This paper establishes new and improved oscillation criteria for second-order nonlinear difference equations with nonlinear damping terms. We develop novel sufficient conditions that generalize and enhance existing results in the literature by employing advanced Riccati transformation techniques and refined analytical methods. Our main contributions include the derivation of more general oscillation theorems that encompass broader classes of nonlinear functions and damping terms, along with the establishment of sharper conditions for oscillatory behavior. The theoretical results are supported by comprehensive examples that demonstrate the effectiveness and applicability of our criteria. Our findings significantly extend the current understanding of oscillatory dynamics in discrete nonlinear systems and provide valuable tools for analyzing complex difference equations arising in various scientific and engineering applications.
Activation functions are essential parts of deep learning models, but most standard activation functions like ReLU, ELU, and GELU have little control over the amount of randomness (variance) they introduce into their output and are also very susceptible to being affected by invalid inputs (i.e. robust). We propose to combine an activ. func. based on the ELU with a new stochastic (random) branch, which we call a "Bernoulli-Mixture-Stochastic-ELU," to provide a method for controlling the randomness while maintaining a simple analytical solution. We derive all analytically solvable characteristics (i.e. mean, variance, covariance) of the output of the proposed function, apply spectral norms to the Jacobians, thus establishing a sound theoretical basis for stability and variance control within stochastic nonlinear mappings. The ability to mathematically model the distributions of outputs of activation functions can provide both mathematically well-defined controls on randomness and stable gradients. We perform empirical validation on common datasets supporting our theoretical conclusions and demonstrate that our activations are capable of sustaining performance at comparable speed and accuracy relative to a noisy input, even in the presence of mislabeled classes. The main contribution of this work lies within the stochastic theory and closed-form analysis that integrates probability theory, functional analysis, and application in computational settings.
The boom in online shopping websites has given rise to the growing demand of accurate sentiment analysis for finding out actionable intelligence from customer reviews. In this paper, we introduce a hybrid sentiment analysis system consisting of the rule-based (VADER) and the deep learning- based transformer model (RoBERTa) to categorize sentiment into three categories, i.e., positive, neutral and negative. The approach employs VADER for processing short reviews in near real time and fine-tunes RoBERTa to model intricate linguistic patterns across longer ones. For model training and testing, we employed Flipkart customer review datasets. We get 1281 jokes giving a precision of 89.2 %, recall of 88.1 % and F1 - score performance of 88.6 %. Power BI is utilized in the visualization of the predictions from models through interactive dashboards which gives live marketing insiughts as well. The hybrid system can deliver a more accurate and scalable sentiment classification, which is invaluable for organisations in the context of the optimization of their customer engagement strategies.
Cubic polynomial equations arise frequently in engineering and applied physics as reduced forms of fundamental governing relations. This paper develops a unified analytical and computational framework for nine representative contexts, including Rayleigh surface waves, cubic equations of state, large-deflection membrane bending, combined bending and tension in elastic members, principal stress analysis, quantum-well eigenvalue problems, signal autocorrelation, cnoidal-wave solutions of the Korteweg–de Vries equation, and travelling waves in the FitzHugh–Nagumo model. For each case, the governing cubic is derived or systematically reformulated, and the physical interpretation of admissible roots is established. Particular attention is given to a numerically stable Lagrange-based formulation, which provides improved robustness and accuracy compared with classical closed-form and iterative approaches across different root regimes. The Rayleigh-wave secular cubic is analysed in detail, including the critical Poisson ratio that separates distinct solution structures. Representative examples from wave propagation, thermodynamics, and stress analysis are used to compare performance with Newton–Raphson and companion-matrix eigenvalue methods. The results demonstrate consistent numerical stability and physical interpretability. The study further highlights an underlying geometric structure of cubic equations in the complex plane, revealing a unifying perspective across diverse engineering applications.
