Related papers: Weak Hadamard Star Configurations and Apolarity
In this paper we provide an analytical procedure which leads to a system of $(n-2)^2$ polynomial equations whose solutions give the parameterisation of the complex $n\times n$ Hadamard matrices. It is shown that in general the Hadamard…
We initiate the combinatorial study of the poset $\mathrm{wIndex}_{\mathcal{T}}$ of weak $\mathcal{T}$-indexing systems, consisting of composable collections of arities for $\mathcal{T}$-equivariant algebraic structures, where $\mathcal{T}$…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
A new type of complex Hadamard matrices of order 9 are constructed. The studied matrices are symmetric, block circulant with circulant blocks ($BCCB$) and form an until now unknown non-reducible and non-affine two-parameter orbit. Several…
We define a new kind quantized enveloping algebra of a generalized Kac-Moody algebra ${\mathcal G}$ by adding a new generator $J$ satisfying $J^m=J$ for some integer $m$. We denote this algebra by $wU_q^{\tau}({\mathcal G})$. This algebra…
A classical theorem of Jones and Journ\'e on weak-star convergence in the Hardy space $H^1$ was generalised to the multiparameter setting by Pipher and Treil. We prove the analogous result when the underlying space is a product space of…
Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard…
The notion of type of quadruples of rows is proven to be useful in the classification of Hadamard matrices. In this paper, we investigate Hadamard matrices with few distinct types. Among other results, the Sylvester Hadamard matrices are…
Let $M$ be G-graded R-module. The idea of a graded weakly primal submodule of $M$, which is a generalization of a graded primal submodule, is introduced and discussed in this paper. Some characteristics and characterizations are assigned to…
We used 1627 faint (15.5< R<23) stars in five fields of the Calar Alto Deep Imaging Survey (CADIS) to estimate the structure parameters of the Galaxy. The results were derived by applying two complementary methods: first by fitting the…
We explore lattice structures on integer binary relations (i.e. binary relations on the set $\{1, 2, \dots, n\}$ for a fixed integer $n$) and on integer posets (i.e. partial orders on the set $\{1, 2, \dots, n\}$ for a fixed integer $n$).…
In 2015, Archdeacon proposed the notion of Heffter arrays in view of its connection to several other combinatorial objects. In the same paper he also presented the following variant. A weak Heffter array $\mathrm{W}\mathrm{H}(m,n;h,k)$ is…
The topic of this article is weak cosmic shear tomography where the line of sight-weighting is carried out with a set of specifically constructed orthogonal polynomials, dubbed TaRDiS (Tomography with orthogonAl Radial Distance polynomIal…
A three-parameter family of complex Hadamard matrices of order 6 is presented. It significantly extends the set of closed form complex Hadamard matrices of this order, and in particular contains all previously described one- and…
First examples of symmetric Hadamard matrices of orders 508 and 764 are constructed. The method used is known as the propus construction. A conjecture regarding this method is formally proposed but it appears implicitly in three previous…
The properties of dense hadronic and quark matter and its relation to compact stars are discussed. In a bottom-up approach one starts with nuclear and hypernuclear physics at low density and extrapolates hadronic matter to large densities.…
This paper provides some new characterizations of the diamond partial order for rectangular matrices by using properties of inner inverses, minus order, and SVD decompositions. In addition, the recently introduced 1MP generalized inverse…
A notable difference between the ordinary and Hadamard products is that the Hadamard product of two singular positive semidefinite matrices can be nonsingular, and one of the factors can even be indefinite. We present an eigenvalue lower…
Let G be a $p$-adic Lie group. We develop a dimension theory for coadmissible G-equivariant $\mathcal{D}$-modules on smooth rigid analytic spaces. We introduce the category of weakly holonomic G-equivariant $\mathcal{D}$-modules, study its…
We replace the group of group-like elements of the quantized enveloping algebra $U_q({\frak{g}})$ of a finite dimensional semisimple Lie algebra ${\frak g}$ by some regular monoid and get the weak Hopf algebra ${\frak{w}}_q^{\sf d}({\frak…