O. Wyler [Notices Amer. Math. Soc. 15 (1968), 169. Abstract #653-306.] has given a Stone-Cech compactification for limit spaces. However, his is not necessarily an embedding. Here, it is shown that any Hausdorff limit space (X, t) can be embedded as a dense subspace of a compact, Hausdorff, limit space (Xi, ri) with the following property: any continuous function from (X, t) into a compact, Hau...

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each ch...

We prove a Weyl Harish-Chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space W. As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space W. We prove that the almost semisimple elements are dense in W. Finally, we provide estimates for the orbital integrals associat...

We give a general overview of the state-of-the-art in subspace system identification methods. We have restricted ourselves to the most important ideas and developments since the methods appeared in the late eighties. First, the basis of linear subspace identification are summarized. Different algorithms one finds in literature (Such as N4SID, MOESP, CVA) are discussed and put into a unifyin...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

Basis properties of exponential and trigonometric systems in grand Lebesgue spaces $ L_{p)} (-\pi,\pi) are studied. Based on a shift operator, we consider the subspace $G_{p)} (-\pi,\pi)$ space $, where continuous functions dense, boundedness singular operator this is proved. We establish basicity system \{{e^{int}}\}_{n\in Z}$ for \{{\sin{nt}}\}_{n\in N }$ \{{\cos{nt}}\}_{n\in N_0}$ (0,\pi)$.

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...

In many applications, such as bioinformatics and cross-market customer relationship management, there are data from multiple sources jointly describing the same set of objects. An important data mining task is to find interesting groups of objects that form clusters in subspaces of the data sources jointly supported by those data sources. In this paper, we study a novel problem of mining mutual...

We prove that on R , there is no n-supercyclic operator with 1 ≤ n < b 2 c i.e. if R has an n-dimensional subspace whose orbit under T ∈ L(R ) is dense in R , then n is greater than b 2 c. Moreover, this value is optimal. We then consider the case of strongly n-supercyclic operators. An operator T ∈ L(R ) is strongly n-supercyclic if R has an ndimensional subspace whose orbit under T is dense i...

This paper considers the automatic design of fuzzy rule-basedclassification systems based on labeled data. The classification performance andinterpretability are of major importance in these systems. In this paper, weutilize the distribution of training patterns in decision subspace of each fuzzyrule to improve its initially assigned certainty grade (i.e. rule weight). Ourapproach uses a punish...