2001 Vol. 27, No. 1

Display Method:
Study of Storage Effect of Super-Strength Steel 37SiMnCrNiMoV
CHEN Yong-lai, CHEN Liang-shan, DONG Xiu-zhong
2001, 27(1): 1-4.
Abstract:
Super-strength steel 37SiMnCrNiMoV is widely used in aerospace and astrospace because of the high specific strength. However the service life of the pressure vessel made of steel 37SiMnCrNiMoV will be decreased after long-term storage in air environment, the phenomenon is called storage effect. Stress corrosion crack test is used to evaluate the storage effect. Effects of storage time and hydrogen-elimination treatment after storage in the buffer solution on the stress corrosion crack time are studied. Results show that the substance of storage effect is a process, in which hydrogen from the environment is induced to material and is gathered at the stress-peak fields by second internal stress, then making the microcracks produced in the tip of the inclusions.
Study on Evaluation of Localized Corrosion of 2024T3 Aluminum Alloy with EIS
HU Yan-ling, LI Di, GUO Bao-lan
2001, 27(1): 5-8.
Abstract:
Alternating immersion test was applied to 2024T3 Al alloy. Electrochemistry Impedance Spectroscopy (EIS) by time domain method was performed on the specimens. Statistic method was also used to deal with data because localized corrosion is a stochastic phenomenon. The results show that the reciprocal of low frequency impedance (1/Rd) was consistent with the Gumbel distribution law. The dynamic variation curve of 1/Rd vs. test period was somewhat of S shape which must be divided into two stages to treat the data, i.e. pitting and intergranular corrosion (Sigmoidal curve) and exfoliation (linear line). Compared with the maximum corrosion depth data (dm) measured by optical microscope, it can be concluded that 1/Rd and dm have similar statistical distribution and time-dependent growth. Quantitative relation between the 1/Rd and dm has been established. According to the relation, EIS by time domain method can enable a nondestructive, quantitative and quick evaluation for localized corrosion of 2024 Al alloy.
Study on Character of Shape Memorizing of EEA/DCP
Lü Zhi, JI Shou-zhen, LI Bing-quan, XU Xiu-cheng
2001, 27(1): 9-11.
Abstract:
The Character of Shape Memorizing of EEA/DCP was systematically studied. The results show that the concentration of DCP has great influence upon Shape-recovering rate, Shape-fixing rate, Shape-recovering temperature, Tensile strength and elongation at break. Furthermore, through the experiments, we can know that when the concentration of DCP is 0.5%, the system of EEA/DCP has the relatively excellent shape memorial character. Additionally, the Dynamical Thermomechanicl Analysis was also taken, that as DCP increasing, the module in room temperature declines and the module in high temperature increases is reflected. And also from the analysis, the high-elastically-module platform of the Shape Memorizing of EEA/DCP is indicated.
Sum-Difference Unified Design of Monopulse Ring-Focus Antenna
CHENG Zhen, Lü Shan-wei, JIANG Xin-fa
2001, 27(1): 12-15.
Abstract:
The relatively poor performance of difference channel of a monopulse ring-focus antenna is accounted for, suitable aperture distribution functions are recommended, formulae of feed difference pattern needed are presented and sum-difference unified design method is put forward. To testify the theoretical method, the authors take a 3.5m C-band monopulse shaped ring-focus antenna with dual-polarization as an example. By using the presented method, the gain difference between the sum channel and the different channel is reduced from 6.5dB to 4.2dB , and the separation angle of the apexes of the different pattern of the antenna from 1.9° to 1.4°. Therefore, the normalized slope of difference pattern arrives at 1.4 with a particular monopulse feed.
Interferometric SAR Phase Noise Reduction
XU Hua-ping, ZHOU Yin-qing, CHEN Jie, LI Chun-sheng
2001, 27(1): 16-19.
Abstract:
The phase noise suppression methods applied on the interferogram of interferometric synthetic aperture radar(INSAR) are studied.Multilook average approach(low pass linear filter) is discussed,and the new concept of range and azimuth critical look number used in multilook approach is proposed and its calculation formulas are deduced.The modified neighborhood field average filter,modified median filter and mode filter are analyzed,and a new practical method,which combines multilook average and nonlinear filter to reduce noise in the wrapped phase map,is presented.At the end of this paper,the characteristics of these approaches are compared and the experimental results by processing ERS-1/2 data are used to confirm that the method is more effective in suppressing noise in the interferogram of INSAR.
