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231 articles for “Differential”
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Numerical Solution of Ordinary Differential Equation and Solution of Partial Differential Equation
Abstract: This research paper explores the fundamental role of various mathematical concepts in engineering and scientific fields like aerospace engineering, materials science, software development, and the energy sector. We delve into the applications of solving algebraic and transcendental equations, finite difference interpolation, numerical methods, solutions to ordinary differential equations (ODEs), and numerical solutions to partial differential equations (PDEs). By examining their applications in these diverse fields, we illustrate the critical importance …
Published in Journal of Aerospace Engineering & Technology · Vol. 14, Issue 3, 2024 · pp. 12–20 Read article
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From Differential Equations to Data Science: A Survey on Analytical Methods in Contemporary Problems
Abstract: The integration of differential equations and data science methods represents a dynamic and evolving approach to solving contemporary challenges across a wide range of disciplines, including engineering, physics, biology, economics, and finance. Differential equations have long served as fundamental tools for modeling continuous systems and processes, offering powerful insights into the behavior of natural and man-made phenomena. For example, they describe how heat diffuses through materials, how populations grow in …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 1–6 Read article
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Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 Read article
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A Review on Design Optimization of Automotive Conventional Differential System for Rear Wheel Drive
Abstract: The following review paper provides a thorough explanation of the limitations of the automotive conventional differential system under various circumstances and suggests a viable solution for each constraint by enhancing the differential unit's design and construction. The conventional differential used in automotive (CAR, TRUCKS etc.) is the system which is used to transmit power from the engine to the rear wheels of the vehicle via the propeller shaft, hence we …
Published in International Journal of Mechanical Dynamics and Systems Analysis · Vol. 1, Issue 2, 2023 · pp. 39–51 Read article
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Optimizing Routing and Placement of VLSI Circuits with Differential Algorithms and Neural Networks
Abstract: The performance of modern VLSI systems is heavily influenced by power constraints, necessitating precise power estimation and effective optimization techniques. Traditional methods, such as gate-level simulations, are often slow and computationally intensive. This paper introduces DRPENN (Differential Algorithm for Routing and Placement Optimization using Neural Networks), an innovative solution that combines a Switching Activity Estimator (SAE) with a neural network-assisted differential algorithm. By leveraging toggle rates from simulations to train …
Published in Journal of VLSI Design Tools and Technology · Vol. 14, Issue 2, 2024 · pp. 14–20 Read article
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Differential Equations in Quantum Mechanics and Schrödinger Equation
Abstract: In this study we investigate how differential equations play a role in quantum mechanics, focusing mainly on the role of a prominent one, Schrödinger's equation, which governs the behavior of quantum systems. In time two the mathematical picture of the wave nature of particles at quantum scales is provided, and the resulting equations are Schrödinger's equation, both in its time dependent as well as in its time independent form. The …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 15–25 Read article
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Optimal Homotopy Analysis Method (OHAM) For the Approximate Series Solution of Non-linear Partial Differential Equation
Abstract: In this article, we have used the Optimal Homotopy Analysis Method (OHAM), which is a basically semi-analytic method to solve differential equations. The ability for the user to choose the convergence control parameter, auxiliary linear operator, auxiliary function, and starting approximation is what sets apart the OHAM technique. We guaranteed the efficacy and efficiency of the procedure by fine-tuning the convergence control parameter. We solved a non-linear partial differential equation …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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Differential Scanning Calorimetry, Thermogravimetric Analysis, and Dynamic Mechanical Analysis for Advanced Medical Materials
Abstract: Modern healthcare depends on advanced medical products that come up with new ways to care for and help patients. Characterizing these products is important to make sure they are safe, effective, and work well. While there are many analysis methods, Differential Scanning Calorimetry (DSC), Thermogravimetric Analysis (TGA), and Dynamic Mechanical Analysis (DMA) are the most important ones for checking the temperature and mechanical qualities of medical materials. By measuring the …
Published in Journal of Polymer & Composites · Vol. 12, Issue 4, 2024 · pp. 57–72 Read article
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Differential Privacy-Aware Data Sanitization for Multi-Level Security
Abstract: Multi-level security (MLS) models are fundamental for enforcing mandatory access control in high-security environments such as government, military, healthcare, and finance. However, traditional MLS frameworks, including the Bell-LaPadula and Biba models, often create rigid data silos, preventing efficient data utilization. Differential privacy (DP) presents a novel solution by enabling controlled information leakage while preserving confidentiality. By injecting statistical noise into query results, DP allows lower-clearance users to access sanitized versions …
Published in International Journal of Computer Science Languages · Vol. 3, Issue 1, 2025 · pp. 42–52 Read article
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Mathematical Modeling of Epidemics Using Stochastic Differential Equations: A Review
Abstract: The accurate modeling of infectious disease dynamics is crucial for predicting outbreaks and informing public health interventions. While deterministic models such as the SIR (Susceptible-Infected-Recovered) framework have traditionally been used to understand disease transmission, they often fail to account for the randomness inherent in real-world scenarios. Disease spread is influenced by numerous uncertain factors, including individual behavioral changes, environmental fluctuations, and imperfect data reporting. These uncertainties can significantly impact model …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 1–6 Read article
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Differential Gene Expression Analysis of Human Atrial Fibroblasts Reveals Dysregulation of RNA Metabolism and Translational Machinery in Atrial Fibrillation
