查询词典 simultaneous differential equation

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

Method］reversed sural neurofasciocutaneous flap with muscle was applied for repairing the soft tissue defect simultaneous open fracture of tibia lower section 6 cases,the soft tissue defect simultaneous chronic osteomyelitis of tibia lower section 5 case,the soft tissue defect of sole of foot simultaneous calcaneus epicarp 3 case, the soft tissue defect of sole of foot simultaneous calcaneus osteomyelitis or dead space 2 case. the scope of the flap was 18 c m×13 cm～11 c m×7 c m and that of the gastrocnemius flap was 4 cm×3 cm～9 c m×6 cm,the thickness was 1～3 cm,the skin flap was bigger than the muscle flap.

方法］自2004年6月以来，应用带肌肉的腓动脉穿支蒂腓肠神经营养血管皮瓣修复小腿下段及足踝部软组织缺损16例，其中胫骨下段开放性骨折伴软组织缺损6例，胫骨下段软组织缺损伴慢性骨髓炎5例，足后跟足底软组织缺损伴跟骨表层组织缺损3例，跟骨骨髓炎伴窦道2例，皮瓣面积30 cm×10 cm～6 cm× 4.5cm，切取的腓肠肌瓣面积4 cm×3 cm～9 cm×6 cm，肌肉厚度1～3 cm，皮瓣面积比肌瓣的面积要大。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

Establish the steady-state and transient model using the three hydrodynamics equations (Continuity equation, Momentum equation and Energy equation). By comparing different state equation, it selects the BWRS state equation which is considered the most accurate state equation in current natural gas measurement. It calculates compression factor, density and other Thermal parameters based on BWRS state equation. In Numerical solution of the steady-state and transient model, compression factor, friction coefficient and all the other Thermal parameters are recalculated in each small time step to reduce the numerical calculation error.

在稳态模型的建立上，利用流体力学三大方程(连续性方程、运动方程和能量方程)，通过比较不同的状态方程选用了目前被认为最精确的用于天然气计量的BWRS状态方程，并以此方程为基础进行压缩因子、密度等热物性参数的计算；在稳态模型的求解上，选用容易计算，精度较高的标准型龙格—库塔(Runge-Kutta)法进行数值求解，并且在迭代过程的每一小步都重新计算燃气的压缩因子，摩阻系数等所有的计算参数，以减少数值计算的误差。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

The topics to be covered in the course are Integration and Economics Applications, Linear, First-Order Difference Equations, Nonlinear First-Order Difference Equations, Linear Second-Order Difference Equations, Linear First-Order Differential Equations, Nonlinear First-Order Differential Equations, Linear Second-Order Differential Equations, Simultaneous Systems of Differential and Difference Equations, and Optimal Control Theory.

讲授内容包括积分与经济的应用、线性一阶差分方程式、非线性一阶差分方程式、线性二阶差分方程式、线性一阶微分方程式、非线性一阶微分方程式、线性二阶微分方程式、差分与微分的联立方程式、最适控制理论。

The researches in this paper have offered solutions to initial value problem for ordinary differential equation involving difference of two monotone functions, ordinary differential equation with integral boundary conditions, and first-order impulsive ordinary differential equation with anti-periodic.

本文结果包含了具有两个函数差的常微分方程初值问题(当 Ik=Gk=0，λ1=λ2=0 时)，常微分方程积分边值问题(当 Ik=Gk=0，g=0，λ1=0，λ2=±1时)，一阶脉冲微分方程反周期边值问题(当 g=0，Gk=0，λ2=d=0 时)的相关结果。

According the connection between the solution of linear fractional differential equation and nonlinear fractional differential equation, the expression of the solution of the nonlinear fractional differential equation is formed.

在一定的条件下，建立了非线性分数阶微分方程在边值条件下有解存在。

In the case of simply supported ends, the Galerkin method is used to simplify the integro-partial-differential equation into an integro -differential equation. The equation is further simplified into a set of ordinary differential equations by introducing an additional variable. Finally, the numerical methods in modern nonlinear dynamics such as phase plane trajectory, power spectrum and Lyapunov exponents are adopted to investigate the dynamical behavior of the beam.

对于两端简支的情形，采用Galerkin方法简化为常微分－积分方程；然后通过引进附加变量的方法进一步简化为常微分方程；最后利用相平面图、功率谱和Lyapunov指数等非线性动力学中的数值方法识别梁的动力学行为。

The paper draws linear unusual differential equation a_0y~(n+a_1y~(n-1+…+a_(n-1)y′+α_ny=∑mi=0k_iδ~(i from the practical problems in the engineering field of electronic technology,circuit analysis,mechanics of materials,mechanical design and civil architecture,discusses the dependence of the solution of the equation on that of homogeneous,gives the algorithm of the equation,and draws the general algorithm of semi-odd number rank unusual Bessel differential equation.

在电子技术、电路分析、材料力学、机械设计和土木建筑等工程技术领域中，常会遇到一类非齐次项为奇异函数的广义线性微分方程，本文给出这类奇异微分方程的解对齐次解的依赖性，从而得出这类奇异微分方程的解法，求出了半奇数阶奇异Bessel微分方程的通解。如下列应用问题中的微分方

Sodium citrate; calcium carbonate; calcium hydroxide; potassium bicorbonate; magnesium carbonate; ferrous sulphate; Zinc sulphate; copper sulphate; manganese sulphate; potassium iodide; sodium selenite.

柠檬酸钠；碳酸钙；氢氧化钙；碳酸氢钾；碳酸镁；硫酸亚铁；硫酸锌；硫酸铜；硫酸锰；碘化钾；亚硒酸钠。

All this to say that I'm glad filmmaking hasn't become completely ironic. I can enjoy an ironic film as much as the next person, but they usually involve a message of some sort. One that's delivered in a smirkingly clever way that requires little in the way of talent.

所有这些都是说，我很高兴电影制作没有变成完全讽刺艺术，我可以和下一个人一样享受讽刺电影的乐趣，虽然他们经常会被划归到一定级别，技术方面不需要很高的才能。