Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

To construct fractional rogue waves, this paper first introduces a conformable fractional partial derivative. Based on the conformable fractional partial derivative and its properties, a fractional Schrödinger (NLS) equation with Lax integrability is then derived and first- and second-order fractional rogue wave solutions of which are finally obtained. The obtained fractional rogue wave solutions possess translational coordination, providing, to some extent, the degree of freedom to adjust the position of the rogue waves on the coordinate plane. It is shown that the obtained first- and second-order fractional rogue wave solutions are steeper than those of the corresponding NLS equation with integer-order derivatives. Besides, the time the second-order fractional rogue wave solution undergoes from the beginning to the end is also short. As for asymmetric fractional rogue waves with different backgrounds and amplitudes, this paper puts forward a way to construct them by modifying the obtained first- and second-order fractional rogue wave solutions.

Study of stimulation impedance myography contractions predictive indicators in occlusion lesions of lower extremities vessels

As a predictive indicator of tissue viability in multiple muscle lesions used the percentage of high-, medium- and low amplitude contracting reactions (СR) or their absence, recorded by stimulation impedance myography contraction (SIMC). After examining the boundaries of the scattering of amp-omic muscle curves of the limbs, the patients determined the distribution of maximum contractile reactions (MSRs) by the angles of tilt curves in the coordinate plane. After examining the boundaries of the scattering of amp-omic muscle curves of the limbs, the patients determined the distribution of maximum contractile reactions (MCRs) by the angles of tilt curves in the coordinate plane. Average sectoral values of MSR were distributed in reverse dependence of amplitudes on the amount of stimulus in the form of hyperbole containing high-, medium-, and low-amplitude MSD, the percentage of which were based on the profiles of histograms of patients with known clinical diagnoses. Comparison of histogram profiles of different stages of chronic ischemic syndrome among themselves showed their high distinguishing ability and correlation of histograms with diagnoses.

A New Redefinition of Geodetic and Plane Coordinates on UTM Geodetic Markers

The entire Peninsular Malaysia is situated on Sunda Tectonic Plate, which is subjected to motion at a prominent rate. All the geodetic infrastructures, including geodetic markers, benchmarks, Continuous Operating Reference Stations and Cadastral Reference Marks have moved away from their original position, and their existing coordinates are no longer reliable and secure to use. There are 10 geodetic markers around UTM that are subjected to the issue above. This study aims to redefine new geodetic and plane coordinates on UTM geodetic markers. Two units of Trimble NetR9 Geodetic Type Receiver are used to execute 3D GNSS Control Network on geodetic markers as well as Standard Benchmarks. Receiver Independent Exchange data of Continuous Operating Reference Stations and gravimetric geoid of MyGeoid model are retrieved from Department of Survey and Mapping Malaysia. Trimble Business Center, Golden Surfer 8 and StarNet are used as post-processing, geoid interpolation and one-dimensional network adjustment software, respectively. New sets of geodetic and plane coordinates along with orthometric heights are produced for these 10 geodetic markers. Eventually, UTM geodetic markers are tied to Geocentric Datum Malaysia 2000 (2016) and National Geodetic Vertical Datum, providing reliable horizontal and vertical reference for land surveying work to fulfil both industrial and educational purposes.Keywords: Coordinate redefinition, geodetic coordinate, plane coordinate, geodetic marker

Continuos Parameterization of the Median Surface of an Ellipsoidal Shell and Its Geometric Parameters

When analyzing the stress-strain state of thin-walled structural elements that have the shape of an ellipsoid, it becomes necessary to calculate the geometric characteristics of the ellipsoidal surface. When using the canonical ellipsoid equation, regions of uncertainty appear in the Cartesian coordinate system at the intersection points of the ellipsoid surface with the horizontal coordinate plane. To exclude these areas of uncertainty, we propose an expression of the radius vector of an ellipsoidal surface whose projections are functions of two parametric representations in mutually perpendicular planes. One of the planes is the vertical plane XOZ, and the other plane is the plane perpendicular to the axis O at the point with the x coordinate. The parameter T of the ellipse obtained from the intersection of the ellipsoid with the XOZ plane was chosen as the argument of the first parametric function. The argument of the second parametric function t is the parameter of an ellipse formed as a result of the intersection of an ellipsoidal surface with a plane perpendicular to the abscissa axis at a distance of x from the origin. The proposed representation of the ellipsoidal surface allowed us to exclude uncertainties at the intersection points of the ellipsoid with the HOWE coordinate plane. By differentiating the proposed radius-vector expression at an arbitrary point on an ellipsoidal surface, we obtain relations for the basis vectors of an arbitrary point and their derivatives represented by components in the same local basis. These relations are necessary for the development of algorithms for numerical analysis of deformation processes of engineering structures that have ellipsoidal surfaces.

