Sentence examples for functions of coefficients from inspiring English sources

where ξ m ( k ) ( k = 1, 2, …, m - 1 ) are polynomial functions of coefficients of system (17).

where X ̃ k, Ỹ k are homogeneous polynomials in x1, x2 of degree k, and their coefficients are polynomial functions of coefficients of the system (2).

We show that the important role is played by the limit behavior of ratios of primitive functions of coefficients in the investigated half-linear equation.

By different choices of the phase functions, we deduce stability theorems in terms of the auxiliary function of coefficients R A ( t ), which is invariant with respect to the lower triangular transformations.

Plots of the extreme GMR values accepted as a function of coefficient of variation (CV) have a convex shape, similar to the classic unscaled 0.80 1.25 limits.

Solving the mass action equations for the triplet motif at steady state yields a generalized Hill function of coefficient 2. Depending on the four reaction rates, this motif is capable of producing a range of quasi-linear, quasi-hyperbolic, and sigmoidal activation and inhibition responses (see Additional file 1).

The matrix distance can be written for any AIP as a sum of functions of LD coefficients, and more precisely for the IBS hap predictor as a sum of concave polynomials of LD coefficients.

The problem of expressing the roots of a polynomial as functions of the coefficients was addressed by several mathematicians independently about 1770.

The second was to express the roots as algebraic functions of the coefficients or to show why it was not, in general, possible to do so.

They are considered as functions of the coefficients of the heat transfer and the width of the heat contact ring between the casting ingot and the copper crucible.

Let ((w_{1} z),w_{2}(z)) ) be a set of meromorphic solutions of (1.2), (S_{1}(r)) means the sum of characteristic functions of all coefficients in (1.2).