For a graph G, we call a set D⊆V(G) a total isolating set of G if G[D] has no isolated vertices and G−N[D] contains no edges, where G[D] is the induced subgraph of G on D and N[D] is the closed neighborhood of D. The total isolation number ιt(G) of G is the minimum cardinality of a total isolating set in G. Recently, Boyer, Goddard and Henning proved that if G is a connected graph with n ≥ 4 vertices and G¬≅C7, then ιt(G)≤n2 and the bound is tight. In this paper, we classify all extremal graphs which achieve the bound. We show that excluding an infinite family of graphs, there exist exactly thirteen sporadic extremal graphs. This solves an open problem proposed by Boyer, Goddard and Henning.
The ever-increasing consumption of fossil fuels has led to environmental crises, which accelerated the quest for sustainable hydrogen energy. Among various production routes, water electrolysis stands out as a promising approach. However, the efficiency of hydrogen evolution reaction is limited by the adhesion of gas bubbles on electrode surfaces, which blocks active sites, increases overpotential, and limits mass transfer. This review highlights the design of micro/nanostructured array electrodes to achieve underwater superaerophobicity, reducing bubble adhesion, facilitating the nucleation and rapid release of ultrasmall bubbles, thereby contributing to reduce in overpotential, faster bubble growth, enhanced mass transport, and improved catalyst stability. We summarize recent advances in fabrication strategies of such electrodes, focusing on micro/nanostructural designs, covering from 0 to 3-dimensional structures. Additionally, the role of hydrophilic gels in optimizing superaerophobicity is discussed. Finally, challenges and future directions are addressed, including bubble dynamics accurate modeling, development of high activity and stability catalysts, intelligent adaptive electrode structure and active bubble regulation, and the integration of artificial intelligence and deep learning for guided electrode design. This review aims to provide a comprehensive perspective on how superaerophobic electrode design address bottlenecks in gas-evolving electrodes, paving the way toward more efficient and economical hydrogen production.
EB irradiation is widely used for starch modification. Nevertheless, modification mechanism and level are blurry especially at a higher dose irradiation, restraining deep functional material design. In this work, pure corn starch was irradiated by an EB in air with dose up to 500 kGy. Then, microstructural and physicochemical property variations were explored via FT-IR, XPS, 13C-NMR, GPC, XRD, SEM, whiteness, TGA and viscosity analysis. Later, its post acceleration effect was explored via AA grafting. Main results reveal that irradiation induced severe starch backbone scission. Cleavage mainly occurred at α-1,4 glycosidic bond and the link of C-1 and C-2 atoms within starch glucose unit. Upon 500 kGy irradiation, number-average molecular mass-Mn-decreased from 2.56 × 105 to 1.33 × 103 Da, conversing macromolecule to small molecule debris. Certain hydroxyls were oxidized to carbonyls. Molecule chain stacking regularity was destroyed. Amorphization occurred shown a crystallinity reduction close to 34
Luminol and Cu2+ bifunctionalized magnetic core-shell Fe3O4@Au nanoparticles (BFCS-Fe3O4@Au NPs) with high chemiluminescence (CL) efficiency were synthesized via an improved approach for pyrophosphate ions (PPi) sensing in complicated samples. First, a uniform Au shell was formed in situ on the Fe3O4 core through the controlled deposition enabled by luminol’s reducing property. This process also resulted in the immobilization of luminol molecules on the Au shell via Au-N coordination, where they functioned as the CL signal units. Subsequently, Cysteine (Cys) was modified onto the Fe3O4@Au surface via Au-S bonds, which introduced specific coordination sites for metal ions. Then, Cu2+ were captured by these sites and fixed onto the Fe3O4@Au surface, which efficiently catalyze the luminol-H2O2 reaction, resulting in a strong “signal-on” state. Finally, the presence of PPi could quantitatively quench this signal by competing with Cys for Cu2+ binding, thereby switching the system “off”. Due to this “signal-on-off” mechanism, an ultrasensitive sensor for PPi was developed, exhibiting a broad linear detection range from 0.1 nM to 10 µM and a low detection limit of 8.37 pM. This sensing strategy provides a reliable and promising pathway for PPi monitoring in biological analysis and environmental water analysis.
This work presents a geometric feature-based structural topology optimization approach based on simple geometric parameters. Here, we hypothesize that the topological configuration is a combination of a set of basic geometries defined by the same Non-Uniform Rational B-spline (NURBS) parameters. Within the design domain, the geometric boundary is distributed by using mesh nodes and geometry boundary normal vectors. The function that identifies the geometry's boundaries is constructed by integrating the field values of all the boundaries within the geometry. This allows for the calculation of the proportion of the mesh that is occupied by the geometry using a step function. By utilizing the element proportion of the basic geometries, the relative density of the element and its corresponding stiffness matrix can be calculated, thereby establishing an optimization model. During the optimization process, the design variables are the geometric parameters of each geometry. The Method of Moving Asymptotes (MMA) is used to update these variables. Numerical examples are shown to validate the correctness and superiority of this proposed method.
