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134 results on '"Wang, Zhenlu"'

1. Some evaluations of interpolated multiple zeta values and interpolated multiple $t$-values

Author

Li, Zhonghua and Wang, Zhenlu

Subjects
Mathematics - Number Theory
Abstract

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in the harmonic algebra.

Published
2024

2. Relations of multiple $t$-values of general level

Author

Li, Zhonghua and Wang, Zhenlu

Subjects
Mathematics - Number Theory
Abstract

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 $_3F_2$, 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., Comment: 24 pages

Published
2022

3. Integrality and some evaluations of odd multiple harmonic sums

Author

Li, Zhonghua and Wang, Zhenlu

Subjects
Mathematics - Number Theory, Mathematics - Classical Analysis and ODEs
Abstract

In 2015, S. Hong and C. Wang proved that none of the elementary symmetric functions of $1,1/3,\ldots,1/(2n-1)$ is an integer when $n\geq 2$. In 2017, Kh. Pilehrood, T. Pilehrood and R. Tauraso proved that the multiple harmonic sums $H_n(s_1,\ldots,s_r)$ are never integers with exceptions of $H_1(s_1)=1$ and $H_3(1,1)=1$. They also proved that the multiple harmonic star sums are never integers when $n\geq 2$. In this paper, we consider the odd multiple harmonic sums and the odd multiple harmonic star sums and show that none of these sums is an integer with exception of the trivial case. Besides, we give evaluations of the odd (alternating) multiple harmonic sums with depth one., Comment: 13 pages

Published
2022

6. A note on the sum of finite multiple harmonic $q$-series on $r\text{-}(r+1)$ indices

Author

Li, Zhonghua and Wang, Zhenlu

Subjects
Mathematics - Number Theory, 11M32, 05A15, 30B10
Abstract

We study the sum of the finite multiple harmonic $q$-series on $r\text{-}(r+1)$ indices at roots of unity with $r=1,2,3$. And we give the equivalent conditions of two conjectures regarding cyclic sums of finite multiple harmonic $q$-series on $1\text{-}2\text{-}3$ indices at roots of unity, posed recently by Kh. Pilehrood, T. Pilehrood and R. Tauraso., Comment: 15 pages

Published
2021

10. Weighted sum formula of multiple $L$-values and its applications

Author

Li, Zhonghua and Wang, Zhenlu

Subjects
Mathematics - Number Theory, 11M32, 11M06, 11M99
Abstract

In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle relations of multiple $L$-values, we give a sum formula and a weighted sum formula of multiple $L$-values. As applications, we give sum formulas and weighted sum formulas of double zeta values of level $2$ and $3$., Comment: 18 pages

Published
2021

15. Photogrammetric Investigation of Storm-Induced Erosion Process on Sandy Beach Profile in Medium-Scale Flume.

Author

Wang, Jun, Yang, Bo, Liang, Bingchen, You, Zai-Jin, Wang, Zhenlu, and Wang, Zhaowei

Subjects
SHORELINES, BEACHES, SEDIMENT transport, BEACH erosion, EROSION, OCEAN wave power, WATER waves, FLUMES, FREE surfaces
Abstract

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]

Published
2024
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23. Experimental Study on Aspect Ratio and Velocity Intensity of Scour Around Submerged Pile Groups

Author

Lu, Youxiang, Wang, Zhenlu, Yin, Zegao, Du, Shengtao, Pan, Xinying, and Liang, Bingchen

Subjects
Global and Planetary Change, Ocean Engineering, Aquatic Science, Oceanography, Water Science and Technology
Abstract

Submerged pile groups are important components of complex piers in hydraulic engineering and are analogs for a range of subsea structures. These may sustain severe damages from local scour. The velocity intensity (U / Uc, the ratio of critical velocity to mean velocity) and aspect ratio (H / Dp, the ratio of pile height to pile diameter) are critical variables in this scour process. However, previous studies on scour around submerged pile groups were conducted in clear-water conditions (U / Uc < 1). In addition, many research studies are being conducted in shallow water flow conditions, which cannot eliminate the effect of the water depth on the scour process. Thus, these research studies cannot directly be applied to live-bed scour around submerged structures. To expand the velocity intensity and aspect ratio of scour around submerged pile groups, flume experiments were conducted with uniform quartz sand in both clear-water and live-bed conditions. Pile groups with different heights are adopted as experimental models. An improved time factor for both clear-water and live-bed scour around submerged structures is determined with the present experiments to extrapolate the scour depth of the present work to the equilibrium scour depth. This new time factor is then tested with experimental data from the literature. The tests demonstrate that this new time factor can reliably predict the scour process and equilibrium scour depth for submerged structures. Empirical relationships to demonstrate the effects of the studied variables including the equilibrium scour depth, scour area, and scour volume are presented. Different methods to predict the effects of the velocity intensity and aspect ratio on the scour depth are compared based on the present work. Furthermore, a correction coefficient is proposed to illustrate the effect of aspect ratio on scour depth. Then, equations of scour area and volume are derived according to the present experiments.

