This paper investigates the regularity and fractal dimensions of the Katugampola fractional integral of the generalized Takagi function Ta,b(x) =infinity & sum;infinity(n=0)a-ndist(bnx,& Zopf;) with parameters satisfying b > a > 1. While fractional integral is known to smooth fractal functions, the precise effect of the Katugampola operator on the generalized Takagi function has remained unexplored. This operator unifies the Riemann-Liouville fractional integral and the Hadamard fractional integral. We aim to characterize how the fractional order alpha > 0 and the auxiliary parameter rho > 0 affect the H & ouml;lder regularity and the fractal dimensions of . Using analytical estimates, the -dimension technique, and H & ouml;lder mapping theory, we obtain sharp uniform H & ouml;lder exponents for all parameter regimes, including critical cases where logarithmic corrections appear. For the Riemann-Liouville case , it has been shown that dim(B)graph(F) = max{1,2 - log(b)a-alpha}, which confirms a linear decay with alpha. For general rho > 0, we provide rigorous upper and lower bounds alongside a conjecture. Numerical experiments also validate these theoretical results. Our findings quantify how the parameter rho interpolates continuously between strong smoothing in the Riemann-Liouville sense and weak smoothing in the Hadamard sense, thereby offering a tunable framework for signal processing and image analysis.
Enhancing lattice oxygen mobility and lowering oxygen vacancy formation energy are among the critical strategies to improve the catalytic oxidation activity of transition metal oxides toward volatile organic compounds (VOCs). Herein, an anion engineering strategy was adopted, where selenium (Se)—an element homologous to oxygen—was used to partially substitute lattice oxygen. This isoelectronic substitution expanded cation transport pathways and induced abundant surface defect sites. The as-constructed Se0.1-CuFe2Ox/SSZ-13 catalyst exhibited superior catalytic performance for NVOC oxidation, achieving 90 % n-butylamine conversion and nearly 100 % N2 selectivity at a low temperature of only 176 °C. Mechanistic investigations revealed that Se primarily existed in the form of Se2- in Se0.1-CuFe2Ox/SSZ-13. Benefiting from the larger ionic radius of Se2- compared with O2–, the interplanar spacing increased from 0.48 nm of pristine CuFe2O4 to 0.50 nm, thus providing more efficient channels for sub-surface lattice oxygen transport. Meanwhile, significant distortion of the (111) crystal plane was triggered, which facilitated the formation of additional oxygen vacancies. This process not only stabilized the catalyst by reducing its total energy but also alleviated the internal stress caused by lattice distortion. Furthermore, the semi-metallic property of Se contributes to a weaker electron-binding ability than oxygen, which not only modulated the chemical states of Fe/Cu active sites but also facilitated electron transfer during redox reactions. This strategy of substituting lattice oxygen in spinel with homologous Se enables simultaneous modulation of the electronic environment of active sites and activation of oxygen species, thereby significantly improving NVOC purification efficiency. It provides novel insights for designing high-performance catalysts toward efficient NVOC oxidation.
To achieve higher muzzle velocity of gun ammunition while minimizing barrel erosion, gun propellants must deliver greater impetus while maintaining lower combustion temperatures. In this study, ZIF-67 was synthesized via hydrothermal methods. The structural and textural properties of ZIF-67 were characterized using scanning electron microscopy (SEM), N2 adsorption/desorption isotherms, X-ray diffraction (XRD), and Fourier-transform infrared spectroscopy (FTIR). Additionally, 3 wt% ZIF-67 was introduced into the NC-TEGDN-RDX triple-base propellant formulation. Closed-vessel experiments were conducted to determine the impetus and covolume, while the thermal decomposition behavior was investigated via thermogravimetry/differential scanning calorimetry coupled with quadrupole mass spectrometry and Fourier-transform infrared spectroscopy (TG/DSCQMS-FTIR). The results demonstrate that the incorporation of ZIF-67 enhanced the impetus of NC-TEGDN-RDX propellants by 45% and increased the covolume by 41.9%, with negligible changes in the system temperature. This effect is attributed to the catalytic activity of ZIF-67, which promotes the decomposition of the propellant matrix to generate more low-molecular-weight gaseous products (e.g., H2), leading to a 38.6% increase in total gas production. Overall, ZIF-67 provides a novel strategy for optimizing energy release in gun propellants, enabling higher launch velocities for tank gun ammunition and mitigating barrel erosion.
Landslide-induced tsunamis produce localized but highly destructive impulse waves that threaten nearby infrastructure, and the two-phase double-point material point method (MPM) has been adopted to analyze the solid–fluid interaction during slide mass penetrating into water. However, the frictional contact between wave flow and slope surface was usually simplified which led to inappropriate prediction and assessment for the generation and propagation of surge wave. In this study, signed distance functions (SDF) is introduced to define interfaces among bedrock, slide mass, and water. By assigning distinct frictional coefficients to fluid-slope and solid-slope interfaces, this method enables simultaneous simulation of landslide failure mechanisms and wave run-up dynamics. After validations against two experimental cases, the method is applied to the 1958 Lituya Bay mega-tsunami. The simulated results reproduced the extreme run-up height (simulated 526 m versus observed 524 m) caused by a massive rock volume impacting Lituya Bay at a velocity greater than 100 m/s. The simulation captures not only the transition from initial rockfall to granular landslide due to progressive fragmentation but also the two-way fluid–solid interaction during both landslide penetration and wave backflow. Furthermore, sensitivity analysis of the fluid-slope frictional coefficient reveals the importance of slope surface roughness in assessing landslide-tsunami hazards. In conclusion, this study demonstrates that the SDF-enriched two-phase double-point MPM framework offers a robust and effective tool for assessing landslide-tsunami hazards in fjords, lakes, and reservoirs.
For positive integers k and ℓ, the digraph C(k,ℓ) comprises two internally vertex-disjoint directed paths of respective lengths k and ℓ that share a common start and end vertex. It was established by Picasarri-Arrieta and Rambaud (European J. Combin., 2024) that any digraph with minimum out-degree at least two and girth no smaller than 8k−6 necessarily contains a C(k,k)-subdivision, and they further exhibited digraphs of minimum out-degree two and girth k−1 containing no such subdivision, thereby raising the question of the optimal girth threshold. We advance their result in two directions: first, we halve the sufficient girth requirement from 8k−6 to 4k+2; second, we construct a digraph family with minimum out-degree two and girth k that avoids C(k,k) subdivisions altogether. Consequently, the sought-after threshold is confined to the interval [k+1,4k+2].
