In this paper we study systems in which the system operator, A, has a Riesz basis of (generalized) eigenvectors. We show that this class is subset of the class of spectral operators as studied by Dunford and Schwartz. For these systems we investigate several system theoretic properties, like stability and controllability. We apply our theory to Euler-Bernoulli beam with structural damping.

The roots of Bernoulli polynomials, Bn(z), when plotted in the complex plane, accumulate around a peculiar H-shaped curve. Karl Dilcher proved in 1987 that, on compact subsets of C, the Bernoulli polynomials asymptotically behave like sine or cosine. Here we establish the asmptotic behavior of Bn(nz), compute the distribution of real roots of Bernoulli polynomials and show that, properly rescal...

In this note, we will point out, as a corollary of Popa’s rigidity theory, that the crossed product von Neumann algebras for Bernoulli shifts cannot have relative property T. This is an operator algebra analogue of the theorem shown by Neuhauser and Cherix-Martin-Valette for discrete groups. Our proof is different from that for groups.

In this paper, a group shift is an expansive action of Zd on a compact metrizable zero dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli shifts; abelian group shifts factor by continuous group homomorphisms onto canonical equalentropy Bernoulli group shifts; and completely positive entropy abelian group shifts are weakly algebraica...

For every countable group G, a family of isomorphism invariants for measurepreserving G-actions on probability spaces is defined. In the special case in which G is a countable sofic group, a special class of these invariants are computed exactly for Bernoulli systems over G. This leads to a complete classification of Bernoulli systems for many countable groups including all finitely generated l...

We generalize some results on success runs for Bernoulli trials to discrete Markovian arrival processes (D-MAP). We study the distribution of the length of an arbitrary success run and the waiting time to the occurrence of a success run of a given length. Formulae for the mean, the variance and the geometric asymptote of the waiting times are presented. Numerical examples illustrate how diieren...

In this work we will use some Sobolev constants to explicitly characterize a class of potentials q(t) ∈ Lp(R/TZ) for which the periodic linear beam equation u(4) = q(t)u is non-degenerate. As an application, we will obtain the uniqueness of periodic solutions of a certain class of superlinear beam equations. © 2008 Elsevier Ltd. All rights reserved.

Associated with a skew-symmetric linear operator on the spatial domain [a, b] we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated with this Dirac structure is an infinite-dimensional system. We parameterize the boundary port variables for which the C0semigroup associate...