intersection line
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Objective. The aim of the study is to develop a method for determining the coordinates of the earthquake hypocenter using various combinations of second and fourth order figures as a geo-locus of the hypocenter position points.Method. It is known that the line of intersection of figures of the second and fourth orders, in the case of coincidence of focuses, is a circle. To determine the coordinates of the earthquake source, data from seismographs are used, which are used to construct figures of the second and fourth order, the intersection point of which is the hypocenter. When using data from two seismic sensors, there are two figures, the intersection line of which is a circle. A sphere with a radius equal to the radius of the circle is constructed through the center of this circle. For the other two pairs of seismic sensors, two more spheres are also formed, The intersection point of the three spheres obtained is the sought-for hypocenter of the earthquake.Result. A method has been developed for determining the coordinates of an earthquake source using different shapes of the second and fourth orders for different pairs of seismic sensors.Conclusion. The method allows one to select one of the second or fourth order figures for different pairs of seismic sensors, which makes it possible to reduce the error in determining the source coordinates.

An investigation of spin waves interacting with antiferromagnetic spin textures is meaningful for future spintronic and magnonic-based memory and logic applications. In this work, we numerically study the skyrmion dynamics driven by circularly polarized spin waves in antiferromagnets and propose a method of suppressing the Hall motion. It is demonstrated that the application of two circularly polarized spin waves with opposite chirality allows the skyrmion motion straightly along the intersection line of the two spin wave sources. The skyrmion speed depending on these parameters of the spin waves and system is estimated, and a comparison with other methods is provided. Furthermore, two depinning behaviors of the skyrmion related to the strengths of the defect are also observed in the simulations. Thus, the proposed method could be used in precisely modulating the skyrmion dynamics, contributing to skyrmion-based memory device design.

A marginal field defines as an oil and/or gas field that has a short production period, low proven reservoir, and could not be exploited using existing technology. As the demand for oil and gas keeps increasing, one of the solutions to tackle the issues is to build the modified platform which came to be more minimalist to conduct the oil and gas production in the marginal field. Naturally, the minimum offshore structures are cost less but low in redundancy, therefore, pose more risks. Although the study on the minimum structures is still uncommon, there are opportunities to find innovative systems that need to have a further analysis toward such invention. Therefore, this study took the modified jacket platform as a minimum structure, and local stresses analysis by using finite element method is applied for the most critical tubular joint with multiplanarity of the joint is taking into account. The analysis was carried out using the finite element program of Salome Meca with three-dimensional solid elements are used to model the multiplanar joint. Various loading types of axial force, in-plane bending moment, and out-of-plane bending moment are applied respectively to investigate the stress distribution along the brace-chord intersection line of the tubular joint. The results show that the hotspot stress occurred at a different point along each brace-chord intersection line for each loading type. Finally, as compared to the in-plane bending moment or out-of-plane bending moment loading types, the axial force loading state is thought to generate greater hotspot stress.

Introduction. Standard eye enucleation (EE) may not always guarantee a sufficient length of resection of the optic nerve (ON) so that the tumor cells do not spread along the optic nerve at the intersection line. Surgical access and the scope of surgical intervention are determined by the spread and localization of the tumor, as well as the qualification of the operating team.Purpose — to evaluate the role of extended surgical interventions in the spread of extraocular tumors on the ON.Materials and methods. The study included 9 patients with retinoblastoma (RB) and macroinvasion of the ON during primary magnetic resonance imaging (MRI) and/or micromorphological invasion of the ON resection line after EE. 4 of the 9 patients were treated with primary/secondary EE, induction chemotherapy (CT) and high-dose CT (HDCT), radiation therapy (RT). 5 out of 9 patients underwent secondary extended surgical interventions: exenteration of the orbit (n = 1), osteoplastic lateral orbitotomy with precanal resection of the ON (n = 2) in combination with EE in one case, subfrontal craniotomy (n = 1) and orbitozygomatic craniotomy (n = 1) with prechiasmal resection of the ON and EE with adjuvant RT (excluding the latter case) and CT, without HDCT.Results. It should be noted that the overall survival (OS) of 5 patients with complete microscopic resection (R0) after extended secondary operations was 75 ± 0.217 % with an average follow-up period of 77.25 ± 18.8 months, while in 4 patients with R1 (n = 4) without secondary extended operations with HDCT reached only 50 ± 0.25 % with an average follow-up period of 57 ± 24.8 months.Conclusion. MRI is mandatory for the primary diagnosis of RB, especially when there is a risk of the tumor spreading through the ON. Secondary surgery with R0-resection has a positive effect on survival. The need for adjuvant RT and CT after surgery should be discussed.

