A Symmetric Discrete-Gradient Finite-Volume Method for Positive Drift–Diffusion Flows

Sergey Drominko; Erina Kovachiskaya

doi:https://doi.org/10.54216/PAMDA.060103

International Journal of Neutrosophic Science | 2026

An Empirical Evaluation of the Stock Market Using Fuzzy Variant Black and Scholes Model Involving Central Fuzzy Measures

This article defines the central tendency fuzzy measures, which include the weighted fuzzy possiblistic mean and the fuzzy probability mean involving octagonal fuzzy numbers. The same is supported by a fuzzy variant of the Black-Scholes option model, in which uncertain pricing parameters such as volatility, interest rate, and stock price are described using octagonal fuzzy numbers.

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K. Meenakshi mail -

Pavithra S. mail -

S. Sathish mail -

Prabakaran N. mail

link https://doi.org/10.54216/IJNS.270224

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

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International Journal of Neutrosophic Science | 2026

On Graded Weakly Jgr-classical Prime Submodules

Let 0 be a group, Υ be a 0-graded commutative ring with unity 1 and M a graded Υ-module. Our goal in this paper, introducing the concept of graded weakly Jgr -classical prime submodule as a generalization of graded weakly classical prime submodule and offering several results pertinent of graded weakly Jgr - classical prime submodules. For instance, we give characterizations of graded weakly Jgr -classical prime submodule. Also, we give some restrictions for graded submodule to be a graded weakly Jgr -classical prime submodule. A proper graded submodule V of M is said to be a graded weakly Jgr -classical prime submodule of M if, whenever 0̸ = abx ∈ V where a, b ∈ h(Υ) and x ∈ h(M), then either ax ∈ V + Jgr (M) or bx ∈ V + Jgr (M), The symbol Jgr (M) indicates the graded Jacobson radical of Υ-module M.

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Malak Alnimer mail -

Khaldoun Al-Zoubi mail

link https://doi.org/10.54216/IJNS.270225

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

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International Journal of Neutrosophic Science | 2026

Interval-Valued Picture Fuzzy Almost Ideals in Semigroups

An interval-valued neutrosophic set is a type of neutrosophic sets where the membership, indeterminacy, and non-membership degrees are represented by closed intervals within the unit interval [0, 1]. An interval-valued picture fuzzy set is one of special cases of interval-valued neutrosophic sets. In this paper, we apply interval- valued picture fuzzy sets on almost ideals of semigroups. Moreover, we study a relationship between each almost ideal in a semigroup and their interval-valued picture fuzzifications.

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Winita Yonthanthum mail -

Anusorn Simuen mail -

Ronnason Chinram mail

link https://doi.org/10.54216/IJNS.270226

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

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International Journal of Neutrosophic Science | 2026

Solution of Intuitionistic Fuzzy System of Linear Volterra Integro-differential Equations by a Novel Hybrid Method

Our study addresses the intuitionistic fuzzy system of linear Volterra-integro-differential equations of the second kind. Intuitionistic fuzzy General Transform (I-F-G-transform) method has been used to find the exact solution of these systems. We present two numerical examples for illustrating the applicability of the Intuitionistic fuzzy General integral transform method.

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Guelfen hanane mail

link https://doi.org/10.54216/IJNS.270227

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

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Fusion: Practice and Applications | 2026

Cryptanalysis In Block Ciphers: A Comprehensive Review and Future Directions

This paper examines the use of cryptography in block ciphers and assesses their security, with a focus on the Advanced Encryption Standards (AES). The study reviews key cryptanalytic techniques, including differential cryptanalysis (8.3%), linear cryptanalysis (4.2%), and integral cryptanalysis (4.2%). They give their share (in percentage) regarding the relative frequency in the cryptanalysis research literature from 2015 to 2024 according to their literature survey. Side-channel attacks showed the highest practical success rates, with some studies showing up to 50.0% effectiveness. Additionally, the study examines more sophisticated attack techniques such as meet-in-the-middle attacks, quantum-related threats, and biclique cryptanalysis (16.0%).The entire round AES is resistant to a wide range of attack techniques thanks to its strong diffusion and confusion mechanisms and reliable key schedule. The study concludes that cryptanalysis is essential for strengthening encryption schemes against emerging threats, particularly those resulting from quantum computing.

