Coordinate Axes Research Articles

Inequalities in homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces

This paper provides equivalence characterizations of homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces, denoted by $ \dot{F}^s_{p,q}(\mathbb R^n) $ and $ \dot{B}^s_{p,q}(\mathbb R^n) $ respectively, in terms of maximal functions of the mean values of iterated difference. It also furnishes the reader with inequalities in $ \dot{F}^s_{p,q}(\mathbb R^n) $ in terms of iterated difference and in terms of iterated difference along coordinate axes. The corresponding inequalities in $ \dot{B}^s_{p,q}(\mathbb R^n) $ in terms of iterated difference and in terms of iterated difference along coordinate axes are also considered. The techniques used in this paper are of Fourier analytic nature and the Hardy-Littlewood and Peetre-Fefferman-Stein maximal functions.

НЕСТАЦІОНАРНА РЕАКЦІЯ ЦИЛІНДРИЧНОЇ ОБОЛОНКИ З ПРУЖНИМ ШАРОМ НА ДІЮ РУХОМОГО РАДІАЛЬНОГО НАВАНТАЖЕННЯ

An analysis of studies and publications on the issues of determining the stress-strain state of constituent structures has shown that the problems of choosing and modeling the operation of structures in the form of infinitely long cylindrical shells with a soft, weightless elastic layer have not received enough attention in the scientific literature today. The use of modern approaches to the construction of mathematical models and algorithms makes it possible to take into account various kinds of dynamic loads that are transferred to structural elements in the form of cylindrical shells.The aim of the article is to develop an analytical method for calculating cylindrical shells with a weightless soft elastic layer under the action of a moving radial load.Based on the principles and approaches to the analysis of non-stationary dynamic processes in complex shells, the paper presents an algorithm based on the application of the integral Fourier transform along the axial coordinate, as well as the use of the Runge-Kutta numerical method for integrating the transformed differential equations of shell motion in the image space. Cases of load movement with different speeds and uniform pressure wave movement are considered. The dependence of the radial displacements of the shell on the reaction of the elastic layer, represented by an approximate model, taking into account only the radial displacement, is determined. The cases of motion of a radial axisymmetric load both with constant and with varying speed are investigated. The distribution of shell deflections along the length is given for different moments of time during the movement of the load at a constant speed, as well as for the slow movement of the ring load.In this work, for the first time, a mathematical model of the non-stationary behavior of a shell with an outer layer under the action of a moving load is constructed. A comparative analysis of various shell models has been carried out and deformation patterns of both accelerated and slow motion have been constructed. The transient processes that occur at the moment of load application and the subsequent time intervals immediately after this moment are considered. The presented materials can be used for dynamic modeling of the operation of structures in the form of plates and shells.

Non-axisymmetric problems of unsteady deformation of cylindrical shells with filler

Circular cylindrical shells, as structural elements, have found wide application in various fields of mechanical engineering. Thin-walled layered shells have also found wide application as components in underwater objects, air and space vehicles and in many other engineering structures. The aim of this work is to study the action of a non-axisymmetric moving wave of normal pressure on a cylindrical shell interacting with an ideal compressible fluid. The problem statement is given, solution methods are developed, and numerical results are obtained for new problems of stationary deformation of infinitely long viscoelastic cylindrical shells on a viscoelastic foundation when a non-axisymmetric normal pressure wave moves along the shell axis with up to resonant velocity. As an example, considered the action of a non-axisymmetric moving wave of normal pressure on a cylindrical shell interacting with an ideal compressible fluid. The solution methods are based on the joint application of the integral Fourier transform along the axial coordinate and the expansion of all given and desired values into Fourier series along the angular coordinate. An efficient algorithm for the joint calculation of integrals and Fourier series has been developed and implemented on a computer. It has been established that paying to attention the viscoelastic properties of the shell material reduces the deflections by 10–15%, and also makes it possible to evaluate the damping capabilities of the system.

