如何提高初中数学学习能力

数学是中小学的重要工具学科,许多同学由于没有正确掌握数学学习方法,有的负担很重但不得要领;有的陷入题海,茫茫然不知所措.因此在学习数学的时候,我们必须学会如何掌握数学知识？掌握数学技能,发展数学能力,以及养成良好的数学心理品质,从掌握数学学习方法进而形成综合学习的能力.

Application of the theory of linear algebra on mathematical modeling practice

The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, mathematics has permeated from natural scientific technology to agricultural construction, from economic activities to all areas of social life. Generally, when the actual problem requires us to provide quantitative results of analysis, forecasting, decision making, control and other aspects for real object under study, we are often inseparable from the application of mathematics. Mathematical modeling is the key to this process, whose purpose is to make mathematics applied to social and social services, and using mathematics to solve practical problems is through mathematical models. When using mathematical methods to solve some practical problems, we usually first transfer practical problems into mathematical language, and then abstract them into a mathematical model.

A new accelerating algorithm for multi-agent reinforcement learning

In multi-agent systems, joint-action must be employed to achieve cooperation because the evaluation of the behavior of an agent often depends on the other agents’ behaviors. However, joint-action reinforcement learning algorithms suffer the slow convergence rate because of the enormous learning space produced by joint-action. In this article, a prediction-based reinforcement learning algorithm is presented for multi-agent cooperation tasks, which demands all agents to learn predicting the probabilities of actions that other agents may execute. A multi-robot cooperation experiment is run to test the efficacy of the new algorithm, and the experiment results show that the new algorithm can achieve the cooperation policy much faster than the primitive reinforcement learning algorithm.

Application of simple array method in one-way traffic synthetic asessment

One-Way Traffic synthetic assessing can not only determine the assessment method, but can also provide an opportunity for further study of road systems. Comparing three Road Traffic Planning methods, which are Value Analysis method, Simple Array method and Step Analysis method, this paper concludes that Simple Array method has one prominent merit, avoiding the complicated relationship of various factors and simplifying the complex problem. Therefore Simple Array method is firstly presented in this paper to be the assessing measure to assess the One-Way Traffic Planning project. Although this assessing method cannot wholly give way to man’s will, through consistently testing on qualitative factors and with the decision-making results of a multi-program, this method is still an effective method. Using an example of Harbin One-Way Traffic planning, with seven assessing indexes including economic benefit index, Simple Array method is applied to synthetically assessing the program. This fully reflects the general function of One-Way Traffic planning program and objectively evaluates the program. It also proves that, as the method of One-Way Traffic synthetic assessing, Simple Array method is rational and practical.

New autocorrelation topological indexes and their application in QSAR study

Considering the problems of classical structure parameters that existed in the study of quantitative structure activity relationship (QSAR). Two new groups of autocorrelation topological indexes V(t), E(t), (P(t)) and A(t), B(t), C(t), D(t) were developed on the basis of molecular topology and autocorrelation function in mathematics. The first group were obtained from Van der Waals volume, electronegativity and topological vertex degree;and the second group were obtained from the different combination of topological vertex degree.Corresponding softwares of ATIJP and ATITP have been developed for calculating these two new groups of indexes. Better results have been obtained from the application of these indexes in QSAR study.

Mathematic Model of Unsteady Penetration Mass Transfer in Randomly Packed Hollow Fiber Membrane Module

Based on the membrane-based absorption experiment of CO2 into water, shell-side flow distribution and mass transfer in a randomly packed hollow fiber module have been analyzed using subchannel model and unsteady penetration mass transfer theory. The cross section of module is subdivided into many small cells which contains only one hollow-fiber. The cross sectional area distribution of these cells is presented by the normal probability density distribution function. It has been obtained that there was a most serious non-ideal flow in shell side at moderate mean packing density, and the large amount of fluid flowed and transferred mass through a small number of large voids. Thus mass transfer process is dominated by the fluid through the larger void area. The mass transfer process in each cell is described by the unsteady penetration theory. The overall mass transfer coefficient equals to the probability addition of the mean mass transfer coefficient in each cell. The comparisons of the values calculated by the model established with the empirical correlations and the experimental data of this work have been done.The predicted overall mass transfer coefficients are in good agreement with experimental data.

Hysteresis model of magnetostrictive actuators and its numerical realization

This paper presents two numerical realization of Preisach model by Density Function Method (DFM) and F Function Method (FFM) for a giant magnetostrictive actuator (GMA). Experiment and simulation showed that FFM is better than DFM for predicting precision of hysteresis loops. Lagrange bilinear interpolation algorithm is used in Preisach numerical realization to enhance prediction performance. A set of hysteresis loops and higher order reversal curves are predicted and experimentally verified. The good agreement between the measured and predicted curves shows that the classical Preisach model is effective for modelling the quasi-static hysteresis of the GMA.

