Search Results (149)

One of the more well-known of Wittgenstein’s thoughts about the nature of religious beliefs is that we go wrong if we try to vindicate or refute religious beliefs in the same way as we do in the sciences. This may make it seem as if Wittgenstein held a view where the world can be divided into two separate spheres, one hard, objective, world of facts where beliefs are held because we have proof for them, and another subjective, softer, vaguer, where our beliefs cannot be proven and are held for completely different reasons. Religious beliefs would thus fall into the second category. In this text, I will argue (1) that even though it is true that Wittgenstein did not think that religious beliefs were on a par with scientific beliefs (held for similar reasons, vindicated in similar ways), he nevertheless did not divide the world into two (in the above mentioned way); and (2) that Wittgenstein’s reflections on the nature of religious beliefs tells us something important about what it means to hold a belief (in general) that challenges several predominant theoretical views about beliefs. I will, with some help from C.S. Lewis, try to show that thinking about the differences in beliefs according to the predominant model—where the “beliefs” are fundamentally different in a scientific and a religious idioms, which leads us to think that one of them has to be endorsing the right, true, belief; or that they are incommensurable—is a model that misrepresents the “conflict.” The matter may not be as intellectual as one may be prone to think—given that the concept of “belief” is at the center—but may rather be best understood (and, hence, the difficulties most efficiently overcome) if we learn to exercise other features of our experience. In particular, we need to learn how to listen and look at things that sound and look strange. A self-critical training of one’s ears is what is needed. (And for these reasons, the article starts in a different register than one might expect.) Full article

This paper proposes an innovative state-sequential sliding mode control (SS-SMC) to suppress chaotic behavior and achieve angular frequency control of incommensurate fractional-order permanent magnet synchronous motor (IFOPMSM) systems. The method is designed to handle both input perturbations and mismatched external disturbances. Conventional sliding mode control (SMC) is robust to matched uncertainties. However, the use of discontinuous sign functions causes chattering. This reduces control accuracy and overall performance. Many methods have been proposed to reduce chattering. Yet, for IFOPMSMs, achieving both robust stabilization and chattering suppression under mismatched disturbances and input uncertainties remains challenging. To address these issues, this study introduces an SS-SMC strategy that combines a fractional-order integral-type sliding surface with a continuous control law. Unlike conventional SMC methods that rely on discontinuous sign functions, the proposed approach uses a continuous control function. This preserves the robustness of traditional SMC while effectively eliminating chattering. The SS-SMC utilizes state-sequential control, allowing a single input to stabilize all system states sequentially and achieve the control objectives while reducing system complexity. Simulation results and comparative analyses confirm the effectiveness of the proposed method. The findings show that the SS-SMC ensures robust angular frequency regulation of the IFOPMSM and suppresses chattering effectively. Full article

Apologies can offer solace and compensate for intangible and emotional harm in social and legal contexts. In some areas of law, an apology offered by a defendant will be factored into the assessment of damages awarded to vindicate the plaintiff’s rights and compensate for loss. This is the case in Australia, the jurisdiction primarily considered in this article, and in many other jurisdictions. There is a danger, however, of assuming that because apologies are compensatory in some sense, they can be used as a basis to reduce damages in tort law more generally. Even though general damages for non-pecuniary loss in fault-based torts are incommensurate to a monetary amount, they are still intended to compensate for actual loss. Empowering defendants to reduce their damages exposure by apologizing might incentivize meaningful apologies which are valued by plaintiffs. It might also create perverse incentives for plaintiffs and defendants alike, further unbalancing a system in which plaintiffs are already at risk of under-compensation. And it raises uncomfortable questions of evidence, reciprocity, agency and expertise which are yet to be fully explored. We argue for these reasons that it is not currently defensible to reduce an award of general damages for negligence, especially for personal injuries, on the basis of an apology by the defendant. Full article