MODELLING AND ANALYSIS OF INITIAL STRESS STATE IN A THIN-WALL CYLINDER WITH VARIABLE CHARACTERISTICS

A linearized model of prestressed elastic body vibrations is described in terms of the nonsymmetric Piola stress tensor, and a weak statement of the original problem is given. With the help of the Lagrange variational principle, we construct a statement of the problem of steady axisymmetric oscillations of a thin-walled (shell-like) cylinder with variable material properties in the presence of an inhomogeneous prestress field. The motion equations, essential and natural boundary conditions are formulated. Integral characteristics are introduced that average the change in prestresses and material properties over the shell thickness. On the basis of the model presented, the problem on steady-state vibrations of a functionally graded prestressed cylindrical shell is numerically investigated via the shooting method; the influence of the laws of change in material modules and prestress components on dynamic characteristics (e.g., amplitude-frequency characteristics, natural vibration frequencies) is analyzed, a comparative analysis of the solutions is carried out depending on the thin-walled parameter. For the considered cylindrical shell with axial inhomogeneity, based on the acoustic sounding data, we study the inverse problem of restoring two laws of prestress inhomogeneity characterizing the nonuniform initial stress-strain state of tension or inflation. As additional information, we consider the measurement data of the displacement components on the cylinder's surface, given in a set of points at a certain frequency of steady-state oscillations; in such a case, the material characteristics are considered to be known and may depend on the axial coordinate, which makes it possible to set an arbitrary functional gradient along the axis of the cylinder. The mode of probing loading is determined by specifying the traction type and oscillation frequency. Explicit formulas for the desired laws of prestress inhomogeneity are obtained, and computational experiments are carried out to restore them. A high accuracy of reconstruction is revealed far from the ends of the cylinder when probing at a frequency in the vicinity of the first resonance.

Optimization of the operation of the mechanism of the cross planer

The subject of the research is the optimization of the mechanism of the cross planer. In the article, on the basis of the condition of closed contours, the equations of the projection of the links on the corresponding coordinate axes are compiled. A functional relationship has been established between the kinematic parameters characterizing the movement of the input and output links of the mechanism. The obtained numerical calculations are presented in the form of graphic dependences. The aim of the work is the optimal metric synthesis of the mechanism of a cross-planer, with parametric restrictions. The conclusions obtained in the article can be used to improve and design modern technological equipment with mechanisms similar to the mechanism of a cross-cutting machine.

Numerical 11-Factor in Half the Genetic Code – A Search for an Explanation in Number Series

Half of 20 + 4 (double-coded) amino acids in the genetic code structure showed1 an astonishing regularity in a 2D-table, including the 11-factor. The regularities have been dismissed by professionals, saying that no known physical-chemical laws can explain them. Here a search for possible explanations or aspects is carried through by investigating the numeral series, as dimensions, of x = integers 5 → 0 with different exponents, treated in earlier papers: x3, 2x2 behind the Periodic system, x2/3 ×102 (the “ES”-series) and further the basic series with its superposed series (as coding for underlying steps) with features like quantum mechanics. The regularities are reproduced in first section. It’s shown how the paired amino acid side chains that give the 11-factor in the 2D-table are derivable in different ways through counter-directed reading of numbers in the different series (2-digit numbers that always give sums with factor 11). Introduced is the concept of step-numbers, related to numeral series, implying a vector character, with this also anti-vectors, a physical and biological reality, expressed e.g. as intervals. A main interval in the ES-series as a whole is the number 77, specially studied, the most obvious organizing principle in the 2D-table. The fact that also sums of mirrored 2-letter codons code for amino acid groups with the 11-factor points to a deeper level of double-direction acting on both levels, here suggested as inherited from the higher dimension 4D. Regarding the coding base pairs G-C and A-U as two coordinate axes, the regularities show up in amino acids with 2-letter codons that join these axes, called Mx-coded ones, the other half of the genetic code not. It seems connected with the two axes of the 2D-table and strengthens the hypothetical dimensional processes from higher to lower D-degree. Finally, factor 9 as difference of numbers read bidirectionally are circa the inversion of 11, inversion existing in physical laws. An eventual relation to centriole structure with factor 9 (×2 or ×3) of microtubules are shortly studied. This paper should be taken as material, inviting other researchers in applied physics and biochemistry to go on with the questions.

