Related papers: Balanced Leonard Pairs

Let $(V, \phi)$ be a holomorphic Lie algebroid over an irreducible smooth complex projective variety $X$ of dimension at least three, and let $E$ be a holomorphic vector bundle on $X$. We establish a necessary and sufficient condition for…

We present a new look at description of real finite-dimensional Lie algebras. The basic element turns out to be a pair $(F,v)$ consisting of a linear mapping $F\in End(V)$ and its eigenvector $v$. This pair allows to build a Lie bracket on…

A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are…

In this paper, we define two relations one by orthogonality in vector lattices named as strong relation and the other by bounded linear functionals in normed spaces named as weak relation. It turns out that strong relation is an equivalence…

Linear systems often involve, as a basic building block, solutions of equations of the form \begin{align*} A_Sx_S&+A_Px_P =0\\ A'_Sx_S & =0, \end{align*} where our primary interest might be in the vector variable $x_P.$ Usually, neither…

Let $V$ be a finite dimensional vector space over a field $\mathrm{k}$ of characteristic $0$. Let $A$ be a linear mapping of $V$ into itself. This paper gives a normal form for $A$, which gives a better description of the structure of $A$…

The paper contains two main results that are obtained by Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector…

Let $b$ be a non-degenerate symmetric (respectively, alternating) bilinear form on a finite-dimensional vector space $V$, over a field with characteristic different from $2$. In a previous work, we have determined the maximal possible…

Graded bundles are a particularly nice class of graded manifolds and represent a natural generalisation of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids we define the notion of a weighted…

An important result on submajorization, which goes back to Hardy, Littlewood and P\'olya, states that $b\preceq a$ if and only if there is a doubly stochastic matrix $A$ such that $b=Aa$. We prove that under monotonicity assumptions on…

A coherent system of type (r,d,k) on a curve C is a pair (E,V) where E is a vector bundle of rank r and degree d and V is a space of sections of E of dimension k. There is a condition of stability on coherent systems that depends on a…

We consider a family of pairs of m-by-p and m-by-q matrices, in which some entries are required to be zero and the others are arbitrary, with respect to transformations (A,B)--> (SAR,SBL) with nonsingular S, R, L. We prove that almost all…

A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose integer translates…

The estimate [\lVert D^{k-1}u\rVert_{L^{n/(n-1)}} \le \lVert A(D)u \rVert_{L^1} ] is shown to hold if and only if (A(D)) is elliptic and canceling. Here (A(D)) is a homogeneous linear differential operator (A(D)) of order (k) on…

Let $(X,d,\mu )$ be a space of homogeneous type in the sense of Coifman and Weiss, i.e. $d$ is a quasi metric on $X$ and $\mu $ is a positive measure satisfying the doubling condition. Suppose that $u$ and $v$ are two locally finite…

In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous…

In \cite{D3}, Donaldson defines a dynamical system on the space of Fubini-Study metrics on a polarized compact K\"ahler manifold. Sano proved that if there exists a balanced metric for the polarization, then this dynamical system always…

An integer linear system is a set of inequalities with integer constraints. The solution graph of an integer linear system is an undirected graph defined on the set of feasible solutions to the integer linear system. In this graph, a pair…

We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$. Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed.…

Let $(P,\leq)$ be a finite poset (partially ordered set), where $P$ has cardinality $n$. Consider linear extensions of $P$ as permutations $x_1x_2\cdots x_n$ in one-line notation. For distinct elements $x,y\in P$, we define…