Evaluation System and Actualization of Selection Supplier in ERP Enterprise

Suppliers become an essential factor of enterprise competitiveness. The analytic hierarchy process is a kind of Decision-making method with the combination of quantity and quality. This paper presents the evaluation system of supplier selection, using Analytic Hierarchy Process (AHP) method to select the optimum supplier in Enterprise Resource Planning (ERP) enterprise. In order to reduce factor of manmade and increase exactitude, this paper innovates to use a real database in ERP system for evaluation. It also gives an example that one enterprise selects supplier.

A Generalized Hankel Transformation Derived by Parametrized Entangled State Representations

Using the parametrized entangled state representations we have found a generalized Hankel transformationwith the integral kernel being a combination of Bessel functions.This generalized Hankel transformation corresponds tothe appropriate quantum mechanical representation transformation.

New Operator Identities and Combinatorics Studied by Virtue of IWOP Technique

Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an essential role in realizing our goal.

APPLICATION OF REMOTE SENSING TECHNOLOGY TO POPULATION ESTIMATION

This paper attempts to explore a new avenue of urban small-regional population estimation by remote sensing technology, creatively and comprehensively for the first time using a residence count method, area (density) method and model method, incorporating the application experience of American scholars in the light of the state of our country. Firstly, the author proposes theoretical basis for population estimation by remote sensing, on the basis of analysing and evaluating the history and state quo of application of methods of population estimation by remote sensing. Secondly, two original types of mathematical models of population estimation are developed on the basis of remote sensing data, taking Tianjin City as an example. By both of the mathematical models the regional population may be estimated from remote sensing variable values with high accuracy. The number of the independent variables in the latter model is somewhat smaller and the collection of remote sensing data is somewhat easier, but the deviation is a little larger. Finally, some viewpoints on the principled problems about the practical application of remote sensing to population estimation are put forward.

Fuzzy prediction and experimental verification of road surface cleaning rate by pure waterjets

The cleaning parameters affecting cleaning rate using pure waterjets to clean road surface was researched. A mathematical model for predicting cleaning rate was established using fuzzy mathematical method. A fuzzy rule base character-izing the relationship between input and output parameters was built through experiments. The prediction of cleaning rate was achieved under the condition of given input parameters by rule-based fuzzy reasoning. The prediction results were analyzed through experimental verification.

Attitude, Secondary Schools and Student Success in a Tertiary Mathematics Unit

There is a consensus in the literature that mathematical ability contributes to student success in tertiary education. More importantly, mathematical skills are necessary when successfully completing mathematics- and/or science-based degrees. Social sciences such as psychology and economics require statistical skills which also require knowledge of mathematics. Even business students, such as marketing and accounting students need the necessary mathematical skills to successfully complete their degrees at university. This paper suggests that student success in a core business subject is dependent on their mathematical aptitude, attitude, and type of secondary schooling whether government or non-government schools. There is urgency for universities to recognize that high failure rates are due to insufficient mathematics exposure in secondary schooling and remedial classes might not be enough. Specifying a minimum （maths, e.g., two units） requirement for entry and/or providing bridging programs to ensure students have the necessary basic mathematical skills would increase student success in quantitative units.

Improving displayed resolution in convolution reconstruction of digital holograms

In digital holographic microscopy, when the object is placed near the COD, the Fresnel approximation is no longer valid and the convolution approach has to be applied. With this approach,the sampling spacing of the reconstructed image plane is equal to the pixel size of the COD. If the lateral resolution of the reconstructed image is higher than that of the COD,Nyquist sampling criterion is violated and aliasing errors will be introduced. In this Letter,a new method is proposed to solve this problem by investigating convolution reconstruction of digital holograms. By appending enough zeros to the angular spectrum between the two FFT＇s in convolution reconstruction of digital holograms,the displayed resolution of the reconstructed image can be improved. Experimental results show a good agreement with theoretical analysis.

An Algorithm for Extracting Contour Lines Based on Interval Tree from Grid DEM

This paper proposes a new algorithm for determining the starting points of contour lines. The new algorithm is based on the interval tree. The result improves the algorithm＇s efficiency remarkably. Further, a new strategy is designed to constrain the direction of threading and the resulting contour bears more meaningful information.

