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In this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+.

The author uses complex integration to obtain integrable functions with vanishing moments sequence, and then the author considers some operators defined on the vanishing moments subspace.

The author gather several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author constructs explicitly Stieltjes classes with center at well-known probability densities. The author gives a lot of examples, including old cases and new ones.

The author computes the Hilbert transform of powers of |ln⁡x| to construct Stieltjes classes by using a recent result connecting the Krein condition and the Hilbert transform.

As the tourism industry becomes more vital for the success of many economies around the world, the importance of technology in tourism grows daily. Alongside increasing tourism importance and popularity, the amount of significant data grows, too. On daily basis, millions of people write their opinions, suggestions and views about accommodation, services, and much more on various websites. Well-processed and filtered data can provide a lot of useful information that can be used for making tourists' experiences much better and help us decide when selecting a hotel or a restaurant. Thus, the purpose of this study is to explore machine and deep learning models for predicting sentiment and rating from tourist reviews.

This paper used machine learning models such as Naïve Bayes, support vector machines (SVM), convolutional neural network (CNN), long short-term memory (LSTM) and bidirectional long short-term memory (BiLSTM) for extracting sentiment and ratings from tourist reviews. These models were trained to classify reviews into positive, negative, or neutral sentiment, and into one to five grades or stars. Data used for training the models were gathered from TripAdvisor, the world's largest travel platform. The models based on multinomial Naïve Bayes (MNB) and SVM were trained using the term frequency-inverse document frequency (TF-IDF) for word representations while deep learning models were trained using global vectors (GloVe) for word representation. The results from testing these models are presented, compared and discussed.

The performance of machine and learning models achieved high accuracy in predicting positive, negative, or neutral sentiments and ratings from tourist reviews. The optimal model architecture for both classification tasks was a deep learning model based on BiLSTM. The study’s results confirmed that deep learning models are more efficient and accurate than machine learning algorithms.

The proposed models allow for forecasting the number of tourist arrivals and expenditure, gaining insights into the tourists' profiles, improving overall customer experience, and upgrading marketing strategies. Different service sectors can use the implemented models to get insights into customer satisfaction with the products and services as well as to predict the opinions given a particular context.

This study developed and compared different machine learning models for classifying customer reviews as positive, negative, or neutral, as well as predicting ratings with one to five stars based on a TripAdvisor hotel reviews dataset that contains 20,491 unique hotel reviews.

This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).

The authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3,1) in all dimensions.

The authors find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).

This paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If so(3,1) is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions.