Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

Analysis of Perioperative Respiratory Care Methods and their Application Value in Children with Congenital Heart Disease

Objective:To analyze the perioperative respiratory care methods and application value in children with congenital heart disease.Methods:60 children with congenital heart disease(treated from January 2021 to October 2023)were screened and divided into two groups randomly.Each group consisted of 30 cases.The perioperative routine was used in the control group.The observation group underwent the perioperative routine along with better respiratory care.Oxygenation indicators,surgical complications,and family satisfaction levels of the groups were compared.Results:There was no significant difference in the oxygenation index between the two groups of children at admission(P>0.05).At discharge,the oxygenation indicators in the observation group were better than those of the control group,and the incidence of surgical complications was lower than that of the control group.The total satisfaction of family members in the observation group was higher than that of the control group(P<0.05).Conclusion:During the perioperative period for children with congenital heart disease,the implementation of respiratory care,which mainly involves symptomatic care,catheter care,sputum suction care,etc.,can actively improve the oxygenation indicators,reduce surgical complications,and promote faster and better recovery,of children with congenital heart disease.

Approximation Maintenance When Adding a Conditional Value in Set-Valued Ordered Decision Systems

The integration of set-valued ordered rough set models and incremental learning signify a progressive advancement of conventional rough set theory, with the objective of tackling the heterogeneity and ongoing transformations in information systems. In set-valued ordered decision systems, when changes occur in the attribute value domain, such as adding conditional values, it may result in changes in the preference relation between objects, indirectly leading to changes in approximations. In this paper, we effectively addressed the issue of updating approximations that arose from adding conditional values in set-valued ordered decision systems. Firstly, we classified the research objects into two categories: objects with changes in conditional values and objects without changes, and then conducted theoretical studies on updating approximations for these two categories, presenting approximation update theories for adding conditional values. Subsequently, we presented incremental algorithms corresponding to approximation update theories. We demonstrated the feasibility of the proposed incremental update method with numerical examples and showed that our incremental algorithm outperformed the static algorithm. Ultimately, by comparing experimental results on different datasets, it is evident that the incremental algorithm efficiently reduced processing time. In conclusion, this study offered a promising strategy to address the challenges of set-valued ordered decision systems in dynamic environments.

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.

AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

Optimized air-ground data fusion method for mine slope modeling

Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized characteristics of mining slopes,this study introduces a new method that fuses model data from Unmanned aerial vehicles(UAV)tilt photogrammetry and 3D laser scanning through a data alignment algorithm based on control points.First,the mini batch K-Medoids algorithm is utilized to cluster the point cloud data from ground 3D laser scanning.Then,the elbow rule is applied to determine the optimal cluster number(K0),and the feature points are extracted.Next,the nearest neighbor point algorithm is employed to match the feature points obtained from UAV tilt photogrammetry,and the internal point coordinates are adjusted through the distanceweighted average to construct a 3D model.Finally,by integrating an engineering case study,the K0 value is determined to be 8,with a matching accuracy between the two model datasets ranging from 0.0669 to 1.0373 mm.Therefore,compared with the modeling method utilizing K-medoids clustering algorithm,the new modeling method significantly enhances the computational efficiency,the accuracy of selecting the optimal number of feature points in 3D laser scanning,and the precision of the 3D model derived from UAV tilt photogrammetry.This method provides a research foundation for constructing mine slope model.

Spatiotemporal Evolution of Ecosystem Service Value in Caohai National Nature Reserve

Wetland ecosystems are important regulators of global climate change.Studying the spatiotemporal changes and driving mechanisms of their ecosystem service values(ESV)is beneficial for the sustainable development of wetlands.This paper uses the equivalent factor method,based on land use changes,to reveal the spatiotemporal evolution of the ecosystem service value in the Caohai National Nature Reserve(CNNR).The results show the following:①from 2000 to 2020,there was a significant decrease in the core zone s arable land area,with an increase in forest and water areas.Construction land mainly increased in the experimental area,and the grassland area showed a fluctuating change of first increasing and then decreasing;②in 2000,2010,and 2020,the ecosystem service value of the study area was 302 million,296 million,and 325 million yuan,respectively,showing a trend of fluctuating growth,with the value of wetland ecosystems playing a dominant role;③regulatory services are the main contributors to the ecosystem service value in the study area,with a contribution rate of 60%.Hydrological regulation is the ecosystem function with the highest value in wetland ecosystem services,contributing more than 35%to the ESV in all three periods;④in terms of spatial distribution,the core zone s ecosystem service value is dominant.Looking at the total ecosystem service value of the region,the core zone>the experimental area>the buffer zone.In terms of ESV per unit area,the core zone(89000 yuan/hm^(2))is significantly higher than the buffer zone(39100 yuan/hm^(2))and the experimental area(15800 yuan/hm^(2)).The study can provide a basis for research and spatial management of ecosystem services in wetland ecosystems and nature reserves.

