Modelling of the reflectance profile of axisymmetrical radiolocation objects using the integral equation method

Based on the first-kind integral equation method for the electric field, the procedure and software for calculating the radar cross-section of axisymmetrical objects, bodies of revolution, are developed. Algorithms are proposed for computation of the matrix of mutual impedances and Green's function of a ring source providing the computation accuracy required for obtaining a stable solution. The method of solution approximation accuracy evaluation by azimuthal harmonics is proposed. Comparison with test examples is carried out and the applicability for solving real-world problems is shown.

A Study on the Development of Carbon Fiber with Electromagnetic Wave Shielding Performance and Sizing Removal State Measurement Algorithm Using Image Processing

In this paper, nickel-plated carbon fiber was fabricated by a dry process method to improve electromagnetic wave shielding performance. In general, carbon fiber is wrapped in a polymer type in manufacturing and is used after removing the sizing in the pretreatment step for dry coating. The existing sizing removal method was used by removing only with a solution or only with compressed air. In this paper, the method of solution and compressed air (hybrid) was added. The state in which the sizing was removed was determined only by the know-how of the experienced person, and in this paper, it is proposed to represent the numerical value by applying the image processing surface analysis technique. As a result, it was possible to numerically indicate that the hybrid method was excellent among the sizing removal methods and it was possible to manufacture the nickel-plated carbon fibers (30 μm, 40 μm, and 100 μm) by a roll-to-roll sputtering method on the sizing-removed spreading carbon fiber roll. The electromagnetic wave shielding performance of 100 nickel-coated carbon fiber measured by the Korea Testing Laboratory showed the highest electromagnetic wave shielding performance from 66.7 (dB) to 73.2 (dB). This is similar to the electromagnetic wave shielding rate of copper, so it can be used as a cable for EV/HEV vehicles, and it is expected to have a great effect of improving the bending characteristics and disconnection phenomenon and improving the lifespan compared to the existing copper wire.

Comparison of the Natural Vibration Frequencies of Timoshenko and Bernoulli Periodic Beams

This paper deals with the linear natural vibrations analysis of beams where the geometric and material properties vary periodically along the beam axis. In contrast with homogeneous prismatic beams, the frequency spectra of such beams are irregular as there exist enlarged intervals between some adjacent frequencies. Presented here are two averaged models of beams based on the tolerance modelling approach. The assumptions of classical Euler–Bernoulli and Timoshenko–Ehrenfest beam theories are adopted as the foundations. The resulting mathematical models are systems of differential equations with constant, weight-averaged coefficients. This makes it possible to apply any classical method of solution suitable for homogeneous beams, such as Galerkin orthogonalization. Here, emphasis is placed on the comparison of natural frequencies neighbouring the frequency band-gaps that are obtained from these two theories. Two basic cases of material and geometric property distribution in a periodicity cell are studied, and the natural frequencies and mode shapes are obtained for a simply supported beam. The results are supported by a comparison with the finite element method and partially exact solutions.

On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations

Multistaged crystallization systems are used in the production of many chemicals. In this article, employing the population balance framework, we develop a model for a column crystallizer where particle agglomeration is a significant growth mechanism. The main part of the model can be reduced to a system of integrodifferential equations (IDEs) of the Volterra type. To solve this system simultaneously, we examine two numerical schemes that yield a direct method of solution and an implicit Runge–Kutta type method. Our numerical experiments show that the extension of a Hermite predictor–corrector method originally advanced in Khanh (1994) for a single IDE is effective in solving our model. The numerical method is presented for a generalization of the model which can be used to study and simulate a number of possible operating profiles of the column.

Synthesis, structure, and visible-light-driven activity of o-YbFeO3/h-YbFeO3/CeO2 photocatalysts

