MathematicsPub Date : 2024-09-11DOI: 10.3390/math12182813
Chia-Ding Hou, Rung-Hung Su
{"title":"An Outlier Detection Approach to Recognize the Sources of a Process Failure within a Multivariate Poisson Process","authors":"Chia-Ding Hou, Rung-Hung Su","doi":"10.3390/math12182813","DOIUrl":"https://doi.org/10.3390/math12182813","url":null,"abstract":"Among attribute processes, the number of nonconformities conforming to a Poisson distribution is among the most crucial quality attributes. Furthermore, owing to the variety of quality attributes, the significance of the multivariate Poisson process in industry cannot be overstated. An out-of-control multivariate Poisson process can be detected using an alarm on a multivariate control chart. Nevertheless, pinpointing the specific quality attributes that led to the process shifts is complex. The study focuses on the causes that lead to process shifts in multivariate Poisson processes, unlike the majority of studies examining shifts in multivariate normal processes. This paper initially presents a statistical method for detecting outliers in a multivariate Poisson distribution. Furthermore, a progressive testing algorithm is then developed to identify the variables responsible for a failure within a multivariate Poisson process. According to simulation results, the proposed approach can effectively determine the sources of a process fault within a multivariate Poisson process.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"42 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-11DOI: 10.3390/math12182818
Ali Yahya Hummdi, Öznur Gölbaşı, Emine Koç Sögütcü, Nadeem ur Rehman
{"title":"Some Equations in Rings Involving Semiprime Ideals and Multiplicative Generalized Semiderivations","authors":"Ali Yahya Hummdi, Öznur Gölbaşı, Emine Koç Sögütcü, Nadeem ur Rehman","doi":"10.3390/math12182818","DOIUrl":"https://doi.org/10.3390/math12182818","url":null,"abstract":"This paper examines the commutativity of the quotient ring F/Y by utilizing specific differential identities in a general ring F that contains a semiprime ideal Y. This study particularly focuses on the role of a multiplicative generalized semiderivation ψ, which is associated with a map θ, in determining the commutative nature of the quotient ring.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"194 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-10DOI: 10.3390/math12182798
Alexandru Dinu
{"title":"Singularity, Observability, and Independence: Unveiling Lorenz’s Cryptographic Potential","authors":"Alexandru Dinu","doi":"10.3390/math12182798","DOIUrl":"https://doi.org/10.3390/math12182798","url":null,"abstract":"The key findings of this study include a detailed examination of the Lorenz system’s observability, revealing that it maintains high observability compared to other chaotic systems, thus supporting its potential use in cryptographic applications. We also investigated the singularity manifolds, identifying regions where observability might be compromised, but overall demonstrating that the system remains reliable across various states. Additionally, statistical tests confirm that the Lorenz system exhibits strong statistical independence in its outputs, further validating its suitability for encryption purposes. These findings collectively underscore the Lorenz system’s potential to enhance cryptographic security and contribute significantly to the field of secure communications. By providing a thorough analysis of its key properties, this study positions the Lorenz system as a promising candidate for advanced encryption technologies.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"88 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Novel Hybrid Model (EMD-TI-LSTM) for Enhanced Financial Forecasting with Machine Learning","authors":"Olcay Ozupek, Reyat Yilmaz, Bita Ghasemkhani, Derya Birant, Recep Alp Kut","doi":"10.3390/math12172794","DOIUrl":"https://doi.org/10.3390/math12172794","url":null,"abstract":"Financial forecasting involves predicting the future financial states and performance of companies and investors. Recent technological advancements have demonstrated that machine learning-based models can outperform traditional financial forecasting techniques. In particular, hybrid approaches that integrate diverse methods to leverage their strengths have yielded superior results in financial prediction. This study introduces a novel hybrid model, entitled EMD-TI-LSTM, consisting of empirical mode decomposition (EMD), technical indicators (TI), and long short-term memory (LSTM). The proposed model delivered more accurate predictions than those generated by the conventional LSTM approach on the same well-known financial datasets, achieving average enhancements of 39.56%, 36.86%, and 39.90% based on the MAPE, RMSE, and MAE metrics, respectively. Furthermore, the results show that the proposed model has a lower average MAPE rate of 42.91% compared to its state-of-the-art counterparts. These findings highlight the potential of hybrid models and mathematical innovations to advance the field of financial forecasting.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-09DOI: 10.3390/math12172783