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Lama Al-Ghamdi mail -

Mawada Al-Sari mail -

Monir Abdullah mail -

Ghassan Ahmed Ali mail

link https://doi.org/10.54216/FPA.210211

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

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Fusion: Practice and Applications | 2026

Development of an Efficient Cluster-Based Hybrid LEACH+TEEN Protocol for Time-Critical WSN Application

Wireless Sensor Networks (WSNs) play a crucial role in monitoring and data collection for various real-time applications, including environmental surveillance, industrial automation, and smart cities. However, achieving energy efficiency and timely data delivery remains a critical challenge, especially in time-sensitive scenarios. This research presents the development of an efficient cluster-based hybrid routing protocol that combines the strengths of Low-Energy Adaptive Clustering Hierarchy (LEACH) and Threshold-sensitive Energy Efficient Network (TEEN) protocols to address these challenges. The proposed Hybrid LEACH-TEEN protocol dynamically adapts to both periodic and event-driven data transmission needs by integrating LEACH’s randomized cluster-head selection and TEEN’s threshold- based data transmission mechanism. This hybrid approach significantly reduces redundant transmissions and optimizes energy consumption across the network. Extensive simulations were conducted to evaluate the protocol’s performance in terms of network lifetime, stability period, energy consumption, and the number of alive nodes over time. Results demonstrate that the Hybrid protocol outperforms traditional LEACH and TEEN protocols, particularly in time- critical applications, by ensuring prompt response to critical events while maintaining energy-efficient operation. This work contributes to the design of intelligent and adaptive routing strategies for next- generation WSNs.

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Basim Jamil Ali mail -

Mohanad Ali Meteab Al-Obaidi mail

link https://doi.org/10.54216/FPA.210212

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

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Journal of Intelligent Systems and Internet of Things | 2026

A Systematic Review on Classification Techniques of Microorganisms: Challenges and Recommendations – Towards Medical Intelligent Systems

Microorganisms are commonly found in our daily living environments and play a crucial role in environmental pollution control, disease prevention, and treatment, as well as food and drug production. To fully utilize the diverse functions of microorganisms, their analysis is essential using Intelligent Systems. Traditional analysis methods can be labor- intensive and time-consuming. As a result, image analysis using Intelligent Systems i.e. machine learning or deep learning have been introduced to improve efficiency. Deep learning networks algorithms such as CNN contain a stack of multi-layer, the first layer and the last are the input and output layers, between them are the hidden layers to extract and learn many features in images, recurrent network algorithms (RNN) combined with convolution neural network (CNN), these networks allow to process a series of images to extract the crucial information from images and also these algorithms help to minimize the size of images and reduce the redundancy in microrganisms images According to previous studies, these algorithms are the most used to classify the images of microorganisms. However, the classification of microorganism images presents several challenges these include the need for robust algorithms due to varying application contexts, the presence of insignificant features, along various analysis tasks that need to be addressed. The research summarizes significant advancements that tackle these challenges through deep learning and machine learning methods. Current obstacles, gaps in knowledge, unresolved issues, limitations, and difficulties in classification techniques are also discussed.

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Marwa T. Albayati mail -

Mohd Ezanee Bin Rusli mail -

Moamin A. Mahmoud mail -

Aws A. Abdulsahib mail -

Mohammed F. Alomari mail -

Sallar S. Murad mail

link https://doi.org/10.54216/JISIoT.180224

Volume & Issue

Vol. Volume 18 / Iss. Issue 2

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Prospects for Applied Mathematics and Data Analysis | 2025

Some Special Types of Neutrosophic Domains

The neutrosophic ring cannot be an integral domain, but the pseudo-neutrosophic ring could be an integral domain. The main objective of this paper is to present and study some special types of neutrosophic domains, which has not been studied before, such as integral domains.

