Establishing environmental background values of selected trace elements and environmental quality assessment of fi negrained sediments in the Jiaozhou Bay catchment,China

With the development of economy,the impact of human activities on ecological environment is increasing,and environmental protection work is important.Trace elements(Co,Ni,Cu,Pb,Zn,Cd,Cr,and Sc)in surface fi ne-grained sediment samples from the Jiaozhou Bay catchment were selected to evaluate their 2015 environmental background values and the environmental quality.Using statistical analysis,the environmental background values(ranges)of Sc,Co,Ni,Cu,Pb,Zn,Cd,and Cr were calculated,being 13.1(10.8-15.4),12.4(8.6-16.2),32.0(22.9-41.2),29.6(13.5-64.9),24.1(13.0-44.6),77.6(38.5-156.5),0.07(0.02-0.20),and 82.5(66.5-104.0)mg/kg,respectively.The enrichment factor,contamination factor,and pollution load index were used to evaluate the pollution status of the Jiaozhou Bay catchment.The environmental background values of most elements are higher than those of the upper continental crust and lower than those of global shale.At present,the pollution in the eastern Jiaozhou Bay is much higher than that in the western part.The results shall be helpful for future management for trace element pollution monitoring in the Jiaozhou Bay catchment.

Optimization approach of background value and initial item for improving prediction precision of GM(1,1) model

A combination method of optimization of the back-ground value and optimization of the initial item is proposed. The sequences of the unbiased exponential distribution are simulated and predicted through the optimization of the background value in grey differential equations. The principle of the new information priority in the grey system theory and the rationality of the initial item in the original GM（1,1） model are ful y expressed through the improvement of the initial item in the proposed time response function. A numerical example is employed to il ustrate that the proposed method is able to simulate and predict sequences of raw data with the unbiased exponential distribution and has better simulation performance and prediction precision than the original GM（1,1） model relatively.

Initial and Boundary Value Problems for Two-Dimensional Non-hydrostatic Boussi nesq Equations

Based on the theory of stratification, the well-posedness of the init ial and boundary value problems for the system of two-dimensional non-hydrosta ti c Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for s ome representative initial and boundary value problems. Several special cases we re discussed.

Non-equal-interval direct optimizing Verhulst model that x(n) be taken as initial value and its application

To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.

The Relationship between Nonconservative Schemes and Initial Values of Nonlinear Evolution Equations

For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given. Based on numerical tests, the relationship between the nonlinear computational stability and the construction of difference schemes, as well as the form of initial values, is further discussed. It is proved through both theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of nonconservative schemes is decided by the form of initial values.

Consistency and Stability Issues in the Numerical Integration of the First and Second Order Initial Value Problem

In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.

EXISTENCE AND NONEXISTENCE FOR THE INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEM OF MULTIDIMENSIONAL NONLINEAR SCHRDINGER EQUATIONS WITH OPERATOR AND THEIR SOLITON SOLUTIONS

The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.

BACKGROUND VALUES AND TREND DISTRIBUTION OF Cu, Zn AND Ni IN SOILS IN CHINA

The background values of Cu, Zn and Ni are discussed based on the analytical data of 21 main soil types collected from various regions in China. According to statistics of many samples, the background value of Cu is 23.4±10.2 mg/ kg (482 samples), Zn 77.9±2.39 mg/ kg (474 samples), Ni 30.0±12.8 mg/kg (482 samples).

THE BACKGROUND VALUES OF RARE EARTH AND RADIOACTIVE ELEMENTS IN WATER SYSTEM OF SOURCE AREA OF THE CHANG JIANG RIVER

Using neutron activation analysis method we determined contents of rare-earth and radioactive elements (La, Ce, Nd, Sm, Eu, Tb, Yb, Lu, Cs, Rb, Sb, Sc, Sr, Ba, U, Th) in source water system of the Changjiang (Yangtze) River, which is mainly composed of the Tuotuo River, the Chumaer River, and the Buqu River. The contents of these elements in the unflltered water have a great variation and a close correlation with the water turbidity. The contents of these elements in filtered water only have a little variation and are lower than those in the unflltered water. The variations in contents of these elements in sediments are also very little. These elements in the unifiltered water are in geometric distribution, except Sc. Most of the elements in sediments are in arithmetic distribution, but Cs, Sb, Th, are in deviation distribution. The contents of most of these elements in the river source area correspond to the contents of fresh water of the earth. Most of these elements have a little variation in their

Growth and Interactions of Multi-Source Perturbations in Convection-Allowing Ensemble Forecasts

