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Research on social‐ecological systems (SES) has highlighted their complex and adaptive character and pointed to the importance of recognizing their intertwined nature. Yet, we often base our analysis and governance of SES on static and independent objects, such as actors and resources which are not well suited to address complexity and intertwinedness. This bias, which is largely implicit, has its roots in substance ontologies that have influenced most of contemporary science. This paper argues that it is useful to critically reflect on this ontological grounding and develop SES research from a process ontological perspective. Key insights are that process ontological concepts such as process, event and possibility space are able to overcome the dichotomy between the social and the ecological and allow for a conceptualization of continuous change (dynamism) that enhances our understanding of SES as truly intertwined and complex systems. This will enable SES researchers to conceptualize problems as well as corresponding solutions in novel ways which will ultimately support the development of novel governance approaches, from rethinking the aims of policies from managing people towards managing relations between and among people and the natural system. To fully tap the potential which comes with a change in worldview towards a process ontology, changing research approaches and ways of ing are required. Résumé La recherche sur les systèmes socio‐écologiques (SSE) a mis en évidence leur caractère complexe et adaptatif et a souligné l'importance de reconnaître l'enchevêtrement du social et de l’écologique. Pourtant, nos analyses et nos modes de gouvernance se basent souvent sur l'existence d'objets statiques et indépendants, tels que des acteurs ou des ressources qui, soit ne permettent pas d'expliquer/communiquer le caractère complexe de ces systèmes, soit ignorent leur nature enchevêtrée. Ce biais, largement implicite, trouve ses racines dans les ontologies de la substance qui ont influencé la plupart des sciences contemporaines. Cet article propose de réfléchir de manière critique sur les fondements ontologiques des SSE et de s'inspirer d'ontologies qui considèrent les relations et processus comme fondamentaux pour développer des recherches sur les SSE, tenant compte de leur caractère complexe, adaptatif et enchevêtré. Des concepts tels que processus, événements et espace de possibilité permettent de dépasser la dichotomie nature/société et de conceptualiser le changement continu (dynamisme) de telle sorte que notre compréhension des SSE se trouve améliorée. Cette nouvelle perspective permettra de repenser les problèmes des SSE et, par conséquent, de développer de nouvelles approches de gouvernance visant à gérer les relations entre les personnes tout aussi bien qu'entre les personnes et leur environnement. Pour exploiter pleinement le potentiel d'une ontologie des processus, il est nécessaire de modifier nos approches de recherche et nos méthodes d'ion. A free Plain Language Summary can be found within the Supporting Information of this article. A free Plain Language Summary can be found within the Supporting Information of this article.

The aim of this paper is to provide new characterizations for polynomial dichotomies of discrete nonautonomous systems on the half-line. First, we establish equivalent structures for the ranges of projections for a polynomial dichotomy with respect to a sequence of norms. Next, we establish the connections between polynomial dichotomies and other dichotomic behaviors. We obtain for the first time a characterization of polynomial dichotomy with respect to a sequence of norms in terms of ordinary dichotomy and exponential dichotomy of suitable systems with respect to well-chosen sequences of norms. The results are obtained in the most general case, without any additional assumptions regarding the coefficients of the underlying systems.

The brake system requires careful attention for continuous monitoring as a vital module. This study specifically focuses on monitoring the hydraulic brake system using vibration signals through experimentation. Vibration signals from the brake pad assembly of commercial vehicles were captured under both good and defective conditions. Relevant histograms and wavelet features were extracted from these signals. The selected features were then categorized using Nested dichotomy family classifiers. The accuracy of all the algorithms during categorization was evaluated. Among the algorithms tested, the class-balanced nested dichotomy algorithm with a wavelet filter achieved a maximum accuracy of 99.45%. This indicates a highly effective method for accurately categorizing the brake system based on vibration signals. By implementing such a monitoring system, the reliability of the hydraulic brake system can be ensured, which is crucial for the safe and efficient operation of commercial vehicles in the market.

Among Zeno paradoxes the most known are Dichotomy, Achilles, Arrow, and Stadium. These argumentations state that movement is impossible since it is not thinkable. According to the ascendant form of dichotomy, a mobile cannot touch its destination since it always must to reach the half of the distance. The solutions of Diogenes, Aristotle and mathematical analysis are not satisfactory. Finally, the difference between rest and movement can be only conventionally established.

