Huy Tuan Nguyen

Huy Tuan Nguyen, Vo Anh Khoa, Mach Nguyet Minh et al.

In this paper, we rigorously investigate the truncation method for the Cauchy problem of Helmholtz equations which is widely used to model propagation phenomena in physical applications. The method is a well-known approach to the regularization of several types of ill-posed problems, including the model postulated by Regi\' nska and Regi\' nski \cite{RR06}. Under certain specific assumptions, we examine the ill-posedness of the non-homogeneous problem by exploring the representation of solutions based on Fourier mode. Then the so-called regularized solution is established with respect to a frequency bounded by an appropriate regularization parameter. Furthermore, we provide a short analysis of the nonlinear forcing term. The main results show the stability as well as the strong convergence confirmed by the error estimates in $L^2$-norm of such regularized solutions. Besides, the regularization parameters are formulated properly. Finally, some illustrative examples are provided to corroborate our qualitative analysis.

Thanh Nam Duong, Trung Kien Hoang, Quoc Khanh Duong et al.

This paper investigates predicting market strength solely from candlestick chart images to assist investment decisions. The core research problem is developing an effective computer vision-based model using raw candlestick visuals without time-series data. We specifically analyze the impact of incorporating candlestick patterns that were detected by YOLOv8. The study implements two approaches: pure CNN on chart images and a Decomposer architecture detecting patterns. Experiments utilize diverse financial datasets spanning stocks, cryptocurrencies, and forex assets. Key findings demonstrate candlestick patterns do not improve model performance over only image data in our research. The significance is illuminating limitations in candlestick image signals. Performance peaked at approximately 0.7 accuracy, below more complex time-series models. Outcomes reveal challenges in distilling sufficient predictive power from visual shapes alone, motivating the incorporation of other data modalities. This research clarifies how purely image-based models can inform trading while confirming patterns add little value over raw charts. Our content is endeavored to be delineated into distinct sections, each autonomously furnishing a unique contribution while maintaining cohesive linkage. Note that, the examples discussed herein are not limited to the scope, applicability, or knowledge outlined in the paper.