Boletim da Sociedade Paranaense de Matemática

Applications of the Cauchy-Schwarz inequality for the numerical radius

2026-02-15T12:43:54+00:00

The main goal of this article is to establish several new norm and numerical radius inequalities for operators based on the angle between two vectors in Hilbert space. These enhancements and extensions are achieved through the use of the polar and Cartesian decompositions of operators. In particular, it is proved that, if $X\in \mathscr B\left( \mathscr{H} \right)$ has the polar decomposition $X=U\vert X\vert $ and $\mu(\psi)=\frac{1}{4}(2+\cos\psi \cot\psi \log(\frac{1+\sin\psi}{1-\sin\psi}))$, then
\begin{equation*}
\omega^{2r}(X)\le \mu^{2r}(\theta)\left\Vert \frac{1}{p}f^{2pr}(\vert X \vert)+\frac{1}{q} g^{2qr}(\vert X^*\vert) \right\Vert,
\end{equation*}
where $\theta_{X,x}=\angle_{ f(\vert X\vert) x, g(\vert X\vert)U^* x }$, either $0\le \theta< \theta_{X,x} \le\frac{\pi}{2}$ or $\frac{\pi}{2}\le \theta_{X,x} <\theta\le\pi $ for all unit vectors $x\in \mathscr{H}$, $f,g$ are nonnegative continuous functions on $[0,+\infty) $ satisfying the relation $f(t)g(t)=t \,\,(t \in [0,+\infty))$, $r\ge1$, $p,q>1$ and $\frac{1}{p}+\frac{1}{q}=1$.

Continuous function by using (1, 2)Sβ - open sets in Bitopological spaces

2026-02-16T13:11:31+00:00

The aim of this paper is to introduce the concept of (1, 2)S_β -continuous function by using (1, 2)S_β -open sets in bitopological space and study some of their properties.

An AI-Enabled Automation Framework to Increase Efficiency and Accuracy in International Logistics Transit Declaration Processes

2026-02-16T13:17:16+00:00

Increasing global trade volumes and increasingly complex customs regulations have increased the need for accurate and traceable document management in international logistics. Manual preparation of transit declarations has become a significant challenge, especially after the transition to NCTS Version 5, which imposes higher data requirements and stricter validation rules. This study proposes a scalable, AI-powered automation framework that combines digital archiving, OCR-based data extraction, machine learning-assisted validation, data normalization, and automated declaration generation. The proposed system performs content analysis on multiple logistics documents, including CMRs, invoices, insurance policies, and T1/T2 forms, while conducting logical consistency checks using learning-based algorithms. Declaration packages are generated end-to-end and transmitted to customs authorities via SGS Transitnet using a REST-based interface. Real-world operational results show that processing time has been reduced from 20 minutes to approximately 3 minutes, and erroneous entries have been reduced by 84.6%. These findings demonstrate the technical and industrial applicability of the proposed model in high-volume transit operations and highlight the potential for fully autonomous, customs-compliant digital declaration execution in future developments.

Transforming Unstructured Customs Data into Strategic Insights with Robotic Process Automation

2026-02-16T13:20:34+00:00

Strategic decision-making in logistics and foreign trade relies on fast, accurate, and analytically actionable data. However, many commercial data platforms do not provide data through an Application Programming Interface (API) and must be manually obtained. Manual processes are error-prone, labor-intensive, and costly for companies. In this study, a sample data analytics framework based on Robotic Process Automation (RPA) has been developed to automatically extract, clean, and transform unstructured customs declaration data into analytical insights. Data was obtained from Datamyne.com using Python and Playwright, cleaned and standardized with Pandas and NumPy, stored in SQL Server, and visualized with Microsoft Power BI dashboards. Empirical findings show that the proposed system reduces daily data collection time by 93%, increases data accuracy from 95% to 98%, and reduces annual operational costs by approximately 94%. Furthermore, the integration of automated data pipelines with dynamic BI dashboards significantly increases analytical agility by enabling real-time monitoring, detailed analysis, and threshold-based KPI alerts. These results demonstrate that RPA-supported automation not only eliminates repetitive manual processes but also provides a measurable and sustainable competitive advantage for logistics and foreign trade operations by strengthening data-driven decision-making.

A new approach to Abel statistical convergence in metric spaces

2026-02-16T14:39:45+00:00

In this study, we first consider the sequences in the sense of Abel statistical together with the functions preserving the convergence of this kind of sequences called Abel statistical continuous functions in a metric space $X$. Then we relate this kind of continuity with some others. A function $f$ is Abel statistically continuous on a subset $E$ of a metric space $X$, if it preserves Abel statistical convergent sequences, i.e. $(f(p_{k}))$ is Abel statistically convergent whenever $(p_{k})$ is an Abel statistical convergent sequence of points in $E$, where a sequence $(p_{k})$ of points in $X$ is called Abel statistically convergent to a point $L$ in $X$ if $\lim_{x \to 1^{-}}(1-x)\sum_{k\in{\N}:d(p_{k}, L)\geq\varepsilon}^{}x^{k}=0$ for every $\varepsilon>0$. Some other types of continuities are also studied and interesting results are obtained.

