Related papers: Answer to question Nr. 55
We present pictorial means of distinguishing contravariant vectors (or simply vectors) from covariant vectors (or linear forms). When one depicts vector as the directed segment, then the pictorial image of a linear form is a family of…
This is the sixth, concluding part of a series of papers the first five of which have been submitted to the present archive in mid 1998 and published as INR preprints in 1999. The present paper was printed as an INR preprint, too, but for…
In this note we present some results that were already conjectured in the work [9] by Bildhauer, Fuchs and Weickert, where they have investigated analytical aspects of coupled variational models with applications to mathematical imaging.…
Vector is a physical quantity and it does not depend on any co-ordinate system. It need to be expanded in some basis for practical calculation and its components do depend on the chosen basis. The expansion in orthonormal basis is…
The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. Werner [{\it J. Phys. A: Math. Gen.} {\bf 34} (2001) 7081], relate it to local operations on maximally entangled vectors bases, find an…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
We give a new proof of Theorem 6 in [L. Qiu and X. Zhan, On the span of Hadamard products of vectors, Linear Algebra Appl. 422 (2007) 304--307].
We describe a correspondence between GL_n-invariant tensors and graphs, and show how this correspondence accomodates various types of symmetries and orientations.
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
It is shown, that for quantum systems the vectorfield associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schr\"odinger and Heisenberg pictures. We illustrate these ambiguities in terms of…
We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative…
Discussion of "Cross-Covariance Functions for Multivariate Geostatistics" by Genton and Kleiber [arXiv:1507.08017].
We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and…
This is an overview of my papers arxiv:1602.04254 and arxiv:1604.01588.
We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their…
This is a short essay about some fundamental results on scalar curvature and the two key methods that are used to establish them.
This paper is devoted to present two counterexamples to the theorem from \cite{MK} Maria R., Katherine T. M., Bernardo S. M., Extremal graphs with bounded vertex bipartiteness number, Linear Algebra Appl. 493 (2016) 28-36. Moreover, the…
In one of his papers, the author introduces the class of Farkas-related vectors for which a version of Farkas' lemma over integers is derived. In this paper, two similar classes are introduced and studied.