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...

In this paper, a new feature which is characterized by the extrema density of 2-D wavelet frames estimated at the output of the corresponding filter bank is proposed for texture segmentation. With and without feature selection, the discrimination ability of features based on pyramidal and treestructured decompositions are comparatively studied using the extrema density, energy, and entropy as f...

We propose a solution to a problem that is encountered in defining a notion of full meet base revision, ensuring that the output can always be re-used as an input. For this purpose, we introduce the concept of a separable belief base and show that separable bases are exactly those for which the full meet revision closure operator satisfies the extended set of A. G. M. postulates. We then define...

From Definition 1.1, checking a polynomial is separable requires building a splitting field to check the roots are distinct. But we will see in Section 2 a criterion for deciding when a polynomial is separable (that is, has no multiple roots) without having to work in a splitting field. In Section 3 we will define what it means for a field extension to be separable and then prove the primitive ...

This paper combines semantics and syntax to study the combining separable slots of V+O separable words in modern Chinese in a comprehensive perspective, namely the [AB+!] form. The paper discusses and analyzes the selection and restriction within the quantitative V+O separable words. It further analyzes the internal semantic features and rules of use for separable words falling into this catego...

Abstract We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in t...

Maschke functors, semisimple functors and separable functors of the second kind. Abstract We introduce separable functors of the second kind (or H-separable functors) and H-Maschke functors. H-separable functors are generalizations of separable functors. Various necessary and sufficient conditions for a functor to be H-separable or H-Maschke, in terms of generalized (co)Casimir elements (integr...

Suppose O is an alternative division algebra that is quadratic over some subfield K of its center Z(O). Then with (O,K), there is associated a dual polar space. We provide an explicit representation of this dual polar space into a (6n + 7)dimensional projective space over K, where n = dimK(O). We prove that this embedding is the universal one, provided |K| > 2. When O is not an inseparable fiel...

This paper will analyse the relationship between interest rate, income, GDP growth and house prices. First, the control power of interest rate for the prices is limited. Second, people’s income increases, thus that also increases the demand for housing. But house prices are too high and will cause buying pressure. Third, the real estate industry’s growth and GDP growth have inseparable relation...

A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of the Euclidean plane, and some explicit examples are constructed. Finally a conjecture on possible generalizations to other classes of systems is discussed: i...