MLP-JCG: Multi-Layer Perceptron With Joint-Coordinate Gating for Efficient 3D Human Pose Estimation

Various structural relations/dependencies exist among human body joints, which makes it possible to estimate 3D poses from 2D sources. The current research on 3D human pose estimation (3D-HPE for short) mainly focuses on structural information from a specific perspective. However, this information cannot facilitate 2D-to-3D pose lifting. This paper presents a novel and efficient multi-layer perceptron with a joint-coordinate gating (MLP-JCG) model, exploring and utilizing both the local and global structural information to perform 3D pose estimations. Specifically, MLP-JCG contains two independent MLP blocks, i.e., joint-mixing MLP and coordinate-mixing MLP, which solely act on the joint and coordinate axes in modelling their local structural information. For the global structural information, we first explore two kinds of global statistics from the pose matrix embeddings, which are referred to as the dynamics aggregated along the joint/coordinate axis. Then, we propose two kinds of gating units to elementwisely contextualize the features learned from MLP blocks. All the model components are designed based on MLP, making the MLP-JCG easy to implement and train. We conduct experiments on three 3D-HPE benchmarks, and the results demonstrate the superior effectiveness and efficiency of the proposed approach.

Підвищення точності та продуктивності обробки плоских поверхонь деталей, що входять до вузлів і агрегатів автомобілів

The use of new reserves of the process of grinding the flat surfaces of parts allows to significantly increase the productivity of processing, reduce the uneven wear of the wheel profile and increase the accuracy and quality of the processed surfaces, therefore, it is an urgent scientific problem, the solution of which is of important national economic importance. The analysis of research and publications showed the importance of the development and implementation of grinding technologies with crossed axes of grinding wheels and workpieces, for which a special profile adjustment of the wheel is carried out, which makes it possible to obtain an area for removing the rough allowance and a calibration area on the surface of the wheel. At the same time, the entire allowance is cut in the area adjacent to the calibration area. The calibration section at the entrance of the parts to the processing area does not participate in cutting the allowance, has high stability and at the exit forms the final accuracy of the end surfaces. The paper describes the calibration area of the tool end when it is profiled on a machine with a diamond pencil using the transformation matrices of coordinate systems that model movements and rotations along and around the coordinate axes, the optimal length of the calibration area and the ratio of the orientation angles of the grinding wheels in the horizontal and vertical planes are proposed, which give the best results in terms of accuracy.

SHAPING OPERATIONS OF EXTRUSION AND ROTATION OF SOLID-STATE MODELING OF GEOMETRIC OBJECTS IN THE POINT CALCULUS

The shaping operations of extrusion and rotation within the framework of point calculus are implemented. The principles of parametrization of bodies in point calculus are described. When considering the extrusion operation, the cases of performing this operation at a right angle and with a variable inclination angle of the generatrix are taken into account. When implementing the rotation operation, the method of polar parameterization of the sketch plane is considered. Due to the use of point calculus, the proposed approach makes it possible to obtain body models in the form of a three-parameter set of points in the three dimensional space, the density of which depends on the parameters of the three dimensional model set by the designer. The analysis of existing systems of solid modeling and their capabilities in the direction of creating solid models of bodies is carried out. It showed that almost all of them provide the user with models presented as surfaces of body shells and are not filled with points. None of the existing CAD makes it possible to model a body in the form of a three parameter set of points. And when trying to use the proposed modeling apparatus within existing computeraided design systems (for example, outputting a model in the form of a set of points through the API of these systems), we risk getting a body model that is simply impossible to work with due to the excessive consumption of PC resources used for modeling (for example, even a model of a simple body with a high density of points can lead to a “freeze” of the system even on a computer with high computing power). In addition, the evaluation of the effectiveness of the mathematical apparatus embedded in the modeling systems cannot be effectively carried out since the mathematical basis of these CAD systems is a trade secret. In this case comparison is necessary, since the proposed three dimensional models consist of the same type of equations along all coordinate axes, which, if used correctly in CAD, can lead to significant savings in computing power due to parallelization of the data processing across different computational threads.

