超数学项目课程(MBTPC)的研究与实践——以“秤课程”为例

超数学项目课程是指基于数学学科,以超越数学内容为项目核心,以项目学习为主要方式,以丰厚文化底蕴、发展综合素养为基本价值取向的一种跨学科课程形态。以某个数学项目为核心,勾连统摄语文等多学科课程,既可增加课程内容的广度,又切实提升了课程内容的高度。

超数学——一种新的数学方法学与计算机科学

超数学作为一种新的数学方法学不同于经典数学的“定义—定理—证明”模型,而是基于“说明—断言—辩明”模型工作的,其基础是“操作逻辑”。它的理论与实现既为计算机科学提供基础。同时又借助于计算机科学的有关理论、技术和方法学,本文就这些方面概要地讨论超数学及其计算机科学的联系。

教应有理 学需思辨——基于超经验数学研究的“无理数”教学设计

无理数的无限不循环特性超出了日常生活经验的范围,学生难以真正理解.面对这样没有实际情境的数学内容（超经验数学）,本节课的设计通过寻找纯数学情境,建立数学知识之间的内在联系,引导学生感受不可公度量,＂造＂无理数,理性证明无理数等,进而使教与学有理有据.

“做思行”圆融 “玩学创”共生——“超脑麦斯”数学课程设计与实施

"超脑麦斯STEM"数学课程是一种融科学、技术、工程在内的综合课程。"做数学""说数学""玩数学"是超脑麦斯课程的精髓。超脑麦斯课程是实施数学创客教育、数学核心素养教育的重要载体。置入超脑麦斯课程之中,学生能够真正做到"做思行"圆融、"玩学创"共生。

上“超市”学数学？

新课程要求课堂教学与生活实际紧密联系，注重学生实际能力的运用，但实际教学中，教师们常常只能做到模拟情境的演练。这种情境是经过“删减”、“过滤”的，更多只是起导入、激趣或者印证的作用，远不如实际生活丰富、复杂，如果将课堂搬到生活中去，给孩子们创造一个用数学知识解决实际问题的机会，相信孩子们的收益要大得多。

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.

Ultrasonically Assisted Extraction of Isoflavones from Stem of Pueraria lobata （Willd.） Ohwi and Its Mathematical Model

Ultrasonically assisted extraction of isoflavones from the stem of Pueraria lobata （Willd.） Ohwi has been carried out with an ultrasonic extracting apparatus （20kHz, electrical power input to the transducer in 0-650W）. The influence of the electrical power input and extraction time on the＇extraction yield is investigated in water, n-butanol, and 95% （by volume） and 50% （by volume） ethanol aqueous solution. The experimental results indicate that the yields of total isoflavones are higher in ultrasonically assisted extraction than those obtained from con-ventional extraction.Moreover,a mathematical model is proposed,by introducing the electrical power input to index the ultrsound intensity,to describe the behavior of ultrasonically assisted extraction.It is found that the model calcuations are in good agreement with the experimental data.

A Mathematical Method for Determination of Absolute Adsorption from Experimental Isotherms of Supercritical Gases

A mathematical method was proposed for the determination of absolute adsorption from experimental isotherms. The method is based on the numerical equality of the absolute and the excess adsorption when either the gas phase density or the amount adsorbed is not quite considerable. The initial part of the experimentalisotherms, which represents the absolute adsorption, became linear with some mathematical manipulations. The linear isotherms were reliably formulated. As consequence, either the volume or the density of the supercritical adsorbate could be determined by a non-empirical way. This method was illustrated by the adsorption data of supercritical hydrogen and methane on a superactivated carbon in large ranges of temperature and pressure.

Kinetic Study on Extraction of Red Pepper Seed Oil with Supercritical CO_2

A mathematical model for extraction of red pepper seed oil with supercritical CO2was proposed.Some factors influencing the process were investigated,including operation pressure,temperature and extraction yield Xe(%).The model was solved by the method of weighted residuals and used to simulate the process numerically.The kinetic equation is expressed as Xe16.8606exp(t/9.98177)16.95457 and the simulation results are in excellent agreement with the experimental data.The optimal operating parameters are 30 MPa,318 K and 60 min.

Physico-Chemical Properties and Laboratory Hyperspectral Reflectance of Coastal Saline Soil in Shangyu City of Zhejiang Province, China

45 and 50 composite soil samples were collected, respectively, from twoagricultural fields, that were enclosed and reclaimed from coastal tidal-flat areas in 1996 and 1984respectively, in Shangyu of Zhejiang Province, China, to investigate the physico-chemicalproperties and the hyperspectral characteristics of the saline soils and to make an assessment ontheir relationships. The reflectance spectra of saline soils were measured using a spectroradiometerin laboratory. The mean spectral curves of the saline soils from the two sites different inreclamation year showed that the saline soil taken from the recently reclaimed land with highersalinity demonstrated a lower reflectance intensity in the spectral region from about 550 nm to 2300nm. In addition, nine absorption bands, i.e., 488 nm, 530 nm, 670 nm, 880 nm, 940 nm, 1400 nm, 1900nm, 2 200 nm and 2 300 nm, were chosen as the spectral bands to investigate the relationshipsbetween soil physico-chemical properties by means of Pearson correlation analysis. Finally, thefirst two principal components were calculated from nine absorption bands and used to discriminatethe saline soil samples taken from two sampled fields. The results indicate that it is feasible todetect physico-chemical properties of saline soils from fields reclaimed for varying time periods onthe basis of the hyperspectral data.

On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.

