Study of Ballast Track Dynamic Behavior Evaluation Comparative Analysis According to the On-Site Laying of Rectangular-Parallelepiped Fiber Reinforcement Sack

The roadbed reinforcement method using cuboidal fiber reinforcement is an eco-friendly method that compensates for the shortcomings of various existing roadbed reinforcement technologies. A rectangular parallelepiped fiber reinforcement was installed in section oo of the existing line where fine-grained gravel, floating sleepers, and sleeper cracks occurred. The basic physical property test of the upper subgrade was conducted, and the vertical displacement and acceleration of rails and sleepers were compared and analyzed according to the train operation of the reinforced and non-reinforced sections. A comparative analysis of the vertical displacement and acceleration according to train operation after laying the rectangular parallelepiped fiber reinforcement demonstrated that the vertical displacement and acceleration were reduced by up to 84% and 80%, respectively. The dynamic movement of the rail was reduced owing to the reinforcing effect of the rectangular parallelepiped reinforcement, thereby improving the roadbed bearing capacity and stability.

Euclidean Distance Degree and Mixed Volume

We initiate a study of the Euclidean distance degree in the context of sparse polynomials. Specifically, we consider a hypersurface $$f=0$$ f = 0 defined by a polynomial f that is general given its support, such that the support contains the origin. We show that the Euclidean distance degree of $$f=0$$ f = 0 equals the mixed volume of the Newton polytopes of the associated Lagrange multiplier equations. We discuss the implication of our result for computational complexity and give a formula for the Euclidean distance degree when the Newton polytope is a rectangular parallelepiped.

Block Ciphers with Matrices Operating Alternately over Columns and Rows

Abstract—In this paper, we present the dynamic cryptographic algorithms for long states named ACDEL-2D and ACDEL-3D. The first one was inspired by Rijndael and the second one was inspired by 3D, a three-dimensional block cipher. In both proposals, MDS matrices are used alternately on rows and columns of the state and all transformations used in the encryption process are randomly selected depending on pseudorandom sequences. In the block cipher ACDEL-3D the state takes the form of a rectangular parallelepiped or cuboid.Tóm tắt—Trong bài báo này, chúng tôi trình bày các thuật toán mật mã động cho các trạng thái dài, có tên là ACDEL-2D và ACDEL-3D. Thuật toán đầu tiên bắt nguồn từ thuật toán Rijndael và thuật toán thứ hai bắt nguồn từ thuật toán 3D, một thuật toán với khối dữ liệu được biểu diễn ở dạng ba chiều. Cả hai đề xuất đều sử dụng xen kẽ ma trận MDS trong các hàng và cột của trạng thái và tất cả các phép biến đổi được sử dụng trong quá trình mã hóa được chọn ngẫu nhiên tùy thuộc vào chuỗi giả ngẫu nhiên. Trong mật mã khối ACDEL-3D, trạng thái có dạng hình chữ nhật song song hoặc hình khối.

Ideas for improving mathematics teaching in fourth grade of primary school by using the mathematical software GeoGebra

In the paper studying some spatial geometric figures in 4th grade mathematics education is explored. To do this the possibilities of GeoGebra are used. For each of the figures – rectangular parallelepiped, cube, pyramid, cylinder, cone, sphere, drawings are given in order to illustrate the geometric figure as well as to ensure following the basic rule in learning and understanding mathematical concepts – varying the insignificant properties of the concept to make its significant ones stand out.

Application of Jacobi Polynomial and Multivariable Aleph- Function in Heat Conduction in Non-Homogeneous Moving Rectangular Parallelepiped

The present paper deals with an application of Jacobi polynomial and multivariable Aleph-function to solve the differential equation of heat conduction in non-homogeneous moving rectangular parallelepiped. The temperature distribution in the parallelepiped, moving in a direction of the length (x-axis) between the limits x = −1 and x = 1 has been considered. The conductivity and the velocity have been assumed to be variables. We shall see two particular cases and the cases concerning Aleph-function of two variables and the I-function of two variables.

The Keldysh problem for a mixed-type three-dimensional equation with three singular coefficients

В данной статье изучена задача Келдыша для трехмерного уравнения смешанного типа с тремя сингулярными коэффициентами в прямоугольном параллелепипеде. На основании свойства полноты систем собственных функций двух одномерных спектральных задач, доказана теорема единственности. Решение поставленной задачи построено в виде суммы двойного ряда Фурье-Бесселя. In this article, we study the Keldysh problem for a three-dimensional mixed-type equation with three singular coefficients in a rectangular parallelepiped. Based on the completeness property of systems of eigenfunctions of two one-dimensional spectral problems, a uniqueness theorem is proved. The solution to the problem posed is constructed as the sum of a double Fourier-Bessel series.

Comparative Analysis of Support Stiffness Based on On-Site Laying of Rectangular Parallelepiped Fiber Reinforcement Sack

The roadbed reinforcement method, in which a rectangular parallelepiped fiber reinforcement sack is used, is ecofriendly and overcomes the disadvantages of the conventional roadbed reinforcement method. Through large-scale tests, the effects of improving the bearing capacity, stability, and constructability according to the train speed were confirmed. Physical property investigations of the field test were conducted to analyze the conditions of the roadbed. The settlement degree of the site, where the reinforced section and unreinforced section were placed, was measured and analyzed. A rectangular parallelepiped fiber reinforcement sack was laid. Based on the physical properties determined during the field tests, this section was found to be soft ground composed of silt sand with a low bearing capacity. In addition, through comparison and analysis of the degree of settlement caused by the laying of rectangular parallelepiped fiber reinforcement sack, the dynamic vertical displacement of rails and sleepers decreased by at least 84%. It was shown that the track stability improved when the rectangular-parallelepiped fiber reinforcement sack was laid, which reduced the dynamic behavior along and improved the track support.

Nonlocal Problem for a Three-dimensional Elliptic Equation with Singular Coefficients in a Rectangular Parallelepiped

The nonlocal problem for an elliptic equation with two singular coefficients in a rectangular parallelepiped is studied. The uniqueness of the solution of the problem is proved with the use of the method of energy integrals. The spectral Fourier method based on the separation of variables is used to prove the existence of solutions. The solution of the problem is constructed as double Fourier series in terms of a sum of trigonometric and Bessel functions. Under some conditions on parameters and given functions the uniform convergence of the constructed series and its derivatives up to the second order inclusive is proved

A micromagnetic study: lateral size dependence of the macroscopic properties of rectangular parallelepiped Cobalt-ferrite nanoferromagnetic

<span lang="EN-US">The purpose of this study is to provide systematic information through micromagnetic simulations related to the impact of particle size on the magnetic characteristics of Cobalt-ferrite MNP. The micromagnetic computations performed were based on LLG equation. The MNPs sample was simulated in the form of a rectangular parallelepiped with a thickness of 20 nm and square surface with lateral length varies from 10 to 80 nm at an interval of 10 nm. </span><span lang="EN-ID">The results of this study indicate that the size changes in Cobalt-ferrite MNP have a significant impact on various magnetic properties, such as the magnitude of the barrier energy, coercive and nucleation fields, magnetization rate, magnetization curve profile, and magnetization mode.</span><span lang="EN-ID">Cobalt-ferrite MNP with a size of 10 nm shows a single domain with a relatively short magnetization reversal time and high coercive field.</span>