Search Results (17)

Base excitation sources significantly impact vehicle-body vibrations in maglev systems, with the dynamic performance of the suspension system playing a crucial role in mitigating these effects. The second-series suspension system of a maglev vehicle typically employs an air spring, which has a great impact on the stability of maglev vehicle operation. Considering that the suspension system has certain dynamic characteristics under the foundation excitation, the present study proposes the fractional-order nonlinear Nishimura model to describe the memory-restoring force characteristics of the air spring. The fractional-order derivative term is made equivalent to a term in the form of trigonometric function, the steady-state response of the system is solved by the harmonic balance method, and the results are compared with a variety of other methods. The influence of the foundation excitation source on the dynamic behavior of the vibration isolation system is discussed significantly. The variation law of the jump phenomenon and the diversity of periodic motion of the multi-value amplitude curve are summarized. The numerical simulation also revealed the presence of multi-periodic motion in the system when variations occurred in the gap of the suspension system. Combined with the cell mapping algorithm, the distribution law of different attractors on the attraction domain of periodic motion is discussed, and the rule of the transition of periodic motion stability with different fundamental excitation amplitudes is summarized with the Lyapunov exponent. Full article

Global efforts aiming to shift towards renewable energy and smart grid configurations require accurate unit commitment schedules to guarantee power balance and ensure feasible operation under different complex constraints. Intelligent systems utilizing hybrid and high-level techniques have arisen as promising solutions to provide optimum exploration–exploitation trade-offs at the expense of computational complexity. To ameliorate this requirement, which is extremely expensive in non-interconnected renewable systems, radically different approaches based on enhanced priority schemes and Boolean encoding/decoding have to take place. This compilation encompasses various mappings that convert multi-valued clausal forms into Boolean expressions with equivalent satisfiability. Avoiding any need to introduce prior parameter settings, the solution utilizes state-of-the-art advancements in the field of artificial intelligence models, namely Boolean mapping. It allows for the efficient identification of the optimal configuration of a non-convex system with binary and discontinuous dynamics in the fewest possible trials, providing impressive performance. In this way, Boolean mapping becomes capable of providing global optimum solutions to unit commitment utilizing fully tractable procedures without deteriorating the computational time. The results, considering a non-interconnected power system, show that the proposed model based on artificial intelligence presents advantageous performance in terms of generating cost and complexity. This is particularly important in isolated networks, where even a-not-so great deviation between production and consumption may reflect as a major disturbance in terms of frequency and voltage. Full article

Despite the indispensable role of traditional electronic computers in modern society, their limitations in parallel processing capabilities, bit-width constraints, and processor bit-width are becoming increasingly apparent, especially when handling large-scale datasets and complex computational tasks. Although hardware technology and algorithm optimization continue to advance, the arithmetic units of traditional computers—adders—remain constrained by carry delay and bit-width limitations. This bottleneck is particularly pronounced in multiplication operations, mainly when adders are used for partial product accumulation. However, since 2018, the emergence of a new type of Reconfigurable Four-Valued Logic Electronic Processor (RFLEP) has provided a potential solution to these traditional limitations. With its large processor bit-width, flexible bit grouping capabilities, and dynamic hardware function reconfiguration features, this processor has brought revolutionary changes to the field of computing. In this context, this paper proposes and implements a Reconfigurable Four-Valued Logic Multiplication Routine (RFLMR) tailored explicitly for the RFLEP. The RFLMR utilizes the Modified Signed-Digit (MSD) representation method in multi-valued logic combined with the M transformation in four-valued logic to generate partial products. These partial products are then efficiently summed in parallel using the JW-MSD parallel adder, achieving the rapid execution of multiplication operations. Experimental results demonstrate that the multiplication routine based on the RFLEP performs multiplication operations accurately and meets theoretical expectations regarding implementation efficiency and performance. This research not only provides new ideas for developing next-generation high-performance computing systems but also paves the way for exploring more efficient and powerful computing models, heralding a profound transformation in future computing technology. Full article

