In this paper, we solve the Cooper-Schmidt equation in a way that is consistent with Jacuzzi and Airfoil foundations. This PDE equation is one of the most important equations in physics and chemistry. This nonlinear equation in mechanical engineering appears as a wave phenomenon, and in plasma physics discusses systems that are composed of positive and negative charged particles that can move freely. Comparison of the level of hot electron production and its surface causes the harmonic emission of some source signals and the heat electrons in the plasma are radiated spherically [1]. The Cooper-Schmidt equation plays an important role in nonlinear wave scattering. Individual waves are propagated in the nonlinear scattering of media. These waves maintain a stable shape. Due to the dynamic equilibrium and nonlinearity of this equation, an approximate solution has been proposed in many papers [12, 13]. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be obtained that can be obtained by the method. Solved nonlinear systems, such as Newton's iterative method. The existence, uniqueness of the answer, and convergence of methods are examined.

In this paper, we present an efficient and accurate method for calculating the Black-Scholes differential equations and solve the Black-Scholes equations using Jacoby and Airfoil orthogonal bases, with the collocation method. The BlackScholes equation is a partial differential equation, which describes the price of choice in terms of time and the collocation method is a method of deter-mining coefficients. Then we show the computational results and examine the performance of the method for the two options, the price of basic assets and its issues. These results show that the Jacoby method is more efficient in solving the Black Scholes equation, and the method error is less and the convergence rate is higher. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be solved by nonlinear solution methods, such as Newton's iterative method. The existence, uniqueness of the solution, and convergence of the methods are examined, and we will show in an example that by repeating then |𝑢, 𝑛, +1−, 𝑢, 𝑛, | |𝑢, 𝑛, | < ε, can be reached and this indicates the accuracy of the response to In this paper, we present an efficient and accurate method for calculating the Black-Scholes differential equations and solve the Black-Scholes equations using Jacoby and Airfoil orthogonal bases, with the collocation method. The BlackScholes equation is a partial differential equation, which describes the price of choice in terms of time and the collocation method is a method of deter-mining coefficients. Then we show the computational results and examine the performance of the method for the two options, the price of basic assets and its issues. These results show that the Jacoby method is more efficient in solving the Black Scholes equation, and the method error is less and the convergence rate is higher. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be solved by nonlinear solution methods, such as Newton's iterative method.

Suppose G is an n-vertex and m-edge simple graph with edge set E(G). An integer-valued function f: E(G)→Z is called a flow. Tutte was introduced the flow polynomial F(G, l) as a polynomial in an indeterminate l with integer coefficients by F(G, l) = (−1)|E(G)| S SÌE(G)(-1)|S|ln-m+c(G:S), where c(G:S) is the number of connected components of G and (G:S) denotes the spanning subgraph of G with edge set S. In this paper the Flow polynomial of some dendrimers are computed.

Suppose G is a graph, A(G) its adjacency matrix and Ψ (G, λ ) = λ n + a1λ n− 1 + … +an is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = m(G, 0)xn – m(G, 1)xn− 2 – m(G, 2)xn− 4 + … , where m(G, k) is the number of k− matchings in G. In this paper, the relationship between 2k-th coefficient of the characteristic polynomial, a2k, and k-th coefficient of the matching polynomial, (− 1)km(G, k), k=0, 1, 2, … , in a regular graph is determined. In addition, these relations for finding 5, 6-matchings of fullerene graphs are applied.

suppose e=uv is an edge connecting the vertices u and v of a graph G, Nu (e|G) is the vertices of G laying colder to u and Nu (e|G) is the number of vertices of G lying closer to v. then the szeged index of the graph G is defined as Sz (G)= åe= uvÎE(G) Nu (e|G) Nu (e|G) .in this paper, the nontion of szeged of a graph is in-troduced. We investigate some of the properties of  this polynomial and computer it for some Well-known graphs.

The polybenzene units BTX_48, X=A (armchair) and X=Z (zig-zag) dimerize forming “eclipsed” isomers, the oligomers of which form structures of five-fold symmetry, called multi-tori. Multi-tori can be designed by appropriate map operations. The genus of multi-tori was calculated from the number of tetrapodal units they consist. A description, in terms of Omega polynomial, of the two linearly periodic BTX-networks was also presented.

This paper deals with the automatic continuity of multiplicative polynomial operators on a class of topological algebras. Several results are derived in this direction. We also support our results by some examples.