On Singularities of Certain Non-linear Second-Order Ordinary Differential Equations

The method of blowing up points of indeterminacy of certain systems of two ordinary differential equations is applied to obtain information about the singularity structure of the solutions of the corresponding non-linear differential equations. We first deal with the so-called Painlevé example, which passes the Painlevé test, but the solutions have more complicated singularities. Resolving base points in the equivalent system of equations we can explain the complicated structure of singularities of the original equation. The Smith example has a solution with non-isolated singularity, which is an accumulation point of algebraic singularities. Smith’s equation can be written as a system in two ways. We show that the sequence of blow-ups for both systems can be infinite. Another example that we consider is the Painlevé-Ince equation. When the usual Painlevé analysis is applied, it possesses both positive and negative resonances. We show that for three equivalent systems there is an infinite sequence of blow-ups and another one that terminates, which further gives a Laurent expansion of the solution around a movable pole. Moreover, for one system it is even possible to obtain the general solution after a sequence of blow-ups.

GEOGRAPHIC INFORMATION SYSTEM MAPPING OF KEROSENE BUSINESSES IN JAYAPURA

The role of BBM is very important in people's lives. Fuel is a basic need for rural and urban communities, both as household needs and as business needs. The existence of kerosene in Jayapura is quite evenly distributed. From the results of survey conducted by the OFFICE OF INDUSTRY, COOPERATIVE TRADE AND SMEs that every year the use of LPG as fuel for cooking is still very low, while the use of kerosene from year to year is widely used by local community, it causes more kerosene bussiness but people have difficulty getting information about the location to get the kerosene, therefore we need a system that can help find the location, namely geographic information system that can provide information about fuel oil base points. This system is in symbols form for making the system using QGIS with the PIECES analysis method, the design using Unified Modeling Language (UML) method and the development method using waterfall method. This research produces a system that can be expected to make it easier for the public to know the distribution of kerosene in Jayapura

Full-factor matrix model of accuracy of dimensions performed on multi-purpose CNC machines

Introduction. One of the main reasons that modern multi-purpose CNC machines do not use the capabilities of multi-tool processing is the lack of recommendations for design in this direction and, accordingly, for adjustment schemes. The study of the possibilities of multi-tool processing on multi-purpose machines is the subject of the work. The purpose of research: The problem of developing full-factor matrix models of dimensional accuracy and its sensitivity to the machining process is considered to increase the machining efficiency while ensuring machining accuracy using the technological capabilities of multi-tool machining on modern multi-purpose CNC machines. For this purpose, full-factor matrix models of the size scattering fields performed on multi-tool double-carriage adjustments have been developed, taking into account the cases of processing parts with dimensions that differ sharply in different directions, which are often encountered in practice, and in this case, the significant influence of the turns of the workpiece on the processing error, especially in directions with sharply different overall dimensions. Results of research: The developed accuracy models make it possible to calculate not only plane-parallel displacements of the technological system for double-carriage adjustments, but also angular displacements around base points, take into account the combined effect of many factors – a complex characteristic of the subsystems of the technological system (plane-parallel matrix of compliance and angular matrix of compliance), the geometry of the cutting tool , the amount of bluntness of the tool, cutting conditions, etc. As a result, based on the developed accuracy models, it is possible to obtain several ways to control multi-tool machining, including improving the structure of multi-tool adjustments, calculating the limiting values of cutting conditions. Based on the developed full-factor matrix models, it became possible to develop recommendations for the design of adjustments and the creation of an automated design system for multi-tool machining for a group of modern multi-purpose CNC lathes. Scope of the results: The results obtained can be used to create mathematical support for the design of operations in CAD-systems provided for multi-tool multi-carriage machining performed on multi-purpose machines. Conclusions: The developed models and methodology for simulating the machining accuracy make it possible to increase the accuracy and efficiency of simultaneous machining, to predict the machining accuracy within the specified conditions.

RSAtrace3D: robust vectorization software for measuring monocot root system architecture

Background The root distribution in the soil is one of the elements that comprise the root system architecture (RSA). In monocots, RSA comprises radicle and crown roots, each of which can be basically represented by a single curve with lateral root branches or approximated using a polyline. Moreover, RSA vectorization (polyline conversion) is useful for RSA phenotyping. However, a robust software that can enable RSA vectorization while using noisy three-dimensional (3D) volumes is unavailable. Results We developed RSAtrace3D, which is a robust 3D RSA vectorization software for monocot RSA phenotyping. It manages the single root (radicle or crown root) as a polyline (a vector), and the set of the polylines represents the entire RSA. RSAtrace3D vectorizes root segments between the two ends of a single root. By utilizing several base points on the root, RSAtrace3D suits noisy images if it is difficult to vectorize it using only two end nodes of the root. Additionally, by employing a simple tracking algorithm that uses the center of gravity (COG) of the root voxels to determine the tracking direction, RSAtrace3D efficiently vectorizes the roots. Thus, RSAtrace3D represents the single root shape more precisely than straight lines or spline curves. As a case study, rice (Oryza sativa) RSA was vectorized from X-ray computed tomography (CT) images, and RSA traits were calculated. In addition, varietal differences in RSA traits were observed. The vector data were 32,000 times more compact than raw X-ray CT images. Therefore, this makes it easier to share data and perform re-analyses. For example, using data from previously conducted studies. For monocot plants, the vectorization and phenotyping algorithm are extendable and suitable for numerous applications. Conclusions RSAtrace3D is an RSA vectorization software for 3D RSA phenotyping for monocots. Owing to the high expandability of the RSA vectorization and phenotyping algorithm, RSAtrace3D can be applied not only to rice in X-ray CT images but also to other monocots in various 3D images. Since this software is written in Python language, it can be easily modified and will be extensively applied by researchers in this field.

