基于跨学科背景下的小学数学品质课堂构建

《课程标准》强调对核心素养培养,并以此为核心来提炼和概括课程目标。文章以学科融合为核心,在数学教学基础上探索“学科+”的跨学科融合教学范式,为开展跨学科教学提供切入口和具体抓手,帮助教师深度促进各学科内容、方法、思想等要素的真正融合,推动小学数学与其他学科有效融合。

Mathe matical model and calculation for heat transfer during condensation on surfaces of corrugated plates

A mathematical model was established for condensation on surfaces of verticalcorrugated plates based on the mechanism of heat transfer enhancement to thin down the liquid filmdue to surface tension effect between corrugated plate surfaces and liquid films. The relative heattransfer coefficients of condensation on corrugation plates were calculated in contrast withequivalent vertical plane ones. The heat transfer enhancement effects for the main geometricparameters such as pitch, height, corrugation angle, tilt angle, and fillet radii of corrugationswere analyzed to guide the optimization of corrugation structure for application. A two-scalecorrugation is suggested, which can compromise both the enhanced heat transfer effect and adequatecross section area for flows, and it makes the heat transfer coefficient 1 to 2 times more than thatof an equivalent plane one.

NUMERICAL SIMULATION OF SUPERSONIC AXISYMMETRIC FLOW OVER MISSILE AFTERBODY WITH JET EXHAUST USING POSITIVE SCHEMES

Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.

Structural Carpentry in Qing Dynasty-A Framework for the Hierarchically Modularized Chinese Timber Structural Design

This article, by using mathematical expressions, offers a scientific framework for understanding how the grading system of Qing′s structural carpentry determines the design and construction in the grand style timber architecture.The Qing′s grand style timber structure, which is ready for prefabrication and assembly, is extremely hierarchical oriented and significantly standardized. The general procedure in designing a grand style timber structure is to start with the grade that defines the basic module (dou kou); next comes with the number of bracket set (cuan), the number of longitudinal bays and the number of purlins which affect its plan and cross section; thirdly choose a roof type that determines its longitudinal section and the facade as well. A series of formulae are conducted to help depict the layout, cross sectional roof curvature and special longitudinal treatments in 4 sloped and 9 spined roofs respectively.

Time-depth conversion of transient electromagnetic method used in coal mines

Accuracy of time-depth conversion in data processing of transient electromagnetic prospecting always affects the accu- rate positioning of water bodies in coal mines. In order to improve the accuracy of time-depth conversion, we established a mathe- matical model of time-depth conversion for a transient electromagnetic method based on the theory of "double smoke ring effect" of full space transient electromagnetic field transmission. Using a 3-layer as well as a 4-layer geo-electric model for roadway floors, we performed the time-depth conversion of theoretical curves of apparent resistance varying over time. In these curves, the depth corresponding to extreme value points is nearly the same as the depth of a geo-electric model. The position of water body deter- mined by our time-depth conversion method agrees well with the result of borehole drilling, indicating that the established time-depth conversion model can clearly improve the accuracy of spatial positioning of water bodies in coal mines.

MATHEMATICAL MODEL FOR ACCESS MODE OF CONTENTION-COLLISION CANCELLATION IN A STAR LAN

I type system model of CCCAM(Contention-Collision Cancellation Access Mode) is studied through mathematical modelling and simulation. There are two innovations: (1) in the process of mathematical modelling, the instance of 'serving customers unsuccessfully' is taken into account; (2) the time at which customers depart after having been served successfully are chosen to be the embedded point, thereby 'free period' is introduced reasonably. So the mathematical modelling and analysis result in this paper are significant for application of wire star LAN and wireless star LAN.

Kinematic Analysis and Trajectory Planning of J-Groove Welding Robot

This paper introduces the complexity and particularity of tube-sphere intersection weld(J-groove weld) and establishes the mathematical model of tube-sphere intersection trajectory.Based on the characteristics of J-groove welds,the computational process of welding gun orientation is first simplified.Then the kinematic algorithm of a welding robot is obtained according to screw theory and exponential product formula.Finally,Solidworks and SimMechanics are employed to simulate the kinematics of the welding robot,which proves the feasibility of the kinematic algorithm.

A Novel Exponential Kinetic Model for Casein Tryptic Hydrolysis to Prepare Active Peptides

The kinetics of casein tryptic hydrolysis to prepare activepeptides was investigated. Taking into account the reaction mechanismincluding single substrate hydrolysis, irreversible enzymeinactivation, and substrate inhibition, a set of exponentialequations was established to characterize the enzymatic hydrolysiscurves. The verification was carried out by a series of experimentalresults and indicated that the average regressive error was less than5/100. According to the proposed kinetic model, the kinetic constantsand thermodynamic constants of the reaction system were alsocalculated.

