WebCohn-Vossen's inequality. In differential geometry, Cohn-Vossen's inequality, named after Stefan Cohn-Vossen, relates the integral of Gaussian curvature of a non-compact surface to the Euler characteristic. It is akin to the Gauss–Bonnet theorem for a compact surface. A divergent path within a Riemannian manifold is a smooth curve in the ... http://www.math.kent.edu/~zvavitch/GARDNER_ZVAVITCH.pdf

Concentration inequality - Wikipedia

Webinequality (2.7). Moreover, by the symmetry of the definition, the variable −Xis sub-Gaussian if and only if X is sub-Gaussian, so that we also have the lower deviation inequality P[X≤ µ−t] ≤ e− t2 2σ2, valid for all t≥ 0. Combining the pieces, we conclude that any sub-Gaussian variable satisfies the concentration inequality WebWe will show that up to change the Riemannian metric on the manifold the control curvature of Zermelo's problem has a simple to handle expression which naturally leads to a generalization of the classical Gauss-Bonnet formula in an inequality. This Gauss-Bonnet inequality enables to generalize for Zermelo's problems the E. Hopf theorem on ... sh-rc702 bicycle shoes

Gaussian isoperimetric inequality - Wikipedia

WebEquations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry ... equations include graphical, substitution, elimination, Newton's method, and iterative methods such as Jacobi and Gauss-Seidel. How do you determine if a system … WebJun 1, 2011 · n this paper a functional defined as the difference between the left-hand and the right-hand side of an extension of the Gauss inequality given in [H. Alzer, On an inequality of Gauss, Rev. Mat ... WebIn probability theory, Gauss's inequality (or the Gauss inequality) gives an upper bound on the probability that a unimodal random variable lies more than any given distance … sba icertify