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A rank-n tensor on a Lorentzian manifold whose contraction with n arbitrary causal future directed vectors is non-negative is said to have the dominant property. These tensors, up to sign, are called causal tensors, and we determine their general mathematical properties in arbitrary dimension N . Then, we prove that rank-2 tensors which map the null cone on… (More)

- G. Bergqvist, Erik G. Larsson
- IEEE Signal Processing Magazine
- 2010

Tensor modeling and algorithms for computing various tensor decompositions (the Tucker/HOSVD and CP decompositions, as discussed here, most notably) constitute a very active research area in mathematics. Most of this research has been driven by applications. There is also much software available, including MATLAB toolboxes [4]. The objective of this lecture… (More)

- Jón B. Hauksson, G. Bergqvist, Urban Bergsten, Michael Sjöström, Ulf Edlund
- Wood Science and Technology
- 2001

This work was undertaken to investigate the feasibility of using near infrared spectroscopy (NIR) and partial least squares regression (PLS) as a tool to characterize the basic wood properties of Norway Spruce (Picea abies (L.) Karst.). The wood samples originated from a trial located in the province of Västerbotten in Sweden. In this trial, the effects of… (More)

©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.: Göran Bergqvist and… (More)

By using geometric methods and superenergy tensors, we find new simple criteria for the causal propagation of physical fields in spacetimes of any dimension. The method can be applied easily to many different theories and to arbitrary fields (such as scalar or electromagnetic ones). In particular, it provides a conservation theorem of the free gravitational… (More)

- G. Bergqvist, Urban Bergsten, B. Ahlqvist
- Wood Science and Technology
- 2004

The effect of radial increment core diameter (comparing the effects of 12, 8 and 4 mm diameters, with sampling from chips used as a control) on the measurement of tracheid mean length and the percentage of broken tracheids was examined for mature wood of Norway spruce. Two methods of measuring tracheid length were used: image analysis, in which arithmetic… (More)

- G. Bergqvist
- 2012

We show that the probability to be of rank 2 for a 2× 2× 2 tensor with elements from a standard normal distribution is π/4, and that the probability to be of rank 3 for a 3× 3× 2 tensor is 1/2. In the proof results on the expected number of real generalized eigenvalues of random matrices are applied. For n × n × 2 tensors with n ≥ 4 we also present some new… (More)

- G. Bergqvist
- 2007

In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to… (More)

We present a survey of some recent developments for decompositions of multi-way arrays or tensors, with special emphasis on results relevant for applications and modeling in signal processing. A central problem is how to find lowrank approximations of tensors, and we describe some new results, including numerical methods, algorithms and theory, for the… (More)

- G. Bergqvist, K Hemmingsson
- Läkartidningen
- 1999