Precision of the Nebra Disc in Astronomical and Geometric Aspect

The astronomical knowledge on the disc has been coded on two planes: horizontal and meridian. The range of sunrise and sunset directions during the year has been described on the horizontal plane. In turn, on the meridian (vertical) plane, the range of changes in the horizontal height and declination of the Sun in the upper culmination during the year and the Moon in its 18.61-year cycle were described. The relationships between the latitude of the place of observation, the horizontal height of the celestial body and its declination were described by means of geometric constructions. The presented article is a continuation of two publications [1] and [2], which describe the decryption of the Nebra disc. These publications were based on the interpretation of the results of angular measurements, made using a protractor with a scale of 0.5 degrees, without the use of a computer. The presented publication is based on a digital disc image obtained by means of its digitization. The obtained data was used for further calculations based on analytical geometry and graphic programs. This allowed to obtain results in a linear measure with a precision of less than 1 mm. PRECYZJA DYSKU Z NEBRY W ASPEKCIE ASTRONOMICZNYM I GEOMETRYCZNYM Wiedza astronomiczna na dysku została zakodowana na dwóch płaszczyznach: horyzontalnej i południkowej. Na płaszczyźnie horyzontalnej (poziomej) opisano zakres kierunków wschodu i zachodu Słońca w ciągu roku. Z kolei na płaszczyźnie południkowej (pionowej) opisano zakres zmiany wysokości horyzontalnej i deklinacji Słońca w kulminacji górnej w ciągu roku oraz Księżyca w jego 18,61-rocznym cyklu. Za pomocą konstrukcji geometrycznych opisano związki między szerokością geograficzną miejsca obserwacji, wysokością horyzontalną ciała niebieskiego i jego deklinacją. Prezentowany artykuł jest kontynuacją dwóch publikacji: [1], [2], w których opisano deszyfrację dysku z Nebry. Publikacje te były oparte na interpretacji wyników pomiarów kątowych, wykonanych za pomocą kątomierza o podziałce 0,5 stopnia, bez użycia komputera. Prezentowana publikacja bazuje na cyfrowym obrazie dysku, uzyskanym za pomocą jego digitalizacji. Uzyskane dane wykorzystano do dalszych obliczeń opartych na geometrii analitycznej oraz programach graficznych.

Linear interpolated multi-objective economic emission scheduling using grey wolf optimizer: a strategic balance and solution with diverse load pattern

Purpose The purpose of this paper is to focus on the cost-effective and environmentally sustainable operation of thermal power systems to allocate optimum active power generation resultant for a feasible solution in diverse load patterns using the grey wolf optimization (GWO) algorithm. Design/methodology/approach The economic dispatch problem is formulated as a bi-objective optimization subjected to several operational and practical constraints. A normalized price penalty factor approach is used to convert these objectives into a single one. The GWO algorithm is adopted as an optimization tool in which the exploration and exploitation process in search space is carried through encircling, hunting and attacking. Findings A linear interpolated price penalty model is developed based on simple analytical geometry equations that perfectly blend two non-commensurable objectives. The desired GWO algorithm reports a new optimum thermal generation schedule for a feasible solution for different operational strategies. These are better than the earlier reports regarding solution quality. Practical implications The proposed method seems to be a promising optimization tool for the utilities, thereby modifying their operating strategies to generate electricity at minimum energy cost and pollution levels. Thus, a strategic balance is derived among economic development, energy cost and environmental sustainability. Originality/value A single optimization tool is used in both quadratic and non-convex cost characteristics thermal modal. The GWO algorithm has discovered the best, cost-effective and environmentally sustainable generation dispatch.

