Abstract
COVID-19 originated from Wuhan, China in December 2019. Declared by the World Health Organization on March 11, 2020; COVID-19 pandemic has resulted in unprecedented negative global impacts on health and economy. International cooperation is required to combat this ”Incompletely Predictable” pandemic. With manifestations of Chaos-Fractal phenomena, we mathematically model COVID-19 and solve [unconnected] open problems in Number theory using our versatile Fic-Fac Ratio. Computed as Information-based complexity, our innovative Information-complexity conservation constitutes a unique all-purpose analytic tool associated with Mathematics for Incompletely Predictable problems. These problems are literally ”complex systems” containing well-defined Incompletely Predictable entities such as nontrivial zeros and two types of Gram points in Riemann zeta function (or its proxy Dirichlet eta function) together with prime and composite numbers from Sieve of Eratosthenes. Correct and complete mathematical arguments for first key step of converting this function into its continuous format version, and second key step of using our unique Dimension (2x -N) system instead of this Sieve result in primary spin-offs from first key step consisting of providing proof for Riemann hypothesis (and explaining closely related two types of Gram points), and second key step consisting of providing proofs for Polignac’s and Twin prime conjectures.
Highlights
Gram[x=0,y=0] points, Gram[y=0] points and Gram[x=0] points are three types of Gram points (GP) dependently computed directly from Riemann zeta function (RζF or ζ(s)) [or its proxy Dirichlet eta function (DηF or η(s))]
Modelling concepts from open problems, COVID-19 and its resulting pandemic using derived Fic-Fac Ratio are outlined whereby we provide concrete examples of ideal gold standard mathematical arguments (MA) and ideal gold standard diagnostic tests (DT) with their associated MA and DT results corresponding to Fic-Fac Ratio = 0
Homogeneity in this research paper for our Incompletely Predictable (IP) problems are perpetually present [intrinsic] complex properties that clearly do not refer to these Completely Predictable (CP) recurring zeroes but instead validly refer to totally different IP recurring zeroes calculated as axes-intercept points in DηF and approximate Net Area Value (NAV) = 0 from Riemann sum interpretation of sim-DηF
Summary
Gram[x=0,y=0] points, Gram[y=0] points and Gram[x=0] points are three types of Gram points (GP) dependently computed directly from Riemann zeta function (RζF or ζ(s)) [or its proxy Dirichlet eta function (DηF or η(s))]. Obtaining rigorous proof for this property consist of recognizing it as IP [and not CP] problem which requires deriving two IP [”∆x −→ 1”] ’varying’ [and not ’non-varying’] discrete-type algorithms Pi+1 = Pi + pGapi and Ci+1 = Ci + cGapi for calculating all prime and composite numbers [as zero-dimensional points]. Observed characteristics of exponents from this first example [and second example below] as CP problems with perpetually present [intrinsic] simple properties could hint at possible invalidity of exact and inexact DA homogeneity as useful analytic tool used for IP problems These are irrelevant (counter)examples since exact and inexact DA homogeneity in this research paper for our IP problems are perpetually present [intrinsic] complex properties that clearly do not refer to these CP recurring zeroes but instead validly refer to totally different IP recurring zeroes calculated as axes-intercept points in DηF and approximate NAV = 0 from Riemann sum interpretation of sim-DηF. Sine and/or cosine f(n)’s IP (virtual) zeroes and F(n)’s IP (virtual) pseudo-zeroes: Property
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