Abstract: Atrial fibrillation (AF) is a complex cardiac arrhythmia characterized by extensive structural remodeling and the activation of atrial fibroblasts, which drive the progression of fibrosis. To identify the underlying transcriptomic alterations, we analyzed six human atrial fibroblast RNA-Seq datasets (three control and three AF) retrieved from the Sequence Read Archive. After performing rigorous quality control and adapter trimming, we aligned the reads to the GRCh38 human reference genome using a …
Published in International Journal of Bioinformatics and Computational Biology · Vol. 4, Issue 2, 2026 · pp. 15–25 Read article
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Differential Model of Wave Vibration on Strings and Rods
Abstract: Vibration, as a physical phenomenon, plays a multifaceted role in both natural and engineered systems. Beyond its essential contribution to communication through sound and speech, it finds critical application in various technological domains. For instance, in the design of stringed musical instruments such as violins and guitars, precise manipulation of string vibrations defines tonal quality and musical resonance. Similarly, metal rods in tuning forks exhibit vibrational properties that are finely …
Published in Research & Reviews : Journal of Physics · Vol. 14, Issue 1, 2025 · pp. 17–21 Read article
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Evaluating the Role of Platelet Indices, with a Focus on Immature Platelet Fraction (IPF), in Differentiating Hyper-Destructive and Hypo-Productive Thrombocytopenia: A Study from Ludhiana, Punjab, India
Abstract: Background: Thrombocytopenia, characterized by a reduction in platelet count, is commonly observed in clinical settings. Its etiology can be broadly classified into hyper-destructive thrombocytopenia, where platelets are destroyed at an accelerated rate, and hypo-productive thrombocytopenia, where platelet production is impaired. Differentiating between these two causes is essential for effective management. The Immature Platelet Fraction (IPF) has emerged as a promising non-invasive diagnostic tool to distinguish these causes. Objectives: The primary …
Published in Research and Reviews: Journal of Oncology and Hematology · Vol. 14, Issue 2, 2025 Read article
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Assessment of Differential Global Positioning System (DGPS Technology for Generating Accurate Topographic Maps and Controls: A Case Study of Farin-Lamba to Kwali College Area
Abstract: This study investigates the application of Differential Global Positioning System (DGPS) for topographic mapping and control point establishment in Farin-Lamba to Kwali College Area. The second order Survey controls extension are critical indices for ensuring structural and border control mechanisms in environmental development projects. However, creating these controls using traditional ways presents major obstacles. Most modern techniques are improvements on ancient approaches, which raises the possibility of environmental dangers and …
Published in International Journal of Land · Vol. 2, Issue 1, 2025 · pp. 11–23 Read article
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Differentiating Real Versus Unreal in Children: An Investigation Using GIF Stimuli
Abstract: Virtual Reality Judgment is a part of cognitive development. With advancing cognitive development children will develop judgmental abilities enabling them to differentiate realty vs myth. This study explores the development of reality judgment abilities in typically developing children aged 3-6 years. Reality judgment, encompassing both character and action ability perception, is crucial for a child's accurate perception of the world. Existing research on reality judgment often stems from Western contexts, …
Published in International Journal of Children · Vol. 1, Issue 1, 2024 · pp. 01–04 Read article
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Analysis of C45 Steel Machining with Differentiated Tool Bits
Abstract: The tool material may be coated or uncoated, and cutting inserts are typically situated along the covered contact region. Work piece remains fixed while tool revolves for cutting and machining. Objective: A NABL-accredited metallurgical evaluation laboratory (machining) assessed two specimens. Machining profile and materials determine insert selection. Analytical results show material composition. The surface qualities of samples 1 and 2 were examined. As DOC, cutting speed and tool tip temperature …
Published in Journal of Polymer & Composites · Vol. 12, Issue 5, 2024 · pp. 244–252 Read article
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A Review on Design Optimization of Automotive Conventional Differential System for Rear Wheel Drive
Published in Trends in Mechanical Engineering & Technology Read article
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The Rise of Fractional Calculus: Novel Applications in Engineering and Biological Systems
Abstract: Fractional calculus (FC) is an advanced mathematical framework that generalizes the classical concepts of differentiation and integration to non-integer, or fractional, orders. This extension of traditional calculus allows for the modeling of complex dynamic systems that exhibit behavior not easily captured by integer-order differential equations. Over the last few decades, fractional calculus has seen a rapid rise in popularity, particularly in applied mathematics, engineering, and biological sciences, due to its …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 7–11 Read article
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Parallel Privacy-Preserving Adaptive Federated Learning on GPU-Enabled Multi-Core Architectures
Abstract: The increasing deployment of parallel and distributed intelligent systems has intensified the need for privacy-preserving learning frameworks that can exploit multi-core and GPU-based architectures without centralizing sensitive data. This work proposes a parallel Adaptive Federated Learning (AFL) framework that integrates Differential Privacy and Secure Aggregation over heterogeneous multi-core and GPU platforms to enhance both data confidentiality and convergence efficiency. The framework dynamically adjusts client participation, learning rates, and aggregation weights …
Published in Recent Trends in Parallel Computing · Vol. 13, Issue 1, 2026 Read article
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Deciphering Th-Related Gene Interactions in Chronic Spontaneous Urticaria: Bioinformatics Insights and Drug Affinity Exploration
Abstract: Objective: There has been a great deal of interest in how inflammatory dermatosis and The cell interact, but the etiopathogenesis of chronic spontaneous urticaria (CSU) is still inadequately comprehended. Through bioinformatics techniques, the purpose of this work is to elucdate the molecular mechanism underlying Th-related genes in CSU and seeks to find the highest affinity drug. Methods: The CSU RNA expression profiling dataset provided the basis for the investigation. The …
Published in International Journal of Genetic Modifications and Recombinations · Vol. 2, Issue 1, 2024 · pp. 1–15 Read article