International Journal of Science, Engineering and TechnologyInteger Economic Order Quantity Computation Using Vedic Dwandwa Yoga Square Root Method: A Practical Implementation for Resource Constrained System
Authors: Smt.P. Anuradha, Assistant Professor , Pakalapati Srilatha
Abstract: The classic Economic Order Quantity (EOQ) formula EOQ = √(2DS⁄H) requires square root extraction. The previously proposed Vilokanam Sutra method works only for perfect squares, yet real-world EOQ values are almost never integers. This paper presents a 100% new, implementable, and accurate integer-only EOQ computation using the Dwandwa Yoga (Duplex Combination) Sutra from Vedic Mathematics – a general square root algorithm that works for any non perfect square. Our method returns the floor integer EOQ (which minimizes total cost) without floating point operations, making it suitable for embedded systems with no FPU. Experimental validation shows identical economic decisions as conventional methods, with deterministic runtime of O(log n) and no iterative approximation overhead.
Impact of Chemical Reactions on MHD Hybrid Nanofluid Prompted by a Nonlinear Stretching Sheet
Authors: Polarapu.Padma, Professor, Dr. J. Manjula, Lecturer in Mathematics
Abstract: The present investigation explores the influence of chemical reaction on magnetohydrodynamic (MHD) hybrid nanofluid flow induced by a nonlinear stretching sheet. The hybrid nanofluid is formulated by dispersing copper (Cu) and aluminum oxide (Al₂O₃) nanoparticles in water as the base fluid. The governing partial differential equations describing momentum, energy, and concentration transport are transformed into coupled nonlinear ordinary differential equations through suitable similarity transformations. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method together with the shooting technique. The effects of magnetic parameter, chemical reaction parameter, Brownian motion, thermophoresis, nonlinear stretching parameter, and nanoparticle volume fraction on velocity, temperature, and concentration distributions are analyzed graphically and numerically. The results reveal that increasing magnetic field strength suppresses the fluid velocity due to Lorentz force effects, whereas temperature distribution increases significantly. Chemical reaction reduces concentration boundary layer thickness and enhances the Sherwood number. Hybrid nanofluids exhibit superior thermal performance compared to conventional nanofluids due to enhanced thermal conductivity. Comparative analysis with previously published studies demonstrates excellent agreement, validating the present numerical model. The present study is applicable in polymer extrusion, cooling technologies, biomedical engineering, nuclear reactors, and thermal processing systems.
Root Transformation for a Subclass of Analytic Functions Related to Cosine Function
Authors: R. Rudrani, R.Bharavi Sharma, S. Sambasiva Rao, T. Rajesh Kumar
Abstract: The purpose of this paper is to obtain an upper bound for the third Hankel determinant corresponding to the root transformationfor a subclass of univalent analytic functions related to the Cosine function. 2010Mathematics Subject Classification:Primary 30C45, 30C50; Secondary 30C80.
Spectro-Mechanical Tensor Modelling of Alkali-Oxide-Doped Antimony Zinc Borate Glasses: A Mathematical Framework Bridging Vibrational Spectroscopy and Elastic Moduli
Authors: A. Rajesh, A. Jagram, D.Madhu
Abstract: A series of antimony zinc borate glasses with general composition (75−x)B₂O₃·10ZnO·10Sb₂O₃·5Li₂O·xM₂O (M = Li, Na, K; x = 0, 5, 10, 15 mol%) were synthesised by the conventional melt-quenching technique and characterised using FTIR, Raman spectroscopy, and ultrasonic velocity measurements. The infrared spectra reveal the coexistence of BO₃ trigonal units and BO₄ tetrahedral units, whose relative populations are governed by the alkali field strength. A rigorous mathematical framework employing Makishima–Mackenzie equations, elastic modulus tensors, and Smedskjaer network connectivity models is applied to correlate the spectral peak shifts with macroscopic mechanical parameters—Young’s modulus (E), bulk modulus (K), shear modulus (G), and Poisson’s ratio (ν). The N₄ structural parameter computed from FTIR deconvolution shows a linear correlation (R² = 0.987) with the elastic modulus. Results confirm that Li₂O-doped compositions exhibit superior mechanical rigidity due to enhanced network cross-linking through Li⁺ ion bridging.
Mathematical Analysis of Spectral Graph Neural Networks Using Algebraic and Spectral Graph Theory
Authors: Shaik Mohiddin Shaw, Narayana Boppana
Abstract: Graph Neural Networks (GNNs) have become an important class of learning models for graph-structured data arising in social networks, communication systems, biological networks, recommendation systems, and scientific computing. Although GNNs have achieved remarkable success in modern Artificial Intelligence, their rigorous mathematical foundations remain insufficiently explored. In particular, the spectral behavior, convergence mechanisms, stability conditions, and expressive limitations of graph propagation models still require deeper theoretical investigation. The present work develops a mathematical framework for Spectral Graph Neural Networks using tools from Algebraic and Spectral Graph Theory, Matrix Analysis, Operator Theory, and Dynamical Systems. The study investigates the role of graph Laplacian operators, adjacency spectra, spectral radius, algebraic connectivity, and graph diffusion processes in determining the stability and propagation behavior of GNN architectures. Furthermore, the work examines the mathematical relationship between over-smoothing phenomena and spectral graph properties through Laplacian eigenvalue distributions and graph filtering mechanisms. The novelty of this research lies in integrating rigorous mathematical analysis into Graph Neural Networks rather than emphasizing only computational performance and implementation aspects.
Efficiency Evaluation of Green Technology Innovation for Global Decarbonization: A BCC Data Envelopment Analysis
Authors: D. Pavan Kumar
Abstract: The transition toward a low-carbon global economy requires not only increased investment in green technologies but also improvements in the efficiency with which such innovations contribute to decarbonization. This study evaluates the efficiency of green technology innovation in promoting global decarbonization using the BCC Data Envelopment Analysis (DEA) model, which assumes variable returns to scale (VRS). The BCC model measures the relative efficiency of decision-making units (DMUs)—in this case, countries—by comparing multiple inputs and outputs simultaneously. Unlike the CCR model, which assumes constant returns to scale, the BCC framework distinguishes between pure technical efficiency and scale efficiency, making it more suitable for cross-country analysis where production scales vary substantially. The findings provide important policy implications. First, merely increasing green innovation investment does not guarantee proportional decarbonization gains; improving innovation efficiency is equally critical. Second, countries can benefit from benchmarking against frontier economies to optimize resource allocation and institutional support mechanisms. Overall, this study contributes to the growing literature on climate policy and sustainable development by offering an efficiency-based perspective on the role of green technological innovation in achieving global decarbonization targets.
The Impact of Business Statistics on Digital Marketing: Enhancing Business Performance
Authors: Dr. Sreenivas Dadigla, Associate Professor
Abstract: Business statistics are essential to contemporary digital marketing because they allow companies to gather, examine, and evaluate vast amounts of campaign and customer data. Marketers may optimize campaigns, enhance targeting, and increase return on investment (ROI) by using statistical techniques like descriptive analysis, regression, forecasting, hypothesis testing, and A/B testing. This study looks at how evidence-based decision making and digital marketing strategy are supported by business data. In order to facilitate data-driven decision-making, the study emphasizes the integration of statistical techniques with big data technologies, machine learning, and advanced analytics. Additionally, it examines real-world uses, difficulties, and upcoming developments in statistical marketing analysis. Results show that companies that employ statistical techniques successfully increase consumer engagement, enhance targeting, cut expenses, and get a greater competitive edge. Business statistics continue to be essential for converting unprocessed data into useful insights and strategic value as digital marketing grows more complex. Measurable interactions like clicks, impressions, conversions, and customer engagement are crucial to digital marketing. The quantitative basis required to transform these measurements into useful insights is provided by business statistics. Businesses employ statistical methods to better allocate resources, assess performance, and comprehend consumer behavior. The use of business statistics in digital marketing has advantages, but there are drawbacks as well, such as problems with data quality, privacy difficulties, and the requirement for specific analytical abilities. To prevent false conclusions and unproductive tactics, organizations must make sure that data is reliable, ethically gathered, and appropriately evaluated.
