Foundations, Volume 5, Issue 1

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunction seeming to be the primary lens. Our topic is a theory showing “where adjoints...

In glass physics, order parameters have long been used in the thermodynamic description of glasses, but their nature is not yet clear. The difficulty is how to find order in disordered systems. This study provides a coherent understanding of the natu...

In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian $H^{\left(IC\right)}=p^2+\mathrm{i}{x}^3$ does not satisfy all of the necessary postulates of quantum mechanics. This failure is due to the “intrinsic exceptional point” (IEP) fe...

In this paper, we consider the application of brute force computational techniques (BFCTs) for solving computational problems in mathematical analysis and matrix algebra in a floating-point computing environment. These techniques include, among other...

Low-grade gliomas are a group of brain tumors that mostly affect people in early adulthood. A glioma is a tumor that originates in glial cells. They are classified into four levels according to their level of proliferation, with grades 1 and 2 called...

This study employs advanced structural characterization techniques, including anomalous small-angle X-ray scattering (ASAXS), small-angle X-ray scattering (SAXS), and X-ray photoelectron spectroscopy (XPS), to investigate erbium (Er³⁺)-doped silica-b...

In fixed item parameter calibration (FIPC), an item response theory (IRT) model is estimated with item parameters fixed at reference values to estimate the distribution parameters within a specific group. The presence of random differential item func...

In this study, we explore the order–disorder transition in the dynamics of a straightforward master equation that describes the evolution of a probability distribution between two states, $p_1$ and $p_2$ (with $p_1+p_2=1$). We fo...

Stocking–Lord (SL) linking is a widely used linking method based on item response theory (IRT). This article examines the variability in SL linking parameter estimates within the two-parameter logistic (2PL) model. The uncertainty in SL linking...

In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delay...