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In this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+.

The author uses complex integration to obtain integrable functions with vanishing moments sequence, and then the author considers some operators defined on the vanishing moments subspace.

The author gather several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author constructs explicitly Stieltjes classes with center at well-known probability densities. The author gives a lot of examples, including old cases and new ones.

The author computes the Hilbert transform of powers of |ln⁡x| to construct Stieltjes classes by using a recent result connecting the Krein condition and the Hilbert transform.

The purpose of this paper is to provide an analysis of the performance of a new five-phase doubly fed induction generator (DFIG).

This paper presents the results of a research work related to five-phase DFIG framing, including the development of an analytical model, FEM analysis as well as the results of laboratory tests of the prototype. The proposed behavioral level analytical model is based on the winding function approach. The developed DFIG model was used at the design stage to simulate the generator’s no-load and load state. Then, the results of the FEM analysis were shown and compared with the results of laboratory tests of selected DFIG operating states.

The paper provides the results of analytical and FEM simulation and measurement tests of the new five-phase dual-feed induction generator. The use of the MATLAB Simscape modeling language allows for easy and quick implementation of the model. Design assumptions and analytical model-based analysis have been verified using FEM analysis and measurements performed on the prototype. The results of the presented research validate the design process as well as show the five-phase winding design advantage over the three-phase solution regarding the control winding power quality.

The main disadvantage of the winding function approach-based model development is the simplification regarding omitting the tangential airgap flux density component. However, this fault only applies to large airgap machines and is insignificant in induction machines. The results of the DFIG analyses were limited to the basic operating states of the generator, i.e. the no-load state, the inductive and resistive load.

The novel DFIG with five phase rotor control winding can operate as a regular three-phase machine in an electric power generation system and allows for improved control winding power quality of the proposed electrical energy generation system. This increase in power quality is due to the rotor control windings inverter-based PWM supply voltage, which operates with a wider per-phase supply voltage range than a three-phase system. This phenomenon was quantified using control winding current harmonic analysis.

The paper provides the results of analytical and FEM simulation and measurement tests of the new five-phase dual-feed induction generator.

The purpose of this paper is to analyze the micro-motion of the cylinder block.

Based on the elasto-hydrodynamic lubrication, a numerical model for the cylinder block/valve plate interface is proposed, with consideration of the elastic deformations, the pressure-viscosity effect and asperity contacts. The influence-function method is applied to calculating the actual deformations of the cylinder block and the valve plate. The asperity contact model simplified from Greenwood assumption is introduced into the numerical model. Furthermore, the relationship between the micro-motion and the operating condition, the sealing belt width is discussed, respectively.

The results show an increase in the discharge pressure causes the tilt state and the vibrating motion getting worse, which can be eased by improving the rotational speed, the sealing belt width and the ratio of external and internal sealing belt width.

The proposed research can provide a theoretical reference for the optimizing design of cylinder block/valve plate pair.

An Autodesk Ember three-dimensional (3D) printer was used to print optical components from Clear PR48 photocurable resin. The cured PR48 was characterized by the per cent of light transmitted and the index of refraction, which was measured with a prism spectrometer. Lenses and diffraction gratings were also printed and characterized. The focal length of the printed lenses agreed with predictions based on the thin lens equation. The periodicity and effective slit width of the printed gratings were determined from both optical micrographs and fits to the Fraunhofer diffraction equation. This study aims to demonstrate the advantages offered by a layer-by-layer DLP printing process for the manufacture of optical components for use in the visible region of the electromagnetic spectrum.

A 3D printer was used to print both lenses and diffraction gratings from Standard Clear PR48 photocurable resin. The manufacturing process of the lenses and the diffraction gratings differ mainly in the printing angle with respect to the printer x-y-axes. The transmission diffraction gratings studied here were manufactured with nominal periodicities of 10, 25 and 50 µm. The aim of this study was to optically determine the effective values for the distance between slits, d, and the effective width of the slits, w, and to compare these values with the printed layer thickness.

The normalized diffraction patterns measured in this experiment for the printed gratings with layer thickness of 10, 25 and 50 µm are shown by the solid dots in Figures 8(a)-(c). Also shown as a red solid line are the fits to the experimental diffraction data. The effective values of d and w obtained from fitting the data are compared to the nominal layer thickness of the printed gratings. The effective distance between slits required to fit the diffraction patterns are well approximated by the printed layer thickness to within 14, 4 and 16 per cent for gratings with a nominal 10, 25 and 50 µm layer thickness, respectively.

Chromatic aberration is present in all polymer lenses, and the authors have not attempted to characterize it in this study. These materials could be used for achromatic lenses if paired with a crown-type material in an achromatic doublet configuration, because this would correct the chromatic aberration issues. It is worthwhile to compare the per cent transmission in cured PR48 resin (approximately 80 per cent) to the percent transmission found in common optical materials like BK7 (approximately 92 per cent) over the visible region. The authors attribute the lower transmission in PR48 to a combination of surface scattering and increased absorption. At the present time, the authors do not know what fraction of the lower transmission is related to the surface quality resulting from sample polishing.

There are inherent limitations to the 3D manufacturing process that affect the performance of lenses. Approximations to a curved surface in the design software, the printing resolution of the Autodesk Ember printer and the anisotropy due to printing in layers are believed to be the main issues. The performance of the lenses is also affected by internal imperfections in the printed material, in particular the presence of bubbles and the inclusion of debris like dust or fibers suspended in air. In addition, the absorption of wavelengths in the blue/ultraviolet produces an undesirable yellowing in any printed part.

