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Andrius Kulikauskas

  • m a t h 4 w i s d o m - g m a i l
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

用中文

  • 读物 书 影片 维基百科

Introduction E9F5FC

Questions FFFFC0

Software

Priorities

Andrius Kulikauskas: Here are my research priorities.

Research priorities

Wondrous Wisdom

Ecotechnology

  • Document Jere's intuition of ecotechnology, his ways of figuring things out, especially his ability to empathize with a biological system, to have a sense that something is wrong.
  • I want to understand the dynamics of human experience in terms of three languages: argumentation (how things come to matter), verbalization (how meaning arises) and narration (how events happen).
    • Study chess compositions for how issues come to matter.
    • Study chess games for how meaning arises.
    • Study the mathematical concepts in the Mathematical Companion to understand how meaning arises.
  • I want to relate the houses of knowledge (ways of figuring things out) in various disciplines related to life, including biology, chemistry, microbiology, ecotechnology and mathematics.

Mathematical physics

  • Work out a physical interpretation of the combinatorics of orthogonal Sheffer polynomials for a new understanding of Schroedinger's equation with the hope of applying that further to quantum field theory.
    • Write up and publish a video of my current understanding: A Combinatorial Alternative to the Wave Function
    • Divide up the understanding I seek into elements and related problems, organize them and note for each element and each problem the progress, if any, that I have made.
    • Understand the Kim Zeng involution.
    • Understand the polynomial coefficients
      • Reinterpret the trees in terms of particle clocks.
      • Interpret {$A(t), u(t)$} and {$u'(t)$} in terms of the combinatorics. Figure out how to calculate these series.
    • Consider what momentum {$\hat p=-i\hbar\frac{\partial}{\partial x}$} and expected momentum would mean combinatorially in the case of the quantum harmonic oscillator
    • Understand the quantum narrative in terms of the combinatorics of the moments.
      • Given the recurrence formula, write out the definitions of the five polynomials.
      • Given the polynomials, understand the moments in terms of combinatorial objects.
        • I want to understand if the Meixner polynomials relate at all with the ordered Bell numbers.
      • Relate the combinatorial objects which express the moments with Zeng's formula for the moments in terms of permutations.
        • I want to compare the expression of the moments of the Meixner polynomials in terms of permutations (by Kim and Zeng) with the expression for the moments of the orthogonal Sheffer polynomials, and also with the generating function for the moments of the Meixner polynomials.
      • I want to understand how the moments transform as we go from the Meixner to the Charlier, Laguerre, Hermite and Meixner-Pollaczek polynomials.
    • Give a combinatorial interpretation of the definite integral of the square of the wave function (the product {$P_n(x)P_n(x)$}) from {$x$} to {$x+\delta$}.
    • Write out Meixner's proof of the classification of the orthogonal Sheffer polynomials.
      • I am trying to understand how to calculate a nice and meaningful expression for {$A(t)$} as I do for {$u(t)$}.
    • I want to understand how the associated distributions likewise transform as we proceed from the Meixner to the other polynomials.
      • I want to understand how these moments ground the distribution associated with the Meixner polynomials.
      • I want to understand how to use complex integration to get the distribution for the Laguerre polynomials.
      • I want to understand how to get the distribution of the Meixner-Pollaczek polynomials.

Geometry

  • Overview the geometrical concepts, branche presented in the Math Companion
    • Consider how they fit within the entirety of mathematics
  • Identify key perspectives on geometrical thinking
  • Compare those key perspectives across eight layers of geometry

Organize my learning paths

  • Start by mapping out my interests related to geometry
  • Map out all of my interests in math
    • List the relevant math structures for me to understand and why
    • Make a diagram relating these structures
    • Add links to related math that would help me understand
  • Improve my existing map of branches of mathematics
    • Consider how my map of interests relates to the map of all of math

Peacemaking

From before - My key wiki pages for learning, studying, investigating math

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This page was last changed on February 18, 2024, at 06:38 PM