This study investigated the growth of forecast errors stemming from initial conditions(ICs),lateral boundary conditions(LBCs),and model(MO)perturbations,as well as their interactions,by conducting seven 36 h convectionallowing ensemble forecast(CAEF)experiments.Two cases,one with strong-forcing(SF)and the other with weak-forcing(WF),occurred over the Yangtze-Huai River basin(YHRB)in East China,were selected to examine the sources of uncertainties associated with perturbation growth under varying forcing backgrounds and the influence of these backgrounds on growth.The perturbations exhibited distinct characteristics in terms of temporal evolution,spatial propagation,and vertical distribution under different forcing backgrounds,indicating a dependence between perturbation growth and forcing background.A comparison of the perturbation growth in different precipitation areas revealed that IC and LBC perturbations were significantly influenced by the location of precipitation in the SF case,while MO perturbations were more responsive to convection triggering and dominated in the WF case.The vertical distribution of perturbations showed that the sources of uncertainties and the performance of perturbations varied between SF and WF cases,with LBC perturbations displaying notable case dependence.Furthermore,the interactions between perturbations were considered by exploring the added values of different source perturbations.For the SF case,the added values of IC,LBC,and MO perturbations were reflected in different forecast periods and different source uncertainties,suggesting that the combination of multi-source perturbations can yield positive interactions.In the WF case,MO perturbations provided a more accurate estimation of uncertainties downstream of the Dabie Mountain and need to be prioritized in the research on perturbation development.

About well posed initial boundary value problem for changing time direction equation by solution and its solvability

The equation of this type should be nonlinear with nonlinearity at the dominant part defining type of equation. The prime model such equations is diffuse equation with U t=[φ(U x)] x nonmonotone state function φ. In this article are presented studies several equations of this sort.

A NONLINEAR TRANSFORMATION AND A BOUNDARY-INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR CONVECTION-DIFFUSION EQUATIONS

With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.

INITIAL-BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM FOR A QUASILINEAR EVOLUTION EQUATION

In the present paper,the local existence of classical solutions to the periodic boundary problem and the Cauchy problem of a quasilinear evolution equation are studied under the assumptions that do not require the monotonicity of σi(s) (i= 1,…, n). The nonexistence of global solutions to the initial-boundary value problem of the equation is also discussed, a blowup theorem is proved and a concrete example is given.

SYMMETRIES， BāCKLUND TRANSFORMATIONS AND BOUNDARY－INITIAL VALUE PROBLEMS FOR NONLINEAR CHROMATOGRAPH

In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series of Backlund transformations of the equation are constructed by means of the symmetries. The exact solutions of two boundary-initial value problems on the half straight line for the equation are given m terms of the solutions of the corresponding linear problems.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞） ×Ω with p 〉 2 and m 〉 0. He deals with the global solutions by D.H.Sattinger＇s potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.

Soil Geochemical Background Value and Environmental Quality Assessment in Jinan City

[Objectives]This study was conducted to accurately assess soil and environmental quality in Jinan City. [Methods] Based on the multipurpose regional geochemical survey data of 1∶250 000 in Shandong Province, the differences between the soil geochemical background values of 54 indexes in Jinan City and the soil in the whole province and the comprehensive geochemical class of soil quality were studied. [Results] The contents of C and Cao in Jinan soil was significantly higher than the background values of Shandong Province. The Cd, Cr, Cu, F, Ni, Sn, MgO, Cao and Na_(2)O contents and pH value were higher than the abundance of the A soil layer in China, but the nutrient index contents of Se, I and OrgC were lower than the national background values. The surface soil quality in the study area was generally good, with the sum of superior, good and medium accounting for 99.76% of the total area of the study area. The distribution area of poor soil was the least, accounting for only 0.24%, and it was scattered near industrial and mining enterprises in the urban area of Jinan City, Laiwu District, Gangcheng District and Zhangqiu District, which was closely related to human activities. [Conclusions] This study has practical guiding significance for improving land use efficiency.

Mean Square Numerical Methods for Initial Value Random Differential Equations

In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.

A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods

This paper mainly presents Euler method and fourth-order Runge Kutta Method (RK4) for solving initial value problems (IVP) for ordinary differential equations (ODE). The two proposed methods are quite efficient and practically well suited for solving these problems. In order to verify the ac-curacy, we compare numerical solutions with the exact solutions. The numerical solutions are in good agreement with the exact solutions. Numerical comparisons between Euler method and Runge Kutta method have been presented. Also we compare the performance and the computational effort of such methods. In order to achieve higher accuracy in the solution, the step size needs to be very small. Finally we investigate and compute the errors of the two proposed methods for different step sizes to examine superiority. Several numerical examples are given to demonstrate the reliability and efficiency.

INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS

Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN

A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.