Sentence examples for with multiplicity of from inspiring English sources

The transmitter employs a concatenated coding scheme where a Multiple-Trellis-Coded Modulation (M-TCM) encoder with multiplicity of is used as an outer code and an super-orthogonal block code is used as the inner code.

However, the references [4 6] are not concerned with multiplicity of positive solutions for the scalar Schrödinger equation or system.

We give an explicit formula for the spectrum, with multiplicity, of the Bochner Laplacian ▽ ∗ ▽ on V, where ▽ is the Riemannian or Riemannian spin connection.

This would have been in keeping with the work of Khot and colleagues [13] who found a reduction in the age at which the index CHD event occurred with multiplicity of risk factors.

In [13], Chen and Tang proved two different solutions for the non-homogeneous KGM equations in the whole R 3. Candela and Salvatore [14, 15] dealt with multiplicity of solutions to non-homogeneous Schrödinger-Maxwell and Klein-Gordon-Maxwell systems with homogenous boundary conditions in a bounded ball, respectively.

The function (D z)={mathcal D}(lambda (z))) is analytic in ({mathbb D}) whose zeros are given by begin{aligned} z_j=z(lambda _j), quad j=1,2,dots, N, end{aligned}where (lambda _j) are zeros (counting with multiplicity) of ({mathcal D}(lambda )) in (Lambda ={mathbb C}{setminus }[-d,d]), i.e., eigenvalues of H (counted with algebraic multiplicity).

Hence, they occur with multiplicities of four.

The eigenvalues of (U_{4}^{intercal}U_{4}) are 2, 1, and 0 with multiplicities of two, three and three, respectively.

Subsequently, we describe the processes that are unique to systems with multiplicities of higher order than for binaries.

Denote the spectrum (sigma(L):={lambda_{n}}_{n=0}^{infty}) of L, (sigma(L)) consisting of the zeros (counting with multiplicities) of the entire function (Delta(lambda)).

In other cases, there is an interaction between the three stars that is unique to systems with multiplicities of higher orders than binaries.