Intrusion Detection Systems (IDS) have become increasingly critical for protecting large-scale enterprise and cloud infrastructures from sophisticated cyber threats. However, traditional IDS implementations face significant challenges including lack of interpretability, vulnerability to adversarial attacks, and scalability issues in distributed environments. This research proposes a novel mathematical framework that integrates explainable artificial intelligence (XAI) techniques with adversarially robust machine learning models for enhanced intrusion detection. The framework incorporates SHAP (SHapley Additive exPlanations) values for model interpretability and adversarial training mechanisms to defend against evasion attacks. We evaluated our approach using the CICIDS2017 and NSL-KDD datasets, demonstrating superior detection accuracy of 98.7% while maintaining resilience against FGSM and PGD adversarial perturbations. The proposed framework achieved a 23% improvement in adversarial robustness compared to baseline models while providing meaningful explanations for security analysts. Our experimental results indicate that the integration of mathematical rigor with explainability significantly enhances both the reliability and trustworthiness of machine learning-based intrusion detection systems in production environments.
Dynamic networks offer numerous advantages for communication and computing processes, particularly due to the constant changes in their topology. Traditionally, measuring network complexity has relied on either entropy measures or resistance distance measures independently. This highlights the need for a combined approach that incorporates both measures for a comprehensive assessment of network complexity in dynamic networks. In this paper, we introduce the Entropy Resistance Index (ERI) as a new metric for measuring network complexity in dynamic settings. We mathematically formulated this proposed metric and conducted simulations using dynamic graph models, including random, scale-free and small-world graphs. These simulations accounted for changing factors such as node failures, edge perturbations and variations in traffic. The results showed that the ERI metric yielded better outcomes compared to classical methods, which relied solely on entropy or resistance metrics. Specifically, the model for the ERI metric achieved a complexity sensitivity value of 0.91, a diffusion efficiency of 0.93, a robustness factor of 0.90 and a stability rating of 0.92 - all of which were superior to those observed in classical approaches. Furthermore, the ERI values effectively detected variations in network topologies and communication patterns. Finally, theoretical proof demonstrated that the proposed metric is always positive, bounded, stable and sensitive to connectivity changes.
The armed conflict in Colombia has generated massive forced displacement, with women being a population with a differentiated vulnerability that requires the development of specific adaptation mechanisms. This study analyzes the development of resilience and coping strategies in women victims of forced displacement, examining their individual resources and collective processes, as well as State intervention within the framework of the post-conflict era. A systematic literature review was conducted by consulting high-impact databases (SciELO, Redalyc, Scopus, Google Scholar) and institutional repositories. Sixty studies published between 2017 and 2023 were selected, of which 80% correspond to descriptive and phenomenological qualitative methodologies. Regarding the results, the findings indicate a transition in academic literature from a focus on passive victimization toward the recognition of women's capacity for agency and social leadership. Among the identified strategies, spirituality, the pedagogy of memory, entrepreneurship, and the strengthening of life skills, such as assertive communication and conflict resolution, stand out. Likewise, the relevance of Law 1448 of 2011 is highlighted as a catalyst for the visibility and reparation of these victims. Resilience in this context is a multidimensional process that arises from the interaction between a woman's internal capacities, community support, and the effectiveness of public policies for the restitution of rights. It is concluded that state support must transcend welfare-based approaches to foster autonomy and the reconstruction of the social fabric.
The digital transformation of education has positioned teacher training in digital competences as a strategic axis of educational policy, pedagogical innovation, and professional development. In response, international organizations, ministries of education, and specialized agencies have produced frameworks, standards, guidelines, and policy documents intended to define what teachers should know and be able to do in digitally mediated educational settings. However, the diversity of approaches, labels, scopes, and levels of operational detail makes it difficult to understand their points of convergence, divergence, and omission in comparative terms. The aim of this study was to comparatively analyze international frameworks, guidelines, and policy documents on teacher training in digital competences. A qualitative study was conducted through a comparative documentary analysis of a corpus of 40 documents published between 2007 and 2026. The corpus was organized in a documentary review matrix and examined through five categories: theoretical-conceptual foundations in ICT and LKT, teacher training pathways, pedagogical integration of ICT and LKT, AI literacy, and digital formative assessment. The findings show that the international field of teacher digital competence is broad but heterogeneous. The dominant discourse is organized around ICT, digital competence, digital literacy, and digital transformation, while LKT appears less explicitly and is more often inferred through pedagogical interpretation. The corpus also reveals flexible and progressive training pathways, broad but uneven models of pedagogical integration, an emerging yet still non-transversal incorporation of AI literacy, and an uneven treatment of digital formative assessment. The study concludes that international reference frameworks provide a robust foundation for teacher training in digital competences, although they require pedagogical and institutional contextualization in order to respond more effectively to contemporary teacher education needs.
