Sentence examples for product of the function from inspiring English sources

Recall from elementary Hilbert space theory that the norm of a function on a Hilbert space is defined as the square root of the inner product of the function with itself.

As is well known, the convolution product of the function u and v is defined by the integral ( u ∗ v ) ( x, t ) = ∫ 0 t u ( x, t − s ) v ( x, s ) d s, ( x, t ) ∈ B × I. Also, let us consider the functions l ( t ) and g ( t ) defined by l ( t ) = 1, g ( t ) = ( l ∗ l ) ( t ) = t, t ∈ I. (25).

The overall impact of a given gene product on the function of a cell, tissue or organism is ultimately defined by myriad interactions with other gene products.

The kernel function is taken as the inner product of the mapping functions.

Moreover, since the addends in (50) are independent, the characteristic function of the total metric will be given by the product of the functions of the individual variables.

It is likely that chronic over-expression of clusterin in cells which survive therapy results in the clustering of tumor cells, platelets and other circulating cells to form emboli, possibly as a by-product of the function of the glycoprotein as an extracellular chaperone, as originally described by Fritz and his colleagues who first described and named the protein [ 46].

Each is the product of the identity function with a sigmoid-like function.

The density function of the distribution of genealogies is then a product of the density function for the divergence times and the distribution function for tree topologies.

These two filters are, respectively, obtained by inner product of the scaling function χ(t) and the wavelet function ψ(t) [16].

One striking position is a denial that any concepts, thoughts, or cognitions are either purely a priori in nature or purely empirical, either the product of the "intellectual" function alone or the product of the "organic" function alone.

The probability measure μ is the abstract counterpart to the product of the density function and the Lebesgue measure in classical statistical mechanics.