Damghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230On Solving a Non-Linear Equation for the Quark Condensate Operator in Holographic QCD153161202610.22128/ansne.2025.3156.1179ENShahin MamedovInstitute for Physical Problems, Baku State University, Z.Khalilov 23, Baku, AZ 1148, Azerbaijan; Institute of Physics, Ministry of Science and Education, H.Javid 33, Baku, AZ 1143, Azerbaijan; Center for Theoretical Physics, Khazar University, 41 Mehseti Str., Baku, AZ1096, AzerbaijanJournal Article20251117We investigate the non-linear structure of an equation arising in the holographic description of strongly coupled QCD. Within the framework of the AdS/QCD correspondence, we analyze the equation of motion for a bulk scalar dual to the quark condensate operator. We present both analytical approximations and numerical solutions, and discuss their implications for chiral symmetry breaking and meson spectra. Our results highlight the importance of non-linearities in capturing dynamical features beyond the probe approximation.https://ansne.du.ac.ir/article_2026_a67e7b01119a741824d2bc554099450a.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230An Improved Time-Delay Grey Verhulst Model Optimized by Multi-Agent Reinforcement Learning for Electricity Market Forecasting162190202710.22128/ansne.2025.3087.1160ENSajedeh Hedayatollahi PourDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranSeyed Ali AlavizadehAlma Mater Studiorum – Università di Bologna, Bologna, ItalyOmid SolaymanifardDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran0000-0003-1105-9676Journal Article20251008Accurate forecasting of electricity prices is still a difficult task because of the volatile and nonlinear nature of energy markets, as well as the limited availability of reliable data. Grey forecasting models are often used for this purpose, but they usually lack enough flexibility to capture delayed effects and complex interactions among several variables. To address these issues, this study aims to present an Improved Time-Delay Grey Multivariable Verhulst Model (ITGMVM), a new grey model developed for short-term electricity price prediction. The model introduces time-delay parameters that represent lagged relationships between variables, helping it respond better to dynamic market behavior. Two optimization methods are designed for parameter calibration: Partial Parameter Estimation (PPE) and Full Parameter Estimation (FPE), where the latter adjusts all parameters at the same time. These methods are supported by a new hybrid optimization framework called MARL-WOA, which combines Multi-Agent Reinforcement Learning (MARL) with Whale Optimization Algorithm (WOA). This combination improves the search process, leading to faster convergence and higher accuracy. The model is evaluated using real-world data from Australia's National Electricity Market (NEM), specifically focusing on Sundays and Wednesdays between December 2023 and March 2024. Results show that ITGMVM, when optimized with FPE-MARL-WOA, outperforms six existing grey and hybrid models across multiple statistical metrics, achieving exceptional forecasting accuracy and robustness. The obtained results demonstrate the strength of integrating adaptive AI techniques with grey modeling to support decision-making in data-constrained energy environments.https://ansne.du.ac.ir/article_2027_149eca2d55ce06ee474fdeed56561988.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Enhanced Nonlinear Solvers for Shear-Dependent Viscosity Models in Fluid Dynamics191199202810.22128/ansne.2025.3154.1178ENDharm Veer SinghDepartment of Physics, Institute of Applied Science and Humanities, GLA University, Mathura 281406, India0000-0002-8101-2745Bhupendra SinghDepartment of Physics, Atma Ram Sanatan Dharma College, University of Delhi, Delhi, IndiaJournal Article20251117Nonlinear constitutive relations arise frequently in fluid mechanics, especially in flows of complex or non-Newtonian fluids where viscosity depends on deformation rates. This paper develops and analyzes a robust solution strategy for a representative nonlinear equation obtained from the steady, fully-developed flow of a shear-thinning fluid in a channel. The governing equation reduces to a nonlinear ordinary differential equation whose nonlinearity couples momentum transport with a rate-dependent effective viscosity. We introduce a hybrid fixed-point and Newton correction scheme, prove its convergence properties under physically realistic conditions, and evaluate its performance against standard iterative methods. The proposed approach shows significant improvements in convergence speed and stability, particularly in regimes where classical Newton iteration fails due to strong degeneracy in the viscosity law.https://ansne.du.ac.ir/article_2028_d462083a0dad422f713080f20627bca4.