Position Vector Research Articles

Simultaneous X-Ray and Optical Polarization Observations of the Blazar Mrk 421

We present near-simultaneous X-ray and optical polarization measurements in the high synchrotron peaked (HSP) blazar Mrk 421. The X-ray polarimetric observations were carried out using Imaging X-ray Polarimetry Explorer (IXPE) on 2023 December 6. During IXPE observations, we also carried out optical polarimetric observations using 104 cm Sampurnanand telescope at Nainital and multiband optical imaging observations using 2 m Himalayan Chandra Telescope at Hanle. From model-independent analysis of IXPE data, we detected X-ray polarization with degree of polarization (ΠX) of 8.5% ± 0.5% and an electric vector position angle (ΨX) of 10.°6 ± 1.°7 in the 2−8 keV band. From optical polarimetry on 2023 December 6, in B, V, and R bands, we found values of Π B = 4.27% ± 0.32%, Π V = 3.57% ± 0.31%, and Π R = 3.13% ± 0.25%. The value of Π B is greater than that observed at longer optical wavelengths, with the degree of polarization suggesting an energy-dependent trend, gradually decreasing from higher to lower energies. This is consistent with that seen in other HSP blazars and favors a stratified emission region encompassing a shock front. The emission happening in the vicinity of the shock front will be more polarized due to the ordered magnetic field resulting from shock compression. The X-ray emission, involving high-energy electrons, originates closer to the shock front than the optical emission. The difference in the spatial extension could plausibly account for the observed variation in polarization between X-ray and optical wavelengths. This hypothesis is further supported by the broadband spectral energy distribution modeling of the X-ray and optical data.

A New Link to Helices in Euclidean $3$-Space

In this paper, we introduce a novel approach for obtaining the parametric expression and description of a general helix, slant helix, and Darboux helix. The new method involves projecting $\alpha $ onto a plane passing through $\alpha \left( 0\right) $ and orthogonal to the unit axis vector $U$ in order to determine the position vector of the general helix $\alpha $. The position vector of the helix with the plane curve $\gamma $ and its axis $U$ is then established. Additionally, a relation between the curvatures of $\alpha $ and $\gamma $ is presented. The proposed technique is then applied to derive the parametric representation of a slant helix and Darboux helix, followed by the provision of various examples obtained through the application of this methodology.

STCA: High-Altitude Tracking via Single-Drone Tracking and Cross-Drone Association

In this paper, we introduce a high-altitude multi-drone multi-target (HAMDMT) tracking method called STCA, which aims to collaboratively track similar targets that are easily confused. We approach this challenge by categorizing the HAMDMT tracking into two principal tasks: Single-Drone Tracking and Cross-Drone Association. Single-Drone Tracking employs positional and appearance data vectors to overcome the challenges arising from similar target appearances within the field of view of a single drone. The Cross-Drone Association employs image-matching technology (LightGlue) to ascertain the topological relationships between images captured by disparate drones, thereby accurately determining the associations between targets across multiple drones. In Cross-Drone Association, we enhanced LightGlue into a more efficacious method, designated T-LightGlue, for cross-drone target tracking. This approach markedly accelerates the tracking process while reducing indicator dropout. To narrow down the range of targets involved in the cross-drone association, we develop a Common View Area Model based on the four vertices of the image. Considering to mitigate the occlusion encountered by high-altitude drones, we design a Local-Matching Model that assigns the same ID to the mutually nearest pair of targets from different drones after mapping the centroids of the targets across drones. The MDMT dataset is the only one captured by a high-altitude drone and contains a substantial number of similar vehicles. In the MDMT dataset, the STCA achieves the highest MOTA in Single-Drone Tracking, with the IDF1 system achieving the second-highest performance and the MDA system achieving the highest performance in Cross-Drone Association.

