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This is the problem of the 7-th international Experimental Physics Olympiad "The Day of the Inductance". A large inductance made by a general impedance converter is measured by the Maxwell-Wien bridge. The youngest students (S category)…

In this paper the proofs are given that the electric and magnetic fields are properly defined vectors on the four-dimensional (4D) spacetime (the 4-vectors in the usual notation) and not the usual 3D fields. Furthermore, the proofs are…

Assume that arc length is measured with the flat spacetime metric. Then, for the most general Poincare group representation for translating 4-vectors, curves with parallel translated tangent vectors must have accelerations that are the…

In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…

This lecture presents recent advances in the theory of errors propagation. We first explain in which cases the propagation of errors may be performed with a first order differential calculus or needs a second order differential calculus.…

We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some…

For generalized coordinate systems, the numerical values of vector and tensor components do not generally equal the physical values, i.e., the values one would measure with standard physical instruments. Hence, calculating physical…

A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…

A data augmentation module is utilized in contrastive learning to transform the given data example into two views, which is considered essential and irreplaceable. However, the predetermined composition of multiple data augmentations brings…

Physics education researchers have developed many evidence-based instructional strategies to enhance physics students' conceptual learning. These strategies have historically been tested using assessments such as the Force Concept Inventory…

In one of his papers, the author introduces the class of Farkas-related vectors for which a version of Farkas' lemma over integers is derived. In this paper, two similar classes are introduced and studied.

This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…

At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…

We examined how introductory physics students' attitudes and approaches to problem solving compare to those of introductory astronomy students, using a previously validated survey, the Attitudes and Approaches to Problem Solving (AAPS)…

A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…

Students' attitudes and approaches to problem solving in physics can greatly impact their actual problem solving practices and also influence their motivation to learn and ultimately the development of expertise. We developed and validated…

We have designed an introductory laboratory course that engaged first-year undergraduate students in two complementary types of iteration: (1) iterative improvement of experiments through cycles of modeling systems, designing experiments,…

Integrating computation into physics teaching is a curricular move that, at present, has been predominately studied for its cognitive impacts. However, if this modality of instruction shifts how students engage with physics, we argue there…

The impact of Lorentz violation on the dynamics of a scalar field is investigated. In particular, we study the dynamics of a scalar field in the scalar-vector-tensor theory where the vector field is constrained to be unity and time like. By…

The ability to categorize problems based upon underlying principles, rather than contexts, is considered a hallmark of expertise in physics problem solving. With inspiration from a classic study by Chi, Feltovich, and Glaser, we compared…