Components Of Vector Research Articles

Comparative analysis of dynamic stability of cylindrical and conical shells under periodic axial compression

A comparative analysis of the dynamic stability of cylindrical and conical shells with the same geometric and mechanical characteristics under periodic uniformly distributed axial compression was presented. The study of the stability of steady periodic vibrations of thin elastic shells was based on the joint use of the method of curvilinear grids, the projection method and the parameter continuation method combined with the Newton–Kantorovich method. Geometrically nonlinear relations of the thin elastic shells theory are formulated on the basis of the vector approximation of the displacements function in the general curvilinear coordinate system in tensor form and satisfy the Kirchhoff-Love hypothesis. The discretization of the differential equations of the steady forced vibrations in the direction of the generating shells using the method of curvilinear grids was carried out. The components of the elements displacement vectors of the shells middle surface in the circular directionare approximated by trigonometric series. Reduction of the number of generalized coordinates of the discrete dynamic model of shells steady forced vibrations was performed by the Bubnov-Galerkin basis reduction method. A transition from vector ordinary differential equations to a nonlinear system of algebraic equations was made. The construction of a mathematical model of the dynamic stability of steady forced nonlinear vibrations of thin elastic shells was performed according to Floquet's theory using the projection method. The criterion for the loss of stability was the equality to zero of the determinant of the matrix of linearized equations of steady forced nonlinear vibrations of shells according to the Lyapunov theorem. A comparative analysis of frequencies and modes of natural vibrations of cylindrical and conical shells with the same geometric and mechanical characteristics and boundary conditions was performed. Nonlinear steady vibrations of the shells due to periodic axial compression were studied. The critical values of the dynamic load and the corresponding forms of loss of shell stability in the range of lower frequencies of their natural vibrations were obtained.

Propionic Acid Groups and Multiple Aromatic Rings Induce Binding of Ketoprofen and Naproxen to the Hydrophobic Core of Bovine Serum Albumin.

Ketoprofen (KP), which causes photosensitivity by interacting with serum albumin (SA), and three drugs, ibuprofen (IBP), naproxen (NPX), and diazepam (DZP), which share the same binding site, were investigated for their interaction with bovine SA (BSA). For KP, DZP, and IBP, where drug-concentration-dependent quenching of BSA-intrinsic fluorescence was observed, a modified Stern-Volmer plot showed that dynamic quenching was dominant for KP and static quenching was dominant for DZP and IBP. However, this alone cannot be compared with NPX. Therefore, by performing singular value decomposition (SVD) fluorescence spectroscopy, we were able to find the behavior of the drug-concentration-dependent Langmuir-type principal component vectors. KSVD obtained by the Langmuir equation showed a high correlation with the static extinction constant V. Therefore, KSVD indicates the association constant of the drug with BSA and it was found that NPX and IBP had higher values than KP. Finally, in the analysis of the temperature factors of amino acid residues in each drug-binding region and Trp residues, KP and NPX significantly reduced these temperature factors whereas DZP and IBP hardly changed them. This result is consistent with the dynamic and static quenching dominance in the total quenching mechanism. Summarizing the results so far, it was shown that penetration into the hydrophobic core inside BSA can be achieved not only by one of the multiple aromatic rings and propionic acid groups but also by the joint effect of both. In this study, SVD enabled us to extract information on drug adsorption to BSA from fluorescence spectra. Furthermore, the application of SVD is expected to make it possible to perform fluorescence analysis for drug binding to proteins without being limited by the fluorescence properties of the drug.

