In Section 2, we prove the exponential and logarithmic convexity of the functions deduced from (1.5).
The aim of this paper is to prove the exponential convexity of the functions deduced from (1.5) and apply these functions to generalize the means of Stolarsky type, and at last we prove the monotonicity property of these new means.
This allows for the correlation of gene function, deduced from the EST data, with expression levels, deduced from the microarray data.
The nonlinear characteristics of the system can be well described by the nonlinear output frequency response function deduced by the Volterra series.
The analytical functions deduced for Δp(D,ε) and W(D,ε) predict a reduction of the range and depth of depletion interaction by an increase in the attraction strength |ε|.
The proofs are mainly based on an estimate for the Heisenberg left-invariant vectors of the special Hermite functions deduced by the Heisenberg group approach.
Even though, the scattering data cover a limited Q space and thus the overall resolution is rather poor, the radial distribution functions deduced at different equilibrium pressures, reveal differences, which could be attributed to changes in the arrangement of CO2 molecules along the 308 K isothermal scan.
Sequence-dependent effects are incorporated into the calculations by taking advantage of "knowledge-based" harmonic energy functions deduced from the mean values and dispersion of the base-pair "step" parameters in high-resolution DNA crystal structures.
So, in the present paper the singular boundary integral equation is solved by using cubic boundary elements, and, for evaluating the singularities, modified shape functions, deduced on Taylor series expansions, are used.
Secondly, a novel nonlinear decoration algorithm with sine-function deduced from nonlinear feedback algorithm is proposed, where the sine function was embedded into the back of original linear controller.