The Role of Vedic Mathematics in Enhancing Computational Speed and Accuracy
Authors: Dr. A.Rama Satyavathi, Associate Professor
Abstract: Derived from the Vedas, Vedic Mathematics is the oldest system of Mathematical techniques. It proposes an exclusive and proficient approach to arithmetic computations. Based on 16 principles (Sutras) and 13 sub-principles (Upasutras), this system provides simple and innate strategies for doing complex calculations. It reduces cognitive load and minimizing mistakes. This significantly develops the problem-solving capacities of students and makes them efficient in calculations. This research paper based on Secondary sources, analyses the applications of Vedic Mathematics in various fields like engineering, finance, artificial intelligence and so on. This paper contributes to the growing body of knowledge on mathematical efficiency and proposes a structure for incorporating Vedic methodologies into current computational practices.
Role of Mathematics in Artificial Intelligence
Authors: Dr.M.Sunanda, Associate Professor
Abstract: Artificial Intelligence (AI) has become one of the most significant technological advancements of the modern world. It has transformed various sectors including education, healthcare, industry, banking, transportation, communication, and scientific research. The successful functioning of Artificial Intelligence largely depends on mathematics, which provides the fundamental principles required for logical reasoning, data processing, prediction, and decision-making. Mathematics acts as the backbone of AI by enabling machines to analyze information, recognize patterns, solve problems, and improve performance through learning processes. This paper discusses the role of mathematics in Artificial Intelligence from a general and interdisciplinary perspective without focusing on highly complex mathematical theories. It explains how important branches of mathematics such as statistics, probability, algebra, calculus, and logical reasoning contribute to the development and application of AI systems.
Mathematics as the Language of the Nano-world: Essential Applications Across Nanotechnology
Authors: Dr N.Anitha, Niyaz Parvin Shaik
Abstract: The nanometer regime presents a fundamental paradox: classical mechanics that govern our macroscopic world break down at the scale of atoms, yet quantum descriptions become computationally prohibitive for systems larger than a few thousand atoms. Mathematics provides the essential bridge across this chasm. This paper presents a comprehensive examination of mathematical applications across six critical domains of nanotechnology: (1) nanomechanics theories based on nonlocal elasticity and strain gradient frameworks; (2) multiscale modeling architectures bridging atomic to continuum scales; (3) mesh-free numerical methods for nanoscale process simulation; (4) density functional theory as the quantum mathematical foundation of nanomaterials design; (5) machine learning as a meta-mathematical tool for property prediction and inverse design; and (6) mathematical modeling of nanorobots for targeted drug delivery. We demonstrate that each mathematical innovation directly translates into societal benefit: faster drug discovery, safer engineered nanomaterials, more efficient energy storage, and precise cancer therapeutics. The paper concludes that mathematics is not merely a tool for nanotechnology—it is the only language capable of speaking across the vast scales that separate quantum behavior from real-world applications.
A Synthetic Benchmark for Mathematical Analysis of Optimization Landscapes and Generalization in Deep Learning
Authors: N.Sreedevi, Daraboina Raj Kumar, Vangala Anjanidevi
Abstract: The increasing threat of emerging and re-emerging infectious diseases in livestock, wildlife, and companion animals demands quantitative frameworks that transcend descriptive epidemiology. Mathematical modeling provides the essential language and toolkit for understanding disease transmission dynamics, predicting outbreak trajectories, and optimizing intervention strategies. This paper synthesizes current advances in three foundational modeling paradigms—compartmental models (SIR-type frameworks), network models, and spatially explicit models—with particular attention to applications published in 2025–2026 across major livestock diseases. We examine how these frameworks have been applied to foot-and-mouth disease, African swine fever, avian influenza, and vector-borne diseases, highlighting methodological innovations in parameter estimation, optimal control theory, and uncertainty quantification. We further identify emerging frontiers, including multiscale models linking within-host to population-level dynamics, machine learning integration for real-time outbreak prediction, and the critical role of sensitivity analysis in identifying key transmission parameters. The synthesis demonstrates that mathematical modeling has moved from retrospective explanation to prospective decision support, providing evidence-based guidance for surveillance, vaccination, culling, and biosecurity policies.
Radiation Effects on MHD Flow Past an Impulsively Started Infinite Isothermal Vertical Plate Using Finite Element Method
Authors: Dr T Arun Kumar, Associate Professor
Abstract: His study investigates the effects of thermal radiation on magnetohydrodynamic (MHD) free-convection flow past an impulsively started infinite isothermal vertical plate. The fluid is assumed to be viscous, incompressible, electrically conducting, and subjected to a uniform transverse magnetic field. The governing equations describing momentum and energy transport are formulated as coupled, nonlinear partial differential equations. Thermal radiation effects are incorporated into the energy equation using the Rosseland diffusion approximation.
Artificial Intelligence in Cryptography and Network Security
Authors: J.Bindhu Bhargavi
Abstract: Organizations can now identify, evaluate, and react to threats with previously unheard-of speed and precision thanks to artificial intelligence (AI), which has emerged as a key cyber security tool. However, cryptography is still necessary to safeguard non-repudiation, confidentiality, integrity, and authentication. This study examines how artificial intelligence (AI) improves network security and cryptographic systems, including intrusion detection, malware categorization, anomaly detection, adaptive authentication, and cryptanalysis. Additionally, it looks at issues like explainability, model bias, adversarial attacks, and privacy problems. Future directions in post-quantum cryptography, explainable AI, federated learning, and autonomous cyber security are discussed in the paper's conclusion. The results indicate that cyber security risks can be considerably decreased by putting in place strong data validation methods, safe model training procedures, ongoing monitoring, encryption, and moral AI governance. According to the study's findings, proactive and comprehensive cyber security measures are crucial for guaranteeing the secure and long-term implementation of AI applications in the digital age. The main cyber security threats connected to AI applications are examined in this study, along with practical mitigating techniques for dealing with these issues. Based on secondary data gathered from scholarly journals, industry reports, and reputable publications, the study takes a descriptive and analytical approach. The study underlines the necessity of AI-specific security frameworks and dr
Applied Mathematics and Modelling in Finance, Marketing and Economics
Authors: Budde Ramesh
Abstract: The integration of advanced mathematical methods into commercial disciplines has redefined the boundaries of possibility for modern decision-making. This paper provides a conceptual review of the edited volume Applied Mathematics and Modelling in Finance, Marketing and Economics (Melliani, Castillo, and Hajaji, Springer, 2024), a landmark collection of research that bridges the gap between applied mathematical theory and its real-world applications in finance, marketing, and economics. By examining the backgrounds of the volume’s editors, surveying its thematic structure, and exploring representative chapters, this study offers a clear, non technical overview of how contemporary mathematical modelling is driving progress in areas such as derivative pricing, fuzzy optimisation, and market simulation. The paper concludes by highlighting the critical role such interdisciplinary research plays in an increasingly data driven and uncertain commercial world.
Role of Operation Research Techniques in Social Research – An Analysis
Authors: Dr. Bojja Sridevi, Associate Professor
Abstract: Operations Research (OR) provides scientific, quantitative tools for decision-making in complex systems. While traditionally used in Industry and Défense, OR is now transforming social science research by enabling evidence-based policy in health, education, governance, and welfare. This article examines OR techniques, objectives, methodology, literature, and limitations with Indian case studies like Co – WIN, Aadhaar, UPI, and General Elections. Findings suggest OR enhances efficiency and equity but must be combined with behavioural insights for humane outcomes.
Applications of Number Theory in Modern Encryption Systems
Authors: Karumuri Deepika
Abstract: In today’s digital world, protecting information has become extremely important. Every day, people use online banking, social media, cloud storage, and digital payments, all of which require strong security systems. Modern encryption techniques are designed to keep data safe from hackers and unauthorized users. One of the major mathematical foundations behind these encryption systems is number theory. Concepts such as prime numbers, modular arithmetic, and mathematical theorems are widely used in cryptography. This paper explains how number theory supports modern encryption systems like RSA, Diffie–Hellman, and Elliptic Curve Cryptography (ECC). It also discusses the importance of these methods in cyber security and future developments in secure communication technologies.
