A Discrete Nonlinear Advection–Diffusion–Reaction Scheme with Vortex Transport: Stability, Convergence, and Algorithmic Complexity

Malika Abdulameer

doi:https://doi.org/10.54216/PMTCS.060202

Prospects for Applied Mathematics and Data Analysis | 2026

Generating Neutrosophic Random Variables Based on Generalized Gamma Distribution

In practice, we encounter many systems that cannot be studied directly, either due to high costs or because some of these systems are not directly detectable. Therefore, we resort to simulation, which involves applying the study to systems similar to real-world systems and then projecting the results if they are suitable for the real system. The simulation process requires a thorough understanding of probability distributions and the methods used to transform random numbers following a regular distribution on [0,1] into random variables that follow it. This allows us to maximize the benefits of the simulation process and obtain more accurate results for all emerging conditions. The generalized gamma distribution is a family of three parameters characterized by high flexibility. It includes several important distributions as special cases, including the gamma, Weibull, exponential, and Rayleigh distributions, making it exceptionally valuable in engineering and reliability analysis. In previous research, we presented a neutrosophic view of the process of generating random numbers and some techniques used to generate random variables. In this research, we present a neutrosophic study for generating neutrosophic random variables following the generalized gamma distribution, a distribution widely used in engineering applications. The neutrosophic approach takes into account the uncertainty and indeterminacy of the parameters, resulting in random intervals for the variables rather than specific values, and thus provides more accurate simulation results that adapt to all the conditions that the system in operation may encounter.

groups

Khalifa AlShaqsi mail

link https://doi.org/10.54216/PAMDA.060104

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

Details open_in_new

Prospects for Applied Mathematics and Data Analysis | 2026

Exact Bias–Variance Decomposition and Degrees of Freedom in Ridge Regression: Theory, Verification, and a Disease-Progression Application

Ridge regression estimates β in the linear model y = Xβ +ε by βˆ (λ) = argminβ ∥y−Xβ∥2+λ∥β∥2, trading bias for variance as λ increases. This paper collects six results about βˆ (λ) into a single self-contained development, each proved and then checked numerically. The estimator is written in closed form through the singular value decomposition of X; its effective degrees of freedom, df(λ)=Σj d2j /(d2j +λ), are shown to be strictly decreasing and convex in λ; its exact bias and variance are derived in closed form; a strictly positive λ is shown always to exist that reduces mean squared estimation error below that of ordinary least squares whenever the noise variance is positive; the estimator is shown to coincide with the posterior mean under a Gaussian prior with precision proportional to λ; and the leave-one-out cross-validation error is shown to admit a closed-form shortcut that generalized cross-validation approximates by averaging its leverage terms. Every derived quantity is verified against data: the leave-one-out shortcut matches brute-force refitting exactly, and a calibrated Monte Carlo simulation confirms the closed-form bias and variance to within simulation error at every tested λ. Applied to a standard diabetes disease-progression dataset (n = 442, ten predictors), the theoretical construction correctly locates a strictly risk-reducing regularization region, and repeated cross-validation shows ridge, lasso, and elastic net all lying within one standard error of ordinary least squares in out-of-sample prediction error—consistent with the closed-form theory, which attributes the available gain to reduced parameter-estimation risk on a well-conditioned design rather than to prediction-error reduction.

groups

Dwi Retnowardani mail

link https://doi.org/10.54216/PAMDA.060105

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

Details open_in_new

Journal of Neutrosophic and Fuzzy Systems | 2026

Neutrosophic–Fuzzy Evidence Fusion for Uncertainty-Aware Cultivar Identification from Viticultural Chemical Profiles

