The Bohr phenomenon for analytic functions on shifted disks

In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \(\Omega_{\gamma}=\bigg\{z\in\mathbb{C} \colon \bigg|z+\frac{\gamma}{1-\gamma}\bigg|<\frac{1}{1-\gamma}\bigg\}\) for \(0\leq \gamma<1.\) We study improved Bohr radius, Bohr-Rogosinski radius and refined Bohr radius for the class of analytic functions defined in \(\Omega_{\gamma}\), and obtain several sharp results.

Pressure reconstruction of a planar turbulent flow field within a multiply-connected domain with arbitrary boundary shapes

Over the past two decades, it has been demonstrated that the instantaneous spatial pressure distribution in a turbulent flow field can be reconstructed from the pressure gradient field non-intrusively measured by Particle Image Velocimetry (PIV). Representative pressure reconstruction methods include the omnidirectional integration (Liu and Katz, 2006; Liu et al., 2016; Liu and Moreto, 2020), the Poisson equation approach (Violato et al., 2011; De Kat and Van Oudheusden, 2012), the least-square method (Jeon et al., 2015), and most recently, the adjoint-based sequential data assimilation method, which also essentially utilizes the Poisson equation to reconstruct the pressure(He et al., 2020). Most of these previous pressure reconstruction examples, however, were applied to simply-connected domains (Gluzman et al., 2017) only. None of these previous studies have discussed how to apply the pressure reconstruction procedures to a multiply-connected domain (Gluzman et al., 2017). To fill in this gap, this paper presents a detailed report for the first time documenting the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply-connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in the current study is the rotating parallelray omni-directional integration algorithm, which, as demonstrated in reference (Liu and Moreto, 2020) based on simply-connected flow domains, offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply-connected domain pressure reconstruction code is conducted using the DNS (Direct Numerical Simulation) isotropic turbulence field available at the Johns Hopkins Turbulence Databases, with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS pressure gradient in the ambient flow field of a shock-induced non-spherical bubble collapse in water (Johnsen and Colonius, 2009). The successful implementation of the parallel ray pressure reconstruction method to multiply-connected domains paves the way for a variety of important applications including, for example, experimental characterization of pressure field changes during the process of cavitation bubble inception, growth and collapse, non-intrusive unsteady aerodynamic force assessment for an arbitrary body shape immersed in flows, and multi-phase flow investigations, etc. In particular, as an immediate follow-up effort, the parallel ray pressure code will be used for the instantaneous pressure distribution reconstruction of the turbulent flow surrounding cavitation inception bubbles occurring on top of a cavity trailing corner based on high-speed PIV measurements.

Recognition Method of Digital Meter Readings in Substation Based on Connected Domain Analysis Algorithm

Aiming at the problem that the number and decimal point of digital instruments in substations are prone to misdetection and missed detection, a method of digital meter readings in a substation based on connected domain analysis algorithm is proposed. This method uses Faster R-CNN (Faster Region Convolutional Neural Network) as a positioning network to localize the dial area, and after acquiring the partial image, it enhances the useful information of the digital area. YOLOv4 (You Only Look Once) convolutional neural network is used as the detector to detect the digital area. The purpose is to distinguish the numbers and obtain the digital area that may contain a decimal point or no decimal point at the tail. Combined with the connected domain analysis algorithm, the difference between the number of connected domain categories and the area ratio of the digital area is analyzed, and the judgment of the decimal point is realized. The method reduces the problem of mutual interference among categories when detecting YOLOv4. The experimental results show that the method improves the detection accuracy of the algorithm.

Approximation by rational functions on doubly connected domains in weighted generalized grand Smirnov classes

UDC 517.5 Let be a doubly connected domain bounded by two rectifiable Carleson curves. In this work, we use the higher modulus of smoothness in order to investigate the approximation properties of -Faber–Laurent rational functions in the subclass of weighted generalized grand Smirnov classes of analytic functions.

Multicoated elastic inhomogeneities of arbitrary shape neutral to multiple fields

We rigorously establish the interesting result that in anti-plane elasticity an elastic epitrochoidal inhomogeneity can be made neutral to multiple uniform fields applied in the matrix via the insertion of two intermediate coatings. Using a two-term conformal mapping function, the simply connected domain occupied by the epitrochoidal inhomogeneity and its surrounding inner and outer coatings is mapped onto the interior of the unit circle in the image plane. The mismatch parameters are determined in an analytical manner by solving a set of two non-linear equations. An elastic inhomogeneity of arbitrary shape can be made neutral to multiple fields through the insertion of N coatings when the proposed mapping function for the simply connected domain occupied by the multicoated inhomogeneity is described in terms of a polynomial of finite degree containing N non-constant terms. In this case, the mismatch parameters are determined by iteratively solving a set of N non-linear equations.

Uniform stresses inside both a non-parabolic inhomogeneity and a non-elliptical inhomogeneity located in the vicinity of a circular Eshelby inclusion

We establish the uniformity of stresses inside both a non-parabolic open inhomogeneity and a non-elliptical closed inhomogeneity interacting with a nearby circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding matrix is subjected to uniform remote anti-plane stresses. Our procedure involves the introduction of a conformal mapping function for the doubly connected domain occupied by the matrix and the circular Eshelby inclusion. Two conditions are established in order to achieve the uniformity property inside each of the two inhomogeneities. Our results indicate that: (a) the internal uniform stresses are independent of the specific shapes of the two inhomogeneities and the existence of the nearby circular Eshelby inclusion; (b) the open and closed shapes of the respective inhomogeneities are significantly affected by the presence of the circular Eshelby inclusion. We also consider the two more complex cases involving: (a) an arbitrary number of circular Eshelby inclusions undergoing uniform eigenstrains; (b) a circular Eshelby inclusion undergoing linear eigenstrains. Detailed numerical results demonstrate the feasibility and effectiveness of the proposed theory.

Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked domain on a tree if and only if it is the pairwise majority rule (also known as the tree-median rule) and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even.