A Lightweight Model Enhancing Facial Expression Recognition with Spatial Bias and Cosine-Harmony Loss

This paper proposes a facial expression recognition network called the Lightweight Facial Network with Spatial Bias (LFNSB). The LFNSB model effectively balances model complexity and recognition accuracy. It has two key components: a lightweight feature extraction network (LFN) and a Spatial Bias (SB) module for aggregating global information. The LFN introduces combined channel operations and depth-wise convolution techniques, effectively reducing the number of parameters while enhancing feature representation capability. The Spatial Bias module enables the model to focus on local facial features while capturing the dependencies between different facial regions. Additionally, a new loss function called Cosine-Harmony Loss is designed. This function optimizes the relative positions of feature vectors in high-dimensional space, resulting in better feature separation and clustering. Experimental results on the AffectNet and RAF-DB datasets demonstrate that the LFNSB model achieves competitive recognition accuracy, with 63.12% accuracy on AffectNet-8, 66.57% accuracy on AffectNet-7, and 91.07% accuracy on RAF-DB, while significantly reducing the model complexity.

Curves of Constant Ratio with Quasi frame in E^3

In the present study we handle a regular unit speed curve by means of the position vector given by the vectorial equation γ (s)=m0 t(s)+m1 nq (s)+m2 bq (s) where bq (s), nq (s) and t(s) are quasi frame vectors. Firstly, we analysis these curves and investigate to being constant ratio curve. Then, we give the parameterizations of T-constant and N- constant curve in accordance with quasi frame. Further, we get the conditions for a regular curve to correspond to be a W- curve in E^3.

Multifrequency polarimetry of high-synchrotron peaked blazars probes the shape of their jets

Multifrequency polarimetry is emerging as a powerful probe of blazar jets, especially with the advent of the Imaging X-ray Polarimetry Explorer (IXPE) space observatory. We studied the polarization of high-synchrotron peaked (HSP) blazars, for which both optical and X-ray emission can be attributed to synchrotron radiation from a population of nonthermal electrons. We adopted an axisymmetric stationary force-free jet model in which the electromagnetic fields are determined by the jet shape. When the jet is nearly parabolic, the X-ray polarization degree is ΠX ∼ 15–50%, and the optical polarization degree is ΠO ∼ 5–25%. The polarization degree is strongly chromatic: ΠX/ΠO ∼ 2–9. This chromaticity is due to the softening of the electron distribution at high energies, and is much stronger than for a uniform magnetic field. The electric vector position angle (EVPA) is aligned with the projection of the jet axis on the plane of the sky. These results compare very well with multifrequency polarimetric observations of HSP blazars. When the jet is instead nearly cylindrical, the polarization degree is large and weakly chromatic (we find ΠX ∼ 70% and ΠO ∼ 60%, close to the expected values for a uniform magnetic field). The EVPA is perpendicular to the projection of the jet axis on the plane of the sky. A cylindrical geometry is therefore practically ruled out by current observations. The polarization degree and the EVPA may be less sensitive to the specific particle acceleration process (e.g., magnetic reconnection or shocks) than previously thought.

Relative position estimation using modulated magnetic field for close proximity formation flight

This paper presents a method to estimate relative position vectors between spacecraft equipped with magnetic coils and magnetic field sensors for close proximity operation. Filters can segregate a magnetic field with a particular frequency if spacecraft drive their coils with this specific frequency. The proposed method utilizes the amplitude of the magnetic field with a particular frequency to estimate relative position vectors. The method consists of an initial position estimator and a sequential position estimator, which is an unscented Kalman filter. The initial position estimator provides a coarse estimate for the relative position vectors using the segregated magnetic field. Relation between the magnetic field and relative position vector is derived analytically in this article for the initial position estimator. The unscented Kalman filter refines the estimation accuracy by initializing the filter with the estimate by the initial position estimator. It is shown that a spacecraft can conduct relative position vector estimation using the magnetic field of a target spacecraft, provided that a few conditions clarified in the article are satisfied. Finally, the proposed estimators are evaluated numerically via simulations.

