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Complex fuzzy soft matrices play a crucial role in various applications, including decision-making, pattern recognition, signals processing, and image processing. The main objective of this study is to introduce the unique notions of complex Pythagorean fuzzy soft matrices (CPFSMs), which provide more flexibility and accuracy in modelling uncertainty. CPFSMs incorporate Pythagorean fuzzy soft matrices, allowing for more sophisticated uncertainty modeling. The key findings of CPFSMs, specific instances, and certain fundamental set-theoretic operations and principles were covered. A set of new distance metrics between two CPFSMs has been defined. In the context of complex Pythagorean fuzzy soft sets and complex Pythagorean fuzzy soft matrices, we created a CPFS decision-making technique. Moreover, the application's numerical example and comparison analysis have been effectively demonstrated. Thus, by integrating the concepts of Pythagorean fuzzy sets, soft matrices, and complex numbers, CPFSMs provide a robust framework with membership and non-membership degrees for complex decision-making modeling and analyzing uncertain data.
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The developed article considers SIR problems for the recent COVID-19 pandemic, in which each component is divided into two subgroups: young and adults. These subgroups are distributed among two classes in each compartment, and the effect of COVID-19 is observed in each class. The fractional problem is investigated using the non-singular operator of Atangana Baleanu in the Caputo sense (ABC). The existence and uniqueness of the solution are calculated using the fundamental theorems of fixed point theory. The stability development is also determined using the Ulam-Hyers stability technique. The approximate solution is evaluated using the fractional Adams-Bashforth technique, providing a wide range of choices for selecting fractional order parameters. The simulation is plotted against available data to verify the obtained scheme. Different fractional-order approximations are compared to integer-order curves of various orders. Therefore, this analysis represents the recent COVID-19 pandemic, differentiated by age at different fractional orders. The analysis reveals the impact of COVID-19 on young and adult populations. Adults, who typically have weaker immune systems, are more susceptible to infection compared to young people. Similarly, recovery from infection is higher among young infected individuals compared to infected cases in adults.
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Heart Failure (HF) is a complex clinical syndrome in which the heart is unable to provide enough blood flow to meet metabolic needs and lacks efficient venous return. HF is a major risk factor for morbidity and mortality with cardiovascular diseases globally. Despite enormous research, the molecular markers relevant to disease prognosis and management remain not well understood. Here, we analyzed the whole transcriptomes of 18 failing hearts and 15 non-failing hearts (predominantly of Caucasian origin), by applying the standard in silico tools. The analyses revealed novel gene-markers including ALKBH5 of mRNA demethylation and KMT2E of histone modification processes, significantly over-expressed in the HF compared with the non-failing hearts (FDR < 0.05). To validate the over-expression of ALKBH5, we determined the global m6A level in hypoxic H9c2 cells using a dot blot assay. The global m6A level was found markedly lower in the hypoxic H9c2 cells than in the control cells. Additionally, the expression of ALKBH5 in the H9c2 cells was quantified by the qPCR and found to be 1.18 times higher at 12â h (p < 0.05), and 1.67 times higher at 24â h of hypoxia (p < 0.01) compared with the control cells, indicating a likely role of ALKBH5 in the failing cardiac cells. Furthermore, we identified several compounds through the virtual screening of 11,272 drug-like molecules of the ZINC15 database to inhibit the ALKBH5 in a molecular docking process. Collectively, the study revealed novel markers potentially involved in the pathophysiology of HF and suggested plausible therapeutic molecules for the management of the disease.
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The unsteady compressible steam laminar flow associated with heat transfer in fluids in a squared cylinder is examined in this work. The current challenge was created utilizing the CFD approach. The laminar flow is chosen with a low Mach number. With the geometric wall, the flow has a no-slip condition. The pressure on the flow is kept at 0 pas, and the temperature in the flow regime is 305.13. A 0.5 m/s velocity is used to start the flow. With the use of graphics, the effects of time on velocity and pressure distributions are discussed. Different outcomes are also mentioned, such as drag coefficients, lift coefficients, and heat distributions. The velocity drops from 2.5 to 1.6 m/s at t = 7 s in the absence of anybody's force and temperature 305.13 K. Pressure increases from 0.00098 to 0.001 Pas in the flow interval of 10 s. Surface temperature increases from 360 to 375 K in time intervals of 10 s keeping pressure constant. And contour temperature increases from 371.56 to 374.2 K in time intervals of 10 s keeping the pressure constant. This information provides us with caution about the emission of steam from the chimneys of furnaces. It implies that when steam flows from a cylindrical geometry like chimneys of furnaces it heats the upper inner and outer parts which may destroy the material. So for safety, that emission should be taken for a short interval of time otherwise it will result in a havoc process. The lift coefficient remains constant and the drag coefficient increases from 0.0005 to 0.065. Under that condition, fluid has to face more resistance. To overcome that difficulty fluid should be provided with high velocity to continue it for a long time. The technique used to solve modeled problems is the Backward Difference Formula.
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Thermal performance can be enhanced due to the mixing of nanoparticles in base fluid. This research discusses the involvement of ternary hybrid nanoparticles in the mixture of pseudo-plastic fluid model past over a two dimensional porous stretching sheet. Modelling of energy equation is carried out in the presence of external heat source or sink and viscous dissipation. The flow presenting equations and derived in Cartesian coordinate system under usual boundary layer theory in the form of complex coupled partial differential equations (PDEs). The derived PDEs have been converted into corresponding ordinary differential equations (ODEs) with the engagement of suitable transformation. The engineers, scientists and mathematicians have great interest in the solution of differential equations because to understand the real physics of the problem. Here, finite element scheme has been used to approximate the solution of the converted problem. The contribution of several emerging parameters on solution have been displayed through graphs and discussed. It is recommended that the finite element method can be engaged to approximate the solution of nonlinear problems arising in modelling the problem in mathematical physics.