The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam.  The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.

Functions are the core of algebra, and the teaching of function concepts is also the main task of high school mathematics Students' learning of functions and their concepts shifts from understanding specific quantitative relationships to understanding abstract quantitative relationships The monotonicity of functions, as the property of the first function that students learn in high school, lays a certain foundation for learning function related knowledge in the future.

This study explores the intricate relationship between family functioning, emotional bonding, parent-child contact, and academic success among students through a serial mediation analysis. The research, conducted on a sample of 200 participants, sheds light on the indirect pathways through which family dynamics influence academic achievements, emphasizing the significance of emotional connections and parent-child interactions. The findings affirm the positive association between family functioning and academic achievement, in alignment with prior research. Additionally, the study identifies parent-child bonds and contact as partial mediators in this relationship, reinforcing previous findings. A noteworthy discovery is the full complementary sequential mediation effect, revealing that family functioning’s influence on academic success becomes substantial when emotional bonds foster increased parent-child contact. In conclusion, this research underscores the importance of emotional bonds and parent-child contact as sequential mediators, emphasizing their role in translating family dynamics into academic achievements among students. While providing valuable insights, the study acknowledges limitations such as sample size, potential sampling bias, self-reported measures, and a cross-sectional design. Addressing these limitations and expanding the scope of outcomes in future research will contribute to a more comprehensive understanding of the complex dynamics within family and educational institutions relationships and their profound impacts on students’ academic success.

The ways of developing functional textiles based on nanomaterials were introduced, and the latest research achievements of nanomaterials in such aspects as flame retardancy, antibacterial, super-hydrophobic, self-cleaning, UV resistance, and anti-static textiles were reviewed. The main technical obstacles to the large-scale application of nanomaterials in functional textiles were pointed out, the possible solutions were discussed, and the development of functional textiles by nanomaterials has been prospected.

Based on the characteristics of liquid lens sparse aperture imaging, a radiative multiplet array structure is proposed; a simplified model of sparse aperture imaging is given, and the analytical expression of the modulation transfer function is derived from the optical pupil function of the multiplet array structure; the specific distribution form of this multiplet array structure is given, and the structure parameters are approximated by the dimensionless method; the two types of radiative multiplet array structures are discussed, and the filling factor, redundancy, modulation transfer function and other characteristic parameters are calculated. The physical phenomena exhibited by the parametric scan are discussed, and the structural features and imaging characteristics of these two arrays are compared. The results show that the type-II structure with larger actual equivalent aperture and actual cutoff frequency and lower redundancy is selected when the average modulation transfer function and the IF characteristics of the modulation transfer function of the two structures are close to each other; the type-II structure has certain advantages in imaging; the conclusion is suitable for arbitrary enclosing circle size because the liquid lens-based multiplet array structure adopts dimensionless approximation parameters; compared with the composite toroidal structure, the radiative multiplet mirror structure has a larger actual cut-off frequency and actual equivalent aperture when the filling factor is the same.