‘Activation Curve’™

Time-Measurable System Reactions

System reaction curves are indicative of what occurs in natural reactions of both types. They are endotropic (solid curve) and exotropic (dashed curve) reactions. In the graphically plotted examples, the system in examination is the external environment - the more convenient system to measure and manage.

The graph makes it possible to measure the full time-evolution of a reaction for the first instance in our history. The functions produce fractional ratios in all results - unity being the greatest, naturally.

In the 2 arbitrary examples, below,

a = 1/10 scale constant or amplification constant

n = count count of measured objects or paticipants in the system being gauged. ( For engineers/scientists it is the quantum count or particle count. They will use Avagadro's number as the extra, count constant to appropriately scale the accretion or decay. )

            f =        frequency the basis of rate. It units are always number/second, harmonics/second or rythms/second

            t =        time ,                       the time variable

     ω =        2 * Pi rad * f the constant or coefficient for all rythms in nature (including human group behaviours/sociological patterns)

            ω =        2 * Pi rad* f  * t , time evolution of natural 'rythm' or oscillation, where time is constant and expanding continuum

Contributive Influence Introduction/

Exothermic (Liberation) Reaction

f(x) ,    y,     A       =        - *n  ( ( ( 1 - ( ( 1/a ) * x ) ^ ( 1/2 ) ) ^ 2 )    +    1 )

A       =        n * ( ( 1 -  ( (1/a ) * ω * t ) ^ ( 1/2 ) ) ^ 2 )

Contributive Influence Suppression/

Endothermic (Absorption) Reaction 

f(x) ,    y,     A       =       - n * ( ( ( 1 - ( ( 1/a ) * n ) ^ ( 1/2 ) ) ^ 2 )    +    1 )

A       =        n * ( ( 1 - ( ( 1/a ) * ω * t ) ^ ( 1/2 ) ) ^ 2 )

Applications in Various Field of Research and Commercialisation

• Sales - Sales cycles for new and progressing campaigns should ideally follow a variance of the endotropic activation curve

• Economic forecasting - system reactions to changes instituted by organisations and population groups

• Commerce - Engineering & IT technology diffusion rate

  
  

• Product Lifecycle - measurable curve

  
  

• Medicine

  • food or medication absorption rates

  • biochemical energy liberation in body tissue (thermal).  Use of a constant and extra-sensitive or well graded thermometer is required

    
    

• Science & Engineering

  • exothermic (heat emission) reaction

  • endothermic (heat absorption/heat induction) reaction

    
    

Economics - Fiscal/Monetary Policy

With respect to reactions outside of the domain of the science laboratory, in testing the theory, is whether the local currency exhibits a reaction similar to either the endotropic or exotropic, time evolution when currency is traded internationally on the derivatives market. Time evolution of a variable is where the rate portion (always per unit of time) is continuously multiplied by time expansion in seconds (s).

Eg. An earnings rate may be expressed as $/month. The time evolution is ( $/month ) * months

= ( $/month ) * ( seconds in 1 hour ) * ( hours per day ) * ( days per Standard Initernational ( SI ) month )

= ( $/month ) * ( 3 600 * 24 * 28 ) * s

= ( $/month ) * 2.419 2 * 10 ^ 6 * s continuously to the limit of the count of seconds in the allocated timeframe.

In some examples, "x" may be a negative variable or a negative 'quantity'. That would place a mirror image of each curve or 'graph' relative to the vertical axis. That returns 4 fundamental event spaces or 'outcomes'.

© Xerqon ABN 97661410108 2025