Sentence examples for matrices and give from inspiring English sources

Moreover, we obtain the Euclidean norms of r-circulant matrices and give lower and upper bounds for the spectral norms of r-circulant matrices with harmonic and hyperharmonic Fibonacci entries.

With that, we propose Transmission Mode Generating Algorithms (TMGAs) to generate TDMA-based scheduling matrices and give our Linear Programming- (LP-) based and Convex Programming- (CP-) based schemes to maximize the network throughput, and to achieve certain fairness (such as weighted fairness, in particular) at the same time.

Accordingly, the multiplication of the two partitioned matrices, and gives the zero matrix.

We establish several classes of ZSC-matrices, and give separate sufficient and necessary conditions for a matrix to be ZSC.

We calculate the fundamental matrix and give integral representations for the velocity, magnetic induction and pressure.

Precisely, we provide a necessary and sufficient criterion of consensus convergence in terms of Hurwitz stability of a matrix and give an analytical expression of the consensus function.

We show that it is given in terms of the R-transform of the spectral measure of the full rank matrix and give a new proof of the fact that the R-transform is additive under free convolution.

In view of the above papers, we define a new circulant matrix which is called geometric circulant matrix and give upper and lower bounds for the spectral norms of this matrix with the generalized Fibonacci and hyperharmonic Fibonacci numbers by using the same method given in [3].

MWCNTs were uniformly distributed in the nickel matrix and gave different morphologies and high surface roughness to the coating.

Following laser sintering, characterisation of the polymer nanocomposite parts by SEM and dynamic mechanical testing showed that the nanofibres were well dispersed within the polymer matrix and gave a 22% increase in the storage modulus compared to the base material.

The use of 2D sheets as surface coatings instead of bulk additives overcomes common issues related to dispersion of graphene in a polymer matrix, and gives a clear advantage in preserving the mechanical properties of the bulk polymer.