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Shawqi Al-lkami mail -

Adel Al-odhari mail

link https://doi.org/10.54216/PAMDA.050103

Volume & Issue

Vol. Volume 5 / Iss. Issue 1

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Prospects for Applied Mathematics and Data Analysis | 2026

Spectrally Matched Fractional Sobolev Tikhonov Regularization for Periodic Deconvolution

Let T = R/Z and Aβ = (I−Δ)−β/2 with β > 0. From data gδ = Aβ f †+η, ∥η∥2 ≤ δ, consider the fractional Sobolev Tikhonov family f δ λ,s = argminf∈Hs(T) Aβ f −gδ 2 2 +λ ∥ f ∥2 Hs, s ≥ 0. Writing μk = (1+4π2k2)1/2 and ρ = s+β, the estimator is diagonal in the Fourier basis, bf δ λ,s(k) = μβ k 1+λ μ2ρ k bgδ (k). If f † ∈ Hr(T) and 0 < r ≤ 2ρ, then f δ λ,s− f † 2 ≤Caδλ−a+CbMrλb, a = β 2ρ , b = r 2ρ , Mr = f † Hr . where Cq = qq(1−q)1−q for 0 < q < 1 and C1 = 1. Direct minimization gives λ∗ ≍ δ2ρ (r+β) and f δ λ∗,s− f † 2 = O δr/(r+β). Thus the pre-saturation exponent is independent of the penalty order s. When r > 2ρ, the bias saturates and the rate becomes O(δ2ρ/(2ρ+β)); hence the least order avoiding saturation is smin = max{0, r/2−β}. The balanced half-power frequency satisfies μc ≍ δ−1/(r+β), whereas its logarithmic roll-off is −ρ/2. The same exponents persist for spectrally equivalent convolution operators c−μ−β k ≤ ak ≤ c+μ−β k . Fourier experiments on N = 2048 modes, using three source regularities, four penalty orders, five noise levels, and 30 perturbations per configuration, reproduce the predicted saturation ordering and transition boundary. For the H6 benchmark at δ = 10−3, the mean L2 error decreases from 1.4013×10−2 for s = 0 to 1.2710×10−3 for s = 2; the latter is the first tested order in the non-saturated regime.

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Takaaki Fujita mail -

Ajoy Kanti Das mail

link https://doi.org/10.54216/PAMDA.060101

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Prospects for Applied Mathematics and Data Analysis | 2026

A Symmetric Discrete-Gradient Finite-Volume Method for Positive Drift–Diffusion Flows

Consider the periodic gradient flow ∂tu = ∂x(m(u)∂xμ) , μ = h′(u)+V, E [u] = Z 1 0 {h(u)+Vu} dx, for strictly positive density u, convex entropy density h, and mobility m > 0. We couple a centered finite-volume flux with a symmetric two-state approximation of the chemical potential. Its entropy component is the divided difference Dh(a,b) = h(a)−h(b) a−b , Dh(a,a) = h′(a), which enforces the discrete chain rule exactly. With midpoint edge mobility and the logarithmic state un+1 i =expzn+1 i , the nonlinear update is self-adjoint and, for every solved algebraic step, satisfies E n+1 h −E n h = −ΔtΣi M n+1/2 i+1/2 (μn+1/2 i+1 −μn+1/2 i )2 Δx ≤ 0. The flux telescopes to conserve mass, the logarithmic parametrization confines finite roots to the positive cone, and states satisfying h′(ui)+Vi = const are fixed points. A midpoint expansion gives second-order consistency in time; the centered flux gives the same order in space. For h(u) = u(logu−1), a manufactured heat-flow calculation gives observed L2 orders 1.998 and 1.999 under coupled refinement. In a confining Fokker–Planck test, the maximum mass defect is 3.20×10−14 and the energy identity is satisfied within 1.42×10−14. Replacing Dh by the midpoint chemical potential in the same one-step problem produces an energy-balance defect 1.60×10−2, isolating the role of the temporal discrete gradient.

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Sergey Drominko mail -

Erina Kovachiskaya mail

link https://doi.org/10.54216/PAMDA.060103

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

Details open_in_new