Related papers: A vector identity for quadrilaterals

Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…

We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space $V$ over an arbitrary field $\mathbb{K}$ to have an orthogonal basis relative to all the inner products. Some applications to…

We give a proof of an analogue of Connes' Hochschild character theorem for twisted spectral triples obtained from twisting a spectral triple by scaling automorphisms, under some suitable conditions. We also survey some of the properties of…

A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…

We study the relationship between the areas of the consecutive quadrilaterals cut from a convex quadrilateral in the plane by means of a finite or infinite number of straight lines intersecting two of its opposite sides. Moreover, we obtain…

In this purely experimental work we try to represent the set of plane maps with 3 vertices and 3 faces as a bipartite ribbon graph. In particular, this construction allows one to estimate the genus of the initial set.

Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies…

A very simple but useful almost sure convergence theorem of probability is given.

Relative to a given factoring of the Hilbert space, the decomposition of an operator into a convex sum of products over sets of distinct 1-projectors, one set linearly independent, is unique.

We present an identity for the derivatives of the arctangent function as an alternative to the Adegoke - Layeni - Lampret formula. We show that algorithmic implementation of the proposed identity can significantly accelerate the computation…

We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.

A form of Williamson's product theorem which applies to Williamson matrices of even order is presented.

We translate Uchimura's identity for the divisor function and whose generalizations into combinatorics of partitions, and give a combinatorial proof of them. As a by-product of their proofs, we obtain some combinatorial results.

Triple linking numbers were defined for 3-component oriented surface-links in 4-space using signed triple points on projections in 3-space. In this paper we give an algebraic formulation using intersections of homology classes (or cup…

The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…

Some idea, which leads to a non-trivial solution of the quantum four-simplex equation, is exposed in this paper. We call this idea "pentagonal algebra". Few examples of the realisation of this idea are given here, and thus few examples of…

The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.

We define a new relation between character triples and prove some Clifford theory properties for weights in terms of character triples.

This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group…

In three-dimensional Euclidean geometry, the scalar product produces a number associated to two vectors, while the vector product computes a vector perpendicular to them. These are key tools of physics, chemistry and engineering and…