Sentence examples for two analytic functions from inspiring English sources

For any two analytic functions.

The convolution or the Hadamard product of two analytic functions and is given by (1.3).

The Hadamard product (or convolution) of two analytic functions (1.2). is defined by the series (1.3).

The concept of the Hadamard product (or the convolution) of two analytic functions is very useful in our present study.

Let f and g be two analytic functions in the open unit disk Δ = { z ∈ C : | z | < 1 }.

The aim is to find two analytic functions, and (a sectionally analytic function ), in the left and right complex semi-planes, respectively, such that the boundary condition is satisfied.

We have developed a new pan-genome analysis pipeline (PGAP), which can perform five analytic functions with only one command, including cluster analysis of functional genes, pan-genome profile analysis, genetic variation analysis of functional genes, species evolution analysis and function enrichment analysis of gene clusters.

The three analytic functions.

Panseq could identify single nucleotide polymorphism on core genome and strain's specific region (Laing et al., 2010), and PGAP was designed to perform five analytic functions with only one command (Zhao et al., 2012).

We extend and prove Abrahamseʼs theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol (i.e., a quotient of two bounded analytic functions), whose analytic and co-analytic parts have the "left coprime factorization", is normal or analytic.

Hankel determinants are useful, for example, in showing that a function of bounded characteristic in D, i.e., a function which is a ratio of two bounded analytic functions with its Laurent series around the origin having integral coefficients, is rational [1].