Physicochemical properties and biological activities of polysaccharides from the peel of Dioscorea opposita Thunb.extracted by four different methods

Polysaccharides are the important biologically active components found in the peel of Dioscorea opposita Thunb.(DTTP).The influences of 4 extraction methods,namely hot water extraction(W),acidic extraction(HA),hot-compressed water extraction(HCW)and enzyme-assisted extraction(EAE),on the yields,physicochemical properties,hypoglycemic and antioxidant activities of polysaccharides from DTTP were studied and compared.Among these DTTP polysaccharides,DTTP-HA was outstanding in several respects.DTTP-HA was the most water soluble;it had the highest total carbohydrate content(85.08%),the highest uronic acid(13.20%)and the highest thermal stability.DTTP-HA and DTTP-W possessed a triple-helix structure.These 4 kinds of polysaccharides have the same types of monosaccharides,but in different molar percentages.Extraction method had a significant impact on the microstructures of the extracted polysaccharides.DTT-HA exhibited irregular structure with many holes.Among the 4 extracted methods,the DTTP-HA and DTTP-W initially exhibited higher hypoglycemic and antioxidant activities.The better bioactivities of DTTP-HA may be related to the above factors.The findings indicated that acid extraction is an effective method to extract polysaccharides with high biological activities from DTTP.

Plastic Deformation of Nano-TiO_2 Ceramics Prepared by Different Methods

The comparative study of the tensile plastic deformation of nano(n)-TiO2 ceramic prepared byphysical gas condensation (P) and chemical hydrolysis precipitation (C) methods was conductedby a gas pressure forming technique at 750~800℃. The results show that n-TiO2 (P) possessesexcellent property of tensile pIastic deformation comparing with n-TiO2(C). The reason for thisis attributed to the surface cleanness and soft agglomeration of n-TiO2 (P) particfe prepared inreIatively cIean vacuum condition.

Urrets-Zavalia syndrome in different methods of keratoplasty

INTRODUCTIONUrrets-Zavalia was first described as a syndrome consisting of a fixed,dilated pupil with iris atrophy following penetrating keratoplasty（PKP）in 1963 and back then it was thought that this syndrome was only related to keratoconus patients.Other findings that were not essential for the diagnosis were posterior synechiae,ectropion uvea,pigment dispersion,anterior subcapsular lens opacities and secondary glaucoma syndrome.

Prevention and Control Effects of New Biological Formulations Sprayed by Different Methods on Proceras venosatus (Walker) and Tryporyza intacta Snellen in Middle and Late Stages

To screen new biological formulations, accurate and efficient application technology, field test was conducted with 72% Bacillus thuringiensis(Bt)·monosultap WP, 8% lambda-cyhalothrin·emamectin benzoate SA and 3.6% lambda-cyhalothrin·Bt SA through manual spraying and unmanned aerial vehicle spraying. Test results and comprehensive evaluation analysis demonstrated that 72% Bt·monosultap WP and 8%lambda-cyhalothrin·emamectin benzoate SA by manual spraying and unmanned aerial vehicle spraying had good prevention and control effect on strains and internodes damaged by Tryporyza intacta Snellen in middle and late stage, which were ideal new biological formulations with high effi-ciency and low risk for prevention and control of T. intacta in middle and late stage, and could be popularized in sugarcane area. 72% Bt·monosultap WP at the dose of 3 000 g/hectare and 8% lambda-cyhalothrin·emamectin benzoate SA at the dose of 750 mL/hectare could be sprayed in mid September at the peak occurrence period of the forth and fifth generations of T. intacta and Proceras venosatus. Agents were diluted with 900 kg water per hectare, and manually sprayed with electric knapsack sprayer; or agents were diluted with 15 kg of Haoyang aerial control special addi-tives and water per hectare, and sprayed with unmanned aerial vehicle. The control effect against borer-damaged strain rate was above 81.3% and that against borer-damaged internode rate was above 88.6%.

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.

Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

Influence of different inoculation methods on the evaluation of the resistance to rice sheath blight(Rhizoctonia solani Kuhn)

To establish a standard system for geneticstudies on sheath blight resistance, a field testwas conducted at the experimental farm ofYangzhou University to compare several pro-cedures for inoculating rice plants with R.solani Kuhn (RH9). The varieties used wereJasmine 85, Teqing (resistant or moderatelyresistant), and Lemont (susceptible). They

High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations

In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme.

Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

Computational Methods for Three Coupled Nonlinear Schrödinger Equations

In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method. The resulting schemes are highly accurate, unconditionally stable. We use the exact single soliton solution and the conserved quantities to check the accuracy and the efficiency of the proposed schemes. Also, we use these methods to study the interaction dynamics of two solitons. It is found that both elastic and inelastic collision can take place under suitable parametric conditions. We have noticed that the inelastic collision of single solitons occurs in two different manners: enhancement or suppression of the amplitude.

Methods for estimating rotational components of seismic ground motion and their numerical comparisons

Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three translational components,but less on rotational ones.As the precision of rotational sensing techniques has increased,many scholars have paid more attention to the seismic rotational motions.Because the rotational observations are not very popular before and now,approximately converting the translational components into rotational components is utilized in rotation analysis.Based on numerical six-component seismic data with the finite difference method,we compare three different conversion methods,the travelling-wave,frequency-domain and the difference method,to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.

Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations

The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.

THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION

The numerical solution of a singularly perturbed problem for the semilinear parabolic differential equation with parabolic boundary layers is discussed. A nonlinear two-level difference scheme is constructed on the special non-uniform grids. The uniform con vergence of this scheme is proved and some numerical examples are given.

SECOND-ORDER ACCURATE DIFFERENCE METHOD FOR THE SINGULARLY PERTURBED PROBLEM OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.

Solution of a One-Dimension Heat Equation Using Higher-Order Finite Difference Methods and Their Stability

One-dimensional heat equation was solved for different higher-order finite difference schemes, namely, forward time and fourth-order centered space explicit method, backward time and fourth-order centered space implicit method, and fourth-order implicit Crank-Nicolson finite difference method. Higher-order schemes have complexity in computing values at the neighboring points to the boundaries. It is required there a specification of the values of field variables at some points exterior to the domain. The complexity was incorporated using Hicks approximation. The convergence and stability analysis was also computed for those higher-order finite difference explicit and implicit methods in case of solving a one dimensional heat equation. The obtained numerical results were compared with exact solutions. It is found that backward time and fourth-order centered space implicit scheme along with Hicks approximation performed well over the other mentioned higher-order approaches.

Application of the Hybrid Differential Transform Method to the Nonlinear Equations

In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented;applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems.