Research works

p-adic Valuations of Generalized Multifactorials: A Legendre-Type Formula

The classical Legendre formula expresses the p-adic valuation of the factorial n! in terms of the base-p digit sum of n. We generalize this result to the α-th order multifactorial, the product of n and every α-th integer below it, for arbitrary integers α at least 2. When α divid...

A Covariant Lorentz Transformation Analysis of Einstein's Train and the Resolution of Relative Simultaneity

This manuscript re‑examines the standard interpretation of relative simultaneity (RS) in Einstein’s train thought experiment by analysing the Lorentz transformation in its fully covariant form. Using the matrix representation of the Lorentz transformation applied to homogeneous c...

Language ideology in Aruban secondary education: A nexus exploration

Aruban language-in-education policy is shaped by a tension between the dominant home language, Papiamento, and Dutch, the primary language of instruction in most schools. This presentation introduces a proposed analysis of three key policies, interviews with teachers (n = 8), foc...

The Cubic Law for Digit-Collision Energy

For an odd prime base b, the lag-one digit-collision energy is a weighted Dedekind-sum average over the prime-square carrier grid. This paper proves the unconditional cubic law E_b = b^3 + O(b^2 (log b)^2), with the leading cubic split exactly into a diagonal contribution b^3/3 a...

The Adaptation–Fidelity Law One Capability-to-Reward Channel and Its Four Derivations on a Concentration Coordinate

Abstract. The complexity, fairness, health, and survival of an open adaptive system are not four independent properties but four derivations of a single information channel that maps internal capability to reward — in organisms, functional contribution to resource allocation; und...

Additive Boundaries and Conductor Energies of Periodic Remainder Orbits

A finite character-sum treatment of the periodic side of long division. The paper develops signedboundary flux for periodic remainder orbits, proves a conductor-energy decomposition for oddcharacter moments, establishes a full-orbit prime-power energy law, gives an index-two mod...

Geometric Theory of Gravity (GTG-DC): A Constitutive-Geometry Framework for Galaxy Dynamics, Gravitational Lensing, and Cosmology

GTG-DC — Constitutive Geometry as a Parent Theory About This Publication This record presents the current form of GTG-DC (Geometric Theory of Gravity — Dynamical/Constitutive Geometry) — an effective theory in which ordinary, observable matter remains the material source of the g...

AXIOM: A Trust-First Neuro-Symbolic Execution Architecture for Self-Explaining Mathematical Reasoning

AXIOM is a trust-first neuro-symbolic math reasoning architecture combining a frozen large language model (Qwen 2.5 7B Instruct, used as rewriter only) with deterministic SymPy CAS handlers organized via a 1:1:1 task-routing discipline (trigger regex + narrow prompt + closed-form...

Hydra-Flux: Operational Addendum Variant B (Layered / Stratified Systems) in High-Seismicity Environments

Conventional offshore production tests in unconsolidated, layered marine gas hydrate reservoirs face two critical, coupled risks: hydraulic conformance failure due to fluid bypass through high-permeability streaks, and severe geomechanical instability leading to massive sand prod...

TUM memories sección 10: Protocolo de Ignición y Captura en Trampa Torsional Resonante

Se presenta el protocolo operativo para iniciar y estabilizar la Botella Boy descrita en DOI:10.5281/zenodo.19993794. Mediante excitación torsional a 142.86 kHz se genera el campo de contención topológica. Se detallan: 1) Secuencia de arranque con plasmas de argón, 2) Inyección d...

The Cohesion UFT Research Calculator, Version 6

Version 6 is a total rebuild of the Research Calculator: sixteen modules, every onecomputing live from the closed-form expressions of the Cohesion UFT series, withthe source paper stated per module and every displayed value verified against thatsource before release. Three change...

MEON R70–R86.4 Continuation: Locked Lensing Fractal Dimension, External Rotation-Curve Stress Tests, IFU Fail-Closed Diagnostics, and MUSE Covariance Localization

This release continues the MEON validation and reproducibility record after the R57–R69 Zenodo package. It documents the subsequent R70–R86.4 analysis chain, including locked lensing/fractal-dimension investigations, external galaxy rotation-curve stress tests, IFU stellar-kinema...

First Covid-19 Vaccination Rates Among Pregnant Tennessee Women by Month of Conception and Urbanization Level: March 2021 – November 2021

Introduction: Throughout the pandemic, COVID-19 vaccination coverage was lower for the general population living in rural counties than in urban counties. In Tennessee (TN), COVID-19 vaccinations became available to pregnant women in March 2021. Little is known about rates of COV...

Exploring Systemic Challenges in the Western North Carolina Dental Safety Net: A Qualitative Analysis

Introduction: Despite statewide growth, rural communities in Western North Carolina (WNC) face persistent barriers to oral health care driven by chronic dental workforce shortages and systemic geographic disparities. Within this Appalachian region, the dental safety net serves as...

Evaluating the Feasibility and Preliminary Effectiveness of a Tailored Diabetes Education Program for Rural Residents

Introduction: Diabetes is a top ten Rural Healthy People 2030 priority for health improvement among rural Americans. Socioeconomic, environmental, geographic and political barriers contribute to the type 2 diabetes (T2D) prevalence and its disparate impact in rural communities. H...

Infective Endocarditis Hospitalizations in Kentucky, 2008-2018: Spatial and Temporal Trends

Introduction: Infective endocarditis (IE) hospitalization rates have increased significantly in the last decade, primarily due to the opioid epidemic. In 2016, Kentucky (KY) ranked among the top ten states for opioid-related overdose deaths, but limited data exist on IE trends in...

Rural Community Perspectives on Hurricane Helene in Western North Carolina

Introduction: After making landfall on the Florida Gulf Coast in September 2024, Hurricane Helene impacted Western North Carolina (WNC) with historic flooding, landslides, and hurricane-force winds. More than 100 deaths in the region were attributed to the storm's direct impacts....

— Commutation-Discriminant Quaternionic Spacetime (CDQS) — A Unified, Algebraic Reconstruction of Spacetime, Quantum Theory, Gauge Dynamics, Gravitation, and Cosmology—Without Cosmological Constants or Particle Dark Matter (Treatise, v1)

Commutation-Discriminant Quaternionic Spacetime (CDQS) is a proposed algebraic reconstruction and unification of spacetime, quantum theory, gauge dynamics, gravitation, and cosmology via quaternionic energy conservation and a common Clifford transport structure. Rather than takin...

A reference genome and transcriptome of haustorial development in Pedicularis groenlandica reveal diverse trajectories of haustoria-associated gene evolution in parasitic plants.

BACKGROUND AND AIMS: Novel traits frequently evolve by co-opting existing genetic pathways through either the direct repurposing of existing genes or neofunctionalization of duplicated genes. Parasitism represents a major innovation in plants, in which a novel organ, the haustori...

On the Uniqueness of Minimal Physically Derivable Theories

This paper proves a metatheorem concerning the class of physical theories derivable from minimal axiom sets. Rather than asking whether two given theories are equivalent — the direction taken by the existing literature on theoretical equivalence — it asks a prior question: given...