探究“数形结合”在解题中的应用

本文揭示了数学中有理数、应用题、不等式、函数及其图象、平面几何内容中所蕴藏着的数形结合思想，以及应用数形结合思想解决相关内容中考试题的思路。

RELATIONSHIP BETWEEN GROWTH AND MORPHOLOGY OF METARRHIZIUM ANISOPLIAE IN BIOTRANSFORMATION OF STEROID

The fermentation with mold metarrhizium anisopliae has been carried out to determine the relationship between mycelial morphology and growth.Like the biomass concentration,the mycelial morphology seems to be coupled to growth phases:the fractal dimension,a feature calculated from the morphological images,increases during the late lag phase and the early exponential phase,and culminates at a value near 2.4 at half of the exponential phase.This can be attributed to the marked change of rough and smooth pellet proportions during growth and the change can be well expressed by the fractal analysis of mycelial morphology.The mycelial morphology is also strongly related to the biotransformation activity:a mycelial sample was withdrawn from the culture to use for fractal analysis before the steroid substrate (16α,17α epoxy 4 pregnene 3,20 dione) was added;the higher fractal dimension corresponds to the higher conversion rate of steroid biotransformation.And the maximum of fractal dimension appeared prior to the maximum of biomass concentration.It is therefore possible to utilize the fractal dimension curve to supervise the fermentation process more timely and availably than to use the conventional biomass curve to do.

EFFECTIVENESS FACTOR FOR IRREGULAR CATALYST PELLET

The fractal theory was introduced into the gas solid catalytic reaction system to describe the influence of the surface irregularity of catalyst on the gas solid catalytic reaction.A fractal reaction diffusion model is proposed for irregular particles.Based on the shape characterization of the irregular particle,the mth order irreversible reactions are theoretically analyzed.A steady state equation of material balance and its solution as the concentration profile of reacting species are given for the reaction diffusion model for irregular particles.Meanwhile,the effectiveness factors are also expressed with fractal dimension.The results indicate that the higher the fractal dimensions,the higher the total reaction rate,and with the increase of the fractal dimension,the utilization factor of the catalyst is deeply increased.

Optimization of AZ80 magnesium alloy squeeze cast process parameters using morphological matrix

The squeeze cast process parameters of AZ80 magnesium alloy were optimized by morphological matrix. Experiments were conducted by varying squeeze pressure, die pre-heat temperature and pressure duration using L9（33） orthogonal array of Taguchi method. In Taguchi method, a 3-level orthogonal array was used to determine the signal/noise ratio. Analysis of variance was used to determine the most significant process parameters affecting the mechanical properties. Mechanical properties such as ultimate tensile strength, elongation and hardness of the components were ascertained using multi variable linear regression analysis. Optimal squeeze cast process parameters were obtained.

Electrochemical and corrosion behaviors of pure Mg in neutral 1.0% NaCl solution

The corrosion behaviors and corresponding electrochemical impedance spectroscopy（EIS） and polarization curves of pure Mg in neutral 1.0% NaCl solution were investigated.The fractal dimension of EIS at different time was studied.The corrosion process and EIS evolution are divided into three stages.In the initial stage,EIS is composed of two overlapped capacitive arcs,the polarization resistance and charge transfer resistance increase rapidly with immersion time,and the corrosion rate decreases.Then,two well-defined capacitive arcs appear,and the charge transfer resistance and corrosion rate remain stable.After a long immersion time,inductive component appears in a low frequency range,the charge transfer resistance decreases and the corrosion rate increases with the immersion time.The fractal dimension obtained from the time records of EIS seems to be a promising tool for the analysis of corrosion morphology because of its direct relationship with the metal surface.

Fractional distribution and risk assessment of heavy metal contaminated soil in vicinity of a lead/zinc mine

The pollution characteristics of Pb, Cd, Zn, Cu and Ni in soil of lead-zinc mining area were studied. The results indicate that the contamination degree followed the sequence of Cd〉Pb〉Zn〉Ni〉Cu and concentrations of Pb, Cd and Zn exceeded corresponding limits of the Chinese National Soil Environmental Quality Standard III. The soil was extremely polluted by Cd（Iego=5.26）, moderately to heavily polluted by Zn（Iego=2.38）, heavily to extremely polluted by Pb（Iego=4.13）. The results of BCR three-step sequential extraction procedure show that the active Cd, Pb and Zn were relatively high and might exert adverse effects on the plants grown in the soil, while Cu and Ni existed in soil with a relatively stable form. Potential ecological risk results indicate that soils were engaging in a high potential ecological risk by pollution of Cd and should be given rise to concern.