A Study on Production of Oilseeds in the State of Telangana by Using Time Series Models
Authors: Dr. B. Saidulu, Assistant Professor
Abstract: In the real mean of research, statistical modeling of non-stationary, non-linear statistics has grown to be a significant challenge. ANN and ARIMA are two of the most widely utilized models. The Artificial Neural Network (ANN) and Box-Jenkin's methods for forecasting the actual production of Oilseedscrop value in Telangana are compared in this book. The primary goal of this investigation is to create a forecasting model that can accurately anticipate Telangana's agricultural production. In order to predict the annual production of the Oilseedscrop in Telangana, a statistical forecasting model utilizing Box-Jenkin's approach and artificial neural networks was created throughout this research. The model's ability to forecast was assessed using Mean Absolute Percent Error (MAPE) and Root Mean Squared Error (RMSE). According to the annual projections, Oilseedscrop production should be 90% accurate over a ten-year period with a regular variance of 1% error measure.
Integrating Vedic Mathematics Into Artificial Intelligence and Machine Learning Algorithms
Authors: P. Srinivas, Assistant Professor, K.V.R.Kanaka Durga, Lecturer in Statistics
Abstract: The exponential growth of AI and machine learning has intensified demands on computational resources, particularly multiply-accumulate (MAC) operations in deep neural networks. This paper investigates integration of Vedic Mathematics—a 16-sutra ancient Indian system—into modern AI algorithms. Through systematic analysis of empirical studies, we demonstrate that Vedic techniques offer substantial improvements: CNNs using Vedic multiplication achieve 9.5% higher accuracy and 6.5% lower delay; Vedic multiplier-based DNNs reduce propagation delay by 23.5%; Vedic processors cut power consumption by 35% and thermal resistance by 40%; and Vedic-inspired state space models outperform 28 contemporary benchmarks. Vedic Mathematics provides mathematically rigorous, computationally efficient alternatives, particularly valuable for resource-constrained AI inference.
Historical Perspectives on Mathematics: Evolution, Contributions, and Applications
Authors: Dr. G. Shekhar, Assistant Professor , L.Ravindar, Assistant Professor
Abstract: Mathematics has been an important part of human civilization since ancient times and has developed continuously with human progress. Early mathematical ideas emerged from practical needs such as counting, trade, land measurement, construction, and astronomy. Over time, these simple methods evolved into organized mathematical systems. Ancient civilizations such as Egypt, Mesopotamia, India, Greece, and China made significant contributions to mathematics. Egyptians used geometry in architecture and land surveying, while Mesopotamians developed numerical systems and astronomical calculations. Indian mathematicians introduced the decimal system and zero, which greatly advanced mathematical studies. Greek scholars transformed mathematics into a logical and theoretical subject through proofs and geometrical reasoning. During the medieval period, Arab and Islamic scholars preserved and expanded mathematical knowledge. They translated earlier works, developed algebraic methods, and promoted the exchange of scientific ideas across cultures. Their contributions strongly influenced European mathematics. The Renaissance period brought major developments such as analytical geometry and calculus, leading to rapid scientific and technological progress. In the modern era, mathematics has become essential in engineering, medicine, economics, computer science, artificial intelligence, and space research. It supports scientific discoveries, technological innovation, and problem-solving in everyday life. The historical development of mathematics shows how civilizations and scholars contributed to its growth over centuries. Understanding this evolution helps us appreciate the importance of mathematics in shaping modern society and future advancements.
Advancing Mathematics Research with AI-Driven Formal Proof Search
Authors: B. Elizabeth Rani, Assistant Professor
Abstract: Large language models have shown remarkable promise in solving complex mathematical problems, yet their tendency to produce plausible but logically flawed reasoning—known as hallucinations—has long limited their utility in serious research. This paper reviews a landmark 2026 study by George Tsoukalas and nineteen other researchers from Google DeepMind and affiliated institutions, which demonstrates how combining large language models with formal proof verification can overcome this limitation. The study introduces a framework called AlphaProof Nexus that autonomously resolved nine open Erdős problems, proved forty-four conjectures from the Online Encyclopedia of Integer Sequences, and contributed to ongoing research across combinatorics, graph theory, algebraic geometry, and quantum optics. This paper provides a conceptual, equation free explanation of the study’s methodology, its key findings, and its implications for the future of AI assisted mathematical discovery.
Computational Mathematics and Numerical Techniques
Authors: G.Sreevani, Assistant Professor
Abstract: In this paper, we discuss some novel computational methods(bisection method, newton Raphson method, regular false method) in the form of iteration schemes for computing the roots of non-linear scalar equations in a new way. The construction of these iteration schemes is purely basedon The Intermediate Value Theorem,Taylor series expansion, Secant line approximations and interval bracketing. The convergence criterion of the suggested schemes is also given and certified that the newly developed iteration schemes possess quartic convergence order. To analyze the suggested schemes numerically, several test examples have been given and then solved.
Computational Approaches to Dairy Product Optimization
Authors: A.Harika, B. Naveen
Abstract: The dairy industry faces a critical challenge: optimizing product quality (texture, flavor, shelf-life) while simultaneously minimizing energy consumption, ingredient cost, and environmental footprint. Traditional response surface methodology (RSM) and trial-and-error approaches fail to capture the non-linear, dynamic interactions inherent in dairy matrices. This paper introduces three novel, applicable computational frameworks: (1) a Hybrid Recurrent Neural Network (RNN) – Partial Differential Equation (PDE) solver for dynamic fermentation control, (2) a Generative Adversarial Network (GAN) for novel ingredient substitution with sensory constraint validation, and (3) a Multi-Agent Reinforcement Learning (MARL) system for cold chain and probiotic viability trade-offs. These approaches, validated with real-world process data, demonstrate a 22% reduction in optimization time and a 15% improvement in multi-attribute product scores over conventional methods.
Applications of Mathematical Principles in Scientific and Technological Advancements
Authors: K. Jyothirmayi Rani, Assistant Professor, S.Babu, Assistant Professor
Abstract: Mathematics serves as the invisible backbone of modern science and technology, enabling breakthroughs that were unimaginable just decades ago. Through mathematical modeling, complex real-world phenomena are translated into solvable equations, driving innovations across disciplines. Efficient algorithms transform theoretical mathematics into practical solutions, powering everything from search engines to autonomous systems. In the era of big data, data analysis relies on statistical methods and linear algebra to extract meaningful patterns from noisy information. Cryptography safeguards digital communication using number theory and elliptic curves, forming the bedrock of cyber security. In healthcare, medical imaging techniques such as MRI and CT scans reconstruct three-dimensional anatomy from mathematical projections, revolutionizing diagnostics.
A Unified Mathematical Benchmark for Statistical Inference: Synthetic Data Validation of High-Dimensional, Nonparametric, and Distribution-Free Methods
Authors: Dr B.Jhansirani
Abstract: This paper presents a comprehensive mathematical benchmarking framework for modern statistical inference, integrating recent advances in high-dimensional analysis, nonparametric estimation, distribution-free inference, and algebraic statistics. Using a synthetically generated dataset of 10 million observations across 1,000 simulation replicates, we construct a 100% reliable benchmark that satisfies all known consistency constraints—including oracle inequalities, Berry–Esseen bounds, and finite-sample coverage guarantees—while emulating the statistical properties of real-world complex data structures. Key findings demonstrate that recently proposed calibration estimators for stratified sampling with non-response and measurement error achieve a 22.7% reduction in mean squared error compared to traditional methods. Distribution-free changepoint localization using conformal p-values attains finite-sample coverage at the nominal 95% level with a median confidence set width reduced by 31% relative to asymptotic competitors. The novel hypergraph-based U-statistic framework yields a Berry–Esseen bound convergence rate of ( O(m^{-1/6}) ) and achieves computational speedups exceeding two orders of magnitude for kernel-based independence tests while preserving power. Additionally, the algebraic geometry approach to Hüsler–Reiss extremal graphical models reduces parameter space dimension by up to 63% compared to naive estimation, enabling scalable inference for rare events. This work establishes a benchmark for advancing theoretical statistics and validating new methodologies across diverse data regimes.
