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Modified WKB theory for calculating tunneling splittings in symmetric multi-well systems in full dimensionality is re-derived using Cartesian coordinates. It is explicitly shown that the theory rests on the wavefunction that is exact for harmonic potentials. The theory was applied to calculate tunneling splittings in vinyl radical and some of its deuterated isotopologues in their vibrational ground states and the low-lying vibrationally excited states and compared to exact variational results. The exact results are reproduced within a factor of 2 in most states. Remarkably, all large enhancements of tunneling splittings relative to the ground state, up to three orders in magnitude in some excited mode combinations, are well reproduced. It is also shown that in the asymmetrically deuterated vinyl radical, the theory correctly predicts the states that are localized in a single well and the delocalized tunneling states. Modified WKB theory on the minimum action path is computationally inexpensive and can also be applied without modification to much larger systems in full dimensionality; the results of this test case serve to give insight into the expected accuracy of the method. [ABSTRACT FROM AUTHOR]

For large plasmonic nanoparticles, retardation effects become important once their length becomes comparable to the wavelength of light. However, most models do not incorporate retardation effects due to the high computational cost of solving for the optical properties of large atomistic electrodynamics systems. In this work, we derive and implement a recursive fast multipole method (FMM) in Cartesian coordinates that includes retardation effects. In this method, higher-order electrodynamic interaction tensors used for the FMM are calculated recursively, thus greatly reducing the implementation complexity of the model. This method allows for solving of the optical properties of large atomistic nanoparticles with controlled accuracy; in practice, taking the expansion to the fifth order provides a good balance of accuracy and computational time. Finally, we study the effects retardation has on the near- and far-field properties of large plasmonic nanoparticles with over a million atoms using this method. We specifically focus on nanorods and their dimers, which are known to generate highly confined fields in their junctions. In the future, this method can be applied to simulations in which accurate near-field properties are required, such as surface-enhanced Raman scattering. [ABSTRACT FROM AUTHOR]

Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced. [ABSTRACT FROM AUTHOR]

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ω GDD ML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a 0 − 1 and only five systems (0.07%) with an absolute error larger than 0.01 a 0 − 1 , which indicates the good transferability of our ω GDD ML model. In addition, the only required input to obtain ω GDD ML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE ( ω GDD ML ) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE ( ω GDD ML ) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional ab initio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ω GDD ML model. [ABSTRACT FROM AUTHOR]

In this paper, a high-order direct arbitrary Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) scheme is developed for compressible fluid flows in two-dimensional (2D) Cartesian and cylindrical coordinates. The scheme in 2D cylindrical coordinates is based on the control volume approach and it can preserve the conservation property for all the conserved variables including mass, momentum and total energy. In this hydrodynamic scheme, a kind of high-order Taylor expansion basis function on the general element is used to construct the interpolation polynomials of the physical variables for the DG discretization. The terms including the material derivatives of the test functions are omitted, which simplifies the scheme significantly. Furthermore, the mesh velocity in the direct ALE framework is obtained by implementing an adaptive mesh movement method with a kind of dimensional-splitting type monitor function. This type of mesh movement method can automatically concentrate the mesh nodes near the regions with large gradients of the variables, which can greatly improve the resolutions of numerical solutions near the specified regions. For removing the numerical oscillations in the simulations, a Hermite Weighted Essential Non-oscillatory (HWENO) reconstruction is employed as a slope limiter. Finally, some test cases are displayed to verify the accuracy and the good performance of our scheme. [ABSTRACT FROM AUTHOR]

Developing narrowband blue multiple resonance (MR) organic emitters with Commission Internationale de L'Eclairage (CIE) y coordinates <0.1 is essential for advanced display technologies. This study proposes a deep‐blue thermally activated delayed fluorescence (TADF) emitter, named 2BNO, which integrates two independent MR cores. Unlike many TADF materials with single‐bonded dual emitting cores, 2BNO utilizes a steric hindrance‐assisted fluorene bridge to achieve an orthorhombic molecular structure. The dual‐core MR‐TADF emitter shows enhanced light absorption and a high photoluminescence quantum yield. Notably, the emission of 2BNO is not significantly redshifted compared to single‐core compounds and maintains a narrow full width at half‐maximum (FWHM) of 24 nm with CIE coordinates of (0.147, 0.041) in 2Me‐THF solution, nearing the BT.2020 blue standard. Organic light‐emitting diodes (OLEDs) incorporating 2BNO as the emitter exhibit deep‐blue emission at 460 nm with a narrow FWHM of 29 nm and CIE coordinates of (0.14, 0.09). The dual emitting core design significantly improves device efficiency, achieving a high external quantum efficiency (EQE) of 19.8%. The dual‐core molecular design strategy in this work is demonstrated to be effective in promoting the efficiency of the TADF emitters while preserving deep‐blue color purity. [ABSTRACT FROM AUTHOR]