Study on the Grey Polynomial Geometric Programming

In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.

A New Type Machine of Mixing-molding for Polyblends

This paper introduces a new type machine for polyblends with excellent mixing capabilities of internal mixer and continuous molding character of extruder.The machine includes two functions - mixing and extrusion molding that have been composed together by rational design,so a tandem production mode - "batch + continuous" are opened up.The mathematical model of continuous mixing molding was established and verified availably by experimental research.The main physical mechanical property of vulcanizate,which had met national waterproof material standard,verified the machine practicability.The essential difference from other similar type machines is that this machine is not only suitable in producing granular and powder rubbers but also lumpish rubbers.

Effect of heterogeneity on mechanical and acoustic emission characteristics of rock specimen

The influence of heterogeneity on mechanical and acoustic emission characteristics of rock specimen under uniaxial compress was studied with numerical simulation methods.Weibull distribution function was adopted to describe the mesoscopic heterogeneity of rocks.The failure process of heterogeneous rock specimen under uniaxial loading was simulated using FLAC 3D software.Five schemes were adopted to investigate the influence of heterogeneity.The results demonstrate that as the homogeneity increases,the peak strength and brittleness of rocks increase,and the macro elastic modulus improves as well.Heterogeneity has great influence on macro elastic modulus and strength when the homogeneity coefficient is less than 20.0.The volume expansion is not so obvious when the homogeneity increases.As the homogeneity coefficient increases the acoustic emissions modes change from swarm shock to main shock.When the homogeneity coefficient is high,the cumulative acoustic emission events-axial strain curve is gentle before the rock failure.The numerical results agree with the previously numerical results and earlier experimental measurements.

Orthogonal moment based texture segmentation

Texture segmentation is a necessary step to identify the surface or an object in an image. We present a Legendre moment based segmentation algorithm. The Legendre moments in small local windows of the image are computed first and a nonlinear transducer is used to map the moments to texture features and these features are used to construct feature vectors used as input data. Then an RBF neural network is used to perform segmentation. A k-mean algorithm is used to train the hidden layers of the RBF neural network. The training of the output layer is the supervised algorithm based on LMS. The algorithm has been successfully used to segment a number of gray level texture images. Compared with the geometric moment-based texture segmentation, we can reduce the error rates using orthogonal moments.

Seepage-stress coupling constitutive model of anisotropic soft rock

To provide a seepage-stress coupling constitutive model that can directly describe the seepage-stress coupling relationship, a series of one-dimensional seepage-stress coupling tests on two kinds of soft rock (argillaceous siltstone and brown mudstone) were performed by using an MTS-815.02 tri-axial rock mechanics test system, with which the stress-strain curves according to the seepage variation were obtained. Based on the experimental results and by employing Hooke's law, the formulation of the coefficient of strain-dependent permeability was presented and introduced to establish a coupling model. In addition, the mathematical expression and the incremental formulation for coupling model were advanced, in which five parameters that can be respectively determined by using the experimental results were included. The calculated results show that the proposed coupling model is capable of simulating the stress-strain relationship with considering the seepage-stress coupling in the nonlinear elastic stage of two kinds of soft rock.

Numerical forecasting surge in a piping of compressor shops of gas pipeline network

This paper presents a method of forecasting stable operation of gas compressor unit (GCU) centrifugal supercharger (CFS) installed on a piping of compressor shops servicing gas pipelines. The stability of superchargers operation is assessed in relation to the phenomenon of surge. Solution of this problem amounts to the development and numerical analysis of a set of ordinary differential equations. The set describes transmission of gas through a compressor shop as a fluid dynamics model with lumped parameters. The proposed method is oriented to wide application by specialists working in the gas industry. The practical application of this method can use all-purpose programming and mathematical software available to specialists of gas companies.

Variation in downwelling diffuse attenuation coefficient in the northern South China Sea

The diffuse attenuation coefficient for downwelling irradiance(Kd(λ)) is an important parameter for ocean studies.Based on the optical profile data measured during three cruises in the northern South China Sea in autumn from 2003 to 2005,variations in the Kd(λ) spectra were analyzed.The variability of Kd(λ) shows much distinct features in both magnitude and spectra pattern,it is much higher in coastal waters than that of open oceanic waters;and the blue-to-green(443/555) ratio of Kd(λ) tends to increase with chlorophyll a concentration([Chl-a]) from open ocean to coastal waters.These characteristics can be explained most by the increase of aw+p(443)/aw+p(555) with [Chl-a].In short waveband,the relation between Kd(λ)-Kw(λ) and [Chl-a] can be well described by a power law function,indicating the large contribution of phytoplankton to the variations in Kd(λ).As for the spectral model of the diffuse attenuation coefficient,there are good linear relationships between Kd(490) and Kd(λ) in other wavelengths with own slope and intercept of a linear functions in the spectral range 412-555 nm.Kd(490) is well correlated with the spectral ratio of remote sensing reflectance;and should enough measurement data are given,this empirical algorithm would be used in the Kd(λ) retrieval from ocean color satellite data.The variation in Kd(λ) provides much useful information for us to study the bio-optical property in the northern South China Sea.