EFFECTS OF IMPACTS OF COVERING ROLLERS ON GENERAL FORCES OF SMALL-SIZED TILLAGE MACHINE

Increasing the efficiency of agricultural production, in particular the production of crop products in personal subsidiary plots, depends on the development and implementation of high-tech machines and their working units. The need for small-sized tillage equipment is increasing from year to year. But in order to increase the functionality of the equipment and the quality of soil preparation for sowing, it is necessary to study the possibility of using various additional working units. The purpose of the work is theoretical studies of the movement and kinematic connection of a trailed slatted-spiral roller with a walk-behind tractor, which make it possible to substantiate rational design and technological parameters of a small-sized tillage tool. The study used the provisions of classical mechanics and analytical geometry, methods of equilibrium and motion of mechanical systems based on differential and integral principles of mechanics. The design of active and passive rollers for a walk-behind tractor is considered, which allows to qualitatively prepare the soil for sowing at the depth of seeding, the influence of potential and non-potential effects on their generalized forces is revealed, the angular velocity and their acceleration are determined, as well as the dynamic characteristics of the moment of inertia of the rollers relative to the axes of rotation X4 and Z4 and their frames relative to the axes of rotation X3 and Z3. The difference in the generalized force for a passive roller relative to the angle φ 5.49 N∙m was obtained. The angular speed of the active roller is 23.0 rad/s higher than that of the passive roller, and as a result of research it was revealed that the moments of inertia of the active roller and its frame relative to the axles are significantly higher than that of the passive roller. Generalized forces for an active roller relative to the angle q = 2.58 N∙m and relative to the angle φ = 1.98 N∙m, for a passive roller - relative to the angle q = 2.32 N∙m and relative to the angle φ = 7.47 N∙m. The generalized forces for the potential effects of an active roller are Qθa=1.58 N∙m, Qφa=2.26 N∙m, for a passive roller Qθn=1.32 N∙m, Qφn= 4.60 N∙m. Mθa = 1 N∙m, Mφa = 114.63 N∙m; passive roller - respectively Mθn = 1 N∙m, Mφn = 178.9 N∙m

Automated handling of complex chemical structures in Z-matrix coordinates - the chemcoord library

In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimisations with non-linear constraints. Analytical gradients for the transformation between the coordinate systems were derived for the first time, which allows analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimisation was coupled with a Symbolic Algebra package to support arbitrary non-linear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. Sample applications are provided for a number of common chemical reactions and illustrative examples where these new algorithms can be used to automatically produce chemically reasonable structure interpolations, or to perform non-linearly constrained optimisations of molecules.

Way to improve efficiency of teaching linear algebra to students with health disabilities by means of enlarged didactic units

Presented is enlarged didactic units developed by P.M. Erdniev for teaching mathematics, that improves the ability of students to understand educational material. This effect is achieved as a result of organizing the educational process according to the principles of complementarity of teaching methods and the spatial and temporal combination of interrelated elements of knowledge. Among the basic mathematical disciplines taught at Bauman Moscow State Technical University for students with disabilities the most difficult discipline is Linear Algebra, which is due to its content and various problems with students’ health. Linear Algebra is largely based on the theory from Analytical Geometry that is quite well perceived by students with disabilities. A comparative analysis of these disciplines shows that the enlarged didactic units linking these disciplines together can significantly simplify the study of Linear Algebra. However, due to difficulties with scheduling the time gap between these disciplines can be up to two semesters, which makes it impossible to directly use the enlarged didactic units. To solve this problem, we introduce the supporting discipline "Cognitive technologies for supporting the discipline Linear Algebra" which runs in parallel with Linear Algebra and which is based on the material of Analytical Geometry. Forming its content in close connection with Linear Algebra in accordance with the main principles of the enlarged didactic units, we smoothly lead students to the understanding of abstract concepts of Linear Algebra, reducing the complexity of learning.