Research on Real-Time Performance of Bandwidth Allocation for LTPB Network
ZHOU Qiang, XIONG Hua-gang, LUO Zhi-qiang
2001, 27(1): 20-23.
Abstract:
The problem of guaranteeing real-time message transmission in LTPB network, linear token passing bus, has been studied. Bandwidth allocation for LTPB aims at real-time message transmission, and the key parameter, the minimum amount of time used for real-time message transmission in unit time, is an important factor to the property and validity of the bandwidth allocation. Having found out a defect in current real-time performance analysis method, we propose a concept of "the worst case situation", develop a reasonable model, get an important result in real-time performance analysis for LTPB network, and establish the analytic foundation to seek the better bandwidth allocation scheme.
Data Fusion of ADS-SSR in Air Traffic Management
ZHANG Xue-jun, ZHANG Qi-shan
2001, 27(1): 24-27.
Abstract:
The application of Secondary Surveillance Radar (SSR) and Automatic Dependent Surveillance (ADS) have been applied in Air Traffic Management (ATM) system widely, especially in terminal domain. The characteristic and limitation of SSR and ADS in civil aviation are analyzed. The different affections of basic ADS contracts and extended ADS contracts to tracking precision are also deeply studied. A model and algorithm of the data fusion of ADS-SSRin civil aviation are presented for improving the tracking precision. The numerical simulation shows that this model and algorithm are effective. It is helpful for ATM system to have a continuous and reliable surveillance in a whole flight.
Multi-Resolution Multi-Model Tracking Algorithm Based on Model-Mixing
FAN Tao, YANG Chen-yang, LI Shao-hong, MAO Shi-yi
2001, 27(1): 28-31.
Abstract:
A model-mixing approach has been introduced into the original multi-resolution multi-model algorithm and a new maneuvering target tracking algorithm based on multi-resolution multi-model method is proposed. The original algorithm adopts hard switching multi-model approach in the multi-resolution frame. It can improve the performance in the nonmaneuvering segment, but it remains the inherent defaults of the hard switching method. The interactive multi-model algorithm can avoid this default because of model-mixing, but its performance isn-t good during non-maneuvering. The new algorithm combines the advantages of the original multi-resolution algorithm and that of the interactive multi-model algorithm. It can not only solve the problems existed in the original algorithm, but also achieve to a better performance than IMM algorithm during the entire tracking procedure.
An Overview of Rotor Blades Optimum Design for Helicopter Vibration Reduction
XIANG Jin-wu, GUO Jun-xian, ZHANG Xiao-gu
2001, 27(1): 32-35.
Abstract:
Helicopter vibration level has been a problem for many helicopter configurations. Due to the great practical importance of the problem a considerable amount of research has been aimed at various aspects of vibration reduction and control. This paper presents the results of a survey of rotor blades optimum design of reducing vibration by modifying blade properties so as to reduce vibratory hub shears and moments, and thereby reduce the vibration level experienced in the fuselage. Important categories relative to this optimum design problems are considered: the integration of various disciplines and the optimum design objectives; structural and aerodynamic analysis model of the rotor blades for optimum design; numerical optimization and sensitivity analysis technology; and the further development on this subject. This paper is intended to put this design method in a proper perspective from the viewpoint of high performance helicopter design.
Study on Reliability Testing of Four Redundancy Servo Control System
WANG Shao-ping, LI Pei-qiong, HE Jian-jun
2001, 27(1): 36-39.
Abstract:
Because four redundancy servo control system is designed by limited life and high reliability, reliability testing base on exponential distribution is difficult to achieve the effect, which need large samples and long testing time. According to the failure mechanism of four redundancy servo control system, this paper studies the reliability testing method, presents a reliability testing and statistical method based on Weibull process. Based on three assumptions, this paper deals with the operational point in the end of life with the linear method. Considering the transient failure rate of Weibull process in little time as the failure rate, this paper contacts the exponential distribution reliability testing method with the Weibull process method. Application of four redundancy servo control stem indicates that the Weibull process reliability testing method can reduce the testing time and samples, and it provides an effective method to high reliability mechatronic products.