This article examines the persistent conceptual and structural obstacles that pluralism faces within the Euro-United-Statesian art system, particularly in the fields of criticism, art history, and aesthetics. The study situates its inquiry within broader debates around the politics of difference and the decolonization of knowledge, aiming to understand how theoretical frameworks historically incorporated plurality in ways that ultimately neutralize its disruptive potential. Methodologically, the article combines philosophical analysis with a critical rereading of canonical texts by figures such as Clement Greenberg and Arthur Danto, juxtaposed with insights from Indigenous, Black, and decolonial thinkers. The findings suggest that pluralism, while rhetorically embraced, is frequently rendered compatible with a teleological and universalizing narrative that privileges Western aesthetic trajectories. As a result, forms of difference are tolerated only insofar as they can be translated into hegemonic terms. The article concludes by advocating for critical practices that sustain rather than resolve difference, calling for frameworks capable of embracing dissonance, incommensurability, and multiple ontologies without collapsing them into sameness. In doing so, it repositions the contemporary struggle over meaning in art not as a problem to be overcome, but as a necessary symptom of epistemic plurality. Full article

The spread of computer viruses represents a major challenge to digital security, underscoring the need for a deeper understanding of their propagation mechanisms. This study examines the stability and chaotic dynamics of a fractional discrete Susceptible-Infected (SI) model for computer viruses, incorporating commensurate and incommensurate types of fractional orders. Using the basic reproduction number $R_0$, the derivation of stability conditions is followed by an investigation of how varying fractional orders affect the system’s behavior. To explore the system’s nonlinear chaotic behavior, the research of this study employs a suite of analytical tools, including the analysis of bifurcation diagrams, phase portraits, and the evaluation of the maximum Lyapunov exponent (MLE) for the study of chaos. The model’s complexity is confirmed through advanced complexity algorithms, including spectral entropy, approximate entropy, and the $0-1$ test. These measures offer a more profound insight into the complex behavior of the system and the role of fractional order. Numerical simulations provide visual evidence of the distinct dynamics associated with commensurate and incommensurate fractional orders. These results provide insights into how fractional derivatives influence behaviors in cyberspace, which can be leveraged to design enhanced cybersecurity measures. Full article

This paper constructs a fundamental mathematical model to depict the therapeutic effects of two drugs on breast cancer patients. The model is described by fractional order differential equations with two control variables. Two scenarios are considered: the constant control and the optimal control. For the constant control scenario, the existence and uniqueness of the solution of the system are proved by using the fixed point theorem and combining with the Caputo–Fabrizio fractional derivative; then, the sufficient conditions for the existence and stability of the system’s equilibriums are derived. For the optimal control scenario, the optimal control solution is obtained by using the Pontryagin’s maximum principle. To further validate the effectiveness of the theoretical results, numerical simulations were conducted. The results show that the parameters have significant sensitivity to the dynamic behavior of the system. Full article

This study advances circular economy initiatives by advocating for the use of Multi-Criteria Decision-Making (MCDM). MCDM methods address the complex multi-faceted aspects of a product or process. They enable conflicting calculations of energy, cost, environmental criteria, and payback periods to be balanced. A systematic critical systematic review and bibliometric analysis were conducted to investigate the contribution of MCDM to the circular economy. The Scopus database was the primary data source reviewed. The geographical distribution, main research sources, and keyword co-occurrences were analyzed across 31 peer-reviewed book chapters, conference papers, and journal articles. The journal Sustainability (Switzerland) had the most publications (4), followed by the Journal of Business Strategy and the Environment and the Journal of Cleaner Production, each with two articles. Recently MCDM has gained popularity as a tool for evaluating the circular economy. This growing interest may be attributed to the complexity of the circular economy, as MCDM effectively balances multiple environmental criteria while integrating evaluations of economic cost and social impact. Criteria are incommensurable as each criterion has a distinct unit of measurement, making it impossible to compare outcomes across different indicators. MCDM is thus an ideal technique for assessing different options by integrating criteria within testable frameworks. However, no established patterns for selecting specific MCDM methods were identified. This is despite some options (e.g., combinations of AHP and TOPSIS) being used more frequently than others. In conclusion, all the studies identified financial factors as the most significant or highly sensitive issue in the transition toward a circular economy. Full article