Due to its high power-to-weight ratio, low weight, and silent operation, shape memory alloy (SMA) is widely used as a muscle-like soft actuator in intelligent bionic robot systems. However, hysteresis nonlinearity and multi-valued mapping behavior can severely impact trajectory tracking accuracy. This paper proposes an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) scheme aimed at enhancing position tracking performance in SMA-actuated systems by addressing hysteresis nonlinearity, uncertain dynamics, and external disturbances. Firstly, a simplified third-order actuator model is developed and a variable gain extended state observer (VGESO) is employed to estimate unmodeled dynamics and external disturbances within finite time. Secondly, a novel nonsingular fast terminal sliding mode control (NFTSMC) law is designed to overcome singularity issues, reduce chattering, and guarantee finite-time convergence of the system states. Finally, the ANFTSMC scheme, integrating NFTSMC with VGESO, is proposed to achieve precise position tracking for the prosthetic hand. The convergence of the closed-loop control system is validated using Lyapunov’s stability theory. Experimental results demonstrate that the external pulse disturbance error of ANFTSMC is 8.19°, compared to 19.21° for the comparative method. Furthermore, the maximum absolute error for ANFTSMC is 0.63°, whereas the comparative method shows a maximum absolute error of 1.03°. These results underscore the superior performance of the proposed ANFTSMC algorithm. Full article

Fixed point theory is a significant area of mathematical analysis with applications across various fields such as differential equations, optimization, and dynamical systems. Recently, multivalued mappings have gained attention due to their ability to model more complex and realistic problems. ln this work, novel classes of nonlinear mappings called k-strictly asymptotically demicontractive-type and asymptotically hemicontractive-type multivalued mappings are introduced in real Hilbert spaces that are symmetric spaces. In addition, we discuss the weak and strong convergence results by considered modified algorithms, and a demiclosedness property, for these classes of mappings are proved. Several non-trivial examples are demonstrated to validate the newly defined mappings. Consequently, the results and iterative methods obtained in this study improve and extend several known outcomes in the literature. Full article

Service-oriented third-party e-commerce platforms have emerged as a new trend in the manufacturing industry. This paper aims to investigate the platforms’ value-added service (VAS) and charging strategies with a dynamic evolution analysis. Considering the change in the user numbers and characteristics of the e-commerce industry, this paper proposes a system dynamics model composed of multi-value chains and a third-party e-commerce platform. The simulation results indicate that the platform should reduce VAS investment and appropriately increase the VAS fee in the early development period. After the number of users stabilizes, the platform should appropriately increase its VAS investment and reduce the VAS fee. When the VAS fee is low, the platform profit first increases and then decreases as the VAS level increases. Differently, the platform profit will first decrease, then increase, and finally decrease as the VAS level improves when the VAS fee is low. This paper further finds that the strong cross-network effect of manufacturers is not always beneficial to the platform. Full article

Hydraulic valves are used to determine the set values of hydraulic quantities (flow rate, pressure, or pressure difference) in a hydraulic system or its part. This is achieved through the appropriate throttling of the stream flowing through the valve, which is automatically set by the operator (e.g., opening the throttle valve). The procedures for determining its static and dynamic properties were described using the example of modeling a two-stage proportional relief valve. Subsequently, the importance of the design and operational parameters was determined using multi-valued logic trees. Modeling began with the determination of equations describing the flow and movement of moving parts in a valve. Based on the equations, a numerical model was then created, e.g., in the Matlab/Simulink environment (R2020b). The static characteristics were obtained as the result of a model analysis of slow changes in the flow rate through the valve. Various coefficients of logical products have not been taken into account in the separable and common minimization processes of multi-valued logic equation systems in any available literature. The results of the model tests can be used to optimize several types of hydraulic valve constructions. Full article

