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On an inequality for the Riemann zeta-function in the critical strip
Riemann zeta-function size of the Riemann zeta-function new inequalities critical strip
2012/6/30
By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\zeta(1-s)| <= |\zeta(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. Moreover, we est...
An Optimal Inequality For The Tangent Function
inequality tangent function power series expansion
2012/5/24
In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents invol...
Constructive Proof of Global Lyapunov Function as Potential Function
Constructive Proof Global Lyapunov Function Potential Function
2010/12/28
We provide a constructive proof on the equivalence of two fundamental concepts: the global
Lyapunov function in engineering and the potential function in physics, establishing a bridge be-tween these...
Separation of variables and explicit theta-function solution of the classical Steklov--Lyapunov systems: A geometric and algebraic geometric background
Separation of variables explicit theta-function solution
2010/4/6
The paper revises the explicit integration of the classical Steklov--Lyapunov systems via separation of variables, which was first made by F. K\"otter in 1900, but was not well understood until recent...