Cultivar identification from viticultural chemical profiles is a multiclass recognition problem in which a hard label alone does not reveal whether global chemometric evidence agrees with the local structure of previously observed samples. This paper proposes Neutrosophic–Fuzzy Viticultural Evidence Fusion (NFVEF), an uncertainty-aware classifier that combines a global discriminant probability vector G(x) ∈ ΔK−1 with a Gaussian fuzzy-neighborhood vector L(x) ∈ ΔK−1. For every cultivar k, the two evidence views are converted into Tk = p GkLk, Fk = p (1−Gk)(1−Lk), Ik = 1−Tk −Fk. where Ik is exactly the squared Hellinger disagreement between the Bernoulli support views Gk and Lk. A logarithmic fuzzy opinion pool Hk ∝ Gηk L1−η k is then attenuated by neutrosophic disagreement, Rk ∝ Hk exp(−κIk), before classification. The winning class is accompanied by an uncertainty score U = 1−Tˆk (1−Iˆk)(1−Fˆk ), enabling uncertain chemical profiles to be flagged rather than reported with unqualified confidence. The method is evaluated on the UCI Wine cultivar dataset using 60 repeated stratified splits at four synthetic analytical-perturbation levels δ ∈ {0,0.1,0.2,0.3} measured relative to training-feature standard deviations. NFVEF obtains mean accuracies of 0.9858, 0.9836, 0.9744, and 0.9728, respectively. At δ = 0.3, its paired accuracy advantage over linear discriminant analysis is 0.00278 with a 95% bootstrap interval [0.00123,0.00463], while RBF-SVM remains slightly better in raw accuracy. The uncertainty score detects NFVEF errors with mean AUC 0.9520 at the strongest perturbation, and retaining the lowest-uncertainty 90% of cases yields 0.9922 accuracy. The contribution is therefore not universal classifier dominance, but a mathematically interpretable fuzzy–neutrosophic evidence layer for cultivar identification from ambiguous chemical measurements.

groups

Amine Saddik mail -

Ika Agustin mail

link https://doi.org/10.54216/JNFS.110101

Volume & Issue

Vol. Volume 11 / Iss. Issue 1

Details open_in_new

International Journal of Neutrosophic Science | 2026

On Division of Symbolic n-Plithogenic Numbers

The main goal of this article is to study the division of symbolic n-plithogenic numbers using the identification method and n-plithogenic AH-isometry. In particular, we discuss the division of symbolic 2-plithogenic numbers and 3-plithogenic numbers, and we generalize these divisions. Additionally, we prove the validity of the formulas using AH-isometry and provide four worked examples to enhance understanding.

groups

P. Arulpandy mail -

S. Kalaiselvan mail -

M. Sundar mail -

G. Govindharaj mail -

P. Sugapriya mail

link https://doi.org/10.54216/IJNS.270228

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

Details open_in_new

Fusion: Practice and Applications | 2026

Optimizing Navigation: Adaptive Map Reshaping and Shortest Path Analysis for Mobile Robots

To facilitate the practical deployment of robotics, efficient path planning is essential to ensure that robotic movement is accurate, safe, and goal-oriented. This study explores new approaches to map adaptation and path optimization for robot navigation between specified locations. The initial phase of the research involves designing an environment that enables the safe operation of robots. Subsequently, the collected data is processed to construct a graph using Dijkstra’s algorithm, which is employed to determine the shortest path between key points. When multiple paths are available, the algorithm selects the most efficient one, while ensuring safety in point-to-point transitions and when navigating around obstacles. In addition to this, a reinforced method is introduced to enhance the security of path planning. This approach expands the original trajectory to incorporate a safety buffer equal to half of the robot’s safety radius, thus maintaining a safe distance along the traveled route. The key contribution of this work lies in the development of novel maps featuring secure pathways, which can be utilized by optimization algorithms to improve navigation in unfamiliar terrains. Experimental results using PRM* and RRT* validate the accuracy of these maps, especially in complex, maze-like environments.

groups

Mohammed Rabeea Hashim Al-Dahhan mail -

Mahmood Abdulrazzaq Alsaadi mail -

Ruqayah R. Al-Dahhan mail -

Salah A. Aliesawi mail -

Omar Q. Mohsin mail

link https://doi.org/10.54216/FPA.210213

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

Details open_in_new

Journal of Intelligent Systems and Internet of Things | 2026

Deep Neural Network Graph with Reinforcement Learning for Test Case Prioritization

