Riemann Hypothesis In Nature

Riemann ξ Function in Nature All Systems conceivable to man are second order systems and is governed by second order Differential Equations. Please refer my proof for the generality of evoking such a system. Now it is left to us to prove that if any Randomly selected system fed back for stability( unstable systems are per se violent) will have it’s Root, reduces to 1/2. If so, we will also know that all second order system functions will have it’s trivial Roots reduce to ½ and non-trivial imaginary roots lie on the ½ plane. For a system to be stable it will have to be an Eliptecal function and if so all of it will have trivial real root on ½ and non-trivial imaginary part lie on ½ plane. So if we randomly design a system feedback for stability, if it’s root reduces to ½ Riemann Hypothesis remain proved, since it’s non-trivial part will be on ½ plane. So Li(x) the Li function describes how stable systems under nature function. Any feedback control system for stability is governed by the Systemic Equation, G(s)/ (1- G(s). H(s)) = -1, where G(s)H(s) is the feed back loop. We randomly select the system (1+2i) and the feed back loop turns out to be, (1 – (1+i)(1+ xi) where the real part of the second term should be equal to the system actuator real value for stability. The system Transfer function then becomes, (1+2i)(1-(1+2i)(1+xi) = -1 (1+2i)/(2x-(2+x)i)/= -1-----------------(1) (-2x+2) –xi=0 Where x = √((-2x+2)2 +x2

√(4x2 – 7x + 4) Solving the Quadratic equation we get, x = 0.875+1.875-------------------------(2) Substituting Equation (2) in the Equation (1) to get the magnitude of the real part or the System Transfer function. (1+2i)/((1.75+3.75i) – (2.875 + 1.875i)) √(5/4.64)= 0.5 The above example shows any feed back system for stability will reduce to an Eleptical function with real part of root at ½ and varying complex parts. Conformal Maping Let, a = (x + i y) or (x + i b) x = (a + i x) then substituting one in the other, a = (a + i x + i y) x = ( x + iy + ix) a+ i x + i y + i x x+ i y + i x + i y x + iy + i x + i y + i x a + ix + i y + i x + i y Subtracting one from the other we get, (x – a) G(s)/ G(s)H(s)=(a + i x+iy)/(x + i y+ix) X – a –a

a=1, x=2, and y=b=1 a, x and y can be any multiples of the above or a should be 0.5 of x For practical purposes G(s)/(1-G(s)H(s)) instead of G(s)/(G(s)H(s))is used without loss of generality. Also, x=( a + i b) can be used instead of (a + i x), then simplification becomes difficult. Theory of Damping in Electrical Cirucuits Take and RLC circuit. The system equation of which is written as. Ri + L di/dt + CL d2i/dt = Vi C can be considered as a feed back for stability. i=C dV/dt and v=L di/dt , substituting and simplifying (CL/V)d2i/dt2 + (L/V) di/dt + 1=1 This equation is of the form ax2 + bx + c = 0 Let A = (CL/V) and B= (L/V) Now theory of damping stipulates that the circuit will sustain oscillation or is stable or normally damped only if A = B/ If A>B the circuit will be under damped and if A
This means that any Randomly selected system fed back for stability can have the real Part of it’s Root ’1/2 and non-trivial roots on ½ plane. If the system is not fed back for stability or error correction then the System will go unstable proving Riemann’s Hypothesis, also that in Nature only Stable systems are generate and unstable systems don’t fall in the purvey of Humans. Proof through Induction is also clearly visible. Reference: “Electronics Circuits”, Bayless et al, Wiley Eastern.