Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive-like operators

In this paper we use the general class of contractive-like operators introduced by Bosede and Rhoades (J. Adv. Math. Stud. 3(2):1-3, 2010) to prove strong convergence and stability results for Picard-Mann hybrid iterative schemes considered in a real normed linear space. We establish the strong convergence and stability of the Picard iterative scheme as a corollary. Our results generalize and improve a multitude of results in the literature, including the recent results of Chidume (Fixed Point Theory Appl. 2014:233, 2014)

Maximizing ENSO as a source of western US hydroclimate predictability

Until recently, the El Niño–Southern Oscillation (ENSO) was considered a reliable source of winter precipitation predictability in the western US, with a historically strong link between extreme El Niño events and extremely wet seasons. However, the 2015–2016 El Niño challenged our understanding of the ENSO-precipitation relationship. California precipitation was near-average during the 2015–2016 El Niño, which was characterized by warm sea surface temperature (SST) anomalies of similar magnitude compared to the extreme 1997–1998 and 1982–1983 El Niño events. We demonstrate that this precipitation response can be explained by El Niño’s spatial pattern, rather than internal atmospheric variability. In addition, observations and large-ensembles of regional and global climate model simulations indicate that extremes in seasonal and daily precipitation during strong El Niño events are better explained using the ENSO Longitude Index (ELI), which captures the diversity of ENSO’s spatial patterns in a single metric, compared to the traditional Niño3.4 index, which measures SST anomalies in a fixed region and therefore fails to capture ENSO diversity. The physically-based ELI better explains western US precipitation variability because it tracks the zonal shifts in tropical Pacific deep convection that drive teleconnections through the response in the extratropical wave-train, integrated vapor transport, and atmospheric rivers. This research provides evidence that ELI improves the value of ENSO as a predictor of California’s seasonal hydroclimate extremes compared to traditional ENSO indices, especially during strong El Niño events

Unique and conserved MicroRNAs in wheat chromosome 5D revealed by next-generation sequencing

MicroRNAs are a class of short, non-coding, single-stranded RNAs that act as post-transcriptional regulators in gene expression. miRNA analysis of Triticum aestivum chromosome 5D was performed on 454 GS FLX Titanium sequences of flow sorted chromosome 5D with a total of 3,208,630 good quality reads representing 1.34x and 1.61x coverage of the short (5DS) and long (5DL) arms of the chromosome respectively. In silico and structural analyses revealed a total of 55 miRNAs; 48 and 42 miRNAs were found to be present on 5DL and 5DS respectively, of which 35 were common to both chromosome arms, while 13 miRNAs were specific to 5DL and 7 miRNAs were specific to 5DS. In total, 14 of the predicted miRNAs were identified in wheat for the first time. Representation (the copy number of each miRNA) was also found to be higher in 5DL (1,949) compared to 5DS (1,191). Targets were predicted for each miRNA, while expression analysis gave evidence of expression for 6 out of 55 miRNAs. Occurrences of the same miRNAs were also found in Brachypodium distachyon and Oryza sativa genome sequences to identify syntenic miRNA coding sequences. Based on this analysis, two other miRNAs: miR1133 and miR167 were detected in B. distachyon syntenic region of wheat 5DS. Five of the predicted miRNA coding regions (miR6220, miR5070, miR169, miR5085, miR2118) were experimentally verified to be located to the 5D chromosome and three of them : miR2118, miR169 and miR5085, were shown to be 5D specific. Furthermore miR2118 was shown to be expressed in Chinese Spring adult leaves. miRNA genes identified in this study will expand our understanding of gene regulation in bread wheat

Accreting Black Holes

This chapter provides a general overview of the theory and observations of black holes in the Universe and on their interpretation. We briefly review the black hole classes, accretion disk models, spectral state classification, the AGN classification, and the leading techniques for measuring black hole spins. We also introduce quasi-periodic oscillations, the shadow of black holes, and the observations and the theoretical models of jets.Comment: 41 pages, 18 figures. To appear in "Tutorial Guide to X-ray and Gamma-ray Astronomy: Data Reduction and Analysis" (Ed. C. Bambi, Springer Singapore, 2020). v3: fixed some typos and updated some parts. arXiv admin note: substantial text overlap with arXiv:1711.1025

Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces

[EN] A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator C acting on the weighted Banach sequence space c0(w) for a bounded, strictly positive weight w. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of c0.The research of the first two authors was partially supported by the Projects MTM2013-43540-P, GVA Prometeo II/2013/013 and ACOMP/2015/186 (Spain).Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Mean ergodicity and spectrum of the Cesàro operator on weighted c0 spaces. Positivity. 20:761-803. https://doi.org/10.1007/s11117-015-0385-xS76180320Akhmedov, A.M., Başar, F.: On the fine spectrum of the Cesàro operator in $$c_0$$ c 0 . Math. J. Ibaraki Univ. 36, 25–32 (2004)Akhmedov, A.M., Başar, F.: The fine spectrum of the Cesàro operator $$C_1$$ C 1 over the sequence space $$bv_p, (1 \le p < \infty )$$ b v p , ( 1 ≤ p < ∞ ) . Math. J. Okayama Univ. 50, 135–147 (2008)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Spectrum and compactness of the Cesàro operator on weighted $$\ell _p$$ ℓ p spaces. J. Aust. Math. Soc. 99, 287–314 (2015)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ ℓ p + and $$L ^{p-}$$ L p - . Glasg. Math. J (to appear)Ansari, S.I., Bourdon, P.S.: Some properties of cyclic operators. Acta Sci. Math. Szeged 63, 195–207 (1997)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. Szeged 26, 125–137 (1965)Curbera, G.P., Ricker, W.J.: Spectrum of the Cesàro operator in $$\ell ^p$$ ℓ p . Arch. Math. 100, 267–271 (2013)Curbera, G.P., Ricker, W.J.: Solid extensions of the Cesàro operator on $$\ell ^p$$ ℓ p and $$c_0$$ c 0 . Integr. Equ. Oper. Theory 80, 61–77 (2014)Curbera, G.P., Ricker, W.J.: The Cesàro operator and unconditional Taylor series in Hardy spaces. Integr. Equ. Oper. Theory 83, 179–195 (2015)Diestel, J.: Sequences and Series in Banach Spaces. Springer, New York (1984)Dowson, H.R.: Spectral Theory of Linear Operators. Academic Press, London (1978)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory, 2nd Printing. Wiley Interscience Publ, New York (1964)Emilion, R.: Mean-bounded operators and mean ergodic theorems. J. Funct. Anal. 61, 1–14 (1985)Goldberg, S.: Unbounded Linear Operators: Theory and Applications. Dover Publ, New York (1985)Hille, E.: Remarks on ergodic theorems. Trans. Am. Math. Soc. 57, 246–269 (1945)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Leibowitz, G.: Spectra of discrete Cesàro operators. Tamkang J. Math. 3, 123–132 (1972)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Megginson, R.E.: An Introduction to Banach Space Theory. Springer, New York (1998)Mureşan, M.: A Concrete Approach to Classical Analysis. Springer, Berlin (2008)Okutoyi, J.I.: On the spectrum of $$C_1$$ C 1 as an operator on $$bv_0$$ b v 0 . J. Aust. Math. Soc. Ser. A 48, 79–86 (1990)Radjavi, H., Tam, P.-W., Tan, K.-K.: Mean ergodicity for compact operators. Studia Math. 158, 207–217 (2003)Reade, J.B.: On the spectrum of the Cesàro operator. Bull. Lond. Math. Soc. 17, 263–267 (1985)Rhoades, B.E., Yildirim, M.: The spectra and fine spectra of factorable matrices on $$c_0$$ c 0 . Math. Commun. 16, 265–270 (2011)Taylor, A.E.: Introduction to Functional Analysis. Wiley, New York (1958

Threat-sensitive anti-predator defence in precocial wader, the northern lapwing Vanellus vanellus

Birds exhibit various forms of anti-predator behaviours to avoid reproductive failure, with mobbing—observation, approach and usually harassment of a predator—being one of the most commonly observed. Here, we investigate patterns of temporal variation in the mobbing response exhibited by a precocial species, the northern lapwing (Vanellus vanellus). We test whether brood age and self-reliance, or the perceived risk posed by various predators, affect mobbing response of lapwings. We quantified aggressive interactions between lapwings and their natural avian predators and used generalized additive models to test how timing and predator species identity are related to the mobbing response of lapwings. Lapwings diversified mobbing response within the breeding season and depending on predator species. Raven Corvus corax, hooded crow Corvus cornix and harriers evoked the strongest response, while common buzzard Buteo buteo, white stork Ciconia ciconia, black-headed gull Chroicocephalus ridibundus and rook Corvus frugilegus were less frequently attacked. Lapwings increased their mobbing response against raven, common buzzard, white stork and rook throughout the breeding season, while defence against hooded crow, harriers and black-headed gull did not exhibit clear temporal patterns. Mobbing behaviour of lapwings apparently constitutes a flexible anti-predator strategy. The anti-predator response depends on predator species, which may suggest that lapwings distinguish between predator types and match mobbing response to the perceived hazard at different stages of the breeding cycle. We conclude that a single species may exhibit various patterns of temporal variation in anti-predator defence, which may correspond with various hypotheses derived from parental investment theory