Construction Of A Rich Word Containing Given Two Factors

A finite word $w$ with $\vert w\vert=n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called \emph{rich}. Let \Factor(w) be the set of factors of the word $w$. It is known that there are pairs of rich words that cannot be factors of a common rich word. However it is an open question how to decide for a given pair of rich words $u,v$ if there is a rich word $w$ such that \{u,v\}\subseteq \Factor(w). We present a response to this open question:\\ If $w_1, w_2,w$ are rich words, $m=\max{\{\vert w_1\vert,\vert w_2\vert\}}$, and \{w_1,w_2\}\subseteq \Factor(w) then there exists also a rich word $\bar w$ such that \{w_1,w_2\}\subseteq \Factor(\bar w) and $\vert \bar w\vert\leq m2^{k(m)+2}$, where $k(m)=(q+1)m^2(4q^{10}m)^{\log_2{m}}$ and $q$ is the size of the alphabet. Hence it is enough to check all rich words of length equal or lower to $m2^{k(m)+2}$ in order to decide if there is a rich word containing factors $w_1,w_2$

On Words with the Zero Palindromic Defect

We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich words which cannot occur simultaneously as factors of a longer rich word

A study of environmental characterization of conventional and advanced aluminum alloys for selection and design. Phase 2: The breaking load test method

A technique is demonstrated for accelerated stress corrosion testing of high strength aluminum alloys. The method offers better precision and shorter exposure times than traditional pass fail procedures. The approach uses data from tension tests performed on replicate groups of smooth specimens after various lengths of exposure to static stress. The breaking strength measures degradation in the test specimen load carrying ability due to the environmental attack. Analysis of breaking load data by extreme value statistics enables the calculation of survival probabilities and a statistically defined threshold stress applicable to the specific test conditions. A fracture mechanics model is given which quantifies depth of attack in the stress corroded specimen by an effective flaw size calculated from the breaking stress and the material strength and fracture toughness properties. Comparisons are made with experimental results from three tempers of 7075 alloy plate tested by the breaking load method and by traditional tests of statistically loaded smooth tension bars and conventional precracked specimens

Proof of Brlek-Reutenauer conjecture

Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = \sum_{n=0}^{\infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n) +2 - P_U(n+1) - P_u(n), where C_u and P_u are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words.Comment: 9 page

Time evolution in linear response: Boltzmann equations and beyond

In this work a perturbative linear response analysis is performed for the time evolution of the quasi-conserved charge of a scalar field. One can find two regimes, one follows exponential damping, where the damping rate is shown to come from quantum Boltzmann equations. The other regime (coming from multiparticle cuts and products of them) decays as power law. The most important, non-oscillating contribution in our model comes from a 4-particle intermediate state and decays as 1/t^3. These results may have relevance for instance in the context of lepton number violation in the Early Universe.Comment: 19 page

Vertical distribution of aerosol optical properties in the Po Valley during the 2012 summer campaigns

Studying the vertical distribution of aerosol particle physical and chemical properties in the troposphere is essential to understand the relative importance of local emission processes vs. long-range transport for column-integrated aerosol properties (e.g. the aerosol optical depth, AOD, affecting regional climate) as well as for the aerosol burden and its impacts on air quality at the ground. The main objective of this paper is to investigate the transport of desert dust in the middle troposphere and its intrusion into the planetary boundary layer (PBL) over the Po Valley (Italy), a region considered one of the greatest European pollution hotspots for the frequency that particulate matter (PM) limit values are exceeded. Events of mineral aerosol uplift from local (soil) sources and phenomena of hygroscopic growth at the ground are also investigated, possibly affecting the PM concentration in the region as well. During the PEGASOS 2012 field campaign, an integrated observing–modelling system was set up based on near-surface measurements (particle concentration and chemistry), vertical profiling (backscatter coefficient profiles from lidar and radiosoundings) and Lagrangian air mass transport simulations by FLEXPART model. Measurements were taken at the San Pietro Capofiume supersite (44°39′ N, 11°37′ E; 11 m a.s.l.), located in a rural area relatively close to some major urban and industrial emissive areas in the Po Valley. Mt. Cimone (44°12′ N, 10°42′ E; 2165 m a.s.l.) WMO/GAW station observations are also included in the study to characterize regional-scale variability. Results show that, in the Po Valley, aerosol is detected mainly below 2000 m a.s.l. with a prevalent occurrence of non-depolarizing particles ( > 50 % throughout the campaign) and a vertical distribution modulated by the PBL daily evolution. Two intense events of mineral dust transport from northern Africa (19–21 and 29 June to 2 July) are observed, with layers advected mainly above 2000 m, but subsequently sinking and mixing in the PBL. As a consequence, a non-negligible occurrence of mineral dust is observed close to the ground (  ~7 % of occurrence during a 1-month campaign). The observations unambiguously show Saharan dust layers intruding the Po Valley mixing layer and directly affecting the aerosol concentrations near the surface. Finally, lidar observations also indicate strong variability in aerosol on shorter timescales (hourly). Firstly, these highlight events of hygroscopic growth of anthropogenic aerosol, visible as shallow layers of low depolarization near the ground. Such events are identified during early morning hours at high relative humidity (RH) conditions (RH  > 80 %). The process is observed concurrently with high PM1 nitrate concentration (up to 15 µg cm−3) and hence mainly explicable by deliquescence of fine anthropogenic particles, and during mineral dust intrusion episodes, when water condensation on dust particles could instead represent the dominant contribution. Secondly, lidar images show frequent events (mean daily occurrence of  ~ 22 % during the whole campaign) of rapid uplift of mineral depolarizing particles in afternoon–evening hours up to 2000 m a.s.l. height. The origin of such particles cannot be directly related to long-range transport events, being instead likely linked to processes of soil particle resuspension from agricultural lands

