“平方法”在解题中的应用

用平方处理数学问题的方法叫做平方法。平方法在数学各个领域中都有广泛的应用，掌握了平方法对提高解能力是大有好处的，那么平方法有何应用呢？

“平方法”活化数学变换

一、平方法活化平方根变换 “两边平方”，棘手的平方根问题会迎刃而解．

Band Structure of Three-dimensional Phononic Crystals

By using the plane-wave-expansion method, the band structure of three-dimension phononic crystals was calculated, in which the cuboid scatterers were arranged in a host with a face-centered-cubic （FCC） structure.The influences of a few factors such as the component materials, the filling fraction of scatterers and the ratio （RHL） of the scatterer＇s height to its length on the band-gaps of phononic crystals were investigated.It is found that in the three-dimension solid phononic crystals with FCC structure, the optimum case to obtain band-gaps is to embed high-velocity and high-density scatterers in a low-velocity and low-density host. The maximum value of band-gap can be obtained when the filling fraction is in the middle value. It is also found that the symmetry of the scatterers strongly influences the band-gaps. For RHL＞1, the width of the band-gap decreases as RHL increases. On the contrary, the width of the band-gap increases with the increase of RHL when RHL is smaller than 1.

FLOW FIELD ANALYSES OF PLANE JET AT LOW REYNOLDS NUMBERS USING LATTICE BOLTZMANN METHOD

A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.

A Fast Method to Compute the Inertia of Bezout Matrix and Its Application

In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.

FITTING CORRECTION METHOD OF RING ARTIFACTS FOR RECONSTRUCTING CONE-BEAM CT IMAGES

In high-resolution cone-beam computed tomography （CBCT） using the flat-panel detector, imperfect or defect detector elements cause ring artifacts due to the none-uniformity of their X-ray response. They often disturb the image quality. A dedicated fitting correction method for high-resolution micro-CT is presented. The method converts each elementary X-ray response curve to an average one, and eliminates response inconsistency among pixels. Other factors of the method are discussed, such as the correction factor variability by different sampling frames and nonlinear factors over the whole spectrum. Results show that the noise and artifacts are both reduced in reconstructed images

Calculation of Valence Subband Structures for Strained Quantum-Wells by Plane Wave Expansion Method Within 6×6 Luttinger-Kohn Model

The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.

Phase field method simulation of faceted dendrite growth with arbitrary symmetries

A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.

Study on the evaluation index system and evaluation method for self-elevating drilling unit design

In the process of designing self-elevating drilling unit, it is important, yet complicated, to use comparison and filtering to select the optimum scheme from the feasible ones. In this research, an index system and methodology for the evaluation of self-elevating drilling unit was proposed. Based on this, a multi-objective combinatorial optimization model was developed, using the improved grey relation Analysis （GRA）, in which the analytic hierarchy process （AHP） was used to determine the weights of the evaluating indices. It considered the connections within the indices, reflecting the objective nature of things, and also considered the subjective interests of ship owners and the needs of designers. The evaluation index system and evaluation method can be used in the selection of an optimal scheme and advanced assessment. A case study shows the index system and evaluation method are scientific, reasonable, and easy to put into practice. At the same time, such an evaluation index system and evaluation method will be helpful for making decisions for other mobile platforms.

Spectral Shift of π→π^＊ Transition for p-Nitroaniline Based on a New Expression of Nonequilibrium Solvation Energy

According to the nonequilibrium solvation theory studies, a constrained equilibrium principle is introduced and applied to the derivations of the nonequilibrium solvation energy, and a reasonable expression of the spectral shift of the electronic absorption spectra is deduced. Furthermore, the lowest transition of p-nitroaniline （pNA） in water is investigated by time-dependent density functional theory method. In addition, the details of excited state properties of pNA are discussed. Using our novel expression of the spectral shift, the value of -0.99 eV is obtained for π→π^＊ transition in water, which is in good agreement with the available experimental result of -0.98 eV.

An Improved Level Set Approach to the Simulation of Drop and Bubble Motion

An improved level set approach for computing the incompressibletwo-phase flow with significantly de- formed free interface ispresented. The control volume formulation with the semi-implicitmethod for pressure-linked equations consistent (SIMPLEC) algorithmincorporated is used to solve the governing equations on a staggeredgrid. Several improvements concerning the computational grid,interface update, reinitialization procedure etc. are tested Andfound to be effective in promoting the convergence and numericalstability.

A level set based segmentation approach for point-sampled surfaces

Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces is proposed, which is based on the level set evolution scheme. To segment the model so as to align the patch boundaries with high curvature zones, the driven speed function for the zero level set inside narrow band is defined by the extended curvature field, which approaches zero speed as the propagating front approaches high curvature zone. The effectiveness of the proposed approach is demonstrated by our ex- perimental results. Furthermore, two applications of model segmentation are illustrated, such as piecewise parameterization and local editing for point-sampled geometry.