Research on Tactic to Delivery Guided Bomb with Laser
PENG Ke-mao, SHEN Gong-zhang, WEN Chuan-yuan
2001, 27(1): 40-43.
Abstract:
The tactic to delivery guided bomb with laser is researched, while the laser bundle is transmitted by the fighter itself, that is to delivery guided bomb with laser in non-wing-level and to egress in turning. The major is to egress in turning, which synthesizes tactical requirement to shoot the target with the laser bundle and motive to egress. It can efficiently improve survival ability of the fighter to delivery bombs in maneuvering motion and to egress in curve. The condition to satisfy the two requirements is proposed with a simplified particle point model of the fighter and through analysis on the process that the fighter egresses in turning while continuously shoot the target with laser bundle. Simulations on the mission process prove that the proposed condition can satisfy the tactical requirements to delivery guided bomb with laser and to egress in turning while the fighter transmits laser bundle to shoot the target itself.
Numerical Simulation for Bent-Swept Blade in Designing Civilian Fan
LI Qiu-shi, LI Ling, LU Ya-jun
2001, 27(1): 44-47.
Abstract:
It present a numerical method, based on 3-D incompressible steady time-averaged N-S equation and K-ε turbulence model equation, using in aerodynamic designing for high efficient civilian fan. The code was adopted limited volume method and was under the non-orthogonal curve coordinate by means of famous SIMPLE. Through calculating and analyzing, it is proved that the bent-swept blade can control aerodynamic allocation, and has a higher efficiency, a nice flow field with less second flow loss when compared with a straight blade.
Affection of Valve Shape on Air Flow of S.I. Engine
LI Feng, ZHAO Qing, LUO Yun-jun
2001, 27(1): 48-50.
Abstract:
Air motion inside the cylinder of engine plays an important role in the processes of fuel spray and combustion, determine the economy, power output, exhaust emissions and combustion noise of the engine. The multidimensional simulation of the flow in cylinder can give the flow field information in detail and economically, show the effects of geometric and flow parameters to the combustion character, compare the combustion effect of different schemes, provide a effect research methods in engine development. It was simulated of air motion in a 4 valve S.I. engine in this thesis, the code used was a the KIVA3 code and the code was compiled by ALE method. Air motion inside the cylinder of 4 valve S.I. engine with two different length valve, and the affection of valve shape on the air flow and tumble flow strength in cylinder was analyzed. The calculated results indicates, the tumble flow was produced by the use of 4 valve S.I. engine, the tumble flow will be different with different shape valve, and the tumble flow strength with long valve will be stronger than that of short valve. These research results can provide some useful information for the design of S.I. engine.
Experimental Studies on Leading-Edge Vortex Breakdown and Control of Flow over 76°/40° Double Delta Wing
WANG Jin-jun, LIU Ji-ying, XUE Qi-zhi
2001, 27(1): 51-53.
Abstract:
The flow visualization techniques has been used to investigate the effects of trailing-edge jets on the leading-edge vortex breakdown and its control of flow over a 76°/40° double Delta wing. The experimental results indicate that the trailing-edge jets can delay the leading-edge vortex breakdown efficiently, and this delay increases with the angle of attack. The trailing-edge jets can greatly improve the asymmetrical characteristics of the leading-edge vortex breakdown at large angle of attack, and the possible occurrence of "rock" phenomenon may be overcome. In addition, the trailing-edge jets may weaken or even eliminate the mixing phenomenon of the leading-edge vortex, which is in advantage of the flight control of aircraft.
Aerodynamic Analysis of Grid Fin-Body Configurations
SHEN Xia-ling, WANG Li-li
2001, 27(1): 54-56.
Abstract:
Aerodynamic analysis is made for grid fin-body configurations in subsonic and supersonic flow. Vortex lattice formulation has been used in predicting the aerodynamic characteristics for grid fin in subsonic flow. An infinite line doublet and imaging vortices inside the body are employed to model body upward and wing-body carry over load.In supersonic flow, the grid fin is assumed to locate in the cross flow of the body, the wing panel theory is used for calculating the aerodynamic interfere factor of the grid fin produced by the body. The aerodynamic characteristics of some grid fin-body configurations have been calculated, the theory agreed quite well with the experimental data.
Stealth Effect Calculation of Aircraft on Condition of Electrical Jamming
ZHANG Yun-fei, ZHANG Kao, HE Qing-zhi
2001, 27(1): 57-61.
