(1) Let V be a real unitary space, A be a subset of V , and x be a set. Then x ∈ Lin(A) if and only if there exists a linear combination l of A such that x = ∑ l. (2) For every real unitary space V and for every subset A of V and for every set x such that x ∈ A holds x ∈ Lin(A). (3) For every real unitary space V holds Lin( / 0the carrier of V ) = 0V . (4) For every real unitary space V and for...

Neural network-based modeling often involves trying multiple networks with different architectures and training parameters in order to achieve acceptable model accuracy. Typically, one of the trained networks is chosen as best, while the rest are discarded. [Hashem and Schmeiser (1995)] proposed using optimal linear combinations of a number of trained neural networks instead of using a single b...

Neural network (NN)-based modeling often involves trying multiple networks with diierent architectures and training parameters in order to achieve acceptable model accuracy. Typically, one of the trained NNs is chosen as best, while the rest are discarded. Hashem and Schmeiser 25] proposed using optimal linear combinations of a number of trained neural networks instead of using a single best ne...

We address here the problem of sorting a set of linear combinations of three arrays of numbers. Though it has many practical signii-cance, the problem was not addressed earlier. We propose an eecient algorithm for this problem. The main contribution of the work is that we identiied ranges of the parameters of linear combinations for which the sorting order is constant. These ranges for all valu...