Olayiwola Babarinsa

Functionally graded (FG) beams have been used more and more in highly designed structures under dynamic loading due to their graded mechanical properties and excellent performance. Their transient response on complex elastic foundations is, however, not easily predicted due to the material heterogeneity, shear deformation, rotary inertia, and coupled effect of the foundation parameters. The purpose of this study is thus to propose an accurate and efficient computational model for the dynamic analysis of FG Timoshenko beams supported by biparametric Vlasov foundations under harmonic excitation. The formulation takes into account the space-varying material properties, Timoshenko shear deformation, rotary inertia, and coupled Winkler–shear interaction of the Vlasov foundation. The governing equations are numerically solved in space with the high-order spectral element method (SEM) and in time with the Hilber–Hughes–Taylor (HHT) scheme. The resulting framework is used to study the transient displacement and vibration response with respect to the excitation frequency, material gradation index, and stiffness and damping properties of the foundation. The numerical results prove that the results converge quickly in space and time and also indicate that the dynamic response is significantly affected by the interaction between the gradation of material and the parameters of the foundation. The displacement amplitude, resonance behavior, and vibration characteristics are significantly altered by any variations in the gradation index and foundation characteristics. The results obtained with the proposed formulation are in good agreement with those available from the benchmark solutions, thus validating the correctness and reliability of the formulation. The SEM–HHT methodology offers a reliable, precise, and low-computational-cost solution for transient analysis of FG Timoshenko beams on biparametric Vlasov foundations under harmonic excitation. The proposed framework offers a powerful predictive tool for vibration analysis, response control, and design of advanced FG beam systems that can be applied in aerospace, marine, smart infrastructure, and other high-performance engineering structures.

Graph theory and numerical analysis meet in numerous real-world applications, including network evolution, dynamic data clustering, and multiscale modelling. Current spectral methods, however, often presume static graph structures, compromising their accuracy and efficiency for developing networks. This work presents an adaptive spectral technique that adjusts solver tolerance dynamically according to structural changes in the graph, quantified through the Frobenius norm of differences between consecutive Laplacians. We tested this on synthetic graphs and compared it with conventional fixed-tolerance techniques. The adaptive method exhibited runtime improvements of up to 50% and substantially reduced eigenvalue errors. These findings attest to its superior numerical stability and computational efficiency. We advocate the application of adaptive tolerance methods in real-time spectral analysis applications and propose follow-up work develop this framework for weighted, directed, or real-world dynamic networks.

Regularized regression techniques such as the least absolute shrinkage and selection operator (LASSO), elastic-net, and the type 1 and type 2 correlation adjusted elastic-net (CAEN1 and CAEN2 respectively) are used for simultaneously carrying out variable selection and estimation of coefficients in machine learning. Modified estimators based on the CAEN1 and CAEN2 are proposed in this study by rescaling the estimates to undo the double shrinkage incurred due to the application of two penalties. The scale factors are derived by decomposing the correlation matrix of the predictors. The derived scale factors, which depend on the magnitude of correlations among the predictors, ensure that the elastic-net is included as a special case. Estimation is carried out using a robust worst-case quadratic solver algorithm. Simulations show that the proposed estimators referred to as corrected correlation adjusted elastic-net (CCAEN1 and CCAEN2) perform competitively with the CAEN1, CAEN2, LASSO, and elastic-net in terms of variable selection, estimation and prediction accuracy with CCAEN1 yielding the best results when the number of predictors is more than the number of observations and CCAEN2 producing the best performance when there is grouping effect, where highly correlated predictors tend to be included in or excluded from the model together. Applications to two real-life datasets further demonstrate the advantage of the proposed methods for machine learning.

Noise and vibration are pervasive challenges in built-up structures, impacting structural integrity, operational efficiency, and occupant well-being. These issues are particularly pronounced in urban and industrial settings, where traditional materials often struggle to deliver effective mitigation across the broad range of relevant frequencies. This paper introduces an integrated mathematical modeling and virtual design framework for the development of advanced metamaterials aimed at reducing noise and vibration in such complex structures. The approach combines finite element analysis, dynamic energy analysis, and optimization algorithms to design metamaterials with frequency-selective properties that create targeted barriers to acoustic and vibrational disturbances. The study not only develops a systematic methodology for designing these metamaterials but also validates their efficacy through comprehensive simulations and benchmarking against established solutions. The results highlight the advantages of the proposed metamaterials in terms of adaptability, efficiency, and performance robustness across various operating conditions. Sensitivity analyses and comparative evaluations further underscore the superiority of the framework in addressing frequency-dependent challenges, offering significant improvements over conventional materials. A unique aspect of this research is the inclusion of natural metamaterials (NMs) as a sustainable alternative for mitigating ground vibrations. The study reviews the potential of NMs for diverse functionalities, particularly in attenuating ground vibrations in urban environments. These findings emphasize the versatility and eco-friendliness of natural materials, providing a roadmap for their development and application in achieving clean and quiet environments. The proposed framework, therefore, bridges theoretical advancements with practical applications, paving the way for resilient and sustainable solutions to noise and vibration challenges in built-up structures.

Graph theory is one of the neglected branches of mathematics in Nigeria but with the most applications in other fields of research. This article shows the paucity, importance, and necessity of graph theory in the development of Nigeria. The adjacency matrix and dual graph of the Nigeria map were presented. The graph spectrum and energies (graph energy and Laplacian energy) of the dual graph were computed. Then the chromatic number, maximum degree, minimum spanning tree, graph radius, and diameter, the Eulerian circuit and Hamiltonian paths from the dual graph were obtained and discussed.

This paper reviews the theory of matrices and determinants. Matrix and determinant are nowadays considered inseparable to some extent, but the determinant was discovered over two centuries before the term matrix was coined. Our review associate determinant with the matrix as part of linear systems but not with polynomials. Thus, the paper first gives the background on matrix with vast applications in all fields of study and then reviews the history of determinants which is based on its major contributors in chronological order from the sixteenth century to the twenty-first century

In this paper, W Z factorization is optimized with a proposed Cramer’s rule and compared with classical Cramer’s rule to solve the linear systems of the factorization technique. The matrix norms and performance time of WZ factorization together with LU factorization are analyzed using sparse matrices on MATLAB via AMD and Intel processor to deduce that the optimized Cramer’s rule in the factorization algorithm yields accurate results than LU factorization and conventional W Z factorization. In all, the matrix group and Schur complement for every Zsystem (2×2 block triangular matrices from Z-matrix) are established.

This article discusses a mixed graph called mixed hourglass graph. The adjacency of a mixed hourglass graph is coined from an hourglass matrix in which the matrix is obtained from quadratic interlocking factorization. Mixed hourglass graph is a weighted graph with loops, but replacing the weights of the graph with 1’s produce an unweighted mixed hourglass graph or simply mixed hourglass graph. Then the total number of arcs and edges and the spanning subgraph of mixed hourglass graph are examined to infer that the graph is a complete mixed graph and acyclic graph.