A Numerical Study on the Effects of Orography During the Landfall Process of Typhoon Haitang

The landfall process of typhoon Haitang which affected East China seriously was simulated by using the MM5 model and the track, intensity, precipitation and structure of typhoon were successfully reproduced. Then through the sensitive test, the effects of terrain were analyzed Results show that the irregular track during the period of typhoon passing through Taiwan and later landfalling at Fujian was in relation to the occurring and developing of orthographic impressed depression. The amount of rainfall was enhanced more than one time and the strength of typhoon was weakened 4 to 5 hPa. It is found that the effect of terrain on the structure of typhoon is limited at low level and is backward in space compared with the one at high level. In addition, the phenomenon that the equivalent temperature in the typhoon＇s moving direction inclines to the west on the eye of landfall may be concerned with the terrain.

Evolution of stresses in metal injection molding parts during sintering

The evolution of stresses due to inhomogeneity in metal injection molding （MIM） parts during sintering was investigated. The sintering model of porous materials during densification process was developed based on the continuum mechanics and thermal elasto-viseoplastic constitutive law. Model parameters were identified from the dilatometer sintering experiment. The real density distribution of green body was measured by X-ray computed tomography （CT）, which was regarded as the initial condition of sintering model. Numerical calculation of the above sintering model was carried out with the finite element soRware Abaqus, through the user-defined material mechanical behavior （UMAT）. The calculation results showed that shrinkages of low density regions were faster than those of high density regions during sintering, which led to internal stresses. Compressive stresses existed in high density regions and tensile stresses existed in low density regions. The densification of local regions depended on not only the initial density, but also the evolution of stresses during the sintering stage.

Study on the Biological Diversity of Nematode-trapping Fungi in Erhai Lake

[Objective]The research aimed to investigate the biological diversity of nematode-trapping fungi in the sediment of Erhai Lake.[Method]616 pieces of sediments were collected from Erhai Lake.The traditional classification and identification methods were used to isolate,purify and identify.[Result]3 genera and 22 species of nematode-trapping fungi were isolated.Arthrobotrys oligospora,A.musiformis and Dactylella leptospora were the dominant species,and their detection rates were 28.05%,16.04% and 8.92% respectively.By analyzing the diversity of nematode-trapping fungi in four seasons,it was found that the biological diversity was richer in summer,spring and autumn,and the diversity indexes were 2.59,2.47 and 2.34 respectively.The diversity index in winter was 1.48 and was lower.Species forming the adhesive nets were predominant;positive rate was 41.00%.[Conclusion]The rich nematode-trapping fungi resource existed in Erhai Lake,and its biological diversity had the seasonal variation characteristic.The nematode-trapping fungi which formed the viscous net were the dominant species in Erhai Lake.

Effects of AlN hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross using response surface methodology

The effects of aluminium nitride(AlN)hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross were studied using response surface methodology.The results show that the fractal dimensions of the residue can be significantly influenced by the AlN hydrolysis from secondary aluminium dross.The hydrolysis of AlN in the dross was spontaneous under temperatures of303-373K.The actual fractal dimensions of residue were significantly affected by the liquid-solid ratio(p<0.05)and changed from1.16to1.80,which accurately aligned with those from the calculations.Moreover,the fractal dimensions of residue were significantly affected by the interactions between hydrolysis temperature and hydrolysis time,liquid-solid ratio and hydrolysis time,respectively(p<0.01).The minimum fractal dimensions of the residue reached1.15under the optimized conditions,which included a hydrolysis temperature of30℃,liquid-solid ratio of5mL/g and hydrolysis time of10min.The results suggest that response surface methodology can guide in optimizing the conditions of AlN hydrolysis in order to obtain the minimum fractal dimensions of residue for improving the reutilization of the dross.