Classification of Unstructured Text for RPA: A Comparative Machine Learning Analysis

2026-02-16T16:31:33+00:00

Effective human-robot collaboration in digital work environments depends on automated systems correctly interpreting human-generated free-text. Unstructured text types such as bug reports, customer requests, call center records, emails, and free comment fields cannot be processed directly by robotic process automation (RPA) due to the contextual expressions, typos, and stylistic inconsistencies they contain. RPA processes operate rule based. Making sense of this unstructured data, which does not conform to the rules, will strengthen human-robot interaction. In this study, it is proposed to use machine learning methods to provide automatic classification of unstructured texts. In this study, five basic classification algorithms (Logistic Regression, Naive Bayes, Support Vector Machines, Decision Trees, and Random Forest) frequently used in the literature were compared in terms of their features and computational methods. The findings reveal that classifying unstructured text has the potential to significantly increase the accuracy of RPA-based workflows. In this way, it is anticipated that improvements can be made by shortening process times through the interpretation of texts in RPA processes. As a result, it is envisaged that robot-human interaction can become more efficient by making sense of the unstructured data in RPA processes.

Type-I Heavy-Tailed Topp-Leone Family of Distributions with Applications to Biomedical Data

2026-02-16T16:37:34+00:00

In this study, a new family of probability distributions is proposed by integrating the tail flexibility of the Type I Heavy Tail family and the Topp Leone generated family of distributions and this is called the Type I Heavy Tailed Topp-Leone Generated (TIHTTL-G) family of distributions. The significant statistical properties of the TIHTTL-G family of distributions such as moments, generating functions, order statistics, stochastic ordering, and Rényi entropy are derived. The estimation of the parameters of a specific sub-model, the TIHTTL-Rayleigh (TIHTTLR), is performed employing ten different estimation techniques, both classical and Bayesian. Bayesian estimators are derived under three different loss functions namely: Square Error Loss Function, Linear Exponential Loss Function and Generalized Entropy Loss Function. Simulation experiments was conducted to examine parameter estimators from the different estimation procedures. Finally, to demonstrate the applicability of the proposed family, the TIHTTLR was fitted to three real-life datasets, and the results show its superior fit compared to competing models.

DNA and MAL-eleven Algebra to Design an Efficient Encryption Cryptosystem

2026-02-16T16:42:59+00:00

In this paper, we present an innovative encryption method based on DNA and MAL-eleven algebra, where both are used to generate public and private keys.This method provides a high level of security by enhancing key confidentiality and ensuring the protection of the original message from any potential threat.

On the Application of a Lusin-Type Theorem to Differential Inclusions

2026-02-16T16:46:54+00:00

In this paper, we establish a special version of Lusin’s theorem and study its application to dif- ferential inclusions. Lusin’s theorem expresses the realization of Littlewood’s second principle and establishes a connection between measurability and continuity. We prove this result and examine its use in the analysis of differential inclusions. As an application, we consider a differential inclusion problem with compact-valued right-hand side and an additional initial derivative condition, which naturally arises in the theory of differential inclusions. By combining the obtained Lusin result with selection methods, we derive sufficient conditions under which classical solutions can be constructed without imposing convexity assumptions on the value sets. The results clarify how Lusin arguments are important in the theory of classical solutions for differential inclusions.

Extensions in UP-Algebras and Related Properties

2026-02-16T17:05:33+00:00

In this work, we present and explore the idea of extensions of UP-algebras, inspired by similar
constructions in KU-algebras. We begin by recalling fundamental notions related to UP-algebras and proposea
formal definition of an extension in this context. Several illustrative examples are provided to demonstrate the
structure and behavior of these extensions. We examine the relationship between extensions and homomorphic
images, ideals, and congruences, and we establish some necessary and sufficient conditions under which a UPalgebra
extension exists. Furthermore, we compare our results with those obtained in the theory of KU-algebra
extensions to highlight similarities and differences. This study opens new directions in the algebraic analysis
of UP-structures.

AI Based Anomaly Detection in Application Performance Monitoring Using Random Forest

2026-02-16T17:08:31+00:00

This study was carried out to investigate the use of artificial intelligence and machine learning in application performance monitoring software systems and to develop anomaly detection methods. In the project, Random Forest algorithm was applied on the performance data obtained from “AdminServer” and “ManagedServer 1” servers, which are JVM processes, and anomalies were successfully detected using dynamic and dynamic thresholds. In the data processing process, data in JSON format were analyzed, dynamic threshold values were calculated with Z-score and data exceeding the determined threshold values were marked as anomalies. Anomaly detection was performed with the Random Forest classification algorithm, and model accuracy and classification performance were evaluated with metrics. In the visualization steps, histogram, KDE and scatter plot techniques were used to present both the data distribution and the detected anomalies in detail. The results obtained aim to provide an effective approach to system management by automating anomaly detection processes.

Approximation of Fuzzy Numbers by Modified Meyer-König and Zeller Operators: Implications for Medical Diagnosis Modeling

2026-02-16T17:13:08+00:00

In this work, the modified Meyer-König and Zeller operators are generalized to arbitrary compact intervals, and their approximation behavior and structural properties are thoroughly analyzed. In particular, we establish that the extended operators maintain key qualitative features such as monotonicity and shape preservation across any compact domain.

To illustrate the practical utility of the framework, the proposed operators are applied to the fuzzy modeling of diagnostic indicators in cancer patients. The accompanying numerical experiments, supported by detailed graphical and tabular analyses, confirm that the modified Meyer-König and Zeller operators yield highly accurate approximations while preserving the interpretability and clinical relevance of fuzzy medical data.