Hongsheng Su, Zonghao Ding, Xingsheng Wang
{"title":"Prediction of Wind Turbine Gearbox Oil Temperature Based on Stochastic Differential Equation Modeling","authors":"Hongsheng Su, Zonghao Ding, Xingsheng Wang","doi":"10.3390/math12172783","DOIUrl":"https://doi.org/10.3390/math12172783","url":null,"abstract":"Aiming at the problem of high failure rate and inconvenient maintenance of wind turbine gearboxes, this paper establishes a stochastic differential equation model that can be used to fit the change of gearbox oil temperature and adopts an iterative computational method and Markov-based modified optimization to fit the prediction sequence in order to realize the accurate prediction of gearbox oil temperature. The model divides the oil temperature change of the gearbox into two parts, internal aging and external random perturbation, adopts the approximation theorem to establish the internal aging model, and uses Brownian motion to simulate the external random perturbation. The model parameters were calculated by the Newton–Raphson iterative method based on the gearbox oil temperature monitoring data. Iterative calculations and Markov-based corrections were performed on the model prediction data. The gearbox oil temperature variations were simulated in MATLAB, and the fitting and testing errors were calculated before and after the iterations. By comparing the fitting and testing errors with the ordinary differential equations and the stochastic differential equations before iteration, the iterated model can better reflect the gear oil temperature trend and predict the oil temperature at a specific time. The accuracy of the iterated model in terms of fitting and prediction is important for the development of preventive maintenance.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"28 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-09DOI: 10.3390/math12172786
Juan Luis González-Santander, Francesco Mainardi
{"title":"Some Fractional Integral and Derivative Formulas Revisited","authors":"Juan Luis González-Santander, Francesco Mainardi","doi":"10.3390/math12172786","DOIUrl":"https://doi.org/10.3390/math12172786","url":null,"abstract":"In the most common literature about fractional calculus, we find that Dtαaft=It−αaft is assumed implicitly in the tables of fractional integrals and derivatives. However, this is not straightforward from the definitions of Itαaft and Dtαaft. In this sense, we prove that Dt0ft=It−α0ft is true for ft=tν−1logt, and ft=eλt, despite the fact that these derivations are highly non-trivial. Moreover, the corresponding formulas for Dtα−∞t−δ and Itα−∞t−δ found in the literature are incorrect; thus, we derive the correct ones, proving in turn that Dtα−∞t−δ=It−α−∞t−δ holds true.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-09DOI: 10.3390/math12172795
Srinivas R. Chakravarthy
{"title":"Quantitative and Qualitative Analysis of Aircraft Round-Trip Times Using Phase Type Distributions","authors":"Srinivas R. Chakravarthy","doi":"10.3390/math12172795","DOIUrl":"https://doi.org/10.3390/math12172795","url":null,"abstract":"One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times by a few minutes will have a significant impact on the number of trips made by an aircraft, as well as enabling improvements in key measures such as the median and 75th and 95th percentiles. Looking at such measures other than the mean is critical as it is well known that the mean can under- or overestimate the performance of any model. While there is considerable literature on the study of strategies to decrease boarding times, the same cannot be said about the study of the boarding time given a particular strategy for boarding. Thus, the focus of this paper is to study analytically (using suitable stochastic models) and numerically the impact of reducing the average time on the key measures to help the system to plan accordingly. This is achieved using a well-known probability distribution, namely the phase type distribution, to model various events involved in the boarding process. Illustrative numerical results show a reduction in the percentile values when the average boarding times are decreased. Understanding the percentiles of the boarding times, as opposed to relying only on the average boarding times, will help management to adopt a better boarding strategy that in turn will lead to an increase in the number of trips that an aircraft can make.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"12 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-09DOI: 10.3390/math12172784
