巧用“区域法”解答函数问题

近几年在各地的中考试卷中，频繁出现已知一次函数与反比例函数两函数值的大小关系，求自变量取值范围的试题，该类试题多以选择题和解答题的形式出现．此类题目一般的设问方式为已知两函数值的大小关系，求解自变量z的取值范围．解题实质是求解反比例函数与一次函数图象的位置问题，并能正确地进行数与形的结合与转化．下面通过几道近几年各地的中考试题，谈谈这类问题的基本解法．

基于TOPSIS和灰色关联投影法的区域碳效率动态综合评价——以泛珠三角为例

为弥补传统碳效率评价偏向绝对量指标或者少数几个指标的单点式评价的不足,选取相对量指标,从经济、人口、福利多个维度并兼顾地区发展实际与公平原则,构建区域碳效率评价指标体系。将TOPSIS法与灰色关联投影分析相结合,并利用时间序列平均算子二次加权以实现对泛珠三角9省(自治区)2011—2020年碳效率的动态综合评价。静态与动态评价研究结果显示:该区域碳效率发展水平存在差异,其中海南省碳效率总体水平较高,为0.530;贵州省碳效率相对较低,为0.162;海南省比贵州省高出227%。福建省碳效率呈上升趋势,由2011年的0.327上升至2020年的0.498,增长了52.3%。研究认为,应该制定差异化减排策略、加大技术经费投入、增强社会福利、引进人才以实现低碳经济发展。

Electrical structure identification of deep shale gas reservoir in complex structural area using wide field electromagnetic method

To fully exploit the technical advantages of the large-depth and high-precision artificial source electromagnetic method in the complex structure area of southern Sichuan and compensate for the shortcomings of the conventional electromagnetic method in exploration depth,precision,and accuracy,the large-depth and high-precision wide field electromagnetic method is applied to the complex structure test area of the Luochang syncline and Yuhe nose anticline in the southern Sichuan.The advantages of the wide field electromagnetic method in detecting deep,low-resistivity thin layers are demonstrated.First,on the basis of the analysis of physical property data,a geological–geoelectric model is established in the test area,and the wide field electromagnetic method is numerically simulated to analyze and evaluate the response characteristics of deep thin shale gas layers on wide field electromagnetic curves.Second,a wide field electromagnetic test is conducted in the complex structure area of southern Sichuan.After data processing and inversion imaging,apparent resistivity logging data are used for calibration to develop an apparent resistivity interpretation model suitable for the test area.On the basis of the results,the characteristics of the electrical structure change in the shallow longitudinal formation of 6 km are implemented,and the transverse electrical distribution characteristics of the deep shale gas layer are delineated.In the prediction area near the well,the subsequent data verification shows that the apparent resistivity obtained using the inversion of the wide field electromagnetic method is consistent with the trend of apparent resistivity revealed by logging,which proves that this method can effectively identify the weak response characteristics of deep shale gas formations in complex structural areas.This experiment,it is shown shows that the wide field electromagnetic method with a large depth and high precision can effectively characterize the electrical characteristics of deep,low-resistivity thin layers in complex structural areas,and a new set of low-cost evaluation technologies for shale gas target layers based on the wide field electromagnetic method is explored.

Heat and mass transfer of a circular porous moist object located in a triangular shaped vented cavity

Heat and mass transfer of a circular-shaped porous moist object inside a two-dimensional triangle cavity is investigated by using finite element method.The porous object is considered to be a moist food sample,located in the middle of the cavity with inlet and outlet ports with different configurations of inlet/outlet ports.Convective drying performance is numerically assessed for different values of Reynolds numbers(between 50 and 250),dry air inlet temperature(between 40 and 80℃)and different locations of the port.It is observed that changing the port locations has significant impacts on the flow recirculaitons inside the triangular chamber while convective drying performance is highly affected.The moisture content reduces with longer time and for higher Reynolds number(Re)values.Case P4 where inlet and outlet ports are in the middle of the walls provides the most effective configuration in terms of convective drying performance while the worst case is seen for P1 case where inlet and outlet are closer to the corners of the chamber.There is a 192% difference between the moisture reduction of these two cases at Re=250,T=80℃ and t=120 min.

A FICTITIOUS DOMAIN METHOD FOR DIRICHLET PROBLEM AND ITS APPLICATIONS TO GENER ALIZED STOKES PROBLEM

This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.

MARS:A General Multilayer Area Router

Based on a ripped-up and rerouted methodology,a multilayer area detailed router is presented by using simulated evolution technique.A modified maze algorithm is also performed for the single net.

Optimal Boundary Control Method for Domain Decomposition Algorithm

To study the domain decomposition algorithms for the equations of elliptic type, the method of optimal boundary control was used to advance a new procedure for domain decomposition algorithms and regularization method to deal with the ill posedness of the control problem. The determination of the value of the solution of the partial differential equation on the interface——the key of the domain decomposition algorithms——was transformed into a boundary control problem and the ill posedness of the control problem was overcome by regularization. The convergence of the regularizing control solution was proven and the equations which characterize the optimal control were given therefore the value of the unknown solution on the interface of the domain would be obtained by solving a series of coupling equations. Using the boundary control method the domain decomposion algorithm can be carried out.

