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

Mechanical properties of aluminum /SiC bulk composites fabricated by aggregate accumulative press bonding and stir-casting process

Today, the emergence of composite structures can be considered a huge transformation on an industrial scale, especially in the transportation industry. Among all the structures made by the composite process, aluminum-based composites (AMMCs) are particularly popular both in the scientific and industrial fields. These structures are very light in weight and, at the same time, have significant strength. The ability to work with the machine in these structures is very high, and their plastic deformation is so high that they can be used in different industry sectors. Today, various methods are used to induce plastic deformation in aluminum-based composites (AMMCs). One of these methods is called aggregate accumulative press bonding (APB). The advantage of this method compared to other methods is that this method can create a homogeneous nanocomposite with ultra-fine grains. In the present study, the investigation of mechanical properties (MP's) of AA5083/5%SiC bulk composites fabricated via APB vs. pressing temperature (Temp) was conducted. All primary composite samples were fabricated via the stir-casting process (SCP). APB process was done on composite samples as a supplementary process. Finally, the effect of pressing Temp on the MP and microstructural properties (MSP) was investigated. The pressing Temp was varied between the ambient Temp's up to T = 300 °C. The MP were measured in this study by the Vickers micro-hardness (VMH) test, tensile test, and scanning electron microscopy (SEM). It was realized that the pressing Temp has a prominent effect on the MS and MP of fabricated 400°C. Samples fabricated at the ambient Temp have low ductility and high strength while for samples fabricated at T = 300 °C, the elongation and toughness values were higher than others. The TS of samples after 2 steps of APB at T = 200°C is 1.31 times more than that of fabricated at T = 300°C. Elongation was reduced sharply to 1.8% after the two steps at the ambient Temp, while it was 21% for the annealed AA5083

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

Simulation of natural convection of nanofluid inside a square cavity using experimental data by lattice Boltzmann method

The Lattice Boltzmann Method (LBM) is one of the suggested numerical approaches that has been shown to accurately estimate the increase in heat transfer caused by nanofluids. Several approaches to the prediction of the characteristics of nanofluids are investigated, and it is shown to what degree the classical models are accurate representations of the experimental data. The first thing that was done in this study was to explain the thermophysical parameters of the Ethylene Glycol (EG)-iron nanofluid that was employed. The effect of the Rayleigh number, the volume fraction of nanoparticles (φ), and the cavity angle (θ) on the isotherms and the average Nusselt number (Nuavg) are investigated. Finally, the effect of the adiabatic fin on the flow is investigated, and it is demonstrated in which scenario the adiabatic vane will be the most effective. The findings demonstrate that raising the Rayleigh number to 105 and 106 causes the heat to be transferred under the adiabatic fin. This finding suggests that the buoyancy force has a stronger influence on the heat transfer process when it is carried out close to the source of the cold. In general, if the Rayleigh number is increased, the rate of heat transfer in the fluid will rise as well. The Nu avg is increased by 44 % when the Ra number is increased from 103 to 105, and it is increased by 118 % when the Ra number is increased from 105 to 106. The chances of heat entering the cold source are reduced when the adiabatic fin is longer and situated lower. There is a wider cold zone within the hollow when Lf = 80 and Hf = 20, indicating that less heat is entering the cold source

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