Physical Sciences and Mathematics Commons^™

A Note On Euler's Definition Of The Sum Of A Divergent Series, Alexander Aycock

Euleriana

We outline Euler's theory of divergent series and present another approach he could have taken to sum his ``factorial series". Finally, we address the contradictions that arise from his concept of a sum of a divergent series.

Euler's Explorations Of Extremal Ellipses, Jonathan David Evans

Euleriana

In the 1770s, Euler wrote a series of papers (E563, E691 and E692) about finding the ellipse with minimal area or perimeter in the family of all ellipses passing through a fixed set of points. This is a translation of all three papers from the original Latin, together with a commentary which discusses Euler's results and an appendix which addresses a question from E691 which Euler left for others to consider.

Arithmetic Theorems, Demonstrated By A New Method: An English Translation Of E271, Brendon Lasell

Euleriana

After defending in general terms the value of arithmetic demonstrations, where, according to Euler, the force of genius shines more brightly than in any other kind of demonstration, he goes on to let the force of his own genius shine forth in demonstrating the fact that, for any pair of relatively prime numbers a and N, a^ϕ(N) − 1 is always divisible by N, where we anachronistically denote by ϕ(N) the number of numbers less than N that are relatively prime to it. He approaches this theorem by considering the remainders that result when the numbers in an arithmetic …

On Double Integral Formulas: An English Translation Of E391, Thomas W. Polaski

Euleriana

In this paper, Euler investigates the theory of double intergrals to uses them to find areas, volumes and surface areas. He considers transformations of variables in double integrals. After showing that simple multiplication of the transformed differentials is not appropriate, he derives the formula for a change of variables in double integrals. Euler then uses such changes of variables to investigate areas and volumes, and then turns his attention to the so-called ``Florentine problem.'' This problem requires one to remove four equal windows from a hemispherical surface so that the remaining area is equal to the area of a square. …

Eulerian Problem Solving, Christopher Goff, Erik Tou

Euleriana

An introduction to the contents in Volume 6 (Issue 2) of Euleriana.

Bitseat: Reimagining The Financing For Airliners Using Nonfungible Tokens (Blockchain Technology), Edwin S. Ongola

Journal of Aviation Technology and Engineering

This essay describes how blockchain technology, particularly nonfungible tokens, can be used to raise funding for airliners. The essay begins with a brief overview on the costs, categories, and acquisition methods of airliners. After that, the essay introduces concepts on blockchain technology, tokens, and smart contracts. The essay then touches on how nonfungible tokens can be used to facilitate fractional ownership of airliners. From there, the essay discusses Bitseat, a conceptual nonfungible token for fractional ownership of airliners, covering its overall design, appeal, marketplace alternatives, and challenges. Finally, in the discussion, the essay summarizes the overall concept and outlines its …

Developing A Deep Learning-Based Artificial Intelligence System For Detecting Scientific Misinformation On Digital Platforms, Shorouq Al-Awawdeh, Ayah Al- Jafari

Objectives: This study develops and evaluates an Arabic scientific misinformation detection system by fine-tuning AraBERT-base-v2. It examines the effects of early stopping and input sequence length on model performance, interprets selected linguistic characteristics associated with misleading content, and discusses the limitations of using machine-translated data.

Methodology: The study adopted a mixed-methods design, employing a systematic integration of quantitative and qualitative approaches, supported by an interpretive qualitative reading. The initial database consisted of 23,546 records, including 123 Arabic articles collected from the Akeed, Sheek, and Taqeen platforms, and 23,423 foreign-language records drawn from the GossipCop and PolitiFact collections within FakeNewsNet. After …

The Evolution Characteristics Of Gas Pressure Around Coal Seam Directional Long Extraction Boreholes With Nonlinear Extraction Negative Pressure, Zhang Qi, Jia Jinlong, Li Zhiguo, Zhang Longgang, Qin Zhengyuan, Zhang Weizhong, Li Jin

