Sentence examples for analytic representations from inspiring English sources

In many cases we obtain analytic representations, at least to a large extent.

Under certain conditions onT, dual analytic representations ofTas a kind of bundle shift and of T* as an "adjoint bundle shift" are constructed.

The practical application of these methods, however, requires analytic representations that lead to well-conditioned linear systems, techniques for error estimation that permit robust mesh refinement, and implementations on high-performance computing platforms.

In this section, we will describe the properties of a five-parameter generalization of the lambda distribution to obtain smoothed analytic representations for grouped data (Tarsitano 2005).

The representation in (2) is essential to the present work as it allows the treatment of logharmonic mappings f through their associated analytic representations h and g (see [3 5], and [6]).

Put u=sum_{l=1}^{r} D^{ l-1)}u_{l}, where (uin D^{ l-1e}u_{l}hcal{L}^{p}}), where shows that (g(z)) is one of the analytic representations of uin

Perdew, J. P. & Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy.

His best-known work concerned the analytic representation of a single-valued function; this work culminated in the Mittag-Leffler theorem, one of the basic theorems in analytic function theory.

Moreover, this terse analytic representation reveals that, for large index, the basis functions behave asymptotically like the single Jacobi polynomial Pn(x).

The nonlinearity detection and identification has been done using an analytic representation of the displacement signal (FREEVIB method) and subsequently a nonlinear decrement method was used for comparison.

In contrast to the conventional repetitive learning control, no exact knowledge (analytic representation) of the target periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning.