Boletim da Sociedade Paranaense de Matemática

Mathematically modelling based on different feed ingredients

Amna Javed, Aliya Fahmi, Amna, Ishtiaq Ali, Saeed Islam — Sun, 15 Mar 2026 19:54:58 +0000

Various feed ingredients including omega oils and oil seeds, have been used worldwide to improve intake among the birds. In this research paper, feed ingredients were analyzed for fat, fiber, protein, tannins and cyanogenic glycosides (HCN) contents along the fatty acid characterization. Different supplemented enriched experimental diets were also developed to estimate the Crude fat, protein, fatty acids content and gross energy estimation. These experimental isocaloric and isonitrogenous diets were evaluated through mathematical model for characterization. TOPSIS technique is applied in feed ingredients, protein, tannins and cyanogenic glycosides. PIS and NIS solution proposed in different protein. To define the collective index of the ranking.

Heat transfer and entrance flow characteristics of viscoplastic fluid in a circular cylinder using the Bingham-Papanastasiou model

Deepa Madivalar, Vishwanath Kadaba Puttanna, A Kandasamy — Sun, 15 Mar 2026 20:02:24 +0000

This study investigates the laminar flow of an incompressible viscoplastic fluid in the entrance region of a circular cylinder, with emphasis on heat transfer characteristics by considering two different thermal boundary conditions: constant wall temperature and constant wall heat flux. The fluid behavior is modeled using the regularized Bingham-Papanastasiou approach, and the analysis is conducted under the assumptions of Prandtl's boundary layer theory using the finite difference method. The study highlights the simultaneous development of the velocity and thermal boundary layers. It presents a detailed analysis of the heat transfer behavior of Bingham fluid flow in the cylindrical geometry. The impact of yield stress on the flow and thermal parameters is thoroughly examined. The presence of yield stress significantly affects flow characteristics such as velocity, pressure, and temperature distributions. It also influences heat transfer performance, particularly the Nusselt number. The effects of key dimensionless parameters, such as the Bingham and the Prandtl number, are also discussed. The obtained results are consistent with previously reported findings in certain limiting cases, validating the current approach.

Pseudo generalized quasi-Einstein warped products manifolds with respect to affine connections

Mohd Vasiulla, Vineet Kumar, Mohabbat Ali, Sanjay Tyagi, Ashish Tyagi — Mon, 16 Mar 2026 15:09:19 +0000

In this paper, we investigate warped products on pseudo-generalized quasi-Einstein manifolds under affine connections. We explore their fundamental properties, establish conditions for their existence, and prove that these manifolds can be nearly quasi-Einstein and pseudo quasi-Einstein. To illustrate, we provide examples in Riemannian and Lorentzian geometries, confirming their existence. Finally, we construct and analyze an explicit example of a warped product on a pseudo-generalized quasi-Einstein manifold with respect to affine connections.

Refined Neutrosophic Rhotrix: A Novel Algebraic Model for Complex Uncertainty Representation

Ananda Priya B, Gnanachandra P — Mon, 16 Mar 2026 15:13:30 +0000

The concept refined neutrosophic rhotrix, an advanced algebraic structure that extends traditional rhotrices by incorporating Refined neutrosophic logic, is introduced. By decomposing indeterminacy into multiple subcomponents, true indeterminacy, contradiction, and uncertainty, the Refined neutrosophic framework allows for more granular representation and analysis of imprecise, inconsistent, and incomplete information. The study defines the algebraic operations of Refined neutrosophic rhotrices and establishes their structural properties, including closure, associativity, and distributivity under specific conditions.

A Fractional-Order Dynamic Modelling and Robust Control of Nonlinear Robotic Manipulators: A Memory-Driven Framework with FOPID and FO-SMC}

Gizachew Tirite Gellow — Mon, 16 Mar 2026 15:18:19 +0000

This paper develops a comprehensive fractional-order dynamic modelling and control framework for nonlinear robotic manipulators by integrating Caputo fractional derivatives to capture memory-dependent effects such as viscoelasticity, structural damping, and hysteresis—phenomena that classical integer-order models cannot represent accurately. Two fractional-order controllers, a fractional-order PID (FOPID) and a fractional-order sliding-mode controller (FO-SMC), are designed to exploit the long-term memory embedded in the system dynamics, thereby enhancing tracking accuracy, robustness, and transient behavior.

