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When multiplied with a matrix, ( J N + L − 1 T ) N shifts the columns of the matrix up by N chips and fills the empty contents with zeros, while J N + L − 1 N shifts the columns of the matrix down by N chips and fills the empty contents with zeros.
Therefore, the matrix, Φ x x, is a 3-level Toeplitz matrix ([20], Definition 1), i.e., Φ x x has an outermost block Toeplitz structure, and each block is still a block Toeplitz matrix, down to the innermost block with the form of an ordinary Toeplitz matrix.
Evidence of grain refinement of the γ-phase matrix down to the nanometre scale as well as partial dissolution of β-phase precipitates was observed.
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The extra-casein protein sample matrix broke down more slowly than the others because the caseins clotted at the gastric pH.
The matrix laid down by the fibroblasts can serve as a scaffold for recipient cells to colonize after implantation, but also provides structural support for arterial blood flow.
The antimicrobial sensitivity test for the composites had a problem in that the PVA matrix melted down at the autoclave temperature of 37 °C.
At the silicon L3,2-edge, the details of Si-Si bonding are also suppressed in these films until 1100°C where the nitride matrix breaks down.
The InAs QD is defined in a spherical crown shape (width 40 nm, height 5 nm) and is enveloped by the InGaAs matrix (SBL down and SRL up), as shown in the inset of Fig. 3.
PMMA shell covered on the surface of nano-sized Sb2O3 particles have enhanced interactions with PVC matrix, breaking down nano-Sb2O3 particle agglomerates and improving their dispersion in the matrix (average particle size of 60 80 nm) and also increasing the particle-matrix interfacial adhesion.
All cited the central importance of a rigid performance matrix handed down by management -- one that rewards and punishes employees almost entirely on the basis of whether they are able to meet six-month recruitment targets.
The extracellular matrix laid down by terminally differentiated chondrocytes serves as a template for invasion of blood vessels, which in turn serve as a conduit for the emigration of osteoblasts from their perichondrial residence onto the cartilaginous template.
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CEO of Professional Science Editing for Scientists @ prosciediting.com