Introduction. Surface plastic deformation is an effective way to improve the operating performance of machine parts. One of the promising approaches to the design of surface hardening technological processes is the technological inheritance mechanics. To calculate the hereditary parameters characterizing the accumulated deformation and damage to the metal, it is possible to simulate spinning as a process of plane fractional deformation, which significantly reduces the time required for modeling the process. However, upon rotation of the plane in which the stress-strain state is considered, the roller profile changes. The aim of the work is to assess the magnitude of the change in the roller profile in the deformation plane during deformation as an important factor ensuring the accuracy of the solution obtained. Research methods. The roll profile in the warp plane is defined by the intersection line of the roll surface and this plane. The paper presents the procedure for calculating the coordinates of the points of intersection lines, which are curves of the fourth order, depending on the geometric dimensions of the roller and the part, as well as the angle of inclination of the deformation plane. Results and discussion. To estimate the value of the roller profile change, the coordinates of the points of the intersection lines of the roller surface and the deformation plane are determined for the rolling modes corresponding to a sufficiently developed plastic deformation, the obtained lines are approximated in the coordinate system associated with the deformation plane, and the relative change in the coordinates of the intersection lines when the plane was rotated are estimated. As a result of the conducted analytical studies, it is found that even with developed plastic deformation, the relative change in the coordinates of the points of intersection lines does not exceed 0.1%. This indicates the possibility of using a stationary roller profile when simulating rolling using the plane fractional deformation model.

The paper is devoted to the consideration of a number of issues related to the creation of an algorithmic complex designed to solve positional and metric problems with quadrics on a projection model . A feature of the complex is the active use of geometric schemes and algorithms involving imaginary geometric images. In the paper has been presented a detailed description of constructive geometric algorithms for constructing of conics, quadrics and associated geometric images in a system of constructive geometric modeling – Simplex. All the discussed algorithms are available for independent repetition by the reader. In the paper have been presented and implemented algorithms for constructing conic from a point, a polar, and three points; constructing conic from two pairs of complex conjugate points and one real point; determination of a point on a quadric’s surface; setting a quadric by nine points in three-dimensional space. A new alternative frame of the quadric has been considered, based on which have been solved problems of constructing a tangent and a normal to the quadric, finding an intersection line of an arbitrary plane with the quadric, and performing polar and inverse transformations with respect to the quadric. Have been proposed algorithms for constructing an autopolar tetrahedron with respect to the quadric, and for constructing a conic from an autopolar triangle and two points. Have been considered problems of determining a collinear transformation in three-dimensional space and control the quadric through it. The implementation of the algorithms considered in the paper allowed conclude that there is an urgent need to develop tools for modeling imaginary conics, without which the complex of solving problems with quadrics cannot be taken for the complete one.

<div>Figure 3. Layer A. Shaded relief map of the Gabbs Valley, Gillis, and Wassuk ranges, Nevada. Layer B. Simplified geologic map of the Gabbs Valley, Gillis, and Wassuk ranges. Sources of geologic mapping: Bingler (1978); Hardyman (1980); Stewart et al. (1981); Ekren and Byers (1985a, 1985b, 1986a, 1986b); Dilles (1992); Hoxey et al. (2020); this study. Layer C. Geographic names for major mountains, valleys, canyons, flats, washes, and lakes; fault names, and other labels. Layer D. Locations photographs (see Fig. 5), cross-section lines (see Fig. 6), and ⁴⁰Ar/³⁹Ar sample locations with ages (see Table 1). Layers E–J. Southern paleovalley wall contacts and measured dextral offsets for paleovalley infilling units Obmg, Osp, Mrc, Mrl, and Mal, respectively. Layer I. Southern contact of unit Mlf and measured dextral offset. Layer K. Intersection line defined by normal fault–hanging-wall contact between units Mlf and Me and measured dextral offset. Maps, labels, and data sets are organized in a series of layers that may be viewed separately or in combination using the capabilities of the Acrobat (PDF) layering function (click “Layers” icon along vertical bar on left side of window for display of available layers; turn layers on or off by clicking the box that encompasses the layer label located within the gray box in the upper right part of the figure). Figure 3 is intended to be viewed at a width of 64 cm.<br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div>