ЕЛЕКТРОМАГНІТНІ МОМЕНТИ УПРАВЛІННЯ ПРЕЦЕСІЙНИМ РУХОМ ТРИСТУПЕНЕВОЇ ЕЛЕКТРИЧНОЇ МАШИНИ

The main known structures and principles of functioning of electric machines with three degrees of freedom of rotational motion of the rotor are considered. The type of such machines in which it is possible to realize a high frequency of the rotor rotation is highlighted, which gives it the property of gyro-stabilization. The structure of the magnetic system of the machine of this type is presented and a hypothesis is put forward about the adequacy of the expressions of the classical analytical mathematical model, but the need for accurate calculation of the concentrated parameters that make up it. The distribution of magnetic flux density is analyzed based on a numerical mathematical model of a three-dimensional mag-netic field. The dependences of electromagnetic torque components and flux linkages on the rotor axis orientation and the angle of its rotation are calculated. It was concluded that the classical analytical mathematical model are adequate pro-vided that the calculating of its coefficients is based on the results of the modeling of three-dimensional magnetic field in the machine active volume and the surrounding space. It is underlined that, the amplitude of the flux linkage vector of the control winding and the fluctuations of the vector components to use in lumped parameter model must be calculated from the corresponding values of the electromagnetic torque components. Taking into account the results of the analysis of the three-dimensional field demonstrates a significant decrease in the speed of controlled precession and an increase in the amplitude of nutation. References 9, figures 10, tables 2.

High-dimensional hypothesis testing for allometric extension model

Allometric extension model is a multivariate mixture model, in which two population distributions have a common first principal component vector of their covariance matrices and the direction of the difference of their mean vectors coincides with the first principal component vector. This paper studies hypothesis testing for the allometric extension model in a high-dimensional setting when the multivariate normal population distributions are assumed. A test statistic is constructed and its asymptotic normality is shown under the null hypothesis. The consistency of the test is discussed under the alternative hypothesis. Several numerical results on the size and power of the test are also presented.

Solar Sail Orbit Raising with Electro-Optically Controlled Diffractive Film

The aim of this paper is to analyze the transfer performance of a spacecraft whose primary propulsion system is a diffractive solar sail with active, switchable panels. The spacecraft uses a propellantless thruster that converts the solar radiation pressure into propulsive acceleration by taking advantage of the diffractive property of an electro-optically controlled (binary) metamaterial. The proposed analysis considers a heliocentric mission scenario where the spacecraft is required to perform a two-dimensional transfer between two concentric and coplanar circular orbits. The sail attitude is assumed to be Sun-facing, that is, with its sail nominal plane perpendicular to the incoming sunlight. This is possible since, unlike a more conventional solar sail concept that uses metalized highly reflective thin films to reflect the photons, a diffractive sail is theoretically able to generate a component of the thrust vector along the sail nominal plane also in a Sun-facing configuration. The electro-optically controlled sail film is used to change the in-plane component of the thrust vector to accomplish the transfer by minimizing the total flight time without changing the sail attitude with respect to an orbital reference frame. This work extends the mathematical model recently proposed by the authors by including the potential offered by an active control of the diffractive sail film. The paper also thoroughly analyzes the diffractive sail-based spacecraft performance in a set of classical circle-to-circle heliocentric trajectories that model transfers from Earth to Mars, Venus and Jupiter.

Construction of bivariate symmetric and asymmetric copulas and its relationship to ratios of conditional hazard rate functions

ABSTRACT A new method for the construction of both symmetric and asymmetric, absolutely continuous bivariate copulas is introduced. This research was inspired by the well-known cross ratio (CR), studied by Clayton (1978), which is a local dependence measure describing the association between the components of a bivariate random vector, as well as by an alternative risk ratio (RR) proposed recently by Abrams et al. (2022), which unravels the local relation between the two components of the vector. The practical meaning of RR is illustrated in two real data sets by the authors. In this article, various properties of the proposed parametric families of copulas are studied, for example quadrant dependence ordering, tail dependence coefficients and several copula-based measures of dependence. Some relationships of the copulas to RR are discussed and illustrative scatterplots are presented.

