Sentence examples for an expanding matrix from inspiring English sources

The self-affine measure μM,D corresponding to an expanding matrix M∈Mn(R) and a finite subset D⊂Rn is supported on the attractor (or invariant set) of the iterated function system {ϕd(x)="M−1(x+d)}d∈D.

During this interval luminal chitin and chitin binding proteins assemble into an expanding matrix.

Theories for the postnatal presence and then reduction of TNC within the articular cartilage include maintenance of the chondrocyte phenotype, capability of the cells to attach and then detach in an expanding matrix, and the utilization of signal transduction for mediating chondrocyte developmental fate [ 38].

An expanding matrix, i.e., linear function on R n, is an n × n matrix such that the modulus of each eigenvalue is greater than 1.

For an AB-multiresolution analysis associated with any expanding matrices, we deduce that there exists a singe scaling function in its reducing subspace.

And on and on, in an infinitely expanding matrix.

A stable chondrocyte number and expanding matrix may be a primary mechanism in achieving the lower cell density observed in adult articular cartilage.

Let μM,D be a self-affine measure associated with an expanding integer matrix M∈Mn Z) and a finite subset D⊂Zn.

We study spectral properties of the self-affine measure μM,D generated by an expanding integer matrix M∈Mn(Z) and a consecutive collinear digit set D= {0,1,…,q−1}v where v∈Zn∖{0} and q≥2 is an integer.

In this paper, we consider the non-spectral problem for the planar self-affine measures μM,D generated by an expanding integer matrix M∈M2(Z) and a finite digit set D⊂Z2.

In the present paper we show that for an expanding integer matrix M∈M2(Z) and the three-elements digit set D given byM="[abdc]andD="{ 00),(10),(01)}, if ac−bd∉3Z, then there exist at most 3 mutually orthogonal exponentials in L2 μM,D), and the number 3 is the best.