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Existence and Qualitative Properties of Radial Solutions to a Nonlinear Equation on Lifshitz Black Hole Backgrounds200218202910.22128/ansne.2025.3097.1166ENSudhaker UpadhyayDepartment of Physics, K.L.S. College, Nawada, Magadh University, Bodh Gaya, Bihar 805110, India0000-0002-3880-7315Journal Article20251012We study a nonlinear scalar equation on a $(d{+}2)$--dimensional Lifshitz black hole background with dynamical critical exponent $z>1$.<br />For static, radially symmetric configurations the Klein--Gordon equation with power-type self-interaction reduces to a non-autonomous second-order ordinary differential equation on the half-line. We formulate the problem in divergence form, identify a natural weighted energy, and prove existence of bounded solutions decaying at infinity via a compactness argument and a monotone iteration scheme built upon the positive Green operator of the linearized problem. We also derive sharp near-horizon and asymptotic expansions, and we discuss uniqueness under a smallness condition on the nonlinearity. An explicit family of backgrounds $f(r)=1-(r_h/r)^{d+z}$ is used to illustrate the boundary behavior and to present a numerically robust shooting strategy consistent with the analysis.https://ansne.du.ac.ir/article_2029_b0a651edf3df4e83da674aeac2512f6f.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Some Properties of the Connectivity Index in Vague Graphs with Application219228203010.22128/ansne.2025.3189.1184ENAlimohammad Fallah AndevariDepartment of Mathematics Education, Farhangian University,
P.O. Box 14665-889, Tehran, IranYahya TalebiDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranJournal Article20251210In this paper, we first introduce simple fuzzy graphs (VGs), vague graphs, and then focus on one of the important indices of vague fuzzy graphs, namely the connectivity index, which measures the degree of coordination among the vertices of a graph. We apply this index to study the degree of coordination among the campuses and higher education centers of Farhangian University in Mazandaran Province, which are considered as the nodes of a vague fuzzy graph. The main question is whether these campuses and centers operate as a coordinated network or not. The membership functions of the vertices (nodes) are determined on the basis of the data of the Evaluation and Supervision Office of Farhangian University in Mazandaran Province, obtained mainly from student questionnaires in different domains such as the president’s office, administration, finance, research, cultural affairs and student services. At the end of the paper we conclude that the campuses and centers of Farhangian University do not yet behave as a perfectly coordinated network; however, by implementing the changes and improvements suggested in this paper they can become fully coordinated. Likewise, some new indices such as Zagreb index, sombor index, wiener index, and average wiener index are introduced.https://ansne.du.ac.ir/article_2030_00fbf1f3c0736dbc5f2ffa300373a5ac.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230On the Existence and Approximation of Solutions to a Nonlinear Schrodinger-Type Equation229236203110.22128/ansne.2025.3165.1182ENVivek KumarSrivastavaDepartment of Physics, Prof. Rajendra Singh (Rajju Bhaiya) Institute of Physical Sciences for Study and Research, Veer Bahadur Singh Purvanchal University, Jaunpur, 222003, Uttar Pradesh, India0009-0003-9124-9396Neha BhatnagarDepartment of Physics, Faculty of Science and Technology, JSPM University, Pune, 412207, Maharashtra, India0000-0003-0943-8108Ayush OjhaDepartment of Mathematics, Faculty of Engineering and Technology, Veer Bahadur Singh Purvanchal University, Jaunpur, 222003, Uttar Pradesh, IndiaJournal Article20251126We investigate the mathematical structure and approximate solutions of a nonlinear equation arising in quantum mechanics. Specifically, we study a stationary nonlinear Schr\"odinger equation with a cubic nonlinearity, which is relevant in models of Bose--Einstein condensates and nonlinear optics. We establish existence results under suitable boundary conditions and develop a perturbative approximation scheme for small coupling. Numerical experiments illustrate the validity of the approximation and the emergence of localized states.https://ansne.du.ac.ir/article_2031_b14f2b2503a366f3f6cc1e196a631558.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Nonlinear Optimization Problems with Bipolar Fuzzy Relation Equations using Neural Networks237254203210.22128/ansne.2025.3161.1181ENAli Abbasi MolaiSchool of Mathematics and Computer Science, Damghan University, Damghan, IranHassan Dana MazraehSchool of Mathematics and Computer Science, Damghan University, Damghan, IranKourosh ParandDepartment of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran; International Business University,Toronto, CanadaJournal Article20251124In this paper, we present a novel application of neural networks for solving nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set for these problems is generally non-convex, which makes conventional nonlinear optimization methods less suitable for solving them. To address this challenge, we propose the use of neural networks {and some rules for simplification of the problem}. To find an input vector \( x \in [0,1]^n \) that satisfies the constraints and minimizes (or maximizes) the objective function, \( n \) neural networks are trained simultaneously. Each neural network identifies the corresponding variable of the vector \( x \in [0,1]^n \). The loss function integrates both the constraints and the objective function. Our experiments demonstrate that the proposed method can solve these problems with high accuracy and reasonable computational time. The proposed method is compared to the existing methods.https://ansne.du.ac.ir/article_2032_ada47fd9d934a1befbf960e271967e13.