Effective Penetration Depth Investigation for Frank Type Dislocation (Deflected TSDs/TMDs) on Grazing Incidence Synchrotron X-Ray Topographs of 4H-SiC Wafers

In 4H-SiC crystals, Frank type dislocations are created through the deflection of threading screw/mixed dislocations onto the basal plane. Grazing-incidence X-ray topographs are often used to evaluate the density of such dislocations and a knowledge of the effective penetration depth is therefore essential. In this study, a systematic analysis is performed to investigate the effective penetration depth, which is the depth from which contrast from the dislocation is still discernible. This is achieved by comparison between observed topographic images and detailed ray tracing simulations. Simulations shows no significant contrast difference between a deflected TSD and a deflected TMD with the same line direction since the large c component is the dominant contributor to the effective misorientation, whereas the effect of a component is rather negligible. Therefore, this effective penetration depth study uses ray tracing simulation images of deflected TSDs with photoelectric absorption applied to compare with all topographically observed Frank type dislocations. Analysis first reveals that the effective penetration depth varies with the line direction of a Frank type dislocation, and the effective penetration depth is significantly deeper compared to that of a BPD. Further, the effective penetration depth on ray tracing simulations with absorption applied matches well with experimentally measured depth. The study also evaluated the effectiveness of a simplified model based on an approximate expression for the effective misorientation of a dislocation modulated by photoelectric absorption. This was also found to yield satisfactory results and can be used as a universal method to determine the effective penetration depth for Frank type dislocations with c component of Burgers vector.

Ultrafast Coupling of Optical Near Fields to Low-Energy Electrons Probed in a Point-Projection Microscope.

We report the first observation of the coupling of strong optical near fields to wavepackets of free, 100 eV electrons with <50 fs temporal resolution in an ultrafast point-projection microscope. Optical near fields are created by excitation of a thin, nanometer-sized Yagi-Uda antenna, with 20 fs near-infrared laser pulses. Phase matching between electrons and near fields is achieved due to strong spatial confinement of the antenna near field. Energy-resolved projection images of the antenna are recorded in an optical pump-electron probe scheme. We show that the phase modulation of the electron by transverse-field components results in a transient electron deflection while longitudinal near-field components broaden the kinetic energy distribution. This low-energy electron near-field coupling is used here to characterize the chirp of the ultrafast electron wavepackets, acquired upon propagation from the electron emitter to the sample. Our results bring direct mapping of different vectorial components of highly localized optical near fields into reach.

Affine Iterations and Wrapping Effect

Affine iterations of the form xn+1=Axn+b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic to real arithmetic may lead to divergence of these iterations, in particular if the spectral radius of the absolute value of A is greater than 1. We will review different approaches to limit the overestimation of the iterates, when the components of the initial vector x(0) and b are intervals. We will compare, both theoretically and experimentally, the widths of the iterates computed by these different methods: the naive iteration, methods based on the QR- and SVD-factorization of A, and Lohner's QR-factorization method. The method based on the SVD-factorization is computationally less demanding and gives good results when the matrix is poorly scaled, it is superseded either by the naive iteration or by Lohner's method otherwise.

RETRACTED ARTICLE: Machine learning in molecular communication and applications for health monitoring networks

The world has been greatly affected by increased utilization of mobile methods as well as smart devices in field of health. Health professionals are increasingly utilizing these technologies' advantages, resulting in a significant improvement in clinical health care. For this purpose, machine learning (ML) as well as Internet of Things can be utilized effectively. This study aims to propose a novel data analysis method for a health monitoring system based on ML. Goal of research is to create a ML-based smart health monitoring method. It helps the doctors keep an eye on patients from a distance as well as take periodic actions if they need to. Utilizing wearable sensors, a set of five parameters—the electrocardiogram, pulse rate, pressure, temperature, and position detection—have been identified. Kernelized component vector neural networks are used to choose the features in the input data. Then, a sparse attention-based convolutional neural network with a structural search algorithm was used to classify the selected features. For a variety of datasets, the proposed technique attained validation accuracy 95%, training accuracy 92%, RMSE 52%, F-measure 53%, and sensitivity 77%.

