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51.
The set of hybrid numbers is a noncommutative number system that unified and generalized the complex, dual, and double (hyperbolic) numbers with the relation ih =− hi =ε+ i. Two hybrid numbers p and q are said to be similar if there exist a nonlightlike hybrid number x satisfying the equality x −1 qx = p . And, it is denoted by p ∼ q . In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations px = xq and qx − xp = c for 相似文献
52.
The aim of this paper is to describe the moduli spaces of degree d quaternionic superminimal maps from 2-spheres to quaternionic projective spaces HPn. We show that such moduli spaces have the structure of projectivized fibre products and are connected quasi-projective varieties of dimension 2nd + 2n + 2. This generalizes known results for spaces of harmonic 2-spheres in S4. 相似文献
53.
Kit Ian Kou Jianyu Ou Joao Morais 《Mathematical Methods in the Applied Sciences》2016,39(10):2722-2736
In the present paper, we generalize the linear canonical transform (LCT) to quaternion‐valued signals, known as the quaternionic LCT (QLCT). Using the properties of the LCT, we establish an uncertainty principle for the two‐sided QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion‐valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternionic signal minimizes the uncertainty. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
54.
为了提高空间域彩色图像零水印算法的水印嵌入和检测精度以及抵抗旋转几何变换的能力,提出了一种基于Radon变换和四元数实矩阵表示的抗旋转攻击空间域零水印算法。首先将原始彩色图像使用四元数实矩阵来表征,并计算实数字矩阵的Radon变换不变矩;然后利用少量低阶Radon变换不变矩来设计和构建零水印信息;在水印检测前,通过Radon变换几何校正算法对可能遭受旋转攻击的待检测图像进行旋转角度的校正,然后进行水印的提取。实验结果表明,该方法可以获得良好的图像视觉效果,对于旋转几何攻击具有很强的鲁棒性,同时对滤波、JPEG压缩和剪切攻击也具有一定的鲁棒性。 相似文献
55.
56.
1 IntroductionandPreliminariesTherealVandermondematrixisausefultoolinthevibrationanalysisofstructureandthecomputingofdiscreteFouriertransformandthetheoryofcontrolandthedecentralizedstabilizationforlargescalesystemsandmanyotherpracticalfields[1~3],iti… 相似文献
57.
本文指出了文[1]中的几个错误,并利用?-方程解的积分表示,获得了其所讨论的超球上的四元数方程的Neumann问题解的积分表示 相似文献
58.
Multi-focus image fusion is an important method used to combine the focused parts from source multi-focus images into a single full-focus image. Currently, to address the problem of multi-focus image fusion, the key is on how to accurately detect the focus regions, especially when the source images captured by cameras produce anisotropic blur and unregistration. This paper proposes a new multi-focus image fusion method based on the multi-scale decomposition of complementary information. Firstly, this method uses two groups of large-scale and small-scale decomposition schemes that are structurally complementary, to perform two-scale double-layer singular value decomposition of the image separately and obtain low-frequency and high-frequency components. Then, the low-frequency components are fused by a rule that integrates image local energy with edge energy. The high-frequency components are fused by the parameter-adaptive pulse-coupled neural network model (PA-PCNN), and according to the feature information contained in each decomposition layer of the high-frequency components, different detailed features are selected as the external stimulus input of the PA-PCNN. Finally, according to the two-scale decomposition of the source image that is structure complementary, and the fusion of high and low frequency components, two initial decision maps with complementary information are obtained. By refining the initial decision graph, the final fusion decision map is obtained to complete the image fusion. In addition, the proposed method is compared with 10 state-of-the-art approaches to verify its effectiveness. The experimental results show that the proposed method can more accurately distinguish the focused and non-focused areas in the case of image pre-registration and unregistration, and the subjective and objective evaluation indicators are slightly better than those of the existing methods. 相似文献
59.
航天器的矢径可以分解为矢径模和单位矢量的乘积,利用该性质将传统轨道动力学方程分解为矢径模和矢径方向的动力学方程组,实现了航天器位置信息的分离;针对两个方程分别采用常数变易法和四元数描述方法,将轨道动力学模型转化为线性无奇异的方程组,同时得到了7 个新轨道变量,且建立了新轨道变量与惯性系下航天器位置速度信息以及轨道六要素之间的相互转换关系. 该轨道模型适用于任意形式的推力和摄动,避免了奇异性,且在虚拟时间的意义下,航天器的旋转角速度只取决于法向力;在常值推力和变推力的情况下,对该模型进行了数值验证,验证了新模型的可适用性、数值稳定性以及计算精度高的优势. 相似文献
60.
Bézier曲线近似合并算法在几何数据压缩方面有着重要的应用.研究了两条相邻Bézier曲线近似合并的问题,用矩阵的形式给出了相邻Bézier曲线可精确合并的条件,并在此基础上通过广义逆矩阵的方法求解合并逼近后的Bézier曲线.同时,对保端点插值条件的近似合并也给出了结果.最后用实例说明了算法的有效性,得到了很好的逼近效果. 相似文献