Journal of Sustainable Mining

Nonlinear pressure of coal seam gas in the directional borehole and surrounding areas affects extraction efficiency. A multi-field coupling numerical model, including gas desorption, diffusion, fracture seepage, and borehole extraction, is developed for the No. 3 coal seam of the GJH mine. Using the numerical simulation method of control variables, extraction was developed to investigate the nonlinear evolution of axial pressure gradients in directional long borehole and the spatiotemporal response characteristics of gas pressure. Results show that coal seam seepage pressure exhibits a nonlinear radial gradient attenuation around the borehole, evolving through rapid pressure change, stabilization, and slow adjustment. The …

From Data To Decision-Making: The Role Of Local Digital Twins In Cross-Domain Management Within Municipalities – A Research-In-Progress Study In Veenendaal, Diana M.E. Boekman, Koen Smit, Guido Ongena, Rob Peters

Communications of the IIMA

Municipalities are facing increasingly complex, interconnected challenges in areas like housing, climate adaptation, mobility, and social policy. Local Digital Twins (LDTs) are seen as a promising tool to make this complexity more understandable and support decision-making. At the same time, both literature and practice show that few initiatives get past the pilot phase, even though getting through that phase is essential for successful long-term adoption.

This paper presents a research-in-progress study on the development and application of an implementation method for LDT technology within the municipality of Veenendaal, based on human values rather than driven by technological possibilities. Based on …

A Novel Entropy Based Maintainability Measurement Algorithm For Java Source Code., Remi M. Yusuf Mr, Md Shadab Mashuk, Julian Bass

Communications of the IIMA

Software metrics play a central role in assessing and managing the quality of software systems providing quantitative insights into attributes such as complexity, reliability, rigidity, modifiability and maintainability. Among these, maintainability is particularly critical, as it directly influences the ease of system evolution, long-term sustainability, and overall cost effectiveness. Despite the widespread use of metric-based maintainability measurement algorithms, capturing a value that reflects the maintainability situation of software source code remains a challenging task, especially in the presence of design deficiencies such as code smells. To measure changes in maintainability, this study experimentaly characterises the relationship between code smells and …

Δ−Scuti Star Hr 1170, Salman A. Nejad

Aquila: The Journal of Embry-Riddle Observatory

HR 1170, a variable star in the constellation Perseus, exhibits multi-periodic pulsations consistent with its classification as a δ−Scuti star. Through photometric and spectroscopic observations using the 1-meter ERAU telescope and the SARA-RM telescope, this study investigates its variability and spectral characteristics. Photometry conducted over several nights reveals pulsation periods that closely align with previously reported values. Time-resolved spectroscopy highlights prominent absorption features, including Balmer lines and metallic elements, offering further insights into the star’s atmospheric dynamics.

Libs-Based Detection And Preliminary Classification Of Microplastic Signatures In Soil Samples., Ekhlas Jabir Mahmood

Al-Bahir

Contamination of terrestrial systems by microplastics (MPs) has become a critical environmental hazard, but detection of such contaminants in a complex soil system is a challenge for conventional analytical techniques. This research aims to assess the potential of Laser-Induced Breakdown Spectroscopy (LIBS) for the detection and differentiation of different types of microplastics, including HDPE, LDPE, PP, PS, and PVC, dispersed in the soil of Al Najaf, Iraq. Soil samples were collected from different functional zones, namely, Industrial, Commercial, Agricultural, Residential, and Roadside, at the surface level and 30 cm depth. Detection was done by measuring the intensity of the C/H …

A Transformer-Based Approach With Data Augmentation For Multilabel Emotional Context Detection, Mohsin Hasan Hussein, Marem H. Abdulabas, Azha Talal Mohammed Ali, Homam Aziz Ghazi

Al-Bahir

Emotion identification in texts is becoming increasingly difficult because of the wide variety of ways emotions are represented. This study uses a fine-tuned Robustly Optimized Bidirectional Encoder Representations from Transformers Approach

(RoBERTa) to offer a Transformer-based model for identifying multilabel emotional context in textual data. To balance emotion categories and enhance the model's capacity for generalization, data augmentation is applied on two different datasets: Semantic Evaluation and Cross-lingual Emotion Dataset (SemEval and XED) English corpus. This stage is considered one of the most important steps in preprocessing as it greatly helps to improve the results. The RoBERTa model was then …