Additive Poisson regression via forced categorical covariates and generalized fused Lasso

In this study, we use the log-linear link function and propose a generalized fused Lasso (GFL) Poisson regression model in which the nonlinear trend is discretely represented by categorical covariates in the additive model. We use the coordinate descent algorithm for the estimation and show that the optimal solution in a coordinate axis can be found explicitly. To demonstrate the proposed approach, we analyze Japanese crime data. Simulation results showed a fitness ratio for true fusion to be more than 90% in total, demonstrating the reliability of the estimates.

A method for calculating two-dimensional spatially extension distances and its clustering algorithm

This paper presents a novel method for calculating the extension distance between a point and a two-dimensional convex set. The proposed method builds upon existing techniques by employing a line traversal approach. By traversing the convex set with a line originating from the point of interest, the extension distance is computed based on the intersection points between the line and the set along the two coordinate axes. The weights assigned to the intersection points play a crucial role in the distance calculation. By summing the extension distances in both directions, the overall extension distance of the point with respect to the set is obtained. Furthermore, a clustering algorithm is introduced, which incorporates the concept of an interaction factor commonly used in engineering experiments. The multidimensional data is projected onto feature planes created by combining pairs of features. The calculation method for extension distances between points and convex sets in two dimensions is applied to determine the distances between points and cluster classes (or cluster centers). The distances on each feature plane are then weighted, summed, and analyzed to establish the relationships between points and cluster classes, thereby achieving clustering. The feasibility of the proposed algorithm is validated through comparative experiments k-means algorithm on the iris dataset and the wine dataset. The experimental results confirm the effectiveness and viability of the proposed approach.

Spatial properties and the influence of the Soret coefficient on the solutions of time-dependent double-diffusive Darcy plane flow

<abstract><p>This paper investigates time-dependent double-diffusive Darcy flow which is defined in a semi-infinite strip pipe, where the generatrix of the pipe is not parallel to the coordinate axis any more. By using several results which have been derived in the literature, the spatial properties and the influence of the Soret coefficient on the solutions are both obtained. We also give some concrete examples.</p></abstract>

Единая система отсчета геометрических характеристик размерных элементов деталей. Часть I. Теория двух размеров максимума и минимума

A unified reference system for geometric characteristics is based on the classification of joints of applied mechanics, in which the class number is determined by the number of degrees of freedom limited by mating elements of parts and has received the short term «informativeness». Different information content of the bases of elements that materialize coordinate systems determines different information content of the coordinate axes – four, two, zero and different information content of design planes – three, two, one. The paper shows that the information content of elements in the functions of auxiliary bases and executive elements determines the number and type of coordinates (linear and angular), with the help of which it is necessary to set their position in the generalized coordinate system of the part. It is shown that the accuracy of coordinating dimensions should be specified by symmetrical tolerances for linear and angular dimensions.

Interpretation of Spatial Models of Forest Landscape in Book Graphics of the Late 19th and Early 20th centuries

The article analyses the peculiarities of construction and symbolic meaning of forest scenes in book graphics of the late 19th and early 20th centuries in their connection with the selected examples of the interpretation of forest motifs in the history of art of previous periods – the Late Middle Ages, the Renaissance and Romanticism. Iconographic research treats the dark space of the legendary “wild” forest in its spatial and semantic meaning as similar to a wall, a curtain, the boundary of the “other worldˮ. The paper highlights sustainable compositional techniques of forest imagery, and points out the differences in forest images of Romanticism and Symbolism emphasising the psychological dramatisation of perception of the woodland scenes in the book graphics of the turn of the 20th century. Particular attention is paid to the analysis of the location of the coordinate axes of forest space, such as the horizon line and the trail, refusal to depict the sky and emphasis on the tier of tree roots.