A 3D computer model of the CaO-MgO-Al2O3 T-x-y diagram at temperatures above 1300 °C

The research analyses the controversies surrounding the technique for the formation of a CaO-Al2O3 binary system and the nature of melting of compounds in it, i.e. whether the 12:7 compound is technically possible and whether the 1:1 and 1:2 compounds are congruently or incongruently melting compounds. It also discusses whether in the CaO-MgO-Al2O3 ternary system the following compounds can be formed: a 3:1:1 compound alone or, in addition to it, two more compounds of 1:2:8 and 2:2:14. A 3D model of the T-x-y diagram was created for the most common version, with six binary and three ternary compounds. Its high-temperature portion (above 1300°C) consisted of 234 surfaces and 85 phase regions. Ternary compounds were formed as a result of three peritectic reactions. Besides them, six quasi-peritectic and three eutecticinvariant reactions occurred in the system with the participation of the melt. The principle of construction for a threedimensional model involved a gradual transition from a phase reaction scheme (which is transformed into a scheme of uni- and invariant states) presented in a tabulated and then in a graphical form (a template of ruled surfaces and isothermal planes corresponding to invariant reactions) to a T-x-y diagram prototype (graphic images of all liquidus, solidus, and solvus surfaces). The design was concluded with the transformation of the prototype into a 3D model of the real system after the input of the base points coordinates (concentrations and temperatures) and the adjustment of curvatures of lines andsurfaces. The finished model provides a wide range of possibilities for the visualisation of the phase diagram, including the construction of any arbitrarily assigned isothermal sections and isopleths. The 3D model was designed with the help of the author’s software PD Designer (Phase Diagram Designer). To assess the quality of the 3D model, two versions of an isothermal section at 1840 °C were compared: model section and a fragment of an experimental section near Al2O3.

Self-Localization of Mobile Robots Using a Single Catadioptric Camera with Line Feature Extraction

This paper presents a novel self-localization technique for mobile robots using a central catadioptric camera. A unified sphere model for the image projection is derived by the catadioptric camera calibration. The geometric property of the camera projection model is utilized to obtain the intersections of the vertical lines and ground plane in the scene. Different from the conventional stereo vision techniques, the feature points are projected onto a known planar surface, and the plane equation is used for depth computation. The 3D coordinates of the base points on the ground are calculated using the consecutive image frames. The derivation of motion trajectory is then carried out based on the computation of rotation and translation between the robot positions. We develop an algorithm for feature correspondence matching based on the invariability of the structure in the 3D space. The experimental results obtained using the real scene images have demonstrated the feasibility of the proposed method for mobile robot localization applications.

Steganographic methods in vector graphics

Various steganographic techniques are used to hide information. Usually, information is hidden in images, audio and video files, text documents, and the like. The article deals with vector images consisting of various mathematical objects (points, lines, curves of the first and second order, Bezier curves, nodes, tangents, base points, etc.). Information hiding techniques alter these mathematical objects, for example, by encoding the coordinates of the base points. The most successful for carrying out steganographic transformations is the SVG vector graphics format, which, due to its structure, makes it easy to manipulate the objects of which it consists. Its broad support across platforms also allows for increased secrecy when transferring sensitive data by sending seemingly ordinary media files. The article discusses two methods (bitwise and the method of patterns) of hiding information in vector images, studied their features, advantages and disadvantages. Various affine transformations that can be used to disrupt the operation of the steganosystem were also investigated. The most common types of affine transformations are the operations of transfer, rotation, shift and scaling with possible variations (offsets along the abscissa and ordinate axes, proportional and non-proportional scaling, with compression and expansion). Most of the methods for embedding information into vector images provide a one-time resistance to affine transformations, while the repeated imposition of operations for changing the position of objects may destroy the message altogether. The methods investigated in the work (bitwise and the method of patterns) implement a higher level of resistance to various kinds of transformations when they are repeated many times, and the conducted experiments clearly demonstrate this. The results obtained show that vector images can indeed be used to hide information, but the resistance against certain affine attacks is not always high.

Investigating the accuracy of the excess determination at the levelling station basing on the results of multiple measurements

The author considers the accuracy of multiple measuring the excess obtained during the work on geodesic support of the definition of certain road sections surface wear-and-tear degree in the Altai region. Basing on these results in nine cycles for seven federal highways’ sections, the accuracy of determining the excess between the reference points and the roadway points was evaluated. It is noted that at performing the work, the standard deviation measuring excess at the station can serve as a criterion for accuracy. Various options of its calculation are considered, depending on which measurements are taken in joint processing. The analysis of the root-mean-square errors obtained as a result of parsing different variants is performed. It is also noted that the data gathered during the research should be considered at engineering-technical leveling as well as in the process of measuring the values of seasonal road base points’ changes in automobile road sections which are surveyed to define the deterioration rate of the road pavement.

Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

We contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.