双线性的

According to Lagrange equation in analytic dynamics, the dynamic equations of the Double-Axis Gyro Stabilized Platform of a certain airborne SAR antenna are derived, its linear model and the transfer functions of other main parts in the DAGSP are given and at last the block diagram of DAGSP is given.

6利用分析力学原理，推导了某机载天线双轴陀螺稳定平台的动力学方程和线性化模型；给出了天线双轴陀螺稳定平台中各主要环节的传递函数及数学模型。

The length of certain bond and the number of conjugate double-bond affected OWF〓 greatly, OWF〓 changed linearly with the change of bond length (for planar azobenzene derivatives and cyanine derivatives) and the change of conjugate double-bond number (for conjugate alkene,β-carotene and lycopene).

3键长和共轭双键数对OWF〓有较大的影响，OWF〓随键长（如平面型的偶氮苯衍生物、菁类和氧杂菁类等）和双键数（如共轭烯烃类、β—胡萝卜素和番茄红素等）的变化而线性变化。

The length of certain bond and the number of conjugate double-bond affected OWFπ-π greatly, OWFπ-π changed linearly with the change of bond length (for planar azobenzene derivatives and cyanine derivatives) and the change of conjugate double-bond number (for conjugate alkene, p-carotene and lycopene).

3键长和共轭双键数对OWF_有较大的影响，OWF_随键长(如平面型的偶氮苯衍生物、菁类和氧杂菁类等)和双键数(如共轭烯烃类、β—胡萝卜素和番茄红素等)的变化而线性变化。

The results show that relationship between flow stress and strain rate is applied to hyperbolic sine equation in the hot compressive deformation of 6061 aluminum alloy; at the same time, relationship between logarithmic hyperbolic sine of its flow stre...

研究表明，6061铝合金热压缩塑性变形时的流变应力和应变速率之间的关系满足双曲正弦函数关系式；其热压缩塑性变形时流变应力的双曲正弦对数项与绝对温度倒数之间满足线性关系，其高温压缩变形受热激活能的控制。

The variation of pH and conductivity of various phosphate solution with the solution temperature were obtained based on the physical chemistry theory and ionization equilibrium theory in electrolytic solutions, and be testified experimentally under radiation of ultrasonic wave. The pH was a linear function with the reciprocal of thermodynamic temperature, and the conductivity was a linear function with the temperature in phosphate solution.

三、超声波对双水相系统组成物质、两相组成及溶质分配影响的研究根据物理化学原理和电解质溶液电离平衡理论分析推导和实验验证，揭示了超声波作用下不同组成磷酸盐溶液的pH值和电导率随溶液主体温度变化的规律：磷酸盐溶液的pH值与溶液主体绝对温度的倒数成线性关系，磷酸盐溶液的电导率与溶液主体温度成线性关系。

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。

We introduce some concepts, such as yon Neumann algebras, factor von Neumann algebras, nest algebras and so on, and give some well-known theorems that we will use in this paper. In Chapter 2, we put our attention on linear maps that preserving zero Jordan triple product on nest subalgebrasof factor yon Neumann algebras.

第二章首先对因子von Neumann代数中套子代数上保Jordan三重零积的线性映射进行了研究，证明了从因子von Neumann代数中套子代数到任一有单位元的Banach代数的保Jordan三重零积的单位线性双射是Jordan同构。

The feedback controls, including linear, speed, doubly-periodic function, hyperbolic function and trigonometric function are used to suppress chaos to one of the three unstable equilibrium. The Routh-Hurwtiz theorem is applied to derive the conditions of stability of the controlled system.

利用反馈控制方法，包括线性、速度、双周期函数、双曲函数和三角函数反馈控制方法将系统的混沌运动控制到稳定态，根据Routh-Huriwtz准则获得了系统达到控制目标时反馈系数所满足的条件。

In latching the feedback random bit sequences, the linear feedback shift register includes a plurality of bi-stable latches for linearly shifting a mixed random bit sequence outputted by an XOR gate, which is combined with the true random bit sequence.

在锁存所述反馈随机比特序列的过程中，所述线性反馈移位寄存器包括多个双稳态锁存器，其用于线性地移位由XOR门输出的混合随机比特序列，所述混合随机比特序列与真实的随机比特序列组合。

A series combined test method tests were performed to determine the liquid-plastic limits of different samples of fine grained soil and silty sand. The result showed that the loglog relationship between the depth of penetration of fall cone and the water content of some samples were clearly not linear, and the liquid-plastic limit could not be obtained according to the linear relation. Effective test data could not be measured within the three arranges of water contents proposed by the present standards. The dependability was necessary to discuss about the liquid-plastic limit test results obtained from three arranges.

采用液、塑限联合测定法针对部分细粒土和粉砂进行液、塑限测定时，发现对于部分细粒土在双对数坐标上圆锥下沉深度与含水率之间的关系并非线性关系，无法依据线性关系确定液、塑限：采用规程建议的三个含水率范围有时根本无法获得有效试验数据；采用规程建议的三个含水率范围确定得到土的液、塑限试验结果的可靠性有待商榷；采用直线段试验数据确定的液、塑限进行分类可能出现相互矛盾甚至错误的结果。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新