Mathematics and Computer Science: Research Updates Vol. 9

Deep Learning-Driven Chatbots for Crop Health Monitoring and Agricultural Decision Support

Anantha Kranthi Suravarapu — Mon, 02 Mar 2026 00:00:00 +0000

Numerous problems in agriculture, including unpredictable crop yields, disease susceptibility, and the consequences of weather variability, put nutrition and farmer livelihoods at risk. In order to increase agricultural yields, detect diseases early, and provide valuable insights on the Crop Yield Prediction Dataset and Plant Village Dataset, this research provides an AI-powered solution to these issues by integrating deep learning, sophisticated machine learning algorithms, and instantaneous data analysis. The system employs a sophisticated methodology that forecasts temperature, humidity, and conditions for the next five days using the PyOWM API; detects crop diseases using data augmentation and deep learning models such as CNN (accuracy 99.14%), DenseNet-201 (accuracy 99.04%), and Visual Geometry Group-VGG19 (accuracy 97%); and predicts crop yield using models such as Multi-Layer Perceptron-MLP (R2 Score: 0.8242), MLP + Regressor, and Random Forest Regressor achieves the highest R2 Score (0.1789). An AI chatbot that provides farmers with recommendations, disease control methods, and personalised suggestions is part of the technology's real-time help. In order to provide an AI-driven system for weather forecasting, disease detection, yield prediction, and real-time assistance via a chatbot, this project integrates models with high accuracy rates. The user-friendly Streamlit UI is available in Telugu, Hindi, and English, and SQLite handles the secure login and registration procedure.

Certainty-Independent Aspects in Fluid Mechanics: Fundamental Laws and Universal Behaviours

K. Chinnadurai, Salahuddin — Mon, 02 Mar 2026 00:00:00 +0000

This chapter explores certainty-independent parts of fluid mechanics, focusing on fundamental concepts that are true regardless of specific initial conditions or parameter uncertainty. It examines how robust frameworks for comprehending fluid behaviour are supplied by conservation laws, dimensional analysis, similarity solutions, and stability theory without requiring exact knowledge of every system variable. The research demonstrates that many fluid processes have universal characteristics that transcend specific experimental configurations, offering reliable forecasting capabilities in a range of applications. Through theoretical analysis and case examples, the importance of these certainty-independent components in both fundamental research and practical engineering applications is highlighted.

Asymptotic and Bootstrap Implementation of the D'Agostino-Berlanger-D'Agostino K\(^2\) Normality Test in R

José Moral de la Rubia — Mon, 02 Mar 2026 00:00:00 +0000

The K² test could be one of the best tests for assessing normality, yet its use is limited, likely because it is not commonly included in standard statistical software, despite being implementable in R through the moments package. Moreover, its asymptotic approximation has been questioned for small samples, and no bootstrap version currently exists, even though it is feasible in R. This simulation study aimed to: (1) verify the linear independence and nonlinear relationship between √b₁ and b₂; (2) develop an R script for the K² test in both asymptotic and bootstrap versions; (3) assess the fit of the bootstrap distribution of the K² statistic to a chi-square distribution with two degrees of freedom; (4) compare the power of both implementations against non-normal distributions; and (5) contrast the bootstrap version of K² with the Shapiro–Wilk test in small samples. A Monte Carlo simulation with 10,000 replications was conducted, using 16 non-normal distributions as alternative hypotheses and sample sizes (n) ranging from 20 to 2,000 in increments of 20. Linear independence and a parabolic relationship between √b₁ and b₂ were confirmed, and the R script was verified to be functional. The script is available for download as a Word document from a GitHub repository. The bootstrap distribution of K² converged to a chi-square distribution for n ≥ 120. The asymptotic version of K² and the Shapiro–Wilk test showed greater power than the bootstrap version, except for mesokurtic asymmetric distributions. Bootstrap implementation is recommended in these cases for n < 120, while the asymptotic version is generally more powerful and appropriate for n ≥ 20. The developed R script is highly useful for assessing the normality assumption required by many parametric tests, such as t-tests and F-tests for comparing means and variances, as well as for characterising the distribution of a sample of quantitative data; therefore, its use is recommended for these purposes.