Photo-Fenton-like oxidation of organic substances is one of the key advanced oxidation processes based on the reversible Fe2+↔Fe3+ transition and the generation of a strong oxidant ·OH in the presence of H2O2 and is currently considered as a promising method for the purification of polluted aqueous media. However, the absence of effective and stable photocatalysts of this process, operating under the action of visible light, necessitates the exploratory studies, mainly among iron oxides and ferrites of various compositions and structures. In this work, using the method of solution combustion followed by heat treatment in air the heterojunction nanocomposites based on ytterbium orthoferrite and cerium dioxide of the composition o-YbFeO3/h-YbFeO3/CeO2 (0–20 mol.%) with high absorption in the visible region and advanced photo-Fenton-like activity were obtained. The nanocomposites were studied by EDS, SEM, XRD, BET, and DRS methods. The photo-Fenton-like activity of the nanocomposites was investigated during the degradation of methyl violet under the action of visible (λmax = 410 nm) radiation. As a result, the formation of I-type heterojunction based on stable rhombic (55.4–79.0 nm) and metastable hexagonal (19.5–24.0 nm) modifications of ytterbium orthoferrite (o-YbFeO3 and h-YbFeO3, respectively) and cubic cerium dioxide CeO2 (13.2–19.2 nm) nanocrystals was established. It was shown that the obtained nanocomposites had foamy morphology and were characterized by a specific surface in the range of 9.1–25.0 m2/g, depending on the CeO2 content. It was found that nanocrystalline components were chemically and phase-pure, uniformly spatially distributed over the nanocomposite, and had multiple contacts with each other. Based on this fact and the established electronic structure of the nanocomposite components, the formation of I-type heterojunction with the participation of o-YbFeO3 (Eg = 2.15 eV), h-YbFeO3 (Eg = 2.08 eV), and CeO2 (Eg = 2.38 eV) was shown, the presence of which increased photocatalytic activity of the resulting nanocomposite. The optimal content of CeO2 in the nanocomposite was 5%, and the o-YbFeO3/h-YbFeO3/CeO2–5% sample was characterized by the highest rate constant of photo-Fenton-like degradation of methyl violet under the action of visible light equal to k = 0.138 min–1, which was 2.5 to 5 times higher than for nanocomposites based on ytterbium orthoferrite. The obtained results obtained indicate that the developed nanocomposites can be considered as a promising basis for the advanced oxidation processes for the purification of aqueous media from organic pollutants.

Survey on Mitigating the Problems of Parabolic Reflectors for Efficient Communication

In this paper, various problems associated with parabolic reflectors, its causes and the approach to mitigate these problems are discussed. The problems include; side lobe radiations, edge diffraction, aperture blockage, cross polarisation, feed spill over, feed illumination taper, pointing error, surface error and phase error. These problems have adverse effect on the overall gain, efficiency and directivity of the antenna thereby inhibiting efficient communication process. The result of the survey reveals that, phase error tends to be the most difficult of the aforementioned problems due to the challenges associated with locating the phase centre at reflector’s focus. The aperture blockage seems to have the least method of solution, because the problem can be solved by changing the centre feed to an offset feed. Detailed investigation of these problems and the relevant solutions are necessary, since parabolic reflectors are among the most common antennas with diverse application.

Synthesis Structural and Optical Properties of CMC/MgO Nanocomposites

Nanocomposites were prepared by the method of solution casting with different proportions of magnesium oxide nanoparticles (0, 1, 3, 5, 7 and 9) wt%. The structural and optical properties of nanocomposites of CMC/MgO have been studied. It was well known that the increased content of MgONPs in the method contributes to the peaks of MgONPs being completely integrated and/or disappearing within the CMC diffraction halos in the experimental results of XRD study. The differences in the XRD spectrum indicate that doping with nanoparticles induced a disparity in the microstructure of the polymer. Nanocomposite film scanning electron microscopy (SEM) reveals that MgONPs appear to form aggregates and scatter well in (CMC/MgO) nanocomposite films and at apply 9 wt. It forms a continuous network within the polymer for the percentage of MgONPs to (CMC) polymer. FTIR spectrum revealed the MgONPs has no destructive influence on the polymer structure as no covalent bonds formed between CMC and MgONPs. The optical properties of CMC/MgO nanocomposites were measured in wavelength range (200–900) nm. Experimental studies have shown that the absorbance, absorption coefficient, extinction coefficient, refractive index, actual and imaginary dielectric constant of CMC polymer is improved with an increase in concentrations of MgONPs in nanocomposites. The transmittance and energy gap of CMC polymer are decreased with the increase in the concentrations of MgONPs.

A Modified Spectral Relaxation Method for Some Emden-Fowler Equations

In this chapter, we present a modified version of the spectral relaxation method for solving singular initial value problems for some Emden-Fowler equations. This study was motivated by the several applications that these equations have in Science. The first step of the method of solution makes use of linearisation to solve the model problem on a small subinterval of the problem domain. This subinterval contains a singularity at the initial instant. The first step is combined with using the spectral relaxation method to recursively solve the model problem on the rest of the problem domain. We make use of examples to demonstrate that the method is reliable, accurate and computationally efficient. The numerical solutions that are obtained in this chapter are in good agreement with other solutions in the literature.

Mathematical Word Problems That Contain a Constant in the Course of Mathematics of Primary School in Ukraine

The article is devoted to the research of the place of the mathematical word problems in the course of mathematics of primary school in Ukraine. The researchers define the results in the study of solving math problems, find out the essence of the process of solving math problems, form primary school students’ ability to solve math problems that contain a constant. Among the mentioned are to find the fourth proportional, do the proportional division and find the unknown number by two differences. The paper deals with the organization of educational research of students in order to identify common and distinctive features of the mathematical structures of these types of math problems and their influence on the method of solution. Based on the methodological system of teaching primary school learners to solve math problems by S. Skvortsova, taking into account the essence of the concept of “ability to solve math problems” and the methodical system of forming the ability to solve certain types of math problems, it has been proposed a system of drilling activities for the generalization of mathematical structures and methods of solving math problems that contain a constant value.