In this paper, we compute various finite sums that alternate according to involving the generalized binary numbers for and even k of the form with .
This article offers zero-truncated version of Geometric-Ishita distribution (GID) as a valid extension to existentIshita distribution. This coalition of discreet and continuousdistribution on zero-pruned setting makes the distributionmore data friendly. We study the behavior of distributionfunction over the values of parameter. Other character-istics, like moments, skewness, kurtosis, entropy are pre-sented. Also, method of maximum likelihood and methodof moments are discussed for estimating parameter. Finally,a real data analysis is furnished accompanied by the perfor-mance of other competitive distributions.
In this paper, we propose an iterative method for solving very large-scale linear problems called the constraints sorting method (CSM), it consists in sorting the constraints of the initial problem, and iteratively solving a serie of sub-problems of increasing size which will converge to the solution sought, the efficiency of this method depends on the choice of constraints to be introduced, we have chosen to add, at each iteration, a set of constraints most orthogonal to the criterion of the problem to be solved, which gave us very good results. In order to compare (CSM) with the interior point method, we have realized a numerical implementation of our (CSM) approach using the Matlab programming language, and numerical results on execution time showing that our approach is competitive are presented.
In a structured survey of fifty industrial professionals covering hundreds of firms, a veritable crucible was employed tomeasure the readiness of Morocco’s industrials for Industry 4.0, comprising both large state-owned companies and small innovative firms belonging to multiple sectors and scattered across different geographic regions. Quantitative statistical techniques in combination with qualitative thematic inter pretation were employed to carry out mixed methods analysis. As a result, this research uncovers serious digital maturity disparities. The study shows that 46 percent of respondents regard their organizations as Digital OperationUnits multinationals exhibits 74 per cent internet adoption rate and national private enterprises only 32 (X2 = 8.47,p < 0.05). Three impeding factors include money deficit technical unskilled mass resistance to change. And whilethe snares abound 72% have hope for the unclear DigitalConversion, that is the name of this epoch. The study offers actual findings which can be used by policymakers, policy experts and strategic planners in Morocco’s future industrial digital conversion.
The customer churn problem has a huge negative impact in different industries so that early prediction of customer churn can protect business by deciding early new business strategies that keep the customer before customers leave the service. The current research is enhancing the customer retaining by investigating architectural design model for predicting customer churn using Artificial Intelligence(AI). This research proposes adaptive Local Binary Social Spider Algorithm using Random Forest(LBSA-RF) model which is an architectural design model for predicting customer churn using artificial intelligence technique. The experiments took place on three datasets from different industries which are Orange dataset, IBM telecom dataset and bank churn dataset. The experiments administer the importance of real-time data analysis to capture a holistic view of customer interactions. The proposed architecture also concludes feedback for continuous model optimization and adaptation to changing customer patterns. The suggested Adaptive LBSA-RF model precision, recall, f1-score and accuracy performance metrics exceeds different related works when applied on the three mentioned datasets due to the intelligent automated feature selection mechanism of the Local Binary Social Spider Algorithm(LBSA) which effectively identifies and isolates the most predictive features, then leveraged by the Random Forest(RF) which is a powerful ensemble learning algorithm to build an accurate and robust classifier.
This work investigates the oscillatory behavior of solutions to a class of second-order differential equations governed by the Generalized Local Derivative (NαF ). Unlike traditional models limited to power-law kernels, our framework employs an arbitrary functional kernel F(t, α) to describe systems with varying memory and dissipation properties. By utilizing the Riccati transformation technique and integral averaging, we establish new oscillation criteria for both divergent and convergent cases of the kernelweight integral. Our analysis demonstrates that the property of oscillation is a functional consequence of the interaction between the kernel structure, the potential term q(t), and the conductance a(t). We validate these theoretical findings through numerical simulations in the phase plane, revealing the critical influence of the kernel’s decay rate on the system’s ability to sustain cyclic dynamics.
This paper introduces a few new outcomes of deformable fractional calculus of multivariable functions for a recently proposed deformable derivative. It proposes a deformable form of Euler’s Theorem on homogeneous functions. As an application, the proposed results are applied to homogeneous functions.