A Hybrid Equation (EHFM) for Face Recognition: Comparison with Statistical Technique

Rusul Mohsen Washeel, Zahraa Fadhil Abd Alhussain, Asmhan Flieh Hassan — Mon, 16 Mar 2026 15:27:36 +0000

In this research we propose a novel equation (technique) for face recognition. Face recognition is very important task in digital image processing (image similarity), which have many applications in security, biometrics, social media, and entertainment. However, that task is still challenging and limited by several factors. The new technique, we call it, a hybrid equation (EHFM), which has been tested versus the famous measure (SSIM). Face recognition via (EHFM) is depend on a test (reference) image and images of database. The new propose mathematical equation (EHFM) is performed by MATLAB R2020a using the very famous database AT&T images, we chose eight subjects and ten views (poses) per subject with various facial expressions. The essential goal of this our new idea is to introduce more accuracy equation (technique) good for face recognition technique that can be perform in real-time environment. Performance of new our proposed (EHFM) equation for face recognition, which is proved experimentally, also it is evidenced to outperform the (SSIM) statistical-based and famous face recognition.

A Note on Eigenvalues Significance in Digital Image Processing

Akshay Prasad, Vineet Bhatt, Richa Sharma, Deepika Jhala — Mon, 16 Mar 2026 15:31:57 +0000

This paper discusses the importance of eigenvalues in the area of digital image processing (DIP). A digital image may be in the form of a matrix data. The properties of eigenvalues, in the case of standard matrices, have been discussed. We started by converting a standard color image a grayscale image to make it easier to understand how the image is represented in a matrix, and then applied the properties and theorems using the MATLAB software. We also give a comparative analysis of different image noise reduction methods that make use of the eigenvalues of the image data. To measure the quality of image compression using various filters, we used mean square error (MSE) and peak signal to noise ratio (PSNR). Mean square error (MSE) and PSNR have also been used to conduct the experiments and to further prove the validity of the proposed theories and methodologies.

A Fuzzy Inference System for Assessing Parental Mental Health and Postpartum Depression

Saumya Richa, Zahoor Lone — Mon, 16 Mar 2026 17:32:42 +0000

ABSTRACT: The period after childbirth for both mothers and fathers is a very crucial time physically, psychologically, and socially, yet standard psychological assessments often restrict these complex feelings into rigid categories. Designing and testing a Mamdani-type Fuzzy Inference System (FIS), which ties together fuzzy logic with well-known psychological concepts, was measured using depression (EPDS), parental stress (PSS), social support (MSPSS), and emotional regulation (ERQ). This study fulfills that gap. The FIS uses linguistic categories-low, moderate, and high-based on data from 400 parents in Aurangabad, Bihar. The theoretical interaction and the application of these methods to these variables are modeled using expert-defined fuzzy rules that produce a continuous, understandable mental health index. The majority of parents showed moderate emotional well-being, with fathers showing somewhat poor results. The cross-sectional design limits causal inference. Parental emotional risks can be identified early using the fuzzy model.

Tracing the Celestial Legacy through Mathematical and Astronomical Advancement during the Vijayanagar Empire

Santosh Kumar, Siddhant Mishra, Shalini Rana — Mon, 16 Mar 2026 17:36:14 +0000

Advances in trigonometry, infinite series, and computational techniques during the late medieval Deccan transformed indigenous mathematical practice and enabled precise astronomical prediction. This study examines the construction of refined sine tables, early calculus-like series expansions, and iterative algorithms for numerical solutions, and observational protocols that underpinned planetary models. Through critical analysis of manuscripts, temple and royal inscriptions, and Sanskrit treatises, I document contributions by mathematicians and astronomers connected with the Vijayanagar sphere such as Madhava, Jyesthadeva, and Nilakantha Somayaji, whose work on trigonometric series, iterative computation, and a quasi-heliocentric planetary model anticipated later methodological shifts. The paper situates these technical advances within institutional contexts of patronage, scholarly networks, and mathematical pedagogy, demonstrating how courtly support fostered practical computation for calendrical, navigational, and ritual needs. Comparative perspectives with contemporaneous Chinese and European practices reveal convergent moves toward empirical measurement and analytic approximation, while underscoring distinct conceptual frameworks. By foregrounding mathematical methods first, the study reorients narratives about the Vijayanagar period from artistic achievements to scientific agency, arguing that its mathematical-astronomical legacy constitutes a critical bridge between classical Indian techniques and early modern scientific trajectories. The findings revise scientific historiography and offer novel frameworks for integrating South Asian mathematical practices into global histories of science.