An Analysis of Students' Errors to Find the Result Reflection in Coordinate Plane Based On in the Newman Error Analysis Nints-Grade Students of Junior High School 2 Sampit

This study aimed to determine the types and the causes of students' errors in finding the results of reflection in the field of coordinates based on the Newman problem-solving. This research used descriptive research with a quantitative approach. The data collection techniques were written test and a structured interview with the research subjects were Nints-grade students of Junior High School 2 Sampit. Based on the results of the data analysis, there were errors made by students, namely: (1) there were no mistakes in the problem of reading stage, (2) students were not able to write down the known and asked even though students understood the questions presented in the stage of understanding the problem, (3) did not change the questions into a coordinate field in the stage of transformation problem, (4) misplaced of the result reflection and miscalculating the result of reflection on the process skill stage, (5) did not writing down the answers or conclusions in the writing answers stage.

Imaginary Points in Cartesian Coordinate System

Geometric models are considered that allow symbolic representation of imaginary points on a real Cartesian coordinate plane XY. The models are based on the fact that through every pair of imaginary conjugate points A~B with complex coordinates x = a ± jb, y = c ± jd one unique real line m passes. For the image of imaginary points, it is proposed to use the graphic symbol m{OL} consisting of the line m passing through the imaginary points, the center O of the elliptic involution σ with imaginary double points A~B on the line m, and the Laguerre point L, from which the corresponding points involutions σ are projected by an orthogonal pencil of lines. According to A.G. Hirsch, the symbol m{OL} is called the marker of imaginary conjugate points A~B. A theorem is proved that establishes a one-to-one correspondence between the real Cartesian coordinates of the points O, L of the marker, and the complex Cartesian coordinates of the pair of imaginary conjugate points represented by this marker. The proved theorem allows us to solve both the direct problem (the construction of a marker depicting these imaginary points) and the inverse problem (the determination of the Cartesian coordinates of imaginary points represented by the marker). A graphical algorithm for constructing a circle passing through a real point and through a pair of imaginary conjugate points is proposed. An example of the graph-analytical determination of the Cartesian coordinates of imaginary points of intersection of two conics that have no common real points is considered.

A Method for Obtaining Optimal Path in Angle and Avoiding Collision for Robotic Belt Grinding

The angular variation of the joints may be large, and collision between workpieces and tools may occur in robotic grinding. Therefore, this paper proposes an optimal robotic grinding path search algorithm based on the recursive method. The algorithm is optimized by changing the position of the tool coordinate system on the belt wheel; thus, the pose of the robot during grinding is adjusted. First, the position adjustment formula of the tool coordinate system is proposed, and a coordinate plane is established to describe the grinding path of the robot based on the position adjustment formula. Second, the ordinate value of this coordinate plane is dispersed to obtain the search field of the optimal robotic grinding path search algorithm. Third, an optimal robotic grinding path search algorithm is proposed based on the recursive method and single-step search process. Finally, the algorithm is implemented on the V-REP platform. Robotic grinding paths for V-shaped workpieces and S-shaped workpieces are generated using this algorithm, and a grinding experiment is performed. The experimental results show that the robotic grinding paths generated by this algorithm can smoothly complete grinding operations and feature a smaller angular variation of the joint than other methods and no collision.

STOCHASTIC CALCULATION OF A QUASI-HOMOGENEOUS BOLTED JOINTS OF THE BODY SHEETS OF THE STEEL SILOS

This paper deals with the study of reliability of quasi-homogeneous bolted joints of the body of thin-walled constructions ofthe steel silos. Heterogeneity of this unit can be caused by number of reasons, in particular by presence of bolts of differentstrength in joint. In such case the reliability of the system is determined trough the probability of trouble-free work of the coefficient of the critical factor. The general conception of stochastic calculation consists in using the Monte-Karlo simulationprocedure for the samples of random values of the large volume. It was formed the system of conditions, under which the reliability of joints is provided and analytical expressions for the value of coefficient of the critical factor is got, and also madepractical calculation example with the following graphic presentation on a special coordinate plane – a critical stochasticscale. It was illustrated that random presence of bolts of less strength in field joint rapidly increases the risk of refusal.