Elliptic Measures and Square Function Estimates on 1-Sided Chord-Arc Domains

In nice environments, such as Lipschitz or chord-arc domains, it is well-known that the solvability of the Dirichlet problem for an elliptic operator in $$L^p$$ L p , for some finite p, is equivalent to the fact that the associated elliptic measure belongs to the Muckenhoupt class $$A_\infty $$ A ∞ . In turn, any of these conditions occurs if and only if the gradient of every bounded null solution satisfies a Carleson measure estimate. This has been recently extended to much rougher settings such as those of 1-sided chord-arc domains, that is, sets which are quantitatively open and connected with a boundary which is Ahlfors–David regular. In this paper, we work in the same environment and consider a qualitative analog of the latter equivalence showing that one can characterize the absolute continuity of the surface measure with respect to the elliptic measure in terms of the finiteness almost everywhere of the truncated conical square function for any bounded null solution. As a consequence of our main result particularized to the Laplace operator and some previous results, we show that the boundary of the domain is rectifiable if and only if the truncated conical square function is finite almost everywhere for any bounded harmonic function. In addition, we obtain that for two given elliptic operators $$L_1$$ L 1 and $$L_2$$ L 2 , the absolute continuity of the surface measure with respect to the elliptic measure of $$L_1$$ L 1 is equivalent to the same property for $$L_2$$ L 2 provided the disagreement of the coefficients satisfy some quadratic estimate in truncated cones for almost everywhere vertex. Finally, for the case on which $$L_2$$ L 2 is either the transpose of $$L_1$$ L 1 or its symmetric part we show the equivalence of the corresponding absolute continuity upon assuming that the antisymmetric part of the coefficients has some controlled oscillation in truncated cones for almost every vertex.

Singular integrals and sublinear operators on amalgam spaces and Hardy-amalgam spaces

In this paper, we establish the extrapolation theory for the amalgam spaces and the Hardy-amalgam spaces. By using the extrapolation theory, we obtain the mapping properties for the Calderón-Zygmund operators and its commutator, the Carleson operators and establish the Rubio de Francia inequalities for Littlewood-Paley functions of arbitrary intervals to the amalgam spaces. We also obtain the boundedness of the Calder{ó}n-Zygmund operators and the intrinsic square function on the Hardy-amalgam spaces.

Measurement of the photon detection efficiency of silicon photomultipliers for the new detector cluster of the Cherenkov gamma-ray telescope TAIGA-IACT equipped with UV filters

This study was devoted to measurements of the UV-range photon detection efficiency (PDE) of OnSemi MicroFJ SiPM detectors use together with custom UV filters and of the transmission coefficient of these filters at 277 nm. The final goal of these measurements was to determine feasibility of the filters for the new detector cluster of the TAIGA-IACT telescope. PicoQuant PLS-270 UV source emitting pulses at 277 nm was calibrated. The obtained dependences of the registered radiation power on the distance between the emission source and the reference detector are well approximated by the inverse square function, hence no significant scattering or absorption influenced the PDE measurements. The dependences of the number of detected photons on the distance between the source and the detector were obtained. These dependencies are also well approximated by the inverse square function. The PDE of SiPM MicroFJ-60035 detector was measured at the level of 10.0 ± 0.7%. The transmission coefficients of the considered set of filters at the wavelength of 277 nm were also obtained. The SL 240-300 filter has a sufficiently high transmission coefficient and it is advisable to use it as a bandpass ultraviolet filter in the new detector cluster of the TAIGA-IACT telescope; the SL 290-590 filter absorbs ultraviolet light quite well and is applicable in the visible range.

Results on exact controllability of second-order semilinear control system in Hilbert spaces

In our manuscript, we extend the controllability outcomes given by Bashirov (Math. Methods Appl. Sci. 44(9):7455–7462, 2021) for a family of second-order semilinear control system by formulating a sequence of piecewise controls. This approach does not involve large estimations which are required to apply fixed point theorems. Therefore, we avoid the use of fixed point theory and the contraction mapping principle. We establish that a second-order semilinear system drives any starting position to the required final position from the domain of the system. To achieve the required results, we suppose that the linear system is exactly controllable at every non-initial time period, the norm of the inverse of the controllability Grammian operator increases as the time approaches zero with the slower rate in comparison to the reciprocal of the square function, and the nonlinear term is bounded. Finally, an example has been presented to validate the results.

