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

Current medical product development for diagnosis, surgical planning and treatment in the areas of Neurosurgery, Orthopeadic and Dental-Cranio-Maxillofacial surgery in Vietnam

With the population of 86 million and good GDP growth in recent decades, the medical market in Vietnam is growing fast. However, most of the medical technology products are imported, and the number of locally manufactured ones is limited and they do not have the high competition capability in term of quality, quantity and types. In this paper, the current product development in Vietnam for diagnosis, surgical planning and treatment in the areas of Rehabilitation, Neurosurgery, Orthopeadic and Dental-Cranio-Maxillofacial surgery is presented. A roadmap for medical technology development in Vietnam is propose

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

Effects of Data Standardization on Hyperparameter Optimization with the Grid Search Algorithm Based on Deep Learning: A Case Study of Electric Load Forecasting

This study investigates data standardization methods based on the grid search (GS) algorithm for energy load forecasting, including zero-mean, min-max, max, decimal, sigmoid, softmax, median, and robust, to determine the hyperparameters of deep learning (DL) models. The considered DL models are the convolutional neural network (CNN) and long short-term memory network (LSTMN). The procedure is made over (i) setting the configuration for CNN and LSTMN, (ii) establishing the hyperparameter values of CNN and LSTMN models based on epoch, batch, optimizer, dropout, filters, and kernel, (iii) using eight data standardization methods to standardize the input data, and (iv) using the GS algorithm to search the optimal hyperparameters based on the mean absolute error (MAE) and mean absolute percent error (MAPE) indexes. The effectiveness of the proposed method is verified on the power load data of the Australian state of Queensland and Vietnamese Ho Chi Minh city. The simulation results show that the proposed data standardization methods are appropriate, except for the zero-mean and min-max methods

Grid search of multilayer perceptron based on the walk-forward validation methodology

Multilayer perceptron neural network is one of the widely used method for load forecasting. There are hyperparameters which can be used to determine the network structure and used to train the multilayer perceptron neural network model. This paper aims to propose a framework for grid search model based on the walk-forward validation methodology. The training process will specify the optimal models which satisfy requirement for minimum of accuracy scores of root mean square error, mean absolute percentage error and mean absolute error. The testing process will evaluate the optimal models along with the other ones. The results indicated that the optimal models have accuracy scores near the minimum values. The US airline passenger and Ho Chi Minh city load demand data were used to verify the accuracy and reliability of the grid search framework

A note on possible interpretations for the DSJ+(2632)D_{SJ}^+(2632) observed by SELEX

We suggest some possible interpretations for the $D_{SJ}^+(2632)$ observed by SELEX. The $D_{SJ}^+(2632)$ could be the first radial excitation of the $1^-$ ground state $\rm{D_s}^*$(2112), and its unusual decay patten might be hopefully explained by the node structure of the wave functions. In addition, the $D_{SJ}^+(2632)$ could also be a $c\bar sg$ hybrid state or a $(cs)_{3^*}-(\bar s\bar s)_{3}$ (diquark-antidiquark) bound state.Comment: final version to appear in Phys. Lett. B, references adde

An Evolving Stellar Initial Mass Function and the Gamma-Ray Burst Redshift Distribution

Recent studies suggest that Swift gamma-ray bursts (GRBs) may not trace an ordinary star formation history. Here we show that the GRB rate turns out to be consistent with the star formation history with an evolving stellar initial mass function (IMF). We first show that the latest Swift sample of GRBs reveals an increasing evolution in the GRB rate relative to the ordinary star formation rate at high redshifts. We then assume only massive stars with masses greater than the critical value to produce GRBs, and use an evolving stellar IMF suggested by Dav\'{e} (2010) to fit the latest GRB redshift distribution. This evolving IMF would increase the relative number of massive stars, which could lead to more GRB explosions at high redshifts. We find that the evolving IMF can well reproduce the observed redshift distribution of Swift GRBs.Comment: 13 pages, 4 figures, accepted for publication in ApJ