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1. On generalizations of the nonwindowed scattering transform

   https://doi.org/10.1016/j.acha.2023.101597  

   Chua, Albert; Hirn, Matthew; Little, Anna (January 2024, Applied and Computational Harmonic Analysis)

   Balan, Radu (Ed.)

   In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as L^q(R^n) norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then provide norms for these operators, prove that these operators are well-defined, and are Lipschitz continuous to the action of C^2 diffeomorphisms in specific cases. Lastly, we extend our results to formulate an operator invariant to the action of rotations and an operator that is equivariant to the action of rotations. 

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2. Antimatter Free-Fall Experiments and Charge Asymmetry

   https://doi.org/10.3390/sym13071192  

   Jentschura, Ulrich David (July 2021, Symmetry)

   null (Ed.)

   We propose a method by which one could use modified antimatter gravity experiments in order to perform a high-precision test of antimatter charge neutrality. The proposal is based on the application of a strong, external, vertically oriented electric field during an antimatter free-fall gravity experiment in the gravitational field of the Earth. The proposed experimental setup has the potential to drastically improve the limits on the charge-asymmetry parameter ϵ¯q of antimatter. On the theoretical side, we analyze possibilities to describe a putative charge-asymmetry of matter and antimatter, proportional to the parameters ϵq and ϵ¯q, by Lagrangian methods. We found that such an asymmetry could be described by four-dimensional Lorentz-invariant operators that break CPT without destroying the locality of the field theory. The mechanism involves an interaction Lagrangian with field operators decomposed into particle or antiparticle field contributions. Our Lagrangian is otherwise Lorentz, as well as PT invariant. Constraints to be derived on the parameter ϵ¯q do not depend on the assumed theoretical model. 

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3. Relations between Poincaré series for quasi-complete intersection homomorphisms

   https://doi.org/10.1090/proc/17078  

   Pollitz, Josh; Şega, Liana (January 2025, Proceedings of the American Mathematical Society)

   In this article we study base change of Poincaré series along a quasi-complete intersection homomorphism $\mathrm{\phi <\#comment/>}:<\#comment/>Q\to <\#comment/>R$, where $Q$is a local ring with maximal ideal $\mathfrak{m}$. In particular, we give a precise relationship between the Poincaré series ${\mathrm{P}}_M^Q\left(t\right)$of a finitely generated $R$-module $M$to ${\mathrm{P}}_M^R\left(t\right)$when the kernel of $\mathrm{\phi <\#comment/>}$is contained in $\mathfrak{m}{\mathrm{a}\mathrm{n}\mathrm{n}}_Q\left(M\right)$. This generalizes a classical result of Shamash for complete intersection homomorphisms. Our proof goes through base change formulas for Poincaré series under the map of dg algebras $Q\to <\#comment/>E$, with $E$the Koszul complex on a minimal set of generators for the kernel of $\mathrm{\phi <\#comment/>}$. 

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4. On regularity of \overline∂-solutions on 𝑎_{𝑞} domains with 𝐶² boundary in complex manifolds

   https://doi.org/10.1090/tran/9315  

   Gong, Xianghong (March 2025, Transactions of the American Mathematical Society)

   We study regularity of solutions $u$to $\stackrel{¯<\#comment/>}{\mathrm{\partial <\#comment/>}}u=f$on a relatively compact $C^2$domain $D$in a complex manifold of dimension $n$, where $f$is a $(0,q)$form. Assume that there are either $(q+1)$negative or $(n-<\#comment/>q)$positive Levi eigenvalues at each point of boundary $\mathrm{\partial <\#comment/>}D$. Under the necessary condition that a locally $L^2$solution exists on the domain, we show the existence of the solutions on the closure of the domain that gain $1/2$derivative when $q=1$and $f$is in the Hölder–Zygmund space ${\mathrm{\Lambda <\#comment/>}}^r\left(D\right)$with $r>1$. For $q>1$, the same regularity for the solutions is achieved when $\mathrm{\partial <\#comment/>}D$is either sufficiently smooth or of $(n-<\#comment/>q)$positive Levi eigenvalues everywhere on $\mathrm{\partial <\#comment/>}D$. 

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5. Compatible ideals in ℚ-Gorenstein rings

   https://doi.org/10.1090/proc/16331  

   Polstra, Thomas; Schwede, Karl (October 2023, Proceedings of the American Mathematical Society)

   Suppose $R$is a $F$-finite and $F$-pure $\mathbb{Q}$-Gorenstein local ring of prime characteristic $p>0$. We show that an ideal $I\subseteq <\#comment/>R$is uniformly compatible ideal (with all $p^{-<\#comment/>e}$-linear maps) if and only if exists a module finite ring map $R\to <\#comment/>S$such that the ideal $I$is the sum of images of all $R$-linear maps $S\to <\#comment/>R$. In other words, the set of uniformly compatible ideals is exactly the set of trace ideals of finite ring maps. 

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