多元点振荡基础平衡数学式的证明

目的证明糖代谢系统在血糖正常或NIDDM人群,空腹状态相关因子和细胞、细胞微单元功能的彼此作用始终处于动态平衡。方法依据空腹间隔30分钟两次肘静脉血糖(G)、胰岛素(I)、C肽(C)检测值较为近似的事实,把G、I、C的首次和再次检测值分别用G_(01),I_(01),C_(01),和G_(02),I_(02),C_(02)表示。其比值G_(02)/G_(01),C_(02)/C_(01),I_(02)/I_(01)称之谓变化度。结论多元点振荡基础平衡数学式式G/l·C·x·y=1/1=1,即:G_(02)/G_(01),C_(02)/C_(01),I_(02)/I_(01)·x·y=1/1=1表达了空腹状态下,糖代谢系统各相关因子和细胞、细胞微单元功能值的变化度,其数学积是1。

应用多媒体技术提高《微积分》的教学质量

微积分是高等数学教学的重要课程内容之一,是高等数学继续学习与深造的基础课程,它的思想方法是学生学习后继课程的重要工具和基础.本文主要分析大学微积分教学中存在的问题,怎样发挥多媒体技术的优势,使微积分课程的教学质量有所提高,并以典型案例介绍如何以学生为中心进行积极的微积分教学改革.

三角洲平原高弯曲分流河道内部结构单元三维建模

以大庆萨尔图油田北三区西部西块SⅡ12小层典型三角洲平原高弯曲分流河道为例,进行了三角洲平原高弯曲分流河道内部结构单元建模。首先根据高弯曲分流河道沉积层次性,以及河流弯曲机理,解剖了分流河道内部结构,识别出点坝以及侧积层单元,提取了侧积层形态参数和统计参数。其次采用椭球形方程建立了侧积层平面数学函数表达式,采用直线方程描述侧积层剖面形态,从而建立侧积层空间三维几何形态。最后,分两步建立了高弯度分流河道内部结构单元三维地质模型。首先采用序贯指示建模建立分流河道微相模型;随后根据侧积层数学模型描述侧积层空间分布。并在分流河道微相内部将侧积层模型嵌入,形成精细的高弯曲分流河道内部结构模型。以此思路为指导建立了SⅡ12小层结构模型,以此结构模型为基础的储层参数模型很好地再现了点坝内部侧积层对流体渗流的遮挡,为油藏数值模拟和剩余油挖潜奠定了基础。

Quantitative Relationship between Leaf Area Index and Canopy Reflectance Spectra of Rice under Different Nitrogen Levels

Monitoring rice growth by spectral remote sensing technology can provide scientific basis for the high yield and efficient production of rice. Field experiments with different nitrogen application amounts using Tianyouhuazhan rice as test sam- ples were set up to study the relationship between rice leaf area index （LAI） and canopy reflectance spectral. The results showed that： the LAI increased with the amount of applied nitrogen; the canopy reflectance spectral showed significant re- sponse characteristics to groups with different nitrogen application levels; the corre- lation coefficient of LAI and canopy spectral reflectance reached the maximum at 720 nm red edge region. The mathematical model was constructed to predict the LAI according to the canopy reflectance spectra of rice.

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.

Method of variation of parameters for solving a constrained Birkhoffian system

For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.

A New Integrable Lattice Hierarchy and Its Two Discrete Integrable Couplings

A new and efficient way is presented for discrete integrable couplings with the help of two semi-direct sum Lie algebras. As its applications, two discrete integrable couplings associated with the lattice equation are worked out. The approach can be used to study other discrete integrable couplings of the discrete hierarchies of solition equations.

Fractal and its application to sedimentology

In the paper,the foundation,development,basic conception and general characteristics of fractal and the calculating method of the fractional dimension are expounded briefly, and the current situation and prospect of the fractal application in sedimentology are discussed stressly. Both sedimentary process and sedimentary record behave the fractal feature of the self similarity structure. External form and internal texture of the sediments and the distribution of the grain size of the sediments are of fractal feature very well, and the size of the fractional dimension is the quantitative index of the complexity of the background when they are formed. The further analysis on the multi fractal feature of the sedimentary body is the base of the fractal simulation and forecast, and it is the key of the application of the fractal theory to sedimentology.

Characteristic Numbers of Matrix Lie Algebras

A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.

A note on the Marcinkiewicz integral operators on F_p^(α,q)

In this paper, we shall prove that the Marcinkiewicz integral operator #n, when its kernel Ω satisfies the L^1-Dini condition, is bounded on the Triehel-Lizorkin spaces. It is well known that the Triehel-Lizorkin spaces are generalizations of many familiar spaces such as the Lehesgue spaces and the Soholev spaces. Therefore, our result extends many known theorems on the Marcinkiewicz integral operator. Our method is to regard the Marcinkiewicz integral operator as a vector valued singular integral. We also use another characterization of the Triehel-Lizorkin space which makes our approach more clear.