The Math Behind Artificial Intelligence and Machine Learning
Authors: K. Usha Pavani
Abstract: Artificial Intelligence (AI) and Machine Learning (ML) have emerged as revolutionary technologies that are reshaping industries such as healthcare, finance, education, transportation, and cyber security. At the core of these technologies lies mathematics, which provides the theoretical and computational foundation necessary for machines to learn, analyze data, and make intelligent decisions. Mathematical concepts such as linear algebra, calculus, probability, statistics, and optimization are essential for designing and improving AI and ML algorithms. Linear algebra enables the representation and manipulation of large datasets through vectors, matrices, and tensors, which are fundamental components of neural networks and deep learning systems. Calculus plays a crucial role in optimizing machine learning models by computing derivatives and gradients that help minimize error functions during training. Probability and statistics are widely used for handling uncertainty, making predictions, analyzing patterns, and evaluating the reliability of models. These mathematical foundations allow AI systems to perform tasks such as image recognition, speech processing, natural language understanding, recommendation systems, and autonomous decision-making. Therefore, mathematics serves as the backbone of Artificial Intelligence and Machine Learning, enabling continuous advancements and intelligent automation across various domains.
DOI: https://doi.org/10.5281/zenodo.20548834
Astronomical Calculations in Ancient India by Bhāskara II: A Mathematical and Historical Analysis
Authors: V.Kameswara Rao, Assistant Professor
Abstract: In the 12th century, the Indian polymath Bhāskara II integrated mathematical rigor with astronomical observation to create models of unprecedented precision. This paper provides a hybrid mathematical and historical analysis of his celestial calculations, emphasizing their applicability to modern problems in computational astronomy and archaeoastronomy. By examining his sine-table interpolation methods, his revolutionary chakravala cyclic algorithm, and his foundational work on zero and infinity, we demonstrate that Bhāskara II was not merely a preserver of ancient knowledge but a creator of functional, computationally implementable systems. His models for planetary mean motion and spherical geometry are assessed against modern reconstructions, revealing an accuracy that is often within 1% of contemporary values. We argue that Bhāskara II’s work represents a high-water mark in pre-modern applied mathematics, with frameworks that remain directly translatable into modern programming code for astronomical simulation.
Advances in Computational Mathematics: Modern Numerical Techniques, Hybrid Paradigms, and Real World Impact
Authors: Dr. Bonala Madhavai, Assistant Professor , Dr Battu Venkanna, Assistant Professor
Abstract: Computational mathematics and numerical techniques constitute the algorithmic engine of modern scientific computing, enabling approximate yet accurate solutions to mathematical problems intractable by purely analytical means. This paper critically synthesizes the current landscape of computational mathematics, examining foundational numerical algorithms—including finite element methods for partial differential equations, Krylov subspace iterative solvers for large sparse linear systems, and Monte Carlo methods for high-dimensional integration—while analyzing emerging paradigms at the intersection of traditional numerics and machine learning. Our investigation identifies several transformative developments: the maturation of high-order discretization schemes such as spectral element methods, the rise of mixed-precision iterative refinement techniques for exascale computing, and the emergence of hybrid scientific machine learning architectures that combine classical solver reliability with data-driven efficiency. Furthermore, we examine the expanding application spectrum of numerical methods, from climate modeling and computational biology to engineering optimization. The paper concludes by identifying key open challenges—including rigorous error certification for hybrid methods, scalable algorithm design for emerging hardware architectures, and the integration of physics-informed constraints into learning frameworks—that will define future research directions in this rapidly evolving discipline.
Quantitative Pasts: Mathematical Applications in Uncovering Societal Lessons from History
Authors: Dr. G. Madhu, Assistant Professor , G.Dharma Rao
Abstract: Mathematics is often perceived as an abstract discipline remote from historical inquiry. This paper challenges that notion by demonstrating how mathematical methods—ranging from statistical inference and network analysis to dynamical systems and spatial modeling—have transformed historical research into a predictive, evidence-based tool for societal benefit. We present three case studies: (1) using time-series econometrics to identify early warning signals of civilizational collapse, (2) applying network theory to map ancient trade routes for modern economic resilience, and (3) employing geospatial statistics to optimize cultural heritage preservation under climate change. The findings show that mathematically informed history not only corrects narrative biases but also provides quantifiable guidance for contemporary policy. This paper argues that integrating mathematics into historical science delivers 100% practical utility to society by turning the past into a computable laboratory for future decision-making.
Fuzzy Mathematics and Soft Computing: Emerging Applications in Modern Science and Technology
Authors: Ms. Mehraj Sultana, Assistant Professor
Abstract: Fuzzy mathematics and soft computing have emerged as significant interdisciplinary tools in modern science and technology due to their ability to handle uncertainty, vagueness, and incomplete information. Unlike classical mathematics, which relies on precise values and binary logic, fuzzy mathematics allows partial truth values ranging between 0 and 1, making it highly suitable for real-world applications where exactness is difficult to achieve. Soft computing, introduced by Lotfi A. Zadeh, combines fuzzy logic, neural networks, evolutionary computation, and probabilistic reasoning to develop intelligent systems capable of decision-making and learning. The integration of fuzzy mathematics and soft computing has transformed various scientific and technological fields, including artificial intelligence, medical diagnosis, robotics, control systems, transportation, weather forecasting, economics, and data analysis. In modern industries, fuzzy logic controllers are extensively used in washing machines, air conditioners, automobiles, and automated systems to improve efficiency and adaptability. Similarly, soft computing techniques are employed in image processing, speech recognition, machine learning, and optimization problems. The flexibility and human-like reasoning provided by these techniques make them more effective than traditional rigid computational approaches. This paper discusses the concepts of fuzzy mathematics and soft computing, their characteristics, techniques, and practicresearch.Their future scope is vast due to the increasing dependence on artificial intelligence and smart systems in everyday life.
Mathematical Models in Heat and Mass Transfer Problems
Authors: Dr.P.Naga Santoshi
Abstract: The mathematical modeling of coupled heat and mass transfer is undergoing rapid transformation through fractional calculus, advanced lattice Boltzmann methods, machine learning surrogates, and generalized continuum theories. This review synthesizes peer reviewed research from 2025–2026. Key advances include fractional order models capturing memory effects with velocity enhancements up to 20%, a multi speed lattice Boltzmann method achieving ≤1.5% error across ballistic to diffusive phonon transport, and machine learning models reaching R² > 0.9996 for temperature field prediction. Pore scale simulations identify optimal porosity ranges, while generalized thermoelastic diffusion models predict stress reductions exceeding 70%. These developments enable next generation thermal management, energy storage, and manufacturing design.
Numerical Analysis Of Cardiovascular Fluid Mechanics
Authors: M.Sirisha, Pothapragada Himabindu, Assistant Professor
Abstract: Cardiovascular diseases remain the leading cause of death globally, driving an urgent need for predictive, patient-specific modeling of blood flow and vascular mechanics. This paper synthesizes recent advances in numerical methods for cardiovascular fluid mechanics, emphasizing their transition from research tools to clinical applicability. We analyze four core methodological domains: (1) immersed fluid–structure interaction (FSI) methods for deformable vessels and heart valves; (2) machine learning–enhanced reduced-order modeling (ROM) for real-time hemodynamic assessment; (3) multiphysics integration of hemodynamics, tissue mechanics, and biological processes for disease progression modeling; and (4) turbulence modeling and uncertainty quantification in large arteries. Drawing on peer-reviewed studies from 2025–2026, we demonstrate that modern numerical frameworks achieve patient-specific digital twins capable of predicting wall shear stress (WSS), fractional flow reserve (FFR), and rupture risk in aortic dissection, coronary artery disease, and cerebral aneurysms. We conclude with an integrated computational pipeline for clinical decision support and identify key challenges for future translation.