Abstract:
It was formulated that the calculation method of stealth performance of aircraft on condition of stand-off jamming and self-screening jamming. They were discussed the influence of various type of jamming and RCS on the stealth performance. The conclusions were made that the effective radiation power of 10kW stand-off jamming and 1kW self-screening jamming would notably reduce the exposed region with equal detection probability and the detection probability. The effect would better when combined with the RCS reduction technology.
Analytical and Experimental Research of Ball-Bar Impact under Low Velocity
LI Min, ZHU De-chao
2001, 27(1): 62-65.
Abstract:
The analytical and experimental investigations of low speed impact of a ball on a bar were reported. The impact tests, which were carried out by means of laser vibrometer, verified the Hertz contact theorem. It was also shown that, the analysis of low speed impact problem can really be reformulated as the analysis of conventional dynamic response problem. Hence, such kind of problems can be calculated by using MSC/NASTRAN program and its special data card. The agreement between the experimental and analytical results is very well. Furthermore, some technical problems related to the impact measurement by using laser vibratormeter were clarified through this relatively fundamental impact test, thus providing the further more complicated structural impact test with experience and technology.
Analysis and Application of Forced Vibration of Piezoceramic
CHEN Wei-min, GUAN De, ZHU De-chao, LI Min
2001, 27(1): 66-68.
Abstract:
The formula of the in-plane forced vibration of piezoelectric materials plates is presented based upon the fundamental piezoelectric equations, then a direct method of measuring the piezoelectric constant of piezoelectric materials is developed by combining the response formula of the in-plane forced vibration of piezoelectric materials plates with the resonance test. The resonance test is carried out by using laser vibratormeter that has high measurement accuracy and do not need sensors, made the test more convenient. Comparing with the traditional method of measuring the piezoelectric constant, the present method has much more advantages. The accuracy of the measuring results is also raised due to the reduction of intermediate links.
A General Theory for Elastic Damage
TANG Xue-song, JIANG Chi-ping, ZHENG Jian-long
2001, 27(1): 69-72.
Abstract:
On the strict basis of irreversible thermodynamics, a general theory for elastic damage is developed. The approximations and limitations of the classical stress-strain constitutive equation based on the strain equivalence hypothesis are argued theoretically. The relations and differences of the existing various definitions of damage (single scalar, double scalar, second rank and fourth rank tensor damage variables) are expounded for the first time. The theoretical rigor of continuum damage mechanics is improved.
Finite Element Analysis of Shape Memory Alloys Reinforced Composite Laminate
YE Ning, LI Zheng-neng
2001, 27(1): 73-75.
Abstract:
The intelligent structure was made up by which the shape memory alloys (SMAs) be embedded in composite laminate.Applied by the loads or the variation of the temperature,the SMAs would change the distributing of the stress and strain of the structure and the shape of the structure.Because of the non-linear brought with the large displacement of the SMAs,a model is calculated and analyzed with the finite element which used for conducting large deformation analysis of laminated shells,the effect of SMAs is changed for a equivalent mechanical load.The accurate result is obtained.
Integrated Aerodynamic-Stealth Optimal Design of Aircraft Configuration Parameters
LI Tian, WU Zhe, LI Jing
2001, 27(1): 76-78.
Abstract:
Basing on the aerodynamic and RCS objectives,the geometrical parameters of the wing and tail planform and few geometrical parameters of fuselage are optimized.According to the requirements of the forth generation of fighter,the desirable and acceptable values of the objectives and constraints were determined. And according to the theory of fuzzy optimization,the satisfactory function of each objectives and constraints were determined. Then, 5 fuzzy optimization model are established by the application of different combinations of general satisfactory function and fluctuant weights or constant weights.So the designers can make choice according to their different design concepts and purposes.
Optimized BLAS and Its Effect on Performance of Parallel Programs
LONG Xiang, LI Zhong-ze, CHEN Jin
2001, 27(1): 79-82.
Abstract:
It is the trend of using SMP board as the compute node of a high performance system. The benefits of multithreading is discussed firstly and the BLAS3 is rewritten to get higher performance on a Dual Pentium II system. To investigate the relation between the performance of a single compute node and the entire parallel system, the SUMMA(Scalable Universal Matrix Multiplication Algorithm) is taken as an instance of our research works afterwards. The result demonstrates that the higher the performance of a SMP compute node is, the more sensitive to the capability of the SAN(System Area Network) the performance of the whole parallel system is.