A Remote Two-Point Magnetic Localization Method Based on SQUID Magnetometers and Magnetic Gradient Tensor Invariants.

In practical application, existing two-point magnetic gradient tensor (MGT) localization methods have a maximum detection distance of only 2.5 m, and the magnetic moment vectors of measured targets are all unknown. In order to realize remote, real-time localization, a new two-point magnetic localization method based on self-developed, ultra-sensitive superconducting quantum interference device (SQUID) magnetometers and MGT invariants is proposed. Both the magnetic moment vector and the relative position vector can be directly calculated based on the linear positioning model, and a quasi-Newton optimization algorithm is adopted to further improve the interference suppression capability. The simulation results show that the detection distance of the proposed method can reach 500 m when the superconducting MGT measurement system is used. Compared with Nara's single-point tensor (NSPT) method and Xu's two-point tensor (XTPT) method, the proposed method produces the smallest relative localization error (i.e., significantly less than 1% in the non-positioning blind area) without sacrificing real-time characteristics. The causes of and solutions to the positioning blind area are also analyzed. The equivalent experiments, which were conducted with a detection distance of 10 m, validate the effectiveness of the localization method, yielding a minimum relative localization error of 4.5229%.

Unified bounded potential function approach for multi-hovercraft connectivity-maintaining and formation maneuvering control without acceleration measurement

This paper addresses the distributed leader–follower connectivity-maintaining and formation maneuvering control issue for underactuated multi-hovercraft without acceleration measurement. Firstly, a novel time-varying offset term is introduced into the position vector, which transforms the motion equation of the hovercraft into a fully actuated form. In addition, an unified bounded potential function strategy is proposed to simultaneously achieve connectivity-maintaining and formation maneuvering error stabilization without the need to design additional formation error stability terms in the controller. Then, in the absence of dynamic leader acceleration measurement, a distributed variable structure robust term is introduced into the bounded formation maneuvering control protocol, which resists entirely the influence of unknown acceleration on the system. The proposed protocol was rigorously analyzed using the Lyapunov theory. Finally, simulation results validate the effectiveness of the proposed control protocol.

Physical interpretation of invariance of vector differential operators in three orthogonal coordinate systems and a case study of wall and globe of death

In the present study, the effect of operators on fundamental physical quantities in three orthogonal coordinate systems was analyzed using differential equations. The mathematical expression for the position vector and its magnitude, velocity, &acceleration in three orthogonal coordinate systems were obtained from the geometry of the figure and differentiation. The derivations of operation of vector differential operators (curl and diversions) on position vectors were derived, and their physical significance was illustrated. Similarly, the operation of the Laplacian operator on the magnitude of the position vector was also studied. The study highlighted the invariance in the results of all operations in three orthogonal coordinate systems. An investigation has been performed to describe the wall of death and the globe of death problem in appropriate orthogonal coordinate systems. The interpretations in terms of velocity, acceleration, and the net force acting on the vehicle are explained in detail.

A secure image steganography based on LSB technique and 2D chaotic maps

This paper introduces a pioneering, effective data-hiding algorithm using different sizes of cover images and different types of secret data (image, txt, and audio). The proposed algorithm is based on a hybrid 1D chaotic map combined with a 2D composite chaotic map paired with optimization and Least Significant Bits (LSB) techniques. We employ chaotic maps to create the initial embedding position vector, and LSB to hide the secret message in the cover image. The optimization technique utilizes the chaotic maps to optimize the random embedding sites, looking for value matches between the cover image pixels and the secret data bits. This partial improvement leads to a high-quality stego-image, a large embedding capacity, imperceptibility to the human eye, undetectability, and enhanced security. The outcomes of the extensive experiments show that when the payload is 4.2 bits per pixel, the peak signal-to-noise ratio value (PSNR), which expresses the visual quality, is above 30 dB. Furthermore, the experimental results illustrate that the system exhibits robustness against various types of attacks. As a final point of strength, the large key space (2^206) prevents the secret data from being resolved if stego-images are accessed by intruders or third parties. Even minor changes in key bits can significantly alter the extracted secret data, resulting in entirely different secret data.