Frustrated magnetic systems arising in geometrically constrained lattices represent rich platforms for exploring unconventional phases of matter, including fractional magnetization plateaus, incommensurate orders and complex domain dynamics. However, determining the microscopic spin configurations that stabilize such phases is a key challenge, especially when in-plane and out-of-plane spin components coexist and compete. Here, we combine neutron scattering and magnetic susceptibility experiments with simulations to investigate the emergence of field-induced fractional plateaus and the related criticality in a frustrated magnet holmium tetraboride (HoB₄) that represents the family of rare earth tetraborides that crystalize in a Shastry–Sutherland lattice in the $ab$ plane. We focus on the interplay between classical and quantum criticality near phase boundaries, as well as the role of material defects in the stabilization of the ordered phases. We find that simulations using classical annealing can explain certain observed features in the experimental Laue diffraction and the origin of multiple magnetization plateaus. Our results show that defects and out-of-plane interactions play an important role and can guide the route towards resolving microscopic spin textures in highly frustrated magnets. Full article

In the present work, a Cauchy (initial) problem for a fractional linear system with distributed delays and Caputo-type derivatives of incommensurate order is considered. As the main result, a new straightforward approach to study the considered initial problem via an equivalent Volterra–Stieltjes integral system is introduced. This approach is based on the existence and uniqueness of a global fundamental matrix for the corresponding homogeneous system, which allows us to prove that the corresponding resolvent system possesses a unique measure resolvent kernel. As a consequence, an integral representation of the solutions of the studied system is obtained. Then, using the obtained results, relations between the stability of the zero solution of the homogeneous system and different kinds of boundedness of its other solutions are established. Full article

This article investigates non-fragile synchronization control and circuit implementation for incommensurate fractional-order (IFO) chaotic neural networks with parameter uncertainties. In this paper, we explore three aspects of the research challenges, i.e., theoretical limitations of uncertain IFO systems, the fragility of the synchronization controller, and the lack of circuit implementation. First, we establish an IFO chaotic neural network model incorporating parametric uncertainties, extending beyond conventional commensurate-order architectures. Second, a novel, non-fragile state-error feedback controller is designed. Through the formulation of FO Lyapunov functions and the application of inequality scaling techniques, sufficient conditions for asymptotic synchronization of master–slave systems are rigorously derived via the multi-order fractional comparison principle. Third, an analog circuit implementation scheme utilizing FO impedance units is developed to experimentally validate synchronization efficacy and accurately replicate the system’s dynamic behavior. Numerical simulations and circuit experiments substantiate the theoretical findings, demonstrating both robustness against parameter perturbations and the feasibility of circuit realization. Full article

Cohesive human–robot collaboration can be achieved through seamless communication between human and robot partners. We posit that the design aspects of human–robot communication (HRCom) can take inspiration from human communication to create more intuitive systems. A key component of HRCom systems is perception models developed using machine learning. Being data-driven, these models suffer from the dearth of comprehensive, labelled datasets while models trained on standard, publicly available datasets do not generalize well to application-specific scenarios. Complex interactions and real-world variability lead to shifts in data that require domain adaptation by the models. Existing domain adaptation techniques do not account for incommensurable modes of communication between humans and robot perception systems. Taking into account these challenges, a novel framework is presented that leverages existing domain adaptation techniques off-the-shelf and uses statistical measures to start and stop the training of models when they encounter domain-shifted data. Statistically informed multimodal (domain adaptation by transfer) learning (SIMLea) takes inspiration from human communication to use human feedback to auto-label for iterative domain adaptation. The framework can handle incommensurable multimodal inputs, is mode and model agnostic, and allows statistically informed extension of datasets, leading to more intuitive and naturalistic HRCom systems. Full article

