hadamard space can be induced by a topology. We provide an answer on what we call weakly proper Hadamard spaces. A notion of dual space is proposed and it is shown…
We develop a general approach to the problem of classification of weak coideal C*-subalgebras of weak Hopf C*-algebras. As an example, we consider weak Hopf C*-algebras and their weak coideal C*-subalgebras associated with Tambara Yamagami…
We introduce the notion of partial representation of a weak Hopf algebra. We present the universal algebra $H_{par}^w$, which factorizes these partial representations by algebra morphisms. Also, it is shown that $\Hp$ is isomorphic to a…
By omitting the unitary constraint from the definition of weak post-Hopf algebras, we introduce the concept of relaxed weak post-Hopf algebras, offering a thorough characterization of all feasible relaxed weak post-Hopf algebraic structures…
Using the ideas of concatenation construction of codes over the $q$-ary alphabet, we modify the known generalized Sylvester-type construction of the Hadamard matrices. The new construction is based on two collections of the Hadamard…
In this paper, we establish some Hadamard-type inequalities based on coordinated quasi-convexity. Also we define a new mapping associated to coordinated convexity and we prove some properties of this mapping.
Small amplitude inhomogeneous plane waves propagating in any direction in a homogeneously deformed Hadamard material are considered. Conditions for circular polarization are established. The analysis relies on the use of complex vectors (or…
In this paper we consider a generic degree $d$ form $ F $ in $n+1$ variables. In particular, we investigate the existence of star configurations apolar to $F$, that is the existence of apolar sets of points obtained by the $ n $-wise…
In this paper, we study weak bialgebras and weak Hopf algebras. These algebras form a class wider than bialgebras respectively Hopf algebras. The main results of this paper are Kaplansky's constructions type which lead to weak bialgebras or…
An Hadamard matrix is a square matrix $H\in M_N(\pm1)$ whose rows and pairwise orthogonal. More generally, we can talk about the complex Hadamard matrices, which are the square matrices $H\in M_N(\mathbb C)$ whose entries are on the unit…
Based on a closed formula for a star product of Wick type on $\CP^n$, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra (with coefficients contained in the…
We present a theoretical and experimental study of a photonic crystal based optical system in terms of weak values that map polarization states onto longitudinal spatial position and show fast and slow light behavior.
One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete…
Star configurations are certain unions of linear subspaces of projective space. They have appeared in several different contexts: the study of extremal Hilbert functions for fat point schemes in the plane; the study of secant varieties of…
We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified…
Complex Hadamard matrices H of order 6 are characterized in a novel manner, according to the presence/absence of order 2 Hadamard submatrices. It is shown that if there exists one such submatrix, H is equivalent to a Hadamard matrix where…
Hadamard matrices are square $n\times n$ matrices whose entries are ones and minus ones and whose rows are orthogonal to each other with respect to the standard scalar product in $\Bbb R^n$. Each Hadamard matrix can be transformed to a…
Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent…