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1. On Uniform Convergence of Diagonal Multipoint Pad� Approximants For Entire Functions

   Lubinsky, Doron S ( January 2019 , Constructive approximation)

   We prove that for most entire functions f in the sense of category, a strong form of the Baker-Gammel-Wills Conjecture holds. More precisely, there is an inÖnite sequence S of positive integers n, such that given any r > 0, and multipoint PadÈ approximants Rn to f with interpolation points in fz : jzj  rg, fRngn2S converges locally uniformly to f in the plane. The sequence S does not depend on r, nor on the interpolation points. For entire functions with smooth rapidly decreasing coe¢ cients, full diagonal sequences of multipoint PadÈ approximants converge. 

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2. An introductory guide to fluid models with anisotropic temperatures. Part 2. Kinetic theory, Padé approximants and Landau fluid closures

   https://doi.org/10.1017/S0022377819000850  

   Hunana, P. ; Tenerani, A. ; Zank, G. P. ; Goldstein, M. L. ; Webb, G. M. ; Khomenko, E. ; Collados, M. ; Cally, P. S. ; Adhikari, L. ; Velli, M. ( December 2019 , Journal of Plasma Physics)

   In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\unicode[STIX]{x1D701})$ , and the associated plasma response function $R(\unicode[STIX]{x1D701})=1+\unicode[STIX]{x1D701}Z(\unicode[STIX]{x1D701})=-Z^{\prime }(\unicode[STIX]{x1D701})/2$ . We then consider a one-dimensional (1-D) (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the fourth-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1-D closures at higher-order moments than the fourth order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3-D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the fourth-order moment level. In appendix A, we provide comprehensive tables with Padé approximants of $R(\unicode[STIX]{x1D701})$ up to the eighth-pole order, with many given in an analytic form. 

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3. Algebraic stability of meromorphic maps descended from Thurston’s pullback maps

   https://doi.org/10.1090/tran/8221  

   Ramadas, Rohini ( January 2021 , Transactions of the American Mathematical Society)

   null (Ed.)

   Let ϕ : S 2 → S 2 \phi :S^2 \to S^2 be an orientation-preserving branched covering whose post-critical set has finite cardinality n n . If ϕ \phi has a fully ramified periodic point p ∞ p_{\infty } and satisfies certain additional conditions, then, by work of Koch, ϕ \phi induces a meromorphic self-map R ϕ R_{\phi } on the moduli space M 0 , n \mathcal {M}_{0,n} ; R ϕ R_{\phi } descends from Thurston’s pullback map on Teichmüller space. Here, we relate the dynamics of R ϕ R_{\phi } on M 0 , n \mathcal {M}_{0,n} to the dynamics of ϕ \phi on S 2 S^2 . Let ℓ \ell be the length of the periodic cycle in which the fully ramified point p ∞ p_{\infty } lies; we show that R ϕ R_{\phi } is algebraically stable on the heavy-light Hassett space corresponding to ℓ \ell heavy marked points and ( n − ℓ ) (n-\ell ) light points. 

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4. On the Kinematics of Cold, Metal-enriched Galactic Fountain Flows in Nearby Star-forming Galaxies

   https://doi.org/10.3847/1538-4357/ac7b88  

   Rubin, Kate H. R. ; Juarez, Christian ; Cooksey, Kathy L. ; Werk, Jessica K. ; Prochaska, J. Xavier ; O’Meara, John M. ; Burchett, Joseph N. ; Rickards Vaught, Ryan J. ; Kulkarni, Varsha P. ; Straka, Lorrie A. ( September 2022 , The Astrophysical Journal)