Improving the Efficiency of Partial Homomorphic Encryption RSA and Developing it into a Hybrid System

Nibras Hadi — Mon, 16 Mar 2026 17:39:08 +0000

Previous research has carried out several investigations into the mechanics of encryption and the approaches that might speed up computations. It became necessary to develop these algorithms and leverage other technologies to achieve greater efficiency and performance in encryption systems by improving RSA encryption technology. RSA is a type of partial homogeneous encryption mechanism that enables and accelerates multiplication on encrypted data that contains large numbers and requires significant computational effort. Therefore, the system was improved to be more efficient by using the Extended Residual System (RNSBE), with a time reduction of up to 75% compared to the previous system. A hybrid RSA-Pa system was also introduced, combining the characteristics of the RSA algorithm and the Paillier algorithm, resulting in a strong and robust hybrid.

On the Arithmetic-Geometric-Harmonic-Mean Inequalities

Mohammad Al-Hawari, Ayat Almomani, Mohammad A. Bani Abdelrahman — Mon, 16 Mar 2026 20:24:08 +0000

In this article, we collect some inequalities concerning, Arithmetic, Geometric, Young and Heinz inequalities, the goal of the thesis is to investigate Young and Heinz inequalities for scalars and matrices. Improvements to the inequality studied of arithmetic and geometric means for scalars and several other auxiliary results; we provided some improvements to the inequality of arithmetic and geometric means by using the convex functions. A fundamental relationship between positive real numbers and the v-weighted arithmetic-geometric mean inequality is presented for any two scalars. Also, we introduce the largest and the smallest eigenvalues inequalities for matrices by using our subjects.

Enumeration of subsets with closedness in finite fields of characteristic 2

Prasanna Poojary, Nithish Kumar R., Vadiraja G R Bhatta — Mon, 16 Mar 2026 20:27:10 +0000

The additive closedness in the subset of an additive group is termed as $r$-value. The nature of closedness in different subsets of fixed size is observed as a spectrum of $r$-values. We enumerate $r$-values of subsets in finite fields of characteristic 2 and represent them as the spectrum of values. Based on these values the subsets can be further studied as partial Steiner triple systems, sum-free sets, Sidon sets, and Schure triples.

A A Brief Account of Computational Vedic and Ancient Indian Mathematics

D. S. Hooda, Avanish Kumar — Mon, 16 Mar 2026 20:32:25 +0000

The Vedas mentioned some rules for mathematical calculations and
their operations. The system of mathematics based on these rules
is known as Vedic mathematics. Vedic mathematics was written in
the Vedic age. In India, the Vedic mathematics was searched by Sri
Bharati Krishna Tirtha ji Maharaja between 1911 and 1918 from an
cient scriptures. In the present communication, the origin and de
velopment of Vedic mathematics are discussed. The applications of
Vedic mathematics are illustrated by solving multiplication problems
in very short time. Its application in computing multiplication and
future plan of its expansion is explained. Ancient Indian mathematics
with important discoveries like decimal system, numerals, zeros and
infinity are also discussed. The important works of four Indian math
ematicians has also been mentioned in the research paper. "a" ’a’ á

Double cyclic and Quantum codes

Shashirekha G., Vadiraja Bhatta G. R. — Mon, 16 Mar 2026 20:37:52 +0000

In this paper, we explore the structure of $ \mathbb{Z}_2 + u \mathbb{Z}_2 = \{0, 1, u, u + 1\} = \mathbb{Z}_2[u]$-additive codes, where $u^2=0$ and their generalization to double cyclic codes. We establish the algebraic framework for these codes over the ring $ \mathbb{Z}_2[u] $ and its extensions. Additionally, we provide explicit generators for double cyclic codes and define the Gray map to derive corresponding binary linear codes and quantum codes. Finally, we present an example illustrating the construction of a binary linear code.

POLYNOMIAL STABILITY OF TIMOSHENKO SYSTEM WITH SINGULAR LOCAL FRACTIONAL DAMPING IN THE TRANSVERSE DISPLACEMENT

haidar Badawi — Mon, 16 Mar 2026 20:41:44 +0000

In this paper, we investigate the stabilization of Timoshenko system with singular local fractional
damping in the transverse displacement. Using frequency domain approach combined with the multiplier
method, we prove that the energy of our system decays polynomially with different rates.

Designing an Encryption System Using MAL-Eleven Algebra and Pythagoriciens Quadruplets

Reem Nayef Alahmad, Basel Hamdo Alarnous, Abdulbaset Alkhatib, Hassan Yassein — Mon, 16 Mar 2026 20:44:37 +0000

The pace of the technological race is accelerating at an unprecedented rate, driven by fierce competition among information security institutions to meet the demands of the digital market for encryption methods that fulfill its aspirations. This paper employs a mathematical construct to design an efficient encryption method by combining an algebraic structure with the concept of Pythagorean quadruplets.