<div>Figure 3. Layer A. Shaded relief map of the Gabbs Valley, Gillis, and Wassuk ranges, Nevada. Layer B. Simplified geologic map of the Gabbs Valley, Gillis, and Wassuk ranges. Sources of geologic mapping: Bingler (1978); Hardyman (1980); Stewart et al. (1981); Ekren and Byers (1985a, 1985b, 1986a, 1986b); Dilles (1992); Hoxey et al. (2020); this study. Layer C. Geographic names for major mountains, valleys, canyons, flats, washes, and lakes; fault names, and other labels. Layer D. Locations photographs (see Fig. 5), cross-section lines (see Fig. 6), and ⁴⁰Ar/³⁹Ar sample locations with ages (see Table 1). Layers E–J. Southern paleovalley wall contacts and measured dextral offsets for paleovalley infilling units Obmg, Osp, Mrc, Mrl, and Mal, respectively. Layer I. Southern contact of unit Mlf and measured dextral offset. Layer K. Intersection line defined by normal fault–hanging-wall contact between units Mlf and Me and measured dextral offset. Maps, labels, and data sets are organized in a series of layers that may be viewed separately or in combination using the capabilities of the Acrobat (PDF) layering function (click “Layers” icon along vertical bar on left side of window for display of available layers; turn layers on or off by clicking the box that encompasses the layer label located within the gray box in the upper right part of the figure). Figure 3 is intended to be viewed at a width of 64 cm.<br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div>

An analysis of publications has shown that mechanically clamped indexable inserts are predominantly used in modern tool manufacturing. Each insert has its shape and geometry in the tool coordinate system. The static system’s required geometry is achieved by the tilting of the insert pocket in the radial and axial directions. Therefore, it is of great importance in the tool design to know the relationships between the insert’s geometry parameters in the tool coordinate system where the geometry paraments of the insert are defined and working geometry parameters of the tool defined in the static coordinate system. The paper presents the developed methodology for determining the insert pocket base surface position to ensure the required values of the tool geometry parameters of the selected indexable insert in the static coordinate system. The graphs of the dependence of each of the angles of the insert geometry on the angles of rotation of this insert in the front and profile planes are presented as the level lines for practical use. Using these graphs, one can optimize all geometric insertion parameters in the static coordinate system. The model of the calculations of the mechanism of the insert clamping by a screw is developed. The basic size and tolerance of the output link determine the distance from the intersection line of the base surfaces to the thread axis on the pocket and the minimum amount of the screw stroke on the insert clamping in the pocket. Keywords: indexable insert, cutting tool, coordinate system, base surfaces, geometric parameters.

Image registration is an important step in remote sensing image processing, especially for images of urban areas, which are often used for urban planning, environmental assessment, and change detection. Urban areas have many artificial objects whose contours and edges provide abundant line features. However, the locations of line endpoints are greatly affected by large background variations. Considering that line intersections remain relatively stable and have high positioning accuracy even with large background variations, this paper proposes a high-accuracy remote sensing image registration algorithm that is based on the line-intersection-line (LIL) structure, with two line segments and their intersection. A double-rectangular local descriptor and a spatial relationship-based outlier removal strategy are designed on the basis of the LIL structure. First, the LILs are extracted based on multi-scale line segments. Second, LIL local descriptors are built with pixel gradients in the LIL neighborhood to realize initial matching. Third, the spatial relations between initial matches are described with the LIL structure and simple affine properties. Finally, the graph-based LIL outlier removal strategy is conducted and incorrect matches are eliminated step by step. The proposed algorithm is tested on simulated and real images and compared with state-of-the-art methods. The experiments prove that the proposed algorithm can achieve sub-pixel registration accuracy, high precision, and robust performance even with significant background variations.