The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Tra...The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal rule.In particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal rule.Additionally,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed approaches.Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.展开更多
In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions...In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.展开更多
In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singula...In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.展开更多
In this paper, we introduce a quadrature rule for the numerical evaluation of certain hyper singular integrals. The rule is obtained by using Hermite interpolation polynomial. Error bound is also made.
Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations,have been useful in a number of engineering applications.In this paper we investigate some numerical methods fo...Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations,have been useful in a number of engineering applications.In this paper we investigate some numerical methods for computing finite-part integrals.展开更多
In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending ...In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending on the number of subintervals ＂n＂ are calculated by using Maple 18 and presented. These results are demonstrated graphically in a particular numerical example. An algorithm of this application is given by using Maple 18.展开更多
The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint ru...The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.展开更多
A systematic method was developed for ice-class propeller modeling,performance estimation,strength and integrity evaluation and optimization.To estimate the impact of sea ice on the propeller structure,URI3 rules,esta...A systematic method was developed for ice-class propeller modeling,performance estimation,strength and integrity evaluation and optimization.To estimate the impact of sea ice on the propeller structure,URI3 rules,established by the International Association of Classification Societies in 2007,were applied for ice loading calculations.An R-class propeller(a type of ice-class propeller)was utilized for subsequent investigations.The propeller modeling was simplified based on a conventional method,which expedited the model building process.The propeller performance was simulated using the computational fluid dynamics(CFD)method.The simulation results were validated by comparison with experimental data.Furthermore,the hydrodynamic pressure was transferred into a finite element analysis(FEA)module for strength assessment of ice-class propellers.According to URI3 rules,the ice loading was estimated based on different polar classes and working cases.Then,the FEA method was utilized to evaluate the propeller strength.The validation showed that the simulation results accorded with recent research results.Finally,an improved optimization method was developed to save the propeller constituent materials.The optimized propeller example had a minimum safety factor of 1.55,satisfying the safety factor requirement of≥1.5,and reduced the design volume to 88.2%of the original.展开更多
Kiwifruit canker disease seriously affects the yield and quality of"Guichang"kiwifruit in Xiuwen County,Guizhou Province.In order to scientifically,safely,greenly and efficiently prevent and control the dise...Kiwifruit canker disease seriously affects the yield and quality of"Guichang"kiwifruit in Xiuwen County,Guizhou Province.In order to scientifically,safely,greenly and efficiently prevent and control the disease,theory was combined with prevention and control techniques to optimize existing prevention and control techniques,so as to improve the production yield and quality of kiwifruit.Specifically,biocontrol strains targeting local kiwifruit canker disease were screened,and reduced and mixed use of agrochemicals with improved efficiency was studied;and the effects and application techniques of disease resistance inducers and bioorganic fertilizers in inducing systemic disease resistance in kiwifruit trees were explored,and finally,an integrated green prevention and control scheme for kiwifruit canker disease that is suitable for kiwifruit production areas in Guizhou Province and has strong operability was proposed.This study provides technical support for green,efficient,standardized production technical services and sustainable and healthy development of kiwifruit industry.展开更多
文摘The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal rule.In particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal rule.Additionally,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed approaches.Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.
文摘In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.
基金The work of Jin Li was supported by National Natural Science Foundation of China(Grant No.11471195)China Postdoctoral Science Foundation(Grant No.2015T80703)+1 种基金Shan-dong Provincial Natural Science Foundation of China(Grant No.ZR2016JL006)Na-tional Natural Science Foundation of China(Grant No.11771398).
文摘In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.
文摘In this paper, we introduce a quadrature rule for the numerical evaluation of certain hyper singular integrals. The rule is obtained by using Hermite interpolation polynomial. Error bound is also made.
文摘Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations,have been useful in a number of engineering applications.In this paper we investigate some numerical methods for computing finite-part integrals.
文摘In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending on the number of subintervals ＂n＂ are calculated by using Maple 18 and presented. These results are demonstrated graphically in a particular numerical example. An algorithm of this application is given by using Maple 18.
文摘The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.
基金The author would like to thank University of Tasmania and Newcastle University for their support。
文摘A systematic method was developed for ice-class propeller modeling,performance estimation,strength and integrity evaluation and optimization.To estimate the impact of sea ice on the propeller structure,URI3 rules,established by the International Association of Classification Societies in 2007,were applied for ice loading calculations.An R-class propeller(a type of ice-class propeller)was utilized for subsequent investigations.The propeller modeling was simplified based on a conventional method,which expedited the model building process.The propeller performance was simulated using the computational fluid dynamics(CFD)method.The simulation results were validated by comparison with experimental data.Furthermore,the hydrodynamic pressure was transferred into a finite element analysis(FEA)module for strength assessment of ice-class propellers.According to URI3 rules,the ice loading was estimated based on different polar classes and working cases.Then,the FEA method was utilized to evaluate the propeller strength.The validation showed that the simulation results accorded with recent research results.Finally,an improved optimization method was developed to save the propeller constituent materials.The optimized propeller example had a minimum safety factor of 1.55,satisfying the safety factor requirement of≥1.5,and reduced the design volume to 88.2%of the original.
基金Supported by Science and Technology Support Program of Guizhou Province(QKHZC[2020]1Y135)General Higher Education Science and Technology Top-notch Talents Project of Guizhou Province(QJH KY Z[2021]037)+5 种基金Science and Technology Program of Guizhou Province(QKHJZ-ZK[2022]ZD 025)High-level Talent Scientific Research Startup Project of Guizhou Institute of Technology(XJGC20190632)Earth Thesis Project of Guizhou Institute of Technology(KJZX20-005)High-Level Talent Initial Funding of Guizhou Industry Polytechnic College(2023-RC-01)Enterprise Commissioned Project of Guizhou Industrial Polytechnic College(2023-HX-01)Enterprise Commissioned Project of Guizhou Industrial Polytechnic College(2023-HX-02).
文摘Kiwifruit canker disease seriously affects the yield and quality of"Guichang"kiwifruit in Xiuwen County,Guizhou Province.In order to scientifically,safely,greenly and efficiently prevent and control the disease,theory was combined with prevention and control techniques to optimize existing prevention and control techniques,so as to improve the production yield and quality of kiwifruit.Specifically,biocontrol strains targeting local kiwifruit canker disease were screened,and reduced and mixed use of agrochemicals with improved efficiency was studied;and the effects and application techniques of disease resistance inducers and bioorganic fertilizers in inducing systemic disease resistance in kiwifruit trees were explored,and finally,an integrated green prevention and control scheme for kiwifruit canker disease that is suitable for kiwifruit production areas in Guizhou Province and has strong operability was proposed.This study provides technical support for green,efficient,standardized production technical services and sustainable and healthy development of kiwifruit industry.