Spherical parametrization of genus-zero meshes by minimizing discrete harmonic energy

The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.

Isolation and characterization of YNTC-1,a novel Alicyclobacillus sendaiensis strain

A heterotrophic acidothermophilic bacterial strain,YNTC-1,was isolated from an acidic hot spring in Tengchong,Yunan,China.YNTC-1 grows at pH value of 1.5-8.0 and temperature of 40-70℃,with optimal pH and temperature at 3.0 and 55℃,respectively.The cells of the strain are in shape of short rod,with 1.0-1.2μm in length and 0.7-0.8μm in diameter,and with distinct spores at both poles of each cell.The predominant fatty acids in cellular membrane of the strain are C18:1ω7c.16s rRNA gene analysis reveals that this strain is closely related to Alicyclobacillus sendaiensis,with over 99%sequence similarity.Based on phenotypic and genotypic analyses,YNTC-1 is identified as a member of A.sendaiensis.Considering some important morphological and biochemical differences between strain YNTC-1 and A.sendaiensis ATCC 27009T,YNTC-1 may be proposed to be a novel subspecies of A.sendaiensis.However,this viewpoint has to be confirmed by further studies.Co-bioleaching of pyrite and chalcopyrite with strain YN22,Sulfobacillus thermosulfidooxidans,shows that strain YNTC-1 has no evident influence on bioleaching rates of these two sulphide minerals.

Characterization of pitting corrosion of 7A60 aluminum alloy by EN and EIS techniques

The pitting corrosion behaviors of 7A60 aluminum alloy in the retrogression and re-aging （RRA） temper were investigated by electrochemical impedance spectroscopy （EIS） and electrochemical noise （EN） techniques, and the microstructure and the second phase content of the alloy were observed and determined by scanning electron microscopy （SEM） and energy dispersive spectrometer （EDS）. The results show that there exist two different corrosion stages for 7A60 alloy in 3.5%NaCl solution, and the corrosion process can be detected by the appearance of EIS spectrum with two capacitive time constants and the wavelet fractal dimension D extracted from EN. SEM and EDS results also demonstrate that severe pitting corrosion in 7A60 alloy is mainly caused by electrochemical active MgZn2 particles, secondly by Al2MgCu and Mg2Si. Al7Cu2Fe particles make little contribution to the pitting corrosion of 7A60 alloy.

Equilibrium morphology of gas–liquid Janus droplets: A numerical analysis of buoyancy effect

In this article, a theoretical model for predicting the equilibrium morphology of gas–liquid Janus droplets was built. Based on this model, the effects of bubble radius and volume ratio on morphology change was systematically studied. The increase of bubble radius causes the two parts(bubble and oil drop) in Janus droplets tend to merge while the impact of volume ratio is complicated. When volume ratio increases, these two parts firstly tend to merge, then gradually separate. The accuracy of this model was verified by experimental results.

Parametric study of natural convection over horizontal annular finned tube

Natural convection heat transfer from annular finned tubes was studied numerically. Effects of fin spacing, temperature difference and tube diameter on flow pathlines and local heat transfer were also studied. It was shown that pathlines remain mostly circular for different geometries. Moreover, the contributions of fin periphery, fin side and bare tube to heat transfer were specified. It was shown that the heat transfer per unit area of fin periphery can be several times that of other parts. Moreover, in higher finspacing, the heat transfer from the bare tube can be more important than fin sides.

