Sentence examples for unity element from inspiring English sources

Let R be any Ring with unity element 1 and let denotes the set of all the central idempotents of R; then it is known that ( B, ∪, ∩, ′ ) is a Boolean algebra, where, by definition, a ∪ b = a + b - ab, a ∩ b = ab and a' = 1 - a.

Darlingside understands nuance and sforzando as they explore the unity element of what's being delivered.

This imagined unity is one element that sets off a star from an actor, however accomplished.

The corresponding MME are (10) (X ′ R − 1 X X ′ R − 1 Z * X ′ R − 1 Z Z * ′ R − 1 X Z * ′ R − 1 Z * + I m ⊗ A − 1 Z * ′ R − 1 Z Z ′ R − 1 X Z ′ R − 1 Z * Z ′ R − 1 Z + Ψ − 1 ⊗ A − 1 ) (β ^ c ^ s ^ ) = (X ′ R − 1 y Z * ′ R − 1 y Z ′ R − 1 y ) Note that Z* is considerably denser than Z, containing m coefficients γ ij in each row compared to a single element of unity in Z.

In our case, the vector u is a vector along one of the coordinate axes and hence has one element equal to unity and the rest of them equal to zero.

Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method.

To alleviate this limitation, the Partition of Unity Finite Element Method (PUFEM) using plane wave functions has been shown to be very effective for solving short wave Helmholtz problems.

In this paper, the stationary Fokker Planck equation (FPE) is solved for nonlinear dynamical systems using a local numerical technique based on the meshless partition of unity finite element method (PUFEM).

Daubechies family of wavelets combined to the Incomplete Lower Upper (ILU) factorization are considered as preconditioners for a block sparse linear system arising from the approximation of the time harmonic elastic wave equations by the Partition of Unity Finite Element Method (PUFEM).

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction radiation problems in diffusive grey media.

Additionally, R was restricted to be diagonal with unity diagonal elements for all liability traits, as described above.