Mobile Cloud Offloading (MCO) addresses resource limitations of mobile devices by migrat- ing compute-intensive tasks to powerful remote servers. This paper presents a predictive MCO framework that incorporates a machine learning-based decision engine to intelligently select the optimal execution environment among local, edge, and cloud resources. The framework is evalu- ated using diverse workloads including matrix multiplication and image processing. Experimental results demonstrate that the ML-driven predictive approach consistently achieves lower execu- tion latency compared to static and reactive offloading strategies, validating the effectiveness of context-aware, proactive decision-making in mobile computing environments.
This study introduces a continuum-level framework designed to integrate concepts from quantum biology into practical biomaterials and tissue engineering. The Quantum-Inspired Micro-Dilatation Theory extends classical micro-dilatation models by incorporating fields that represent effective coherence, enzymatic activity, and cellular energetics, while maintaining computational tractability for macroscopic simulations. Rather than presuming long-lived quantum coherence in entire tissues, the framework models quantum-associated effects as additional internal variables that subtly modulate stiffness, growth, and degradation at biomaterial–tissue interfaces. This approach establishes a mathematically consistent context for investigating phenomena such as coherence-assisted transport and tunnelling-influenced reactions at the scale of devices and scaffolds. The paper presents the governing equations, delineates typical parameter regimes and numerical behavior, and identifies experimental strategies to assess the relevance of such couplings in regenerative medicine. All quantum-associated effects are strictly treated as phenomenological internal variables at the continuum level, with no assumptions regarding persistent quantum coherence at tissue or organ scales.
Intestinal protozoan infections are a major cause of gastrointestinal illness in low- and middle-income countries, yet recent epidemiological data from eastern Libya remain limited. This cross-sectional study examined 480 stool specimens collected in 2025 from symptomatic patients attending Al-Bayda Medical Center. Parasitological diagnosis was performed using direct wet-mount microscopy, and participants were categorized by gender, age group, and season. Intestinal protozoa were detected in 57 samples, corresponding to an overall prevalence of 11.9%. Entamoeba histolytica was overwhelmingly predominant, accounting for 96.5% of positive cases, while Entamoeba coli and Giardia lamblia were each identified in 1.8% of cases. Infections were more common among adults (91.2%) and females (71.9%), and the highest frequency occurred during winter, followed by summer and autumn, with the lowest in spring. Statistical analysis revealed no significant associations between parasite species and gender, age group, or season. These findings highlight the continued predominance of Entamoeba histolytica among symptomatic patients in eastern Libya and underscore the need for enhanced diagnostic strategies and ongoing epidemiological surveillance to better characterize and control intestinal protozoan infections in the region.
The symbol class Λ(R × R × R × R) is discussed and it is shownthat the product of any two symbols from this class is again in Λ. The Pseudodifferential operators (p.d.o.) A(x, y,Dx0,y) and A (x, y,Dx0,y) involving the coupledfractional Fourier transform Fα1,α2associated with symbol classes are defined.Product and Commutator for the p.d.o. and their boundedness results are obtained
Stem cell transplantation is a vital treatment for various hematologic diseases, where finding a compatible donor is crucial for the success of the procedure. Traditionally, the donor-recipient matching process involves complex evaluation of genetic markers and Human Leukocyte Antigen (HLA) typings, which requires advanced analytical techniques to ensure compatibility. The proposed research presents an advanced stem cell donor matching methodology using a Hybrid Random Forest and Variational Autoencoder (VAE) framework. The model leverages the VAE for complex feature extraction, compressing high-dimensional donor-recipient characteristics into an informative latent space, and integrates this with a Random Forest classifier for predicting compatibility. The enriched feature set, derived by combining latent features and original data, enables the model to capture nuanced relationships between genetic markers, HLA typings, and other biological factors. The model was implemented in Jupyter Notebook and achieved a remarkable accuracy of 80.17%, outperforming nine existing models, including Standard Random Forest, XGBoost, and LightGBM, by an average margin of 4%. Additionally, the model demonstrated high precision, recall, F1-score, and AUC-ROC values, indicating its robustness in correctly identifying compatible donor-recipient pairs. The effectiveness of this approach suggests its potential to enhance decision-making in clinical settings, providing a reliable and efficient solution for stem cell donor matching.
