The density of metallic materials, along with strength and corrosion-resistance, is one of the main physical characteristics. This property is critical for nickel alloys, which are widely used in space and aeronautics, where it is extremely important to minimize the mass of each part. When developing new types of the alloys, it is essential to have a reliable and accurate method for estimating density. Unfortunately, no unified method for calculating the density has yet been proposed, except several regression models that give more or less accurate results. In this paper, we analyze and critically evaluate the available approaches, and provide a group of advanced analytical equations that accurately calculate the density of a nickel alloy based on its chemical composition. The method takes into account the spatial fcc structure of the alloys, the molar mass and molar volume of the alloying elements, as well as, the behavior of light ligands. We verify the accuracy of the equation based on real density and chemistry data for 69 nickel alloys. Using all equations, we calculate the density and compare the calculated data with real values. Comparison of the results shows that the proposed method provides the best accuracy of all those considered. The RMSE between the calculated values and the real ones is about 0.07. The error of the regression methods is 0.5 at best. Thus, the proposed approach increases the accuracy of calculating the density of nickel alloys by about an order of magnitude, while significantly simplifying it.

The accuracy and repeatability of the color reproduction in print is determined by the fine tuning of the tone reproduction curves of the basic printing colorants (most often this is CMYK). However, the diversity of manufacturers of printing equipment and dyes introduces an element of significant uncertainty about color uniformity. In addition, the traditional approach does not take into account the effect of hue change when applying the original dyes, as well as, the non-linearity of the hue rise in high and low density areas. Determining the color of base colorants that produces the most uniform tone change is an important engineering challenge. Previously, there was no scientific basis for such calculations. We recently proposed an alternative color correction model based on gradation trajectories as an analogue of gradation curves in the CIE Lab space. We have also described the extension of the approach to double color overlay (gradation surfaces) and its analytical and discrete implications. The trajectories are the geodetic lines on gradation surfaces. In this paper, we propose using the gradation trajectories to determine “ideal” or “true” initial printing dyes for electrophotography. To simplify calculations, natural color discretization in digital printing is used.

Nickel alloys are widely used in the production of gas turbine parts. The alloys show resistance to mechanical and chemical degradation under severe long-term stress and high temperatures. One of the major mechanical properties of the alloys is the high-temperature rupture strength, which is measured after a specimen is heated to a certain temperature and held for a certain time considering deformation. Determining the influence of certain elements on the properties of an alloy is a complex scientific and engineering problem that affects the time and cost of developing new materials. Simulation is a great chance to cut costs. In this paper, we predict a high-temperature strength based on the composition of refractory elements in alloys using a deep learning artificial neural network. We build the model based on prior knowledge of the composition of the alloys, information on the role of alloying elements, type of crystallization, test temperature and time, and the tensile strength. Successful simulation results show the applicability of this method in practice.

Quantifying the spatial characteristics of information stored and disseminated electronically is a complex computational challenge. Flat vector objects such as symbols, tracks, routes, etc. are described using the mathematical apparatus of Bezier curves. Finding the perimeters of such objects, especially in the case of curves of order higher than the third, is associated with certain difficulties. Reducing the order of curves by dividing or splitting them into sub-curves of lower orders, accompanied by some decrease in the accuracy of the estimate, is a convenient method for fast calculating the perimeters of plane figures described by Bezier curves. In this work, we propose an iterative algorithm for determining the arc length of a Bezier curve, which compares different criteria for splitting a curve into sub-curves.

Plane shapes are one of the broadest domains for electronically stored information. Such vector objects, including texts, routes, etc. are often described using Bezier curves. Many data analysis tasks require determination of the perimeters of vector objects, which is associated with significant computational complexity; however, it is far from always necessary to calculate metrics with high accuracy. In this work, we propose splitting Bezier curves into arcs to reduce dimension. Thus, we quickly compute the perimeter of an arbitrary flat figure with limited precision.