Functions
... Let A and B be nonempty sets. A function f from A to B is an assignment of exactly one element of B to each element of A. If b is the unique element of B assigned by the function f to the element a of A, we write f(a) = b. If f is a function from A to B, we write f: A B. ...
... Let A and B be nonempty sets. A function f from A to B is an assignment of exactly one element of B to each element of A. If b is the unique element of B assigned by the function f to the element a of A, we write f(a) = b. If f is a function from A to B, we write f: A B. ...
A single hidden layer feedforward network with only one neuron in
... Chui and Li [6] proved that a single hidden layer network with a continuous sigmoidal activation function having integer weights and thresholds can approximate an arbitrary continuous function on a compact subset of R. Ito [18] established a density result for continuous functions on a compact subse ...
... Chui and Li [6] proved that a single hidden layer network with a continuous sigmoidal activation function having integer weights and thresholds can approximate an arbitrary continuous function on a compact subset of R. Ito [18] established a density result for continuous functions on a compact subse ...
Fourier Series
... The numbers an and bn are called the Fourier coefficients of f. When an and bn are given by (2), the trigonometric series (1) is called the Fourier series of the function f. Remark 1 If f is any integrable function then the coefficients an and bn may be computed. However, there is no assurance that ...
... The numbers an and bn are called the Fourier coefficients of f. When an and bn are given by (2), the trigonometric series (1) is called the Fourier series of the function f. Remark 1 If f is any integrable function then the coefficients an and bn may be computed. However, there is no assurance that ...
On the Computation of Confluent Hypergeometric Functions for
... These type of integrals can be solved using specialized adaptive routines, such as the routine gsl integration qawo from the GNU Scientific Library [2]. This routine combines Clenshaw-Curtis quadrature with Gauss-Kronrod integration. Numerical examples can be found in [8], which show that this metho ...
... These type of integrals can be solved using specialized adaptive routines, such as the routine gsl integration qawo from the GNU Scientific Library [2]. This routine combines Clenshaw-Curtis quadrature with Gauss-Kronrod integration. Numerical examples can be found in [8], which show that this metho ...
Part II. Optimization methods
... functional I, so its numerator is a number. But what is the sense of the division of the number I (v h ) I (v ) to the element h of the set V. It is clear, if h is a number. However it can be a vector or a function. Unfortunately the considered fraction does not have any sense in this case. So w ...
... functional I, so its numerator is a number. But what is the sense of the division of the number I (v h ) I (v ) to the element h of the set V. It is clear, if h is a number. However it can be a vector or a function. Unfortunately the considered fraction does not have any sense in this case. So w ...
Functions I - Australian Mathematical Sciences Institute
... Union and intersection are familiar operations on sets. Another useful operation on sets is set difference. For two sets A and B , we define A \ B = { x ∈ A | x ∉ B }. That is, A \ B is the set of all elements of A that are not in B . We can read A \ B as ‘A take away B ’ or ‘A minus B ’. For exampl ...
... Union and intersection are familiar operations on sets. Another useful operation on sets is set difference. For two sets A and B , we define A \ B = { x ∈ A | x ∉ B }. That is, A \ B is the set of all elements of A that are not in B . We can read A \ B as ‘A take away B ’ or ‘A minus B ’. For exampl ...