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Forecasting Key Global Factors using Hybrid Artificial Neural Networks and the Mackey-Glass Nonlinear Differential Equation255263203310.22128/ansne.2025.3152.1177ENShahram BadamchizadehBiosystem department, Agricultural Research Institute, Iranian Research Organization for science and TechnologyAli ZenouziBiosystem department, Agricultural Research Institute, Iranian Research Organization for science and TechnologySharareh HarirchiDepartment of Biotechnology, Iranian Research Organization for Science and Technology, Tehran P.O. Box 3353-5111, IranNavid BaseriGeneral Office of Information Technology, Iranian Research Organization for Science and TechnologyAbbas TamjidiDepartment of Wood and Paper Science and Technology, Ka.C., Islamic Azad University, Karaj, IranJournal Article20251116Accurate prediction of environmental and socio-economic indicators is of great importance for global development in all areas and for assessing risks related to climate change. In this study, artificial neural networks (ANNs) based on multilayer perceptron (MLP), long short-term memory (LSTM) and hybrid artificial neural networks, with and without the Mackey-Glass Nonlinear Differential Equation (MG), were used to predict world population, per capita gross domestic product (GDP), fossil fuel consumption and CO$_2$ emissions. Historical data were collected from official and reliable international sources for the years 1990 to 2022. To evaluate the performance of the proposed models, a set of reliable indicators including root mean square error (RMSE), mean absolute percentage error (MAPE) and coefficient of determination ($R^2$) were used. The results show that the hybrid neural network models that used the Mackey-Glass delayed differential equation significantly reduced the forecast error in all evaluation indices for all different variables. The Mackey-Glass equation improved the MAPE index by 12.5\% {}{}and increased the $R^2$ index by 8.7\%. In addition, the results of the sensitivity analysis show that the models are sensitive to the choice of input features, data preprocessing, and network architecture design. The differences between the model outputs highlight the need to pay close attention to the model complexity and how to represent the time series dynamics in long-term forecasts. Overall, the findings indicate that the hybrid neural models augmented with the nonlinear delayed differential equation provide a more accurate and reliable picture of future global trends. The results have important implications for climate policy design, global energy planning, and sustainable development strategies.https://ansne.du.ac.ir/article_2033_a2fa0d575cfa615519ccf5ded4f05992.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Connected 2-Dominating Sets and Connected 2-Dominating Polynomials in Friendship Graphs264270203410.22128/ansne.2025.3089.1161ENHamed MahmoudzadehDepartment of Mathematics, Faculty of Mathematics, Statistics, and Computer Science, Semnan University, Semnan, Iran0009-0002-7264-3796Saeed Mohammadian SemnaniDepartment of Mathematics, Faculty of Mathematics, Statistics, and Computer Science, Semnan University, Semnan, Iran0000-0001-6755-4911Journal Article20251010Let \( G = (V, E) \) be a simple graph. A subset \( D \subseteq V \) is called a connected 2-dominating set of \( G \) if every vertex in \( V \setminus D \) is adjacent to at least two vertices of \( D \), and the induced subgraph \( G[D] \) is connected. The minimum size of such a set is referred to as the connected 2-domination number of \( G \), denoted by \( \gamma_2^c(G) \). In this work, we investigate the enumeration of connected 2-dominating sets in graphs. For this purpose, we define a generating polynomial, called the connected 2-domination polynomial, which encodes the number of such sets of different cardinalities. Furthermore, several fundamental properties of this polynomial are studied, and explicit forms are derived for certain graph families, in particular the friendship graphs \( F_n \).https://ansne.du.ac.ir/article_2034_fe2324aa571b224e39995170457933a0.