Discrete search-based determination of a local orbital frame in unknown environments

A local orbital frame is an important and often applied coordinate frame in attitude and orbit control. Usually, a navigation filter estimates the position and velocity vector, which are used to build up this reference frame. It is beneficial for many space applications, such as communication or Earth observation missions, or for conducting orbit control maneuvers to change the orbit plane. Furthermore, satellite formation flying can require an orbital frame to describe relative motion. This work investigates the feasibility of determining the local-vertical local horizontal (LVLH) frame without full knowledge of the orbit. This scenario often applies to non-characterized small bodies like asteroids or comets. A discrete search method is used to determine the complete LVLH frame in real-time, assuming that one axis, a line-of-sight vector to the body’s center of mass, is known. By minimizing an objective function, the remaining axes can be determined. The estimated parameters are the inclination and the right ascension of the ascending node of the osculating orbit plane. This study investigates the feasibility of this concept and then applies it to perturbed orbits and sensor noise. The proposed method demonstrates that a discrete search can determine the LVLH frame. The approach can be seen as a step toward increasing the autonomy of a spacecraft near small bodies with unknown environments.

The Pedal Curves Generated by Alternative Frame Vectors and Their Smarandache Curves

In this paper, pedal-like curves are defined resulting from the orthogonal projection of a fixed point on the alternative frame vectors of a given regular curve. For each pedal curve, the Frenet vectors, the curvature and the torsion functions are found to provide the common relations among the main curve and its pedal curves. Then, Smarandache curves are defined by using the alternative frame vectors of each pedal curve as position vectors. The relations of the Frenet apparatus are also established for the pedal curves and their corresponding Smarandache curves. Finally, the expressions of the alternative frame apparatus of each Smarandache curves are given in terms of the alternative frame elements of the pedal curves. Thus, a set of new symmetric curves are introduced that contribute to the vast curve family.

Generation of cubic Hermite spline-based trochoidal milling toolpath by introducing a coefficient factor in machining curved slots

Trochoidal milling has become popular in high-speed milling due to its ability to reduce cutting force, enhance thermal dissipation, and prolong tool life. Among other toolpath patterns, the cubic Hermite spline offers significant advantages in generating trochoidal milling toolpath in machining complex and curved slots. However, determining those two different relation coefficients in the polynomial function of cubic Hermite spline remains complicated and empirical. This paper introduces a coefficient factor to simplify the determination process, which only requires the position and tangent vector parameters of each endpoint pair. The coefficient factor combines an instantaneous in-process slot width (IISW)-related width factor and a tangent vector direction-related direction factor. Two complex-curved slots are used to validate the performance of the proposed method. The results show that this method is straightforward and effective in generating trochoidal milling toolpaths for machining complex-curved slots while matching the slot geometry. Additionally, compared with a direct 5-axis trochoidal milling (one-step slotting strategy) in trochoidal milling of 3D slots on both serial and hybrid machining tools, a two-step slotting strategy (3-axis trochoidal milling and a successive 5-axis perpetual milling) is preferable in improving machining efficiency.

Some classification of affine homothetical surfaces of finite type in 𝕀

Abstract A Euclidean submanifold is said to be of Chen finite type if its coordinate functions are a finite sum of eigenfunctions of its Laplacian Δ. In this paper, we classify two types of affine homothetical surfaces of finite type in isotropic 3-space 𝕀 3 {\mathbb{I}^{3}} under the condition Δ ⁢ r i = λ i ⁢ r i {\Delta r_{i}=\lambda_{i}r_{i}} , where ( r i ) {(r_{i})} is the i-component function of the position vector r ( i = 1 , 2 , 3 {i=1,2,3} ), λ i ∈ ℝ {\lambda_{i}\in\mathbb{R}} and Δ denotes the Laplace operator.

