Let G = V , E be a connected finite graph and Δ p be the p -Laplacian on G with p > 1. We consider a perturbed p -th Yamabe equation Δ p u λ u p 2 u = h u α 2 u ε f , where h , f : V are functions with h , f > 0 ; 1 < p < α ; λ...
Suppose that x1(t) and x2(t) are solutions of our equation system. If the system of equations is linear, it is easy to show that x3(t) = a x1(t) + b x2(t) is also a solution, where a and b are constants. This is known as the principle of linear superposition. If the ...
Explore the properties of a straight line graph y mx + c m c m y c the effects of changing the slope,m the effects of changing they-intercept,c the effects of a positive and a negative value of the slope,m the effects of a positive and negative value of they-intercept,c ...
We study an exact solution to a singular ordinary differential equation and use the solution to give a new estimate on the lower bound of the first non-zero eigenvalue of a closed Riemannian manifold with a negative lower bound on the Ricci curvature in terms of the lower bound on the Ricc...
Note: This quadratic equation will have twocomplexsolutions involving imaginary numbers, but the focus is on real solutions here. Look at what the graph of a quadratic equation with no real solutions looks like: Lesson Summary Register to view this lesson ...
You may also try plotting the polynomial and guessing its root from the graph. If you don't succeed, use the cubic equation formula, which is not the most user-friendly method in mathematics but always yields the correct result! What is the cubic equation formula? The cubic equation formula...
This leads us to imaginary and complex numbers. Before about 1800, most mathematicians would have told you that the quadratic equation with negative discriminant has no solutions. Associated with this point of view, the square root of a negative number has acquired the designation “imaginary.” ...
The Arrhenius equation is an expression that relates the rate constant, absolute temperature, and the A factor. Graph of Arrhenius equation provided here.
The current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite differen
In this research, we study traveling wave solutions to the fractional extended nonlinear SchrÖdinger equation (NLSE), and the effects of the third-order dispersion parameter. This equation is used to simulate the propagation of femtosecond, plasma physic and in nonlinear optical fiber. To accomplis...