International Journal Of Mathematics And Computer Research

An Investigation on Jacobian Integral of the Equations of Motion of the System in the Elliptic Orbit of the Centre of Mass

2025-01-03T11:03:17+00:00

In this article, we discuss the effect of earth’s oblateness and magnetic force on the motion and stability of the system for elliptic orbit of the centre of mass. We have got a set of non-linear, non-homogenous and non-autonomous equations. Generally, a system moving in space has to face some perturbative forces. These forces compel the system to change its orbit from circular to elliptic orbit. On account of this we have studied in details the problem in elliptic orbit of the centre of mass. This is simply the generalization of the particular case of the Keplerian orbit i.e. circular orbit. So, we analysed the effect of the earth’s oblateness and magnetic force on the existence and behavior of different equilibrium position of the system. Also, discuss the Jacobian Integral of the averaged equations of motion of the system, Two equilibrium solutions of the problem and after Hooke’s modulus of elasticity.

Analytical Solution of Fractional Order Mathematical Model in the Time of COVID-19 by Fractional Differential Transform Method

2025-01-05T04:49:32+00:00

In this paper, we will discuss an analytical solution and numerical simulation of fractional order mathematical model on COVID-19 under Caputo sense with the help of fractional differential transform method for different values of q, where q ∈ (0,1]. The underlying mathematical model on COVID-19 is consist of two compartments, like, healthy individual and infected individual. We show the reliability and simplicity of the method by comparing our solution of given model with the solution obtained by Laplace Adomian decomposition method via graphically and numerically. Further, we analyse the stability of model using Lyapunov direct method under Caputo sense. We conclude that use of fractional epidemic model provides better understanding and biologically more insights about the disease dynamics.

Mathematics Subject Classification: 2010 MSC: 26A33, 37M05

A NOTE ON PRABHAKAR DERIVATIVE

2025-01-07T10:05:44+00:00

Prabhakar's derivative is an important milestone in the history of fractional calculus. By introducing the generalized Mittag-Leffler function and showing how it can solve singular integral equations, Prabhakar provided a powerful mathematical tool. This contribution remains highly valuable and continues to influence modern science and engineering, ensuring its importance for many years ahead. This survey explores the mathematical foundation, properties, and applications of the Prabhakar fractional derivative in diverse scientific and engineering fields. The paper provides an overview of its recent historical development, mathematical formulation, key properties, and potential research directions.

Neighborhood Approach for Solving One Class of Mixed Integer Non-Linear Programming

2025-01-10T12:18:49+00:00

Integer programming is not new subject in optimization. However, given its practical applicability, we face computational difficulties in solving the large-scale problems. In this paper we solve a class of mixed-integer nonlinear programming problem by adopting a strategy of releasing non-basic variables from their bounds found in the optimal continuous solution in such a way to force the appropriate non-integer basic variables to move to their neighborhood integer points.

Road Accident Emergency Reporting Management System using Neural Network

2025-01-11T10:48:32+00:00

Given the high number of road accidents that result in deaths every day, victims may lose their lives if emergency medical personnel or concerned parties fail to arrive promptly to intervene in an accident or if they do so, because they are unaware of the location of a nearby hospital or medical facility, they may not be able to provide the much-needed help. To avert this scenario, this research work seeks to deploy a Deep Learning Road Accident Emergencies Management model, which by examining of video and sensors’ data, identifies and reports traffic incidents in real time. A Neural Network (NN) is used by the model to recognize accident scenarios based on anomalous motion patterns inside video frames, including sudden halts and crashes. Put into practice in python, the program incorporates deep learning libraries such as OpenCV and TensorFlow for strong data processing and analysis in real time. To train and evaluate the model, an 80/20 data split, which results in reduced latency and high accuracy in accident detection. The Key performance metrics include a testing accuracy of 96%, an F1-score of 87.5%, and a response time of less than two seconds on average. The study advances the domains of artificial intelligence, transportation safety, and emergency management by offering a practical, real-time solution for automated accident reporting. This quick detection capability allows for timely emergency alerts, which are sent to responders via a web-based interface, giving them precise location details. The model's promise as a life-saving tool in smart city infrastructures is highlighted by its capacity to deliver precise and prompt replies. The Road Accident Emergency Reporting Model has important ramifications for increasing road safety, decreasing emergency response times, and boosting public safety in general due to its strong design and low latency.

On The Infinity of Twin Primes and other K-tuples

2025-01-11T10:45:54+00:00

The paper uses the structure and math of Prime Generator Theory to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.

