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The Fisher information matrix I([GAMMA]) is given by the K x K symmetric matrix whose (u, v)th element is the covariance between uth and vth first partial derivatives of the log-likelihood:

Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

The partial derivatives of the magnetic components (2) in the laboratory system are

Magneto-kinematical and electro-kinematical fields

The first partial derivative of C3S with respect to f becomes:

Mathematics: a tool of quality control

After making use of relation (10), it is very easy to show that the partial derivatives of the equilibrium quantities of loans ([L.sub.i]) with respect to parameters [alpha] and r and variables [D.sub.i] and [D.sub.j] have as follows:

Monetary policy implications on banking conduct and bank clients' behavior

The way each of the three functionally relevant parameters E, D, and K depends upon each of the three governing growth-related parameters [alpha], [rho], and [delta] may be quantified by considering the corresponding partial derivatives [partial derivative]E/[partial derivative][alpha], [partial derivative]E/[partial derivative][rho], [partial derivative]E/[partial derivative][delta], [partial derivative]D/[partial derivative][alpha], [partial derivative]D/[partial derivative][rho], [partial derivative]D/[partial derivative][delta], [partial derivative]K/[partial derivative][alpha], [partial derivative]K/[partial derivative][rho], [partial derivative]K/[partial derivative][delta].

Covariations between shell-growth parameters and the control of the ranges of variation of functionally relevant shell-shape parameters in bivalves: a theoretical approach

The assumption that u [member of] [C.sup.2] enables the examination of partial derivatives signs.

The individual taxpayer utility function with tax optimization and fiscal fraud environment

The following partial derivatives obtained from differentiating the functions [F.sub.1] and [F.sub.2] are needed to determine the sign of [absolute value of [J.sub.1]]:

The Baland-Robinson theory of child labor efficiency: a proposed extension

The notation [U.sub.X]k = [[[partial derivative].sup.k]U(X,t)]/[[partial derivative][X.sup.k]] takes care of all possible partial derivatives where k is the highest partial derivatives of U w.

A novel approach to model turbulence Part I: theoretical formulation

where the partial derivatives within the parentheses are normalized by the Compton radius [r.sub.c].

A modern interpretation of the Dirac-electron continuity equation

More formally, the expansion of the preceding determinant in (45) verifies that a symmetric matrix is obtained for [partial derivative][h.sub.i](P,k)/[partial derivative][P.sub.j] due to the commutation of second-order partial derivatives of [P.sub.j]

Numerical reduced variable optimization methods via implicit functional dependence with applications

where partial derivatives of potential are the following:

Computation of electric wind parameters in direct current corona field/Vienpolio vainikinio islydzio elektrinio vejo parametrij skaiciavimas