From Dissertation To Deployment: A Unified Software Platform Operationalizing Clinical-Prediction And Sequential-Security Ai For Healthcare, Olsi Shehu, Damiana Teliti, Jasmin Kevrić, Bekir Karlik

Communications of the IIMA

Advances in machine learning for healthcare are abundant, yet most validated models remain confined to research notebooks and never reach secure, usable clinical software. This paper addresses that deployment gap by presenting a unified, security-hardened software platform that operationalizes two complementary streams of doctoral research inside a single, role-based hospital information system. The first stream contributes a clinical-prediction capability: an ultra-hybrid ensemble that couples a quantum-inspired feature transformation, particle-swarm feature selection, and calibrated soft voting for cancer-outcome prediction (96.41% accuracy, AUC-ROC 0.983 on TCGA-BRCA), survival stratification, multi-cancer generalization, and pharmacogenomic drug-response classification (89.31% mean accuracy across 25 compounds). The second …

Gc-Ms Profiling And Antibacterial Activity Of Cold-Macerated Garlic Extracts Against Multidrug-Resistant Uropathogens, Fatima A. Khalaf, Saeed A. Fayadh

Karbala International Journal of Modern Science

The growing number of cases of multidrug-resistant (MDR) urinary tract infections has made the clinical management of urinary tract diseases a significant challenge; therefore, the need for effective adjunctive therapies cannot be overemphasized. This study evaluated the bioactive components and antibacterial efficacy of cold-macerated garlic extracts obtained using distilled water, 70% ethanol and hexane solvents against antimicrobial-resistant urinary isolates. Out of 250 urine samples that were analyzed, 124 (49.6%) showed significant microbial growth, with Escherichia coli being the most frequently isolated organism. The results of the phytochemical screening and Gas Chromatography-Mass Spectrometry (GC-MS) analysis showed that the ethanolic extract had …

Hyperlattice-Valued And Superhyperlattice-Valued Uncertain Sets With Decision Applications, Takaaki Fujita, Ajoy Kanti Das, Sankar Prasad Mondal, Arif Mehmood, Arkan Ghaib

Neutrosophic Systems with Applications

Fuzzy set theory enriches classical sets by assigning to each element a graded membership in [0,1], thereby capturing partial inclusion and uncertainty. The notion of an Uncertain Set further abstracts this idea by allowing membership to take values in a general degree-domain, providing a unified language that subsumes fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and related models. On the algebraic side, a hyperlattice replaces one lattice operation by a multivalued hyperoperation, enabling the representation of ambiguous or non-deterministic combinations, while a superhyperlattice iterates this structure through powerset lifting to obtain higher-order layers of interaction. Motivated by these developments, we introduce HyperLattice-valued …

A Neutrosophic Event-Graph Legal Ai System For Detecting Contradictions In Witness Testimonies Under Egyptian Law, Shimaa Abdelghany Attalla, Alaa Elmor, Nada Hesham, Abduallah Gamal

Neutrosophic Systems with Applications

Witness testimony is an important source of evidence in criminal proceedings, but it may contain contradictions, incomplete details, or conflicts with other case-file materials. This paper proposes a neutrosophic event-graph legal AI framework for detecting materially contested claims in witness testimonies under the Egyptian criminal-procedure context. The framework converts testimony and related records into structured claims containing actor, action, object, time, location, source, and modality. These claims are then connected through an event graph and evaluated using neutrosophic components of support, indeterminacy, and opposition. The system produces source-grounded legal-review alerts when a claim has sufficient opposition from other claims or …

An Interval-Valued Spherical Fuzzy Critic–Waspas Framework For Prioritizing Healthcare Delivery Models To Enhance Patient Satisfaction Under Uncertainty, Mariam Hamada, Ahmed Samy, Mohamed M. Abdelhafeez, Shrouk El-Amir

