This article considers the task of handwritten text recognition using attention-based encoder–decoder networks trained in the Kazakh and Russian languages. We have developed a novel deep neural network model based on a fully gated CNN, supported by multiple bidirectional gated recurrent unit (BGRU) and attention mechanisms to manipulate sophisticated features that achieve 0.045 Character Error Rate (CER), 0.192 Word Error Rate (WER), and 0.253 Sequence Error Rate (SER) for the first test dataset and 0.064 CER, 0.24 WER and 0.361 SER for the second test dataset. Our proposed model is the first work to handle handwriting recognition models in Kazakh and Russian languages. Our results confirm the importance of our proposed Attention-Gated-CNN-BGRU approach for training handwriting text recognition and indicate that it can lead to statistically significant improvements (p-value < 0.05) in the sensitivity (recall) over the tests dataset. The proposed method’s performance was evaluated using handwritten text databases of three languages: English, Russian, and Kazakh. It demonstrates better results on the Handwritten Kazakh and Russian (HKR) dataset than the other well-known models.

Tables are everywhere, from scientific journals, articles, websites, and newspapers all the way to items we buy at the supermarket. Detecting them is thus of utmost importance to automatically understanding the content of a document. The performance of table detection has substantially increased thanks to the rapid development of deep learning networks. The goals of this survey are to provide a profound comprehension of the major developments in the field of Table Detection, offer insight into the different methodologies, and provide a systematic taxonomy of the different approaches. Furthermore, we provide an analysis of both classic and new applications in the field. Lastly, the datasets and source code of the existing models are organized to provide the reader with a compass on this vast literature. Finally, we go over the architecture of utilizing various object detection and table structure recognition methods to create an effective and efficient system, as well as a set of development trends to keep up with state-of-the-art algorithms and future research. We have also set up a public GitHub repository where we will be updating the most recent publications, open data, and source code. The GitHub repository is available at https://github.com/abdoelsayed2016/table-detection-structure-recognition.

: We consider the continuation problem from the time-like surface for the 2D Maxwell equation. The problem is formulated in an operator form . We describe and justify gradient methods for minimizing the cost functional for the continuation and coefficient inverse problems. The results of a computational experiment are presented.

: We investigate the continuation problem for the elliptic equation. The continuation problem is formulated in operator form . The singular values of the operator A are presented and analyzed for the continuation problem for the Helmholtz equation. Results of numerical experiments are presented.

We consider an ill-posed initial boundary value problem for the Helmholtz equation. This problem is reduced to the inverse continuation problem for the Helmholtz equation. We prove the well-posedness of the direct problem and obtain a stability estimate of its solution. We solve numerically the inverse problem using the Tikhonov regularization, Godunov approach, and the Landweber iteration. Comparative analysis of these methods is presented.

A numerical method for solving the Dirichlet problem for the wave equation in the two-dimensional space is proposed. The problem is analyzed for ill-posedness and a regularization algorithm is constructed. The first stage in the regularization process consists in the Fourier series expansion with respect to one of the variables and passing to a finite sequence of Dirichlet problems for the wave equation in the one-dimensional space. Each of the obtained Dirichlet problems for the wave equation in the one-dimensional space is reduced to the inverse problem with respect to a certain direct (well-posed) problem. The degree of ill-posedness of the inverse problem is analyzed based on the character of decreasing of the singular values of the operator A. The numerical solution of the inverse problem is reduced to minimizing the objective functional . The results of numerical calculations are presented.