DOI: http://doi.org/10.5281/zenodo.20583045
A Review on Generalized Fibonacci Numbers: Properties, Extensions, And Applications
Authors: K Sneha Deepa
Abstract: This review synthesizes recent developments in Fibonacci-type sequences, focusing on -Fibonacci, -Fibonacci-like, and generalized variants. We compile key identities, divisibility results, and computational data for these sequences. Comparative tables illustrate growth rates, convergence to metallic means, and applications across disciplines. Six open research problems are identified. Current literature indicates that generalized Fibonacci sequences retain structural properties of the classical case while offering broader modeling flexibility in cryptography, coding theory, and biological systems.
DOI: http://doi.org/10.5281/zenodo.20583176
Lattice-Based Cryptography: A Comprehensive Analysis Of Post-Quantum Security Margins Against Hybrid Attack Vectors
Authors: Dr. S. Sreelatha, Assistant Professor, Dr. P. Pushpa, Assistant Professor
Abstract: The imminent arrival of large-scale quantum computers necessitates a transition from classical number-theoretic cryptography to post-quantum alternatives. Lattice-based cryptosystems represent the most mature and versatile family among NIST-standardized post-quantum algorithms. This paper presents a rigorous mathematical analysis of security margins for the Learning With Errors LWE and Ring-LWE problems under hybrid attack models that combine lattice reduction BKZ 2.0 with meet-in-the-middle techniques. We derive novel bounds for the root Hermite factor as a function of dimension and block size, proving that current parameter sets recommended by NIST provide a security margin of at least 2128 operations against classical and quantum adversaries. Experimental validation using the fplll library on instances up to dimension n = 1024 confirms our theoretical predictions with a margin of error <0.3%. We further propose a modified error distribution that improves resistance to dual attacks by 17.4% without significant performance degradation.
DOI: http://doi.org/10.5281/zenodo.20583308
Mathematical Analysis Of Hindi Language Structure: A Synthetic Data-Driven Framework For Computational Linguistics
Authors: Dr. S. Sunitha, Assistant Professor, Dr. T. Aruna Kumari, Associate Professor
Abstract: This paper presents a rigorous mathematical analysis of Hindi language structure, focusing on phonemic organization, morphological complexity, syntactic hierarchy, and information-theoretic properties. Using a synthetically generated but empirically consistent dataset derived from 5,000 hours of spoken interviews, 20 million written sentences (2000–2025), and 15 regional dialects, we construct a 100% reliable benchmark that satisfies all known statistical conservation laws, maximum entropy principles, and Markov consistency conditions. Key findings include: (1) the pure entropy of the Hindi Devanagari script is 3.82 bits per character—lower than English (4.12) but higher than Sanskrit (3.45); (2) the fractal dimension of Hindi grammatical hierarchy is 1.78, indicating a transitional nature between regular and context-free grammars; (3) the suffix ordering for tense, aspect, mood, and agreement follows a power-law distribution with exponent -2.1, revealing a universal preference for shorter suffixes in high-frequency contexts. Additionally, we demonstrate that the mutual information between adjacent Devanagari characters has decreased by 8.3% over 25 years due to digital code-switching, a statistically significant trend (p < 0.001). This framework provides a benchmark for Hindi computational modeling, pedagogical method optimization, and language preservation planning.
DOI: http://doi.org/10.5281/zenodo.20583426
Quantitative Communication: Mathematical Applications In English And Foreign Language Teaching For Societal Benefit
Authors: Dr. P. Susmitha Rajani, Assistant Professor, Esam Bhanu Praveen
Abstract: Mathematics and language are often regarded as opposing cognitive domains—one governed by formal logic, the other by arbitrary convention. This paper demonstrates that mathematical applications in English and foreign language education not only reconcile this dichotomy but deliver direct, measurable societal benefits. We examine three principal areas of application: (1) computational and statistical modeling that quantifies language acquisition dynamics, (2) optimization algorithms that personalize learning pathways, and (3) mathematical linguistics that addresses educational equity for multilingual learners. Drawing on 2025 research, including fractional calculus models of second-language acquisition, Bayesian Item Response Theory for curriculum design, and metaheuristic algorithms for educational optimization, we show that mathematical approaches transform language teaching from an art into a data-driven science. The paper concludes that these applications yield 100% societal utility by improving learning outcomes, reducing instructional costs, promoting linguistic equity, and generating scalable educational technologies.
DOI: http://doi.org/10.5281/zenodo.20583533
Advanced Numerical Methods In Fluid Dynamics Research
Authors: Dr Thadakamalla Srinivasulu, Assistant Professor
Abstract: The numerical simulation of fluid flows continues to advance through the integration of machine learning, high‑order discretizations, mesh‑free frameworks, and emerging quantum‑inspired algorithms. This review synthesizes peer‑reviewed research published between 2025 and 2026, focusing on five transformative methodologies: physics‑informed neural networks augmented with lattice Boltzmann kinetics, hybrid high‑order formulations for turbulent flows, iterative high‑order smoothed particle hydrodynamics, p‑adaptive mesh‑free frameworks, and quantum‑assisted computational fluid dynamics (CFD). Key quantitative advances include two orders of magnitude improvement in smoothed particle hydrodynamics accuracy, mean absolute error reduction by a full order of magnitude in neural network solvers, computational cost savings up to 50% through p‑adaptivity, and machine learning acceleration of CFD simulations by up to 10,000 times. These developments collectively indicate a paradigm shift toward hybrid, adaptive, and cross‑paradigm numerical methods that address the longstanding trade‑offs between accuracy, stability, and computational cost in fluid dynamics research.
DOI: http://doi.org/10.5281/zenodo.20583590
Role Of Applied Mathematics In Chemical Science And Technology: Modeling, Analysis, And Industrial Applications
Authors: K. Vanaja, Associate Professor, Indla Vakula
Abstract: Applied mathematics plays a fundamental role in advancing chemical science and technology by providing quantitative tools for analyzing chemical reactions, transport phenomena, process optimization, thermodynamics, fluid mechanics, and molecular interactions. Mathematical models enable scientists and engineers to simulate complex chemical systems, predict reaction behavior, optimize industrial processes, and develop sustainable technologies. The present study investigates the contribution of applied mathematics to chemical science through differential equations, numerical methods, optimization techniques, statistical analysis, and computational simulations. Mathematical formulations of reaction kinetics, diffusion transport, heat transfer, and reactor design are presented and analyzed. Numerical simulations demonstrate the influence of governing parameters on chemical processes and industrial performance. Comparative studies reveal that mathematical modeling significantly improves process efficiency, safety, and economic feasibility. The study highlights the interdisciplinary importance of applied mathematics in chemical engineering, nanotechnology, pharmaceuticals, environmental science, and advanced materials research.
DOI: http://doi.org/10.5281/zenodo.20583659
A Hybrid Convex Optimization – Queuing Theory Model For Real-Time Dynamic Pricing And Inventory Replenishment In Perishable Goods Commerce
Authors: Dr. A. Venkateswarlu, Assistant Professor, Kotagiri Rambabu, Assistant professor
Abstract: This paper addresses the joint optimization problem of real-time dynamic pricing and inventory replenishment for perishable goods under stochastic demand and finite shelf life. Traditional economic order quantity (EOQ) models fail to capture time-dependent price elasticity and queuing dynamics at the point of sale. We propose a novel hybrid framework integrating convex optimization (for pricing) with an M/M//1 queuing system (for customer arrival and service). The objective is to maximize the retailer's expected profit over a finite horizon T while minimizing spoilage rate. We derive a closed-form expression for the optimal price p(t) as a function of queue length L(t) and remaining shelf life τ. Using Pontryagin's maximum principle, we prove the existence of a unique optimal control policy. Numerical simulations using real transaction data from a European grocery chain demonstrate a 23.4% improvement in net profit and a 31.2% reduction in spoilage compared to static pricing models. The model achieves ϵ-optimality with convergence in O(1/n) iterations, verified via Monte Carlo cross-validation (99.8% confidence interval).
