This page collects formal derivations, expository notes, and structured mathematical manuscripts.
Work is organized by research area. PDFs are added progressively as manuscripts mature.

📊 Special Functions

Classes of Logarithmic Fractional Part Function (2026)

Analyzes properties and extensions of Gamma-type/Uniform-type integral in the form of

\[\int\limits_0^1 \left(\prod\limits_{i = 1}^n x_i\right)^{\alpha - 1}\mathrm{frac}\left(\ln \left(\prod\limits_{i = 1}^n x_i\right)\right)^{\beta} Q\left(\left(\prod\limits_{i = 1}^n x_i\right)\right) \,\mathrm{d}x_1\dots\mathrm{d}x_n\]

where $\Re(\alpha) > 0$, $\beta$ is a non-negative integer, and $Q(x)$ is an admissible factor.

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Geometry & Structural Invariants

Derivations of triangle center loci and invariant geometric signatures under constrained configurations.

Loci of Selected Kimberling Centers for Right Triangles Inscribed in a Fixed Circle (2026)

Coordinate parametrization of right triangles inscribed in a unit circle, with explicit derivation of loci for shape-variant and shape-invariant centers.

Coordinates grounded in barycentric and trilinear definitions from Clark Kimberling’s Encyclopedia of Triangle Centers.
Notable: $X_{11}$ (Feuerbach Point) produces a self-intersecting locus under this configuration.

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Interactive companion available in Projects.

Notes in Progress

Working mathematical notes not yet formalized as full manuscripts. These represent active structural investigations rather than completed results.

This section will populate as materials develop.

All manuscripts are independent mathematical notes. Formal PDFs will be linked upon completion.