The emergence of higher-dimensional evolution equations in dissimilar scientific arenas has been on the rise recently with a vast concentration in optical fiber communications, shallow water waves, plasma physics, and fluid dynamics. Therefore, the present study deploys certain improved analytical methods to perform a solitonic analysis of the newly introduced three-dimensional nonlinear dynamical equations (all within the current year, 2024), which comprise the new (3 + 1) Kairat-II nonlinear equation, the latest (3 + 1) Kairat-X nonlinear equation, the new (3 + 1) Boussinesq type nonlinear equation, and the new (3 + 1) generalized nonlinear Korteweg–de Vries equation. Certainly, a solitonic analysis, or rather, the admittance of diverse solitonic solutions by these new models of interest, will greatly augment the findings at hand, which mainly deliberate on the satisfaction of the Painleve integrability property and the existence of solitonic structures using the classical Hirota method. Lastly, this study is relevant to contemporary research in many nonlinear scientific fields, like hyper-elasticity, material science, optical fibers, optics, and propagation of waves in nonlinear media, thereby unearthing several concealed features.

Solar collectors play a crucial role in harnessing solar radiation and converting it into thermal energy, functioning as efficient heat exchangers. Among them, solar dish concentrators are particularly notable for their ability to operate at high temperatures, making them an effective solution for both heat and electricity generation. Owing to their high efficiency in capturing and utilizing solar energy, dish collectors have attracted significant interest in solar thermal applications. These concentrators come in various cavity receiver designs—such as open, spiral, hollow, and volume configurations—allowing for versatile energy conversion. Building on this concept, the present study investigates natural convection heat transfer within a two-dimensional ‘C’-shaped cavity filled with a porous medium and hybrid nanofluids, specifically Ag-MgO (silver-magnesium oxide) and Ag-TiO $$_2$$ 2 (silver-titanium dioxide oxide). The cavity features adiabatic upper and lower surfaces, with a heated slit on the left and a cooled wall on the right. As solar devices become more compact and efficient, the shape of the cavity plays a critical role in ensuring proper thermal management to prevent overheating and sustain optimal performance. To enhance heat transfer in solar collectors, the study applies a machine learning technique, evaluating the influence of two distinct hybrid nanoparticles. Furthermore, machine learning is used to analyze how different parameters vary with the type of nanoparticle, aiming to determine the most effective combination for optimizing heat transfer. The governing equations are solved using the finite difference method coupled with the Marker and Cell (MAC) technique. The findings indicate that an increase in the Rayleigh number improves heat transfer owing to intensified buoyancy-driven convection, with Ag-MgO exhibiting greater efficacy compared to Ag-TiO $$_2$$ 2 . Raising the nanoparticle volume fraction significantly boosts heat transfer at $$\textrm{Ra}=10^6$$ Ra = 10 6 , with Ag-MgO and Ag-TiO $$_2$$ 2 nanofluids showing improvements of 12.32% and 11.93%, respectively. ANN analysis identifies Darcy number, Rayleigh number, and nanoparticle volume fraction as primary influencers of Nusselt number. For Ag-MgO, their impacts are 37.15%, 22.15%, and 13.79%, while Ag-TiO $$_2$$ 2 shows similar contributions: 37.07%, 23.51%, and 13.79%. At 5% volume fraction, Ag-MgO outperforms Ag-TiO $$_2$$ 2 by 11.35% at $$\textrm{Ra}=10^5$$ Ra = 10 5 and maintains a 0.451% lead at $$\textrm{Ra}=10^6$$ Ra = 10 6 , indicating consistently superior thermal performance.

This study investigates the geometry of osculating type-2 ruled surfaces in Minkowski 3-space ${\mathbf{E}}_1^3$, formulated through the Type-2 Bishop frame associated with a spacelike curve whose principal normal is timelike and binormal is spacelike. Using the hyperbolic transformation linking the Frenet–Serret and Bishop frames, we analyze how the Bishop curvatures ${\zeta }_1$ and ${\zeta }_2$ affect the geometric behavior and formation of such surfaces. Explicit criteria are derived for cylindrical, developable, and minimal configurations, together with analytical expressions for Gaussian and mean curvatures. We also determine the conditions under which the base curve behaves as a geodesic, asymptotic line, or line of curvature. Several illustrative examples in Minkowski 3-space are provided to visualize the geometric influence of ${\zeta }_1$ and ${\zeta }_2$ on flatness, minimality, and developability. Overall, the Type-2 Bishop frame offers a smooth and effective framework for characterizing Lorentzian geometry and symmetry of osculating ruled surfaces, extending classical Euclidean results to the Minkowski setting.

The Hitchcock-Koopmans transportation problem is a well-known and fundamental optimization problem which focuses on minimization of the objective function which is basically the transportation cost from multiple sources to multiple destinations. In this article, we present some novel results on the spectral properties of structured matrices appearing in Hitchcock-Koopmanstransportation problems. The results on the computation of singular values are presented with usage of tools from linear algebra and matrix analysis. The new results are derived on interconnection between structured singular values of pseudo-inverse and D-stable matrices of Hitchcock-Koopmans transportation models. The numerical experimentation shows the behavior of singular values. The Matlab EigTool is used for the computation of pseudo-spectrum of pseudo-inverse matrix corresponding to the transportation model.

In this study, we introduce an algorithm that utilizes the Haar wavelet collocation method to solve the time-dependent Emden–Fowler equation. This proposed method effectively addresses both linear and nonlinear partial differential equations. It is a numerical technique where the differential equation is discretized using Haar basis functions. A difference scheme is also applied to approximate the time derivative. By leveraging Haar functions and the difference scheme, we form a system of equations, which is then solved for Haar coefficients using MATLAB software. The effectiveness of this technique is demonstrated through various examples. Numerical simulations are performed, and the results are presented in graphical and tabular formats. We also provide a convergence analysis and an error analysis for this method. Furthermore, approximate solutions are compared with those obtained from other methods to highlight the accuracy, efficiency, and computational convenience of this technique.

Matrices have significant contribution in the field of science and technology. It is often seen that fuzzy matrix theory theory cann’t address all types of uncertanity. In order to solve real life problems containing the neutrosophic phenomena, determinant and adjoint of a neutrosophic fuzzy matrix are required. The article introduces the notions of determinant and adjoint of neutrosophic fuzzy matrices. We shall define the idea of the neutrosophic matrix in which everyelement will appear with the degree of membership values of independent functions, namely membership, indeterminacy, and non-membership functions. Each degree of these membership values will be taken from the interval [0, 1]. With the help of this notion, we shall introduce the determinant and adjoint of a square neutrosophic fuzzy matrix. We shall investigate some basic properties, theorems and results of the determinant and adjointof a square neutrosophic fuzzy matrix. We shall justify these concepts by providing proof. Some properties and results shall be verified by providing suitable numerical examples. We shall give some definitions based on the newly defined concepts. The article reveals an innovative idea which contributes to find determiant and adjoint of neutrosophic fuzzy matrices generated from real-life problems. These newly introduced definitions will have applications in relevant science and technology research fields such as to solve linear equations containing neutrosophic fuzzy matrices.