The direction vector assisted INS/spectral redshift integrated navigation system for spacecraft

Abstract A reliable and autonomous navigation system is crucial for the achievement of high survivability of spacecraft. As a novel autonomous navigation system, inertial/spectral redshift(INS/SRS) integrated navigation system can correct the navigation error of INS through redshift and direction vector information from celestial body. However, Since SRS need to obtain the position measurement by integrating the velocity information of the spacecraft, the position error from INS/SRS is diverged. Thus, this paper investigates a direction vector assisted INS/SRS integrated navigation system for the spacecraft. In this paper, the relationship among the position of spacecraft, redshift and direction vector from celestial body are investigated. And then a direction vector assisted SRS is proposed which can solve the position information of spacecraft directly by redshift and direction vector information. Finally, the direction vector assisted SRS has been combined with INS as the direction vector assisted INS/SRS integrated navigation system. Simulations and comprehensive analysis have demonstrated the proposed integrated navigation system has better navigation performance than INS/SRS integrated navigation system.

Relation Between the Single Orths of a Point on the Axis of the Deformed Thread in the Case of Euler and Lagrange Coordinates

The values of the position vectors and unit tangents have been determined by research, defining the positions of points on the axis of the deformed thread using Eulerian and Lagrangian coordinates. The position vector defines the point's position on the line relative to the moving coordinate system. It determines the point's position on the line relative to the stationary coordinate system. Consequently, when the thread is displaced, the point moves to a new position. The new position vector defines the point's position on the line. The displacement vector of the point on the thread axis characterizes the shift of points due to deformation at the thread intersection. This has made it possible to use these theoretical relation at the initial stage of designing the technological process to derive equations for determining thread tension in the fabric and knit forming zone, reduce thread breakage rates, and enhance the quality of the finished products

Research on relative reachable domain in target orbit for maneuvering spacecraft

PurposeLots of successful space missions require that the maneuvering spacecraft can reach the target spacecraft. Therefore, research on relative reachable domain (RRD) in target orbit for maneuvering spacecraft is particularly important and is currently a hot-debated topic in the field of aerospace. This paper aims at analyzing and simulating the RRD in target orbit for maneuvering spacecrafts with a single fixed-magnitude impulse and continuous thrust, respectively, to provide a basis for analyzing the feasibility of spacecraft maneuvering missions and improving the design efficiency of spacecraft maneuvering missions.Design/methodology/approachBased on the kinematics model of relative motion, RRD in target orbit for maneuvering spacecraft with a single fixed-magnitude impulse can be calculated via analyzing the relationship between orbital elements, position vector and velocity vector of spacecrafts, and relevant studies are introduced to compare simulation results for the same case and validate the method proposed in the paper. With analysis of the dynamic model of relative motion, the calculation of RRD in target orbit for maneuvering spacecraft with continuous thrust can be transformed as the solution of the optimal control problem, and example emulations are carried out to validate the method.FindingsFor the case with a single fixed-magnitude impulse, simulation results show preliminarily that the method is in agreement with the method in Ref. (Wen et al., 2016), which treats the same case and thus is plausibly correct and feasible. For the case with continuous thrust, analysis and simulation results confirm the validity of the proposed method. The methods based on relative motion in this paper can efficiently determining the RRD in target orbit for maneuvering spacecraft.Originality/valueBoth theoretical analyses and simulation results indicate that the method proposed in this paper is comparatively simple but efficient for determine the RRD in target orbit for maneuvering spacecraft swiftly and precisely.