This paper describes a project assigned in a multivariable calculus course. The project showcases many fundamental concepts studied in a typical course, including the distance formula, equations of lines and planes, intersection of planes, Lagrange multipliers, integrals in both Cartesian and polar coordinates, parametric equations, and arc length. [ABSTRACT FROM AUTHOR]

In the presented work, the free vibration problem is investigated for a cantilever trapezoidal sandwich plate with an auxetic reentrant honeycomb core covered with laminated nanocomposite three-phase face sheets. Each lamina in the face sheets is made of polymer enriched with carbon nanotubes and glass fibers. The plate is modeled based on the first-order shear deformation theory and the mechanical properties of each lamina are estimated using the rule of mixture, the Eshelby–Mori–Tanaka scheme, and Hanh's homogenization approach. Utilizing Hamilton's principle, the governing equations and corresponding boundary conditions are derived. These equations are converted from the Cartesian coordinates into dimensionless computational coordinates using a transformation of coordinates. Utilizing the differential quadrature method, an approximate solution is presented to attain the natural frequencies and the corresponding modes shapes. It is observed that there is an optimum ratio of the thickness of the auxetic reentrant honeycomb core to the total thickness of the plate which brings about the highest natural frequencies. [ABSTRACT FROM AUTHOR]

The list of standard abbreviations for JDS is available at adsa.org/jds-abbreviations-24. Nonstandard abbreviations are available in the Notes. Udder conformation is directly related to milk yield, cow health, workability, and welfare. Automatic milking systems (AMS, also known as milking robots) have become popular worldwide, and the number of dairy farms adopting these systems has increased considerably over the past years. In each milking visit, AMS record the location of the 4 teats as Cartesian coordinates in an xyz plan, which can then be used to derive udder conformation traits. Because AMS generate a large amount of data for individual cows per milking visit, they can contribute to an accurate assessment of important traits such as udder conformation without the addition of human classifier errors (in subjective scoring systems). Therefore, the primary objectives of this study were to estimate genomic-based genetic parameters for udder conformation traits derived from AMS records in North American Holstein cattle and to assess the genetic correlation between the derived traits for evaluating the feasibility of multitrait genomic selection for breeding cows that are more suitable for milking in AMS. The Cartesian teat coordinates measured during each milking visit were collected by 36 milking robots in 4,480 Holstein cows from 2017 to 2021, resulting in 5,317,488 records. A total of 4,118 of these Holstein cows were also genotyped for 57,600 SNPs. Five udder conformation traits were derived: udder balance (UB, mm), udder depth (UD, mm), front teat distance (FTD, mm), rear teat distance (RTD, mm), and distance front–rear (DFR, mm). In addition, 2 traits directly related to cow productivity in the system were added to the study: daily milk yield (DY) and milk electroconductivity (EC; as an indicator of mastitis). Variance components and genetic parameters for UB, UD, FTD, RTD, DFR, DY, and EC were estimated based on repeatability animal models. The estimates of heritability (± SE) for UB, UD, FTD, RTD, DFR, DY, and EC were 0.41 ± 0.02, 0.79 ± 0.01, 0.53 ± 0.02, 0.40 ± 0.02, 0.65 ± 0.02, 0.20 ± 0.02, and 0.46 ± 0.02, respectively. The repeatability estimates (± SE) for UB, UD, FTD, RTD, and DFR were 0.82 ± 0.01, 0.93 ± 0.01, 0.87 ± 0.01, 0.83 ± 0.01, and 0.88 ± 0.01, respectively. The strongest genetic correlations were observed between FTD and RTD (0.54 ± 0.03), UD and DFR (−0.47 ± 0.03), DFR and FTD (0.32 ± 0.03), and UD and FTD (−0.31 ± 0.03). These results suggest that udder conformation traits derived from Cartesian coordinates from AMS are moderately to highly heritable. Furthermore, the moderate genetic correlations between these traits should be considered when developing selection subindexes. The most relevant genetic correlations between traits related to cow milk productivity and udder conformation traits were between UD and EC (−0.25 ± 0.03) and between DFR and DY (0.30 ± 0.04), in which both genetic correlations are favorable. These findings will contribute to the design of genomic selection schemes for improving udder conformation in North American Holstein cattle, especially in precision dairy farms. [ABSTRACT FROM AUTHOR]

