Author: Ahmed Gossa

This page documents the author identity and the early works that preceded the formalization of Hierarchical Calculus. It also provides direct links to archived PDF works and ready-to-copy IEEE citations.

Name: Ahmed Gossa (GOSSA AHMED)
Email: gossaahmed@yahoo.fr
Official Website: Hierarchical Calculus Website
Concept DOI: 10.5281/zenodo.17917302

Research note: The 2011 and 2012 documents represent the conceptual bridge from differential change → proportional change → logarithmic change, which later becomes an explicit rank–degree structure in Hierarchical Calculus.

1) Short Academic Biography

The author’s work focuses on describing “multiple languages of change” in calculus. While classical differentiation is powerful, many phenomena are more naturally described through proportional variation (relative scaling) or logarithmic hierarchies.

These ideas were presented early in two independent manuscripts: Proportional Calculus (2011) and Logarithmic Calculus (2012), which later converge into the unified framework now named Hierarchical Calculus.

2) Timeline of Key Works

2011 — Proportional Calculus

Independent manuscript | Nov. 12, 2011 | Author: GOSSA AHMED

Introduces proportional (relative) differentiation, proportional integration, and approximation ideas based on structural invariance.

Open PDF

2012 — Logarithmic Calculus

Independent manuscript | May 21, 2012 | Author: GOSSA AHMED

Extends the proportional approach by defining logarithmic differentiation and logarithmic integration, with applications to hierarchical growth mechanisms.

Open PDF

2025 — Hierarchical Calculus (Official Website + DOI)

Official reference | Zenodo Concept DOI

Unifies differential, proportional, logarithmic, and higher layers into a structured rank–degree system \(D_r^n\).

Open DOI

Scientific connection: These works illustrate an explicit shift from unit-dependent change to scale-aware and multi-layer change, which is the essential motivation behind Hierarchical Calculus.

3) IEEE Citation + BibTeX

3.1 IEEE — Concept DOI (General Reference)

[1] A. Gossa, “Hierarchical Calculus — Official Website,” Zenodo, 2025. doi: 10.5281/zenodo.17917302.

3.2 IEEE — 2011 Proportional Calculus

[2] GOSSA AHMED, “Proportional Calculus,” Nov. 12, 2011. (PDF available in the official repository).

3.3 IEEE — 2012 Logarithmic Calculus

[3] GOSSA AHMED, “Logarithmic Calculus,” May 21, 2012. (PDF available in the official repository).

3.4 BibTeX

@misc{gossa_proportional_2011, author = {Gossa, Ahmed}, title = {Proportional Calculus}, year = {2011}, note = {PDF available in the official repository}, url = {https://gossaahmed.github.io/gossa-math/PROPORTIONAL_CALCULUS.pdf} } @misc{gossa_logarithmic_2012, author = {Gossa, Ahmed}, title = {Logarithmic Calculus}, year = {2012}, note = {PDF available in the official repository}, url = {https://gossaahmed.github.io/gossa-math/LOGARITMIC_CALCULUS.pdf} } @software{gossa_hierarchical_calculus_2025, author = {Gossa, Ahmed}, title = {Hierarchical Calculus — Official Website}, year = {2025}, doi = {10.5281/zenodo.17917302}, url = {https://gossaahmed.github.io/gossa-math/index-en.html} }

Tip: If you want maximum academic strength, we can archive the PDFs on Zenodo with individual DOIs, then replace [2] and [3] with DOI citations.

4) Contact

Email: gossaahmed@yahoo.fr
GitHub: GOSSAAHMED/gossa-math
DOI: 10.5281/zenodo.17917302