Among the systems involved with data and knowledge that give answers, solutions, or diagnoses, based on available information; those based on feature selection are very important since they allow us to solve important tasks into pattern recognition and decision making areas. Feature selection consists in finding a minimum subset of attributes that preserves the ability to discern between object...

A point $p\in\mathbb{P}^N$ of a projective space is $h$-identifiable, with respect to variety $X\subset\mathbb{P}^N$, if it can be written as linear combination $h$ elements $X$ in unique way. Identifiability implied by conditions on the contact locus general spaces called non weak defectiveness and tangential defectiveness. We give ensuring an irreducible non-degenerated we apply these results...

We present an explicit procedure to determine the $C_5$-cone of a reduced complex analytic curve $X \subset \mathbb{C}^n$ at singular point $0 \in X$, which is known be union finite number planes. also give upper bounds on these The comes out with collections integers that we call auxiliary multiplicities and prove they Lipschitz type singularities. finish presenting example shows irreducible c...

Let X be an irreducible affine algebraic variety that is spherical with respect to action of a connected reductive group G. In this paper, we provide sufficient conditions, formulated in terms weight combinatorics, for the existence one-parameter additive actions on $$X$$ normalized by Borel subgroup $$B \subset G$$ . As application, prove every G-stable prime divisor can open G-orbit means sui...

Let $\mathfrak{g}$ be a semisimple Lie algebra. We establish new relation between the Goldie rank of primitive ideal $\mathcal{J}\subset U(\mathfrak{g})$ and dimension corresponding irreducible representation $V$ an appropriate finite W-algebra. Namely, we show that $\operatorname{Grk}(\mathcal{J}) \leqslant \dim V/d_V$, where $d_V$ is index suitable equivariant Azumaya algebra on homogeneous s...

The moduli space of stable maps Mg,k(X, β) to a complex projective manifold X (where g is the genus, k is the number of marked points, and β ∈ H2(X,Z) is the image homology class) is the central tool and object of study in Gromov-Witten theory. The open subset corresponding to maps from smooth curves is denoted Mg,k(X, β). The protean example is M0,k(P , d). This space is wonderful in essential...

In their fundamental studies of the finite dimensional representations of associative algebras, Artin and Procesi proved that the primitive ideals corresponding to irreducible n-dimensional representations (for fixed n, over an algebraically closed field) can be homeomorphically parameterized by a locally closed subset of the maximal spectrum of a suitably chosen affine commutative trace ring. ...

Two invertible dynamical systems (X,A, μ, T ) and (Y,B, ν, S) where X, Y are metrizable spaces and T , S are homeomorphisms on X and Y , are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping φ from a subset X0 of X of full measure to a subset Y0 of Y of full measure such that φ|X0 is continuous in the relative topology on X0, φ|Y0 is continuous in t...

Various kinds of nonseparating subcontinua were studied by a number of authors, see, for example, the expository paper [2], where a large amount of information on this subject is given. In the topological literature, or in continuum theory (to be more precise), the term “terminal,” when applied either to subcontinua of a given continuum or to points, and the same name “terminal” was assigned to...