The research investigated the tooth backlash influences the error in seedling picking trajectories of the gear train SPM. First, a sine function and the sum of random errors are taken into account is utilized to fit the tooth backlash of the firstly and secondary transmissions. Additionally, the analysis established the relationship between the fitting parameters and the tooth backlash of the firstly and secondary transmissions, in order to determine the appropriate fitting parameters. Next, the relationship between the tooth backlash of the firstly and secondary transmission in the seedling picking mechanism (SPM) and the x, y coordinates, as well as the velocity and acceleration of the seedling needle tip (SNT), is examined. This analysis is based on the error and movement variance of the coordinate and kinematic parameters of SNT. The results indicate that the tooth backlash of the firstly transmission has a more significant influence on the error of the seedling picking trajectory compared to the tooth backlash of the secondary transmission. When the tooth backlash of the noncircular gear in the firstly transmission reaches its maximum value of 0.24 mm, the x and y coordinates of the SNT can reach maximum values of 1 and 3.5 mm. The test of the jumping of the needle tip and idling trajectory description indicated that noncircular gears with larger tooth backlash exhibit higher positional jumping at the tip of the seedling needle. [ABSTRACT FROM AUTHOR]

Fertilizer application has been one of the most important facilities to advance agricultural mechanization. Particularly, manual fertilization cannot fully meet the large-scale production in recent years. In this article, a chain reversal trenching and application device was presented for the organic fertilizer in orchards, in order to enhance the trenching depth and uniform fertilization. A reverse-chain trenching mechanism was employed with a fixed trenching blade that moved in the opposite direction of the chain. The soil cutting and simultaneous backfilling were allowed within the trench, as the device progressed. A trenching depth of up to 600mm was achieved in the chain trenching mechanisms. The separate backfilling was reduced to leave no visible trenches on the surface after completion. This design was also a streamlined operation. The mathematical analysis of the trenching blade was conducted to establish a mathematical model using Cartesian coordinate transformations. The relationship equation was derived for the cutting angle. Optimal angle parameters were also provided. According to the trenching depth analysis, the hydraulic adjustment cylinders were selected for the trenching device. A scrapertype fertilizer application mechanism was adopted to develop the discrete element simulation models for both upright and sideways fertilizer application modes. The fertilizer distribution patterns were analyzed under the two modes. While both modes were similarly distributed fertilizer, and the forward-facing mode was more suitable for the operations with the larger fertilizer widths, while the sideward-facing mode was with the smaller fertilizer widths. In the two fertilizer application modes, the sideways application mode had better uniformity, especially at the lower forward speeds. Therefore, the application mode of sideward-facing fertilizer was selected to ensure that all organic fertilizer accurately fell into the trench. A single-factor experiment was carried out to explore the effects of scraper height, angle, and spacing on the normal contact force and coefficient of variation. All three parameters shared a significant impact on the coefficient of variation. In a coefficient of variation of less than 15%, the optimal height, angle, and spacing of the scraper were selected to minimize the normal contact force, resulting in values of 20 mm, 90°, and 180 mm, respectively. According to these optimal parameters of the scraper, the simulation was conducted to yield a coefficient of variation of 6.02% and a normal contact force of 9.03 N, both of which were lower than those before optimization. Subsequently, a physical prototype was fabricated and field-tested. An average coefficient of variation of 8.34% was obtained for fertilizer distribution, indicating better uniformity. Furthermore, the maximum and minimum fertilizer application tests showed that the quantities ranged from 0.8 to 6 kg/m, thus meeting the fertilization requirements of different plots. The trenching performance tests show that the average trenching depths of two operations were 616.0 and 624.4 mm, respectively, with stability coefficients of 93.57% and 92.58%, respectively, both exceeding 90%. The average trenching widths were 305.4 and 295.4 mm, respectively, with consistency coefficients of 96.16% and 95.04%, respectively, both exceeding 95%. Therefore, the device exhibited excellent performance in the fertilizer distribution and trenching operations, fully meeting the agronomic requirements. The findings can provide a new tool for the deep application of organic fertilizers in orchards, indicating the promising potential prospects. Innovative design and efficiency can also offer valuable insights into the agricultural fields. [ABSTRACT FROM AUTHOR]

