Sentence examples for functions for the first from inspiring English sources

Applications for some special functions such as polylogarithm, hypergeometric and Bessel functions for the first kind are presented as well.

Toward this scope, we introduce experimental site-specific amplification functions for the first time in the area to be utilized in future small-scale earthquake hazard models.

In addition, many students study the derivatives of trigonometric functions for the first time in their first year at a university.

In this section, we give some inequalities for some special functions such as polylogarithm, hypergeometric, Bessel and modified Bessel functions for the first kind.

The comparison is completed with a representation of P D versus SNR for the best detectors obtained with the different error functions, for the first case study.

Figure 5 shows the probability density functions for the first 3 years of variable costs (upper level) and the first 3 years of maintenance costs (lower level).

The article deals with the existence of uncountably many positive solutions which are bounded below and above by positive functions for the first-order nonlinear neutral differential equations.

Then, under the condition of simultaneous triangularization of the connection matrices, a common Lyapunov function (for the first problem) and a single Lyapunov and multiple Lyapunov functions (for the second problem) are systematically constructed respectively by those of several lower-dimensional dynamic systems.

Using the approximation of the high signal-to-noise ratio (SNR), upper bound functions for the second term and that for the fourth term in (14) can be, respectively, obtained as (15).

Moreover, as the first estimation phase (flux estimation) depends only on the assumption of the topology of the metabolic network, the flux estimates can subsequently be used to guide the selection of the most appropriate flux functions for the second phase or to detect inconsistencies in the assumed topology of the network separately from the flux equations [ 14].

Open image in new window Fig. 3 Detail function for the first level of decomposition for the clean signal (top), detail function for the first level of decomposition for the signal with SNR = 100 along with its Fourier spectrum (middle) and detail function for the seventh level of decomposition for the signal with SNR = 100 along with its Fourier spectrum (bottom).