During the last years the dynamics of linear operators on infinite dimensional spaces has been extensively studied, see the survey articles [3], [6], [7], [8], [9], [11]. Let us recall the notion of hypercyclicity. Let X be a separable Banach space and T : X → X be a bounded linear operator. The operator T is said to be hypercyclic provided there exists a vector x ∈ X such that its orbit under ...

what features and advantages does the prophet have which distinguish him from others? to answer this question, the writer names three approaches: 1. epistemical approach, 2. responsibility approach, and 3, situational approach. in the first approach, he examines various viewpoints which all view divine knowledge (ma‘rifat) as the prophet's distinctive feature. in the second approach, the s...

We provide a Hilbert-Mumford Criterion for actions of reductive groups G on Q-factorial complex varieties. The result allows to construct open subsets admitting a good quotient by G from certain maximal open subsets admitting a good quotient by a maximal torus of G. As an application, we show how to obtain all invariant open subsets with good quotient for a given G-action on a complete Q-factor...

In order to obtain better generalization performance in supervised learning, model parameters should be determined appropriately, i.e., they should be determined so that the generalization error is minimized. However, since the generalization error is inaccessible in practice, the model parameters are usually determined so that an estimator of the generalization error is minimized. The regulari...

The application of this work is to decision making with financial time series, using learning algorithms. The traditional approach is to train a model using a prediction criterion, such as minimizing the squared error between predictions and actual values of a dependent variable, or maximizing the likelihood of a conditional model of the dependent variable. We find here with noisy time series t...