Sentence examples for determinant expression from inspiring English sources

The following determinant expression is originally given in [17]; other proofs are seen in [3,26].

Corresponding to Theorem 2, another determinant expression for this zeta function (tilde {mathbf {Z}}_{G} u)) can be obtained.

(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.

Seeing the determinant expression in the above, we may say the Ihara zeta function Z G (u) of a graph is derived by the positive support (U + of the Grover matrix U.

From the definitions of a 2-step-cycle and an equivalence class, applying the usual method, which can be seen in [26,36] for instance, we can give the exponential expression and a determinant expression for the modified zeta function (tilde {mathbf {Z}}_{G} u)): Let G be a connected graph with n vertices and m unoriented edges.

By Proposition 1, an analytic continuation (tilde {mathbf {Z}}_{G} u)) has the following determinant expression: begin{array}rcl@ tilde{mathbf{Z}}_{G} u)&=& 1/det left(mathbf{I}_{2m} -u left(mathbf{U}^{2} right)^ right) &=& prod_{lambdain Specleft left(mathbf{U}^{2}right)^ right)} (1-u lambda)^{-1}; end{array}.

Then we give to such a function two types of determinant expressions and derive from it some geometric properties of a finite graph.

In Section 3, we introduce and discuss a modified zeta function (tilde {mathbf {Z}}_{G} u)) related to (U2)+ on a graph G and present two types of determinant expressions, properties of poles and geometric information derived from (tilde {mathbf {Z}}_{G} u)).

They differed not only in the CD14 but also in other determinants expression and functional activity [ 17].

To what extent do microorganisms of the cariogenic flora exemplified by S. mutans differ in virulence determinants "expression" from microorganisms of physiological flora?

By spelling out the definition of the determinant, the expression on the left hand side can be seen to be a polynomial function in, called the characteristic polynomial of.