Foundations, Volume 3, Issue 3

Diagnostic classification models (DCMs) are statistical models with discrete latent variables (so-called skills) to analyze multiple binary variables (i.e., items). The one-parameter logistic diagnostic classification model (1PLDCM) is a DCM with one...

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t³ scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of var...

A method without memory as well as a method with memory are developed free of derivatives for solving equations in Banach spaces. The convergence order of these methods is established in the scalar case using Taylor expansions and hypotheses on highe...

Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute. Exploring the convergence properties of such metho...

Numerous applications from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert, or Banach, to mention a few. Researchers worldwide are developing methodologies to han...

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A brief review of the classical and quantum description of the interaction of electromagnetic radiation with matter based on the model of a harmonic oscillator is presented. This review includes the generalized Bohr correspondence principle, the exci...

The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics ($\mu$NEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension...

Living beings are composite thermodynamic systems in non-equilibrium conditions. Within this context, there are a number of thermodynamic potential differences (forces) between them and the surroundings, as well as internally. These forces lead to fl...

Any two points are close together in a θ-contraction by a factor of θ. The function Δ is implied to be a contraction under this condition, but with a tighter bound on the contraction factor. In this paper, we introduce the notions of orthogonal θ-con...

This article shows the life and work of Gerty Cori, a woman born in Czechoslovakia and who later became a naturalized American, who spent her whole life researching, together with her husband, in the laboratory to find the cause of some diseases, par...