Reconstruction of LWD-NMR T2 water spectrum and fluid recognition based on microscopic pore structure constraints

The existing fluid property identification methods are not applicable to low resistivity reservoirs. In order to accurately identify low-resistivity oil reservoirs, the effects of fluid properties on the NMR T2 spectrum under different pore structures were analyzed. The results show that the T2 spectrum of the low-resistivity oil section shows a broad and gentle hilly shape, and the T2 spectrum of the water section shows a steep and mountainous shape. Based on the difference characteristics of T2 spectrum of reservoirs with different fluid properties, a new NMR water spectrum reconstruction and fluid property identification method based on microscopic pore structure constraint is innovatively proposed. Based on the drilling NMR logging data, three parameters characterizing the microscopic pore structure are firstly extracted from the NMR T2 spectrum of standard water reservoirs, which reflect the overall shape of the T2 spectrum in terms of transverse relaxation time, longitudinal pore fraction and These three parameters reflect the pore structure, water and oil and gas information of the reservoir in terms of the transverse relaxation time, the longitudinal pore fraction and the overall morphology of the T2 spectrum. Secondly, the microscopic pore structure parameters are used as the coordinate axes to construct a 3D water spectrum sample library, and the standard water formation T2 spectrum samples of the target block are stored in the 3D water spectrum library through the constraints of the three parameters. Finally, the NMR T2 spectrum parameters are extracted from the whole well section and the samples in the water spectrum library are called to realize the water spectrum reconstruction. The parameters that can distinguish oil and water formations are extracted from the measured T2 spectrum and the reconstructed water spectrum and fluid identification is performed. The results show that the reconstructed water spectrum is highly similar to the actual measured T2 spectrum in the production-proven standard water layer, which verifies the accuracy of the water spectrum reconstruction technique; in Caofeidian A oilfield, the fluid identification was performed on 20 production-proven test sections, of which 18 reservoirs were correctly identified, and the identification compliance rate reached 90%. The method circumvents the influence of pore structure in NMR T2 spectrum and highlights the information of its fluid properties, which improves the fluid property identification capability of logging with drilling (LWD) NMR logging.

Methods of calculating areas of overlapping inks of ellipsoidal raster elements

The mechanisms of moire occurrence during dot-to-dot printing for various forms of raster elements (circle, square, rhombus, ellipse) are considered. The algorithms for calculating the areas of common overlay of raster elements of neighboring inks of round, square and rhombic form are presented. An algorithm and methodology for calculating the areas of common overlay of raster elements of ellipsoidal form with arbitrary misalignment along the coordinate axes has been developed. The program code for calculating the areas of common overlay of ellipses using the Pascal 7.0 programming language was writtеn. The Monte Carlo method was used to calculate the area of the common overlap of two ellipses. The optimal geometric parameters for the stochastic process of the Monte Carlo method were found. The dependences of the areas of common overlay of ellipsoidal raster elements on misalignment along the x-axis for different misalignments along the y-axis were obtained

A New Approach for Improving GNSS Geodetic Position by Reducing Residual Tropospheric Error (RTE) Based on Surface Meteorological Data