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.

The Calculation of Parameters for DNA Kinetic Structure Based on Monte-Carlo Multiple Integrals

Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.

Application of Eigenkets of Bosonic Creation Operator in Deriving Some New Formulas of Associated Laguerre Polynomials

Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L^ρm （｜z｜^2） and its generalized generating function formula. A series of recursive relations regarding to L^ρm （｜z｜^2） are also deduced in the context of the Fock representation by algebraic method.

Integrability and Gauge Fixing for Bosonic String on AdS_3×S^3

The integrability and the TST transformation of the bosonic string on AdS3× S^3 are studied. The Lax connection for gauge fixed theory is constructed and proved to be fiat.

On the Braided Monoidal Categories of T-smash Products A ■_T H

Let A and H be Hopf algebra, T-smash product AT H generalizes twisted smash product A ＊ H. This paper shows a necessary and sufficient condition for T-smash product moduie category AT HM to be braided monoidal category.

Modeling of dynamic recrystallization volume fraction evolution for AlCu4SiMg alloy and its application in FEM

To improve the understanding of coupling effect between dynamic recrystallization(DRX)behaviors and flow behaviors of as-cast AlCu4 SiMg, a finite element(FE) simulation equipped with the models of DRX evolution was implemented. A series of isothermal compression tests were performed primarily on a Gleeble-3500 thermo-mechanical simulator in a temperature range of 648-748 K and a strain rate range of 0.01-10 s-1.According to the measured true stress-strain data,the strain hardening rate curves(dσ/dε versus σ) were plotted to identify the critical strains for DRX initiation(εc). By further derivation of the related material constants, the DRX volume fraction equation and the strain for 50% DRX(ε0.5) equation were solved. Accordingly, the aforementioned DRX equations were implanted into the FE model to conduct a series of simulations for the isothermal compression tests. The results show that during the evolution of DRX volume fraction at a fixed strain rate, the strain required for the same amount of DRX volume fraction increases with decreasing temperature. In contrast, at a fixed temperature, it increases with increasing strain rate. Ultimately, the DRX kinetics model of AlCu4 SiMg alloy and the consequence of the FE analysis were validated by microstructure observations.

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A^-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hicrarchy of soliton equations is generated, which possesses the multi.component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi.component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.

Integrability of a New Type of Deformed XXZ Model

A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.

Greek Texts and the Rigorization of Analysis:An Inquiry into J.L.Lagrange's Work on the History of Mathematics

This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and exerted his influence on other scholars in the translation and diffusion of ancient Greek texts.Second,investigating Lagrange's style in doing and writing history of mathematics,this paper takes a new perspective and elucidates his motivation in these activities.In particular,it focuses on Lagrange's presentation of the history of calculus while he was teaching analysis at the Ecole Polytechnique(1795-1799)so as to clarify the function of history in Lagrange's mathematical works.My thesis is that Lagrange's intention in examining the different methods employed by his predecessors was to find inspiration and useful contents in his search for the proper approach to mathematical problems.I thus argue in this paper that history served as a guide or methodology for Lagrange's mathematics.Meanwhile,through an analysis of his historical writing,this paper points to four epistemological values according to which Lagrange judged various historical methods of differential calculus:generality,simplicity,clarity,and rigor.Lagrange's move to rigorize analysis was connected to his interest in and research of Greek texts;he was attempting to introduce the rigor of the ancient Greeks'demonstration in his works of analysis.

Microstructure and mechanical properties of Al-Si alloy modified with Al-3P

Al-Si alloy was modified with Al-3P master alloy at 740℃.The effects of Si content(7,8,9,10 and 11 wt.%) and adding amount of alterant A1-3P(0,0.1,0.3,0.6,1.0 and 1.5 wt.%) on microstructures and tensile properties of the alloy were investigated with optical microscope(OP),Image Pro Plus 6.0,scanning electron microscope(SEM) and universal testing machine.When the content of Al-3P is 0.6 wt.%,the area fraction of primary a(Al) in the Al-Si alloy increases more compared to the unmodified alloy with an increase in Si content,which could be explained by the movement of non-equilibrium eutectic point.When the Si content is constant(Al-lOSi),with the increase of Al-3P content,the increased rate in area fraction of primary a(Al) phase in the Al-lOSi alloy increases first and then decreases.And when 0.6 wt.% Al-3P is added,the increase in area fraction of primary a(Al) phase is the largest.Compared to the unmodified Al-lOSi alloy,the tensile strength and elongation of Al-lOSi alloy increase by 2.3% and 47.0%,respectively,after being modified with 0.6 wt.% Al-3P alloy.The fracture mode of the modified Al-lOSi alloy is ductile fracture.