The probability measure generated by typical chaotic orbits of a dynamical system can have an arbitrarily Sne-scaled interwoven structure of points with different singularity scalings. Recent work has characterized such measures via a spectrum of fractal dimension values. In this paper we pursue the idea that the infinite number of unstable periodic orbits embedded in the support of the measure...

We show that the periodic orbits of an area-contracting horseshoe map can be partitioned into subsets of orbits of minimum period k, 2k, 4k, 8k, ..., for some positive integer k. This partition is natural in the following sense: for any parametrized area-contracting map which forms a horseshoe, the orbits in one subset of the partition are contained in a single component of orbits in the full p...

Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-kno...

background: lymphocyte subsets enumeration is considered prominent in the management of primary and acquired immunodeficiency disorders. because of local variations due to race, age, gender, and environmental conditions on lymphocyte subsets, and to improve the accuracy of interpretation of laboratory findings, reference intervals must be determined in every population. objective: to establish ...

In finite dimensions, the Poincaré recurrence theorem can be proved from the basic properties of a finite measure. In infinite dimensions, it is difficult to establish a natural finite measure, especially by extending a finite dimensional finite measure. A natural alternative is the Banach norm which can be viewed as a counterpart of the probability density. An interesting problem is to study t...

The evaluation of atomic polar tensors and Born Effective Charge (BEC) from Density Functional Perturbation Theory (DFPT) has been implemented in the CP2K code package. This implementation is based on a combination Gaussian plane wave approach for description basis functions arising potentials. presence non-local pseudo-potentials considered, as well contributions being centered atoms. Simulati...

We define a family B(t) of compact subsets the unit interval which generalizes sets numbers whose continued fraction expansion has bounded digits. study how set changes as one moves parameter t, and see that undergoes period-doubling bifurcations displays same transition pattern from periodic to chaotic behavior usual quadratic polynomials. The E bifurcation parameters is fractal measure zero H...

Polynomials orthogonal on the unit circle with random recurrence coefficients and finite band spectrum are investigated. It is shown that the coefficients are in fact quasiperiodic. The measures associated with these quasi-periodic coefficients are exhibited and necessary and sufficient conditions relating quasi-periodicity and spectral measures of this type are given. Analogs for polynomials o...

A subset A of a group G is called symmetric with respect to the element g ∈ G if A = gA−1g. It is proved that in any 2-coloring, every infinite group G contains monochrome symmetric subsets of arbitrarily large cardinality < |G|. A topological space is called resolvable if it can be partitioned into two dense subsets [8]. In [4] W. Comfort and J. van Mill proved that each nondiscrete topologica...