RESEARCH ON IMPERFECTION SENSITIVE REGION OF SINGLE-LAYER LATTICED DOMES

The concept of the imperfection sensitive region is given. The advanced stochastic imperfection method is used to research the imperfection sensitive region of single-layer latticed domes. Taking a K6 single-layer latticed dome with a diameter of 50 m as an example, its imperfection sensitive region is made up of the first 12 kinds of joints. The influence of the imperfections of support joints on the stability of the K6 single-layer latticed dome is negligible. Influences of the joint imperfections of the main rib and the secondary rib on the structural stability are similar. The initial deviations of these joints all greatly lower the critical load of the dome. Results show that the method can analyze the structural imperfection sensitive region quantitatively and accurately.

High-temperature thermal stability of C/C−ZrC−SiC composites via region labeling method

To investigate the thermal stability of ceramic-matrix composites,three kinds of C/C−ZrC−SiC composites with different Zr/Si molar ratios were synthesized by reactive melt infiltration.Employing region labeling method,the high-temperature thermal stability of the composites was systematically studied by changing the temperature and holding time of thermal treatment.Results show that the mass loss rate of low Si composites has a growth trend with increasing temperature,and a crystal transformation from β-SiC toα-SiC occurs in the composites.In the calibrated area,SiC phase experiences Ostwald ripening and volume change with location migration,while ZrC phase experiences a re-sintering process with diffusion.Moreover,it is found that increasing temperature has a more obvious effect on the thermal stability than extending holding time,which is mainly attributed to the faster diffusion rate of atoms.

Using Statistical Learning Algorithms in Regional Landslide Susceptibility Zonation with Limited Landslide Field Data

Regional Landslide Susceptibility Zonation(LSZ) is always challenged by the available amount of field data, especially in southwestern China where large mountainous areas and limited field information coincide. Statistical learning algorithms are believed to be superior to traditional statistical algorithms for their data adaptability. The aim of the paper is to evaluate how statistical learning algorithms perform on regional LSZ with limited field data. The focus is on three statistical learning algorithms, Logistic Regression(LR), Artificial Neural Networks(ANN) and Support Vector Machine(SVM). Hanzhong city, a landslide prone area in southwestern China is taken as a study case. Nine environmental factors are selected as inputs. The accuracies of the resulting LSZ maps are evaluated through landslide density analysis(LDA), receiver operating characteristic(ROC) curves and Kappa index statistics. The dependence of the algorithm on the size of field samples is examined by varying the sizes of the training set. The SVM has proven to be the most accurate and the most stable algorithm at small training set sizes and on all known landslide sizes. The accuracy of SVM shows a steadilyincreasing trend and reaches a high level at a small size of the training set, while accuracies of LR and ANN algorithms show distinct fluctuations. The geomorphological interpretations confirm the strength of SVM on all landslide sizes. Our results show that the strengths of SVM in generalization capability and model robustness make it an appropriate and efficient tool for regional LSZ with limited landslide field samples.

On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

Road traffic states estimation algorithm based on matching of regional traffic attracters

To effectively solve the traffic data problems such as data invalidation in the process of the acquisition of road traffic states,a road traffic states estimation algorithm based on matching of the regional traffic attracters was proposed in this work.First of all,the road traffic running states were divided into several different modes.The concept of the regional traffic attracters of the target link was put forward for effective matching.Then,the reference sequences of characteristics of traffic running states with the contents of the target link's traffic running states and regional traffic attracters under different modes were established.In addition,the current and historical regional traffic attracters of the target link were matched through certain matching rules,and the historical traffic running states of the target link corresponding to the optimal matching were selected as the initial recovery data,which were processed with Kalman filter to obtain the final recovery data.Finally,some typical expressways in Beijing were adopted for the verification of this road traffic states estimation algorithm.The results prove that this traffic states estimation approach based on matching of the regional traffic attracters is feasible and can achieve a high accuracy.

Application of Integration of Spatial Statistical Analysis with GIS to Regional Economic Analysis

This paper summarizes a few spatial statistical analysis methods for to measuring spatial autocorrelation and spatial association, discusses the criteria for the identification of spatial association by the use of global Moran Coefficient, Local Moran and Local Geary. Furthermore, a user-friendly statistical module, combining spatial statistical analysis methods with GIS visual techniques, is developed in Arcview using Avenue. An example is also given to show the usefulness of this module in identifying and quantifying the underlying spatial association patterns between economic units.

Multi-path routing algorithm in WSN using an improvedparticle swarm optimization

To slove the problems of constrained energy and unbalanced load of wireless sensor network(WSN)nodes,a multipath load balancing routing algorithm based on neighborhood subspace cooperation is proposed.The algorithm adopts the improved particle swarm optimization(PSO)algorithm,takes the shortest distance and minimum energy consumption as optimization target and divides the nodes in one-hop neighborhood near the base station area into different regions.Furthermore,the algorithm designs a fitness function to find the best node in each region as a relay node and forward the data in parallel through the different paths of the relay nodes.The simulation results show that the proposed algorithm can reduce energy consumption and average end-to-end delay,balance network load and prolong network lifetime effectively.

