Essays on Mathematical Models

Nonlinear evolution equations (NLEEs) have a widespread application in the field of mathematical physics and engineering such as fluid, plasma, nonlinear optics, marine science and so on. In soliton theory [1-3], finding exact solutions of NLEEs is one of the hot topics in this field….

I love Mathematics. It is an imagined world with a consistent system of rules that are meaningful, which can used in a wide range of real-life applications. Whether it’s tricky calculus problems or normal probabilities; it captivates my mind every time I study it and…

The algebraic method of deriving general solutions to problems is one of the most rewarding parts of mathematics as it allows knowledge to be built on by thinking outside the box. Calculus and algebra often allow me to be innovative with mathematical ideas and draw…

I have decided to center my mathematical exploration around the topic of Card tricks. Card tricks is one of the topic that has mathematical connections. First of all, I am going to explore the mathematics behind “21 card tricks”. After that, I will use probability…

Andrew Wiles is a British mathematician who was born on April 11, 1953 In Cambridge England. He was born to mother Patricia Wiles and Father Maurice Frank Wiles, who was the Regius Professor of Divinity at England’s finest, University of Oxford. Wiles was born in…

Basically there are two types of models in GIS: Vector Data Model (representation of the world using points, lines and polygons) Raster Data Model (representation of the world as a surface divided into regular grid of cells). What is raster data? In its handiest shape,…

Introduction The numbers have always been interesting since I was a little kid. Especially the numbers that I saw in everyday life, whether in newspapers, magazines, or advertisement boards which I see on the streets, showed me how much mathematics processed into our lives. Seeing…

Question 1 Canine Crunchies Inc. (CCI) sells large bags of dog food to warehouse clubs. CCI uses an automatic filling process to fill bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25…

The comprehension of polynomials is important throughout multiple tasks because it holds a large position in other academic subjects, improves work performance, and allows mathematical calculations to be simpler and quicker, making daily and complex situations easier. Polynomials are the core to algebra. Algebra is…

Sentiment Analysis is the process of determining whether a piece of writing is positive, negative or neutral. In our approach, we proposed a machine learning approach to analyze emotions in text and social media content in EMMA. The core component of this model is a…

Abstract— In 1900, less than 20 percent of the world populace lived in cities, in 2007, fair more than 50 percent of the world populace lived in cities. In 2050, it has been anticipated that more than 70 percent of the worldwide population (about 6.4…

Java is known for its interoperability, portability and the ease with which a programmer can carry out all the tasks. Java also provides reusability for its code. The main reason why programmers prefer java is due to its object-oriented approach which makes it very easy…

In this paper, we offer and investigate stability (local and global) and bifurcation (Hopf-Andronov) analyses of a Crowley-Martin predator-prey model system with Qiwu’s growth for prey species and intra-specific competition among predator species. Initially, by virtue of the comparison principle, we achieve boundedness results for…

Mathematics, an advantageous subject and an useful tool in our everyday lives. Without further notice, we surely use mathematics in most cases. If you relate with us, we look at a clock before we go to bed to calculate how many hours we can rest…

Throughout our IA, we managed to analyze our statistical modeling with new fields of mathematics. We defined and applied linear algebra with Matrix multiplication, and derived some significant probabilities of the model. We started with 2 by 2 matrix to gain some insight, where it…