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Abstract. In this paper, we study the interpolation properties of anisotropic net spaces Np,q(M), where p = (p1; ...., pn), q = (q1 ...., qn). It is shown that, with respect to the multidimensional interpolation method, the following equality holds [ABSTRACT FROM AUTHOR]

This paper discussed the synchronization of impulsive fuzzy neural networks (FNNs) with uncertainty of information exchange. Since the data of neural networks (NNs) cannot be completely measured in reality, we designed an observer-based impulsive controller on the basis of the partial measurement results and achieved the purpose of reducing the communication load and the controller load of FNNs. In terms of the Lyapunov stability theory, an impulsive augmented error system (IAES) was established and two sufficient criteria to guarantee the synchronization of our FNNs system were obtained. Finally, we demonstrated the validity of the results by a numerical example. [ABSTRACT FROM AUTHOR]

This paper mainly considered the finite-time lag synchronization for two-layer complex networks with impulsive effects. Different types of controllers were designed to achieve the lag synchronization of two-layer complex networks. Several sufficient conditions on lag synchronization in the sense of finite time were derived. The time for synchronization was also estimated. It is important to note that synchronization time was influenced by the initial value, as well as the impulses and impulse sequence. This implied that different impulse effects result in varying synchronization times. Additionally, desynchronizing impulses can extend the synchronization time, whereas synchronizing impulses have the opposite effect. Finally, a numerical example was presented to showcase the practicality and validity of the proposed theoretical criteria. [ABSTRACT FROM AUTHOR]

In this paper, a class of matrices, namely, Drazin-dagger ma- trices, in which the Drazin inverse and the Moore-Penrose inverse com- mute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated. Moreover, some results about the Moore- Penrose inverse, the Drazin inverse and the numerical range of some re- ciprocal matrices are obtained. In particular, the relations between re- ciprocal matrices, Drazin-Dagger matrices and star order are established. Also, some properties of the generalized inverses of the conjugate EP ma- trices are studied. To illustrate the results, some numerical examples are also given. [ABSTRACT FROM AUTHOR]

We analyze the SCARDO model in the case of the 3-element opinion space under specific constraints on the transition table parameters that allows to link the problem at stake to the case of the 2-element opinion space that has been thoroughly studied previously. We characterize the properties of fixed points and support our findings by numerical experiments. Further, we manage to find out those settings that ensure the system almost surely reaches a specific domain in the phase space, after which its behavior can be predicted analytically. [ABSTRACT FROM AUTHOR]

In medical imaging, noise can significantly obscure critical details, complicating diagnosis and treatment. Traditional denoising techniques often struggle to maintain a balance between noise reduction and detail preservation. To address this challenge, we propose an “Efficient Transfer-Learning-Based Fractional Order Image Denoising Approach in Medical Image Analysis (ETLFOD)” method. Our approach uniquely integrates transfer learning with fractional order techniques, leveraging pre-trained models such as DenseNet121 to adapt to the specific needs of medical image denoising. This method enhances denoising performance while preserving essential image details. The ETLFOD model has demonstrated superior performance compared to state-of-the-art (SOTA) techniques. For instance, our DenseNet121 model achieved an accuracy of 98.01%, precision of 98%, and recall of 98%, significantly outperforming traditional denoising methods. Specific results include a 95% accuracy, 98% precision, 99% recall, and 96% F1-score for MRI brain datasets, and an 88% accuracy, 91% precision, 95% recall, and 88% F1-score for COVID-19 lung data. X-ray pneumonia results in the lung CT dataset showed a 92% accuracy, 97% precision, 98% recall, and 93% F1-score. It is important to note that while we report performance metrics in this paper, the primary evaluation of our approach is based on the comparison of original noisy images with the denoised outputs, ensuring a focus on image quality enhancement rather than classification performance.

The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings (F-N-V-Ms), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard (H⋅H) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes.

This paper investigates the dynamics of the SIR infectious disease model, with a specific emphasis on utilizing a harmonic mean-type incidence rate. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. A sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V-L) matrices, is developed to examine the overall trajectory of the model globally. In addition to that, we describe the transmission of infectious disease through a mathematical model using fractal-fractional differential operators. We prove the existence and uniqueness of solutions in the SIR model framework with a harmonic mean-type incidence rate by using the Banach contraction approach. Functional analysis is used together with the Ulam–Hyers (UH) stability approach to perform stability analysis. We simulate the numerical results by using a computational scheme with the help of MATLAB. This study advances our knowledge of the dynamics of epidemic dissemination and facilitates the development of disease prevention and mitigation tactics.