This paper is motivated by a claim in the classical textbook of Muskhelishvili concerning the Cauchy singular integral operator
S
on Hölder functions with parameters. To the contrary of the claim, a ...counter example was constructed by Tumanov which shows that
S
with parameters fails to maintain the same Hölder regularity with respect to the parameters. In view of the example, the behavior of the Cauchy singular integral operator with parameters between a type of Log-Hölder spaces is investigated to obtain the sharp norm estimates. At the end of the paper, we discuss its application to the
∂
¯
problem on product domains.
The asymptotic profiles of the endemic equilibrium play an important role in determining whether or not eliminating the infectious disease when considering the dispersal rates of populations approach ...to zero or infinity. This paper aims to provide a qualitative analysis of a reaction–diffusion Susceptible–Infective–Recovered–Susceptible epidemic model with standard incidence mechanism and a logistic source in a spatially heterogeneous environment. For this purpose, we first estimate the uniform bounds of the solution of the model. By the theory of uniform persistence, we explore the threshold-type result of the model in terms of the basic reproduction number
ℜ
0
. Compared to the results in Han et al. (Z Angew Math Phys 71:190, 2020) where the growth of susceptible population is adopt by linear source, our theoretical results reveal that controlling the dispersal rates of population cannot eradicate the disease, and the infection component of the steady state solution approaches to nonzero level when the dispersal rates of populations approach to zero or infinity. We also obtain that varying total population enhances persistence of infectious disease, the results are consistent with Li et al. (Z Angew Math Phys 68:96, 2017).
In this paper, we obtain a higher order derivative formula of the solid Cauchy integral operator on smooth bounded domains in
C
. The formula can be used to prove a Calderón–Zygmund type theorem for ...higher order singular integrals, and to obtain a criterion for the solvability of the
∂
¯
problem in the flat category.
We construct examples of twice differentiable functions in
R
n
with continuous Laplacian and unbounded Hessian. The same construction is also applicable to higher order differentiability.
We demonstrate an intermolecular reaction cascade to control the force which triggers crosslinking of a mechanochromic polymer of spirothiopyran (STP). Mechanochromism arises from rapid reversible ...force‐sensitive isomerization of STP to a merocyanine, which reacts rapidly with activated C=C bonds. The concentration of such bonds, and hence the crosslinking rate, is controlled by force‐dependent dissociation of a Diels–Alder adduct of anthracene and maleimide. Because the adduct requires ca. 1 nN higher force to dissociate at the same rate as that of STP isomerization, the cascade limits crosslinking to overstressed regions of the material, which are at the highest rate of material damage. Using comb polymers decreased the minimum concentration of mechanophores required to crosslinking by about 100‐fold compared to previous examples of load‐strengthening materials. The approach described has potential for controlling a broad range of reaction sequences triggered by mechanical load.
A mechanochemical reaction cascade for controlling load‐strengthening of a mechanochromic polymer is realized by using two comb polymers, each containing either spirothiopyran or a Diels–Alder adduct in the proximity of the branch points. The threshold force to trigger crosslinking is increased by ca. 1 nN and the minimum concentration of mechanophores required for crosslinking is decreased by 100‐fold compared to previous examples.
Multi-network elastomers are both stiff and tough by virtue of containing a pre-stretched stiff network that can rupture and dissipate energy under load. However, the rupture of this sacrificial ...network in all described covalent multi-network elastomers is irreversible. Herein, we describe the first example of multi-network elastomers with a reformable sacrificial network containing mechanochemically sensitive anthracene-dimer cross-links. These cross-links also make our elastomers mechanochromic, with coloration that is both persistent and reversible, because the fluorogenic moiety (anthracene dimer) is regenerated upon irradiation of the material. In proof-of-concept experiments we demonstrate the utility of incorporating anthracene dimers in the backbone of the sacrificial network for monitoring mechanochemical remodeling of multi-network elastomers under cycling mechanical load. Stretching or compressing these elastomers makes them fluorescent and irradiating them eliminates the fluorescence by regenerating anthracene dimers. Reformable mechanochromic cross-links, exemplified by anthracene dimers, hold potential for enabling detailed studies of the molecular origin of the unique mechanical properties of multi-network elastomers.
Multi-network elastomers with a reformable sacrificial network containing mechanochemically sensitive anthracene-dimer cross-links manifest reversible mechanochromism and remodeling.
Electric Vehicles (EVs) have been encouraged to penetrate deeper in the vehicle market for the green transportation system. One of the key issues to promote EV industry is to deploy Battery Swapping ...Stations (BSSs) that can satisfy the electricity demand of EV users. Since large scale data of vehicles such as GPS locations and electricity requests can be collected, the data-driven approach can be a cost-effective and useful method to select the locations of BSSs. In this paper, we propose a data-driven framework to solve the BSS location selection problem based on a large scale of GPS data of taxies in metropolitan area. The proposed solution consists of three main steps: Hidden Markov Model (HMM) based map matching and trajectory extraction, electricity consumption rate model based battery swapping demand estimation and clustering strategy based BSS location determination. Compared to the state-of-art deployment baseline, our proposed scheme is more easily to implement in reality and the mean distance error between the location that battery swapping demand is generated and the nearest BSS is reduced by 52.5% and 62.7%, which will definitely reduce the range anxiety of EV users and help improve the will of using EVs.
In this paper, an intelligent insole that contains five wide-range flexible capacitive pressure sensors is developed. The output signal of these five sensors is collected and processed by a portable ...microprocessor system, which is then transmitted to a cloud platform via a Wi-Fi module. The ensuing data visualization is constructed with a WeChat mini-program. The wide-range flexibility is achieved by employing composition materials with a high pressure-sensitive effect. A novel approach is proposed to fabricate flexible pressure-sensitive dielectrics, thereby significantly enhancing the sensitivity and detection range of pressure sensors. The fabrication process involves utilizing polydimethylsiloxane (PDMS) as a flexible substrate, incorporating nano-iron powder and polyvinylidene fluoride as sensitizing materials, and applying an external magnetic field to control the distribution of iron nanoparticles during the curing process of PDMS. Furthermore, a motion detection system tailored for these flexible sensors is developed. By integrating sensor networks with Internet of things technology, the application potential of wide-range flexible pressure sensors in kinematics and medical rehabilitation fields can be effectively realized.
In this paper, we get a Schwarz lemma for pluriharmonic mappings between the unit balls of any dimensions, which generalizes classical Schwarz lemma for bounded harmonic functions to higher ...dimensions. As an application of the Schwarz lemma obtained, a boundary Schwarz lemma is established for pluriharmonic mappings between unit balls with any dimensions.
This paper is concerned with fault detection for a class of nonlinear networked control systems with stochastic transfer delays and data drops. A modified T-S fuzzy model is used to represent the ...considered system. The infinitely distributed time delays are introduced to describe the delays in the controllers. In the fault detection filter, a sequence of stochastic variables is introduced to govern the random occurrence of the stochastic transfer delays and data drops in the measurements, and all of the stochastic variables are mutually independent. Sufficient conditions using regular and piecewise Lyapunov functions are derived for the existence of the designed filter. An example is employed to show the effectiveness and applicability of the proposed fault-detection method.
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