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We study the relations of multiple t -values of general level. The generating function of sums of multiple t -(star) values of level N with fixed weight, depth and height is represented by the generalized hypergeometric function 3 F 2 , which generalizes the results for multiple zeta(-star) values and multiple t -(star) values. As applications, we obtain formulas for the generating functions of sums of multiple t -(star) values of level N with height one and maximal height and a weighted sum formula for sums of multiple t -(star) values of level N with fixed weight and depth. Using the stuffle algebra, we also get the symmetric sum formulas and Hoffman's restricted sum formulas for multiple t -(star) values of level N. Some evaluations of multiple t -star values of level 2 with one–two–three indices are given. [ABSTRACT FROM AUTHOR]

Foundation scour is the erosion of sediments around pile foundations by wave and current in offshore wind energy. This phenomenon destabilizes foundations and poses a threat to pile safety. Therefore, scour protection becomes a crucial challenge in offshore wind projects. This paper reviews and synthesizes recent publications and patented technologies related to scour protection. Considering the primary engineering concerns, the paper proposes design principles for effective scour protection schemes to standardize evaluation criteria. These principles prioritize efficacy, independence, and cost-efficiency, enabling the analysis of scour protection scheme applicability. In addition, this paper summarizes and describes common protection schemes in the literature. The effectiveness of their protection is analyzed and summarized, and their economic and performance independence is evaluated. This paper categorizes flow-altering scour protection schemes found in the literature. Based on a comprehensive understanding of the mechanisms and engineering requirements of scour protection, the paper proposes a focus on determining the erosion reduction rate curve ( E p − U / U c curve) as a key criterion for evaluating the effectiveness of protection schemes under varying flow velocities and the erosion reduction rate of scour protection schemes under extreme conditions. The study highlights the necessity of establishing a comprehensive design evaluation methodology, which is crucial for addressing the significant challenges related to scour encountered in offshore wind power projects. [ABSTRACT FROM AUTHOR]

Covalent organic frameworks (COFs) are crystalline organic porous polymers that can be precisely integrated by building blocks to achieve pre‐designed composition, components, and functions, making them a powerful platform for the development of molecular devices in the field of electrocatalysis. The precise control of channel/dopant positions and highly ordered network structures of COFs provide an ideal material system for the applications of advanced electrocatalysis. In this paper, the topological structure design and synthesis methods of COFs are reviewed in detail, and their design principles are deeply analyzed. In addition, the applications of COFs and their derivatives in the field of electrocatalysis are systematically summarized and the optimization strategies are proposed. Finally, the application prospects of COFs and their derivatives in electrocatalysis and the challenges that may be encountered in the future are prospected, providing helpful guidance for future research. [ABSTRACT FROM AUTHOR]

Covalent organic frameworks (COFs) are porous organic materials with well‐defined and uniform structure. The material is an excellent candidate as a solid adsorbent for iodine adsorption. In the present study, we report the synthesis of COF with porphyrin moiety, TF‐TA‐COF, by solvothermal reaction, which was characterized by XRD, solid‐state 13C NMR, IR, TGA, and nitrogen adsorption‐desorption analysis. TF‐TA‐COF showed a high specific surface area of 443 m2 g−1, and exhibited good adsorption performance for iodine vapor, with an adsorption capacity of 2.74 g g−1. XPS and Raman spectrum indicated that a hybrid of physisorption and chemisorption took place between host COF and iodine molecules. The electric properties of iodine‐loaded TF‐TA‐COF were also studied. After doped with iodine, the conductivity of the material increased by more than 5 orders of magnitude. The photoconductivity of I2‐doped COF was also studied and TF‐TA‐COF showed doping‐enhanced photocurrent generation. [ABSTRACT FROM AUTHOR]

