ON CAPABLE GROUPS OF ORDER p4

A group $H$ is said to be capable, if there exists another group$G$ such that $\frac{G}{Z(G)}~\cong~H$, where $Z(G)$ denotes thecenter of $G$. In a recent paper \cite{2}, the authorsconsidered the problem of capability of five   non-abelian $p-$groups of order $p^4$ into account. In this paper, we continue this paper by considering three other groups of order $p^4$.  It is proved that the group $$H_6=\langle x, y, z \mid x^{p^2}=y^p=z^p= 1, yx=x^{p+1}y, zx=xyz, yz=zy\rangle$$ is not capable. Moreover, if $p > 3$ is  prime and $d \not\equiv 0, 1 \ (mod \ p)$ then the following groups are not capable:\\{\tiny $H_7^1=\langle x, y, z \mid x^{9} = y^3 = 1, z^3 = x^{3}, yx = x^{4}y, zx = xyz, zy = yz \rangle$,\\$H_7^2= \langle x, y, z \mid x^{p^2} = y^p = z^p = 1, yx = x^{p+1}y, zx = x^{p+1}yz, zy = x^pyz \rangle,$ \\$H_8^1=\langle x, y, z \mid x^{9} = y^3 = 1, z^3 = x^{-3}, yx = x^{4}y, zx = xyz, zy = yz \rangle$,\\$H_8^2=\langle x, y, z \mid x^{p^2} = y^p = z^p = 1, yx = x^{p+1}y, zx = x^{dp+1}yz, zy = x^{dp}yz \rangle$.

A high-order nonlinear Schrödinger equation with the weak non-local nonlinearity and its optical solitons

Abstract The present paper explores a high-order nonlinear Schrodinger equation in a non-Kerr law media with the weak non-local nonlinearity describing solitons' propagation through nonlinear optical fibers. To this end, the real and imaginary parts of the model are firstly extracted using a wave variable transformation. The modified Kudryashov method and symbolic computations are then adopted to successfully retrieve optical solitons of the model. The results presented in the current study demonstrate the great performance of the modified Kudryashov method in handling high-order nonlinear Schrodinger equations

Construction of 2-Gyrogroups in Which Every Proper Subgyrogroup Is Either a Cyclic or a Dihedral Group

In this paper, a 2-gyrogroup G(n) of order 2n, n≥3, is constructed in which every proper subgyrogroup is either a cyclic or a dihedral group. It is proved that the subgyrogroup lattice and normal subgyrogroup lattice of G(n) are isomorphic to the subgroup lattice and normal subgroup lattice of the dihedral group of order 2n, which causes us to use the name dihedral gyrogroup for this class of gyrogroups of order 2n. Moreover, all proper subgyrogroups of G(n) are subgroups

The effect of initial pressure on the thermal behavior of the silica aerogel/PCM/CuO nanostructure inside a cylindrical duct using molecular dynamics simulation

Amidst escalating fuel expenses and growing concerns over greenhouse gas pollution, the adoption of renewable alternative energy sources has become increasingly imperative. In response, scientists are fervently dedicated to identifying energy-saving solutions that are readily adaptable. Notably, silica aerogels have demonstrated remarkable efficacy in temperature management under both hot and cold conditions, while phase change materials are renowned for their capacity to store thermal energy. The study examines the effect of initial pressure on the thermal performance of silica aerogel/PCM/CuO nanostructure in a cylindrical duct. This was investigated using MD simulations and the LAMMPS software. The study will investigate several elements, such as density, velocity, temperature patterns, heat flux, thermal conductivity, and charge time or discharge time of the simulated structure. According to the results, with an increase in the initial pressure, the maximum density increases from 0.0838 atom/Å3 to 0.0852 atom/Å3, and the maximum velocity decreases from 0.0091 Å/fs to 0.0081 Å/fs. Also, the findings show that, by increasing the initial pressure, the temperature decreases from 931.42 K to 895.63 K, and thermal conductivity and heat flux decrease to 1.56 W/m.K and 56.66 W/m2 with increasing the initial pressure to 5 bar. Finally, the results show that charging time increases to 6.34 ns at 5 bar. The increase in charging time with increasing initial pressure may be attributed to the reduced mobility of particles within the structure as a result of the higher pressure. The findings of this study can help for a better understanding of energy-saving solutions, advanced thermal management systems, and the design of efficient energy storage technologies tailored to specific pressure-related operating conditions

Intraspecific interactions in a high density leopard population

Although less studied than interspecific interactions, interactions among members of the same species can influence space use and temporal activity. Using techniques commonly applied to the analysis of interspecific interactions – multi-species occupancy modelling and the analysis of temporal activity patterns – we studied intraspecific interactions within a high density population of Persian leopards (Panthera pardus saxicolor) in Tandoureh National Park, northeastern Iran. Using camera trap data, we investigated spatiotemporal interactions between male leopards, lone female leopards and families (cubs / females with cubs). While we hypothesised that male and female leopards would display different temporal activity patterns, we did not predict spatial avoidance between these groups. We also predicted that leopard families would exhibit spatiotemporal avoidance from male leopards due to the risk of infanticide. Contrary to our expectations we did not find any evidence for spatial or temporal avoidance between leopard families and adult male leopards. Male and lone female leopards exhibited positive pairwise co-occurrence, consistent with reports of high overlap between male and female leopard home ranges. While a high level of overlap in temporal activity patterns was found between males/lone females and males/families, there was evidence for variation in the proportion of time each leopard group was active in particular periods of the diel cycle. Male leopards showed cathemeral activity, while lone females and families were more active during daylight hours. The application of these techniques to interactions within a species has improved understanding of the ecology and behaviour of this endangered solitary carnivore

Ultra-low-dose chest CT imaging of COVID-19 patients using a deep residual neural network

Objectives The current study aimed to design an ultra-low-dose CT examination protocol using a deep learning approach suitable for clinical diagnosis of COVID-19 patients. Methods In this study, 800, 170, and 171 pairs of ultra-low-dose and full-dose CT images were used as input/output as training, test, and external validation set, respectively, to implement the full-dose prediction technique. A residual convolutional neural network was applied to generate full-dose from ultra-low-dose CT images. The quality of predicted CT images was assessed using root mean square error (RMSE), structural similarity index (SSIM), and peak signal-to-noise ratio (PSNR). Scores ranging from 1 to 5 were assigned reflecting subjective assessment of image quality and related COVID-19 features, including ground glass opacities (GGO), crazy paving (CP), consolidation (CS), nodular infiltrates (NI), bronchovascular thickening (BVT), and pleural effusion (PE). Results The radiation dose in terms of CT dose index (CTDIvol) was reduced by up to 89%. The RMSE decreased from 0.16 ± 0.05 to 0.09 ± 0.02 and from 0.16 ± 0.06 to 0.08 ± 0.02 for the predicted compared with ultra-low-dose CT images in the test and external validation set, respectively. The overall scoring assigned by radiologists showed an acceptance rate of 4.72 ± 0.57 out of 5 for reference full-dose CT images, while ultra-low-dose CT images rated 2.78 ± 0.9. The predicted CT images using the deep learning algorithm achieved a score of 4.42 ± 0.8. Conclusions The results demonstrated that the deep learning algorithm is capable of predicting standard full-dose CT images with acceptable quality for the clinical diagnosis of COVID-19 positive patients with substantial radiation dose reduction