One of the most interesting results from this study was the manufacture of diffraction gratings using 3D printing. An analysis of the diffraction pattern produced by these printed gratings yielded estimates for the slit periodicity and effective slit width. These gratings are unique because the effective slit width fills the entire volume of the printed part. This aspect makes it possible to integrate two or more optical devices in a single printed part. For example, a lens combined with a diffraction grating now becomes possible.

This paper aims to analyze the bearing characteristics of the high speed train window glass under aerodynamic load effects.

In order to obtain the dynamic strain response of passenger compartment window glass during high-speed train crossing the tunnel, taking the passenger compartment window glass of the CRH3 high speed train on Wuhan–Guangzhou High Speed Railway as the research object, this study tests the strain dynamic response and maximum principal stress of the high speed train passing through the tunnel entrance and exit, the tunnel and tunnel groups as well as trains meeting in the tunnel at an average speed of 300 km·h-1.

The results show that while crossing the tunnel, the passenger compartment window glass of high speed train is subjected to the alternating action of positive and negative air pressures, which shows the typical mechanic characteristics of the alternating fatigue stress of positive-negative transient strain. The maximum principal stress of passenger compartment window glass for high speed train caused by tunnel aerodynamic effects does not exceed 5 MPa, and the maximum value occurs at the corresponding time of crossing the tunnel groups. The high speed train window glass bears medium and low strain rates under the action of tunnel aerodynamic effects, while the maximum strain rate occurs at the meeting moment when the window glass meets the train head approaching from the opposite side in the tunnel. The shear modulus of laminated glass PVB film that makes up high speed train window glass is sensitive to the temperature and action time. The dynamically equivalent thickness and stiffness of the laminated glass and the dynamic bearing capacity of the window glass decrease with the increase of the action time under tunnel aerodynamic pressure. Thus, the influence of the loading action time and fatigue under tunnel aerodynamic effects on the glass strength should be considered in the design for the bearing performance of high speed train window glass.

The research results provide data support for the analysis of mechanical characteristics, damage mechanism, strength design and structural optimization of high speed train glass.

This paper is concerned with the existence of mild solutions for a class of fractional semilinear integro-differential equations having non-instantaneous impulses. The result is obtained by using noncompact semigroup theory and fixed point theorem. The obtained result is illustrated by an example at the end.

As of July 30, 2020, more than 17 million novel coronavirus disease 2019 (COVID-19) cases were registered including 671,500 deaths. Yet, there is no immediate medicine or vaccination for control this dangerous pandemic and researchers are trying to implement mathematical or time series epidemic models to predict the disease severity with national wide data.

In this study, the authors considered COVID-19 daily infection data four most COVID-19 affected nations (such as the USA, Brazil, India and Russia) to conduct 60-day forecasting of total infections. To do that, the authors adopted a machine learning (ML) model called Fb-Prophet and the results confirmed that the total number of confirmed cases in four countries till the end of July were collected and projections were made by employing Prophet logistic growth model.

Results highlighted that by late September, the estimated outbreak can reach 7.56, 4.65, 3.01 and 1.22 million cases in the USA, Brazil, India and Russia, respectively. The authors found some underestimation and overestimation of daily cases, and the linear model of actual vs predicted cases found a p-value (<2.2e-16) lower than the R2 value of 0.995.

In this paper, the authors adopted the Fb-Prophet ML model because it can predict the epidemic trend and derive an epidemic curve.

This study aims to provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation.

The authors shall use the averaging theory, more precisely Theorem $6$.

The main results on the periodic solutions of the fifth-order differential equation (equation (1)) are given in the statement of Theorem 1 and 2.

In this article, the authors provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation.

The purpose of the study is to obtain and analyze vibro-acoustic characteristics.

A unified analysis model for the rotary composite laminated plate and conical–cylindrical double cavities coupled system is established. The related parameters of the unified model are determined by isoparametric transformation. The modified Fourier series are applied to construct the admissible displacement function and the sound pressure tolerance function of the coupled systems. The energy functional of the structure domain and acoustic field domain is established, respectively, and the structure–acoustic coupling potential energy is introduced to obtain the energy functional. Rayleigh–Ritz method was used to solve the energy functional.

The displacement and sound pressure response of the coupled systems are acquired by introducing the internal point sound source excitation, and the influence of relevant parameters of the coupled systems is researched. Through research, it is found that the impedance wall can reduce the amplitude of the sound pressure response and suppress the resonance of the coupled systems. Besides, the composite laminated plate has a good noise reduction effect.

This study can provide the theoretical guidance for vibration and noise reduction.

An appropriate equivalent model is the key to the effective analysis of the system and structure in which permanent magnet takes part. At present, there are several equivalent models for calculating the interacting magnetic force between permanent magnets including magnetizing current, magnetic charge and magnetic dipole–dipole model. How to choose the most appropriate and efficient model still needs further discussion.

This paper chooses cuboid, cylindrical and spherical permanent magnets as calculating objects to investigate the detailed calculation procedures based on three equivalent models, magnetizing current, magnetic charge and magnetic dipole–dipole model. By comparing the accuracies of those models with experiment measurement, the applicability of three equivalent models for describing permanent magnets with different shapes is analyzed.

Similar calculation accuracies of the equivalent magnetizing current model and magnetic charge model are verified by comparison between simulation and experiment results. However, the magnetic dipole–dipole model can only accurately calculate for spherical magnet instead of other nonellipsoid magnets, because dipole model cannot describe the specific characteristics of magnet's shape, only sphere can be treated as the topological form of a dipole, namely a filled dot.

This work provides reference basis for choosing a proper model to calculate magnetic force in the design of electromechanical structures with permanent magnets. The applicability of different equivalent models describing permanent magnets with different shapes is discussed and the equivalence between the models is also analyzed.