On Design and Implementation of NET-RAM
LONG Xiang, LIAO Hong-bin, GAO Xiao-peng
2001, 27(1): 83-87.
Abstract:
A NVM(Network Virtual Memory) system treats all the memories distributed on the network as the memory of a single node so that an application can take the advantage of much larger memory resources on the network. This is especially suitable for such applications which are not time-sensitive but need a large amount of memories. A method of implementing a NVM system by simplifying the distributed shared memory management, which is used in our SNOW clustering system, is introduced. After giving the concept of network virtual memory, we describe the architecture of a network virtual system-NET-RAM and expatiate the structure of soft-cache. The prototype of NET-RAM is tested and the result is analyzed. Finally, we discuss our feature work to improve the NET-RAM system.
Non-Newtonian Effects on Ferrofluid Lubrication
CHI Chang-qing
2001, 27(1): 88-92.
Abstract:
The load carrying capacity of the ferrofluid lubricating films can be controlled directly by means of the applied magnetic field, since the viscosity of the ferrofluid increases in the case of magnetic field. The experimental investigations showed that the ferrofluid is an non-Newtonian fluid: it behaves simultaneously as a Binghamoplastic and as a pseudoplastic. The non-Newtonian behavior of the ferrofluid is dependent both on oreintation and on intensity of the applied magnetic field. The constitutive equation of the ferrofluid can be expressed as τ(H,D)= τs(H)+η1(H)D+η2(H)D2. It is possible that the "solid" cores appear and adhere to the surfaces of bearing, since the ferrofluid has a yield shear stress τs(H). The pseudoplastic behaviors of the ferrofluid have an effect on the condition for core occurrence. The cross section C0 of a pure Couette flow in the ferrofluid lubricated bearing is different from that in the ordinary Binghamoplastic lubricated bearing. The solutions of load carrying capacity and friction force of plane slider lubricated with ferrofluid are given as an actual example.
On Performance of Ferrofluid-Lubricated Plane Sliderin Uniform Magnetic Field
CHI Chang-qing
2001, 27(1): 93-96.
Abstract:
The calculated results show that the performance of the ferrofluid-lubricated plane sliders is different obviously from the performance of plane sliders lubricated with Newtonian fluid or Bingham plastic. The yield stress causes the attached cores and increases the load carrying capacity of plane slider. In the case of a low velocity lubrication, the high applied magnetic field strength is of benefit to the load carrying capacity, since it can increase viscosity of a ferrofluid and can cause the attached cores in the lubricating film. When the adhered cores occur, the magnitude of optimum film thickness ratio of a plane slider lubricated with ferrofluid is much larger than 2.2 and increases with increasing applied magnetic field strength. In the case of a high speed lubrication, it is possible that no adhered cores appear and the film thickness ratio of 2.2 is advisable to reach a maximum load carrying capacity. The friction coefficient of a ferrofluid-lubricated plane slider is larger under the condition of a high magnetic field strength and a high shear rate.
Using Genetic Algorithms to Solve Sub-Link-s Parameters of Flexible Link
WU Li-cheng, LU Zhen, YU Shou-qian, ZHENG Hong
2001, 27(1): 97-100.
Abstract:
A genetic algorithm of real number type is used to solve the equations of the sub-link-s parameters when modeling a flexible robot manipulator with the sub-links approach. It is the key of successfully using the sub-links approach that how to solve the equations of the sub-link-s parameters. However, the set of equations is high non-linear. The general solving approach is hardly fit for it because of lack of initial vector that enough close to the solution. Some approach possessed the ability of large-scale convergence is failing too because of the singularity of the Jacobian matrix of the equations. The proposed approach based on genetic algorithm can smoothly solve the equations by optimization method that replace some complicated symbolic calculation by solving simple algebra equations. Then the validity and high efficiency of the proposed approach are showed by a practical example.
Simulation Analysis on Kinematics and Force of Hexapod
GUO Zu-hua, CHEN Wu-yi, CHEN Ding-chang
2001, 27(1): 101-104.
