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.