We consider separately radial (with corresponding group ${\mathbb{T}}^n$) and radial (with corresponding group
${\rm U}(n))$ symbols on the projective space ${\mathbb{P}^n({\mathbb{C}})}$, as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^*$-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the commutativity of the $C^*$-algebras is a consequence of the existence of multiplicity-free representations. Furthermore, our method shows how to extend the current formulas for the spectra of the corresponding Toeplitz operators to any closed group lying between ${\mathbb{T}}^n$ and ${\rm U}(n)$., Raul Quiroga-Barranco, Armando Sanchez-Nungaray., and Obsahuje bibliografii
Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the description of the given convex polyhedral set. We provide also a lot of examples carried out on PC.
Let $\kappa $ be a cardinal number with the usual order topology. We prove that all subspaces of $\kappa ^2$ are weakly sequentially complete and, as a corollary, all subspaces of $\omega _1^2$ are sequentially complete. Moreover we show that a subspace of $(\omega _1+1)^2$ need not be sequentially complete, but note that $X=A\times B$ is sequentially complete whenever $A$ and $B$ are subspaces of $\kappa $.
We study sequential convergences defined on a Boolean algebra by systems of maximal filters. We describe the order properties of the system of all such convergences. We introduce the category of 2-generated convergence Boolean algebras and generalize the construction of Novák sequential envelope to such algebras.
In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.
The elements of economic interest in coastal sediments are characterized by a relative high concentration in minerals as the ilmenite, rutile, monazite and manganite. The objective of this work has been to carry out a study of selective sequential extractions of lanthanide elements and metals that are toxic. It started with rare earth phosphate minerals, using the technology established in the American continent (Tessier), applicable to sludge and sediments. The study is concerned with the outcrops of REE's minerals reported in Mexico as pegmatite, in the settlement "The Dead”, Telixtlahuaca, Oaxaca and of “Lagoon Mother” and “Saw of San Carlos”, Tamaulipas. There were evaluated in addition samples of Cuarzomonzodiorite, of “The Incarnation”, Hidalgo. Two modifications interfere to the above mentioned scheme of extractions and for the reached results it was possible to find the existence of some elements lanthanides as well as of toxic metals, praseodymium, neodymium, ytterbium and lead, associated with these minerals. The procedure of sequential selective extractions according to Tessier's methodology, does not manage to extract significant quantities of these elements, except in the conditions of maximum aggressiveness, of a digestion with HNO3/HClO4 concentrates and warming.
In this paper, processing of sonar signals has been carried out using
the Minimal Resource Allocation Network (MRAN) and the Probabilistic Neural Network (PNN) in differentiating of commonly encountered features in indoor environments. The stability-plasticity behavior of both networks has been investigated. The experimental result shows that the MRAN possesses lower network complexity but experiences higher plasticity in comparison with PNN. The study also shows that the MRAN performance is superior in terms of on-line learning to PNN.
In this paper we prove the following result: an inductive limit $(E,t) = \text{ind}(E_n,t_n)$ is regular if and only if for each Mackey null sequence $(x_k)$ in $(E,t)$ there exists $n=n(x_k)\in \mathbb N$ such that $(x_k)$ is contained and bounded in $(E_n,t_n)$. From this we obtain a number of equivalent descriptions of regularity.