Digital-Twin Approach Predicts Fatigue Damage of Marine Risers

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper OTC 30985, “From Data to Assessment Models, Demonstrated Through a Digital Twin of Marine Risers,” by Ehsan Kharazmi and Zhicheng Wang, Brown University, and Dixia Fan, SPE, Massachusetts Institute of Technology, et al., prepared for the 2021 Offshore Technology Conference, Houston, 16–19 August. The paper has not been peer reviewed. Copyright 2021 Offshore Technology Conference. Reproduced by permission. Assessing fatigue damage in marine risers caused by vortex-induced vibrations (VIV) serves as a comprehensive example of using machine-learning methods to derive assessment models of complex systems. A complete characterization of the response of such complex systems usually is unavailable despite massive experimental data and computation results. These algorithms can use multifidelity data sets from multiple sources. In the complete paper, the authors develop a three-pronged approach to demonstrate how tools in machine learning are used to develop data-driven models that can be used for accurate and efficient fatigue-damage predictions for marine risers subject to VIV. Introduction In this study, machine-learning tools are developed to construct a digital twin of a marine riser. The digital twin uses various sources of training data, including field data, experimental data, computational-fluid-dynamics simulations, extracted databases, semiempirical codes, and existing knowledge of underlying physical models. The authors also show that a well-trained digital twin can use the streaming data from a few field sensors efficiently to provide an accurate reconstruction of motion and to provide fatigue-damage prediction. Several machine-learning algorithms have been developed in the literature to predict the life span of the structure through the changes in parameters. To the best of the authors’ knowledge, most existing methods are developed as black boxes that return parameters by only feeding experimental data and therefore are ignorant of the underlying physics. In the first of three approaches, the authors enhance the capabilities of semiempirical codes by developing efficient databases through active learning. In the second approach, the LSTM-ModNet framework is applied to reconstruct and analyze the entire motion of a riser in deep water from sensor measurements through modal decomposition in space and the sequence-learning capability of recurrent neural networks in time. The formulation described in the paper provides a tool that efficiently combines different types of sensor measurements, such as strain and acceleration. In the third approach, a higher level of abstraction is introduced and the nonlinear operator that maps the inflow current velocity to the root-mean-square function of the riser response is approximated. In particular, the newly developed neural network DeepONet is used as a black box to learn the mapping between the input parameters (the inflow velocity, riser bending stiffness, and tension as a function of water depth) to the output parameters (strain, amplitude, and exciting frequencies as a function of water depth). In these approaches, data from the high-mode VIV test is used to train the networks.

The Regularity Problem for Uniformly Elliptic Operators in Weighted Spaces

This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the boundary data belongs to Lebesgue spaces with weights in the Muckenhoupt classes. Our results generalize those of S. Mayboroda (and those of P. Auscher and S. Stahlhut employing the first order method) who considered the unweighted case. To obtain our main results we use the weighted Hardy space theory associated with elliptic operators recently developed by the last two named authors. One of the novel contributions of this paper is the use of an “inhomogeneous” vertical square function which is shown to be controlled by the gradient of the function to which is applied in weighted Lebesgue spaces.

A Smoothed GFEM Based on Taylor Expansion and Constrained MLS for Analysis of Reissner–Mindlin Plate

Based on the Taylor Expansion and constrained moving least square function, a smoothed GFEM (SGFEM) is proposed in this paper for static, free vibration and buckling analysis of Reissner–Mindlin plate. The displacement function based on SGFEM is composed of classical linear finite element shape function and nodal displacement function, which are obtained by introducing the gradient smoothed meshfree approximation in Taylor expansion of nodal displacement function. A constrained moving least square function is proposed for constituting meshfree nodal displacement function. The merits of the proposed SGFEM, including high accuracy, rapid error convergence, insensitive to mesh distortion, free of shear-locking problem, no extra DOFs and temporal stability, etc., are demonstrated by several typical examples and comparisons with other numerical methods.

VAT Efficiency—A Discussion on the VAT System in the European Union

The effectiveness of the tax system can be analysed in various ways. According to the authors one of manifestations of such effectiveness is resistance to tax evasion. This phenomenon is influenced by multiple factors, with few being the level of VAT rates and the number of rates in force in the country concerned. The aim of the considerations is therefore to analyse how the standard VAT rate as well as the number of rates affect the effectiveness of this tax. The research was based on a literature query in the field of value added tax in the European Union. In addition, the problem of tax evasion was indicated and the aggregated data on the size of the tax gap in the Member States were presented. Then, there are the results of the research for 27 European Union countries for 2011–2019. The efficiency of VAT collection was modelled using square function, determining the significance of the parameters of this function, as well as the value of abscissa, which made it possible to group the countries based on how they maintained the efficiency of VAT collection over the analysed period of time. The final part of the study concentrates on the relationship between the efficiency of tax collection and the amount of both the basic rate and the number of rates. The conclusions of the research are as follows: a tax system with a small number of reduced rates, and preferably with one relatively low standard rate, is the system least susceptible to tax fraud. The research also shows a positive correlation between the value of the basic VAT rate along with the number of preferential rates and the scale of the tax gap, i.e., in countries with a higher standard VAT rate and a greater number of preferential rates, the tax gap is greater. The study will enable further investigation into the strategy of determining the optimal VAT rate and the process of its unification. Proposed changes may contribute to increasing the efficiency of VAT administration in EU countries, reducing the shadow economy, tax fraud and positively influencing economic growth.