Journal of Jishou University(Natural Sciences Edition)

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25 May 2022, Volume 43 Issue 3

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Mathematics

Existence and Uniqueness of Solutions for a Class of Fractional Differential Equations with Boundary Value Problems

LI Yiyun, XIE Jingli

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 1-6.

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With Banach contraction mapping principle and Krasnoselskii's fixed point theorem,we obtain the existence and uniqueness of solutions for nonlocal boundary value problems of nonlinear fractional differential equations with Caputo and Hilfer-Hadamard fractional derivative.

Lattice Boltzmann Model for Solving Nonlinear Coupled Long and Short Wave Equations

SONG Tongzheng, DAI Houping, FENG Shuting, WEI Xuedan

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 7-14.

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With Taylor expansion and Chapman-Enskog multi-scale expansion techniques,the equilibrium distribution functions and the correction functions are derived,and the two functions are introduced into the D1Q3 lattice Boltzmann model with two distribution functions.With this model,the initial-boundary value problem for a class of nonlinear coupled long-short wave equations is solved.For the plane wave and solitary wave solutions,the numerical simulation results verify the validity of the model for solving the nonlinear coupled initial-boundary value problems of the long-short wave equation.

Global Polynomial Stabilization of Proportional Delayed Neural Networks

WANG Yu, ZHANG Shiru, ZHANG Yuji, ZHOU Liqun

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 15-25.

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For a class of proportional delayed neural networks,a state feedback controller is used.With the condition that the activation function is bounded and satisfies the Lipschitz condition,we analyze the global polynomial stabilization (GPS) and global asymptotic stabilization (GAS) of the studied system are analyzed by constructing appropriate Lyapunov functionals and using mean value inequality and inequality analysis skills.Several delay-dependent GPS and GAS conditions are obtained.

Relaxed Total Lagrange Duality and Optimality Conditions for the Convex Infinite Programming

ZHENG Qinghui, HU Xingxing, WANG Xianyun

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 26-31.

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With the properties of subdifferential of functions and some new weaker constraint qualifications,the total duality and optimality condition between the convex infinite optimization problem and its relaxed Lagrange dual problem are established.

Approximate Optimality Conditions for DC Composite Optimization Problems

HU Xingxing, ZHENG Qinghui, TIAN Liping

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 32-37.

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With the properties of function ε-subdifferential and the new constraint qualification,the characteristic characterization of approximate optimal solution for DC composite optimization problem is established.

Electrical Technology

Harmonic Parameter Estimation Based on Classical Cosine Window Three Spectral Line Interpolation FFT

LI Minghao, WANG Xuming, ZHANG Zhiwei, TAN Yuhao, LEI Kejun

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 38-43.

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Aiming at the problems of spectrum leakage and fence effect in signal processing by fast Fourier transform（FFT）,based on the analysis of the characteristics of main-lobe and side-lobe of several classical cosine windows,a harmonic analysis method based on cosine window three spectral line interpolation FFT is proposed by using the spectral lines with the largest amplitude near the real frequency point and the spectral lines on both sides. Combined with the least square and polynomial fitting methods,the correction formula of harmonic parameters is derived.The simulation results show that,compared with the traditional FFT method,the proposed method can better suppress the influence of spectrum leakage and fence effect,and the detection accuracy of harmonic parameters has been further improved.

FFT Dielectric Loss Angle Measurement of Improved Rife-Vincent(Ι) Window

ZHANG Zhiwei, PENG hao, TAN Yuhao, LI Minghao, WANG Xuming

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 44-47.

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Due to the asynchronous sampling of the signal,there will be spectrum leakage when using FFT to process the signal,resulting in the low measurement accuracy of FFT dielectric loss angle.In order to improve the measurement accuracy of dielectric loss angle,the side lobe characteristics of different window functions are analyzed.A new cosine window is constructed through the self-multiplication operation of Rife-Vincent (Ι) window,and an FFT dielectric loss angle measurement method based on improved Rife-Vincent (Ι) window is proposed.The new window function has better sidelobe characteristics than the traditional window function,and improves the suppression effect of spectrum leakage.The simulation results show that the measurement accuracy of using Rife-Vincent (Ι) self-multiplication window method is higher than that of using Hanning window and Blackman window method.