Modal identification to non-stationary random excitation based on wavelet transform and co-integration theory

A kind of method of modal identification subject to ambient excitation is presented. A new synthesis stationary signal based on structural response wavelet transform and wavelet coefficient processes co-integration is obtained. The new signal instead of structural response is used in identifying the modal parameters of a non- stationary system, combined with the method of modal identification under stationary random excitation-the NExT method and the adjusted continuous least square method. The numerical results show that the method can eliminate the non-stationarity of structural response subject to non-stationary random excitation to a great extent, and is highly precise and robust.

Effect of Long-Term Fertilization on Organic Nitrogen Forms in a Calcareous Alluvial Soil on the North China Plain

In order to illustrate the change of nitrogen （N） supply capacity after long-term application of manure and chemical fertilizer, as well as to properly manage soil fertility through fertilizer application under the soil-climatic conditions of the North China Plain, organic N forms were quantified in the topsoil with different manure and chemical fertilizer treatments in a 15-year fertilizer experiment in a Chinese calcareous alluvial soil. Soil total N （TN） and various organic N forms were significantly influenced by long-term application of chemical fertilizer and manure. TN, total hydrolysable N, acid-lnsoluble N, amino acid N and ammonium N in the soil increased significantly （P 〈 0.05） with increasing manure and fertilizer N rates, but were not influenced by increasing P rates. Also, application of manure or N fertilizer or P fertilizer did not significantly influence either the quantity of amino sugar N or its proportion of TN. Application of manure significantly increased （P 〈 0.05） hydrolysable unknown N, but adding N or P did not. In addition, application of manure or N fertilizer or P fertilizer did not significantly influence the proportions of different soil organic N forms.

A Dynamic Load Balancing Method of Cloud-Center Based on SDN

In order to balancing based on data achieve dynamic load flow level, in this paper, we apply SDN technology to the cloud data center, and propose a dynamic load balancing method of cloud center based on SDN. The approach of using the SDN technology in the current task scheduling flexibility, accomplish real-time monitoring of the service node flow and load condition by the OpenFlow protocol. When the load of system is imbalanced, the controller can allocate globally network resources. What＇s more, by using dynamic correction, the load of the system is not obvious tilt in the long run. The results of simulation show that this approach can realize and ensure that the load will not tilt over a long period of time, and improve the system throughput.

Nitrogen Recommendations for Summer Maize in Northern China Using the N_min Test and Rapid Plant Tests

A field experiment with a split-plot design was carried out at Dongbeiwang Farm in Beijing Municipality to establish reliable N fertilizer recommendation indices for summer maize (Zea mays L.) in northern China using the soil Nmin (mineral N) test as well as the plant nitrate and SPAD (portable chlorophyll meter readings) tests. The results showed that Nmin sollwert (NS) 60 kg N ha-1 at the third leaf stage and N rate of 40 to 120 kg N ha-1 at the tenth leaf stage could meet the N requirement of summer maiz…

Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method

A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.

Numerical simulation of single bubble rising in shear-thinning fluids by level set method

The behavior of single bubble rising in quiescent shear-thinning tlmds was lnvestlgateO numerically by level set metnoa. number of bubbles in a large range of Reynolds number and Eotvos number were investigated including spherical, oblate and spherical. The bubble shape and drag coefficient were compared with experimental results. It is observed that the simulated results show good conformity to experimental results over a wide range of Reynolds number. In addition, the detailed flow field based on the reference coordinate system moving with the bubble is obtained, and the relationship among flow field, bubble shape and velocity is discussed.

Evaluation of the possible slip surface of a highly heterogeneous rock slope using dynamic reduction method

A new method, the dynamic reduction method(DRM) combined with the strain-softening method, was applied to evaluate the possible slip surface of a highly heterogeneous rock slope of the Dagangshan hydropower station in Southwest China.In DRM, only the strength of the failure elements is reduced and the softening reduction factor K is adopted to calculate the strength parameters. The simulation results calculated by DRM show that the further slip surface on the right slope of the Dagangshan hydropower station is limited in the middle part of the slope, while both SRM(strength reduction method) and LEM(limit equilibrium method) predict a failure surface which extends upper and longer. The observations and analysis from the three recorded sliding events indicate that the failure mode predicted by DRM is more likely the scenario.The results in this study illustrate that for highly heterogeneous slopes with geological discontinuities in different length scales, the proposed DRM can provide a reliable prediction of the location of the slip surface.