Sentence examples for matrix and elements from inspiring English sources

(3) Relationship between the nodal displacement and the cross-sectional area is derived, following the conjecture about the determinant expression of stiffness matrix and elements of adjoint matrix.

Key sector analysis is grounded in the theoretical formulation by Sherman and Morrison (1949, 1950) of the relationship between changes in elements of the inverse matrix and elements of the input coefficient matrix.

The SDEs in Equation (3) comprise three types of tunable parameters: ODE model parameters, elements of the matrix and elements of the set of measurement covariance matrices, and we denote the set of all potential parameters by.

In the analysis, it is convenient to parameterise the actual relationship between family members i and j in terms of deviations from mean pedigree-based relationships: r ij  =  A ij - A. The n ×  n covariance matrix V of observations y within a family of n sibs is then var y = V = I σ W 2 + R σ A 2, where I is the identity matrix and elements of R are r ij, i ≠ j, and r ii  = 0.

left[ {M_{e} } right]left{ {ddot{q}_{e} } right} + left[ {K_{e} } right]left{ {{q}_{e} } right} = left{ {F_{e} } right} (12 where [K e ], [M e ], and {F e } are the element stiffness matrix, element mass matrix, and element nodal load vector, {q e } is nodal displacement vector, and (left{ {ddot{q}}_{e} right}) is the second derivative of the displacements of the element with respect to time.

A mesh of 3D hexahedron quadratic elements with reduced integration (C3D20R) elements was employed with 820 elements in the matrix and 60 elements in each fibril.

Open image in new window Fig. 13 a Generated subsurface fracture map using object-based model and (b) three dimensions mesh (tetrahedral elements for matrix and triangle elements for fractures) used in simulation process.

Three special element types, called yarn element, matrix element and mixed element, are derived.

Gaussian random measurement matrix is the most commonly used measurement matrix, and its elements have enough randomness to satisfy the design requirement of measurement matrix in CS.

The transformation matrix in this type of chaos synchronization is a non-diagonal square matrix, and its elements are complex numbers.

where the equality holds if and only if ( M 1 † M 1 ) − 1 is a diagonal matrix and all elements on the diagonal are equal to 1/(4K) [11] 11].