In this paper we investigate a diffusive logistic model with a free boundary in one space dimension. We aim to use the dynamics of such a problem to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. We prove a spreading-vanishing dichotomy for this model, namely the species either successfully spreads to all the new environment and stabilizes at a positive equilibrium state, or it fails to establish and dies out in the long run. Sharp criteria for spreading and vanishing are given. Moreover, we show that when spreading occurs, for large time, the expanding front moves at a constant speed. This spreading speed is uniquely determined by an elliptic problem induced from the original model. [PUBLICATION ABSTRACT]

We give new admissibility criteria for dichotomic behaviours of discrete nonautonomous systems, in infinite dimensional spaces. First, we present admissibility conditions for uniform and exponential dichotomy. Next, our study is focused on polynomial dichotomy, providing new characterizations for this notion by means of some double admissibilities. We obtain two categories of criteria for polynomial dichotomy, based on input-output conditions imposed to some suitable systems such that, for each one, the input sequences belong to certain ℓ p -spaces and the outputs are bounded. We point out the importance of the assumptions regarding the complementarity of the stable subspaces at the initial time and we also discuss the relevance of the concept of solvability (unique or not) in the admissibility criteria for polynomial dichotomies on the half-line. All the results are obtained in the general case, without any additional hypotheses on the systems coefficients and without assuming any growth type properties for the associated propagators. Furthermore, as an application of the admissibility results we establish a robustness property of the polynomial dichotomy under small perturbations.

In order to solve the problem of finding out the frequency of signal through adaptive filter as soon as possible, the adaptive frequency search of adaptive filter has been focused in this paper. According to the change of the signal frequency, the proposed adaptive filter based on the technology of dichotomy decides the frequency of the input signal, realizes the narrowband filtering and the large dynamic variation of specific frequency signal. And the single frequency sinusoidal signal has been theoretically analyzed by the way of DTFT and discrete Fourier transform. Finally, the estimated value of the signal frequency has been preliminary measured by the method of DFT, then based on the characteristic of DFT, the dichotomy search for the real signal frequency has been designed so that the accuracy of frequency measurement would be guaranteed within 2Hz.

This paper introduces a new approach to integral characterizations in the study of dynamical systems, utilizing the connection between uniform dichotomy with differentiable growth rates and uniform exponential dichotomy. Within this framework, we establish integral conditions for these dichotomies, considering both invariant projection-valued functions and projection-valued functions compatible with a skew-evolution cocycle. The method relies on incorporating differentiable growth rates, which extend existing results and provide a broader perspective on dichotomy theory. We hope that these results may contribute to the dichotomy theory of nonautonomous dynamical systems.

This paper presents integral charaterizations for nonuniform dichotomy with growth rates and their correspondents for the particular cases of nonuniform exponential dichotomy and nonuniform polynomial dichotomy of skew-evolution cocycles in Banach spaces. The connections between these three concepts are presented.

The isotopic dichotomy between non-carbonaceous (NC) and carbonaceous (CC) meteorites indicates that meteorite parent bodies derive from two genetically distinct reservoirs, which presumably were located inside (NC) and outside (CC) the orbit of Jupiter and remained isolated from each other for the first few million years of the solar system. Here we review the discovery of the NC–CC dichotomy and its implications for understanding the early history of the solar system, including the formation of Jupiter, the dynamics of terrestrial planet formation, and the origin and nature of Earth’s building blocks. The isotopic difference between the NC and CC reservoirs is probably inherited from the solar system’s parental molecular cloud and has been maintained through the rapid formation of Jupiter that prevented significant exchange of material from inside (NC) and outside (CC) its orbit. The growth and/or migration of Jupiter resulted in inward scattering of CC bodies, which accounts for the co-occurrence of NC and CC bodies in the present-day asteroid belt and the delivery of presumably volatile-rich CC bodies to the growing terrestrial planets. Earth’s primitive mantle, at least for siderophile elements like Mo, has a mixed NC–CC composition, indicating that Earth accreted CC bodies during the final stages of its growth, perhaps through the Moon-forming giant impactor. The late-stage accretion of CC bodies to Earth is sufficient to account for the entire budget of Earth’s water and highly volatile species.