Recently, Deep learning (DL) models are increasingly used in Test Case Prioritization (TCP) tasks combining partial and imperfect test case (TC) information into accurate prediction models. Various DL algorithms have been created to improve TC failure prediction and prioritization in CI settings. Among them, Deep Reinforcement Prioritizer (DeepRP) model is developed using Deep Reinforcement Learning (DRL) and Deep Neural Network (DNN) for efficient TCP on huge test suites. But, the model's labelling task is interrupted early, creating difficulty in learning TC features for unlabeled training TCs due to limited resources. To solve this, Deep Graph Reinforcement Prioritizer (DeepGRP) is proposed in this paper to learn the TC features from unlabeled training data for efficient TCP in Regression Testing (RT). In this method, graph neuron stimulation attributes for TCs are created to retrieve the activation graph across DNN layers of DeepRP. The connectivity neuron link defines the activation graph. The proposed deep graph (DG) recognizes the DNN neurons as nodes and the adjacency matrix as the connectivity link among the nodes. Also, the message passing mechanism is applied to aggregate the structural information from the adjacency matrix with neighbouring node features to enhance TCP. By applying this mechanism, DeepGRP captures the high-order dependencies among neurons for efficient activation features which overcomes the traditional activation models and improves the TCP at large scale RT.  The DG model prioritizes TCs using Learning-to-Rank (L2R) which learns node attributes from TCs. This enables for better DNN testing efficiency by detecting vulnerabilities early and lower development time for efficient TCP and tackling the difficulty of learning TC characteristics for efficient TCP. Finally, the testing findings suggest that the DeepRP can improve the TCP for large TSs when compared to other common algorithms.

groups

Shankar Ramakrishnan mail -

E. K. Girisan mail

link https://doi.org/10.54216/JISIoT.180225

Volume & Issue

Vol. Volume 18 / Iss. Issue 2

Details open_in_new

Journal of Intelligent Systems and Internet of Things | 2026

Emotion Recognition Using Deep Learning via Facial Expression

Human-computer interaction (HCI), artificial intelligence (AI), and HI are in high demand these days. In fields like marketing, client feedback analysis, security, and healthcare, facial expression- grounded emotion recognition becomes a pivotal tool for comprehending mortal feelings. Facial expressions like fear, disgust, surprise, anger, sadness, and happiness are pivotal pointers of emotional countries. Businesses can ameliorate client gests by relating these pointers and measuring client satisfaction with goods or services. The discovery of mortal feelings has been achieved with machine literacy algorithms like support vector machines and arbitrary timbers. The effectiveness of deep literacy models for emotion discovery has been validated by earlier studies that employed Convolutional Neural Networks (CNNs) to reliably classify feelings grounded on facial expressions. Likewise, recent developments in deep literacy, particularly the operation of Convolutional Neural Networks (CNNs), have significantly increased the delicacy of facial emotion recognition and interpretation from images and live camera aqueducts. In order to reuse face images with CNN models for real- time emotion recognition, our exploration attempts to produce an emotion recognition system using Python and OpenCV. The current study describes how to watch live videotape aqueducts for facial expressions to identify which of the seven linked feelings is most likely to do. This system provides emotional behavior in real time when needed.

groups

Santosh B. Dhekale mail -

S. S. Nikam mail -

D. K. Shedge mail

link https://doi.org/10.54216/JISIoT.180226

Volume & Issue

Vol. Volume 18 / Iss. Issue 2

Details open_in_new

International Journal of Neutrosophic Science | 2026

A Comparative Study of Neutrosophic Subalgebras in Sheffer Stroke UP-algebras

In this paper, we conduct a comprehensive study of neutrosophic subalgebras of various types within the framework of Sheffer stroke UP-algebras (SUP-algebras). Specifically, we introduce and characterize (∈, ∈), (∈, ∈ ∨q), and (q, ∈ ∨q)-neutrosophic subalgebras based on neutrosophic ∈-subsets, q-subsets, and (∈ ∨q)-subsets. Necessary and sufficient conditions are established for these subsets to form subalgebras under the Sheffer stroke operation. Several theorems demonstrate how these types interrelate and differ in their structural properties, with illustrative examples provided. Furthermore, we identify the conditions under which certain canonical subsets, such as X1 0 = {x ∈ X | T (x) > 0, I(x) > 0, F (x) < 1}, form subalgebras across differ- ent neutrosophic configurations. These results offer a unified perspective and deeper insight into the algebraic behavior of neutrosophic systems in the context of SUP-algebras.