Physics and Computer

Theoretical Derivation of the Kramers-Kronig Relationship Based on the Fourier Transform

SU Hongmei

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 48-51.

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From the causal law of physical experimental facts,without concrete microscopic physical model, this paper discusses the physical mechanism and theoretical derivation of the Kramers-Kronig relationship based on Fourier transform,dispersion theory,and residue theorem.

Design of Controller for Pure Electric Bus Based on STM32

WANG Guoyi, YUAN Tao, YU Xingguo, LI Hao

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 52-56.

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A pure electric bus controller based on STM32 is designed through analyzing the function and running state of pure electric bus control. The function of each module of the controller is analyzed,and the power supply circuit and voltage detection circuit are designed. The controller adjusts the speed of the DC motor through outputting pulse width modulation with different duty cycles.The information collected by the sensor is transmitted to the microprocessor in real time through the CAN bus,and the microprocessor analyses the collected information and sends commands through CAN bus to control the running state of the bus safely,accurately and in real time.

Geotechnical Engineering

Analytical Solution of Matric Suction for Advanced-Peak Pattern Rainfall Infiltration into a Two-Layered Foundation

XU Ruilin, QIN Weixing, HE Yong, HU Huiren, YANG Le, WANG Cong, XIONG Xuanyu

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 57-65.

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In order to reveal the influence of advanced-peak rainfall infiltration on the matrix suction distribution of a two-layered foundation,the following research work is carried out.Firstly,based on Richards transient unsaturated seepage equation and Gardner soil water characteristic function,the water transport model of a two-layered unsaturated foundation for advanced-peak rainfall infiltration is established,and the transient analytical solution of matrix suction for advanced-peak pattern rainfall infiltration into a two-layered foundation is established by Laplace transform.Then,the analytical results are compared with those obtained from the finite element simulation,which indicates that the analytical solution is reasonable.The research results provide a convenient means to predict the evolution characteristics of matrix suction of a two-layered foundation for non-uniform rainfall infiltration,and can provide technical support for the evaluating bearing performance and reducing disaster of a foundation in rainy season.

Significance Analysis of the Influencing Parameters of Maximum Leachate Depth in Landfill Drainage Layer

LIU Jinlong, QIN Weixing, XU Ruilin, HU Huiren, LIU Zechen, DENG Chuanxiong

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 66-71.

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In order to predict the maximum leachate depth in landfill drainage layer and determine the significance of its influening parameters,the following research work is carried out.Firstly,an analytical solution to leachate depth along drainage layer is obtained during leachate infiltration based on the extended Dupuit assumption;the distribution law of leachate depth along drainage layer is analyzed with different leachate infiltration intensity.Then,orthogonal design method is used for comparing the effectiveness of the five main parameters influencing maximum leachate depth,which are leachate infiltration intensity,permeability coefficient,horizontal drainage distance,layout slope as well as water head at the drainage blind ditch ,and the most influential parameters for changing maximum leachate depth are obtained.The variance analysis gives the degrees of impact for each parameter on the maximum leachate depth.The results show that:(1) the analytical solution of leachate depth obtained above considers the actual hydraulic state of the drainage blind ditch in the drainage layer more reasonably,and the distribution characteristics of leachate depth are accurately described;(2) leachate infiltration intensity and horizontal drainage distance have significant impact on the maximum leachate depth in the landfill drainage layer.The findings will facilitate the optimization of design parameters of landfill drainage layer and the prevention of landfill instability caused by high leachate depth.

Chemistry and chemical engineering

Preparation of Li₄Ti₅O₁₂ by Solid-State Method and Exploration of Calcination Temperature

LONG Ruilai, WU Xianming, WU Xiuting, YIN Caishuo

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 72-78.

