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In this article, we study two classes of Kirchhoff-type equations as follows: −a+b∫R3∣∇u∣2dxΔu+V(x)u=(Iα∗∣u∣p)∣u∣p−2u+f(u),inR3,u∈H1(R3),\left\{\begin{array}{l}-\left(a+b\underset{{{\mathbb{R}}}^{3}}{\overset{}{\int }}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+V\left(x)u=({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u+f\left(u),\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3},\\ u\in {H}^{1}\left({{\mathbb{R}}}^{3}),\end{array}\right.\hspace{1.85em} and −a+b∫R3∣∇u∣2dxΔu+V(x)u=(Iα∗∣u∣p)∣u∣p−2u+m∣u∣l−2u,inR3,u∈H1(R3),\left\{\begin{array}{l}-\left(a+b\underset{{{\mathbb{R}}}^{3}}{\overset{}{\int }}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+V\left(x)u=({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u+m| u{| }^{l-2}u,\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3},\\ u\in {H}^{1}\left({{\mathbb{R}}}^{3}),\end{array}\right. where a>0a\gt 0, b≥0b\ge 0, α∈(0,3)\alpha \in \left(0,3), (3+α)/30m\gt 0, V:R3→RV:{{\mathbb{R}}}^{3}\to {\mathbb{R}} is a potential function and Iα{I}_{\alpha } is a Riesz potential whose order is α∈(0,3)\alpha \in \left(0,3). Under some assumptions on V(x)V\left(x) and f(u)f\left(u), we can prove that the equations have ground state solutions by variational methods.

Background: Post-stroke spasticity (PSS) is a common complication after stroke and is an important cause of high rates of disability after stroke. At present, modern medicine has made great progress in the treatment of PSS, 'early detection, early treatment' has become a general consensus for the treatment of PSS in the clinic. Clarifying the risk factors of PSS can help to detect and treat the functional disorders caused by PSS at an earlier stage. Methods: This is a retrospective study. 436 stroke patients who visited the Neurology Department of the Third Affiliated Clinical Hospital of Changchun University of Chinese Medicine from June 2020 to November 2020 were selected as study subjects, and finally 257 patients were included in the final analysis, and divided into 101 cases with spasticity and 156 cases without spasticity, depending on whether or not the stroke victim had a spasm at the time of admission. Results: The multivariate regression analysis showed that basal ganglia as the cerebral hemorrhage or infarction site (OR = 4.930, 95%CI = 2.743–8.86, p = 0.000), cerebral hemorrhage or infarction volume (OR = 1.087, 95%CI = 1.016–1.164, p = 0.016) and NIHSS scores (OR = 1.232, 95%CI = 1.089–1.393, p = 0.001) are independent influencing factors and independent risk factors for spasticity (p < 0.05). A risk prediction model for spasticity in stroke patients is derived with the multivariate logistic regression analysis Logit (P) = 1.595 * Basal ganglia +0.084 * infarct volume + 0.208 * NIHSS scores – 2.092. An evaluation of the goodness of fit using the ROC curve showed AUC (95% CI) = 0.786 (0.730–0.843), an indication of a high degree of model fit. Conclusion: Independent risk factors for Post-stroke spasticity include basal ganglia as the cerebral hemorrhage or infarction site, cerebral hemorrhage or infarction volume and NIHSS scores. [ABSTRACT FROM AUTHOR]

In the fields of information science and artificial intelligence, dealing with uncertainty, fuzziness, and complexity has always been a hot and difficult research topic. Especially in modern society, with the continuous development of science and technology, people are facing more and more complex problems. Interval‐valued hesitant fuzzy set (IVHFS) is an extended form of a fuzzy set. It can more flexibly express and handle uncertainty and fuzziness in decision‐making processes. However, in the practical application of the IVHFS, its information measurement is crucial, which is directly related to the application value of the IVHFS in various fields. Therefore, studying the information measurement of the IVHFS has important theoretical significance and practical value for the fields of information science and artificial intelligence. In spite of significant advances, entropy and similarity as the well‐known information measures for interval‐valued hesitant fuzzy information have not yet been thoroughly researched. In this contribution, we investigate information measures in the IVHFS, including nonprobabilistic entropy, similarity, and cross‐entropy. We first analyze the change law of hesitating uncertainty and fuzzy uncertainty in geometric space, and a nonprobabilistic entropy measurement method and its axiomatic definition for IVHFS are further developed. Then, a novel similarity measurement formula for IVHFS and its axiomatic requirements are proposed on the basis of the two nonfuzzy elements (0¯ and 1¯). Furthermore, the novel similarity measure is used to construct the cross‐entropy measure for IVHFS and its axiomatic requirements based on the association between the similarity and the cross‐entropy. Lastly, a MAGDM method is proposed by using the developed three information measures, and the efficacy of the proposed method is demonstrated by a numerical example of emergency communication support capacity evaluation. Comparative analysis and computational cost analysis are implemented to demonstrate the superiority and validity of the proposed information measures. [ABSTRACT FROM AUTHOR]

Summary: This article considers the problem of edge‐based event‐triggered output feedback control for linear multi‐agent systems (MASs) with state‐independent process and measurement noise under undirected communication topologies. The main breakthroughs are the design of distributed event‐triggered output feedback control strategy and the stochastic stability analysis. Toward this, first, according to Kalman filtering theory, An observer is contrasted to optimally estimate the state of each agent. Next, a novel edge‐based event‐triggered mechanism (EBETM) is designed to reduce the communication frequency among agents effectively, and a positive interval between events is enforced in EBETM, which can eliminate the Zeno behavior. Then, stability of the estimation error and the consensus error systems is analyzed, the execution error is estimated and the almost sure consensus is achieved. Finally, a numerical example is given to show that MASs achieves almost sure consensus and there is a positive interval between the events of all edges. [ABSTRACT FROM AUTHOR]

Semi‐additive process (SAP) is a pivotal technique for fabricating integrated circuit (IC) packaging substrates, achieving fine line/space resolution below 20 μm. The adhesion strength between the epoxy composite dielectric layer and electroplated copper is critical for ensuring the long‐term service reliability of high‐performance substrates. Herein, an epoxy composite film suitable for SAP is deposited with copper layer via electroless plating followed by electroplating. The effects of lamination and pre‐curing temperatures in SAP on the butter layer thickness, desmear weight, surface roughness (Ra), and adhesion strength of the plated copper are systematically investigated. The desmear weight decreases with the rising of lamination temperature attributed to the increased butter layer thickness. The lamination temperature is demonstrated to be one of the most influential factors in determining the adhesion strength between the plated copper and the epoxy composite. A high and stable peel strength exceeding 6.0 N cm−1 is achieved under the circumstance of a low Ra of merely 0.95 μm, indicating significant potential for these epoxy composite films in the fabrication of fine‐line and high‐density packaging substrates. [ABSTRACT FROM AUTHOR]

In this paper, we define expanding mappings in the setting of partial metric spaces analogous to expanding mappings in metric spaces. We also obtain some results for two mappings to the setting of partial metric spaces