Calcium isotope fractionation in alpine plants

In order to develop Ca isotopes as a tracer for biogeochemical Ca cycling in terrestrial environments and for Ca utilisation in plants, stable calcium isotope ratios were measured in various species of alpine plants, including woody species, grasses and herbs. Analysis of plant parts (root, stem, leaf and flower samples) provided information on Ca isotope fractionation within plants and seasonal sampling of leaves revealed temporal variation in leaf Ca isotopic composition. There was significant Ca isotope fractionation between soil and root tissue \Updelta^{44/42}\hbox{Ca}_{\rm root-soil} \approx -0.40\,\permille in all investigated species, whereas Ca isotope fractionation between roots and leaves was species dependent. Samples of leaf tissue collected throughout the growing season also highlighted species differences: Ca isotope ratios increased with leaf age in woody species but remained constant in herbs and grasses. The Ca isotope fractionation between roots and soils can be explained by a preferential binding of light Ca isotopes to root adsorption sites. The observed differences in whole plant Ca isotopic compositions both within and between species may be attributed to several potential factors including root cation exchange capacity, the presence of a woody stem, the presence of Ca oxalate, and the levels of mycorrhizal infection. Thus, the impact of plants on the Ca biogeochemical cycle in soils, and ultimately the Ca isotope signature of the weathering flux from terrestrial environments, will depend on the species present and the stage of vegetation successio

Conformal dimension and random groups

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where $l$ is the relator length, going to infinity. (a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model, and (b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at densities $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to density < 1/16. Many minor improvements. To appear in GAF

τ→ρππν\tau\to\rho\pi\pi\nu decays

Effective chiral theory of mesons is applied to study the four decay modes of $\tau\to\rho\pi\pi\nu$. Theoretical values of the branching ratios are in agreement with the data. The theory predicts that the $a_{1}$ resonance plays a dominant role in these decays. There is no new parameter in this study.Comment: 12 pages and one figur

Localization of tenascin in human skin wounds

A total of 56 surgically treated human skin wounds with a wound age between 8h and 7 months were investigated. Tenascin was visualized by immunohistochemistry and appeared first in the wound area pericellularly around fibroblastic cells approximately 2 days after wounding. A network-like interstitial positive staining pattern was first detectable in 3-day-old skin wounds. In all wounds with an age of 5 days or more, intensive reactivity for tenascin could be observed in the lesional area (dermal-epidermal junction, wound edge, areas of bleeding). In wounds with an age of more than approximately 1.5 months no positive staining occurred in the scar tissue. In conclusion, for forensic purposes, positive staining for tenascin restricted to the pericellular area of fibroblastic cells indicates a wound age of at least 2 days. Network-like structures appear after approximately 3 days or more. Since tenascin seems to be regularly detectable in skin wounds older than 5 days, the lack of a positive reaction in a sufficient number of specimens indicates a wound age of less than 5 days. The lack of a positive reaction in the granulation tissue of wounds with advanced wound age indicates a survival time of more than about 1.5 months, but a positive staining in older wounds cannot be excluded

Weighted composition operators on Korenblum type spaces of analytic functions

[EN] We investigate the continuity, compactness and invertibility of weighted composition operators W-psi,W-phi: f -> psi(f circle phi) when they act on the classical Korenblum space A(-infinity) and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map phi has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.Gomez-Orts, E. (2020). Weighted composition operators on Korenblum type spaces of analytic functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(4):1-15. https://doi.org/10.1007/s13398-020-00924-1S1151144Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics. Amer. Math. Soc., 50 (2002)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ and $$L^{p-}$$. Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263–281 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the Fréchet sequence spaces $$ces(p+), 1\le p\le \infty$$. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 1533–1556 (2019)Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces $$ces(p-), 1\le p\le \infty$$. Descriptive topology and functional analysis. II, 43–67, Springer Proc. Math. Stat., 286, Springer, Cham (2019)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Austral. Math. Soc. 1–32. https://doi.org/10.1017/S1446788719000235Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic funcions. Israel J. Math. 141, 263–276 (2004)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 54(1), 70–79 (1993)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. RACSAM 114, 63 (2020). https://doi.org/10.1007/s13398-020-00788-5Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 64(1), 101–118 (1998)Bourdon, P.S.: Essential angular derivatives and maximum growth of Königs eigenfunctions. J. Func. Anal. 160, 561–580 (1998)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289–299 (2014)Carleson, L., Gamelin, T.: Complex Dynamics. Springer, Berlin (1991)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc., Ser. A 69, 41–60 (2000)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and $$H^\infty$$ spaces. J. Math. Anal. Appl. 445, 1300–1309 (2017)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Kamowitz, H.: Compact operators of the form $$uC_{\varphi }$$. Pac. J. Math. 80(1) (1979)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Köthe, G.: Topological Vector Spaces II. Springer, New York Inc (1979)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Grad. Texts in Math. 2, New York, (1997)Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(3), 872–884 (2000)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287–302 (1971)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs, Amer. Math. Soc. 138 (2007

Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the Asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.Comment: 17 pages, 8 figures. During preparation of this manuscript the authors became aware of the work of Mileyko at al., concurrently submitted for publicatio

Preferences and skills of Indian public sector teachers

With a sample of 700 future public sector primary teachers in India, a Discrete Choice Experiment is used to measure job preferences, particularly regarding location. General skills are also tested. Urban origin teachers and women are more averse to remote locations than rural origin teachers and men respectively. Women would require a 26-73 percent increase in salary for moving to a remote location. The results suggest that existing caste and gender quotas can be detrimental for hiring skilled teachers willing to work in remote locations. The most preferred location is home, which supports decentralised hiring, although this could compromise skills

Positive and negative streamers in ambient air: modeling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.Comment: 18 pages, 10 figure

Probing photo-ionization: Experiments on positive streamers in pure gasses and mixtures

Positive streamers are thought to propagate by photo-ionization whose parameters depend on the nitrogen:oxygen ratio. Therefore we study streamers in nitrogen with 20%, 0.2% and 0.01% oxygen and in pure nitrogen, as well as in pure oxygen and argon. Our new experimental set-up guarantees contamination of the pure gases to be well below 1 ppm. Streamers in oxygen are difficult to measure as they emit considerably less light in the sensitivity range of our fast ICCD camera than the other gasses. Streamers in pure nitrogen and in all nitrogen/oxygen mixtures look generally similar, but become somewhat thinner and branch more with decreasing oxygen content. In pure nitrogen the streamers can branch so much that they resemble feathers. This feature is even more pronounced in pure argon, with approximately 10^2 hair tips/cm^3 in the feathers at 200 mbar; this density could be interpreted as the free electron density creating avalanches towards the streamer stem. It is remarkable that the streamer velocity is essentially the same for similar voltage and pressure in all nitrogen/oxygen mixtures as well as in pure nitrogen, while the oxygen concentration and therefore the photo-ionization lengths vary by more than five orders of magnitude. Streamers in argon have essentially the same velocity as well. The physical similarity of streamers at different pressures is confirmed in all gases; the minimal diameters are smaller than in earlier measurements.Comment: 28 pages, 14 figures. Major differences with v1: - appendix and spectra removed - subsection regarding effects of repetition frequency added - many more smaller change