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Li₄Ti₅O₁₂ powders were prepared by solid-state reaction and two-step calcination method with Li₂CO₃ and TiO₂ as starting materials and anhydrous ethanol as dispersant.The microstructure and morphology of the materials were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM).The electrochemical properties of the materials were tested by constant current charge-discharge,AC impedance and cyclic voltammetry.The results show that the pure phase Li₄Ti₅O₁₂ with complete crystal structure could be synthesized after calcination at 800 ℃ for 6h,and uniform dispersion with particle size of 200~400 nm.The first reversible specific capacity of the Li₄Ti₅O₁₂ sample was 157.67 mA·h/g at the rate of 0.5 C,and the coulombic efficiency was 96.1%,the capacity retention was 94.3% after 100 cycles.The first reversible specific capacity was 107.0 mA·h/g at the rate of 0.5C,the coulombic efficiency was 96.1% and capacity retention was 84.1% after 1 000 cycles.

Optimization Model for C4 Olefin Preparation Based on Random Forest and L-M Algorithm

JIANG Zihao, REN Tao, ZHOU Qi, LUO Jiamian

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 79-83.

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It is important to investigate the catalyst combination and temperature on the preparation of olefins by ethanol coupling.Firstly,ANOVA was used to screen the important influencing factors;then,the importance of the influencing factors on ethanol conversion and C4 olefin selectivity was analyzed by random forest algorithm:temperature>catalyst mass>ethanol concentration>Co loading>charging ratio;finally,multiple non-linear regression was performed by L-M algorithm,and the optimal C4 olefin yield was obtained with particle swarm algorithm.The optimal value was 42.548 5%.

Characteristic column：Study on Wuling Mountain Area

Temporal and Spatial Changes of Healthy City Construction in Wulingshan Area

HE Linhai, LI Jiajia, WU Jilin, DENG Ziyi, ZHONG Ying

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 84-92.

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Taking six key cities in Wuling Mountain Area as the research object,this paper proposes a healthy city construction evaluation index system composed of five subsystems (including 21 indexes) of economy,society,environment,culture and medical treatment,determines the index weight by using the entropy weight method,and analyzes the spatial-temporal changes of healthy city construction by using the comprehensive index method and ArcGIS software.The results show that the comprehensive index of Huaihua City in healthy city construction of ranks the highest among the six key cities in 2010,2015 and 2020,followed by Jishou City,Qianjiang District,Tongren City,Zhangjiajie City and Enshi City.In terms of temporal dimension,the ranking of Tongren City has been greatly improved.The ranking Enshi City has always been in the low.The ranking of Zhangjiajie City declined at first and then rebounded.The ranking of Jishou City and Huaihua City has always been stable in the top three,and the ranking of Qianjiang District has always been in the middle.In terms of spatial dimension,the construction level of the five subsystems of economy,society,environment,culture and medical treatment is slightly different.The overall pattern has changed from "low in the northwest and high in the Southeast" to "low in the north and high in the South",and finally to "low in the northeast and high in the southwest" .In order to promote the high-quality development of the key cities in Wuling mountain area,according to the spatio-temporal change results of the healthy city construction of the six key cities,suggestions are put forward to improve the healthy city construction level of each city from the five aspects of economy,society,environment,culture and medical treatment.

Medical Science

Correlation Analysis of Serum Selenium and Gestational Diabetes Mellitus

YANG Yan, XU Xiaoyan, CHEN Zaiwang

Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 93-96.

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Objective:To explore the correlation between serum selenium and gestational diabetes mellitus.Methods:From March 2020 to September 2021,360 pregnant women were selected as subjects according to the inclusion criteria,180 of whom were normal physical examination subjects with negative GDM diagnosis and were classified as control group,and 180 with positive GDM diagnosis received hospitalization and were classified as observation group.Methods:Selenium levels in different pregnancy periods of the same group and the selenium levels in same pregnancy period of the two groups were compared.Pregnancy outcomes and neonatal outcomes of the two groups were compared.Results:The serum selenium level of pregnant women in the third trimester was lower than that in the middle and early trimesters in the two groups (P<0.05),and the serum selenium level of pregnant women in the second trimester was lower than that in the early trimesters in the observation group (P<0.05).The incidence of adverse pregnancy outcomes and adverse neonatal outcomes in the observation group were higher than those in the control group.Conclusion:There is a strong correlation between serum selenium and gestational diabetes mellitus,and it is of positive significance for pregnant women to supplement selenium by detecting trace elements during pregnancy.