Circumcentering approximate reflections for solving the convex feasibility problem

The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Since reflections are based on exact projections, their computation might be costly. In this regard, we introduce the circumcentered approximate-reflection method (CARM), whose reflections rely on outer-approximate projections. The appeal of CARM is that, in rather general situations, the approximate projections we employ are available under low computational cost. We derive convergence of CARM and linear convergence under an error bound condition. We also present successful theoretical and numerical comparisons of CARM to the original CRM, to the classical method of alternating projections (MAP), and to a correspondent outer-approximate version of MAP, referred to as MAAP. Along with our results and numerical experiments, we present a couple of illustrative examples.

Исследование этапов превращения кремния в карбид кремния в процессе атомного замещения методами полного внешнего отражения рентгеновских лучей и рентгеновской дифрактомерии

X-ray diffraction and total external reflection of X-rays (X-ray reflectometry) methods were used to study the successive stages of synthesis of epitaxial SiC films on Si (100) X-ray diffraction and total external X-ray reflection (XRD) methods were used to study successive stages of synthesis of epitaxial SiC films on Si (100) surfaces, (110) and (111) surfaces by the atom substitution method. The data on the transformation evolution of (100) surfaces were studied, (110) and (111) Si, into SiC surfaces. A comparative analysis of the X-ray structural quality of the SiC layers grown on Si by the atom substitution method with the quality of SiC layers grown by Advanced Epi by the standard CVD method. A modified technique for the total outer X-ray reflection method, based on measurements of the intensity of the reflected X-rays using a special parabolic mirror. It is shown that the method of total external reflection method makes it possible to obtain important information about the degree of surface roughness of SiC layers, the evolution of their crystal structure and plasmon energy in the process of Si to SiC conversion.

High-Temperature Superconducting Cable Fault Location Method Based on Improved Time-Frequency Domain Reflection Method and EEMD Noise Reduction

Aiming at the operation and maintenance requirements of the fault location of high-temperature superconducting cables, a fault location method of high-temperature superconducting cables based on the improved time-frequency domain reflection method and EEMD noise reduction is proposed. Considering the cross-term interference problem in the traditional time-frequency domain reflection method, this paper introduces the affine transformation to project the time-frequency distribution of the self-term and the cross term and further highlights the characteristic differences between the two through coordinate transformation, and the particle swarm algorithm is employed to solve the optimal stagger angle of the affine transformation. The unscented particle filter is adopted to separate the cross term, and EEMD noise reduction is introduced to solve the signal noise problem. Finally, two software programs, PSCAD and MATLAB, are employed for joint simulation to build a model of high-temperature superconducting cable. The simulation example shows that the proposed method in this paper can eliminate the cross-term interference of the traditional time-frequency domain reflection method, effectively locate the fault of the high-temperature superconducting cable, and improve the positioning accuracy.

Analysing detection bands of two-spectral reflection method to identify forest species composition

The optical reflection method is considered for detection of the forest areas where coniferous or broadleaved trees are dominant. Statistical modelling of correct detection and false alarm probabilities for identifying dominant (coniferous or broadleaved) tree species by the two-spectral reflection method has been conducted. It has been shown that monitoring enables us to identify dominant (coniferous or broadleaved) tree species with correct detection probability close to 1 and false alarms probability ~ second decimal places for the temperate climate zone at the wavelengths of 532 and 1540 nm or 532 and 1480 nm. As to the subtropical climate zone, due to a great variety of reflection spectra of vegetation, a selection of the spectral detection bands for reliable identification of dominant coniferous or broadleaved tree species is possible only for specific forestlands where the number of evergreen broadleaved and coniferous tree species is relatively small.

Validation of the Effectiveness of Near-Infrared Spectroscopy for Detecting Impurities in Milk Powder using ANN and SVM

Nowadays, there are so many productions on the market that based on dairy product that include milk powder. The milk powder has different categories which is for children, adult and others. The milk powder involves the local product until the import product. The transparency of the content in the milk powder cannot be identified easily and can cause food poisoning to be happened. Hence, with the use of near-infrared spectroscopy, NIRS it can be use easily to detect the content in the food simply. There are many methods in NIRS which is reflectance and absorbance. This method being uses to detect which milk powder is adulterated. Ocean Optic XR-1 ES, USA device and Ocean View software have been used in this project to take data from the sample. The device use wavelength between 200nm-1025nm. The milk powder obtained from the supermarket and nearby stores. Data that have been taken then transferred into suitable table and will go through two different analysis method which is SVM and ANN. The reflection method is not suitable to detect the adulterated milk powder. From the result ANN shows the higher accuracy to classify the pure and Adulterant milk powder.