Boltzmann Suppression of Interacting Heavy Particles

Matsumoto and Yoshimura have recently argued that the number density of heavy particles in a thermal bath is not necessarily Boltzmann-suppressed for T << M, as power law corrections may emerge at higher orders in perturbation theory. This fact might have important implications on the determination of WIMP relic densities. On the other hand, the definition of number densities in a interacting theory is not a straightforward procedure. It usually requires renormalization of composite operators and operator mixing, which obscure the physical interpretation of the computed thermal average. We propose a new definition for the thermal average of a composite operator, which does not require any new renormalization counterterm and is thus free from such ambiguities. Applying this definition to the model of Matsumoto and Yoshimura we find that it gives number densities which are Boltzmann-suppressed at any order in perturbation theory. We discuss also heavy particles which are unstable already at T=0, showing that power law corrections do in general emerge in this case.Comment: 7 pages, 5 figures. New section added, with the discussion of the case of an unstable heavy particle. Version to appear on Phys. Rev.

Quantum skyrmions and the destruction of long-range antiferromagnetic order in the high-Tc superconductors La(2-x)Sr(x)CuO(4) and YBa(2)Cu(3)O(6+x)

We study the destruction of the antiferromagnetic order in the high-Tc superconductors La(2-x)Sr(x)CuO(4) and YBa(2)Cu(3)O(6+x) in the framework of the CP1-nonlinear sigma model formulation of the 2D quantum Heisenberg antiferromagnet. The dopants are introduced as independent fermions with appropriate dispersion relations determined by the shape of the Fermi surface. The energy of skyrmion topological defects, which are shown to be introduced by doping, is used as an order parameter for antiferromagnetic order. We obtain analytic expressions for this as a function of doping which allow us to plot the curves T_N(x_c)\times x_c and M(x)\times x, for both YBCO and LSCO, in good quantitative agreement with the experimental data.Comment: 4 pages, revtex, 5 embeeded figure

Protective role of PI3-kinase-Akt-eNOS signalling pathway in intestinal injury associated with splanchnic artery occlusion shock.

Background and purpose: Endothelial NO synthase (eNOS) is a dynamic enzyme tightly controlled by co- and post-translational lipid modifications, phosphorylation and regulated by protein-protein interactions. Here we have pharmacologically modulated the activation of eNOS, at different post-translational levels, to assess the role of eNOS-derived NO and of these regulatory mechanisms in intestinal injury associated with splanchnic artery occlusion (SAO) shock. Experimental approach: SAO shock was induced by clamping both the superior mesenteric artery and the celiac trunk for 45 min followed by 30 min of reperfusion. During ischemia, 15 min prior to reperfusion, mice were given geldanamycin, an inhibitor of hsp90 recruitment to eNOS, or LY-294002 an inhibitor of phosphatidylinositol 3-kinase (PI3K), an enzyme that initiates Akt-catalysed phosphorylation of eNOS on Ser 1179. After 30 min of reperfusion, samples of ileum were taken for histological examination or for biochemical studies. Key results: Either LY-294002 or geldanamycin reversed the increased activation of eNOS and Akt observed following SAO shock. These molecular effects were mirrored in vivo by an exacerbation of the intestinal damage. Histological damage also correlated with neutrophil infiltration, assessed as myeloperoxidase activity, and with an increased expression of the adhesion proteins: ICAM-I, VCAM, P-selectin and E-selectin. Conclusions and implications: Overall these results suggest that activation of the Akt pathway in ischemic regions of reperfused ileum is a protective event, triggered in order to protect the intestinal tissue from damage induced by ischaemia/reperfusion through a fine tuning of the endothelial NO pathway. © 2007 Nature Publishing Group All rights reserved