[001]-textured 0.4P(Mg1/3Nb2/3)O3-0.25PbZrO3-0.35PbTiO3-0.5%MnO2 (Mn-PMN-PZT) ceramics were fabricated by templated grain growth using 2 vol. % BaTiO3 in this paper. Full matrices of dielectric (ɛij), elastic (sij, cij), and piezoelectric (dij) parameters were obtained by the resonance–antiresonance method. The dielectric constant ɛ33T of textured ceramics reaches 2600, which is four times that of random ceramics. Textured Mn-PMN-PZT ceramics exhibit high d33 = 984 pC/N and high k33 = 0.89, which is much larger than d33 = 223 pC/N and k33 = 0.70 of random ceramics. However, ɛ11T of ceramics decreases by about 30% after texturing, and the corresponding shear coupling coefficient k15 also decreases from 0.66 to 0.44, which may be due to the reduction in the angle between spontaneous polarization and transverse direction. Furthermore, the temperature stability of the textured ceramics was evaluated as well. The phase transition temperature TR−T was determined by the impedance method to be 120 °C. The textured Mn-PMN-PZT ceramic shows high temperature stability, which is better than PMN-PT.

In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning. For the first three topics, we primarily review research in the past five years, updating and expanding on the previous survey by Shiebler et al. The fourth topic, which delves into higher category theory, particularly topos theory, is surveyed for the first time in this paper. In certain machine learning methods, the compositionality of functors plays a vital role, prompting the development of specific categorical frameworks. However, when considering how the global properties of a network reflect in local structures and how geometric properties and semantics are expressed with logic, the topos structure becomes particularly significant and profound.

In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring Q, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincare series of Q.

The rapid development of new energy electric vehicles (NEEVs) has garnered significant attention globally. This paper aims to analyze and understand the factors influencing the development of NEEVs and their potential impact on both the domestic and global automotive industries. Initially, this paper identifies key factors that significantly impact the industry's development and establish a multiple linear regression model to analyze these factors. Subsequently, this paper applies exponential smoothing and grey correlation analysis to conduct a comprehensive forecast of trends from multiple perspectives. Our analysis predicts that NEEVs will experience a steady rise over the next decade, especially in market share, making them increasingly competitive against traditional vehicles. Furthermore, NEEVs are poised to significantly disrupt the traditional energy vehicle industry through technological innovation and market demand.