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One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
The paper revisits the concepts of instantaneous active and reactive powers and provides a novel definition for basic circuit elements based on quantities utilized in classical mechanics, such as absolute and relative velocity, momentum…
Writing and argumentation are critical to both professional physics and physics education. However, the skill of making an extended argument in writing is often overlooked in physics classrooms, apart from certain practices like lab…
Motivated by the problem of finding resistances among vertices in a hypercube, we derive exact expressions, generating functions, and asymptotic expansions for these resistances, then study the combinatorial interpretations of the…
Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems…
Capacitors are typically connected together in one of two configurations: either in series, or in parallel. Here we study a capacitor-within-capacitor (CWC). Simulations and experiments indicate that the overall capacitance of the…
Conceptors provide an elementary neuro-computational mechanism which sheds a fresh and unifying light on a diversity of cognitive phenomena. A number of demanding learning and processing tasks can be solved with unprecedented ease,…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.
General physics approach is applied to analysis of power components in electrical systems under sinusoidal and non-sinusoidal conditions. Physical essence of active, reactive and distorting powers are determinate. It is shown that the all…
This lecture notes are intended for the students taking courses in mathematical control theory. They are concerned with the attainability problem with constraints. The exposition is oriented to the linear control problems with the impulse…
Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments…
We generalize the weighted cumulative entropies (WCRE and WCE), introduced in [5], for a system or component lifetime. Representing properties of cumulative entropies, several bounds and inequalities for the WCRE is proposed
This paper aims to provide physics teachers with tools to help deepen the understanding of the laws of electromagnetism. The fundamental contributions of our proposal are: a) to use quotes from mythical characters in the history of science…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…
We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.
In this article, we reflect upon our positive experiences incorporating or working on extra credit projects in algebra-based introductory physics that asked students to connect physics with humanities, social sciences, and everyday life. We…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and divergence terms. Our main interest is to provide graph and…
This expository manuscript presents generalized expressions for the low-frequency voltage gain and terminal impedances of each of the three fundamental bipolar-amplifier topologies (i.e., common emitter, common base, and common collector).…