Aaron Lloyd-Jones, Academic Publications

Here is a link ( ClickThis 🖱 ) for a listing of facebook meta posts.

List and Timeline of Academic Documents

1. (2008) log-normal theory of mortality (actuarial honours)
   To download 🖙 click here 🖱🖘 (dozens of new equations for actuarial science)
   This is actually a derivative (applications of) of my actuarial honours thesis which I will eventually put here as well.
   
2. (2011) phd financial derivatives (finance phd)
   To download BOOK1 🖙 TBA 🖘
   To download BOOK2 🖙 TBA 🖘
   To download BOOK3 🖙 TBA 🖘
   To download compendium of random walks 🖙 TBA 🖘
   
3. (2013) raison detre (this is a summary of BOOK2 of the PhD)
   To download 🖙 click here 🖱🖘
4. (2017) power series
   To download 🖙 click here 🖱🖘
5. (2018) random walk theory of light
   To download 🖙 click here 🖱🖘
6. (2021) complex numbers
   To download 🖙 click here 🖱🖘
7. (2022) dihedral groups
   To download 🖙 click here 🖱🖘
8. (2022) Lagrangian of basis exponential
   To download 🖙 click here 🖱🖘
9. (2023) polar complex numbers
   To download 🖙 click here 🖱🖘
10. (2022) change of principal rotation axis
    To download 🖙 click here 🖱🖘
11. (2023) almighty cross product
    To download 🖙 click here 🖱🖘
12. (2024) circular relations of i=kx
    To download 🖙 click here 🖱🖘
13. (2024) hyperbolic relations of kxkx and ixjx+jxix
    To download 🖙 click here 🖱🖘
14. (2025) relative motion kinematics
    To download 🖙 click here 🖱🖘

🎝 Click here to listen to some robot boxing 🎜🔊 (Patrick Patrikios)

Some Highlights of Original Equations and Research

• Log-Normal Theory of Mortality (human lifespan)
  Life insurance actuaries model population lifespan; histogram of deaths at each age
  

• New Theory of Financial Derivatives (with full recognition of μ)
  Π = S∂V/∂S - V
  dΠ/dt = (μ+0.5σ²)S∂V/∂S - rV
  rV - ∂V/∂t = 0.5σ²S²∂²V/∂S² + (μ+0.5σ²)S∂V/∂S
  

  Correcting Previous Theory (surreptitiously debased of μ)
  dΠ/dt = rΠ
  Δ = μ+0.5σ² - r (introduced by the contraint dΠ/dt = rΠ)
  rV - ∂V/∂t = 0.5σ²S²∂²V/∂S² + (μ + 0.5σ² - Δ)S∂V/∂S
  rV - ∂V/∂t = 0.5σ²S²∂²V/∂S² + rS∂V/∂S
  
  

• New Theory of Complex Numbers; Quaternion Vector Operator Interpretation i = k̂×
  i = 𝐤𝐱, 𝐣𝐱, and 𝐢𝐱
  𝐞𝐱𝐩𝐤, 𝐞𝐱𝐩𝐣, and 𝐞𝐱𝐩𝐢
  𝐜𝐨𝐬𝐤, 𝐜𝐨𝐬𝐣, 𝐜𝐨𝐬𝐢
  𝐬𝐢𝐧𝐤, 𝐬𝐢𝐧𝐣, 𝐬𝐢𝐧𝐢
  𝐭𝐚𝐧𝐤, 𝐭𝐚𝐧𝐣, 𝐭𝐚𝐧𝐢
  𝐬𝐞𝐜𝐤, 𝐬𝐞𝐜𝐣, 𝐬𝐞𝐜𝐢
  𝐜𝐨𝐬𝐞𝐜𝐤, 𝐜𝐨𝐬𝐞𝐜𝐣, 𝐜𝐨𝐬𝐞𝐜𝐢
  𝐜𝐨𝐭𝐚𝐧𝐤, 𝐜𝐨𝐭𝐚𝐧𝐣, 𝐜𝐨𝐭𝐚𝐧𝐢
  𝐋𝐨𝐠𝐤, 𝐋𝐨𝐠𝐣, 𝐋𝐨𝐠𝐢
  𝐥𝐨𝐠𝐤, 𝐥𝐨𝐠𝐣, 𝐥𝐨𝐠𝐢
  