Statistical Techniques in Ecology: Descriptive Statistics and Normal Distribution

B. K. Singh, Rajan Singh, Anshul Dubey, Nidhi Tiwari, Nidhi Prabhakar — Mon, 02 Mar 2026 00:00:00 +0000

Ecological science relies on robust estimates of the abundance, diversity, and spatial distribution of individuals and species, but these quantities are notoriously difficult to observe directly. Statistics may be considered as the science and technique of collecting, analysing, and making inferences from data, and these references are stated as probabilities. The study aims to explore and apply quantitative and statistical methods in ecology to understand the relationships between populations and their environment, assess the effects of environmental hazards on animal and plant populations, and evaluate overall ecological balance. Fundamental statistical concepts, including descriptive statistics, probability distribution, regression and correlations, and the chi-square distribution, are demonstrated to show their function in analysing ecological data. On the other hand, specialised methods, such as species-abundance relations and species-diversity measures, provide insights into community structure and ecosystem stability. The study recommends the use of logarithmic distributions to accurately fit species-abundance data and enhance the reliability of ecological analyses.

Exploring Cramer-Rao Lower Bounds and Uniformly Minimum Variance Unbiased Estimators (UMVUE): Counterexamples

S. C. Bagui, K. L. Mehra — Mon, 02 Mar 2026 00:00:00 +0000

Cramer-Rao Lower Bound (CR-LB) is a fundamental tool for determining the minimum variance of unbiased estimators. The main goal of this chapter is to present counterexamples where the variance of the UMVUE does not reach the Cramer-Rao lower bound. We provided many motivating counterexamples and demonstrated that these UMVU estimators are, in fact, asymptotically efficient. All counterexamples are either new or not typically found in standard textbooks. To illustrate the process, we included numerous definitions related to UMVUE and explained various methods and step-by-step approaches for finding UMVUEs.

This chapter will be valuable for senior undergraduates and first-year graduate students taking courses in statistical inference. The material should also interest teachers of statistical estimation theory. They could include the examples from this paper in various exams. Certainly! The article also has significant pedagogical value.

Analysis of Hydromagnetic Flow and Heat Transfer of a Boussinesq-Stokes Suspension over an Exponentially Stretching Sheet

Mon, 02 Mar 2026 00:00:00 +0000

There are numerous uses for boundary layer flow on a continually stretched sheet, wire drawing, including hot rolling, the manufacture of glass fibre, and the making of paper. Most previous studies mainly focus on boundary layer flows over stretching surfaces, where it is considered that the surface's velocity stretches in a quadratic proportion to the distance from the static origin. The current chapter presents the investigation of heat transfer properties and velocity profiles in a hydromagnetic Boussinesq-Stokes suspension (BSS) flow over an exponentially stretching impermeable sheet. The fundamental equations that describe the transfer of heat and flow are partial differential equations. A suitable local similarity transformation was applied to convert the equations into nonlinear ordinary differential equations. The differential transform method (DTM) was used to obtain the series solutions of the transformed equations with guaranteed convergence. The influence of the Chandrasekhar number, couple stress parameter, Prandtl number, and Eckert number on velocity profiles and heat transfer was investigated. The study showed that magnetic field strength, couple stress, Prandtl number, and Eckert number significantly influence the velocity and thermal boundary layers in hydromagnetic Boussinesq–Stokes suspension flow over an exponentially stretching sheet, with important implications for industrial heat and material processing applications.

Arithmetic Modelling and Routing Algorithms for an Edge–Fog–Cloud Continuum Structured as a Full k-ary Tree

Pedro J. Roig, Salvador Alcaraz, Katja Gilly, Cristina Bernad, Carlos Juiz — Mon, 02 Mar 2026 00:00:00 +0000

Remote computing is currently widely deployed in production networks, although its performance could be optimised through an appropriate architectural design. Accordingly, a mathematical model of an edge-fog-cloud hierarchy is presented, where all devices are organised as a full complete k-ary tree. When devices across layers are sequentially indexed, integer division and modular arithmetic can be used to determine the devices and ports involved along the path between a source and a destination end device. Two pseudocode algorithms are proposed, where one considers only a single cloud server, while the other extends the approach to multiple cloud servers. The key properties of both algorithms are simplicity and scalability, highlighting their technical relevance in remote computing architectures. The proposed model may have a practical impact on IoT, edge AI, and network design as it simplifies how packets are forwarded between end devices in remote computing environments.

Meekly SC\(^∗\)-Normal Spaces in Topological Spaces

Neeraj K. Tomar, Saroj Rani — Mon, 02 Mar 2026 00:00:00 +0000

This chapter develops the concept of meekly SC^∗-normality, a novel generalization of the classical notion of normality in topology. The proposed framework simultaneously broadens SC^∗-normality and other established forms of normality, offering a unified perspective on generalized separation axioms. Fundamental properties are systematically derived, several equivalent characterizations are obtained, and the relationships between meekly SC∗-normal spaces and a range of existing normal-type spaces are rigorously analyzed. By establishing these structural connections, the chapter not only enriches the theory of generalized closed sets and separation axioms but also opens new directions for further research in advanced topological studies.