In this study, laboratory experiments were conducted to investigate the influence of changes in storm wave height and water level on beach response in a medium-scale wave flume. A schematic storm was simulated (rising, apex, and waning phases). A non-intrusive photogrammetric method was used to collect high-resolution and synchronous data regarding the free surface water elevation and bed level, from which shoreline location, sandbar position, cross-shore sediment transport rates, and nonlinear wave parameters were derived. The cross-shore sediment transport was in agreement with previous laboratory measurements, including the monotonous exchange from foreshore erosion to shoaling zone accretion in most stages of the storm simulation. The surf zone was the main region supplying sediment for beach morphology modification and sandbar generation. The degree of storm erosion was not completely determined by the largest wave height and water level or the cumulative wave power of the apex phase. The largest gradients of the wave parameter sequence change occurred in the rising phase, and this was the main factor generating efficient beachface erosion. It induced an increase in sandbar size, accompanied by the cross-shore motion of maximum velocity amplitude, more violent disturbances of wave nonlinearity, and increased surf zone erosion, with these factors increasing beach instability and leading to more severe storm erosion. The large wave height and water level resulted in shoreline retreat, with a more significant swash zone erosion under a higher runup. The offshore sediment transport turned toward the onshore direction as the original large sandbar deteriorated under the decreasing wave parameter sequence in the waning phase. [ABSTRACT FROM AUTHOR]

Estuarine sediment transport is driven by the combined action of a multitude of influencing factors, including astronomical tides, waves dynamics, and river discharges. This study focuses on the effects of wave forces on sediment transport patterns in micro-tidal estuaries near Wanbao Beach, China. Numerical simulations are carried out using Delft3D. Modeling scenarios are configured using different wave characteristics, spanning from typical waves to those with a return period of 50 years. Results show that waves have a positive effect on landward sediment transport, resulting a larger active range of sediment. By comparing the spatial geomorphic variations under varying wave conditions, we find that modifications in significant wave height (Hs) primarily impact the position of erosion and deposition zones, whereas alterations in spectral peak period (Tp) predominantly influence the magnitude of these changes. The finding is further demonstrated by a comparison of residual currents under different wave intensities. Analysis of sediment transport rates in different transects indicates that the sediment transport rate is highest at the mouth transects and lowest at the alongshore transects. Moreover, variations in sediment transport rates exhibit distinctive patterns between the two outlet transects, even when subjected to identical wave conditions. The disparities are attributed to differences in runoff and the topographical features in proximity to the estuaries. Additionally, we find the sediment transport rate becomes insensitive to the variations in Hs when Hs is larger than a threshold value. The threshold decreases with increasing Tp. [ABSTRACT FROM AUTHOR]

This study aims to obtain safe working condition of the electrothermal U-shaped actuator (EUA). The finite difference method is applied for modeling and solving the steady electric-thermal state and maximum temperature of the microactuator. The critical voltages causing beam buckling and overheating phenomena are determined to avoid the axial instability as well as melting deformation of the actuator. The relationships between temperature and the frequency or amplitude of the AC are analyzed. The results showed that the structure and the applied voltage levels have significant influence on the temperature distributions and the value of the stress. It is confirmed that the temperature between 300 to 600 °C is comparatively suitable for microactuator according to theoretical and experimental analysis, and the microactuator is able to provide accurate and stable number of cycles for tens of millions. [ABSTRACT FROM AUTHOR]

We study the sum of the finite multiple harmonic q-series on r-(r + 1) indices at roots of unity with r = 1, 2, 3. Mainly, we give equivalent conditions of two conjectures regarding cyclic sums of finite multiple harmonic q-series on 1-2-3 indices at roots of unity, posed recently by Kh. Pilehrood, T. Pilehrood and R. Tauraso. [ABSTRACT FROM AUTHOR]

Copper is the only metal that can convert CO2 into C2 and C2+ in electrocatalytic carbon dioxide reduction (CO2RR). However, the Faraday efficiency of CO2 conversion to C2 and C2+ products at high current densities is still low, which cannot meet the actual industrial demand. Here, the design methods of single‐atom copper catalysts (including regulating the coordination environment of single‐atom copper, modifying the carbon base surface and constructing diatomic Cu catalysts) are reviewed, and the current limitations and future research directions of copper‐based single‐atom catalysts are proposed, providing directions for the industrial conversion of CO2 into C2 and C2+ products. [ABSTRACT FROM AUTHOR]