We propose a framework for dealing with binary hard-margin classification in Banach spaces, centering on the use of a supporting semi-inner-product (s.i.p.) taking the place of an inner-product in Hilbert spaces. The theory of semi-inner-product spaces allows for a geometric, Hilbert-like formulation of the problems, and we show that a surprising number of results from the Euclidean case can be...

Sparse tensor product spaces provide an efficient tool to discretize higher dimensional operator equations. The direct Galerkin method in such ansatz spaces may employ hierarchical bases, interpolets, wavelets or multilevel frames. Besides, an alternative approach is provided by the so-called combination technique. It properly combines the Galerkin solutions of the underlying problem on certain...

In [FS] we introduced a product construction for locally compact, complete , geodesic hyperbolic metric spaces. In the present paper we define the hyperbolic product for general Gromov-hyperbolic spaces. In the case of roughly geodesic spaces we also analyse the boundary at infinity.

the choice of which products to stock among numerous competing products and how much space to allocate to those products are central decisions for retailers. this study aimed to apply data mining approach so that, we got needed information from large datasets of sale transactions to find the relations between products and to make product assortments. thus, we represented a model for product ass...

We present a new method to obtain Willmore-Chen submanifolds in spaces endowed with warped product metrics and fibers being a given homogeneous space. The main points are: First the invariance of the variational problem of WillmoreChen with respect to the conformal changes in the ambient space metric. Second, the principle of symmetric criticality which allows us to relate the problem with that...

In a series of papers [66, 65, 62, 63, 64] TSIRELSON constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by ARVESON [4] for classifying E0-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So we connect each continuous tensor product systems o...