Road Layout Cuts Volume Evaluation by Electrical Resistivity Tomography: Case Study of Gagnoa-Gueyo-Bamenadou Road Project

A study of excavated material on the Gagnoa-Guéyo-Bamenadou road project in southwest Côte d’Ivoire was carried out using electrical resistivity tomography with a dipole-dipole configuration. This study aimed to determine the nature and volume of the studied cuts. Based on the cumulative distances of the longitudinal sections of the road alignment superimposed on the tomographic profiles, a cumulative volume of 104681 m3 of material was determined. This volume comprises 88557 m3 of soft cuts and 16,124 m3 of rocky cuts, which can be reused in specific embankment zones. This work may, therefore be useful in the characterization of cuts in a preliminary design study, in order to anticipate changes during the road’s development and asphalting.

Using a Spatial Convolution Method to Estimate Ecosystem Services Values at Regional Level: a Case Study in Northeast China

Since the introduction of the concept, studies on valuation of ecosystem services have been overwhelming, in cognizance of its great significance. In this article, the authors took Northeast China as the study area and applied the published coefficients for the world by Costanza to calculate the ecosystem services values through a spatial convolution method. The convolution analysis was done with a square processor with 5×5 neighborhood cells. The results showed that the ecosystem services value for the study area in the year 2003 was US$44 990 million which is US$89 million less than the value without operation, and the main contributions for that decrease were from water bodies, wetlands and estuaries. It is expected that this article can attract more interest to explore this field adopting geographic methods.

A Comparative Study of the Hydroxyl Value and Iodine Value in Polyoxyl Stearyl Ether in United States Pharmacopeia Specifications

The iodine value (iodine number) and hydroxyl value are important analytical characteristics of fats and oils. The iodine (I2) required saturating the fatty acids present in 100 grams of the oil or fat. Iodine value is a measure of the total number of double bonds (-C=C-) present in fats and oils. Unsaturated compounds contain molecules with double and triple bonds which are very reactive towards iodine. The iodine value has been determined according to Hanus with iodine monobromide in glacial acetic acid, and then the amount of iodine remaining unreacted is determined by titration using sodium thiosulfate volumetric standard solution. The hydroxyl value is the amount of potassium hydroxide in milligrams that is equivalent to the hydroxyl amount of 1 gram of the sample (mg KOH/g sample). Poloxyl Stearyl Ether is a mixture of the monostearyl ethers of mixed polyethylene glycols. It may contain various amounts of free stearyl alcohol and some free polyethylene glycol. In this study, the iodine value and hydroxyl value have been determined by titration in polyoxyl stearyl ether. Iodine value 1.84 g of I2 absorbed/100g sample, and hydroxyl value 162.65 mg KOH/g sample have been found in poloxyl stearyl ether. The iodine value and hydroxyl value results met the United States Pharmacopeia specifications for Polyoxyl Stearyl Ether.

Implications of vitamin D for flesh quality of grass carp(Ctenopharyngodon idella):antioxidant ability,nutritional value,sensory quality,and myofiber characteristics

Background Muscle represents a unique and complex system with many components and comprises the major edible part of animals.Vitamin D is a critical nutrient for animals and is known to enhance calcium absorption and immune response.In recent years,dietary vitamin D supplementation in livestock has received increased attention due to biological responses including improving shear force in mammalian meat.However,the vitamin D acquisition and myofiber development processes in fish differ from those in mammals,and the effect of vitamin D on fish flesh quality is poorly understood.Here,the influence of dietary vitamin D on fillet quality,antioxidant ability,and myofiber development was examined in grass carp(Ctenopharyngodon idella).Methods A total of 540 healthy grass carp,with an initial average body weight of 257.24±0.63 g,were allotted in 6 experimental groups with 3 replicates each,and respectively fed corresponding diets with 15.2,364.3,782.5,1,167.9,1,573.8,and 1,980.1 IU/kg vitamin D for 70 d.Results Supplementation with 1,167.9 IU/kg vitamin D significantly improved nutritional value and sensory quality of fillets,enhancing crude protein,free amino acid,lipid,and collagen contents;maintaining an ideal pH;and reduc-ing lactate content,shear force,and cooking loss relative to respective values in the control(15.2 IU/kg)group.Average myofiber diameter and the frequency of myofibers>50μm in diameter increased under supplementation with 782.5–1,167.9 IU/kg vitamin D.Levels of oxidative damage biomarkers decreased,and the expression of antioxi-dant enzymes and nuclear factor erythroid 2-related factor 2 signaling molecules was upregulated in the 1,167.9 IU/kg vitamin D treatment compared to respective values in the control group.Furthermore,vitamin D supplementation activated cell differentiation by enhancing the expression of myogenic regulatory factors and myocyte enhancer factors compared to that in the control group.In addition,supplementation with 1,167.9 IU/kg vitamin D improved protein deposition associated with protein synthesis molecule(target of rapamycin)signaling and vitamin D receptor paralogs,along with inhibition of protein degradation(forkhead box protein 1)signaling.Conclusions Overall,the results demonstrated that vitamin D strengthened antioxidant ability and myofiber devel-opment,thereby enhancing nutritional value and sensory quality of fish flesh.These findings suggest that dietary vitamin D supplementation is conducive to the production of nutrient-rich,high quality aquaculture products.

