Motivation The motivation for this discussion is to look at the cognitive and logical rationales of e-Learning objects, which reside in computer-based e-Learning artefacts. e-Learning objects, the system to which they belong, and the sequence of messages that form a discourse between the system and its environment are inseparable. Altogether, they formulate the “Universe of Discourse” (Wieringa...

e-mail: [email protected] Abstract. The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finall...

In this paper we prove that a free product of conjugacy separable groups A and B, amalgamating a cyclic subgroup, is conjugacy separable if A and B are subgroup separable, cyclic conjugacy separable, 2-free, and residually p-finite, for all prime numbers p. The following result is an example of the applications we obtain as consequences of our main theorem. Let A and B each be a free product of...

We show that the convex set of separable mixed states of the 2 × 2 system is a body of a constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert– Schmidt (Euclidean) measure. An analogous pr...

If G is a Polish group, then the category of Polish G-spaces and continuous G-mappings has a universal object. §0. Preface It is known from [2] that 0.1. Theorem (de Vries). Let G be a separable locally compact metric group. Then the category of continuous G-maps and separable complete metric G-spaces has a universal object. In other words, there is a separable complete metric space X on which ...

The well-known results about the existence of separable, measurable resp., modifications of stochastic processes (e.g., [4, 5]) are generalized to the case of real valued random fields indexed by a separable, separable and locally convex resp., metric space.

We provide a complete work-flow, based on the language of quantum information theory, suitable for processing data for the purpose of pattern recognition. The main advantage of the introduced scheme is that it can be easily implemented and applied to process real-world data using modest computation resources. At the same time it can be used to investigate the difference in the pattern recogniti...

Table of Contents 1. Introduction. 2. The isomorphic classification of separable C(K) spaces. A. Milutin's Theorem. B. C(K) spaces with separable dual via the Szlenk index 3. Some Banach space properties of separable C(K) spaces. A. Weak injectivity. B. c 0-saturation of spaces with separable dual. C. Uncomplemented embeddings of C([0, 1]) and C(ω ω +) in themselves. 4. Operators on C(K)-spaces.