Scientific Resource Catalog
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This paper proposes a novel approach to algorithm design termed "Algorithm Crystallization." Instead of traditional optimization methods which rely on iterative refinement of parameters, Algorithm Crystallization posits that algorithms evolve through a process analogous to crystal formation. The co…
Modern society faces socio-environmental challenges related to solid waste. In this context, sustainable and design and social innovation can play a significant role in addressing these issues. This study aimed to valorize two types of waste, sugarcane bagasse ash (CBC waste) and ornamental stone s…
A presentation explaining the proof https://doi.org/10.5281/zenodo.22019186 of determining the maximum "diameter" of a Miura-ori folded sheet at any "n" sizing
Interface engineering represents an effective strategy for passivating interfacial defects and suppressing dark current in photodetectors. Numerical simulations of an ITO/TiO 2 /MoS 2 /RbGeI 3 /Cu 2 O/Au n-i-p heterojunction demonstrate the efficacy of a MoS 2 interlayer in enhancing device perform…
In this paper, we develop an evolutionary generalized transferable neural network (Evo-GTransNet) solver for parabolic partial differential equations, formulated as a retained-space fixed-feature Galerkin method of lines. A GTransNet provides the prescribed spatial dictionary, while only the retain…
Abstract Simulating spacetime metric deformations and trans-relativistic coordinate transitions within continuous gen-eral relativity presents an intractable tensor bottleneck. This paper resolves these computational barriers byapplying the unified TONE-Tang method to a mechanical, non-point-partic…
The notion of minimality pervades many branches of mathematics and physics, from the study of surfaces that minimize area to the optimization of energy functions in variational calculus. Despite the apparent diversity of minimal structures, there exists a deep, underlying unity that can be captured…
FINDING: The golden angle (≈137.51°) governs phyllotaxis, the spiral arrangement of leaves and seeds, arising from the golden ratio's irrationality to optimize packing and light exposure. MATH: Golden angle = 360° × (1 – 1/φ) = 360° × (2 – φ) ≈ 137.507764°; φ = (1 + √5)/2 ≈ 1.6180339; related to Fi…
FINDING: Decoherence is the process by which quantum superpositions decay into classical mixtures due to environmental entanglement, with recent advances in exact master equations for quantum dot systems enabling precise modeling of non-Markovian decoherence. | MATH: Exact master equation derived f…
The notion of alignment has long been a guiding principle in mathematics, especially in the context of dualities and correspondences between seemingly disparate structures. In this paper, we propose a unified framework, the Universal Mathematical Alignment Theory (UMAT), that formalizes the process…
This paper explores the concept of "Computational Symmetry Dynamics," a novel approach to optimization and problem-solving that shifts from passively leveraging existing symmetries to actively generating and evolving them during a training process. The core idea is to design algorithms that iterati…
This paper introduces and investigates a novel theoretical framework called Structural Mismatch Theory. The central notion is the mismatch measure M(A,B) defined for any pair of abstract structures A and B. We explore the circumstances under which the mismatch vanishes, i.e., M(A,B)=0, and examine…
Resonant-state expansion (RSE) is a powerful modal framework for the perturbative analysis of open resonant systems, providing direct access to complex eigenfrequencies and eigenmodes. While RSE is well developed in electromagnetism, a comparably systematic formulation for acoustics remains less es…
FINDING: The golden angle (≈137.51°) governs phyllotaxis in sunflowers and other plants, arising from the golden ratio's irrationality to optimize seed/leaf packing. MATH: - Golden ratio φ = (1 + √5)/2 ≈ 1.6180339887 - Golden angle = 360° / φ² = 360° / (φ + 1) ≈ 137.507764° (or equivalently 360° -…
This work presents "The Cosmic Landscape Map: Taiji Duality & Geometric Morphogenesis Blueprint", establishing a comprehensive 5-layer cosmological map where physical distance fundamentally emerges and evolves through geometric morphogenesis in accordance with the Fibonacci sequence and the Golden…
Halide perovskites have garnered significant attention due to their exceptional properties, with the efficiency of small perovskite cells nearing that of the best silicon crystal solar cells. However, long-term stability remains a critical challenge for perovskite solar cells (PSCs). This research…
ENGLISH The 600-Cell and the Binary Icosahedral Group 2I: Spectra, Pseudodeterminants and Galois Structure. With the audited state of the CPSD programme Abstract This monograph collects only computationally verified and fully reproducible results obtained from a single 114 kB data file (600cell_hod…
Iterative latent workspaces offer an alternative computational paradigm for maintaining, routing, and transforming structured relational information during neural sequence processing. However, repeatedly updating a shared continuous latent workspace across unconstrained recurrent iterations frequen…
The concept of vacancies—missing constituents—in physical crystals has inspired a parallel framework in pure mathematics. This paper introduces the Mathematical Vacancy Theory (MVT), a systematic study of missing positions or elements in various mathematical structures and their influence on global…
🇬🇧 Abstract (English) Title: Observer Position, Topological Suture, and Dual Gravity in UCT Quasicrystalline Cosmology v6.1.4 Abstract (English) Within the framework of Unification Topological Cosmology (UCT v6.1.4), the macroscopic structure of spacetime is modeled by the Poincaré dodecahedral spa…