The uniform Turán density πu(F) of a (3-uniform) hypergraph F is the supremum of d for which there are infinitely many F-free hypergraphs with the property that every induced subhypergraph of H on a linearly sized vertex set has edge density at least d. Determining πu(F) for given hypergraphs F was suggested by Erdős and Sós in the 1980s. However, there are very few hypergraphs whose uniform Turán density has been determined. In this paper, we are the first to establish a verifiable condition for hypergraphs F with πu(F)=1/4. In particular, currently known hypergraphs whose uniform Turán density is 1/4, such as K4(3)- studied in Glebov et al. (Israel J Math 211:349–366, 2016) and Reiher et al. (J Eur Math Soc 20:1139–1159, 2018), and F5⋆ studied in Chen and Schülke (Beyond the broken tetrahedron, 2022, arXiv:2211.12747), satisfy this condition. Moreover, we also identify some new hypergraphs whose uniform Turán density is also 1/4.

The significant in situ multicolored patterning without changing printing tools nor substrate media still remains challenging, especially toward practical applications for anti-counterfeiting. This research invented a unique universal approach for the laser-induced in situ synthesis of colorful fluorescent patterns (from blue: CIE 0.15, 0.18 to red orange: CIE 0.36, 0.39) through the controlled formation of N, S doped carbon dots (CDs) in solid composite polymer films or hydrogel with a hierarchical and physically unclonable microsurface architecture for anti-counterfeiting. The in situ patterning approach, coupled with multi-layer technique, yielding designable blue, yellow, orange, and red orange color under 365 nm in the same pattern. A 5 cm² colorful pattern can be efficiently finished within 5 min without changing the substrate and the line width accuracy can be up to 300 μm. The absolute quantum efficiency of the blue pattern reached as high as 23%. The fluorescent patterns can be survived at indoor for 24 months. The hydrogen bonding interactions between the CDs precursor and polymer facilitated the generation, uniform dispersion and stabilization of CDs during the laser irradiation. The hypothesis that laser irradiation induced photochemical reactions of CD precursors within a polymer matrix was supported by thermodynamic assessments. The universality of in situ fluorescent patterning strategy was demonstrated by developing fluorescent patterns on both solid polymer films, hydrogel, pharmaceutical packaging and textile.

Systematic experimental investigations concerning the influence of α morphology on the fretting wear behaviors of metastable β titanium alloys are carried out. A Ti-10V-2Fe-3Al titanium alloy was subjected to different heat treatment routes to create dual phase microstructures consisted of β phase plus α phase with three different morphologies. The effect of α morphology on the fretting wear resistance, the resulting failure mechanisms, and stress induced martensite transformation (SIMT) were unraveled. Results show that the α morphology has a significant influence on fretting wear behaviors depending on the fretting run regimes. In the partial slip regime (PSR) and mixed fretting regime (MFR), the microstructure with lath α morphology has a lowest fretting wear volume accompanied by relatively strong SIMT effect. While in gloss slip regime (GSR), the globular α microstructure has a lowest fretting wear volume along with strongest SIMT response, yet a highest fretting wear volume for the acicular α morphology microstructure due to its brittleness nature. The subsurface observations demonstrates that a compacted and thick plastic deformation layer, especially for the mechanical mixture layer, can well protect the material surface against the fretting wear damage.