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Aims to propose a new dynamic model for the solution of the three‐dimensional structural analysis problem of a non‐linear (non‐symmetrical) structure which is subjected under seismic forces.

This problem is reduced to the solution of a system of ordinary differential equations of the second kind and such a system is numerically solved by using a special kind of finite elements and by solving the corresponding eigenvalues‐eigenvectors problem.

The proposed finite element method is much smaller in degree of freedom size than commercial software, as classical linear stiffness matrices of three‐dimensional beam element have six degrees of freedom per node.

Future research should concentrate on the application of the new dynamic model to solve more complicated forms of non‐symmetrical structures.

Practical implications are given to structural analysis problems to the determination of the eigenvalues‐eigenvectors. As an example, an application is given to the determination of the eigenvalues and eigenvectors of a 15‐floor building consisting of reinforced concrete and subjected to an horizontal seismic vibration.

The new dynamic model which is proposed is addressed to researchers of dynamic analysis and civil engineers.

Aims to present a boundary integral equation method for solving Laplace's equation Δu=0 with nonlinear boundary conditions.

The nonlinear boundary value problem is reformulated as a nonlinear boundary integral equation, with u on the boundary as the solution being sought. The integral equation is solved numerically by using the collocation method on smooth or nonsmooth boundary; the singularities of solution degrade the rates of convergence.

Variants of the methods for finding numerical solutions are suggested. So these methods have been compared with respect to number of iterations.

Numerical experiments show the efficiency of the proposed methods.

Provides new methods to solve nonlinear weakly singular integral equations and discusses difficulties that arise in particular cases.

The purpose is to present a new formal approach based on a partial integro‐differential equation, the space‐time state transition equation (STSTE), and on a set of general equations with which space‐time dynamical models of complex systems, such as social systems and ecosystems, can be built.

The STSTE provides the partial derivative of the density of a state‐variable with regard to time as a sum of time rates and space‐time rates. Time rates describe the dynamics of the system for each space‐point irrespectively of the other points, whilst space‐time rates describe this evolution as a consequence of the relation of each space‐point with a given set of other points of the space. This relation contains integrals over the accessibility domains (sets of space‐points with which each space‐point is related).

The STSTE is provided for any system of space‐coordinates and is compared with the reaction‐diffusion models (RD). The reason why it is more convenient to work with the STSTE than with the RD to model complex systems in the context of social systems and ecosystems is indicated.

An urban system (the city of Valencia, Spain) is presented as an application; an analytical solution strategy is stated under the simplest hypothesis for computing space‐time rates, and a computer program for the situation is developed to obtain numerical solutions.

A numerical comparison between the new STSTE model and the RD shows that, the STSTE model produces better results than the reaction diffusion model in validation.

Accurate numerical differentiation of approximate data by methods based on Green's second identity often involves singular or nearly singular integrals over domains or their boundaries. This paper applies the finite part integration concept to evaluate such integrals and to generate suitable quadrature formulae. The weak singularity involved in first derivatives is removable; the strong singularities encountered in computing higher derivatives can be reduced. To find derivatives on or near the edge of the integration region, special treatment of boundary integrals is required. Values of normal derivative at points on the edge are obtainable by the method described. Example results are given for derivatives of analytically known functions, as well as results from finite element analysis.

Providing a comprehensive literature review to consolidate existing knowledge, advancements and future directions in the field. By synthesizing the state of research, this work enhances the understanding of Prescriptive Maintenance (PsM) methodologies, applications and potential benefits to assist researchers in identifying fruitful avenues for further investigation, and guide practitioners in implementing PsM strategies to improve maintenance outcomes in their industries.

Through a systematic, multistage, specialists audited analysis of peer-reviewed articles, conference papers, books sections, thesis, magazines and industry reports, this work provides a literature review analyzing PsM origins, definitions, enablers, outputs and emerging trends.

PsM concept evolved in recent years representing a shift from traditional maintenance, leveraging prescriptive analytics, data-driven modeling and optimization techniques to enable proactive decision-making and optimal resource allocation. By harnessing PsM, organizations can anticipate and mitigate failures, optimize maintenance actions and enhance asset reliability.

Existing literature points out the following challenges for PsM implementation: prescriptive analytics improvement, scalability of frameworks, development of prototypes, processes integration; PsM maturity assessment; asset health prognostics assertiveness, real-time data availability and adoption of cost functions to grasp business and environmental, social and governance (ESG) costs.

Optimal deployment of resources with little or no human intervention in the maintenance decision process and the creation of new services improving reliability and operational performance.

By optimizing maintenance, not only direct costs diminish but also environmental, social and governance (ESG) related costs decrease by reducing energy waste during equipment’s operating phase, assessing the ecological impact of providing maintenance to operators and line maintenance stakeholders and, consequently, minimizing or even eliminating harmful effects on the environment and the human.

Work consolidating existing PsM-related knowledge and indicating future work is a gap in the literature. This paper fills this gap.