Documents

Many systems encountered in nature and engineering exhibit complex and hierarchical geometric structures. Fractal geometry provides a powerful tool for understanding and modeling these structures. However, existing deterministic circle packing fractals, such as the Apollonian gasket, often adhere to fixed geometric rules and may fall short in accurately reflecting the diversity of observed structures. Addressing the need for greater flexibility in modeling physical and mathematical systems, this ...

Bu çalışma, özgün bir algoritmik yapıya sahip olan Keçeci Sayı dizilerinin tanım kümesini, standart sayı sistemlerinin ötesine taşıyarak nötrosofik ve hipergerçek sayılar gibi ileri düzey matematiksel yapılarla genişletmektedir. Keçeci Sayıları, temel olarak bir başlangıç değeri ve bir artış skalerine dayanan, bölünebilirlik ve asallık testlerine bağlı özyinelemeli bir algoritma ile üretilen dizilerdir. Bu çalışmanın temel amacı, bu deterministik algoritmanın, belirsizlik (nötrosofik) ve sonsuz ...

Keçeci Varsayımı'nın Hesaplanabilirliği: Sonlu Adımda Kararlı Yapıya Yakınsama Sorunu

Mehmet Keçeci ORCID: https://orcid.org/0000-0001-9937-9839, Independent Researcher

Received: 03.08.2025

Abstract:

Bu çalışma, "Keçeci Varsayımı" olarak adlandırılan yeni bir matematiksel hipotezi sunar ve bu varsayımın, klasik Collatz Varsayımı'nın çok daha genel bir çerçevede formüle edilmiş hali olabileceğini ileri sürer. Keçeci Varsayımı, belirli bir yinelemeli süreç boyunca, herhangi bir başlangıç değerinin ...

This study comprehensively examines the profound technological and methodological synergies existing between observations made via interferometric detectors such as LIGO and Virgo, which have revolutionized the field of gravitational wave (GW) astrophysics, and the rapidly advancing quantum computing (QC) technologies. As both disciplines aim to perform measurements pushing the limits of precision, the effective control and mitigation of environmental and quantum-originated noise pose a critical ...

Nodal-line semimetals constitute a fascinating subclass within the family of topological materials in condensed matter physics. These unique materials are characterized by the intersection of their electronic energy bands along one or more closed or open lines within the Brillouin Zone, rather than at isolated points. These lines of intersection are termed "nodal lines," and along these lines, electrons can behave as if they were massless, leading to extraordinary electronic properties. The ...

The development of quantum computers represents one of the most exciting and challenging endeavours in modern science. Progress in this field, particularly with the advent of the second quantum revolution, necessitates a profound interplay between diverse disciplines such as materials science, condensed matter physics, and quantum information theory. The primary aim of this work is to explore the potential of layered quantum structures containing exotic particles—Weyl and Majorana fermions—to ...

The Limits of Python in Computational Mathematics and Their Extension with JAX: An Application on Harmonic Numbers

Mehmet Keçeci ORCID: https://orcid.org/0000-0001-9937-9839, Independent Researcher

Received: 29.07.2025

Abstract:

This study presents a comparative analysis of a traditional, pure Python-based approach and a modern, JAX library-based approach for calculating the harmonic series, focusing on performance, scalability, and efficiency. The harmonic series is a divergent series of significant ...

This study presents a comparative analysis of static and dynamic number sequences, using the classical Oresme numbers and the novel Keçeci numbers, developed by Mehmet Keçeci, as primary case studies. Static sequences are characterized by a fixed, predictable recurrence relation. The Oresme numbers—the partial sums of the harmonic series (Η_n=∑(k=1)^n 1/k)—exemplify this category. Their generation follows a simple, deterministic rule (Η_n= Η(n-1)+1/n), and their predictable divergence, proven ...