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1. Notes on solutions of KZ equations modulo $p^s$ and $$p$$-adic limit $$s\to\infty$$

   Alexander Varchenko (January 2022, Contemporary mathematics)

   We consider the KZ equations over C in the case, when the hypergeometric solutions are hyperelliptic integrals of genus g. Then the space of solutions is a 2g-dimensional complex vector space. We also consider the same equations modulo ps, where p is an odd prime and s is a positive integer, and over the field Q_p of p-adic numbers. We construct polynomial solutions of the KZ equations modulo ps and study the space Mps of all constructed solutions. We show that the p-adic limit of Mps as s→∞ gives us a g-dimensional vector space of solutions of the KZ equations over Qp. The solutions over Qp are power series at a certain asymptotic zone of the KZ equations. In the appendix written jointly with Steven Sperber we consider all asymptotic zones of the KZ equations in the case g=1 of elliptic integrals. The p-adic limit of Mps as s→∞ gives us a one-dimensional space of solutions over Qp at every asymptotic zone. We apply Dwork's theory and show that our germs of solutions over Qp defined at different asymptotic zones analytically continue into a single global invariant line subbundle of the associated KZ connection. Notice that the corresponding KZ connection over C does not have proper nontrivial invariant subbundles, and therefore our invariant line subbundle is a new feature of the KZ equations over Qp. We describe the Frobenius transformations of solutions of the KZ equations for g=1 and then recover the unit roots of the zeta functions of the elliptic curves defined by the equations y2=βx(x−1)(x−α) over the finite field Fp. Here α,β∈F×p,α≠1 

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2. Measurement of the inclusive isolated photon production cross section in $$\text{ p }\text{ p }$$pp collisions at $$\sqrt{s}=7$$s=7 TeV

   https://doi.org/10.1140/epjc/s10052-019-7389-9  

   Acharya, S.; Adamová, D.; Adhya, S. P.; Adler, A.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; et al (November 2019, The European Physical Journal C)
3. Crustal Anisotropy from the Birefringence of P-to-S Converted Waves: Bias Associated with P-Wave Anisotropy

   https://doi.org/10.4401/ag-8882  

   Park, Jeffrey; Chen, Xiaoran; Levin, Vadim (January 2023, Annals of Geophysics)

   Many researchers have used the birefringence of P‑to‑S converted waves from the Moho discontinuity to constrain the anisotropy of Earth’s crust. However, this practice ignores the substantial influence that anisotropy has on the initial amplitude of the converted wave, which adds to the splitting acquired during its propagation from Moho to the seismometer. We find that large variations in Ps birefringence estimates with back-azimuth occur theoretically in the presence of P‑wave anisotropy, which normally accompanies S‑wave anisotropy. The variations are largest for crustal anisotropy with a tilted axis of symmetry, a geometry that is often neglected in birefringence interpretations, but is commonly found in Earth’s crust. We simulated globally-distributed P‑coda datasets for 36 distinct 4‑layer crustal models with combinations of elliptical shear anisotropy or compressional anisotropy, and also incorporated the higher-order anisotropic Backus parameter C. We tested both horizontal and tilted symmetry-axis geometries and tested the birefringence tradeoff associated with Ps converted phases at the top and bottom of a thin high‑ or low‑velocity basal layer. We computed composite receiver functions (RFs) with harmonic regression over back azimuth, using multipletaper correlation with moveout corrections for the epicentral distances of 471 events, to simulate a realistic data set. We estimate Ps birefringence from the radial and transverse RFs, a strategy that is similar to previous studies. We find that Ps splitting can be a useful indicator of bulk crustal anisotropy only under restricted circumstance, either in media with no compressional anisotropy, or if the symmetry axis is horizontal throughout. In other, more-realistic cases, the inferred fast polarization of Ps birefringence estimated from synthetic RFs tends either to drift with back-azimuth, form weak penalty-function minima, or return splitting times that depend on the thickness of an anisotropic layer, rather than the birefringence accumulated within it.   

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4. A. Squicciarini, S. Rajtmajer, P. Umar, T. Blose.

   A. Squicciarini, S. Rajtmajer (October 2020, 2nd IEEE International Conference on Cognitive Machine Intelligenc)

   null (Ed.)
5. The dimensions of scatterers in the lower mantle using USArray recordings of S-wave to P-wave conversions

   https://doi.org/10.1016/j.pepi.2020.106541  

   Ritsema, Jeroen; Kaneshima, Satoshi; Haugland, Samuel M. (September 2020, Physics of the Earth and Planetary Interiors)

   null (Ed.)