Extraction of Pumpkin Polysaccharide by Complex Enzyme Method and Its Antioxidant Research

[Objective] This paper aims to study a new method of extracting pumpkin polysaccharide from pumpkin. Single factor experiments were conducted to examine the effects of extracting time,temperature,the solid-liquid ratio and pH value on the extraction yield of polysaccharide from pumpkin. [Method] The best enzyme ratio and extraction conditions for complex enzymes extraction were determined through orthogonal tests. Scavenging ·OH and O-2 activities of pumpkin polysaccharides were also investigated by salicylic acid and improved self-oxidation of o-pheno methods respectively. [Results] The results showed that the biggest extraction yield of polysaccharide from pumpkin can be got when adding 1% cellulose enzyme,1.5% pectinase,1.0% papain and Na2HPO4-citric acid buffer solution (pH was 4.6),and oscillating for 30 min under water at 40 ℃ with the solid-liquid ratio of 1:30. In addition,pumpkin polysaccharides had a strong activity of eliminating ·OH,but very weak activity to scavenge O-2. [Conclusion] This study provided basic data for research and application of Pumpkin polysaccharide.

Analytical investigations of in situ stress inversion from borehole breakout geometries

This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collected and three failure criteria were studied.Based on the Kirsch equations,relatively accurate major horizontal stress(sH)estimations from known minor horizontal stress(sh)were achieved with percentage errors ranging from 0.33%to 44.08%using the breakout width.The Mogi-Coulomb failure criterion(average error:13.1%)outperformed modified Wiebols-Cook(average error:19.09%)and modified Lade(average error:18.09%)failure criteria.However,none of the tested constitutive models could yield reasonable sh predictions from known sH using the same approach due to the analytical expression of the redistributed stress and the nature of the constitutive models.In consideration of this issue,the horizontal stress ratio(sH/sh)is suggested as an alternative input,which could estimate both sH and sh with the same level of accuracy.Moreover,the estimation accuracies for both large-scale and laboratory-scale breakouts are comparable,suggesting the applicability of this approach across different breakout sizes.For breakout depth,conformal mapping and complex variable method were used to calculate the stress concentration around the breakout tip,allowing the expression of redistributed stresses using binomials composed of sH and sh.Nevertheless,analysis of the breakout depth stabilisation mechanism indicates that additional parameters are required to utilise normalised breakout depth for stress estimation compared to breakout width.These parameters are challenging to obtain,especially under field conditions,meaning utilising normalised breakout depth analytically in practical applications faces significant challenges and remains infeasible at this stage.Nonetheless,the normalised breakout depth should still be considered a critical input for any empirical and statistical stress estimation method given its significant correlation with horizontal stresses.The outcome of this paper is expected to contribute valuable insights into the breakout stabilisation mechanisms and estimation of in situ stress magnitudes based on borehole breakout geometries.

Species distribution of polymeric aluminium ferrum——timed complexation colorimetric analysis method of Al-Fe-Ferron

The effects of the calorimetric buffer solutions were investigated while the two colorimetric reactions of AI-ferron complex and Fe-ferron complex occurred individually, and the effects of the testing wavelength and the pH of the solutions were also investigated. A timed complexatian colorimetric analysis method of Al-Fe-ferron in view of the total concentration of {AI + Fe} was then established to determine the species distribution of polymeric Al-Fe. The testing wavelength was recommended at 362 net and the testing pH value was 5. With a comparison of the ratios of n(Al)/n(Fe), the standard adsorption curves of the polymeric Al-Fe solutions were derived from the experimental results. Furthermore, the solutions' composition were carious in both the molar n(Al)/n(Fe) ratios, i.e. 0/0, 5/5, 9/1 and 0/10, and the concentrations associated with the total ( Al + Fe which ranged from 10(-5) to 10(-4) mol/L..

A new complex variable element-free Galerkin method for two-dimensional potential problems

In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.

Complex variable element-free Galerkin method for viscoelasticity problems

Based on the complex variable moving least-square （CVMLS） approximation, the complex variable element-free Galerkin （CVEFG） method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin （EFG） method, with the same node distribution, the CVEFG method has higher precision, and to obtain the similar precision, the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method.

LOWER BOUND LIMIT ANALYSIS OF THREE-DIMENSIONAL ELASTOPLASTIC STRUCTURES BY BOUNDARY ELEMENT METHOD

Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.

An improved complex variable element-free Galerkin method for two-dimensional elasticity problems

In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares （CVMLS） approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin （EFG） method and the ICVMLS approximation, the improved complex variable element-free Galerkin （ICVEFG） method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFC method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.

Species analysis methods for hydrolysis polymerization of aluminum

Al Ferron timed complex colorimetric method (AFM) and 27 Al NMR spectroscopy method(ANM) were discussed. For the former, the different colorimetric reagent preparation methods' results indicate that there are some differences beteween them, and the combined method can be used as a simplified procedure. For the latter, the small tube method is more accurate. Eventually, the Al 13 (ANM) was compared to the Al b (AFM).

Extended Complex tanh-Function Method and Exact Solutions to （2＋1）-Dimensional Hirota Equation

In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 （2004） 1037]. Abundant new solutions o[ （2q-1）-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.

Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems

Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.

New complex variable meshless method for advection-diffusion problems

In this paper,an improved complex variable meshless method（ICVMM） for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square（ICVMLS） approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency.

Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method

In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

Complex coordinate rotation method based on gradient optimization

In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.

Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.

Determination of Critical Slip Surface of Soil Slope by New Complex Method

A new complex method is presented considering not only the improvement upon the ＂bad ＂design point, but also the diversity of the newly generated complex, which is obtained by replacing the ＂bad ＂design point with the better design point located at the line between the ＂bad ＂design point and the ceotroid of the remaining design points of the old complex. The new complex method is applied to searching for the critical slip surface of two non-homogeneous soil slopes. The comparison of the results obtained by the new complex method with that by the basic complex method shows that the new complex method is much more likely to find the true critical surface for the randomly generated initial complex.

Study on Process Conditions of Preparation of Microporous Potatoes Starch by Complex Enzyme Method

[Objective] The technology of using c-amylase and glucoamylase to prepare microporeus potato starch was studied.[ Method ] Taking potato starch as raw materials, starch hydrolysis rate and the oil absorption as a measure of index, the influences of the reaction temperature, two enzymes proportion, the quantity of enzyme, the chroma of substrate, buffer solution pH and reaction time on microporous potato starch were inves- tigated. [ Result] The experimental results showed that the best technological conditions were reaction temperature 45 ℃, enzyme ratio （ glucoamy- lase/α-amylase）6, the quantity of enzyme （amount of enzyme and starch quality than） is 1.0%, the substrate quantity chroma of 0.14 g/ml, buffer solution pH 4, the reaction time 8 h. In such process condition, the oil adsorption rate of hydrolyzed potato starch was as high as 70.2%, starch hydrolytic ratio was 34.16%. [ Condmion] The study provided a basis for the development and utilization of microporous starch. Key words Microporous starch; Hydrolysis rate; Oil absorption rate; Preparation; Complex enzyme method; China

COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.