Killing-Yano tensors was introduced in 1952 by Kentaro-Yano from mathematically point of view.The physical interpretation of KillingYano tensors of rang higher than two was unclear. We found the conditions when a Killing-Yano tensor becomes a Nambu tensor. We found that in flat space case all the Killing-Yano tensors are Nambu tensors. Permanent address: Institute of Space Sciences,Bucharest-Ma...

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition we correct and extend some results concerning Ki...

In this talk, we presented the Birkhoff-von Neumann type theorem for a multistochastic tensors. In particular, we give a necessary and sufficient condition such that a multi-stochastic tensor is a convex combination of finitely many permutation tensors. It is well-known that extreme points in the set of doubly-stochastic matrices are just permutation matrices. However, we find that extreme poin...

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space [Formula: see text...

The tensors produced by diffusion tensor magnetic resonance imaging (DTMRI) represent the covariance in a Brownian motion model of water diffusion. Under this physical interpretation, diffusion tensors are required to be symmetric, positive-definite. However, current approaches to statistical analysis of diffusion tensor data, which treat the tensors as linear entities, do not take this positiv...

Diffusion tensor imaging provides the ability to study white matter connectivity and integrity noninvasively. The information contained in the diffusion tensors is very complex. Therefore a simple way of dealing with tensors is to compute rotationally invariant scalar quantities. These scalar indices have been used to perform population studies between controls and patients with neurological an...

We consider the problem of identifying unknown inclusions inside an elastic body by means of traction–displacement relations measured on the boundary. Based on the asymptotic formula of Ammari et al (2003 J. Elast. at press), we propose an algorithm to reconstruct unknown inclusions. The algorithm of this paper detects the location and the elastic moment tensors (elastic Pólya–Szegö tensors) of...

The results of Strassen [25] and Raz [19] show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we construct field-independent explicit 0/1 tensors T : [n]d -+ F with rank at least 2n td/ 2j + n 8(d Ig n). This improves the lower-order terms in known low...

A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski space is proposed and its properties examined. In this scheme the structure of spacetime is intrinsically quantum mechanical. It is shown that the causal ge...