Trust Region Algorithm for a Class of Nonlinear Complementarity Problem

In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.

Application of different clustering approaches to hydroclimatological catchment regionalization in mountainous regions, a case study in Utah State

With respect to the different hydrological responses of catchments, even the adjacent ones, in mountainous regions, there are a great number of motivations for classifying them into homogeneous clusters. These motivations include prediction in ungauged basins(PUB), model parameterization, understanding the potential impact of environmental changes, transferring information from gauged catchments to the ungauged ones. The present study investigated the similarity of catchments through the hydro-climatological pure time-series of a 14-year period from 2001 to 2015. Data sets encompass more than 13,000 month-station streamflow, rainfall, and temperature data obtained from 27 catchments in Utah State as one of the eight mountainous states of the USA. The identification, analysis, and interpretation of homogeneous catchments were investigated by applying the four approaches ofclustering, K-means, Ward, and SOM(Self-Organized Map) and a newly proposed Wavelet-Entropy-based(WE-SOM) clustering method. By using two clustering evaluation criteria, 3, 5, and 6 clusters were determined as the best numbers of clusters, depending on the method employed, where each cluster represents different hydro-climatological behaviors. Despite the absence of geographic characteristics in input data matrix, the results indicated a regionalization in agreement with topographic characteristics. Considering the dependency of the hydrological behavior of catchments on the physiographic field aspects and characteristics, WE-SOM method demonstrated a more acceptable performance, compared to the other three conventional clustering methods, by providing more clusters. WE-SOM appears to be a promising approach in catchment clustering. It preserves the topological structure of data which can, as a result, be proofed in a greater number of clusters by dividing data into higher numbers of distinct clusters withsimilar altitudes of catchments in each cluster. The results showed the aptitude of wavelets to quantify the time-based variability of temperature, rainfall and streamflow, in the way contributing to the regionalization of diverse catchments.

Design of push-pull system to control diesel particular matter inside a dead-end entry

Diesel particulate matter （DPM） is considered to be carcinogenic after prolonged exposure. With more diesel- powered equipment used in underground mines, miners＇ exposure to DPM has become an increasing concern. This paper used computational fluid dynamics method to study the DPM dispersion in a dead-end entry with loading operation. The effects of different push-pull ventilation systems on DPM distribution were evaluated to improve the working conditions for underground miners. The four push-pull systems considered include： long push and short pull tubing; short push and long pull tubing, long push and curved pull tubing, and short push and curved pull tubing. A species transport model with buoyancy effect was used to examine the DPM dispersion pattern with unsteady state analysis. During the 200 s of loading operation, high DPM levels were identified in the face and dead-end entry regions. This study can be used for mining engineer as guidance to design and setup local ventilation, select DPM control strategies and for DPM annual training for underground miners.

Control of combustion area using electrical resistivity method for underground coal gasification

Underground coal gasification （UCG） is one of the clean technologies to collect heat energy and gases （hydrogen, methane, etc.） in an underground coal seam. It is necessary to further developing environ- mentally friendly UCG system construction. One of the most important UCG＇s problems is underground control of combustion area for efficient gas production, estimation of subsidence and gas leakage to the surface. For this objective, laboratory experiments were conducted according to the UCG model to iden- ti[y the process of combustion cavity development by monitoring the electrical resistivity activity on the coal samples to setup fundamental data for the technology engineering to evaluate combustion area. While burning coal specimens, that had been sampled from various coal deposits, electrical resistivity was monitored. Symmetric four electrodes system （ABMN） of direct and low-frequency current electric resistance method was used for laboratory resistivity measurement of rock samples. Made research and the results suggest that front-end of electro conductivity activity during heating and combusting of coal specimen depended on heating temperature. Combusting coal electro conductivity has compli- cated multistage type of change. Electrical resistivity method is expected to be a useful geophysical tool to for evaluation of combustion volume and its migration in the coal seam.

An Explicit-Implicit Predictor-Corrector Domain Decomposition Method for Time Dependent Multi-Dimensional Convection Diffusion Equations

The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.

Determination of Vitamins B2,B3,B6 and B7 in Corn Steep Liquor by NIR and PLSR

Corn steep liquor(CSL) is an important raw material that has high nutritional value and serves as a nitrogen source.Biotin in CSL is especially of great importance to fermentation.In order to develop a fast,versatile,cheap,and environmentally safe analytical method for quantifying vitamins B2(VB2),B3(VB3),B6(VB6) and B7(VB7) in CSL,the near-infrared spectroscopy(NIR) measurements of 66 samples(22 batches) of CSL were analyzed by partial least-square regression(PLSR).Multivariate models developed in the NIR regions showed good predictive abilities for VB2,VB3,VB6 and VB7.Results confirmed the probability of the multivariate spectroscopic approach as a replacement for expensive and time-consuming conventional chemical methods.