Neutrosophic Systems with Applications

Selecting an appropriate healthcare delivery model is important for improving the quality of healthcare services and enhancing patient satisfaction. However, this decision is complex because it involves several criteria, uncertainty, and different expert opinions. To handle this uncertainty, this paper uses Interval-Valued Spherical Fuzzy Sets (IVSFSs), which allow experts to express their evaluations more flexibly. This paper proposes an integrated interval-valued spherical fuzzy CRITIC-WASPAS approach to prioritize healthcare delivery models. The CRITIC method is used to determine the objective weights of the evaluation criteria, while the WASPAS method is used to rank the healthcare delivery models. Expert evaluations are expressed …

20 Years Of Neutrosophic Statistics: A Bibliometric Analysis, Hammad Khalid, Arshad Hameed

Neutrosophic Systems with Applications

Florentin Smarandache introduced neutrosophic statistics (NS), a formalism for representing uncertainty and indeterminacy in observations, parameters and statistics in an extension to classical and interval statistics. Although widespread in various contexts, such as statistical quality control, hypothesis testing, medical diagnosis, and decision science, and increasingly used and developed, the scientific evolution and conceptual framework of the science of decision making remain largely unexamined. To fill this gap, the present study has been conducted with a comprehensive bibliometric analysis of NS research articles published between 2003 to 2025 from Scopus which has been conducted following the SPAR-4-SLR protocol. In all, 501 …

A Unified Framework For Neutrosophic Estimation Using Fractional Power, Exponential, And Logarithmic Functions With Bivariate Auxiliary Information, Anchal Yadav, Anuj Yadav

Neutrosophic Systems with Applications

This study develops a generalized neutrosophic ratio-type estimator for estimating the population mean by incorporating information from two auxiliary variables under Simple Random Sampling Without Replacement (SRSWOR). The proposed methodology extends the conventional single-auxiliary-variable approach by jointly incorporating bivariate auxiliary information within the neutrosophic framework, thereby accounting for uncertainty, indeterminacy, and inconsistency in the available information. The bias and mean squared error of the proposed estimator are derived using first-order approximations, and the corresponding efficiency conditions are established through theoretical comparisons with existing neutrosophic estimators. The performance of the proposed estimator is further examined using a real medical dataset represented …

Monitoring System In The Georeactor Area During The Underground Coal Gasification Process, Aleksandra Tokarz, Jacek Grabowski, Krzysztof Korczak

Journal of Sustainable Mining

Safety control of the underground coal gasification (UCG) process involves ensuring that the process runs smoothly, monitoring changes occurring on the surface and in the rock mass, and counteracting the negative environmental impact of the process. The article presents the application of a monitoring system implemented in Poland, both in pilot tests conducted in shallow coal seams at the Barbara Experimental Mine and in deep coal seams at the Wieczorek mine, where a full-scale gasification process was tested. The analysis of the monitoring results carried out during the gasification experiment in an operating mine allowed for the identification of key …

Microwave Thermal Pre-Treatment To Improve Nickel Extraction From Lateritic Ore, Johana Borda, Daniel Sosa, Robinson Torres

Journal of Sustainable Mining

Two heat treatment processes for a nickeliferous laterite sample are presented, one by the conventional muffle route and the other by microwave. The heating was carried out in order to improve the dissolution of nickel in an acid medium. The study describes the changes observed in the mineral for the increase in temperature as a consequence of radiation in the microwave and in the muffle. The changes in the mineral crystalline phases were analyzed by X-ray diffraction. The leaching media consisted of a 1 M sulfuric acid solution at ambient conditions for 7 h. The interaction between the reagent and …

On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci

Journal of Stochastic Analysis

We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian motion (GBM) and the constant elasticity of variance (CEV), offering flexibility to capture complex dynamics while posing analytical challenges. Using a fixed-point approach, we prove existence and uniqueness, analyze higher-order moments, derive asymptotic estimates, and assess stability. Finally, we illustrate an application where Poisson’s equation admits a probabilistic representation via a timehomogeneous nonlinear SDE with state-dependent variable exponents.

Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver

Journal of Stochastic Analysis

Starting with a stochastic matrix, we study the behavior of powers of an associated companion matrix, which has the same characteristic polynomial as the original matrix. In general the companion matrix will have negative entries while maintaining rowsums equal to 1. We will find the growth rate even if the Ces`aro limit of the sums of the companion matrix diverge. Surprisingly, in the irreducible aperiodic case the powers of the companion matrix will converge even though the norm of the matrix exceeds 1 and it has possibly negative entries.

Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar

Journal of Stochastic Analysis

The goal of this article is to study in depth the subclass of Z+- valued additive processes in law with nonnegative increments. We establish key distributional properties of these processes and obtain some existence results under a variety of conditions. We show that they form a subclass of the family of inhomogeneous Markov chains with spatial homogeneity. We extend the notion of factoring introduced by Sato (2004, [9]) for Rd-valued additive processes in law to their Z+-valued counterparts with nonnegative increments. We give a sufficient condition for the existence of a factoring for these processes. Lastly, we obtain their representation …

Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger

CODEE Journal

Students in introductory differential equations courses often learn to associate specific equation types with familiar physical systems. While this approach supports procedural fluency, it can inhibit transfer learning: students recognize familiar forms rather than construct models from first principles. This paper presents a modeling-first instructional approach designed to help students recognize the shared structure of second-order differential equations across diverse contexts. Students derive governing equations from fundamental physical laws for multiple systems, including an Inductor, Resistor, and Capacitor (LRC) electrical circuit, a simple pendulum, and viscous pipe flow. Through guided comparison, students identify common components such as inertia, damping, restoring …

Geographical Pattern Analysis Of Gis Images With Deep Learning And Voronoi Network, Nidaa Kareem, Tawfiq A. Al-Assadi

Journal of Intelligent Informatics, Networking, and Cybersecurity

Localization is not enough for the analysis of spatial patterns; a principled geometric and statistical framework is required. This paper proposes an integrated spatial intelligence system combining deep learning, computational geometry, and spatial statistics, which is a unified and interpretable system. It is based on segmentation localization that accurately localizes the centroid of each object without the disadvantages of the bounding box. These centroids form a natural Voronoi tessellation of regions of spatial influence intrinsic to the data instead of imposing any artificial restrictions. A geometry-based density formulation is used to improve representation, which includes Voronoi cell areas and neighborhood …

Generalized Spectral Bound For Quasi-Twisted Codes, Buket Özkaya

Turkish Journal of Mathematics

Minimum distance bounds play a central role in the analysis of algebraic codes. For cyclic and constacyclic codes, several bounds based on their zero set have been developed. However, analogous results for quasi-twisted (QT) codes are comparatively limited. In this paper, we further investigate the spectral theory of QT codes and derive a general spectral bound on their minimum distance. Our bound unifies and generalizes previously known spectral bounds for quasi-cyclic (QC) and QT codes, and contains them as special cases. We present a new proof technique and show that the bound can be formulated with respect to an arbitrary …

A Novel Iterative Algorithm For Approximating Common Fixed Points Of Generalized Α-Nonexpansive Multivalued Mappings In Kohlenbach Hyperbolic Spaces, Makbule Kaplan Özekes

Turkish Journal of Mathematics

In this paper, we propose a new iterative scheme involving three multivalued mappings in Kohlenbach hyperbolic spaces. Strong and ∆-convergence theorems are established for approximating common fixed points of nonexpansive multivalued mappings under suitable conditions. A numerical example is also presented to illustrate the efficiency and faster convergence of the proposed method. The results obtained extend and unify several related contributions in the existing literature.

On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos

Turkish Journal of Mathematics

In this paper, we answer some natural questions concerning symmetrisation and more general combinations of Finsler metrics, with a view to applications to Funk and Hilbert geometries and metrics on Teichmüller spaces. The metrics on Teichmüller space that we consider are the Thurston metric and the earthquake metric, both introduced by Thurston. The first metric has been thoroughly studied over the last couple of decades, and the second over the last few years. The Funk metric and its symmetrisation, the Hilbert metric, are classical metrics that have been investigated in the contexts of hyperbolic geometry and geometric function theory and, …