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The fractional regularized long wave equation and the fractional nonlinear shallow-water wave equation are the noteworthy models in the domains of fluid dynamics, ocean engineering, plasma physics, and microtubules in living cells. In this study, a reliable and efficient improved F-expansion technique, along with the fractional beta derivative, has been utilized to explore novel soliton solutions to the stated wave equations. Consequently, the study establishes a variety of reliable and novel soliton solutions involving trigonometric, hyperbolic, rational, and algebraic functions. By setting appropriate values for the parameters, we obtained peakons, anti-peakon, kink, bell, anti-bell, singular periodic, and flat kink solitons. The physical behavior of these solitons is demonstrated in detail through three-dimensional, two-dimensional, and contour representations. The impact of the fractional-order derivative on the wave profile is notable and is illustrated through two-dimensional graphs. It can be stated that the newly established solutions might be further useful for the aforementioned domains.

Statistical process control basically involves inspecting a random sample of the output from a process and deciding whether the process is producing products with characteristics that fall within a predetermined range. It is used extensively in the field of reliability engineering. The reliability of the production process is thoroughly monitored for any internal variation using the SPC. The aim is always to settle such variations through a proper control monitoring. If the underlying distribution of the process is known to the researcher than the use of parametric control charts are useful but in many cases when there is doubt about the distribution of the process then it is preferred to use non parametric control charts. In this paper we propose the modified Exponentially weighted moving average (EWMA), Double Exponentially weighted moving average (DEWMA), Hybrid Exponentially weighted moving average (HEWMA), Extended Exponentially weighted moving average (EEWMA), Modified Exponentially weighted moving average (MEWMA) and mix- type control charts by mixing these control charts with Tukey control chart EWMA-TCC, DEWMA-TCC, HEWMA-TCC, EEWMA-TCC, MEWMA-TCC for the shape parameter of the Kumaraswamy Lehmann-2 Power function distribution (KL2PFD).

This research investigates the influence of the combined effect of the chemically reactive and thermal radiation on electrically conductive stagnation point flow of nanofluid flow in the presence of a stationary magnetic field. Furthermore, the effect of Newtonian heating, thermal dissipation, and activation energy are considered. The boundary layer theory developed the constitutive partial differential momentum, energy, and diffusion balance equations. The fundamental flow model is changed to a system of coupled ordinary differential equations (ODEs) via proper transformations. These nonlinear-coupled equations are addressed analytically by implementing an efficient analytical method, in which a Mathematica 11.0 programming code is developed for numerical simulation. For optimizing system accuracy, stability and convergence analyses are carried out. The consequences of dimensionless parameters on flow fields are investigated to gain insight into the physical parameters. The result of these physical constraints on momentum and thermal boundary layers, along with concentration profiles, are discussed and demonstrated via plotted graphs. The computational outcomes of skin friction coefficient, mass, and heat transfer rate under the influence of appropriate parameters are demonstrated graphically.

In this paper, long-wave anti-plane shear motion in a multilayered laminate composed of pre-stressed compressible elastic layers is investigated. The layers of the laminate are perfectly bonded, while a fixed-free boundary condition is prescribed on the outer faces of the laminate. The solution of the model is determined analytically via the propagator matrix and numerically through the asymptotic approach. Moreover, the numerical results featuring harmonic curves are presented graphically, together with an asymptotic long-wave analysis of the vibration modes. As a special case of materials, linear isotropic with one shear modulus is considered. A polynomial long-wave low-frequency approximation of the related dispersion relation is also studied. It governs dispersion curves including the lowest harmonic. It is revealed that a low-frequency mode exists in both the two- and three-layered laminates, which are taken as prototypical structures. Lastly, comparisons between the exact and approximate asymptotic results are presented, and excellent agreement is observed.

In this article, two flexible classes called the modified Kavya–Manoharan-G (MKM-G) and discrete modified Kavya–Manoharan-G (DMKM-G) families are investigated. The two proposed families provide more flexibility for modeling real-lifetime and count data from environmental, medical, engineering, and educational fields. Due to the new extra shape parameter of the two proposed families, their special sub-models are capable of modeling monotonic and non-monotonic hazard rates. The basic properties of the MKM-G family are studied. Eight classical approaches of estimation are used for estimating the MKM-exponential (MKME) parameters. The performances of the estimators are explored using simulation results. Additionally, the DMKM-exponential (DMKME) distribution is defined. Finally, the importance and flexibility of the MKME and DMKME distributions are addressed by fitting seven real-lifetime and count data from aforementioned applied fields. The real data analysis shows that the special models of the two classes are good candidates and can provide close fit as compared to well-known competing continuous and discrete distributions.

The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency.

(1) Background: ESports is a new trend of sports, which has gained considerable popularity worldwide. There is a scarcity of evidence that focuses on the lifestyle of ESports players (eSP) particularly on symptoms of nomophobia, level of anxiety, sleep quality, food consumption and physical activity. (2) Objective: to determine the prevalence and relationship between symptoms of nomophobia, psychological aspects, insomnia and physical activity of eSP in Saudi Arabia. (3) Methods: A cross-sectional study was conducted between March and April 2021 using a convenient self-selection adult sample. A total of 893 (216 eSP vs. 677 non-eSP (NeSP)) participants aged over 18 years were included. All participants answered a seven-part validated questionnaire that included: (i) sociodemographic questions; (ii) a symptoms of nomophobia questionnaire; (iii) general anxiety disorder questions, (iv) an insomnia severity index, (v) an Internet addiction scale, (vi) the Yale food addiction scale 2.0 short form and (vii) an international physical activity questionnaire. (4) Results: Among the entire population, the prevalence of moderate to severe nomophobia, anxiety, insomnia, Internet addiction and low physical activity were 29.8%, 13.9%, 63.3%, 27% and 2.8%, respectively. The eSP and NeSP differed significantly in nomophobia scale, anxiety and insomnia values. Compared to NeSP, eSP had a higher level of severe nomophobia p = 0.003, a severe level of anxiety p = 0.025 and symptoms of insomnia p = 0.018. Except for food addiction and physical activity, a positive correlation was identified between symptoms of nomophobia, anxiety and insomnia among eSP. (5) Conclusion: This study reported high prevalence of nomophobia, anxiety and insomnia among eSP compared to NeSP.

Knowledge of the ion composition in the near-Earth’s magnetosphere and plasma sheet is essential for the understanding of magnetospheric processes and instabilities. The presence of heavy ions of ionospheric origin in the magnetosphere, in particular oxygen (O + ), influences the plasma sheet bulk properties, current sheet (CS) thickness and its structure. It affects reconnection rates and the formation of Kelvin-Helmholtz instabilities. This has profound consequences for the global magnetospheric dynamics, including geomagnetic storms and substorm-like events. The formation and demise of the ring current and the radiation belts are also dependent on the presence of heavy ions. In this review we cover recent advances in observations and models of the circulation of heavy ions in the magnetosphere, considering sources, transport, acceleration, bulk properties, and the influence on the magnetospheric dynamics. We identify important open questions and promising avenues for future research.