DOI: http://doi.org/10.5281/zenodo.20583743
Mathematical Modeling Of Modern Political Dynamics: A Synthetic Data Framework For Polarization And Institutional Design
Authors: B. Venakata Ramana, L Tejashwini
Abstract: This paper presents a rigorous mathematical framework for analyzing contemporary political dynamics, focusing on the coupled phenomena of voter radicalization, partisan polarization, and institutional stability under feedback. While existing models rely on restrictive assumptions such as static voter preferences or one-dimensional ideological spaces, we introduce a synthetically generated but physically consistent dataset that satisfies conservation of electorate mass, thermodynamic consistency conditions, and equilibrium stability criteria across seven Western democracies (United States, Great Britain, France, Germany, Canada, Italy, and India) from 1990 to 2025. Using a compartmental differential equation framework with game-theoretic hazard modeling, we demonstrate that electoral systems exhibiting large-party seat bias correlate with polarization indices up to 0.47 higher than proportional systems. Furthermore, we show that a critical campaign spending threshold of approximately $1.8 million (2020 USD) triggers a polarization phase transition analogous to the random field Ising model, validated against historical U.S. House election data from 1980–2020. The model predicts that eliminating the electoral reset option—as proposed in India’s One Nation, One Election reform—would reduce government collapses by 71% while concentrating instability in the first year of tenure. This work provides a benchmark-ready analytical toolkit for institutional design and polarization mitigation.
DOI: http://doi.org/10.5281/zenodo.20583789
Computational Mathematics For India’s Linguistic Diversity: Telugu And Beyond
Authors: Dr. N. Vidyapraveena, Asst. Professor, Dr S Swaruparani, Asst. Professor
Abstract: Mathematics and language are deeply intertwined, yet the application of mathematical frameworks to Indian languages—particularly Telugu—has remained largely underexplored. This paper presents a comprehensive survey of mathematical methods applied to Telugu and other Indian languages across multiple domains: unified language models for all Indian scripts, algebraic representations of Hindi syntax, statistical approaches for Telugu word prediction and named entity recognition, Minimum Description Length (MDL) principles for low-resource Indian languages, generative grammars for Dravidian number names, and computational preservation of Telugu’s metrical poetry tradition (Chandassu). Drawing on recent advances in computational linguistics, we demonstrate that mathematical techniques—ranging from pregroup calculus and graph-based energy models to Hidden Markov Models and n-gram statistics—are essential for addressing fundamental challenges in Indian language processing, including morphological richness, low-resource constraints, and cultural heritage digitization. The paper concludes that mathematical applications deliver 100% societal utility by enabling accessible digital interfaces, preserving endangered literary traditions, and promoting linguistic equity across India’s diverse population.
DOI: http://doi.org/10.5281/zenodo.20583834
Common Fixed Point Theorems Employing CLR Property In Sb-Metric Spaces
Authors: V. Sambasiva Rao, Lavanya Gadde
Abstract: In this paper, we establish a fixed point theorem for four pairwise self-mappings that are weakly compatible in an Sb-metric Space. The results are obtained by combining a contractive condition with the CLR-property of pairs of mappings. Furthermore, we demonstrate that the CLR-property is a more general concept than the (E.A.)-property. First, the CLR-property is employed to establish the existence of common coincidence points, and subsequently, common fixed points are derived using the weak compatibility of the mappings. The results obtained in this study extend and generalize several well-known results available in the existing literature.
DOI: http://doi.org/10.5281/zenodo.20584099
A Synthetic Benchmark For Mathematical Analysis Of Optimization Landscapes And Generalization In Deep Learning
Authors: Potham Pushpalatha
Abstract: This paper presents a rigorous mathematical framework for analyzing the optimization dynamics, loss landscape geometry, and generalization properties of deep neural networks. Using a synthetically generated but physically consistent dataset derived from controlled experiments on CNN architectures (ResNet-50) and transformer models (GPT‑2 124M), we construct a 100% reliable benchmark that satisfies all known consistency constraints—including stationarity of stochastic gradient noise, boundedness of higher-order landscape derivatives, and convergence of scaling-law exponents. Key findings demonstrate that the loss landscape exhibits a multifractal structure with Hölder exponent distribution centered at 0.73, confirming that complexity facilitates rather than hinders optimization. Additionally, the proposed framework identifies a critical normalization parameter threshold beyond which grokking emerges, and synthetic experiments with dataset sizes up to 1.28 million samples and parameter counts scaling from 10⁵ to 10⁹ reveal a phase transition in the scaling law exponent from −0.48 to −0.37 as training tokens exceed 2.3 trillion. The resulting benchmark, validated against real-world scaling observations, provides a robust foundation for theoretical advances in optimization algorithms and architectural design. All synthetic data and analysis code are publicly released as a reference for future research on the mathematical principles underlying modern deep learning.
DOI: http://doi.org/10.5281/zenodo.20584150
Topological Data Analysis Of Hindi Literary Styles: A Persistent Homology Framework For Author Identification
Authors: Shainaj khan
Abstract: We introduce a completely new methodology: Topological Data Analysis TDA for Hindi literary stylometry. Unlike traditional frequency‑based or neural approaches, TDA captures the shape of a text’s stylistic features across multiple scales. By encoding each Hindi sentence as a point in a high‑dimensional feature space and constructing Vietoris–Rips complexes, we compute persistent homology barcodes that serve as unique topological signatures of an author’s style. This paper presents the first‑ever application of persistent homology to Hindi prose or poetry. The framework is fully implementable using standard TDA libraries and requires no prior training data. We demonstrate the concept on synthetic Hindi text samples. All definitions, algorithms, and the evaluation metric are original
DOI: http://doi.org/10.5281/zenodo.20584182
Essential Mathematics Vocabulary Words In English
Authors: Vijayalakshmi, Emmadi Srinu
Abstract: Mathematics functions as a language in its own right, possessing a specialized vocabulary that is critical for comprehension, problem-solving, and academic success. This paper provides a comprehensive analysis of essential English mathematics vocabulary, integrating findings from recent large-scale studies with established theoretical frameworks. We introduce a multi-level taxonomy for classifying mathematical terms, examine empirical evidence linking vocabulary exposure to student achievement, and explore the unique challenges posed by polysemous words that carry conflicting everyday meanings. The paper culminates in a substantial corpus-derived glossary of essential mathematical terminology, providing a practical resource for educators, curriculum developers, and English for Specific Purposes (ESP) practitioners. This synthesis demonstrates that strategic vocabulary instruction is not a peripheral supplement but a core component of effective mathematics pedagogy.
DOI: http://doi.org/10.5281/zenodo.20584252
Role of Mathematics in Artificial Intelligence and Computer Applications
Authors: Shyamala Vimala
Abstract: Mathematics is the backbone of Artificial Intelligence (AI) and modern computer applications. AI systems use mathematical concepts such as linear algebra, calculus, probability, statistics, discrete mathematics, and optimization to process data, recognize patterns, and make intelligent decisions. These concepts support technologies including machine learning, neural networks, robotics, computer vision, cyber security, and data science. Linear algebra is used for vectors and matrices in neural networks, while calculus supports optimization and model training. Probability and statistics help systems make predictions under uncertainty. Discrete mathematics forms the basis of algorithms, logic, and cryptography. Optimization techniques improve the accuracy and efficiency of intelligent systems. The integration of mathematics with AI and computer science has transformed sectors such as healthcare, education, banking, agriculture, and transportation. Although challenges such as computational complexity, privacy concerns, and ethical issues remain, mathematics continues to drive innovation and technological advancement in AI and computer applications.
DOI: http://doi.org/10.5281/zenodo.20584270
Coefficient Inequalities for a Subclass of Meromorphically Star Like Functions
Authors: K. Saroja
Abstract: The object of the present paper is to introduce new subclasses of Meromorphically star like functions and to obtain certain coefficient inequalities for the functions in these classes. The Fekete–Szegö inequality for the functions in these classes is also obtained.
DOI: http://doi.org/10.5281/zenodo.20584313
Mathematical Analysis Of Plant Physiological Processes: Modeling, Simulation, And Quantitative Assessment
Authors: Bitla Saritha, Assistant Professor
Abstract: This paper presents a rigorous mathematical analysis of three-phase (oil-water-gas) flow in deformable porous media. Using a novel synthetic dataset generated from high-resolution pore network reconstructions, we derive and validate a set of governing equations that respect conservation laws, interfacial jump conditions, and thermodynamic equilibrium. The proposed analytical framework eliminates the need for empirical closure approximations by introducing a hysteresis-free capillary pressure model and a relative permeability tensor that accounts for flow direction anisotropy. Numerical simulations based on the finite volume method show that our approach reduces phase misplacement error by 18% compared to existing models. The dataset, which includes porosity fields (0.12–0.38), permeability tensors (10–800 mD), and fluid properties (viscosity ratios up to 1:100), is made available for benchmarking. Our findings demonstrate that mathematical consistency between the hyperbolic saturation transport equation and elliptic pressure equation ensures stability even for adverse mobility ratios. This work provides a foundation for developing next-generation reservoir simulators with verified accuracy.
DOI: http://doi.org/10.5281/zenodo.20584343
Applied Mathematics As A Catalyst For Scientific And Technological Advancement
Authors: S. Lavanya, Assistant Professor
Abstract: Mathematics is the foundational language through which modern science and technology describe, analyse, and predict complex phenomena. From the micro-architecture of quantum systems to the macro-dynamics of global climate, mathematical structures provide the rigor and abstraction necessary to convert observations into actionable knowledge. This paper surveys the critical and expanding role of mathematics across contemporary scientific and technological domains, demonstrating that progress in these fields is inseparable from mathematical innovation. In computer science and artificial intelligence, mathematics is not peripheral but constitutive. Linear algebra enables the representation of data in high-dimensional vector spaces, forming the basis for neural networks, word embeddings, and transformer models. Calculus and optimization theory drive gradient descent, backpropagation, and reinforcement learning. Discrete mathematics, graph theory, and combinatorics underlie algorithms, database theory, cryptography, and network security. Number theory and algebraic geometry now secure global communications through RSA, elliptic curve cryptography, and emerging post-quantum protocols. Probability and statistics provide the inference frameworks for machine learning, uncertainty quantification, and generative models that power applications from medical diagnosis to autonomous driving. The physical sciences remain deeply mathematized. Newtonian mechanics, Maxwell’s electromagnetism, and Einstein’s relativity are all expressed through differential equations and tensor calculus. Quantum mechanics formalized physical states as vectors in Hilbert space and observables as Hermitian operators. Modern pursuits like string theory and quantum field theory rely on topology, category theory, and complex analysis to reconcile quantum mechanics with gravitation. Experimental physics depends on Fourier analysis for signal extraction, as demonstrated by LIGO’s detection of gravitational waves, and on statistical methods for data analysis in particle accelerators like CERN. Engineering translates mathematical models into functioning systems. Control theory uses differential equations and Laplace transforms to stabilize aircraft, robots, and power grids. Signal and image processing depend on Fourier, wavelet, and discrete cosine transforms for compression, denoising, and transmission, enabling technologies from MRI to 5G. Finite element methods solve partial differential equations to simulate stress, heat flow, and fluid dynamics in bridges, vehicles, and turbines. Operations research applies linear programming, integer programming, and game theory to logistics, scheduling, and resource allocation. In life sciences, mathematics has moved from descriptive to predictive. Mathematical biology models population dynamics, enzyme kinetics, and neural activity using ordinary and partial differential equations. Epidemiology employs compartmental models such as SIR and SEIR to forecast outbreaks and evaluate interventions, a role made globally visible during COVID-19. Medical imaging reconstructs internal anatomy using the inverse Radon transform. Bioinformatics uses dynamic programming for sequence alignment, hidden Markov models for gene prediction, and graph algorithms for protein interaction networks. The 2021 breakthrough of Alpha Fold applied geometric deep learning to solve the 50-year protein folding problem. Quantitative finance and economics are built on stochastic calculus, partial differential equations, and time series analysis. The Black-Scholes-Merton model for option pricing, Monte Carlo methods for risk, and network models for systemic risk all derive from mathematical theory. Modern fintech uses machine learning for fraud detection, credit scoring, and algorithmic trading. Environmental and climate science depend on large scale PDE simulations of atmosphere and ocean dynamics, coupled with statistical models for uncertainty and extreme event prediction. Optimization guides renewable energy deployment, smart grid design, and carbon capture networks. This paper argues that the relationship between mathematics, science, and technology is symbiotic. Scientific challenges inspire new mathematics, and mathematical advances enable new technologies. The rise of data science, quantum computing, and computational biology exemplifies this feedback loop. We conclude that strengthening mathematical education, fostering interdisciplinary collaboration, and investing in foundational research are essential to address global challenges in health, sustainability, security, and digital transformation.
DOI: http://doi.org/10.5281/zenodo.20584385
Cryptography And Mathematical Security Systems
Authors: U. Naga Rekha Rani
Abstract: The impending arrival of cryptographically relevant quantum computing threatens classical public‑key infrastructures. This paper reviews the latest developments (2025–2026) in post‑quantum cryptography (PQC), fully homomorphic encryption (FHE), and zero‑knowledge proofs (ZKP). NIST has advanced nine signature candidates to its third evaluation round and selected HQC as a backup encryption standard. Novel primitives include bio‑inspired RNA‑based cryptography, algebraic hash signatures, and topology‑mined lattice schemes. FHE has reached its fifth generation with the GL scheme and the MadPanthera virtual processor, while lightweight ZKPs such as Microsoft’s Vega enable mobile‑friendly verification. These advances demonstrate rapid maturation toward deployable quantum‑safe systems.
DOI: http://doi.org/10.5281/zenodo.20584405
Applications Of Biostatistics In Modern Botanical Research
Authors: D. Ramesh, Assistant Professor
Abstract: Contemporary botanical research integrates genomic, phenotypic, and environmental data across unprecedented spatial and taxonomic scales. This paper synthesizes recent advances in biostatistical methods applied to plant science, emphasizing their interconnected use rather than isolated application. We systematically review four methodological domains: (1) phylogenetic comparative methods, including relaxed molecular clocks and network inference for divergence timing; (2) genome-wide association studies (GWAS) and quantitative trait locus (QTL) mapping, with innovations in population structure handling, meta-analysis, and machine learning; (3) adaptive evolution inference via genome-environment association (GEA) and quantitative genetic approaches; and (4) spatial statistics and species distribution modeling, including joint and deep-learning-based frameworks. Drawing on 30+ peer-reviewed studies from 2024–2026, we propose an integrative analysis pipeline that bridges these methods. This framework enables researchers to move from pattern description to causal inference in plant evolutionary ecology, biodiversity conservation, and crop breeding.
DOI: http://doi.org/10.5281/zenodo.20584468
A Synthetic Benchmark For Mathematical Analysis Of Optimization Landscapes And Generalization In Deep Learning
Authors: Potham Pushpalatha, Shainaj khan
Abstract: This paper presents a rigorous mathematical framework for analyzing the optimization dynamics, loss landscape geometry, and generalization properties of deep neural networks. Using a synthetically generated but physically consistent dataset derived from controlled experiments on CNN architectures (ResNet-50) and transformer models (GPT‑2 124M), we construct a 100% reliable benchmark that satisfies all known consistency constraints—including stationarity of stochastic gradient noise, boundedness of higher-order landscape derivatives, and convergence of scaling-law exponents. Key findings demonstrate that the loss landscape exhibits a multifractal structure with Hölder exponent distribution centered at 0.73, confirming that complexity facilitates rather than hinders optimization. Additionally, the proposed framework identifies a critical normalization parameter threshold beyond which grokking emerges, and synthetic experiments with dataset sizes up to 1.28 million samples and parameter counts scaling from 10⁵ to 10⁹ reveal a phase transition in the scaling law exponent from −0.48 to −0.37 as training tokens exceed 2.3 trillion. The resulting benchmark, validated against real-world scaling observations, provides a robust foundation for theoretical advances in optimization algorithms and architectural design. All synthetic data and analysis code are publicly released as a reference for future research on the mathematical principles underlying modern deep learning.
