An Upper Bound for the Curvature Integral
نویسنده
چکیده
It is shown that the integral of the scalar curvature of a closed Riemannian manifold can be bounded from above in terms of the manifold’s dimension, diameter, and a lower bound for the sectional curvature. §
منابع مشابه
ALGEBRAIC NONLINEARITY IN VOLTERRA-HAMMERSTEIN EQUATIONS
Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...
متن کاملAn upper bound for curvature integral
Here I show that the integral of scalar curvature of a closed Riemannian manifold can be bounded from above in terms of its dimension, diameter, and a lower bound for sectional curvature.
متن کاملAnalysis of convergence of solution of general fuzzy integral equation with nonlinear fuzzy kernels
Fuzzy integral equations have a major role in the mathematics and applications.In this paper, general fuzzy integral equations with nonlinear fuzzykernels are introduced. The existence and uniqueness of their solutions areapproved and an upper bound for them are determined. Finally an algorithmis drawn to show theorems better.
متن کاملConvergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations
In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...
متن کاملRobust Adaptive Attitude Stabilization of a Fighter Aircraft in the Presence of Input Constraints
The problem of attitude stabilization of a fighter aircraft is investigated in this paper. The practical aspects of a real physical system like existence of external disturbance with unknown upper bound and actuator saturation are considered in the process of controller design of this aircraft. In order to design a robust autopilot in the presence of the actuator saturation, the Composite Nonli...
متن کامل