Benjamin F. Akers, Kristina O. F. Williams
{"title":"Coarse-Gridded Simulation of the Nonlinear Schrödinger Equation with Machine Learning","authors":"Benjamin F. Akers, Kristina O. F. Williams","doi":"10.3390/math12172784","DOIUrl":"https://doi.org/10.3390/math12172784","url":null,"abstract":"A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data are to the training set.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"34 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-09DOI: 10.3390/math12172788
Ekaterina V. Orlova
{"title":"A Novel Brillouin and Langevin Functions Dynamic Model for Two Conflicting Social Groups: Study of R&D Processes","authors":"Ekaterina V. Orlova","doi":"10.3390/math12172788","DOIUrl":"https://doi.org/10.3390/math12172788","url":null,"abstract":"We consider a two-group social conflict under the corporates’ research and development (R&D) business processes. Conflict participants are divided into two groups depending on their attitude to new ideas, technologies, and behavioral style for R&D creative problems—innovators and adapters. We reveal the contradiction that arises between the need to include both types of employees in one project team and their objectively antagonistic positions regarding the methods and approaches to R&D processes. The proposed research methodology is based on a modern post-non-classical paradigm formed on the principles of coherence, interdisciplinarity, openness, and nonlinearity, as well as a sociophysical approach to the social conflicts modeling. We use the general theories of magnetism, paramagnetism, and functions of P. Langevin and L. Brillouin to describe the dynamics of group participants’ preferences regarding the style of conflict behavior. The analogy of paramagnetism, consisting in the orienting effect of the magnetic field, is used to describe social groups interactions that have not only their own interests, but are also influenced by the opinions of opposite social groups. A two-dimensional, four-parameter map represents the dynamics of group conflict. Modeling results show that regardless of the initial states and with certain parameters of intra-group and intergroup interactions, the trajectories eventually converge to an attractor (limit cycle) in a two-dimensional space. No non-periodic or chaotic modes are identified in the two-group conflict, which determines the controllability of the described conflict. The results of the simulation experiments are used as decision support and contradictions resolution aimed at forming the required modes of the corporates’ research and development business processes and ensuring the group participants’ cohesion and depolarization. The results of testing the model at an industrial enterprise are presented.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"7 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MathematicsPub Date : 2024-09-09DOI: 10.3390/math12172791
Guoquan Yuan, Xinjian Zhao, Liu Li, Song Zhang, Shanming Wei
{"title":"Few-Shot Learning Sensitive Recognition Method Based on Prototypical Network","authors":"Guoquan Yuan, Xinjian Zhao, Liu Li, Song Zhang, Shanming Wei","doi":"10.3390/math12172791","DOIUrl":"https://doi.org/10.3390/math12172791","url":null,"abstract":"Traditional machine learning-based entity extraction methods rely heavily on feature engineering by experts, and the generalization ability of the model is poor. Prototype networks, on the other hand, can effectively use a small amount of labeled data to train models while using category prototypes to enhance the generalization ability of the models. Therefore, this paper proposes a prototype network-based named entity recognition (NER) method, namely the FSPN-NER model, to solve the problem of difficult recognition of sensitive data in data-sparse text. The model utilizes the positional coding model (PCM) to pre-train the data and perform feature extraction, then computes the prototype vectors to achieve entity matching, and finally introduces a boundary detection module to enhance the performance of the prototype network in the named entity recognition task. The model in this paper is compared with LSTM, BiLSTM, CRF, Transformer and their combination models, and the experimental results on the test dataset show that the model outperforms the comparative models with an accuracy of 84.8%, a recall of 85.8% and an F1 value of 0.853.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}