A SURVEY OF DIMENSION OF POSETS

2025-01-15T14:52:36+00:00

In 1930, E. Szpilrajn proved that any order relation on a set $X$ can be extended to linear order on $X$. It also follows that order relation is the intersection of its linear extensions. In 1941 Dushnik and Miller introduced the concept of dimension of a poset $(X,P)$, denoted $Dim(X,P)$, as the smallest positive integer $n$ for which there exist linear extensions $L_1, L_2, ..., L_n$ of $P$ so that $P=L_1\cap L_2\cap ...\cap L_n$.
In this paper, we do literature survey of the research articles on dimension theory of posets. This survey provides an overview of key concepts, results, and challenges in dimension theory of posets. The survey also examines advanced topics like fractional dimension, geometric representations, and topological considerations. Open problems and future research directions, emphasizing the interdisciplinary potential of dimension theory in mathematics and computer science.

New theorems of Laplace Kernels with Radon measures in Galerkin Markov-State Models: about time evolution of eigenvalues and about errors

2025-01-16T11:09:16+00:00

New theorems apt to the methods of the Markov-State Models in the Galerkin representation are derived directly from the Markov-chains theories. The analytical expressions of the time evolution of the eigenvalues and those of the relative error are derived. The new theorems are descended from measuretheory methodologies. The newly-written theorems therefore provide wit the analytical expressions of the time evolution of the eigenvalues and with that of the relative error from the measure-theoretical foundations of the Markov-chains models; the applications to protein folding are originated form the orthogonality of the committor functions in the appropriate description(s). The newly-found theorems are indicated of use for the other necessitated errors calculations. The modellisation used is one apt to recover the items of information about the originating chains.

Markov-chains models offer the suitable tools of a wide range of investigation branches: protein-folding, catalysis, polymeric materials, further moleculardynamics processes, kinetic-network models, electron spin resonance, etc.

A Screenlock Application Using Yoruba Characters for Android Devices

2025-01-17T11:06:33+00:00

A lock screen is a user interface that appears on a mobile device when it is in a locked state. The purpose of a lock screen is to prevent unauthorized access to the device and its content, such as personal contacts, photos, and other sensitives information. A lock screen typically requires the user to enter a password, pattern or use biometric authentication such as fingerprint recognition to unlock the device. English characters and patterns were often used for screen lock on mobile devices because English language is the most official language in some country most especially in Nigeria and other African countries, However, most illiterate and adult that are not familiar with these languages find it difficult to use. To combat this problem, there is need to develop a user-friendly Yoruba lock-screen app that takes Yorùbá characters as input and also allow users to unlock their android devices with this newly developed application.

Moreover, Yorùbá is one of the largest ethnic groups in Nigeria. and also, there is need to promote our local language. The system was built using various programming languages and comparative study of different technique is done as per stages.

The system is made flexible and versatile and application has a user-friendly screen. The application has been tested by various student (who uses Android APP) and has provided a successful result

Extended Modified Sub-Equation Method for Solving Nonlinear Travelling Wave Equation

2025-01-20T11:06:32+00:00

We considered the third order nonlinear Schrodinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. We extended modified sub-equation method to obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic. Trigonometric and rational solutions that are more general than classical ones. We followed analytical mathematical metod by constructed the transformation groups which help us using vector fields and Lie symmetry groups. We discussed the dynamic behavior and structure of the exact solutions for distinct solution of arbitrary constants .We obtained the symmetry reductions and exact of the equation. In addition to group-invariant solutions which are Jacobi elliptic function and exponential type.

A Hybrid Model High-Order Hesitant Fuzzy Time Series and Multilayer Perceptron with Mean Aggregated Membership Value for Enhanced Air Pollutant Concentration Forecasting

2025-01-20T11:08:50+00:00

This study introduces an advanced hybrid model integrating High-Order Hesitant Fuzzy Time Series (HOHFTS) with a Multilayer Perceptron (MLP) to improve the accuracy of air pollutant concentration forecasting. The model utilizes Hesitant Fuzzy Sets to define fuzzy sets, mean aggregated membership values to handle hesitant fuzzy elements, and MLP neural networks to capture complex relationships. A distinguishing feature is the determination of the optimal fuzzy time series (FTS) order, set to 24 in this study, to effectively capture daily temporal dependencies in the hourly air pollutant data. A case study using Semarang City’s air pollution dataset demonstrates the model's effectiveness, with preprocessing addressing missing values and interval-based discretization. Performance evaluation with Mean Absolute Error (MAE) and Symmetric Mean Absolute Percentage Error (SMAPE) indicates outstanding accuracy, with SMAPE values below 10% for most pollutants. Further exploration of hyperparameter optimization and order determination is recommended to enhance generalization and computational efficiency.