Estimating the value of a statistical life in China: A contingent valuation study in six representative cities

The value of a statistical life(VSL)is a crucial tool for monetizing health impacts.To explore the VSL in China,this study examines people’s willingness to pay(WTP)to reduce death risk from air pollution in six representative cities in China based on face-to-face contingent valuation interviews(n=3936)from March 7,2019 to September 30,2019.The results reveal that the WTP varied from CNY 455 to 763 in 2019(USD 66-111),corresponding to a VSL range of CNY 3.79-6.36 million(USD 549395-921940).The VSL in China in 2019 is estimated to be CNY 4.76 million(USD 689659).The statistics indicate that monthly expenditure levels,environmental concerns,risk attitudes,and assumed market acceptance,which have seldom been dis‐cussed in previous studies,significantly impact WTP and VSL.These findings will serve as a reference for ana‐lyzing mortality risk reduction benefits in future research and for policymaking.

A Study on the Factors Influencing Value-Added in the Cruise Ship Value Chain Based on the DEMATEL-ISM Model

Cruise value chain is to take the exchange of cruise products and services as the core in a certain spatial scope,and enterprises with core advantages within or between different industries establish associations in accordance with certain technical and economic conditions,so as to realise the multi-dimensional extension and value appreciation of the cruise value chain in the vertical and horizontal links,and ultimately establish a chain-network type of enterprise strategic alliance.This paper tries to analyse the value-added factors of the cruise industry chain by constructing a multi-level hierarchical structural model with reference to the influencing factor analysis methods of relevant literature-DEMATEL(Decision Making Experiment and Evaluation Experiment)and ISM(Interpretative Structural Model).The study shows that the innovation and scale value-added module in the upstream of the cruise industry chain is the core module of value-added of the whole cruise industry chain,and the value-added mainly originates from the design and manufacturing of cruise ships.The middle reaches of the cruise industry chain are mainly cruise operation enterprises,and the specificity of cruise operation determines that its brand value-added is mainly accomplished through the global layout of multinational corporations,and the cruise brand is able to drive the consumption demand and has value-added ability.The downstream value-added of the cruise industry chain is mainly realised through the increase in profits of cruise tourism service products.

Landslide susceptibility mapping using an integrated model of information value method and logistic regression in the Bailongjiang watershed,Gansu Province,China

Bailongjiang watershed in southern Gansu province, China, is one of the most landslide-prone regions in China, characterized by very high frequency of landslide occurrence. In order to predict the landslide occurrence, a comprehensive map of landslide susceptibility is required which may be significantly helpful in reducing loss of property and human life. In this study, an integrated model of information value method and logistic regression is proposed by using their merits at maximum and overcoming their weaknesses, which may enhance precision and accuracy of landslide susceptibility assessment. A detailed and reliable landslide inventory with 1587 landslides was prepared and randomly divided into two groups,(i) training dataset and(ii) testing dataset. Eight distinct landslide conditioning factors including lithology, slope gradient, aspect, elevation, distance to drainages,distance to faults, distance to roads and vegetation coverage were selected for landslide susceptibility mapping. The produced landslide susceptibility maps were validated by the success rate and prediction rate curves. The validation results show that the success rate and the prediction rate of the integrated model are 81.7 % and 84.6 %, respectively, which indicate that the proposed integrated method is reliable to produce an accurate landslide susceptibility map and the results may be used for landslides management and mitigation.

Estimation of conservation value of myrtle(Myrtus communis)using a contingent valuation method:a case study in a Dooreh forest area,Lorestan Province,Iran

Background： Around 2000 plant species occur naturally in Lorestan Province of which 250 species are medicinal and myrtle is one of them. Myrtle is a shrub whose leaves and fruits have medicinal value and thus, if managed and harvested properly, could produce sustained economic benefits. In recent years, however, over half of the myrtle site areas was destroyed, due to inappropriate management and excessive harvesting practices. Thus, coming up with a practical harvesting approach along with identifying those factors damaging the sites, seems to be very crucial. Methods： In our investigation, we calculated the conservation value per hectare of myrtle in the Dooreh forest area in Lorestan Province. Using the Contingent Valuation （CV） and Double Bounded Dichotomous Choice （DBDC） methods, we determined the willingness to pay （VVTP） for myrtle conservation. The VVTP was estimated with a Iogit model for which indices were obtained based on a maximum precision criterion. Results： The results showed that 86.67 per cent of people were willing to pay for the conservation of these myrtle sites. Average monthly WTP per family was calculated as $0.79. The annual conservation value in terms of WTP for the preservation of the myrtle sites in Dooreh was estimated as $102,525. Among the variables of the model presented, education had a positive impact, while the amount proposed for payment and family size had a negative impact on the WTP. Conclusions： Our estimate of the value of myrtle conservation should provide justification for policy makers and decision making bodies of natural resources to implement policies in order to conserve the natural sites of this species more effectively.

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

SUPERCONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR ELLIPTIC BOUNDARY VALUE PROBLEM

Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.