Discrete Optimal Transport with Independent Marginals is #P-Hard

We study the computational complexity of the optimal transport problem that evaluates the Wasserstein distance between the distributions of two -dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in the maximum of the number of atoms of the two distributions. However, if the components of either random vector are independent, then this number can be exponential in even though the size of the problem description scales linearly with . We prove that the described optimal transport problem is #P-hard even if all components of the first random vector are independent uniform Bernoulli random variables, while the second random vector has merely two atoms, and even if only approximate solutions are sought. We also develop a dynamic programming–type algorithm that approximates the Wasserstein distance in pseudo-polynomial time when the components of the first random vector follow arbitrary independent discrete distributions, and we identify special problem instances that can be solved exactly in strongly polynomial time.

Использование топологического анализа данных для визуализации выходной информации приборов

The article discusses Takens embedding for 2D and 3D visualization of 1D time series data. The paper considers the use of topological data analysis in conjunction with Takens embedding to analyze the output information of a dynamic system - a rigid body. 3D images of curves constructed from three components of the angular velocity vector of a rigid body for various values of the main moments of inertia are constructed. Three-dimensional images of the curves constructed on the basis of the Takens embedding for the component of the angular velocity of a rigid body for various values of the principal moments of inertia are constructed. Distances between 3D images of curves are determined by constructing persistent landscape functions. Using the method of topological data analysis in conjunction with Takens embedding for image comparison allows you to classify and identify images and output information of the instrumental composition.

Bridge Cable Anomaly Detection Based on Local Variability in Feature Vector of Monitoring Group Cable Forces

The cable is the key supporting component of the cable-stayed bridges, and damaged cables will directly affect the safety and stability of the bridge in operation. Therefore, this paper proposes a bridge cable anomaly detection and localization method based on the variation in the group cable force feature vector. First, mechanical analysis was carried out on the correlation of cable forces between two cables on the same side induced by the single-vehicle case and a cable force feature vector was established to reflect the mechanical characteristics of the group cable forces. Second, a bridge cable anomaly detection method was proposed based on the variation in the group cable force feature vector. Third, the isolation of abnormal components of the cable force feature vector, which can accurately localize abnormal cables, was presented. The long-term monitoring data of an in-service cable-stayed bridge were utilized to validate the effectiveness of the proposed method. The results demonstrated that the proposed method could effectively detect abnormal cable conditions and accurately localize abnormal cables. In addition, the proposed bridge cable feature index and anomaly detection method were robust to the situation of partially missing data due to sensor fault.

Statistical Inferences for Complex Dependence of Multimodal Imaging Data

Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this article, we propose rigorous statistical testing procedures for making inferences on the complex dependence of multimodal imaging data. Motivated by the analysis of multi-task fMRI data in the Human Connectome Project (HCP) study, we particularly address three hypothesis testing problems: (a) testing independence among imaging modalities over brain regions, (b) testing independence between brain regions within imaging modalities, and (c) testing independence between brain regions across different modalities. Considering a general form for all the three tests, we develop a global testing procedure and a multiple testing procedure controlling the false discovery rate. We study theoretical properties of the proposed tests and develop a computationally efficient distributed algorithm. The proposed methods and theory are general and relevant for many statistical problems of testing independence structure among the components of high-dimensional random vectors with arbitrary dependence structures. We also illustrate our proposed methods via extensive simulations and analysis of five task fMRI contrast maps in the HCP study. Supplementary materials for this article are available online.