Steganalysis of the methods of concealing information in graphic containers

Aim. Today, there is a pressing matter of protection against steganography-based attacks against information systems. These attacks present a danger as they use the most common data files – especially graphics files – as containers that deliver malicious code to a system or cause a leak of sensitive information. Developing methods of detecting such hidden information is the responsibility of a special subsection of steganography, the steganalysis. Such methods should be extensively used in computer forensics as part of security incident investigation, as well as in automated security systems with integrated modules for analyzing data files for malicious or dangerous information. An important feature of such activities is the need to examine a wide variety of elements and containing files. In particular, it is required to verify not only the colour values of the pixels in images, but their frequency characteristics as well. This raises a number of important questions associated with the best practices of applying steganalysis algorithms and making correct conclusions based on the outputs. The paper aims to briefly analyse the most important and relevant methods of steganalysis, both spatial and frequency, as well as to make conclusions regarding their performance and ways to analyse the outputs based on the test results of the software that implements such methods. Methods. The steganalysis of concealment within the least significant bits of an image’s pixels uses Pearson’s Chi-square statistical analysis, as well as the Regular-Singular method that involves signature analysis of pixel groups and analytical geometry tools for estimating the relative volume of the hidden message. The Koch-Zhao method of steganalysis is used for the purpose of detecting information embedded in the frequency-domain image representation. It also allows identifying the parameters required for extracting the hidden message. Results. A software suite was created that includes the software implementations of the analysed methods. The suite was submitted to a number of tests in order to evaluate the outputs of the examined methods. For the purpose of testing, a sample of images of various formats was compiled, in which information was embedded using a number of methods. Based on the results of the sample file analysis, conclusions were made regarding the efficiency of the analysed methods and interpretation of the outputs. Conclusion. Based on the test results, conclusions were made on the accuracy of the steganalysis methods in cases of varied size of the embedded message and methods of its concealment. The patterns identified with the help of the analysis outputs allowed defining a number of rules for translating the outputs into conclusions on the identification of the fact of detection of hidden information and estimation of its size.

Surface Texture Measurement with Profile Method Using Six-Axis Coordinate Measuring Machine

Currently the measurement of surface texture in mechanical engineering is traditionally carried out using profilometers. Modern profilometers do not allow measuring of surfaces with complex shapes. This is due to the different sensitivity of the sensor and the discreteness of the movements along the axes of the Cartesian coordinate system. Coordinate Measuring Machines are devoid of such a drawback. However, stylus of the coordinate measuring machine has a diameter many times larger than the diamond stylus of the profilometer. Therefore, there is a mechanical filtering effect, that affects the results of measuring the parameters of the surface texture. In this paper a mathematical model of the contact of the spherical stylus and a rough surface based on analytical geometry is proposed. Influence of the diameter of the spherical stylus on the maximum measurement errors of a amplitude parameters are investigated. Seven amplitude parameters Rp, Rv, Rz, Ra, Rq, Rsk, Rku of the surface texture are modeled. Coordinate measuring machine and profilometer with stylus diameter of 2 μm measurement results are compared. it was concluded that the stylus diameter of the coordinate measuring machine when measuring the surface texture should be no more than 20 μm.

ANALISIS KEBUTUHAN MAHASISWA CALON GURU MATEMATIKA TERHADAP APLIKASI GEOGEBRA PADA PEMBELAJARAN GEOMETRI ANALITIK

The purpose of this study was to analyze the needs of the GeoGebra application in mathematics learning, especially the learning of analytic geometry for prospective mathematics teacher students. This research is descriptive quantitative research with a survey method. Participants in this study were prospective teacher students who had taken a course in analytic geometry at a university in Bandung, Indonesia. The sample of this research is student-teacher candidates in the sixth, fourth and second semesters. The total sample was 72 students with 20 males and 52 females. The data collection instruments used questionnaires and interviews. Based on the results of the study, it is known that when learning analytical geometry, most students have difficulty visualizing geometric shapes so that students feel they need GeoGebra as a learning medium in lectures on analytic geometry.

Antoni Wyrwicz – professor of higher mathematics at the Vilnius university (1817–1831)

Antoni Wyrwicz (1791–1865) was a professor of higher mathematics at the Vilnius university in the period from 1817 until 1831. Wyrwicz taught algebra by tractate of Sniadecki and Burdon, spherical trigonometry by Sniadecki, Cagnoli, Delambre Neper, astronomy by Delambre and Biot. Wyrwicz in 1819 published translation of Biot Analytical geometry. From 1824 until 1831 Wyrwicz taught differential and integral calculus by Lacroix and Lagrange. He translated 6 school books for algebra from Lacroix and 6 school books for geometry from Legendre.