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Making use of the cyclic property of the trace, it can be expressed in the form: (54).
On the other hand, by making use of the joint convexity and concavity of trace functions obtained by Bekjan [5] we generalize a variational inequality for positive definite matrices due to Hansen to the case of noncommutative L p spaces.
Making use of the zero curvature equation and the tri-trace identity, the two generalized AKNS hierarchies and their Hamiltonian structures are obtained, respectively.
Analytics make use of the digital traces left by learners in online learning environments in order to improve teaching and learning and the environments in which these take place.
Derivation of Eq. (19) makes use of the properties of trace operation, i.e., mathrm{t}mathrm{r}left(Delta APDelta {B}^{mathrm{T}}{R}^{mathrm{T}}right)=mathrm{t}mathrm{r}left({left(Delta APDelta {B}^{mathrm{T}}{R}^{mathrm{T}}right)}^{mathrm{T}}right)=mathrm{t}mathrm{r}left RDelta BPDelta {A}^{mathrm{T}}right).
The proposed method is to make use of the Fourier domain directional field to trace an appropriate candidate for the scar pixels to be replaced with.
Finally, it is possible to map the SatiX data with estimated locations making use of a trace-based location service (see e.g., [12]).
Figure 1 b makes use of the time series on labour shortages to trace the euro area Beveridge curve since 1990.
First, we implement our method by only imposing the trace-norm regularization, denoted as 'Ours (Trace-norm only)', which only makes use of the SNPs' correlations, but does not select longitudinal imaging markers.
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