The classical Gleason–Kahane–Żelazko theorem for complex Banach algebras was generalized for not necessary linear functionals by Kowalski and Słodkowski. We prove a version of the Kowalski–Słodkowski theorem for real Banach algebras and also for real and complex -pseudoconvex algebras.
We define and study a holomorphic functional calculus for a single element in complex and real complete A-pseudoconvex algebras with unit. As a consequence of the main result we obtain the spectral mapping theorem and existence of the logarithm and the nth root of an algebra element.
In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement...
This paper is a collection of numerous methods and results concerning a design of kernel functions. It gives a short overview of methods of building kernels in metric spaces, especially and . However we also present a new theory. Introducing kernels was motivated by searching for non-linear patterns by using linear functions in a feature space created using a non-linear feature map.
The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this...
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