Spatio-temporal variation of water conservation and its impact factors on the southern slope of Qilian Mountains

The ecology of Qilian Mountains has been seriously threatened by uncontrolled grazing and wasteland reclamation. This study examined the ecological changes on the southern slope of Qilian Mountains in China from the perspective of water conservation by classifying different clusters of water conservation functional areas to efficiently use limited human resources to tackle the water conservation protection problem. In this study, we used Integrate Valuation of Ecosystem Services and Tradeoffs(InVEST) model to estimate water conservation and analyzed the factors that influence the function. The results of this study include:(1) from 2000 to 2015, the water conservation of the southern slope of Qilian Mountains generally showed an increasing trend, and the total water conservation in 2015 increased by 42.18% compared with that in 2000.(2) Rainfall, fractional vegetation cover(FVC), and evapotranspiration have the most significant influence on the water conservation of the study area. Among them, water conservation is positively correlated with rainfall and FVC(P<0.05) and negatively correlated with evapotranspiration(P<0.05).(3) The importance level of water conservation functional areas gradually increases from northwest to southeast, and the region surrounding Menyuan Hui Autonomous County in the southeast of the southern slope of Qilian Mountains is the core water conservation functional area. And(4) the study area was divided into five clusters(Cluster Ⅰ–Cluster Ⅴ) of water conservation, with the areas of Clusters Ⅰ through Ⅴ accounting for 0.58%, 13.74%, 41.23%, 32.43%, and 12.01% of the whole study area, respectively.

Auto-Bcklund transformation and exact solutions of Wick-type stochastic Burgers equation

Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.

Effect of Silicon-on-Insulator Substrate on Residual Strain in 3C-SiC Films

One group of SiC films are grown on silicon-on-insulator （SOI） substrates with a series of silicon-overlayer thickness. Raman scattering spectroscopy measurement clearly indicates that a systematic trend of residual stress reduction as the silicon over-layer thickness decreases for the SOI substrates. Strain relaxation in the SiC epilayer is explained by force balance approach and near coincidence lattice model.

Solitary Waves for Cubic-Quintic Nonlinear Schroedinger Equation with Variable Coefficients

The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients （vCQNLS） are derived with the aid of a set of subsidiary high-order ordinary differential equations （sub-equations for short）. The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.

Compositions,Proportions,and Equilibrium Temperature of Coexisting Two-feldspar in Crystalline Rocks

Compositions, proportions, and equilibrium temperature of coexisting two-feldspar in crystalline rocks are of great importance to classification in petrography and interpretation of petrogenesis. Crystalline rocks are usually composed of 4-6 minerals （phases）, depending on their independent chemical components and the equilibrium temperature of crystallizations. In general, number of mineral phases can be determined by the ＂Phase Rule＂. According to the mass balance principle, bulk composition of coexisting two-feldspar could be evaluated from the bulk chemistry of a rock, provided that the compositions of the coexisting mafic mineral phases containing calcium, sodium, and potassium oxides are determined, e.g., by microprobe analysis. The compositions, proportions, and temperature of two-feldspar in equilibrium can thus be simultaneously resolved numerically from bulk composition of the rock, by incorporating the activity/composition relations of the ternary feldspars with the mass balance constraints. Upon the numerical approximation method presented in this paper, better-quality, internally consistent data on feldspar group could usually be obtained, which would be expected more realistic and accurate in consideration of thermodynamic equilibria in the system of crystalline rocks, as well as bulk chemistry of a rock and the composing minerals.

Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.

Analysing chaos in fractional-order systems with the harmonic balance method

In this paper, the fractional-order Genesio-Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results.

Exact Solutions of Discrete Complex Cubic Ginzburg-Landau Equation and Their Linear Stability

The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.

Detailed balance limit efficiency of silicon intermediate band solar cells

The detailed balance method is used to study the potential of the intermediate band solar cell （IBSC）, which can improve the efficiency of the gi-based solar cell with a bandgap between 1.1 eV to 1.7 eV. It shows that a crystalline silicon solar ceil with an intermediate band located at 0.36 eV below the conduction band or above the valence band can reach a limiting efficiency of 54% at the maximum light concentration, improving greatly than 40.7% of the Shoekley-Queisser limit for the single junction Si solar cell. The simulation also shows that the limiting efficiency of the silicon-based solar cell increases as the bandgap increases from 1.1 eV to 1.7 eV, and the amorphous Si solar cell with a bandgap of 1.7 eV exhibits a radiative limiting efficiency of 62.47070, having a better potential.

A Simplified Hirota Method and Its Application

By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.

Computer Implementation of the Passage Arrangement for Plate-Fin Heat Exchangers According to Local Balance Principle

A two-step method for stacking arrangement of passages in multistream plate-fin heat exchanger is proposed. The first step (predict step) is to initialize the arrangement according to a local-balance principle, and the second step (correct step) is to resadust the arrangement according to the results of differential computation of the temperature distribution. The computer implementation process of the local balance principle is described in detail and three examples are illustrated to show the feasibility of this principle. A subroutine program is provided to facilitate the reader to adopt this principle.

Exact Solitary Wave Solutions of Nonlinear Evolution Equations with a Positive Fractional Power Term

The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.

The Underground Sewer Drainage Design Analysis of Highway Subgrade Under Evaporation

According to the water balance principle, the expression of the phreatic table is established by considering evaporation and considering evaporation ＆ drainage respectively. The law of phreatic table variation under the combined effects of considering evaporation ＆ drainage is obtained. Based on Newton-Raphson iterarive method, calculation and analysis programs are done to solve the first order implicit differential equation of the sewer drainage calculation considering phreatic evaporation. The calculation results show： after considering phreatic evaporation, in the need of reducing the same height of phreatic, the sewer spacing is appropriately larger than the case which didn＇t consider the affection of phreatic evaporation; the phreatic drop speed in both effects of evaporation and drainage is faster than the case of just considering the drainage effect. Phreatic evaporation has a great influence to the subgrade sewer distance, phreatic evaporation needs to be considered in the subgrade drainage design.

Multi-parameter Tikhonov Regularization—An Augmented Approach

We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.