PaIRS-UniNa: A Robust And Accurate Free Tool For Digital Particle Image Velocimetry And Optical Camera Calibration

This contribution presents PaIRS-UniNa (PArticle Image Reconstruction Software – University of Naples “Federico II”), a free software application designed to perform digital particle image velocimetry (PIV). PaIRS-UniNa relies on a powerful C library designed for speed, robustness and accuracy, and a user-friendly graphical interface (Figure 1) running in Python environment on all operating systems, including Windows, Linux and MacOS. At the current stage, it features modules to perform two-component (2C) PIV, stereoscopic PIV and optical camera calibration for multi-camera systems. The processing of PIV and stereoscopic PIV data is based on an iterative image deformation method, which can be customized by the user varying different parameters in such a way to find the best compromise between accuracy and computational speed. These parameters include the size, shape and number of interrogation windows, the number of process iterations and the type of interpolating functions for both image deformation and displacement interpolation (such as bilinear, bicubic, methods based on simplexes or the FFT shift theorem and B-splines of varying orders). Additionally, it is possible to select a range of weighting windows for cross-correlation estimation and velocity field filtering, including rectangular, Blackman, Gaussian, Harris, Hann windows, among others, and several vector validation strategies for outlier detection and replacement. Such a level of customization enables to effectively adjust the modulation transfer function of the PIV process to meet specific application requirements. For the stereoscopic PIV process two different approaches are possible: mapping, which involves applying PIV to de-warped images for 2D-2C displacement fields, and warping, which applies PIV to raw images and combine 3C reconstruction and image dewarping in a single subsequent step. In order to accurately estimate the laser sheet plane location and correct errors due to misalignment and inaccurate displacement vector positions, a disparity correction procedure is also available. The calibration module (CalVi) supports accurate calibration with the camera models mostly used in the PIV community: polynomials, rational functions and the pinhole camera model. Moreover, it supports the integration of the pinhole camera model with a refractive correction model for cylindrical geometries and camera calibration procedures working with unknown positions and orientations of the calibration target. In such a way, the target may be moved by hand without losing accuracy in comparison with a conventional calibration, in which the target is displaced with the aid of translational and rotational stages and knowledge of the target positions is strictly required. Already used in numerous experimental studies by the Experimental Thermo-Fluid Dynamics group of University of Naples “Federico II” and international collaborating groups, PaIRS-UniNa offers a rapid and effective free alternative to commercial PIV software for research and industrial use.

Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness

In this paper, a three-dimensional vector field model is proposed, whose dimensions are the Hansen Solubility Parameters: dispersion parameter (δD), polarity parameter (δP), and hydrogen bonding parameter (δH). The vector space that defines the field has the peculiarity of having a dispersion vector with a magnitude of 2 as its base vector, while the polarity and hydrogen bonding vectors have a magnitude of 1. A substance is characterised as a position vector, and the interaction between two substances is determined by calculating the vector difference of both, known as the interaction vector. The interaction among substances may involve solubility, swelling, cracking, surface tension, interface tension, and any physical phenomena where the intermolecular energies of dispersion, polarity or hydrogen bonding come into play. This paper studies free surface energy (surface and interfacial tension). It has been found that free surface energy is directly proportional to the square of the magnitude of the interaction vector. The proportionality constant, τ, is expressed in length units, has a value of 0.025 nm, and does not depend on the chemical nature of the substance or state of matter (solid, liquid or gas). The constant value τ appears universal and aligns with the thickness of interfaces, thereby supporting Guggenheim’s hypothesis. This hypothesis asserts that interfaces possess actual thickness and are not merely mathematical surfaces, as originally postulated by Gibbs. Moreover, it also has been found that the interface thickness, τ, is approximately equal to half of the Bohr radius, a0, which is defined by universal constants. Because the solubility parameters of thousands of substances are known and can be easily determined from their molecular structure, a good approximation of the surface and interfacial tension of any given substance can now be calculated. It has also been found that the contact angles of sessile droplets in three-phased systems can be calculated from the interaction vectors of the implicated substances.