Numerical Simulation of Dynamic Performance of the Molten Carbonate Fuel Cell

A three dimension of dynamic mathematical model of the molten carbonate fuel cell is established,in which the heat generation, mass transfer and electrochemical characteristics are described. The performance of the fuel cell including the distributions of the temperature and the velocity is predicted numerically. Then the experimental data including the output performance of the fuel cell generation system and the temperature distributions are compared. The numerical results are in agreement with the experiment results.

Error assessment of laser cutting predictions by semi-supervised learning

Experimentation data of perspex glass sheet cutting, using CO2 laser, with missing values were modelled with semi-supervised artificial neural networks. Factorial design of experiment was selected for the verification of orthogonal array based model prediction. It shows improvement in modelling of edge quality and kerf width by applying semi-supervised learning algorithm, based on novel error assessment on simulations. The results are expected to depict better prediction on average by utilizing the systematic randomized techniques to initialize the neural network weights and increase the number of initialization. Missing values handling is difficult with statistical tools and supervised learning techniques; on the other hand, semi-supervised learning generates better results with the smallest datasets even with missing values.

Mechanical response features and failure process of soft surrounding rock around deeply buried three-centered arch tunnel

Due to the extreme complexity of mechanical response of soft surrounding rock(SR) around a tunnel under high geostatic stress conditions, the integration of physical and numerical modeling techniques was adopted. Based on the similarity theory, new composite-similar material was developed, which showed good agreement with the similarity relation and successfully simulated physico-mechanical properties(PMP) of deep buried soft rock. And the 800 mm×800 mm×200 mm physical model(PM) was conducted, in which the endoscopic camera technique was adopted to track the entire process of failure of the model all the time. The experimental results indicate that the deformation of SR around a underground cavern possessed the characteristics of development by stages and in delay, and the initial damage of SR could induce rapid failure in the later stage, and the whole process could be divided into three stages, including the localized extension of crack(the horizontal load(HL) was in the range of 130 k N to 170 k N, the vertical load(VL) was in the range of 119 k N to 153.8 k N), rapid crack coalescence(the HL was in the range of 170 k N to 210 k N, the VL was in the range of 153.8 k N to 182.5 k N) and residual strength(the HL was greater than 210 k N, the VL was greater than 182.5 k N). Under the high stress conditions, the phenomenon of deformation localization in the SR became serious and different space positions show different deformation characteristics. In order to further explore the deformation localization and progressive failure phenomenon of soft SR around the deeply buried tunnel, applying the analysis software of FLAC3 D three-dimensional explicit finite-difference method, based on the composite strain-softening model of Mohr-Coulomb shear failure and tensile failure, the calculation method of large deformation was adopted. Then, the comparative analysis between the PM experiment and numerical simulation of the three centered arch tunnels was implemented and the relationship of deformation localization and progressive failure of SR around a tunnel under high stress conditions was discussed.

Numerical simulation on influence of jet angle on jet's characteristics in flowing ambient fluid

Based on the stress-algebraic model, the turbulent buoyant jet with variable density was studied by the relation between density and concentration. A simple expression for buoyancy coefficient was proposed. The governing equations of turbulent buoyant jet with variable density were closed by introducing the expression of β and the relation between density and concentration. Numerical results for the jet axis with density difference agree well with experimental ones. By finite volume method, the 2 - D vertical jet＇s flow field with different jet angles was studied. The analysis of the relation among the vortex center, the position of separation point and jet angles shows that the circumfluenee field is the largest when the jet angle is 90°. The area turbulent kinetic energy ka is proposed and the relationship between mixing intensity and jet angles is analyzed based on it. Results show that the jet angle of is the optimum condition for jet water mixing with environment water;and the reduced rate of difference between the centerline density of jet and the density of ambient water is the largest at the jet angle of 90°.

Mass Transfer During Osmotic Dehydration Using Acoustic Cavitation

An experimental study on intensifying osmotic dehydration was carried out ina state of nature and with acoustic cavitation of different cavitating intensity (0.5A, 0.7A and0.9A) respectively, in which the material is apple slice of 5mm thickness. The result showed thatacoustic cavitation remarkably enhanced the osmotic dehydration, and the water loss was acceleratedwith the increase of cavitating intensity. The water diffusivity coefficients ranged from1.8x10^(-10)m^2·s^(-1) at 0.5A to 2.6x10^(-10)m^2·s^(-1) at 0.9A, and solute diffusivitycoefficients ranged from 3.5x10^(-11) m^2·s^(-1) at 0.5A to 4.6X10^(-11)m^2·s^(-1) at 0.9A. On thebasis of experiments, a mathematical model was established about mass transfer during osmoticdehydration, and the numerical simulation was carried out. The calculated results agree well withexperimental data, and represent the rule of mass transfer during osmotic dehydration intensified byacoustic cavitation.