CALCULATION AND EXPERIMENTAL STUDY OF THE STRESS-STRAIN STATE OF ELEMENTS OF TECHNOLOGICAL SYSTEMS WITH USING OF THE METHOD OF FINITE ELEMENTS AND HOLOGRAPHIC INTERFEROMETRY

The work describes computational and experimental studies of the stress-strain state of elements of technological systems. The distribution of movements of individual surfaces is determined on the example of vice-type adjustable machine tools. In the course of experimental studies, normal displacements are determined from the pattern of stripes on the hologram. The components of the displacement vector in the plane of the investigated surfaces are determined by scanning speckle interferograms. The obtained distributions of the displacement components were compared with the distributions determined by the finite element method. Satisfactory convergence of the results of numerical and experimental studies has been confirmed. The constructed calculation models can be used for further studies of the behavior of the housings of vice-type devices under the action of complex loads. The advantage of the developed version of the calculation-experimental method of studying the stress-strain state is its direct focus on the verification of the calculation model. The basic results are the results of experimental studies in the form of patterns of interference bands. These pictures describe the distribution of displacement fields of points on the surfaces of the bodies under study. With this picture, which was obtained on a natural object, the pictures of displacement fields, which were obtained during calculations with the application of the finite element method, are compared. Numerically calculated pictures are modified depending on the boundary conditions that are applied, as well as on the characteristics of the finite element models that are being built. In order to determine adequate boundary conditions and acceptable variants of finite-element models, the functional of the discrepancy of the displacement distribution fields obtained, on the one hand, numerically, and on the other - experimentally, is minimized. This construction of the calculation model verification algorithm demonstrated its efficiency and effectiveness. Keywords: stress-strain state; technological system; machine tool; finite element method; contact interaction

Weak trimer distortion and planar spin configuration in hexagonal Lu0.6In0.4FeO3

Improper ferroelectricity and canted ferromagnetism in antiferromagnetically ordered hexagonal ferrites with A2-type spin configuration have been intensely studied due to their potential for room-temperature multiferroicity with strong magnetoelectric couplings. However, the subtle interplay between the magnetic structure and trimer structural distortion, which is a critical ingredient for ferroelectricity, has not been clearly verified in experiments due to the lack of control over trimer distortion. In this study, we report on Lu0.6In0.4FeO3, which exhibits weaker trimer distortion primarily related to the smaller tilting of the FeO5 bipyramids. The reduced vertical displacement of the equatorial oxygen of FeO5 located at the center of the trimer lowers the magnitude of the in-plane Dzyaloshinskii–Moriya vector component, resulting in the absence of canted ferromagnetism with the planar A1-type spin configuration, rather than the canted A2-type observed in other hexagonal ferrites. Our findings demonstrate that the degree of trimer distortion plays an important role in determining the spin configuration in related hexagonal systems.

STUDY OF AN OSCILLATING CHARGE IN A DIPOLE-QUADRUPOLE SYSTEM

The solution of the problem of determining the magnitude of the component of the electric field intensity vector generated by an oscillating charge in a dipole-quadrupole system in a homogeneous medium is obtained. Two mutually perpendicular directions of charge oscillations in a cylindrical coordinate system are considered. From the analysis of the obtained dependences for the oscillation frequencies, it can be seen that in the first case, the frequency of «vertical» oscillations exceeds the frequency of «horizontal» oscillations. Knowing the maximum and minimum frequencies of the oscillating charge radiation spectrum, it is possible to calculate the molecular parameters. The analysis of the parameters of the radiation spectrum of a harmonically oscillating charge performing a non-relativistic motion can be used in the analysis of the electromagnetic radiation spectra of atoms and molecules in an excited state, as well as the parameters of the crystal lattice.