Published
2022

32. Optimizing the Microstructure, Mechanical, and Tribological Properties of Si-DLC Coatings on NBR Rubber for Its Potential Applications

Author

Liu Guangqiao, Bin Zhang, Kui Chen, Li Qiang, Wang Zhenlu, Dong Limei, and Zedong Wen

Subjects
tribological behaviors, Toughness, Materials science, Si/Si-DLC film, Doping, Surfaces and Interfaces, Tribology, mechanical properties, Microstructure, Surfaces, Coatings and Films, Volumetric flow rate, Brittleness, Natural rubber, deposition parameters, lcsh:TA1-2040, NBR rubber, visual_art, Materials Chemistry, visual_art.visual_art_medium, Growth rate, Composite material, lcsh:Engineering (General). Civil engineering (General)
Abstract

Si doped diamond-like carbon (Si-DLC) films were deposited on nitrile-butadiene rubber (NBR), and the effects of deposition parameters on the mechanical and tribological properties of an Si-DLC top layer on NBR were investigated. Then, the sample with the best performance is selected to investigate its tribological behaviors and mechanism under different contact loads. The results show that the growth rate and the doped Si content are also decreased with increasing the CH4 flow rate. The Si atom exists in the form of Si-C bonds at low CH4 flow rate (&le, 40 sccm) and Si-C + Si-O-C bonds at high CH4 flow rate (&ge, 60 sccm). Furthermore, the sp3 content increases monotonously, while the hardness and H3/E2 ratio firstly decreases and then increases. As a result, the friction and wear behaviors are in line with the change trend of the hardness. The lowest friction coefficient (~0.19) and a slight wear were achieved for the Si-DLC3 film under the relatively high load of 3 N. The tribological results indicate that the friction coefficient and wear increase monotonously with the increase of load, which is mainly attributed to the brittle fragmentation of films at a higher load, and thus a high strength and super toughness DLC films should be needed. Furthermore, the friction and wear behaviors of samples depend critically on its surface topography, and the wear is lower when the friction direction is parallel to the stripes.

Published
2020
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34. Taurine can play a positive role in growth, liver health and resistance to Aeromonas hydrophilaof yellow catfish Pelteobagrus fulvidracoexposed to ammonia stress for a long time

Author

Zhang, Muzi, Qin, Chuanjie, Sun, Zhuo, Jiang, Haibo, Wang, Zhenlu, Lin, Yanhong, and Li, Ming

Abstract

Ammonia is an important environmental pollutant that is toxic to most aquatic animals, and nutrient manipulation is an effective regulatory pathway. To assess the influence of taurine supplementation on growth, liver detoxification and anti-bacterial infection of yellow catfish subjected to ammonia exposure for a long time, three experiment diets with different taurine levels (0.50, 1.00, and 2.00 %) were formulated and fed to fish (7.28 ± 0.05) g under three ammonia levels (0.00, 25.00 and 50.00 mg/L total ammonia nitrogen) for 56 days. The results showed that hepatic glycogen and whole-body protein contents were reduced, suggesting that energy deficiency caused by ammonia poisoning plays an important role in growth inhibition; elevated serum alanine aminotransferase and aspartate aminotransferase levels suggest liver injury, which may be caused by oxidative stress (decreased activities of superoxide dismutase and catalase, and expressions of SODand CAT) and inflammation (increased contents of tumor necrosis factor α, interleukin 1 and interleukin 8, and expressions of TNF α, IL 1and IL8), analysis of tissue sections further confirmed this finding. Furthermore, after injection with Aeromonas hydrophila, cumulative mortality increased proportionally with the rise in ammonia levels, the observed decrease in serum complements C3, C4, immunoglobulin M, and antibody titer contents emerged as a crucial factor contributing to the decreased disease resistance. The exogenous taurine was found to alleviate the negative impact of the above-mentioned ammonia poisoning. This study provides valuable insights into the mechanism of ammonia-induced aquatic toxicology in fish.

Published
2024
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