Soil Heavy Metal Pollution Around the Dabaoshan Mine,Guangdong Province,China

Soil contamination in the vicinity of the Dabaoshan Mine, Guangdong Province, China, was studied through determi- nation of total concentrations and chemical speciation of the toxic metals, Cu, Zn, Cd, and Pb, using inductively coupled plasma mass spectrometry. The results showed that over the past decades, the environmental pollution was caused by a combination of Cu, Zn, Cd, and Pb, with tailings and acid mine drainage being the main pollution sources affecting soils. Significantly higher levels （P ≤ 0.05） of Cu, Zn, Cd, and Pb were found in the tailings as compared with paddy, garden, and control soils, with averages of 1486, 2516, 6.42, and 429 mg kg^-1, respectively. These metals were continuously dispersed downstream from the tallings and waste waters, and therefore their concentrations in the paddy soils were as high as 567, 1 140, 2.48, and 191 mg kg^-1, respectively, being significantly higher （P ≤ 0.05） as compared with those in the garden soils. The results of sequential extraction of the above metals from all the soil types showed that the residual fraction was the dominant form. However, the amounts of metals that were bound to Fe-Mn oxides and organic matter were relatively higher than those bound to carbonates or those that existed in exchangeable forms. As metals could be transformed from an inert state to an active state, the potential environmental risk due to these metals would increase with time.

Thermal decomposition kinetics of Algerian Tamazarte kaolinite by thermogravimetric analysis

The decomposition kinetics of Algerian Tamazarte kaolinite(TK)was investigated using thermogravimetric analysis(TG).Differential thermal analysis(DTA)and TG experiments were carried out between room temperature and1400°C,at differentheating rates from10to40°C/min.The activation energies,measured by DTG from isothermal treatments usingJohnson-Mehl-Avrami(JMA)and Ligero methods and by non-isothermal treatments using Ozawa,Boswell and Kissinger methods,were around151and144kJ/mol,respectively.The Avrami parameter of growth morphology(indicating the crystallization mode)was found to be around1.57using non-isothermal treatments;however,when using isothermal treatments it is found to be equal to1.35.The numerical factor,which depends on the dimensionality of crystal growth,is found to be1.53using Matusita equation.Thefrequency factor calculated by the isothermal treatment is equal to1.55×107s-1.The results show that the bulk nucleation is followedby three-dimensional growth of metakaolinite with polyhedron-like morphology controlled by diffusion from a constant number ofnuclei.

Exponential synchronization of general chaotic delayed neural networks via hybrid feedback

This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model,which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator,and covers several well-known neural networks,such as Hopfield neural networks,cellular neural networks(CNNs),bidirectional associative memory(BAM)networks,recurrent multilayer perceptrons(RMLPs).By virtue of Lyapunov-Krasovskii stability theory and linear matrix inequality(LMI)technique,some exponential synchronization criteria are derived.Using the drive-response concept,hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria.Finally,detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

SYSTEM FOR AUTOMATIC GENERALIZATION OF TOPOGRAPHIC MAPS

With the construction of spatial data infi＇astructure, automated topographic map generalization becomes an indispensable component in the community of cartography and geographic information science. This paper describes a topographic map generalization system recently developed by the authors. The system has the following characteristics： 1） taking advantage of three levels of automation, i.e. fully automated generalization, batch generalization, and interactive generalization, to undertake two types of processes, i.e. intelligent inference process and repetitive operation process in generalization; 2） making use of two kinds of sources for generalizing rule library, i.e. written specifications and cartographers＇ experiences, to define a six-element structure to describe the rules; 3） employing a hierarchical structure for map databases, logically and physically; 4） employing a grid indexing technique and undo/redo operation to improve database retrieval and object generalization efficiency. Two examples of topographic map generalization are given to demonstrate the system. It reveals that the system works well. In fact, this system has been used for a number of projects and it has been found that a great improvement in efficiency compared with traditional map general- ization process can be achieved.

Numerical study on forming complex fitting body on end of integrated stainless steel pipe without welds

It is necessary to use the integrated stainless steel pipe having two fitting bodies without welds while train travelling at high speed. In order to form this type of integrated stainless steel pipe, the method of preforming combined finish forming process is developed. The preforming process is characterized by flaring combined upsetting for left fitting body which is like a flange, and is characterized by tube axial compressive process under die constraint for right fitting body which is like a double-wall pipe. The finite element simulations of the processes are carried out by software package DEFORM, and the results indicate that: 1) left or right fitting body can be formed by a two-step forming process without folding and under-filling defects; 2) by using two-step forming, strain and stress in left fitting body are larger than those in right fitting body, and deformation in right fitting body is more homogenous than the deformation in left fitting body; 3) two or more preforming steps may be needed for left fitting body considering the distributions of strain and stress.