The Central Limit Theorem on SU(n,1)/S(U(n)×U(1))

Let G = SU（n, 1）, K = S（U（n） × U（1））, and for l ∈Z, let {T;},l∈Z be a one- Dimensional K-type and let Et be the line bundle over G/K associated to Tl. In this work we obtain a central limit theorem for the space Et.

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.

Fractal Interpretation of Ultrasonic Crystallization of Solutions

Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dimension of crystals equals 2.45, which is consistent with the literature data. Crystal growth is represented as the N-rd translation of each side of the crystal lattice with its own speed and with relation to the formation of similar structures--fractals. A mathematical model of ultrasonic crystallization of a CuSO4 solution was proposed. The model is based on the combined use of differential transport equations of momentum, mass, energy and sound waves and a method of similarity and dimensional analysis. The calculated formulas for the concentration of Ccr, the equivalent diameter of the formed crystals dcr and the intensity of internal energy source Ф, associated with the interaction of crystals with the hydro mechanical, heat and sound fields were obtained. Fractal interpretation of ultrasonic crystallization of the CuSO4 solution was made. It was found that on the growth of crystal size d^r directly affects translation N, i.e., an increase in the number of sets of crystals of infinitely small size e, correspond to the size of the crystal lattice. In turn, translation of crystals depends on the geometry of the crystallizer and the physical parameters of external force fields, acting on the CuSO4 solution. A connection of results of the mathematical modeling with the results of fractal analysis of the ultrasonic crystallization of solutions was established.

Positive solutions of singular superlinear fourth order boundary value problem

The cone theorem and the fixed point index are used to investigate the positive solution of singular superlinear boundary value problem for a fourth order nonlinear differential equation.

The Derivation Algebra of the Cartan-type Lie Superalgebra H

In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH = adH（H＂ ＋ Fh） （{（adDi）^pt ｜ i = 1,2,…,m, t=1,2,…,ti-1}）.

Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory

Spaces of equivalence modulo a relation of congruence are constructed on field solutions to establish a theory of the universe that includes the theory QFT （Quantum Field theory）, the SUSY （Super-symmetry theory） and HST （heterotic string theory） using the sheaves correspondence of differential operators of the field equations and sheaves of coherent D - Modules [1]. The above mentioned correspondence use a Zuckerman functor that is a factor of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry [2, 3]. The obtained development includes complexes of D - modules of infinite dimension, generalizing for this way, the BRST-cohomology in this context. With it, the class of the integrable systems is extended in mathematical physics and the possibility of obtaining a general theory of integral transforms for the space - time （integral operator cohomology [4]）, and with it the measurement of many of their observables [5]. Also tends a bridge to complete a classification of the differential operators for the different field equations using on the base of Verma modules that are classification spaces of SO（l, n ＋ 1）, where elements of the Lie algebra al（1, n ＋ 1）, are differential operators, of the equations in mathematical physics [1]. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field （Verma modules） and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic L G - bundles category with a special connection （Deligne connection）. The corresponding D - modules may be viewed as sheaves of conformal blocks （or co-invariants） （images under a version of the Penrose transform [1, 6]） naturally arising in the framework of conformal field theory.

Study on Excess Thermodynamic Parameters and Theoretical Estimation of Ultrasonic Velocity Using Scaled Particle Theory in Binary Liquid Mixtures of 2-Methyl-2-propanol and Nitriles at Different Temperatures

Density, ρ, ultrasonic speed, u, and viscosity, η, of binary mixtures of 2-methyl-2-propanol (2M2P) with acetonitrile (AN), propionitrile (PN) and butyronitrile (BN) including those of pure liquids are measured over the entire composition range at temperatures 298.15, 303.15 and 308.15 K. From these experimental data, the excess available volume, E a V , excess free volume, E f V , excess isothermal compressibility, E T β , excess thermal expansion coefficient, E α , and excess internal pressure, E i π , are calculated. The variation of these properties with composition and temperature are discussed in terms of molecular interactions between unlike molecules of the mixtures. It is found that the values of E a V , E f V , E T β and E α are positive and those of E i π are negative for all the mixtures at each temperature studied, indicating the presence of weak interactions between 2M2P and AN/PN/BN molecules. The variations of E a V , E f V , E T β , E α and E i π values with composition indicate that the interactions in these mixtures follow the order: AN<PN<BN, i.e., the 2M2P-nitrile interaction decreases with the increase of alkyl chain length in these nitrile molecules. In addition, the theoretical ultrasonic velocity is calculated using the scaled particle theory and compared with the experimental values.

Effects of R-Parity Violating Supersymmetry in Top Pair Production at Linear Colliders with Polarized Beams

In the minimal supersymmetric standard model with R-parity violation, the lepton number violating top quark interactions can contribute to the top pair production at a linear collider via tree-level u-channel squark exchange diagrams. We calculate such contributions and find that in the allowed range of these R-violating couplings, the top pair production rate as well as the top quark polarization and the forward-backward asymmetry can be significantly altered. By comparing the unpolarized beams with the polarized beams, we find that the polarized beams are more powerful in probing such new physics.

The Role of Potential Structure in Excitation Functions of Synthesizing Superheavy Nuclei

The excitation functions of two very similar reaction channels, 58Fe＋ 208pb→ 265Hs ＋ 1n and 58Fe＋ 209Bi → 266Mt ＋1n are studied in the framework of the dinuclear system conception. The fusion probabilities are found to be strongly subject to the structure of the driving potential. Usually the fusion probability is hindered by a barrier from the injection channel towards the compound nuclear configuration. The barrier towards the mass symmetrical direction, however, also plays an important role for the fusion probability, because the barrier hinders the quasi-fission, and therefore helps fusion.