PURPOSE Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. METHODS Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates th...

the energy equation for turbulent flow of fiber suspensions was derived in terms of second order correlation tensors. fiber motion of turbulent energy including the correlation between pressure fluctuations and velocity fluctuations was discussed at two points of flow field, at which the correlation tensors were the functions of space coordinates, distance between two points, and time.

This note deals with preservation of tensor sum and tensor product of Hilbert space operators. Basic operations with tensor sum are presented. The main result addresses to the problem of transferring properties from a pair of operators to their tensor sum and to their tensor product. Sufficient conditions are given to ensure that properties preserved by ordinary sum and ordinary product are pre...

We study the tensor rank of the tensor corresponding to the algebra of n-variate complex polynomials modulo the dth power of each variable. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a counterexample to a conjecture of Rhodes. At the same time we obtain a new lower bound on the tensor rank of tensor powers of the generalised W-state tensor....

Tensor models and tensor field theories admit a $1/N$ expansion melonic large $N$ limit which is simpler than the planar of random matrices richer vector models. They provide examples analytically tractable but non-trivial strongly coupled quantum lead to new class conformal theories. We present compact introduction topic, covering both some classical results in field, like details expansion, a...

The topic of this paper is the so-called trifocal tensor (TFT), which describes the relative orientation of three uncalibrated images. The TFT is made up of 27 homogenous elements but only has 18 DOF. Therefore, its elements have to fulfil 8 constraints a new form for these constraints is presented in this paper. Furthermore, a new minimal parameterization for the TFT is presented having exactl...

A tensor is a multidimensional array, where the order of tensor denotes the dimension of the array. For example, a scalar is simply an order-0 tensor, a vector order-1, a matrix order-2, and any tensor with order-3 or greater is described as a higher order tensor. For this paper I will be focusing on the simplest higher-order tensor, the order-3 tensor, which can be visualized as a sort of Rubi...

A “conformal tensor” is constructed from the metric tensor gMN (or Vielbein e A M ) and is invariant against Weyl rescaling gMN → egMN (or eM → eeM ). Moreover, it vanishes if and only if the space is conformally flat, gMN = e ηMN (or e A M = eδ M ). In dimension four or greater the conformal tensor is the Weyl tensor. In three dimensions the Weyl tensor vanishes identically, while the Cotton t...