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Exploiting Pairing Attribute-Based VDM for Enhanced Similarity Learning271286203510.22128/ansne.2025.3107.1169ENSomaye DolatikalanDepartment of Computer Science, Yazd University, Yazd, IranMohammad Reza HooshmandaslDepartment of Computer Science, University of Mohaghegh Ardabili, Ardabil, Iran0000-0002-3834-3610Seyed Abolfazl Shahzadeh FazeliDepartment of Computer Science, Yazd University, Yazd, Iran0000-0002-3724-8689Elham AbbasiDepartment of Computer Science, Yazd University, Yazd, IranSeyed Mehdi KarbassiDepartment of Mathematics, Yazd University, Yazd, IranJournal Article20251022The value difference metric (VDM) is a well-established similarity measure for nominal attributes in classification tasks. However, it suffers from a critical limitation: it assigns a zero distance to differing attribute values with identical class distributions, reducing discriminatory power. To address this, we propose the pairing attribute value difference metric (PAVDM), which enhances similarity evaluation by jointly considering pairs of attribute values. While PAVDM improves discrimination, it introduces higher computational costs. To mitigate this, we introduce two optimization strategies: CSPAVDM, which leverages Cramér’s $V$ for correlation-based pairing, and ASPAVDM, which employs AdaBoost to prioritize impactful attributes. Results show that PAVDM and its optimized variants outperform classical VDM in accuracy, precision, F1-score, and ROC AUC under a fair evaluation protocol.https://ansne.du.ac.ir/article_2035_25a08caf2ff4e6212019e36b56ef0008.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Nonlinear Elliptic Equations in Black Hole Holography: Existence, Uniqueness, and Asymptotics287299203610.22128/ansne.2025.3129.1171ENSudhaker UpadhyayDepartment of Physics, K.L.S. College, Nawada, Magadh University, Bodh Gaya, Bihar 805110, India0000-0002-3880-7315Journal Article20251106We investigate a nonlinear elliptic boundary value problem that arises naturally in the mathematical formulation of black hole holography. The equation under study is a scalar model that captures the interaction between geometry and exponential nonlinearities on conformally compact manifolds. Our main results establish the existence of weak and strong solutions for all values of the coupling parameter, prove uniqueness in the regime of small coupling, and analyze the breakdown of uniqueness through blow-up phenomena as the parameter increases. We further provide a detailed description of the asymptotic behavior of solutions near the conformal boundary, showing that the leading divergence is universal while the subleading term encodes freely prescribable boundary data. From a variational perspective, the problem admits a natural energy functional whose critical points correspond to solutions, and whose structure reflects stability, multiplicity, and phase transitions. These results illustrate the deep interplay between nonlinear partial differential equations, conformal geometry, and holographic dualities, and they point to further applications of geometric analysis in mathematical physics.https://ansne.du.ac.ir/article_2036_2dea74e260f7824413c773fc2e332429.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X10220251230Nonlinear Eigenvalue Methods for Quantifying Quantum Entanglement300313203710.22128/ansne.2025.3141.1175ENAbrar AhmedNaqashDepartment of Physics, National Institute of Technology Srinagar, Jammu and Kashmir, 190006, India0000-0003-3891-4740Fardeen AhmadSofiDepartment of Physics, University of Kashmir, Srinagar 190006, India0009-0004-0792-5353Mohammad HarisKhanDepartment of Physics, University of Kashmir, Srinagar 190006, India0009-0007-8927-484XSundus AbdiDepartment of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada0000-0002-7810-653XJournal Article20251111We present a hybrid analytical numerical method to evaluate the geometric measure of entanglement for pure multipartite states by formulating the closest separable state problem as a coupled nonlinear eigenvalue condition. We develop a hybrid analytical numerical framework in which a formal perturbative linearization around a reference product state is combined with an iterative fixed-point scheme. The approach combines a Gauss-Seidel block fixed-point iteration with a controlled first order linearization about a stationary reference product state. The perturbative analysis provides local structural insight and initialization guidance, while the iterative method yields accurate numerical estimates of the geometric measure of entanglement. We make explicit and prove an equal multiplier stationarity identity showing that, at an optimum, all block Lagrange multipliers coincide and are fixed by the optimal fidelity to the target state. A normalization preserving linearization is obtained by projecting onto local tangent spaces, which yields an explicit first order correction and a corresponding scalar shift in the effective eigenvalue. We further establish a monotonic block ascent property: the overlap with the target state increases at every update, remains bounded, and converges to a stationary value. For standard three qubit benchmarks, the hybrid solver converges smoothly and reproduces the known exact optima for the GHZ and W states.https://ansne.du.ac.ir/article_2037_26abd9c4509320a2089c51fab82388d6.pdf