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1. Sensitivity-improved Polarization Maps at 40 GHz with CLASS and WMAP Data

   https://doi.org/10.3847/1538-4357/ad5313  

   Shi_时, Rui_瑞; Appel, John_W; Bennett, Charles_L; Bustos, Ricardo; Chuss, David_T; Dahal, Sumit; Denes_Couto, Jullianna; Eimer, Joseph_R; Essinger-Hileman, Thomas; Harrington, Kathleen; et al (August 2024, The Astrophysical Journal)

   Abstract Improved polarization measurements at frequencies below 70 GHz with degree-level angular resolution are crucial for advancing our understanding of the Galactic synchrotron radiation and the potential polarized anomalous microwave emission and ultimately benefiting the detection of primordialBmodes. In this study, we present sensitivity-improved 40 GHz polarization maps obtained by combining the CLASS 40 GHz and Wilkinson Microwave Anisotropy Probe (WMAP)Q-band data through a weighted average in the harmonic domain. The decision to include WMAPQ-band data stems from similarities in the bandpasses. Leveraging the accurate large-scale measurements from the WMAPQband and the high-sensitivity information from the CLASS 40 GHz band at intermediate scales, the noise level atℓ∈ [30, 100] is reduced by a factor of 2–3 in the map space. A pixel domain analysis of the polarized synchrotron spectral index (β_s) using the WMAPKband and the combined maps (mean and 16th/84th percentiles across theβ_smap: $-{3.08}_{-0.20}^{+0.20}$) reveals a stronger preference for spatial variation (probability to exceed for a uniformβ_shypothesis smaller than 0.001) than the results obtained using WMAPKandKabands ( $-{3.08}_{-0.14}^{+0.14}$). The cross-power spectra of the combined maps follow the same trend as other low-frequency data, and validation through simulations indicates negligible bias introduced by the combination method (subpercent level in the power spectra). The products of this work are publicly available onLAMBDA(https://lambda.gsfc.nasa.gov/product/class/class_prod_table.html). 

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2. Introducing isodynamic points for binary forms and their ratios

   https://doi.org/10.1007/s40627-022-00112-4  

   Hägg, Christian; Shapiro, Boris; Shapiro, Michael (January 2023, Complex Analysis and its Synergies)

   Abstract The isodynamic points of a plane triangle are known to be the only pair of its centers invariant under the action of the Möbius group$${\mathcal {M}}$$ $M$on the set of triangles, Kimberling (Encyclopedia of Triangle Centers,http://faculty.evansville.edu/ck6/encyclopedia). Generalizing this classical result, we introduce below theisodynamicmap associating to a univariate polynomial of degree$$d\ge 3$$ $d\ge 3$with at most double roots a polynomial of degree (at most)$$2d-4$$ $2d-4$such that this map commutes with the action of the Möbius group$${\mathcal {M}}$$ $M$on the zero loci of the initial polynomial and its image. The roots of the image polynomial will be called theisodynamic pointsof the preimage polynomial. Our construction naturally extends from univariate polynomials to binary forms and further to their ratios. 

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3. Scaling laws and exact results in turbulence ^*

   https://doi.org/10.1088/1361-6544/ad6057  

   Novack, Matthew (July 2024, Nonlinearity)

   Abstract In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000Nonlinearity13249–55) and Eyink (2003Nonlinearity16137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s $\frac{4}{5}$, $\frac{4}{3}$, $\frac{4}{15}$laws. We apply these computations to improve a recent result of Hofmanovaet al(2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruèet al(2023Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giriet al(2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws. 

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4. Improving Cosmological Constraints from Galaxy Cluster Number Counts with CMB-cluster-lensing Data: Results from the SPT-SZ Survey and Forecasts for the Future

   https://doi.org/10.3847/1538-4357/ac6a55  

   Chaubal, P. S.; Reichardt, C. L.; Gupta, N.; Ansarinejad, B.; Aylor, K.; Balkenhol, L.; Baxter, E. J.; Bianchini, F.; Benson, B. A.; Bleem, L. E.; et al (June 2022, The Astrophysical Journal)

   Abstract We show the improvement to cosmological constraints from galaxy cluster surveys with the addition of cosmic microwave background (CMB)-cluster lensing data. We explore the cosmological implications of adding mass information from the 3.1σdetection of gravitational lensing of the CMB by galaxy clusters to the Sunyaev–Zel’dovich (SZ) selected galaxy cluster sample from the 2500 deg²SPT-SZ survey and targeted optical and X-ray follow-up data. In the ΛCDM model, the combination of the cluster sample with the Planck power spectrum measurements prefers ${\sigma }_8{\left({\mathrm{\Omega }}_m/0.3\right)}^{0.5}=0.831\pm 0.020$. Adding the cluster data reduces the uncertainty on this quantity by a factor of 1.4, which is unchanged whether the 3.1σCMB-cluster lensing measurement is included or not. We then forecast the impact of CMB-cluster lensing measurements with future cluster catalogs. Adding CMB-cluster lensing measurements to the SZ cluster catalog of the ongoing SPT-3G survey is expected to improve the expected constraint on the dark energy equation of statewby a factor of 1.3 toσ(w) = 0.19. We find the largest improvements from CMB-cluster lensing measurements to be forσ₈, where adding CMB-cluster lensing data to the cluster number counts reduces the expected uncertainty onσ₈by respective factors of 2.4 and 3.6 for SPT-3G and CMB-S4. 

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5. Global Well-Posedness for $$H^{-1}(\mathbb {R})$$ Perturbations of KdV with Exotic Spatial Asymptotics

   https://doi.org/10.1007/s00220-022-04522-7  

   Laurens, Thierry (November 2022, Communications in Mathematical Physics)

   Abstract Given a suitable solutionV(t, x) to the Korteweg–de Vries equation on the real line, we prove global well-posedness for initial data$$u(0,x) \in V(0,x) + H^{-1}(\mathbb {R})$$ $u(0,x)\in V(0,x)+H^{-1}\left(R\right)$. Our conditions onVdo include regularity but do not impose any assumptions on spatial asymptotics. We show that periodic profiles$$V(0,x)\in H^5(\mathbb {R}/\mathbb {Z})$$ $V(0,x)\in H^5(R/Z)$satisfy our hypotheses. In particular, we can treat localized perturbations of the much-studied periodic traveling wave solutions (cnoidal waves) of KdV. In the companion paper Laurens (Nonlinearity. 35(1):343–387, 2022.https://doi.org/10.1088/1361-6544/ac37f5) we show that smooth step-like initial data also satisfy our hypotheses. We employ the method of commuting flows introduced in Killip and Vişan (Ann. Math. (2) 190(1):249–305, 2019.https://doi.org/10.4007/annals.2019.190.1.4) where$$V\equiv 0$$ $V\equiv 0$. In that setting, it is known that$$H^{-1}(\mathbb {R})$$ $H^{-1}\left(R\right)$is sharp in the class of$$H^s(\mathbb {R})$$ $H^s\left(R\right)$spaces. 

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