groups

Aiyared Iampan mail -

Vennila Ramasamy mail -

V. Vijaya Bharathi mail -

K. Geetha mail -

Neelamegarajan Rajesh mail

link https://doi.org/10.54216/IJNS.270229

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

Details open_in_new

Pure Mathematics for Theoretical Computer Science | 2025

On the Formal Foundations of D-Off Numbers and Neutrosophic D-Numbers

A variety of uncertainty-handling frameworks—such as Fuzzy Sets,1 Hyperfuzzy Sets,2 Bipolar Fuzzy Sets,3 Neutrosophic Sets,4 Vague Set,5 Hesitant Fuzzy Sets,6, 7 Picture Fuzzy Sets,8 Soft Sets,9, 10 Rough Sets,11 and Plithogenic Sets12, 13—have been extensively studied for modeling and reasoning under vagueness and imprecision. A fuzzy set extends classical set theory by assigning each element a membership value in the unit interval [0, 1], thereby capturing partial inclusion.1 Neutrosophic Sets further generalize this idea by introducing three independent membership functions—truth, indeterminacy, and falsity—each mapping into [0, 1]. Many of these frameworks have been enriched by incorporating offset concepts, which permit membership degrees to take values beyond the unit interval. Similarly, D-numbers extend Dempster–Shafer belief functions by assigning to each subset B ⊆ X a mass D(B) ∈ [0, 1] with P B D(B) ≤ 1, thus accommodating incomplete uncertainty.14 In this work, we introduce and formally define four new constructs: D-OffNumber, D-OverNumber, D-UnderNumber, and Neutrosophic D-Number, and we investigate their mathematical foundations, structural properties, and interrelationships. The present study focuses exclusively on theoretical development, leaving potential applications—such as their integration into decision-making frameworks—for future research.

groups

Takaaki Fujita mail -

Arif Mehmood mail -

Arkan A. Ghaib mail

link https://doi.org/10.54216/PMTCS.050105

Volume & Issue

Vol. Volume 5 / Iss. Issue 1

Details open_in_new

Pure Mathematics for Theoretical Computer Science | 2026

A Discrete Nonlinear Advection–Diffusion–Reaction Scheme with Vortex Transport: Stability, Convergence, and Algorithmic Complexity

This paper develops a two-dimensional discrete mathematical model for a nonlinear advection–diffusion–reaction equation under a divergence-free vortex field. The formulation is treated as a finite-dimensional dynamical system generated by an explicit finite-difference algorithm: first-order upwind operators approximate advection, secondorder centered operators approximate diffusion, and explicit Euler time stepping advances the nonlinear reaction. The resulting update rule is analyzed through Courant–Friedrichs–Lewy restrictions, a diffusion constraint, and a frozen-coefficient von Neumann argument. A Gaussian initial state and homogeneous Neumann boundary conditions define the computational problem. Numerical experiments show stable vortex-driven redistribution, diffusion-induced smoothing, decay of total mass in the presence of the linear loss term, and localized changes caused by the quadratic reaction. Grid-refinement, time-step-sensitivity, and analytical diffusion benchmarks support convergence of the discrete approximation. For an Nx by Ny grid, each time step requires O(NxNy) arithmetic operations and O(NxNy) storage, so the method provides a transparent algorithmic bridge between nonlinear PDE analysis and discrete computation. The study emphasizes the mathematical structure, stability conditions, convergence behavior, and computational complexity of the scheme while retaining pollutant transport as an illustrative application.

groups

Malika Abdulameer mail

link https://doi.org/10.54216/PMTCS.060202

Volume & Issue

Vol. Volume 6 / Iss. Issue 2

Details open_in_new