##Startup On startup, the program will print the message to the screen, saying welcome to the chat room. The console will be used for all input. Typing text will attempt to send a message to other ...

For y= a0.x^0 + a1.x^1 + a2.x^2 + ..... + aN.x^N We input a polynomial function as: a0,a1,a2,a3,.....,aN For example, If we want a graph of y= x^3 + 4x^2 + 5 we feed in the values: 5,0,4,1 then input ...

Last summer in Barcelona, Joachim Kock floated the idea that there might be a connection between two invariants of graphs: the Tutte polynomial and the magnitude function. Here I’ll explain what these ...

Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

Abstract: Understanding the underlying graph structure of a nonlinear map over a particular domain is essential in evaluating its potential for real applications. In this paper, we investigate the ...

In this article, we will see how the Taylor series can help us simplify functions like cos(θ) into polynomials for ease of computation. How do you define Taylor Series? Taylor series is a modified ...

Polynomial and special function theory remains a vibrant area of mathematical research, interweaving classical algebra with advanced analysis. At its core, the study concerns algebraic expressions ...

Abstract: This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability analysis of the polynomial ...

The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics. In this paper we present the explicit generalized ...