Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
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01 Oct 2020
TL;DR: In this article, three weight functions: Inverse trigonometric function, Hyperbolic tangent function and Log function are proposed for the purpose of improving the robustness and time efficiency of IR3C algorithm.
Abstract: The need for occlusion face recognition in daily life, professional fields like criminal investigation and the recent epidemic is increasing, so it is still a hot issue in the current research and many researchers are pursuing the technical excellence for the face recognition of random occlusion. In the previous research, RRC model is proposed for the excellent performance in the occlusion face recognition and the IR3C algorithm is adopted to solve this model. Among them, the weight function in this algorithm plays a big role, which will directly affect the recognition rate and running time of the experiment. In this paper, three weight functions: Inverse trigonometric function, Hyperbolic tangent function and Log function are proposed for the purpose of improving the robustness and time efficiency of IR3C algorithm. Applying these functions on the comparable types and levels of random occlusion and then comparing them with the previous research, the experimental results indicate that the inverse trigonometric function is superior to other functions with better recognition rates and shorter running time.
TL;DR: In this paper , the gamma derivative of sine and cosine functions is defined for non-orthogonal systems, where the y-axis is at a variable angle to the x-axis.
Abstract: Derivatives in trigonometry have always been defined in orthogonal contexts (i.e., where the y-axis is set perpendicular to the x-axis). Within the context of trigonometric, the present work expands the concept of derivative (operating by the principle of 90 degrees phase shift when applicable to sine and cosine functions) to the realm where the y-axis is at a variable angle $\gamma$ to the x-axis (i.e., non-orthogonal systems). This gives rise to the concept of the \emph{gamma derivative} --- which expands the classical derivative to impart phase shifts of $\gamma$ degrees. Hence, the ordinary derivative (with respect to $\alpha$) or $d/d \alpha$ is a particular case of the more general \emph{gamma derivative} or $d_\gamma/d_\gamma \alpha$. Formula for the $n^{th}$ gamma derivative of the extended sine and cosine functions are defined. For applied mathematics, the gamma derivatives of the extended sine function $\sin^*(\alpha,\gamma)$ and cosine function $\cos^*(\alpha,\gamma)$ determine the extended governing equation of the energy-coupled mass-spring oscillatory system, and by extended analogy that of the electrical LC (Inductance-Capacitance) circuit.
18 Mar 2022
TL;DR: Both Bifurcation Diagram & Lyapunov Exponent Spectrum manifest that the new mapping possesses wonderful chaotic properties, and a pseudorandom bit generator is designed based on it, which owns great application prospect.
Abstract: In the literature, little attention is paid to devising and analyzing novel one dimensional chaotic mappings. In our previous efforts, we have tried fold, translation & scale on arctangent function & sigmoid function respectively, which brings good results. In this paper, we do the same to obtain a variant of Hyperbolic Sine Function. Both Bifurcation Diagram & Lyapunov Exponent Spectrum manifest that the new mapping possesses wonderful chaotic properties. Then, a pseudorandom bit generator is designed based on it. Pseudorandom tests demonstrate that the generator is much better than our previous ones. It owns great application prospect.
TL;DR: The combination of data transformation and optimization model can improve the accuracy of diagnosis from two aspects of data structure and classification algorithm.
Abstract: A new method of dissolved gas analysis is proposed to improve the accuracy of transformer fault diagnosis. The slime mold optimized support vector machine (SMA‐SVM), and logarithmic arctangent transform (LOG‐ACT) are combined. On the one hand, the better global optimization performance of SMA is used to optimize SVM parameters to solve the difficulty of SVM parameter selection. On the other hand, corresponding transformations are carried out for different features: the logarithmic(LOG) transformation is carried out for the original DGA data to retain the order of magnitude information. The arctangent (ACT) transformation is carried out for the ratio features to improve the data structure. Therefore, the combination of data transformation and optimization model can improve the accuracy of diagnosis from two aspects of data structure and classification algorithm. The performance of the proposed method was compared with IEC three ratio method, artificial neural network, optimized artificial neural network, GA‐SVM, and PSO‐SVM. Experimental results using published data show that the proposed method can significantly improve the accuracy of transformer fault diagnosis. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.