• Quaternion Vector form of Euler's equation
  𝐞𝐱𝐩𝐤(θ) = 𝐜𝐨𝐬𝐤(θ) + 𝐬𝐢𝐧𝐤(θ) k̂×
  𝐞𝐱𝐩𝐣(θ) = 𝐜𝐨𝐬𝐣(θ) + 𝐬𝐢𝐧𝐣(θ) ĵ×
  𝐞𝐱𝐩𝐢(θ) = 𝐜𝐨𝐬𝐢(θ) + 𝐬𝐢𝐧𝐢(θ) î×
  
  Quaternion Vector form of De Moivre's Theorem
  𝐞𝐱𝐩𝐤(nθ) = 𝐜𝐨𝐬𝐤(nθ) + 𝐬𝐢𝐧𝐤(nθ) k̂×
  𝐞𝐱𝐩𝐣(nθ) = 𝐜𝐨𝐬𝐣(nθ) + 𝐬𝐢𝐧𝐣(nθ) ĵ×
  𝐞𝐱𝐩𝐢(nθ) = 𝐜𝐨𝐬𝐢(nθ) + 𝐬𝐢𝐧𝐢(nθ) î×
  

• Dihedral Group of Order 4, D₄
  the rotations

  {i, i², i³, i⁴} = {k̂×, (k̂×)², (k̂×)³, (k̂×)⁴} 

  plus the relected rotations

  {i*, i*², i*³, i*⁴} = {(ĵĵ'+ĵ×)², (ĵĵ'+ĵ×)² k̂×, (ĵĵ'+ĵ×)²(k̂×)², (ĵĵ'+ĵ×)²(k̂×)³} 

  for the full group

  D₄ = {i, i², i³, i⁴, i*, i*², i*³, i*⁴}
     = {k̂×, (k̂×)², (k̂×)³, (k̂×)⁴, (ĵĵ'+ĵ×)²(k̂×)¹, (ĵĵ'+ĵ×)²(k̂×)², (ĵĵ'+ĵ×)²(k̂×)³, (ĵĵ'+ĵ×)²(k̂×)⁴}
  

Resume and Transcripts 🎓

1. (2001-2006) Macquarie University: BCom-Actuarial Studies BSc-Statistics
   To download transcript 🖙 click here 🖱🖘
   To download graduation certificate 🖙 click here 🖱🖘
   To download legacy resume 🖙 click here 🖱🖘
   
2. (2008-2012) The University of Sydney: PhD-Finance (financial derivatives, unpassed)
   To download documentation 🖙 TBA 🖘
   To download examiner reports 🖙 TBA 🖘
   
3. Legacy resume (2012)
   To download legacy resume 🖙 click here 🖱🖘
   I will eventually write an up-to-date one that focuses now on science and engineering.

Areas of Expertise, Knowledge, and Research 🎓📐🧩⌬📡∰

1. (2006-2026) Developing new applied mathematics (primary research area)🎓∰
   Linear algebra, complex numbers, calculus, brownian motion, financial derivatives, life-insurance mathematics, and so on.
2. Computer Aided Design (CAD) and Computer Aided Manufacture (CAM)
   📐 Click here to watch an SOLIDWORKS assembly and disassembly📐
   📐 Click here to see the SOLIDWORKS assembly drawing and bill of materials📐
   📐 Click here to see one of the SOLIDWORKS component drawings📐
   📐 Click here to watch FUSION computer numerical control manufacture📐
   
3. C and Python (and the mathematical and statistical software packages) - not a full professional programmer
   but more than proficient for doing maths and technical computing which is my primary research interest.
   
4. Rubiks quaternions and derivatives (dynamic Euclid and Pythagorus on steriods) (a primary reserach interest)
   I'll be putting some nice pictures of my collection here and probably some videos of my solves.

© Copyright Aaron Lloyd-Jones

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