Epidemic Spread in Networks Induced by Deactivation Mechanism

We have studied the topology and epidemic spreading behaviors on the networks in which deactivation mechanism and long-rang connection are coexisted. By means of numerical simulation, we find that the clustering coefficient C and the Pearson correlation coefficient r decrease with increasing long-range connection μ and the topological state of the network changes into that of BA model at the end （when μ = 1）. For the Susceptible-Infect-Susceptible model of epidemics, the epidemic threshold can reach maximum value at μ = 0.4 and presents two different variable states around μ= 0.4.

The foundation and analysis of polarized magnetic system’s unified mathematical model in aerospace electromagnetic relay

Polarized magnetic system has a series of features, such as small volume, light weight, low power consumption, high sensitivity, quick movement and so on, widely used in the products of the military aerospace electromagnetic relay. The typical polarized magnetic system has mainly four structures and its simplified equivalent magnetic circuits model is the base of the design of the electromagnetic relay with permanent magnet. In the past, the analysis method that people used was difficult to build the unified mathematical models, which divided the work gap magnetic flux into "permanent magnet flux" and "electromagnetic flux". Based on the analysis method of the work gap magnetic voltage, this paper founds the unified mathematical model of the polarized magnetic system and divides the attractive torque into permanent magnet torque, polarized torque and electromagnetic torque through the energy balance formula. It analyses the influence of permanent magnet sizes on permanent magnet torque, polarized torque and electromagnetic torque through the energy balance formula and the conclusions can direct the design of aerospace electromagnetic relay with permanent magnet.

Hydrodynamic Performance of Multiple-Row Slotted Breakwaters

This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.

Shallow Water Modal Evolution Due to Nonlinear Internal Waves

Acoustic modal behavior is reported for an L-shape hydrophone array during the passage of a strong nonlinear internal wave packet. Acoustic track is nearly parallel to the front of nonlinear internal waves. Through modal decomposition at the vertical array, acoustic modes are identified. Modal evolution along the horizontal array then is examined during a passing internal wave. Strong intensity fluctuations of individual modes are observed before and during the internal waves packet passes the fixed acoustic track showing a detailed evolution of the waveguide modal behavior. Acoustic refraction created either uneven distribution of modal energy over the horizontal array or additional returns observable at the entire L-shape array. Acoustic ray-mode simulations are used to phenomenologically explain the observed modal behavior.

Mathematical model of absorption and hybrid heat pump

Recovering waste heat from industrial processes is bene ficial in order to reduce the primary energy demands and heat pumps can be used to this purpose.Absorption heat pumps are energy-saving and environment-friendly because use working fluids that do not cause ozone depletion and can reduce the global warming emissions.The hybrid heat pump processes combine the conventional vapor-compression and the absorption heat pump cycles.Studies about the simulations and modeling of hybrid heat pumps are few in literature.In this research a mathematical model for single effect absorption and hybrid heat pump is carried out with Chem Cad? 6.0.1.LiBr–H_2O is used as working fluid while electrolytic NRTL and electrolytes latent heat are used as thermodynamic model due to the better results.Binary parameters of activity coef ficients are regressed from experimental vapor pressure data while default constants are used for the solubility expressions.A design of heat pumps is developed and a new modeling of generator is analyzed.The coef ficient of performance of absorption heat pump and hybrid heat pump is equal to 0.7 and 0.83 respectively.For absorption heat pump a sensitivity analysis is carried out to evaluate the effect of temperature and pressure generator,the concentration of Li–Br solution on coef ficient of performance,cooling capacity and working fluid temperature.For hybrid heat pump,the different coef ficients of performance,the primary energy ratio,the generator heat,and the compressor power are analyzed for different values of compressor proportion.Results show that comparing the two systems the hybrid pump allows to save more primary energy,costs and carbon dioxide emissions with respect to absorption heat pump with the increasing of compressor proportion parameter.Future researches should focus on the construction of this heat pumps integrated in chemical processes as a biogas plant or trigeneration systems.