   We use medium-resolution Keck/Echellette Spectrograph and Imager spectroscopy of bright quasars to study cool gas traced by Caiiλλ3934, 3969 and Naiλλ5891, 5897 absorption in the interstellar/circumgalactic media of 21 foreground star-forming galaxies at redshifts 0.03 <z< 0.20 with stellar masses 7.4 ≤ logM_*/M_⊙≤ 10.6. The quasar–galaxy pairs were drawn from a unique sample of Sloan Digital Sky Survey quasar spectra with intervening nebular emission, and thus have exceptionally close impact parameters (R_⊥< 13 kpc). The strength of this line emission implies that the galaxies’ star formation rates (SFRs) span a broad range, with several lying well above the star-forming sequence. We use Voigt profile modeling to derive column densities and component velocities for each absorber, finding that column densitiesN(Caii) > 10^12.5cm⁻²(N(Nai) > 10^12.0cm⁻²) occur with an incidencef_C(Caii) = 0.63^+0.10_−0.11(f_C(Nai) = 0.57^+0.10_−0.11). We find no evidence for a dependence off_Cor the rest-frame equivalent widthsW_r(CaiiK) orW_r(Nai5891) onR_⊥orM_*. Instead,W_r(CaiiK) is correlated with local SFR at >3σsignificance, suggesting that Caiitraces star formation-driven outflows. While most of the absorbers have velocities within ±50 km s⁻¹of the host redshift, their velocity widths (characterized by Δv₉₀) are universally 30–177 km s⁻¹larger than that implied by tilted-ring modeling of the velocities of interstellar material. These kinematics must trace galactic fountain flows and demonstrate that they persist atR_⊥> 5 kpc. Finally, we assess the relationship between dust reddening andW_r(CaiiK) (W_r(Nai5891)), finding that 33% (24%) of the absorbers are inconsistent with the best-fit Milky WayE(B−V)-W_rrelations at >3σsignificance.

    

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5. Zetaproteobacteria Pan-Genome Reveals Candidate Gene Cluster for Twisted Stalk Biosynthesis and Export

   https://doi.org/10.3389/fmicb.2021.679409  

   Koeksoy, Elif ; Bezuidt, Oliver M. ; Bayer, Timm ; Chan, Clara S. ; Emerson, David ( June 2021 , Frontiers in Microbiology)

   Twisted stalks are morphologically unique bacterial extracellular organo-metallic structures containing Fe(III) oxyhydroxides that are produced by microaerophilic Fe(II)-oxidizers belonging to the Betaproteobacteria and Zetaproteobacteria. Understanding the underlying genetic and physiological mechanisms of stalk formation is of great interest based on their potential as novel biogenic nanomaterials and their relevance as putative biomarkers for microbial Fe(II) oxidation on ancient Earth. Despite the recognition of these special biominerals for over 150 years, the genetic foundation for the stalk phenotype has remained unresolved. Here we present a candidate gene cluster for the biosynthesis and secretion of the stalk organic matrix that we identified with a trait-based analyses of a pan-genome comprising 16 Zetaproteobacteria isolate genomes. The “ s talk f ormation in Z etaproteobacteria” (sfz) cluster comprises six genes ( sfz1-sfz6 ), of which sfz1 and sfz2 were predicted with functions in exopolysaccharide synthesis, regulation, and export, sfz4 and sfz6 with functions in cell wall synthesis manipulation and carbohydrate hydrolysis, and sfz3 and sfz5 with unknown functions. The stalk-forming Betaproteobacteria Ferriphaselus R-1 and OYT-1, as well as dread-forming Zetaproteobacteria Mariprofundus aestuarium CP-5 and Mariprofundus ferrinatatus CP-8 contain distant sfz gene homologs, whereas stalk-less Zetaproteobacteria and Betaproteobacteria lack the entire gene cluster. Our pan-genome analysis further revealed a significant enrichment of clusters of orthologous groups (COGs) across all Zetaproteobacteria isolate genomes that are associated with the regulation of a switch between sessile and motile growth controlled by the intracellular signaling molecule c-di-GMP. Potential interactions between stalk-former unique transcription factor genes, sfz genes, and c-di-GMP point toward a c-di-GMP regulated surface attachment function of stalks during sessile growth. 

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