Search results for "Combinatorics"

Stochastic Processes on Ends of Tree and Dirichlet Forms

2016

We present main ideas and compare two constructions of stochastic processes on the ends (leaves) of the trees with varying numbers of edges at the nods. In one of them the trees are represented by spaces of numerical sequences and the processes are obtained by solving a class of Chapman-Kolmogorov Equations. In the other the trees are described by the set of nodes and edges. To each node there is naturally associated a finite dimensional function space and the Dirichlet form on it. Having a class of Dirichlet forms at the nodes one can under certain conditions build a Dirichlet form on L2 space of funcions on the ends of the trees. We show that the state spaces of two approaches are homeomo…

Two groups with isomorphic group algebras

1990

Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras: A New Method

2014

In this paper we introduce a topological approach for extending a representable linear functional \({\omega}\), defined on a topological quasi *-algebra without unit, to a representable linear functional defined on a quasi *-algebra with unit. In particular, we suppose that \({\omega}\) is continuous and the positive sesquilinear form \({\varphi_\omega}\), associated with \({\omega}\), is closable and prove that the extension \({\overline{\varphi_\omega}^e}\) of the closure \({\overline{\varphi_\omega}}\) is an i.p.s. form. By \({\overline{\varphi_\omega}^e}\) we construct the desired extension.

Partial spreads in finite projective spaces and partial designs

1975

A partial t-spread of a projective space P is a collection 5 p of t-dimensional subspaces of P of the same order with the property that any point of P is contained in at most one element of 50. A partial t-spread 5 p of P is said to be a t-spread if each point of P is contained in an element of 5P; a partial t-spread which is not a spread will be called strictly partial. Partial t-spreads are frequently used for constructions of affine planes, nets, and Sperner spaces (see for instance Bruck and Bose [5], Barlotti and Cofman [2]). The extension of nets to affine planes is related to the following problem: When can a partial t-spread 5 ~ of a projective space P be embedded into a larger part…

Bounded Bi-ideals and Linear Recurrence

2013

Bounded bi-ideals are a subclass of uniformly recurrent words. We introduce the notion of completely bounded bi-ideals by imposing a restriction on their generating base sequences. We prove that a bounded bi-ideal is linearly recurrent if and only if it is completely bounded.

"Indexing structures for approximate string matching

2003

In this paper we give the first, to our knowledge, structures and corresponding algorithms for approximate indexing, by considering the Hamming distance, having the following properties. i) Their size is linear times a polylog of the size of the text on average. ii) For each pattern x, the time spent by our algorithms for finding the list occ(x) of all occurrences of a pattern x in the text, up to a certain distance, is proportional on average to |x| + |occ(x)|, under an additional but realistic hypothesis.

On the spectrum of linear combinations of two projections inC*-algebras

2010

In this note, we study the spectrum and give estimations for the spectral radius of linear combinations of two projections in C*-algebras. We also study the commutator of two projections.

Comparing the relative volume with a revolution manifold as a model

1993

Given a pair (P, M), whereM is ann-dimensional connected compact Riemannian manifold andP is a connected compact hypersurface ofM, the relative volume of (P, M) is the quotient volume(P)/volume(M). In this paper we give a comparison theorem for the relative volume of such a pair, with some bounds on the Ricci curvature ofM and the mean curvature ofP, with respect to that of a model pair\(\left( {\mathcal{P},\mathcal{M}} \right)\) where ℳ is a revolution manifold and\(\mathcal{P}\) a “parallel” of ℳ.

The Jordan-Hölder theorem and prefrattini subgroups of finite groups

1995

by A. BALLESTER-BOLINCHES and L. M. EZQUERRO(Received 26 January, 1994)Introduction. All groups considered are finite. In recent years a number ofgeneralizations of the classic Jordan-Holder Theorem have been obtained (see [7],Theorem A.9.13): in a finite group G a one-to-one correspondence as in the Jordan-Holder Theorem can be defined preserving not only G-isomorphic chief factors but eventheir property of being Frattini or non-Frattini chief factors. In [2] and [13] a newdirection of generalization is presented: the above correspondence can be defined in sucha way that the corresponding non-Frattini chief factors have the same complement(supplement).In this paper we present a necessary a…

Tighter Relations between Sensitivity and Other Complexity Measures

2014

The sensitivity conjecture of Nisan and Szegedy [12] asks whether the maximum sensitivity of a Boolean function is polynomially related to the other major complexity measures of Boolean functions. Despite major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004 [11].