DOI: http://doi.org/10.5281/zenodo.20584500
Mathematical Analysis Of Plant Physiological Processes: Modeling, Simulation, And Quantitative Assessment
Authors: Bitla Saritha, Assistant Professor
Abstract: This paper presents a rigorous mathematical analysis of three-phase (oil-water-gas) flow in deformable porous media. Using a novel synthetic dataset generated from high-resolution pore network reconstructions, we derive and validate a set of governing equations that respect conservation laws, interfacial jump conditions, and thermodynamic equilibrium. The proposed analytical framework eliminates the need for empirical closure approximations by introducing a hysteresis-free capillary pressure model and a relative permeability tensor that accounts for flow direction anisotropy. Numerical simulations based on the finite volume method show that our approach reduces phase misplacement error by 18% compared to existing models. The dataset, which includes porosity fields (0.12–0.38), permeability tensors (10–800 mD), and fluid properties (viscosity ratios up to 1:100), is made available for benchmarking. Our findings demonstrate that mathematical consistency between the hyperbolic saturation transport equation and elliptic pressure equation ensures stability even for adverse mobility ratios. This work provides a foundation for developing next-generation reservoir simulators with verified accuracy.
DOI: http://doi.org/10.5281/zenodo.20584343
Role Of Numerical Methods In Scientific Computing
Authors: Potlapuvvu Srinivasa Rao, Assistant Professor, Dr. K. Rajitha
Abstract: Scientific computing has emerged as one of the most important interdisciplinary fields in modern science and technology. It combines mathematical models, computational algorithms, and high-performance computing techniques to solve complex scientific and engineering problems. Numerical methods play a central role in scientific computing because many real-world problems cannot be solved analytically using exact mathematical formulas. Numerical methods provide approximate yet highly accurate solutions for differential equations, optimization problems, integration, interpolation, and matrix operations. These methods are extensively applied in physics, chemistry, biology, climate modeling, artificial intelligence, engineering simulations, finance, and medical sciences. The development of modern computers has significantly enhanced the efficiency and applicability of numerical techniques. Methods such as the Newton-Raphson method, finite difference method, finite element method, Runge-Kutta methods, and iterative matrix solvers enable scientists and engineers to model complex systems with high precision. Scientific computing relies heavily on these algorithms to process large datasets and simulate physical phenomena. Numerical methods also reduce computational complexity and improve the stability and convergence of mathematical models. This research paper discusses the role of numerical methods in scientific computing by examining their theoretical foundations, mathematical modeling techniques, applications, and computational significance. The study explores different numerical algorithms and their effectiveness in solving scientific problems. A comparative analysis of traditional analytical methods and numerical approaches is presented to highlight the advantages of computational techniques. Mathematical equations, tables, and graphical interpretations are included to demonstrate the practical importance of numerical methods. The paper further proposes an efficient computational framework integrating iterative numerical algorithms for solving nonlinear scientific problems. Experimental observations reveal that numerical methods provide reliable, scalable, and accurate solutions for high-dimensional problems where analytical methods fail. The study comes to the conclusion that numerical techniques are the foundation of scientific computing and continue to propel advancements in engineering, research, and contemporary technology.
DOI: http://doi.org/10.5281/zenodo.20584574
Applications Of Mathematics In E‑Commerce And Finance
Authors: Parelli Sreenivas, Assistant Professor, Kondapaka Aruna
Abstract: The rapid expansion of digital commerce and financial technology has dramatically increased the use of advanced mathematics. This paper explores how mathematical models, optimization techniques, and intelligent systems are applied in e‑commerce and finance. It discusses topics such as optimization in e‑commerce, portfolio selection in finance, fraud detection using machine learning, algorithmic trading, and blockchain technology. By synthesizing findings from recent research, this study highlights the crucial role of mathematics in enhancing decision‑making, risk management, and security in modern commercial and financial systems. The paper concludes with an overview of emerging trends that promise to deepen the integration of mathematics with commerce and finance.
DOI: http://doi.org/10.5281/zenodo.20584614
Optimization Techniques and Operation Research
Authors: Vadika Wooha Rani
Abstract: Operations Research (OR) is a multidisciplinary field that applies advanced analytical methods to support decision-making, resource allocation, and problem-solving in complex systems. Rooted in mathematics, statistics, and optimization techniques, OR provides systematic frameworks for analyzing challenges where competing objectives and constraints exist. By employing models such as linear programming, queuing theory, simulation, and network optimization, OR enables organizations to minimize costs, maximize efficiency, and improve service quality. Its applications span manufacturing, logistics, healthcare, finance, and public policy. For instance, OR helps industries streamline supply chains, hospitals optimize patient scheduling, and governments design efficient transportation systems. In essence, Operations Research bridges theory and practice, offering decision-makers structured tools to navigate uncertainty, evaluate alternatives, and achieve optimal outcomes in dynamic environments.
DOI: http://doi.org/10.5281/zenodo.20584659
Neural Discovery In Mathematics: Do Machines Dream Of Colored Planes
Authors: E. Balalaxminarayana, Mullagiri Venkatakrishna
Abstract: This paper reviews the 2025 research work titled "Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?" by Konrad Mundinger, Max Zimmer, Aldo Kiem, Christoph Spiegel, and Sebastian Pokutta. The study presents a novel approach that uses neural networks to drive mathematical discovery. Focusing on the Hadwiger-Nelson problem—a long-standing open question in discrete geometry and combinatorics—the researchers reformulated a complex geometric coloring challenge into an optimization task that neural networks could solve. Through this method, they discovered two novel six-colorings of the Euclidean plane, achieving the first improvement in thirty years to a variant of the original problem. This paper provides a conceptual, equation‑free explanation of the research, its methodology, key findings, and broader implications for the use of artificial intelligence in mathematical discovery.
DOI: http://doi.org/10.5281/zenodo.20584780
Mathematical Analysis Of Multiphase Fluid Flow Systems In Heterogeneous Porous Media: A Synthetic Benchmark Study
Authors: E Bitla Saritha, Assistant Professor
Abstract: This paper presents a rigorous mathematical analysis of three-phase (oil-water-gas) flow in deformable porous media. Using a novel synthetic dataset generated from high-resolution pore network reconstructions, we derive and validate a set of governing equations that respect conservation laws, interfacial jump conditions, and thermodynamic equilibrium. The proposed analytical framework eliminates the need for empirical closure approximations by introducing a hysteresis-free capillary pressure model and a relative permeability tensor that accounts for flow direction anisotropy. Numerical simulations based on the finite volume method show that our approach reduces phase misplacement error by 18% compared to existing models. The dataset, which includes porosity fields (0.12–0.38), permeability tensors (10–800 mD), and fluid properties (viscosity ratios up to 1:100), is made available for benchmarking. Our findings demonstrate that mathematical consistency between the hyperbolic saturation transport equation and elliptic pressure equation ensures stability even for adverse mobility ratios. This work provides a foundation for developing next-generation reservoir simulators with verified accuracy.
DOI: http://doi.org/10.5281/zenodo.20584826
Game Theory In Business And Economics
Authors: Kareema Tabassum
Abstract: Game theory is an important mathematical and economic tool used for analyzing strategic decision-making among individuals, organizations, and businesses. It helps understand how participants make decisions when the outcome depends not only on their own actions but also on the actions of others. In modern business and economics, game theory has become highly significant in areas such as pricing strategies, market competition, negotiation, advertising, investment decisions, and consumer behavior. The present study examines the applications of game theory in business and economics based on primary data collected from business professionals, commerce students, and entrepreneurs. The study aims to understand the awareness, practical applications, and effectiveness of game theory in business decision-making. Primary data were collected through a structured questionnaire distributed among respondents from different business and educational backgrounds. The collected data were analyzed using percentage analysis and simple statistical interpretation. The findings indicate that game theory plays an important role in competitive business environments and economic planning. Most respondents agreed that strategic thinking, cooperation, negotiation, and competitive analysis are essential for business success. The study further reveals that game theory concepts are increasingly used in marketing strategies, pricing decisions, business negotiations, and risk management. The paper concludes that game theory is not only a theoretical concept but also a practical decision-making tool that improves business efficiency and economic analysis. The study recommends increasing awareness and practical training related to game theory in commerce and management education.
DOI: http://doi.org/10.5281/zenodo.20584942