Good Banach spaces for piecewise hyperbolic maps via interpolation

We introduce a weak transversality condition for piecewise C^1+α and piecewise hyperbolic maps which admit a C^1+α stable distribution. We show bounds on the essential spectral radius of the associated transfer operators acting on classical anisotropic Sobolev spaces of Triebel–Lizorkin type which are better than previously known estimates (when our assumption on the stable distribution holds). In many cases, we obtain a spectral gap from which we deduce the existence of finitely many physical measures with basin of total measure. The analysis relies on standard techniques (in particular complex interpolation) but gives a new result on bounded multipliers. Our method applies also to piecewise expanding maps and to Anosov diffeomorphisms, giving a unifying picture of several previous results on a simpler scale of Banach spaces.     

On almost periodic processes in impulsive competitive systems with delay and impulsive perturbations

In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with the general impulsive nonautonomous Lotka–Volterra system of integro-differential equations with infinite delay. The impulses are at fixed moments of time, and by using the techniques of piecewise continuous Lyapunov’s functions, new sufficient conditions for the global exponential stability of the unique positive almost periodic solutions of these systems are given.     

A solid molecular basket sorbent for CO2 capture from gas streams with low CO2 concentration under ambient conditions

In this paper, a solid molecular basket sorbent, 50 wt% PEI/SBA-15, was studied for CO(2) capture from gas streams with low CO(2) concentration under ambient conditions. The sorbent was able to effectively and selectively capture CO(2) from a gas stream containing 1% CO(2) at 75 °C, with a breakthrough and saturation capacity of 63.1 and 66.7 mg g(-1), respectively, and a selectivity of 14 for CO(2)/CO and 185 for CO(2)/Ar. The sorption performance of the sorbent was influenced greatly by the operating temperature. The CO(2)-TPD study showed that the sorbent could be regenerated under mild conditions (50-110 °C) and was stable in the cyclic operations for at least 20 cycles. Furthermore, the possibility for CO(2) capture from air using the PEI/SBA-15 sorbent was studied by FTIR and proved by TPD. A capacity of 22.5 mg g(-1) was attained at 75 °C via a TPD method using a simulated air with 400 ppmv CO(2) in N(2).     

Population turnover and adaptation in heterogeneous environments

We study adaptive dynamics in a structured population model of asexual individuals which takes into account environmental heterogeneity among the subpopulations. The key purpose of the present work is to address how population turnovers, i.e. extinction events followed by recolonization, affect the rate of fixation of advantageous mutations. This model is a generalization of our previous model to address the interplay between environmental correlation and evolutionary forces on the adaptive process. The incorporation of population turnovers into the model enables us to make a direct correspondence between the model and host-parasite dynamics (epidemiological models). Strikingly, contrary to the intuitive and usual deleterious effect associated to extinction events, it is observed that population turnovers can in fact speed up adaptation as heterogeneity rises. On the other side, in nearly homogeneous population turnovers have a neutral effect on fixation rates, but a detrimental outcome is also achieved when extinction events become very common. In resume, population turnover outcomes on fixation rates of advantageous mutations are strongly influenced by the selective correlation among the subpopulations (demes).     

On ℤ<Subscript>2</Subscript>-graded identities of the super tensor product of <Emphasis Type="Italic">UT</Emphasis><Subscript>2</Subscript>(<Emphasis Type="Italic">F</Emphasis>) by the Grassmann algebra

Let F be a field of characteristic zero and E be the unitary Grassmann algebra generated over an infinite-dimensional F-vector space L. Denote by \(\mathcal{E} = \mathcal{E}^{(0)} \oplus \mathcal{E}^{(1)}\) an arbitrary ?₂-grading of E such that the subspace L is homogeneous. Given a superalgebra A = A ⁽⁰⁾ ⊕ A ⁽¹⁾, define the superalgebra \(A\hat \otimes \mathcal{E}\) by \(A\hat \otimes \mathcal{E} = (A^{(0)} \otimes \mathcal{E}^{(0)} ) \oplus (A^{(1)} \otimes \mathcal{E}^{(1)} )\). Note that when E is the canonical grading of E then \(A\hat \otimes \mathcal{E}\) is the Grassmann envelope of A. In this work we find bases of ?₂-graded identities and we describe the ?₂-graded codimension and cocharacter sequences for the superalgebras \(UT_2 (F)\hat \otimes \mathcal{E}\), when the algebra UT ₂(F) of 2 ×2 upper triangular matrices over F is endowed with its canonical grading.     

Comparison of Singer's Formant, Speaker's Ring, and LTA Spectrum Among Classical Singers and Untrained Normal Speakers

Many studies have described and analyzed the singer's formant. A similar phenomenon produced by trained speakers led some authors to examine the speaker's ring. If we consider these phenomena as resonance effects associated with vocal tract adjustments and training, can we hypothesize that trained singers can carry over their singing formant ability into speech, also obtaining a speaker's ring? Can we find similar differences for energy distribution in continuous speech? Forty classically trained singers and forty untrained normal speakers performed an all-voiced reading task and produced a sample of a sustained spoken vowel /a/. The singers were also requested to perform a sustained sung vowel /a/ at a comfortable pitch. The reading was analyzed by the long-term average spectrum (LTAS) method. The sustained vowels were analyzed through power spectrum analysis. The data suggest that singers show more energy concentration in the singer's formant/speaker's ring region in both sung and spoken vowels. The singers' spoken vowel energy in the speaker's ring area was found to be significantly larger than that of the untrained speakers. The LTAS showed similar findings suggesting that those differences also occur in continuous speech. This finding supports the value of further research on the effect of singing training on the resonance of the speaking voice.     

New families of hypohamiltonian graphs

We construct three new infinite families of hypohamiltonian graphs having respectively 3k+1 vertices (k?3), 3k vertices (k?5) and 5k vertices (k?4); in particular, we exhibit a hypohamiltonian graph of order 19 and a cubic hypohamiltonian graph of order 20, the existence of which was still in doubt. Using these families, we get a lower bound for the number of non-isomorphic hypohamiltonian graphs of order 3k and 5k. We also give an example of an infinite graph G having no two-way infinite hamiltonian path, but in which every vertex-deleted subgraph G - x has such a path.     

A model of longitudinal dispersion in non–homogeneous porous media

This paper is concerned with a model of the longitudinal dispersion of a set of tagged particles in a flow through nonhomogeneous stratified porous media. The model is a particular homogeneous Markov jump process, the successive states visited forming a non-homogeneous Poisson process. The passage time of alevel x of this Markov process is an additive stochastic process.This property is used to evaluate the general form of the longitudinal concentration function of the tagged particles in the flow.