If a mechanical or acoustical impedance modification is introduced between two positions, the effect of that modification can be plotted in the complex plane at a given frequency. It has been shown that the mechanical or acoustical response will trace a circle in the complex plane for straight-...
Define a transformation presenting the mapping in the complex plane z -> w = z^3. > w≔evalcx+Iy3 w≔I3x2y−y3+x3−3xy2 (2) We use the real and imaginary parts of w to define the components of the transformation. We can set up the transforma...
a2) the Mobius transformation defined by the three point correspondences can be computed in a closed form, as a rational linear function in the complex plane, 2)三封点书信定义的Mobius变革在封闭形状在复平面可以被计算,作为一个合理的线性函数,[translate]...
The Watson transformation is essentially the idea that a series can be converted into an integral in the complex plane via an "inverse residue" calculation. This idea has a long history of being used to convert expressions for the solutions of boundary value problems (BVPs) into alternative expr...
but all of the following are linear operators: contraction (of ℝn), dilation (of ℝn), reflection of space through the xy-plane (or xz-plane or yz-plane), rotation of the plane about the origin through a given angle θ, projection (of ℝn) in which one or more of the coordi...
If rotations are parallel to the xy plane, an additional translation and rescaling occurs along the z-axis. Likewise, if rotations are parallel to the yz plane, additional translation and rescaling occur along the x-axis. For any magnification factor that is not unity, some point in space ...
We derive a Bu00e4cklund transformation for the self-dual Yang-Mills fields by using the method of special Riemann problem with one zero, in which the moving poles in the complex parameter plane are incorporated. This BT is more general than a previously given one and is capable of generat...
摘要: In this paper we proved that the limit set produced by a transforation group have the fractal construction if it is generated by tow Mobiustransformations on complex plane C and the conditions (1—6) in definition 1 are satisfied.关键词: mobius transformation invariant set fractal ...
genetic transformation technologies have emerged as effective solutions. Despite various difficulties in genetic transformation for forest trees, including prolonged life cycles, genetic diversity, interspecies variations, and complex regeneration systems, significant research progress has been achieved in tree ge...
In Eq. (1), the nonlinear term has a self-induced nonlinear potential V(x,z)=q(x,z)q∗(−x,z) satisfying the parity-time-symmetric condition V(x,z)=V∗(−x,z). It has been shown that Eq. (1) is completely integrable in the sense that it can be solved by the ...