Square character degree graphs yield direct products

If $G$ is a solvable group, we take $\Delta (G)$ to be the character degree graph for $G$ with primes as vertices. We prove that if $\Delta (G)$ is a square, then $G$ must be a direct product

A multi-degree-of-freedom reconfigurable ankle rehabilitation robot with adjustable workspace for post-stroke lower limb ankle rehabilitation

Introduction: A multi-degree-of-freedom ankle rehabilitation robot with an adjustable workspace has been designed to facilitate ankle joint rehabilitation training. It features a rotation center adapted to the human body, making it suitable for patients with ankle dysfunction following a stroke.Method: In this study, a multi-degree-of-freedom reconfigurable ankle rehabilitation robot (RARR) with adaptable features, based on the principles of ergonomics, has been proposed to cater to the varying needs of patients. This robot offers an adjustable workspace, allowing for different types of ankle joint rehabilitation exercises to be performed. By adjusting the assembly of the RARR, personalized and targeted training can be provided to patients, circumventing issues of redundancy in degrees of freedom during its use. A kinematic model of the robot has been established, and finite element simulation has been employed to analyze the strength of critical components, ensuring the safety of the robot. An experimental platform has been set up to assess the smoothness of the rehabilitation process with RARR, with angle measurements conducted using an Inertial Measurement Unit (IMU).Results and discussion: In conclusion, both simulation and experimental results demonstrate that the robot offers an adjustable workspace and exhibits relatively smooth motion, thereby confirming the safety and effectiveness of the robot. These outcomes align with the intended design goals, facilitating ankle joint rehabilitation and advancing the field of reconfigurable robotics. The RARR boasts a compact structure and portability, making it suitable for various usage scenarios. It is easily deployable for at-home use by patients and holds practical application value for wider adoption in rehabilitation settings

Fabrication and Investigation of Two-Component Film of 2,5-Diphenyloxazole and Octafluoronaphthalene Exhibiting Tunable Blue/Bluish Violet Fluorescence Based on Low Vacuum Physical Vapor Deposition Method

Organic luminescent materials play an important role in the fields of light-emitting diodes and fluorescent imaging. Moreover, new synthetic approaches towards π-conjugated molecular systems with high fluorescence quantum efficiency are highly desired. Herein, different 2,5-diphenyloxazole-octafluoronaphthalene (DPO-OFN) films with tunable fluorescence have been prepared by Low Vacuum Physical Vapor Deposition (LVPVD) method. DPO-OFN films showed some changed properties, such as molecular vibration and fluorescence. All films exhibited blue/bluish violet fluorescence and showed blue shift, in comparison with pristine DPO. This work introduced a new method to fabricate two-component molecular materials with tunable blue/bluish violet luminescence properties and provided a new perspective to prepare organic luminescent film materials, layer film materials, cocrystal materials, and cocrystal film materials. Importantly, these materials have potential applications in the fields of next generation of photofunctional materials

Nonlinear Electrical Conductivity Properties of Au Films Prepared by Sputtering

Metal-based films with tunable electrical conductivity have played an important role in developing new types of electric devices for future application. In this work, a sputtering method was used to obtain Au films on silicon substrate in a hypobaric atmosphere. Scanning electron microscope (SEM) shows that the interspaces between the Au nanoparticles were highly uniform and orderly distributed, with the width of several nanometers at the surface. By measuring the I-V curves of the films with thickness less than 20 nm, the nonlinear behaviors of electrical resistivity became gradually obvious as the decrease of the film thickness. For example, upon the thickness reducing to 10 nm, remarkable discontinuous step phenomenon appeared. Moreover, a computational simulation was carried on the electrical conductivity of films under normal temperature based on the Coulomb blockade theory and scattering theory, in which the electric current was in the range from 0 to 1.5 × 10−5 A. The computational results were consistent well with the experimental observations, which confirm that the nonlinear and step phenomenon can be assigned to the Coulomb blockade effect when electrons transfer occurs in the interspaces between the nanoparticles