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In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium.

In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known.

Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal.

The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

To compute an optimal control of non‐linear reaction diffusion equations that are modelling inhibitor problems in the brain.

A new numerical approach that combines a spectral method in time and the Adomian decomposition method in space. The coupling of these two methods is used to solve an optimal control problem in cancer research.

The main conclusion is that the numerical approach we have developed leads to a new way for solving such problems.

Focused research on computing control optimal in non‐linear diffusion reaction equations. The main idea that is developed lies in the approximation of the control space in view of the spectral expansion in the Legendre basis.

Through this work we are convinced that one way to derive efficient numerical optimal control is to associate the Legendre expansion in time and Runge Kutta approximation. We expect to obtain general results from optimal control associated with non‐linear parabolic problem in higher dimension.

Coupling of methods provides a numerical solution of an optical control problem in Cancer research.

This paper describes a non‐linear reaction‐diffusion equation, which models how a substance spreads in the surface of the cortex so as to avoid a massive destruction of neurones when cerebral tissue is not oxygenated correctly. For the explicit finite differences method, the necessary stability condition is provided by a reaction‐diffusion equation with non‐linearity given by a decreasing function. The solution to the non‐linear reaction‐diffusion equation of the model can be obtained via one of the two methods: the finite differences (explicit schema) method and the Adomian method.

A new approach of the decomposition method (Adomian) in which the Adomian scheme is obtained in a more natural way than in the classical presentation, is given. A new condition for obtaining convergence of the decomposition series is also included.

This study investigates how federated learning (FL) and human–robot collaboration (HRC) can be used to manage diverse industrial environments effectively. We aim to demonstrate how these technologies not only improve cooperation between humans and robots but also significantly enhance productivity and innovation within industrial settings. Our research proposes a new framework that integrates these advancements, paving the way for smarter and more efficient factories.

This paper looks into the difficulties of handling diverse industrial setups and explores how combining FL and HRC in the mark of Industry 5.0 paradigm could help. A literature review is conducted to explore the theoretical insights, methods and applications of these technologies that justify our proposal. Based on this, a conceptual framework is proposed that integrates these technologies to manage heterogeneous industrial environments.

The findings drawn from the literature review performed, demonstrate that personalized FL can empower robots to evolve into intelligent collaborators capable of seamlessly aligning their actions and responses with the intricacies of factory environments and the preferences of human workers. This enhanced adaptability results in more efficient, harmonious and context-sensitive collaborations, ultimately enhancing productivity and adaptability in industrial operations.

This research underscores the innovative potential of personalized FL in reshaping the HRC landscape for manage heterogeneous industrial environments, marking a transformative shift from traditional automation to intelligent collaboration. It lays the foundation for a future where human–robot interactions are not only more efficient but also more harmonious and contextually aware, offering significant value to the industrial sector.

Contemporary governmentality combines biopolitical and necropolitical logics to establish social, political and physical borders that classify and stratify populations using symbolic and material marks as, for example, nationality, gender, ethnicity, race, sexuality, social class and/or disability. The social sciences have been prolific in the analysis of alterities and, in turn, implicated in the epistemologies and knowledge practices that underpin and sustain the multiplication of frontiers that define essential differences between populations. The purpose of this paper is to develop a strategy that analyze and subvert the logic of bordering inherent in the bio/necropolitical gaze. In different ways, this paper examines operations of delimitation and differentiation that contribute to monolithic definitions of subject and subjectivity.

The authors question border construction processes in terms of their static, homogenizing and exclusionary effects.

Instead of hierarchical stratification of populations, the papers in this special issue explore the possibilities of relationship and the conditions of such relationships. Who do we relate to? On which terms and conditions? With what purpose? In which ethical and political manner?

A critical understanding of the asymmetry in research practices makes visible how the researcher is legitimized to produce a representation of those researched, an interpretation of their words and actions without feedback or contribution to the specific context where the research has been carried out. Deconstructive and relational perspectives are put forward as critical strands that can set the basis of different approaches to research and social practice.

Faltung equations (closed cycle type) have a wide range of biological applications, nonetheless, they are poorly studied. We use a Volterra‐Kostitzin model (which is a Faltung equation) to study the dynamics of a certain species, where the integral term represents a residual action. The complexity of resolution of this non‐linear equation using classical numeric methods is here solved with the Adomian decomposition method. Our method provides the same graphic solution as others do, such as the numeric method Miladie. However, the decomposition method of Adomian has the advantage that neither time nor space are considered discontinuous and that it gives an analytical solution with a reliable approximation.

In some papers G. Adomian has presented a decomposition technique in order to solve different non‐linear equations. The solution is found as an infinite series quickly converging to accurate solutions. The method is well‐suited for physical problems and it avoids linearization, perturbation and other restrictions, methods and assumptions which may change the problem being solved – sometimes seriously – unnecessarily. Proofs of convergence are given by Cherruault and co‐authors. Many numerical studies for physical phenomena, such as Fisher’s equation, Lorentz’s equation and Edem’s equation are given and solved. In this work, the general equation given by ∂ p \over ∂ t = (∇ ⋅(q(x)⋅ ∇p)) + f(x, t) is solved by using decomposition methods, and is compared to other techniques. This equation can be used to describe the motion of a fluid flow in the so‐called reservoir region, where p(x, t) represents the pressure distribution, f(x, t) describes the withdrawal or injection of the fluid, and q(x) is the transmissibility in the reservoir region.

The purpose of this paper is to describe the experience of the Agriculture Engineering School of Barcelona (ESAB), where undergraduate students were involved in field research experiments on organic waste use in agricultural systems.

The paper outlines how the formation of professionals oriented to work for OWM companies has been successfully promoted.

Agricultural systems can assimilate self‐produced organic wastes (OW) and others from different sources. Their management for crop production can generate enormous economic and environmental benefits which can contribute to sustainable development. The implementation of an integrated strategy for OW treatment (OWT) and management (OWM) must be adapted to the characteristics of the specific geographical region and must consider the interrelations among diverse subjects such as: soil science, fertilizer management, plant production, animal husbandry, farm machinery, climate and culture.

The education of future specialists in OWM requires a multidisciplinary education which can be effectively achieved if those topics are incorporated into the educational programs of agriculture engineering schools.

The paper shows how agricultural systems can assimilate self‐produced organic wastes from different sources.