Fourier-space generalized magneto-optical ellipsometry

The magneto-optical Kerr effect (MOKE) is widely exploited in laboratory-based setups for the study of thin films and nanostructures, providing magnetic characterization with good spatial and temporal resolutions. Due to the complex coupling of light with a magnetic sample, conventional MOKE magnetometers normally work by selecting a small range of incident wave-vector values, focusing the incident light beam to a small spot, and recording the reflected intensity at that angular range by means of photodetectors. Using this approach, additional methodologies and measurements are required for full vectorial magnetic characterization. Here, we computationally investigate a Fourier-space MOKE setup, where a focused beam ellipsometer using high numerical aperture optics and a camera detector is employed to simultaneously map the intensity distribution for a wide range of incident and reflected wave vectors. We employ circularly incident polarized light and no analyzing optics, in combination with a fitting procedure of the light intensity maps to the analytical expression of the Kerr effect under linear approximation. In this way, we are able to retrieve the three unknown components of the magnetization vector as well as the material' s optical and magneto-optical constants with high accuracy and short acquisition times, with the possibility of single-shot measurements. Fourier MOKE is thus proposed as a powerful method to perform generalized magneto-optical ellipsometry for a wide range of magnetic materials and devices.

Properties of singular points in a special case of orthorhombic media

The position of singular lines for orthorhombic (ORT) media with fixed diagonal elements of the elasticity matrix cij, i=1…6 is studied under the condition that c11, c22, c33&gt;c66&gt;c44&gt;c55. In this case, the off-diagonal coefficients of the elasticity matrix c12, c13, c23 are chosen so that some of the values of d12=c12+c66, d13=c13+c55, d23=c23+c44 are zero. For orthorhombic medium, where the only one of d12, d13, d23 is zero, contains only singular points in the planes of symmetry. If two or all three dij are zero, then the ORT medium contains singular lines and discrete singular points. We call such media pathological. A degenerate ORT medium with positive d12, d13, d23 has at most two singular lines, which are the intersection of a quadratic cone with a sphere. The pathological media may have up to 6 singular lines on the surface of the slowness. Singular lines for pathological media are described by more complex equations than conventional degenerate ORT models. The article proposes to using squares x, y, z of the components of the slowness vector in the equations. In a new coordinate system, equations defining singular lines for pathological media become linear or quadratic. Intersecting with the plane x+y+z =1, they define the straight lines, ellipses, or hyperbolas. If non-zero values d12, d13, d23 increase, the singular lines pass through four fixed points on the plane x+y+z =1, which makes it possible to describe the evolution of their change. Conditions are derived under which the singular curves of pathological ORT models are limiting the singular curves for degenerate ORT models with positive values of d12, d13, d23. Formulas are derived for transforming surfaces of slowness and singular lines of pathological media into the region of group velocities. The results are demonstrated with examples of pathological models obtained from the standard model of the ORT medium by changing the elasticity coefficients c12, c13, c23 so that some of the values d12, d13, d23 are zero

Path planning and pose correction of robot laser cleaning process for specific surfaces of parts

The purpose of this paper is to solve a series of problems, such as the difficulty in accurately controlling the specific surfaces, and the interference between the laser beam and the part, when the laser is used to clean mechanical parts with complex surfaces by using robots. Firstly, a region segmentation algorithm of the stereo lithography (STL) model was designed, and the feature surfaces of the model were obtained by using the dihedral angle as the criterion. Then the path points which could easily cause interference between the laser beam and the part to be cleaned were detected by the method of ray intersection, and the pose of the robot was modified according to the normal vectors of two non-interference points that were adjacent to the continuous interference points respectively. Finally, the proposed method was validated by scanning path visualization and robot laser cleaning process experiments. The generated path in the unit of feature surface according to the variation components of normal vectors proved the effectiveness of the STL model region segmentation algorithm based on dihedral angle division criteria; the change of the normal vectors of the path points on the current feature surface was continuous and smooth, which meant that the path points did not cause sudden change of the robot pose after the pose correction. The robot cleaned the specific surfaces of the test workpiece safely and effectively in the actual laser cleaning experiments, and the effective cleaning area reached 96.87%, 99.56%, 94.53% and 91.62% of the target cleaning area, which further proved the effectiveness of this study. The method is also useful for the path planning of robots in other processing fields.