Positioning error components related to tropospheric and ionospheric delays are caused by the atmosphere in positioning determined by global navigation satellite systems (GNSS). Depending on the user’s requirements, the position error caused by tropospheric influences, which is commonly referred to as zenith tropospheric delay (ZTD), must be estimated during position determination or determined later by external tropospheric corrections. In this study, a new approach was adopted based on the reduction of residual tropospheric error (RTE), i.e., the unmodeled part of the tropospheric error that remains included in the total geodetic position error, along with other unmodeled systematic and random errors. The study was performed based on Global Navigation Satellite System (GLONASS) positioning solutions and accompanying meteorological parameters in a defined and harmonized temporal-spatial frame of three locations in the Republic of Croatia. A multidisciplinary approach-based analysis from a navigational science aspect was applied. The residual amount of satellite positioning signal tropospheric delay was quantitatively reduced by employing statistical analysis methods. The result of statistical regression is a model which correlates surface meteorological parameters with RTE. Considering the input data, the model has a regional character, and it is based on the Saastamoinen model of zenith tropospheric delay. The verification results show that the model reduces the RTE and thus increases the geodetic accuracy of the observed GNSS stations (with horizontal components of position accuracy of up to 3.8% and vertical components of position of up to 4.37%, respectively). To obtain these results, the Root Mean Square Error (RMSE) was used as the fundamental parameter for position accuracy evaluation. Although developed based on GLONASS data, the proposed model also shows a considerable degree of success in the verification of geodetic positions based on Global Positioning System (GPS). The purpose of the research, and one of its scientific contributions, is that the proposed method can be used to quantitatively monitor the dynamics of changes in deviations of X, Y, and Z coordinate values along coordinate axes. The results show that there is a distinct interdependence of the dynamics of Y and Z coordinate changes (with almost mirror symmetry), which has not been investigated and published so far. The resultant position of the coordinates is created by deviations of the coordinates along the Y and Z axes—in the vertical plane of space, the deviations of the coordinate X (horizontal plane) are mostly uniform and independent of deviations along the Y and Z axes. The proposed model shows the realized state of the statistical position equilibrium of the selected GNSS stations which were observed using RTE values. Although of regional character, the model is suitable for application in larger areas with similar climatological profiles and for users who do not require a maximum level of geodetic accuracy achieved by using Satellite-Based Augmentation Systems (SBAS) or other more advanced, time-consuming, and equipment-consuming positioning techniques.

The Procedure of Identifying the Geometrical Layout of an Exploited Railway Route Based on the Determined Curvature of the Track Axis.

This paper presents a detailed algorithm for determining the curvature of a track axis with the use of a moving chord method, and then discusses the procedure for identifying the geometric layout of an exploited railway route on the basis of the determined curvature. In the moving chord method, the measured coordinates of the track axis allow one to directly determine the existence of the horizontal curvature without the need for additional measurements. This enables comprehensively identifying the existing geometric elements-straight lines, circular arcs, and transition curves. The conducted activities were illustrated with a calculation example, including a 5.5 km long test section with five areas of directional change. This showed a sequential procedure that led to the solution of the given problem. Based on the curvature diagram, the coordinates of the segmentation points, which define the connections of the existing geometric elements with each other, were determined.

TreeKDE: clustering multivariate data based on decision tree and using one-dimensional kernel density estimation

In this paper, we present an algorithm for clustering multidimensional data, which we named TreeKDE. It is based on a tree structure decision associated with the optimization of the one-dimensional kernel density estimator function constructed from the orthogonal projections of the data on the coordinate axes. Among the main features of the proposed algorithm, we highlight the automatic determination of the number of clusters and their insertion in a rectangular region. Comparative numerical experiments are presented to illustrate the performance of the proposed algorithm and the results indicate that the TreeKDE is efficient and competitive when compared to other algorithms from the literature. Features such as simplicity and efficiency make the proposed algorithm an attractive and promising research field, which can be used as a basis for its improvement, and also for the development of new clustering algorithms based on the association between decision tree and kernel density estimator.

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

The purpose of this paper is to report the feasibility of constructing high-order rogue waves with controllable fission and asymmetry for high-dimensional nonlinear evolution equations. Such a nonlinear model considered in this paper as the concrete example is the (3 + 1)-dimensional generalized Boussinesq (gB) equation, and the corresponding method is Zhaqilao’s symbolic computation approach containing two embedded parameters. It is indicated by the (3 + 1)-dimensional gB equation that the embedded parameters can not only control the center of the first-order rogue wave, but also control the number of the wave peaks split from higher-order rogue waves and the asymmetry of higher-order rogue waves about the coordinate axes. The main novelty of this paper is that the obtained results and findings can provide useful supplements to the method used and the controllability of higher-order rogue waves.