We derive an effective transmission condition for acoustic subwavelength resonators, modeled as small-scaled bubbles distributed not necessarily periodically along a smooth, bounded hypersurface, which need not be flat. The transmission condition relates the jump in the normal derivative of the acoustic field to its second time derivative, convoluted in time with a sinusoidal kernel. This kernel has a period determined by the common subwavelength resonance (specifically, the Minnaert resonance in this case). This dispersive transmission condition can also be interpreted as a Dirac-like surface potential that is convoluted in the time domain and spatially supported on the specified hypersurface, unveils distinct regimes of acoustic behavior: 1. Low resonance: The surface becomes fully transparent, allowing complete acoustic transmission; 2. Moderate resonance: The surface exhibits memory effects, acting as a dispersive acoustic screen; 3. High resonance: The surface functions as a partially reflective or transmissive state with negligible memory effect. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Let q be a prime power and r a positive even integer. Let Fq be the finite field with q elements and Fqr be its extension field of degree r. Let chi be a nontrivial multiplicative character of Fqr and f(X) a polynomial over Fqr with exactly one simple root in Fqr. In this paper, we improve estimates for character sums Sigma g is an element of G of sparse elements, with respect to some fixed basis of Fqr which contains a basis of Fqr/2, or a subset avoiding affine hyperplanes in general position. While such sums have been previously studied, our approach yields sharper bounds by reducing them to sums over the subfield Fqr /2 rather than sums over general linear spaces. These estimates can be used to prove the existence of primitive elements in G in the standard way. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Improving the efficiency of electrical machines requires a fundamental understanding of the mechanisms that govern magnetic and eddy-current losses in magnetic core materials, which are inherently controlled by the microstructural features. With FeSi alloys serving as a representative model system, this work assesses both hysteresis and eddy-current losses in additively manufactured electrical steel using a multiphysical framework that combines the demagnetization simulation based on the Landau-Lifshitz theory and the computational homogenization based on the magneto-quasi-static (MQS) Maxwell's equations. The microstructures were digitized and generated from experimental characterization of the additively manufactured FeSi electric steel with different Silicon and Boron contents. By conducting parameter studies on a series of digital microstructures, the effects of average grain size and grain boundary (GB) phase thickness on hysteresis and eddy-current losses were revealed. An average grain size around 120 mu m has the lowest hysteresis loss, although the eddy-current loss increases with the grain size. Increasing GB-phase thickness helps reduce both losses. Results indicate the potential to reduce energy losses in magnetic core materials through microstructural optimization.