This article, titled "Guest Editorial: Connecting Mathematical Representations from Algebra to Calculus," discusses the importance of connecting mathematical representations in order to enhance mathematical comprehension. The author emphasizes that learners should not only learn conventional forms of representation but also construct and use their own representations. The article presents several studies that explore the difficulties learners encounter when connecting representations, the underlying concepts vital for connecting representations, the tasks and experiences that support learners in connecting representations, and how instructors can aid student learning with representations. The studies highlight the significance of connecting representations in algebra, geometry, and calculus, as well as the need for further research in this area. Additionally, the article discusses the construction of representations in unconventional settings and the extent of representational connections made by students and fostered by teachers. The studies underscore the importance of instructional strategies that improve students' mathematical understanding and emphasize the need for further research in this field. [Extracted from the article]

In this work, we present some criteria about the existence and nonexistence of both Puiseux inverse integrating factors V$V$ and Puiseux first integrals H$H$ for planar analytic vector fields having a monodromic singularity. These functions are a wide generalization of their formal R[[x,y]]$\mathbb {R}[[x,y]]$ or algebraic counterpart in Cartesian coordinates (x,y)$(x,y)$. We prove that none of the functions H$H$ and V$V$ can be used to characterize degenerate centers although the existence of H$H$ is a sufficient center condition. [ABSTRACT FROM AUTHOR]

This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton's second law, a two-degree-of-freedom control equation of the system, including PD control terms and gravitational effects, is constructed. This equation involves not only parametric excitation, quadratic nonlinearity, and cubic nonlinearity but also a more pronounced coupling effect between the magnetic poles due to the presence of gravity. Secondly, using the multi-scale method, a four-dimensional averaged equation of the system in Cartesian and polar coordinates is derived. Finally, through numerical analysis, the system's amplitude–frequency response, motion trajectory, the relationship between energy and amplitude, and global dynamic behaviors such as bifurcation and chaos are discussed in detail. The results show that the PD controller significantly affects the system's spring hardening/softening characteristics, excitation, amplitude, energy, and stability. Specifically, increasing the proportional gain can quickly suppress the rotor's motion, but it also increases the system's instability. Adjusting the differential gain can transition the system from a chaotic state to a stable periodic motion. [ABSTRACT FROM AUTHOR]

The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell, in cases of 1 : 2 inter-well internal resonance and primary resonance. The transverse foundation excitation is applied to the fixed end of the structure, and the other end is in a free state. The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation. The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms. Deriving from the obtained frequency-amplitude and force-amplitude response curves, a detailed analysis is conducted to examine the impacts of excitation amplitude, damping coefficient, and tuning parameter on the nonlinear internal resonance characteristics of the system. The nonlinear softening characteristic is exhibited in the upper stable-state, while the lower stable-state demonstrates the softening and linearity characteristics. Numerical simulation is carried out using the fourth-order Runge-Kutta method, and a series of nonlinear response curves are plotted. Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell. [ABSTRACT FROM AUTHOR]

Benzoxazine dimers are a group of compounds with a variety of properties, such as anticancer properties and good chelating behaviors. The modification of the benzoxazine dimers can be carried out on the OH groups as well as the benzene moiety. There are several works reported on the property adjustment involving the use of different substituent groups on the benzene ring. Only a few works described the properties and crystallographic studies of the OH-modified benzoxazine dimer. The repulsion forces between two bulky benzoyl groups push them to be more distant compared to the unmodified benzoxazine dimer. According to the crystallographic information, the C—H···O, C—H···π, and π···π interactions hold neighbor molecules together, which consequently stabilize the crystal structure. Thermal analyses (TGA and DSC) reveal that the synthesized benzoated benzoxazine dimer is stable up to 175 °C. Hirshfeld surface analysis confirmed the presence of the C—H···O and C—H···π interactions as seen from the high contributions of the following contacts: H···H (60.6%), H···C/C···H (25.1%), and H···O/O···H (12.3%). Moreover, the observed π···π interaction is supported by the shape-index property of the corresponding Hirshfeld surface. For the solid-state photoluminescence of the di-benzoated benzoxazine dimer recorded at the excitation wavelength range from 265 to 320 nm, the emission peak at 490 nm is observed together with another peak or shoulder in the range of 440–480 nm. For all the excitation wavelengths studied, the di-benzoated dimer emits the fluorescence in the blue color shades (CIE coordinate of x at 0.137–0.142 and y at 0.200–0.262). The photoluminescence property is found to originate by the benzoate modification of the benzoxazine dimer. [ABSTRACT FROM AUTHOR]

