Sentence examples for maximum modulus of from inspiring English sources

In this paper, we obtain new results concerning the maximum modulus of a polar derivative of a polynomial with restricted zeros.

We can demonstrate that the maximum modulus of B occurs when α ΔX = mπ and β ΔY = nπ, where m and n are integers; hence, B is real.

In the situation of water logging after subsidence, the maximum modulus of erosion would decrease if the accumulated slope length were reduced.

A matrix M is an M-matrix if M = s I − A, where A ≥ O and s ≥ ρ ( A ), where ρ denotes the spectral radius of a matrix, that is, the maximum modulus of its eigenvalues.

In the same paper, some results of the lower bound for the characteristic functions, poles and maximum modulus of transcendental meromorphic solutions of some complex difference equations are obtained as follows.

If f ( z ) is an analytic function in Δ, then the hyper-order about maximum modulus of f ( z ) is also defined by σ M, 2 ( f ) = lim r → 1 − ¯ log 3 + M ( r, f ) log 1 1 − r.

In view of the Nevanlinna theory, we study the growth and poles of solutions of some classes of systems of complex difference equations and obtain some interesting results such as the lower bounds for Nevanlinna lower order, a counting function of poles and maximum modulus for solutions of such systems.

The maximum modulus for bECM also occurred at a lower strain rate, indicating possible disruption of the hydrogel structure.

In our previous study, chemically converted graphene (CCG) without functionalization showed limited dispersion in the PS matrix at a higher graphene loading, resulting in a maximum modulus increase of 28% at 4 wt.% loading of CCG [4].

Hence, The convergence rate is where ρ lv(B) of a matrix B is a notation for the maximum modulus eigenvalue of B. The final equality follows from a general property for a square matrix form Cvv' where v is a vector, saying that it only has one eigenvalue different from zero which is equal to v' Cv.

Since the function (overline{ zeta_{1}}f(lambdazeta_{1},ldots,lambdazeta_{n})- overline{ zeta_{2}}g(lambdazeta_{1},ldots,lambdazeta_{n})) is holomorphic on the unit disk (|lambda|<1), by the maximum modulus principle of one complex variable, it follows that overline{ zeta_{1}}f(lambdazeta_{1},ldots,lambda zeta_{n})- overline{ zeta_{2}}g(lambdazeta_{1}, ldots,lambdazeta_{n})=0 for all (lambdain D).