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All Journal Mikailalsys Journal of Advanced Engineering International Mikailalsys Journal of Mathematics and Statistics
Yadav, Dipendra Prasad
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Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering

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Lebesgue Measure and Integration on Subsets of R^d Kumar, Nand Kishor; Pokhrel, Chudamani; Yadav, Dipendra Prasad
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 1 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i1.3958

Abstract

Henri Lebesgue, a French mathematician, discovered centuries ago that the Riemann Integral does not work well on unbounded functions. It prompts him to consider another way to integration known as Lebesgue Integral. This paper discusses the Riemann integral's shortcomings and introduce a more thorough concept of integration, the Lebesgue integral, repeated integration. There is also some debate about the Lebesgue measure, which determines the Lebesgue integral. Some examples are given, such as F_σ -set, G_δ -set and Cantor function. In this article, we first look into a unified theory for d-dimensional volume based on the concept of a measure, and then we will use that theory to build a stronger and more flexible theory for integration.
Distance Metrics for Machine Learning and it's Relation with Other Distances Yadav, Dipendra Prasad; Kumar, Nand Kishor; Sahani, Suresh Kumar
Mikailalsys Journal of Mathematics and Statistics Vol 1 No 1 (2023): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v1i1.1990

Abstract

In machine learning, distance metrics play a crucial role in measuring the degree of dissimilarity among data points. When creating and optimizing machine learning models, data scientists and machine learning practitioners can make more informed choices by understanding the features of popular distance metrics and their relationships. The effectiveness and interpretability of the model's output can be greatly influenced by selecting the appropriate distance metric. We explain distance metrics and their relevance in machine learning with various examples of metrics, including Minkowski distance, Manhattan distance, Max Metric for R^n, Taxicab distance, Relative distance, and Hamming distance.
Mathematical Analysis of Fertility in Nepal Using Arriaga's Approach Kumar, Nand Kishor; Yadav, Dipendra Prasad
Mikailalsys Journal of Advanced Engineering International Vol 1 No 1 (2024): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v1i1.2759

Abstract

This article has judged how well the P/F changing ratio technique and Arriaga's approach forecast fertility levels in Nepal. The study's goal was accomplished and the logistic curve function was legalized by estimating national fertility rates. Using information from the 2011 till 2021 censuses together with Arriaga's methodology, the following factual investigates the calculation of fertility rates in Nepal. By using cutting edge indirect fertility estimation techniques on a national level, this study seeks to evaluate the fertility change in Nepal. Utilizing information from the 2011 and 2021 Censuses, fertility estimates were produced with an emphasis on last-year births. The findings show that Nepal's fertility rates have recently dropped.
Concept of Bilinear Transformation, Jacobian, and Conformal Mapping with Applications Kumar, Nand Kishor; Yadav, Dipendra Prasad
Mikailalsys Journal of Advanced Engineering International Vol 1 No 1 (2024): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v1i1.1970

Abstract

This article explores the concepts of bilinear transformation, Jacobian transformation, and conformal mapping, focusing on their essential properties and presenting key results. The discussion revolves around isogonal transformation, conformal transformation, Jacobian transformation, and bilinear transformation, as well as critical points and fixed points.
Mathematical Models of Biological Control of Dengue Kumar, Nand Kishor; Yadav, Dipendra Prasad
Mikailalsys Journal of Advanced Engineering International Vol 1 No 2 (2024): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v1i2.2874

Abstract

Dengue fever, transmitted by Aedes mosquitoes, poses a significant public health threat in tropical and subtropical regions worldwide. Despite efforts to control its spread through various means, including vector control strategies and vaccine development, dengue remains a formidable challenge. Mathematical modeling has emerged as a valuable tool in understanding the complex dynamics of dengue transmission and evaluating control strategies, particularly those involving biological control methods.
Co-Authors Kumar, Nand Kishor Pokhrel, Chudamani Sahani, Suresh Kumar