The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.

Existence of wandering and periodic domain in given angular region

Dynamics of composition of entire functions is well related to it's factors, as it is known that for entire functions f and g, fog has wandering domain if and only if gof has wandering domain. However the Fatou components may have different structures and properties. In this paper we have shown the existence of domains with all possibilities of wandering and periodic in given angular region θ.

Fault Detection for Turbine Engine Disk Based on One-Class Large Vector-Angular Region and Margin

Fault detection is an important technique to detect divergence based on unknown abnormalities, which involves establishing a computational model exclusively originated from the key features of the normal samples. The multimodality of process data distribution of engine turbine disk is inevitably affected by incorporation of ambient disturbance; the mean and covariance would vary significantly, resulting in decayed detecting accuracy. By adopting a strategy to maximize vector-angular mean and minimize vector-angular variance simultaneously in the feature space, a one-class large vector-angular region and margin (one-class LARM) framework is systematically conducted for fault detection of turbine engine disk which will enhance the robustness of the dynamic multimode process monitoring. Simulation based on the single mode and multimode of turbine engine disk is thoroughly performed and compared that the results of which solidly validated the favorable efficiency of the proposed method.

A Time-domain Double Diffraction for Non-perfectly Conducting Wedges

A time-domain (TD) double diffraction solution is proposed with the source illumination for one or both sides of non-perfectly conducting wedges. The frequency domain redefined reflection angles as well as modified reflection coefficients are used in the different angular region of wedges for developing TD double diffraction. The accuracy of the proposed model is confirmed with IFFT- FD solution. Finally, the table of computational efficiency has been given for both the methods (TD and IFFT-FD) for hard polarization.

A method for measuring angular bearing errors in the “antenna - radome” system in the phased-array beam scanning region

The paper introduces a method for measuring angular bearing errors in an antenna-radome system in a two-dimensional angular region of scanning of electronically steerable antenna, i.e. phased array antenna, active phased array antenna. The measurements were based on an antenna measuring collimator system - “compact testing ground”. The mathematical expressions used in processing the obtained data are given. To make a matrix of angular bearing errors, measurements are carried out at different angles of the heel of the antenna - radome system when the phased array antenna beam is deflected in oblique planes. To perfect the method at the initial stage, we used a quick-release model of the radome, which has the ability to introduce angular bearing errors

Comparative Study of the Trueness of the Inner Surface of Crowns Fabricated from Three Types of Lithium Disilicate Blocks

This study set out to compare the three-dimensional (3D) trueness of crowns produced from three types of lithium disilicate blocks. The working model was digitized, and single crowns (maxillary left second molar) were designed using computer-aided design (CAD) software. To produce a crown design model (CDM), a crown design file was extracted from the CAD software. In addition, using the CDM file and a milling machine (N = 20), three types of lithium disilicate blocks (e.max CAD, HASS Rosetta, and VITA Suprinity) were processed. To produce a crown scan model (CSM), the inner surface of each fabricated crown was digitized using a touch-probe scanner. In addition, using 3D inspection software, the CDM was partitioned (into marginal, axis, angular, and occlusal regions), the CDM and CSM were overlapped, and a 3D analysis was conducted. A Kruskal–Wallis test (α = 0.05) was conducted with all-segmented teeth with the root mean square (RMS), and they were analyzed using the Mann–Whitney U-test and the Bonferroni correction method as a post hoc test. There was a significant difference in the trueness of the crowns according to the type of lithium disilicate block (p < 0.001). The overall RMS value was at a maximum for e.max (42.9 ± 4.4 µm), followed by HASS (30.1 ± 9.0 µm) and then VITA (27.3 ± 7.9 µm). However, there was no significant difference between HASS and VITA (p = 0.541). There were significant differences in all regions inside the crown (p < 0.001). There was a significantly high trueness in the angular region inside the crown (p < 0.001). A correction could thus be applied in the CAD process, considering the differences in the trueness by the type of lithium disilicate block. In addition, to attain a crown with an excellent fit, it is necessary to provide a larger setting space for the angular region during the CAD process.