Algebraic structure underlying spherical, parabolic and prolate spheroidal bases of the nine-dimensional MICZ-Kepler problem

Octonion algebra $\mathbb{O}$ has recently been used to study the fundamental physics of the Standard Model, such as its three-generation structure and its possibility of unifying gravity and quantum mechanics. Interestingly, this octonion algebra $\mathbb{O}$ has also been related to the $SO(8)$ monopole and, consequently, links to the nine-dimensional MICZ-Kepler problem. This problem has been solved exactly by the variables separation method in three different coordinate systems, spherical, parabolic, and prolate spheroidal. In the present study, we establish a relationship between the variable-separation and the algebraic structure of $SO(10)$ symmetry. Each of the spherical, parabolic, or prolate spheroidal bases is proved to be a set of eigenfunctions of a corresponding nonuplet of algebraically-independent integrals of motion. This finding also helps us to establish connections between the bases by the algebraic method. This connection, in turn, allows calculating a complicated integral of confluent Heun, generalized Laguerre, and generalized Jacobi polynomials, which may be engaging in analytics.Comment: 21 pages, no figures. Submitted to Physica Script

Revisiting the Approaches for Exploring Students’ Drive in Japanese Studies

Japanese Studies undergraduate programs offer students an engaging curriculum that provides a deep understanding of the Japanese language and culture. A degree in Japanese Studies equips students with valuable skills that are relevant in various fields, making it a popular choice worldwide. College students’ motivation is a critical factor in academic success and has been extensively studied in education. The paper aims to review the existing theories related to study motivation, language acquisition, study abroad drives, and motivation, then to consider the approaches and details that we could prioritize for investigating the motivations and drives of students majoring and minoring in Japanese Studies in universities

The multi-vehicle profitable pick up and delivery routing problem with uncertain travel times

Abstract This paper addresses a variant of the known selective pickup and delivery problem with time windows. In this problem, a fleet composed of several vehicles with a given capacity should satisfy a set of customers requests consisting in transporting goods from a supplier (pickup location) to a customer (delivery location). The selective aspect consists in choosing the customers to be served on the basis of the profit collected for the service. Motivated by urban settings, wherein road congestion is an important issue, in this paper, we address the profitable pickup and delivery problem with time windows with uncertain travel times. The problem under this assumption, becomes much more involved. The goal is to find the solution that maximizes the net profit, expressed as the difference between the collected revenue, the route cost and the cost associated to the violation the time windows. This study introduces the problem and develops a solution approach to solve it. Very preliminary tests are performed in order to show the efficiency of developed method to cope with the problem at hand

Thermal effect on magnetoexciton energy spectra in monolayer transition metal dichalcogenides

It is widely comprehended that temperature may cause phonon-exciton scattering, enhancing the energy level's linewidth and leading to some spectrum shifts. However, in the present paper, we suggest a different mechanism that allows the thermal motion of the exciton's center of mass (c.m.) to affect the magnetoexciton energies in monolayer dichalcogenides (TMDCs). By the nontrivial but precise separation of the c.m. motion from an exciton in a monolayer TMDC with a magnetic field, we obtain an equation for the relative motion containing a motional Stark term proportional to the c.m. pseudomomentum, related to the temperature of the exciton gas but neglected in the previous studies. Solving the Schr\"odinger equation without omitting the motional Stark potential at room temperature shows approximately a few meV thermal-magnetic shifts in the exciton energies, significant enough for experimental detection. Moreover, this thermal effect causes a change in exciton radius and diamagnetic coefficient and enhances the exciton lifetime as a consequence. Surprisingly, the thermoinduced motional Stark potential breaks the system's SO(2) symmetry, conducting new peaks in the exciton absorption spectra at room temperature besides those of the $s$ states. This mechanism could be extended for other magnetoquasiparticles such as trions and biexcitons.Comment: 8 pages, 4 figures, 3 tables for main manuscript; 20 pages, 6 figures, 6 tables for supplementary. Published on Physical Review

Retrieval of material properties of monolayer transition-metal dichalcogenides from magnetoexciton energy spectra

Reduced exciton mass, polarizability, and dielectric constant of the surrounding medium are essential properties for semiconduction materials, and they can be extracted recently from the magnetoexciton energies. However, the acceptable accuracy of the previously suggested method requires very high magnetic intensity. Therefore, in the present paper, we propose an alternative method of extracting these material properties from recently available experimental magnetoexciton s-state energies in monolayer transition-metal dichalcogenides (TMDCs). The method is based on the high sensitivity of exciton energies to the material parameters in the Rytova-Keldysh model. It allows us to vary the considered material parameters to get the best fit of the theoretical calculation to the experimental exciton energies for the $1s$, $2s$, and $3s$ states. This procedure gives values of the exciton reduced mass and 2D polarizability. Then, the experimental magnetoexciton spectra compared to the theoretical calculation gives also the average dielectric constant. Concrete applications are presented only for monolayers WSe$_2$ and WS$_2$ from the recently available experimental data. However, the presented approach is universal and can be applied to other monolayer TMDCs. The mentioned fitting procedure requires a fast and effective method of solving the Schr\"{o}dinger of an exciton in monolayer TMDCs with a magnetic field. Therefore, we also develop such a method in this study for highly accurate magnetoexciton energies.Comment: 8 pages, 4 figures, 4 table

HybridMingler: Towards Mixed-Reality Support for Mingling at Hybrid Conferences

Mingling, the activity of ad-hoc, private, opportunistic conversations ahead of, during, or after breaks, is an important socializing activity for attendees at scheduled events, such as in-person conferences. The Covid-19 pandemic had a dramatic impact on the way conferences are organized, so that most of them now take place in a hybrid mode where people can either attend on-site or remotely. While on-site attendees can resume in-person mingling, hybrid modes make it challenging for remote attendees to mingle with on-site peers. In addressing this problem, we propose a collaborative mixed-reality (MR) concept, including a prototype, called HybridMingler. This is a distributed MR system supporting ambient awareness and allowing both on-site and remote conference attendees to virtually mingle. HybridMingler aims to provide both on-site and remote attendees with a spatial sense of co-location in the very same venue location, thus ultimately improving perceived presence