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1. Global Gradient Estimate for a Divergence Problem and Its Application to the Homogenization of a Magnetic Suspension

   Dang, T (April 2022, Association for Women in Mathematics series)

   Español, M (Ed.)

   "This paper generalizes the results obtained by the authors in Dang et al. (SIAM J. Appl. Math. 81(6):2547--2568, 2021) concerning the homogenization of a non-dilute suspension of magnetic particles in a viscous flow. More specifically, in this paper, a restrictive assumption on the coefficients of the coupled equation, made in Dang et al. (SIAM J. Appl. Math. 81(6):2547--2568, 2021), that significantly narrowed the applicability of the homogenization results obtained is relaxed and a new regularity of the solution of the fine-scale problem is proven. In particular, we obtain a global L∞-bound for the gradient of the solution of the scalar equation −divax∕$$\epsilon$$∇$$\phi$$\epsilon$$(x)=f(x){\$$}{\$$}- {\backslash}operatorname {\{}{\{}{\backslash}mathrm {\{}div{\}}{\}}{\}} {\backslash}left [ {\backslash}mathbf {\{}a{\}} {\backslash}left ( x/{\backslash}varepsilon {\backslash}right ){\backslash}nabla {\backslash}varphi ^{\{}{\backslash}varepsilon {\}}(x) {\backslash}right ] = f(x){\$$}{\$$}, uniform with respect to microstructure scale parameter $$\epsilon$${\thinspace}≪{\thinspace}1 in a small interval (0, $$\epsilon$$0), where the coefficient a is only piecewise H{\"o}lder continuous. Thenceforth, this regularity is used in the derivation of the effective response of the given suspension discussed in Dang et al. (SIAM J. Appl. Math. 81(6):2547--2568, 2021)." 

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2. Polarization and domains in wurtzite ferroelectrics: Fundamentals and applications

   https://doi.org/10.1063/5.0249265  

   Fichtner, Simon; Schönweger, Georg; Lee, Cheng-Wei; Yazawa, Keisuke; Gorai, Prashun; Brennecka, Geoff_L (April 2025, Applied Physics Reviews)

   The 2019 report of ferroelectricity in (Al,Sc)N [Fichtner et al., J. Appl. Phys. 125, 114103 (2019)] broke a long-standing tradition of considering AlN the textbook example of a polar but non-ferroelectric material. Combined with the recent emergence of ferroelectricity in HfO2-based fluorites [Böscke et al., Appl. Phys. Lett. 99, 102903 (2011)], these unexpected discoveries have reinvigorated studies of integrated ferroelectrics, with teams racing to understand the fundamentals and/or deploy these new materials—or, more correctly, attractive new capabilities of old materials—in commercial devices. The five years since the seminal report of ferroelectric (Al,Sc)N [Fichtner et al., J. Appl. Phys. 125, 114103 (2019)] have been particularly exciting, and several aspects of recent advances have already been covered in recent review articles [Jena et al., Jpn. J. Appl. Phys. 58, SC0801 (2019); Wang et al., Appl. Phys. Lett. 124, 150501 (2024); Kim et al., Nat. Nanotechnol. 18, 422–441 (2023); and F. Yang, Adv. Electron. Mater. 11, 2400279 (2024)]. We focus here on how the ferroelectric wurtzites have made the field rethink domain walls and the polarization reversal process—including the very character of spontaneous polarization itself—beyond the classic understanding that was based primarily around perovskite oxides and extended to other chemistries with various caveats. The tetrahedral and highly covalent bonding of AlN along with the correspondingly large bandgap lead to fundamental differences in doping/alloying, defect compensation, and charge distribution when compared to the classic ferroelectric systems; combined with the unipolar symmetry of the wurtzite structure, the result is a class of ferroelectrics that are both familiar and puzzling, with characteristics that seem to be perfectly enabling and simultaneously nonstarters for modern integrated devices. The goal of this review is to (relatively) quickly bring the reader up to speed on the current—at least as of early 2025—understanding of domains and defects in wurtzite ferroelectrics, covering the most relevant work on the fundamental science of these materials as well as some of the most exciting work in early demonstrations of device structures. 

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3. Non-Galvin filters

   https://doi.org/10.1142/S021906132450017X  

   Benhamou, Tom; Garti, Shimon; Gitik, Moti; Poveda, Alejandro (March 2024, Journal of Mathematical Logic)

   We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Theorem 2.3]. 

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4. A Stochastic Analysis of Queues with Customer Choice and Delayed Information

   https://doi.org/10.1287/moor.2019.1024  

   Pender, Jamol; Rand, Richard; Wesson, Elizabeth (August 2020, Mathematics of Operations Research)

   Many service systems provide queue length information to customers, thereby allowing customers to choose among many options of service. However, queue length information is often delayed, and it is often not provided in real time. Recent work by Dong et al. [Dong J, Yom-Tov E, Yom-Tov GB (2018) The impact of delay announcements on hospital network coordination and waiting times. Management Sci. 65(5):1969–1994.] explores the impact of these delays in an empirical study in U.S. hospitals. Work by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] uses a two-dimensional fluid model to study the impact of delayed information and determine the exact threshold under which delayed information can cause oscillations in the dynamics of the queue length. In this work, we confirm that the fluid model analyzed by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] can be rigorously obtained as a functional law of large numbers limit of a stochastic queueing process, and we generalize their threshold analysis to arbitrary dimensions. Moreover, we prove a functional central limit theorem for the queue length process and show that the scaled queue length converges to a stochastic delay differential equation. Thus, our analysis sheds new insight on how delayed information can produce unexpected system dynamics. 

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5. A generalized Walsh system for arbitrary matrices

   https://doi.org/10.1515/dema-2019-0006  

   Harding, Steven N.; Picioroaga, Gabriel (January 2019, Demonstratio Mathematica)

   Abstract In this paper we study in detail a variation of the orthonormal bases (ONB) of L2[0, 1] introduced in [Dutkay D. E., Picioroaga G., Song M. S., Orthonormal bases generated by Cuntz algebras, J. Math. Anal. Appl., 2014, 409(2), 1128-1139] by means of representations of the Cuntz algebra ON on L2[0, 1]. For N = 2 one obtains the classic Walsh system which serves as a discrete analog of the Fourier system. We prove that the generalized Walsh system does not always display periodicity, or invertibility, with respect to function multiplication. After characterizing these two properties we also show that the transform implementing the generalized Walsh system is continuous with respect to filter variation. We consider such transforms in the case when the orthogonality conditions in Cuntz relations are removed. We show that these transforms which still recover information (due to remaining parts of the Cuntz relations) are suitable to use for signal compression, similar to the discrete wavelet transform. 

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