Abstract:
Hexapod is one example of a parallel connection mechanism. This paper simulates the movement of a hexapod, analyses the velocity and acceleration of the movable platform and the force acted on the rods. Inside a specific workspace, the cure of velocity and acceleration of the platform and the force of the rods when the platform moves is drawn by a simulation program. According to the results, the factors that influence the veracity and stability of the platform's movement are discovered. The relation between the maximum force of rods and maximum acceleration of platform indicates the mechanism has good dexterity and the platform can move with high velocity and acceleration. The results also provide reference for the control of the mechanism.
FEM Design of Cruciform Biaxial Tensile SpecimenBased on Limit Strain Analysis
FEM Design, YU Yong, WAN Min
2001, 27(1): 105-108.
Abstract:
A cruciform biaxial tensile specimen with chamfer in arm and center region is designed by the method of finite element numerical simulation in order to realize the complex loading using cruciform biaxial tensile test and study the limit strains of sheet metals under the complex strain loading paths. Finite element calculated model is established. An optimum shape of specimen is obtained on the basis of the following conditions: the stress distribution in the center region is uniform and large deformation is obtained easily during stretching of the specimen. Different strain paths in the center region can be realized by adjusting the velocity boundary conditions. This paper provides the basis for the study of sheet forming limit under the complex strain loading paths.
Fabrication of SIMOS/SOI CMOS IC-s
WEN Meng-quan
2001, 27(1): 109-111.
Abstract:
SOI-SIMOX(Silicon On Insulator-Separation by Implanted Oxygen) materials were formed by large dose(1.5×1018/cm2) oxygen ion implantation into p-type (100) Si wafers at energy of 170keV and annealing in nitrogen at 1300℃ for 6 h.The carriers in the top silicon layers of the SIMOX are reversed from P-type into N-type.The reversion is resulted from the residual oxygen atoms in the top Si layers,which play the role of donors and over-compensate the acceptors in the virgin p-type Si.The oxygen donor ionization energy is 0.15eV.The MOSFET-s and CMOS triple 3-input NAND gate circuits(CC4023) were fabricated on SIMOS/SOI materials.The CMOS/SIMOX process is briefly introduced.
A New Associative Memory System via Tchebycheff Interpolation
YAN Shou-feng, LIU Zhong-kan, MAO Shi-yi
2001, 27(1): 112-116.
Abstract:
A new high-order associative memory system via Tchebycheff interpolation is proposed. It offers the error-free approximation to multi-variable polynomial functions with arbitrarily given order. Tchebycheff interpolation nears to the best uniform approximation, this ensures theoretically the approximation precision as a whole to multi-variable continuous functions with arbitrarily given order. Particularly, comparing with other AMS, it also has distinctive advantage in approximation to some discontinuous functions such as rectangular pulse function. Theoretic analysis and numerical simulations have shown that the proposed TI-AMS has the advantages in much less computational, high-precision of learning, fast convergence rate and much less required whole memory size. It has great potential in the application areas of picture compression, pattern recognition, and controller implementation for high-precision real-time intelligent control.
Synchronous Motion of Center Symmetry Plane Three Connecting Rod
LEI Jin-zhi, GUAN Ke-ying
2001, 27(1): 117-120.
Abstract:
Center symmetry plane three connecting rod is studied. This model can be used to describe the movement of satellite with symmetry solar pane in outer space with weak gravitation. Since the system is nonintegrable, in general, the movement of such system is complicated. The Lagrange motion equation of the system is established, and synchronous movement is studied.Exact solution of synchronous movement is presented and movement disciplinarian is studied. It proved that under certain condition, it exist periodic motion. Results will be helpful to analysis the complicity of near synchronous movement of the system.
Research on Method of Circuits Tolerance Analyses Based EDA Technology
SHI Jun, KANG Rui
2001, 27(1): 121-124.
Abstract:
The basic theory of tolerance analysis technology is discussed. The technology precept of circuits tolerance analyses and design based on the EDA software PSpice is given. The methods of Monte Carlo analyses and worst-case analyses are discussed in detail. Three aspects of the application fortolerance analyses, circuits parameter deflection, effecting of temperature and degradation, are studied. An example of Monte Carlo analyses is given, the upper limit value and the lower limit value of system performance reliability are computed. The effecting between system performance and variance of circuit component parameter is analyzed by running multiple simulation. Feasibility of the precept is proved by the analyses of the example.