Perovskite-type materials containing Bi³⁺ cations at A sites are interesting from the viewpoints of applications and fundamental science as the lone pair of Bi³⁺ cations often stabilizes polar, ferroelectric structures. This can be illustrated by a lot of discoveries of different new functionalities in bulk and thin films of BiFeO₃ and its derivatives. In this work, we investigated solid solutions of BiCr_1−xFe_xO₃ with 0.1 ≤ x ≤ 0.4 prepared by a high-pressure (HP) method and post-synthesis annealing at ambient pressure (AP). HP-BiCr_1−xFe_xO₃ modifications with 0.1 ≤ x ≤ 0.3 were mixtures of two phases with space groups C2/c and Pbam, and the amount of the C2/c phase decreased with increasing x. The amount of the C2/c phase was also significantly decreased in AP-BiCr_1−xFe_xO₃ modifications, and the C2/c phase almost disappeared in AP-BiCr_1−xFe_xO₃ with 0.2 ≤ x ≤ 0.3. Fundamental, strong reflections of HP-BiCr_1−xFe_xO₃ and AP-BiCr_1−xFe_xO₃ were almost unchanged; on the other hand, weak superstructure reflections were different and showed clear signs of strong anisotropic broadening and incommensurate positions. These structural features prevented us from determining their room-temperature structures. On the other hand, HP-BiCr_1−xFe_xO₃ and AP-BiCr_1−xFe_xO₃ showed high-temperature structural phase transitions to the GdFeO₃-type Pnma modification at T_srt = 450 K (x = 0.1), T_srt = 480 K (x = 0.2), T_srt = 510 K (x = 0.3), and T_srt = 546 K (x = 0.4). Crystal structures of the GdFeO₃-type Pnma modifications of all the samples were investigated by synchrotron powder X-ray diffraction. Magnetic properties of HP-BiCr_1−xFe_xO₃ and AP-BiCr_1−xFe_xO₃ were quite close to each other (HP vs. AP), and the x = 0.2 samples demonstrated negative magnetization phenomena without signs of the exchange bias effect. Full article

This manuscript presents new fractional difference equations; we investigate their behaviors in-depth in commensurate and incommensurate order cases. The work exploits a range of numerical approaches involving bifurcation, the Maximum Lyapunov exponent (LEm), and the visualization of phase portraits and also uses the $C_0$ complexity algorithm and the approximation entropy ApEn to evaluate the intricacy and verify the chaotic features. Thus, the outcomes indicate that the suggested fractional-order map can display a variety of hidden attractors and symmetry breaking if it has no fixed points. Additionally, nonlinear controllers are offered to stabilize the fractional difference equations. As a result, the study highlights how the map’s sensitivity to the fractional derivative parameters produces different dynamics. Lastly, simulations using MATLAB R2024b are run to validate the results. Full article

Lanthanide molybdates are materials known for their mixed proton–ionic conductivity. This study investigates the effects of Pr content and Nb-doping on the crystal structure and electrical properties of the La_5.4−xPr_xMo_1−yNb_yO_12−δ (x = 0, 1.35, 2.7, 4.05, 5.4; y = 0, 0.1) series. The research focuses on two primary objectives: (i) enhancing the electronic conductivity through the use of Pr⁴⁺/Pr³⁺ redox pairs and (ii) increasing the ionic conductivity through Nb⁵⁺ aliovalent doping. The materials were thoroughly characterized by X-ray powder diffraction (XRD), X-ray photoelectron spectroscopy (XPS), transmission and scanning electron microscopy (TEM and SEM), and complex impedance spectroscopy. The average crystal structure of the materials depended significantly on the Pr content. In general, compositions with a higher Pr content crystallize in a cubic fluorite-type structure, whereas those with a lower Pr content stabilize a rhombohedral polymorph. However, detailed TEM studies reveal a more complex local crystal structure characterized by nanodomains and incommensurate modulations. The highest conductivity values were observed in a N₂ atmosphere for compositions with an elevated Pr content, with values of 0.17 and 204.4 mS cm⁻¹ for x = 0 and x = 5.4, respectively, at 700 °C, which is attributed to electronic conduction mediated by the Pr⁴⁺/Pr³⁺ redox pair, as confirmed by XPS. These findings highlight the potential of tailored doping strategies to optimize the conducting properties of lanthanide molybdates for specific high-temperature electrochemical applications. Full article

Systems of incommensurate delay fractional differential equations (DFDEs) with non-vanishing constant delay of retarded type are investigated. It is shown that the mild solutions are well-posed in Hadamard sense on the space of continuous functions. The analysis is local and carried out for finite intervals. The strong results are obtained with weak conditions by using state-of-the-art new methods. No condition on the Lipschitz parameter is added for well-posedness results. Application of this theorem for the Hopfield neural network is carried out. Full article