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.

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.

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.

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.

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.

A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting （CZC） method is proposed in this paper, by combining the Duffing oscillator＇s phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high- efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent （MLE） method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

Discussion of the Evaluation Method and Value of Green Building's POE in the Era of Large Data

China vigorously is carrying out the construction of green building and ecological city during " The 12 th five-Year plan". Now,although the identification system of design and operation have been implemented in the evaluation of green building,lacking of appropriate evaluation after use. The actual operation results of many buildings,which have got a green building logo,are not satisfied from the user 's perspective. In this paper,an evaluation method that combines the actual building energy consumption and users' satisfaction has been discussed,based on the post occupancy evaluation( POE) theory and the Big data technology. Through the comparison and analysis of building objective operational metrics and users subjective feelings indicators,the green buildings' POE has been achieved. Finally,the study analyzes the assessed value of green building's POE from the three-time dimensions,short-term,medium-term and long-term. And the outlook of the direction is looking forward to the follow-up study.

The height-width ratio limited value for rubber bearing isolated structure computed by uniform design method

Rubber isolation is the most mature control technology in practical application, and is widely used by short rigid buildings. However, many high isolation buildings have been built around the world in recent years, which do not follow the existing criterions and codes. Many researchers began to research the special problems caused by larger height-width ratio isolation structures. The overturning effect of high height-width ratio structures with rubber bearing is firstly studied. Considering the main factors, such as the height-width ratio of structures, type of site, the designed basic acceleration of ground motion and the decouple factor in horizon, computing experiment is defined with the Uniform Design Method, which is also known as designing isolation structure. The forces of the bearing under edge of structures based on the position of the rubber bearing are calculated. The result indicates that the rubber bearings will lose its functionality under very high tension and compressing force of earthquake motion in horizon and vertical, when the height-width ratio is over a certain value. Thus, based on the calculation result of isolation structures defined in the uniform design method, regression analysis is conducted, and also the rubber edge force regression formula are gotten, which has higher correlation and smaller standard deviation. This formula can be used to roughly calculate whether the pull force occurs at the edge of the building. By the edge bearings of isolation structure minimum force formula, the height-width ratio limited value of the isolation structure is deducted when rubber bearing has minimum force of zero.

THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

In this article,we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation.This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem.We prove the error estimates between the regularization solution and the exact solution by using an a priori regularization parameter and an a posteriori regularization parameter choice rule.Some numerical results in one-dimensional case and two-dimensional case show that our method is efficient and stable.

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.

Measuring Recreational Value of World Heritage Sites Based on Contingent Valuation Method:A Case Study of Jiuzhaigou

World heritage possesses various kinds of use value and non-use value. Measuring the recreational value of world heritage sites is a key issue in the heritage tourism. This paper employs Contingent Valuation Method (CVM), which is an evaluation instrument on the basis of tourists′ attitude and preference, to measure the recreational value of Jiuzhaigou, one of the World Natural Heritage sites in China, and analyzes the biases in the survey. The results show that: 1) In 2009, Jiuzhaigou′s recreational value was 3.46×108 yuan (RMB), and the per capita Willingness to Pay (WTP) was 137.31 yuan by CVM. Compared with the results of other methods, this result is significantly low. 2) Among the factors that influence Jiuzhaigou tourists′ WTP, psychological perception factors have the greatest effect while demographic and socio-economic characteristics have a small effect on WTP. 3) The virtuality in CVM creates biases both from CVM itself and in the procedures that CVM was implemented. The former includes hypothetical bias, information bias, protest response bias, and strategic bias; and the latter includes the questionnaire design, population and sample definition, sampling and data processing. The paper analyses those biases and illustrates their potential in-fluences on the accuracy of CVM measurement. 4) Although there are various defects in CVM measurement, it is still an effective valuation method.

Valuing options to renew at future market value:the case of commercial property leases

In this study,we develop and empirically test a valuation model for a commonly encountered option in office leases:a tenant’s option to renew at future market rent(a fair market value)with lease termination as the maturity date.The model integrates decision analysis with real options analysis and market risk with private risks.“Option value”is defined as the private value of the option to either party pre-contract,while“option price”assumes a fair agreement between transacting parties and can be positive(rental premium paid)or negative(rental discount offered).Without manifest expectations,an analysis of a sample of office leases supports the model’s logic with price estimates in a practical range.The tenants’option price/value is shown to have a negative relationship with the original/renewal lease term;conversely,the landlords’option value is positively related to the original/renewal term.Comparative analyses show that transaction costs have a positive effect on tenants’option value and on prices,while vacancy costs and the vacancy period are both positively related to the landlords’option value and negatively related to price.Market rent is found to have a negative relationship with option price.Overall,this study provides a theoretical analysis and empirical tests of the value of a real option that allows option holders to renew/extend their contracts at a fair market value.

Hazard Assessment of Co-seismic Landslides Based on Information Value Method:A Case in 2018 MW6.6 Hokkaido Earthquake,Japan

An MW6.6 earthquake occurred in eastern Hokkaido,Japan on September 6th,2018.Based on the pre-earthquake image from Google Earth and the post-earthquake image from high resolution(3 m)planet satellite,we manually interpret 9293 coseismic landslides and select 7 influencing factors of seismic landslide,such as elevation,slope,slope direction,road distance,flow distance,peak ground acceleration(PGA)and lithology.Then,9293 landslide points are randomly divided into training samples and validation samples with a proportion of 7:3.In detail,the training sample has 6505 landslide points and the validation sample has 2788 landslide points.The hazard risk assessment of seismic landslide is conducted by using the information value method and the study area is further divided into five risk grades,including very low risk area,low risk area,moderate risk area high risk area and very high risk area.The results show that there are 7576 landslides in high risk area and very high risk area,accounting for81.52%of the total landslide number,and the landslide area is 22.93 km^2,accounting for 74.35%of the total area.The hazard zoning is in high accordance with the actual situation.The evaluation results are tested by using the curve of cumulative percentage of hazardous area and cumulative percentage of landslides number.The results show that the success rate of the information value method is 78.50%and the prediction rate is 78.43%.The evaluation results are satisfactory,indicating that the hazard risk assessment results based on information value method may provide scientific reference for landslide hazard risk assessment as well as the disaster prevention and mitigation in the study area.