Real-world data obtained from integrating heterogeneous data sources are often multi-valued, uncertain, imprecise, error-prone, outdated, and have different degrees of accuracy and correctness. It is critical to resolve data uncertainty and conflicts to present quality data that reflect actual world values. This task is called data fusion. In this paper, we deal with the problem of data fusion based on probabilistic entity linkage and uncertainty management in conflict data. Data fusion has been widely explored in the research community. However, concerns such as explicit uncertainty management and on-demand data fusion, which can cope with dynamic data sources, have not been studied well. This paper proposes a new probabilistic data fusion modeling approach that attempts to find true data values under conditions of uncertain or conflicted multi-valued attributes. These attributes are generated from the probabilistic linkage and merging alternatives of multi-corresponding entities. Consequently, the paper identifies and formulates several data fusion cases and sample spaces that require further conditional computation using our computational fusion method. The identification is established to fit with a real-world data fusion problem. In the real world, there is always the possibility of heterogeneous data sources, the integration of probabilistic entities, single or multiple truth values for certain attributes, and different combinations of attribute values as alternatives for each generated entity. We validate our probabilistic data fusion approach through mathematical representation based on three data sources with different reliability scores. The validity of the approach was assessed via implementation into our probabilistic integration system to show how it can manage and resolve different cases of data conflicts and inconsistencies. The outcome showed improved accuracy in identifying true values due to the association of constructive evidence. Full article

In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets $p\left(\ge 2\right)$ of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed. Full article

In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an application of the obtained results to dynamical systems. Full article

In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing that the problem undergoes the same cascade of bifurcations as in the Chafee-Infante equation. Second, we study the stability of the fixed points and establish that the semiflow is a dynamic gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections. Full article

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information ($\mathsf{\Phi }$). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements. Full article

With the miniaturization of micro-electro-mechanical system (MEMS) gyroscopes, it is necessary to study their nonlinearity. The phase-frequency characteristics, which affect the start-up time, are crucial for guaranteeing the gyroscopes’ applicability. Nevertheless, although the amplitude-frequency (A-f) effect, one of the most obvious problems in nonlinearity, has been well studied, the phase response of nonlinear gyroscopes is rarely mentioned. In this work, an elaborate study on the characteristics and locking process of nonlinear MEMS gyroscopes is reported. We solved the dynamic equation using the harmonic balance method and simulated the phase-locked loop (PLL) actuation process with an iterative calculation method. It was shown that there existed an apparent overhanging and multi-valued phenomenon in both the amplitude–frequency and phase–frequency curves of nonlinear gyroscopes. Meanwhile, it was ascertained by our simulations that the locking time of PLL was retarded by the nonlinearity under certain conditions. Moreover, experiments demonstrating the effect of nonlinearity were aggravated by the high quality factor of the drive mode due to the instability of the vibration amplitude. A nonlinear PLL (NPLL) containing an integrator was designed to accelerate the locking process. The results show that the start-up time was reduced by an order of magnitude when the appropriate integral coefficient was used. Full article

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution $\omega$ that is optimal in the sense that the error $\sigma (\omega ,\mathcal{J}\omega )$ assumes the global minimum value $\sigma (\theta ,\vartheta )$ . The aim of this paper is to define the notion of Suzuki $\alpha$ - $\Theta$ -proximal multivalued contraction and prove the existence of best proximity points $\omega$ satisfying $\sigma (\omega ,\mathcal{J}\omega )=\sigma (\theta ,\vartheta ),$ where $\mathcal{J}$ is assumed to be continuous or the space $\mathcal{M}$ is regular. We derive some best proximity results on a metric space with graphs and ordered metric spaces as consequences. We also provide a non trivial example to support our main results. As applications of our main results, we discuss some variational inequality problems and dynamical programming problems. Full article

The computational applications of fuzzy sets are pervasive in systems with inherent uncertainties and multivalued logic-based approximations. The existing fuzzy analytic measures are based on regularity variations and the construction of fuzzy topological spaces. This paper proposes an analysis of the general fuzzy measures in n-dimensional topological spaces with monoid embeddings. The embedded monoids are topologically distributed in the measure space. The analytic properties of compactness and homeomorphic, as well as isomorphic maps between spaces, are presented. The computational evaluations are carried out with n = 1, considering a set of translation functions with different symmetry profiles. The results illustrate the dynamics of finite fuzzy measure in a monoid topological subspace. Full article