Heimburg and Jackson devised a mathematical model known as the Heimburg model to describe the transmission of electromechanical pulses in nerves, which is a significant step forward. The major objective of this paper was to examine the dynamics of the Heimburg model by extracting closed-form wave solutions. The proposed model was not studied by using analytical techniques. For the first time, innovative analytical solutions were investigated using the exp$\left(-\phi \left(\xi \right)\right)$-expansion method to illustrate the dynamic behavior of the electromechanical pulse in a nerve. This approach generates a wide range of general and broad-spectral solutions with unknown parameters. For the definitive value of these constraints, the well-known periodic- and kink-shaped solitons were recovered. By giving different values to the parameters, the 3D, 2D, and contour forms that constantly modulate in the form of an electromechanical pulse traveling through the axon in the nerve were created. The discovered solutions are innovative, distinct, and useful and might be crucial in medicine and biosciences.

The current evaluation described the flow features of Darcy Forchhemier hybrid nanoliquid across a slender permeable stretching surface. The consequences of magnetic fields, second order exothermic reaction, Hall current and heat absorption and generation are all accounted to the fluid flow. In the working fluid, silicon dioxide (SiO₂) and titanium dioxide (TiO₂) nano particulates are dispersed to prepare the hybrid nanoliquid. TiO₂ and SiO₂ NPs are used for around 100 years in a vast number of diverse products. The modeled has been designed as a nonlinear set of PDEs, Which are degraded to the dimensionless system of ODEs by using the similarity transformation. The reduced set of nonlinear ODEs has been numerically estimated through bvp4c package. The outcomes are tested for validity and consistency purpose with the published report and the ND solve technique. It has been noted that the energy curve lessens with the influence of thermodiffusion, Brownian motion and rising number of nanoparticles, while boosts with the result of magnetic field. Furthermore, the concentration outline of hybrid nanoliquid improves with the upshot of chemical reaction.

The study of convective heat transfer in differently shaped fins with radiation, internal heat generation and variable thermal conductivity was considered. The energy equation of the model was converted into the dimensionless form by adopting the proper variables, which was later solved using the differential transformation method. The impact of the parameters on the thermal performance, efficiency and heat transfer of the fins was analyzed graphically and also by performing thermal analysis on the fins. It was noticed that there was a significant effect on the thermal performance of the fins with different shapes, and also the heat transfer rate of the fin increased for improved values of the internal heat generation and radiation parameters. The exponential profile showed better results than other profiles, and the results obtained were supported by thermal analysis using ANSYS software.

Potential biomarkers which include S100 calcium binding protein A9 (S100A9), mucin 5AC (MUC5AC), transforming growth factor β1 (TGF-β1), and angiopoietin-2 have previously been shown to be effective for cholangiocarcinoma (CCA) diagnosis. This study attempted to measure the sera levels of these biomarkers compared with carbohydrate antigen 19-9 (CA19-9). A total of 40 serum cases of CCA, gastrointestinal cancers (non-CCA), and healthy subjects were examined by using an enzyme-linked immunosorbent assay. The panel of biomarkers was evaluated for their accuracy in diagnosing CCA and subsequently used as inputs to construct the decision tree (DT) model as a basis for binary classification. The findings showed that serum levels of S100A9, MUC5AC, and TGF-β1 were dramatically enhanced in CCA patients. In addition, 95% sensitivity and 90% specificity for CCA differentiation from healthy cases, and 70% sensitivity and 83% specificity for CCA versus non-CCA cases was obtained by a panel incorporating all five candidate biomarkers. In CCA patients with low CA19-9 levels, S100A9 might well be a complementary marker for improved diagnostic accuracy. The high levels of TGF-β1 and angiopoietin-2 were both associated with severe tumor stages and metastasis, indicating that they could be used as a reliable prognostic biomarkers panel for CCA patients. Furthermore, the outcome of the CCA burden from the Classification and Regression Tree (CART) algorithm using serial CA19-9 and S100A9 showed high diagnostic efficiency. In conclusion, results have shown the efficacy of CCA diagnosis and prognosis of the novel CCA-biomarkers panel examined herein, which may prove be useful in clinical settings.

In this new era of the fluid field, researchers are interested in hybrid nanofluids because of their thermal properties and potential, which are better than those of nanofluids when it comes to increasing the rate at which heat is transferred. Compared to the dynamics of radiative Ethylene Glycol-Zinc Oxide (nanofluid) and Ethylene Glycol-Zinc Oxide-Titanium Dioxide (hybrid nanofluid) flows between two permeable expanding/contracting walls, nothing is known in terms of Lorentz force, heat source, and the activation energy. The thermo-physical characteristics of Ethylene Glycol, Zinc Oxide nanoparticles, and Titanium Dioxide nanoparticles are used in this study to derive the governing equations for the transport of both dynamics. Governing equations are converted as a set of nonlinear ordinary differential equations (with the aid of suitable similarity mutations), and then the MATLAB bvp4c solver is used to solve the equations. This study’s significant findings are that rise in the reaction rate constant increases mass transfer rate, whereas an increase in the activation energy parameter decreases it. The mass transfer rate decreases at a rate of 0.04669 (in the case of hybrid nanofluid) and 0.04721 (in the case of nanofluid) when activation energy ($E$) takes input in the range $0\le E\le 5$. It has been noticed that the velocity profiles are greater when the walls are expanding as opposed to when they are contracting. It is detected that the heat transfer rate reduces as the heat source parameter increases. The heat transfer rate drops at a rate of 0.9734 (in the case of hybrid Nanofluid) and 0.97925 (in the case of nanofluid) when the heat source parameter ($Q$) takes input in the range $0\le Q\le 0.3$. In addition, it has been observed that the entropy generation increases as the Brinkmann number rises.

In this paper, we propose two scaled Dai–Yuan (DY) directions for solving constrained monotone nonlinear systems. The proposed directions satisfy the sufficient descent condition independent of the line search strategy. We also reasonably proposed two different relations for computing the scaling parameter at every iteration. The first relation is proposed by approaching the quasi-Newton direction, and the second one is by taking the advantage of the popular Barzilai–Borwein strategy. Moreover, we propose a robust projection-based algorithm for solving constrained monotone nonlinear equations with applications in signal restoration problems and reconstructing the blurred images. The global convergence of this algorithm is also provided, using some mild assumptions. Finally, a comprehensive numerical comparison with the relevant algorithms shows that the proposed algorithm is efficient.