Related papers: On quasi-orthogonal cocycles
A cohomology theory is proposed for the recently discovered heptagon relation -- an algebraic imitation of a 5-dimensional Pachner move 4--3. In particular, `quadratic cohomology' is introduced, and it is shown that it is quite nontrivial,…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
An $n\times n$ real matrix $Q$ is quasi-orthogonal if $Q^{\top}Q=qI_{n}$ for some positive real number $q$. If $M$ is a principal sub-matrix of a quasi-orthogonal matrix $Q$, we say that $Q$ is a quasi-orthogonal extension of $M$. In a…
Finite quasi semimetrics on $n$ can be thought of as nonnegative valuations on the edges of a complete directed graph on $n$ vertices satisfying all possible triangle inequalities. They comprise a polyhedral cone whose symmetry groups were…
In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…
In this work it is shown that certain interesting types of quasi-orthogonal system of subalgebras (whose existence cannot be ruled out by the trivial necessary conditions) cannot exist. In particular, it is proved that there is no…
Solutions which are quasimodular forms to a second order differential equation attached to a triangular group are explicitly described in terms of certain orthogonal polynomials.
In this paper we illustrate that paraorthogonality on the unit circle $\mathbb{T}$ is the counterpart to orthogonality on $\mathbb{R}$ when we are interested in the spectral properties. We characterize quasi-paraorthogonal polynomials on…
The determinant is a main organizing tool in commutative linear algebra. In this review we present a theory of the quasideterminants defined for matrices over a division algebra. We believe that the notion of quasideterminants should be one…
We develop a quasisymmetric analogue of the theory of Schubert cycles, building off of our previous work on a quasisymmetric analogue of Schubert polynomials and divided differences. Our constructions result in a natural geometric…
We present a criterion, based on three commutator relations, that allows to decide whether two self-adjoint matrices with non-overlapping support are simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they can be…
We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family…
We develop the theory of coregular sequences and codepth for modules that need not be finitely generated or artinian over a Noetherian ring. We use this theory to give a new version of a theorem of Hellus characterizing set-theoretic…
The notion of unbiased orthogonal designs is introduced as a generalization among unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several constructions for mutually…
We give elementary applications of quasi-homomorphisms to growth problems in groups. A particular case concerns the number of torsion elements required to factorise a given element in the mapping class group of a surface.
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…
We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe…
A real matrix $Q$ is quasi-orthogonal if $Q^{\top}Q=qI$, for some positive real number $q$. We prove that any $n\times n$ skew-symmetric matrix $S$ is a principal sub-matrix of a skew-symmetric quasi-orthogonal matrix $Q$, called a…
The aim of this paper is twofold. The first part is concerned with the associated and the so-called co-polynomials, i.e. new sequences obtained when finite perturbations of the recurrence coefficients are considered. In the second part we…
One of the most promising structural approaches to resolving the Hadamard Conjecture uses the family of cocyclic matrices over ${\mathbb Z} _t \times {\mathbb Z}_2^2$. Two types of equivalence relations for classifying cocyclic matrices…