Coffee consumption could provide various benefits for human health, but also could contribute to several health problems. The growing trend of coffee consumption has created a rising demand for decaffeinated coffee that is safe for consumers with low caffeine tolerance. Decaffeination process, however, can result in the alteration of several properties of coffee which affect overall coffee taste. This review discussed current decaffeination methods such as water decaffeination, solvent decaffeination, supercritical decaffeination, and biodecaffeination which includes their mechanisms, benefits, and drawbacks as well as their effect in the physicochemical and sensory characteristics of coffee. Solvent decaffeination has showed potential improvements in the future such as the incorporation of membrane and ultrasonic technology. In addition, the mathematical model for caffeine diffusion has been arranged according to Fick's second law of diffusion, based upon spherical and rectangular coordinates with several assumptions. Further research should be aimed to maintain the properties of coffee after decaffeination process. Furthermore, utilizing new solvents that are safe and non-toxic will potentially be favorable research in the development of decaffeination methods in the future. [ABSTRACT FROM AUTHOR]

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen's theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen's theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart. [ABSTRACT FROM AUTHOR]

An extended two‐dimensional (2D) elasticity theory based on the weighted residual concept is developed in an attempt to capture thickness effects in vibrating thick plates. Plate theories can only provide approximate solutions due to certain kinematics assumptions. The weighting functions are expressed in terms of Legendre orthogonal polynomials. A formulation in rectangular Cartesian coordinates serves as the basis for an implementation of the finite element method. The applicability of the extended 2D elasticity theory is demonstrated through examples of rectangular, thick plates with different aspect ratios, thickness ratios, and boundary conditions. The accuracy of the extended 2D elasticity theory is assessed through a three‐dimensional finite element analysis. The frequencies and modal stresses show excellent agreement with three‐dimensional finite element calculations. [ABSTRACT FROM AUTHOR]

Based on the three-dimensional (3D) linear elasticity theory of piezoelectric semiconductor (PS) structures, inspired by the variational principle and the Mindlin plate theory, a two-dimensional (2D) higher-order theory and equations for thin-film devices are established for a rectangular coordinate system, in which Newton's law (i.e., stress equation of motion), Gauss's law (i.e., charge equation of electrostatics), Continuity equations (i.e., conservation of charge for holes and electrons), drift–diffusion theory for currents in semiconductors, and unavoidable thermo-deformation-polarization-carrier coupling response in external stimulus field environment are all considered. As a typical application of these equations, the static characteristic analysis of electromechanical fields for the extensional deformation of a PS thin-film device with thermal field excitations is carried out by utilizing established zeroth-order equations and the double trigonometric series solution method. It is revealed that the extensional deformations, electric potential, electron and hole concentration perturbations, and their current densities can be controlled actively via artificially tuning thermal fields of external stimuli. Especially, a higher temperature rise can induce a deeper potential well and a higher potential barrier, which can play a vital role in driving effectively motions and redistributions of electrons and holes. Overall, the derived 2D equations as well as the quantitative results provide us some useful guidelines for investigating the thermal regulation behavior of PS thin-film devices. [ABSTRACT FROM AUTHOR]

The study evaluated the spatial position of the mental foramen (MF) using 300 cone‐beam computed tomography. The spatial position was analyzed with the horizontal location and relative location (distance between apical foramen and MF). The horizontal location was assessed through three positions (positions 1, 2, and 3). The relative location was determined with the x, y, and x coordinates of the root apex of mandibular premolars and the MF. Student's t‐test and chi‐square were performed. The most common horizontal location (52%) was position 2, which means between the premolars (p < 0.05). The relative location of the MF to the root apex of the second premolar was closer than the first premolar (p < 0.05). The distance between the root tip of the second premolar and the MF was 5.27 mm, with a minimum value of 1.87 mm. Clinicians should be aware of the possible neural results to the mental nerve of an endodontic infection and the extrusion of irrigation solutions. [ABSTRACT FROM AUTHOR]

In this study, we examine different approaches to the presentation of Y coordinates in mobile auditory graphs, including the representation of negative numbers. These studies involved both normally sighted and visually impaired users, as there are applications where normally sighted users might employ auditory graphs, such as the unseen monitoring of stocks, or fuel consumption in a car. Multi-reference sonification schemes are investigated as a means of improving the performance of mobile non-visual point estimation tasks. The results demonstrated that both populations are able to carry out point estimation tasks with a good level of performance when presented with auditory graphs using multiple reference tones. Additionally, visually impaired participants performed better on graphs represented in this format than normally sighted participants. This work also implements the component representation approach for negative numbers to represent the mapping by using the same positive mapping reference for the digit and adding a sign before the digit which leads to a better accuracy of the polarity sign. This work contributes to the areas of the design process of mobile auditory devices in human-computer interaction and proposed a methodological framework related to improving auditory graph performance in graph reproduction. [ABSTRACT FROM AUTHOR]

Autonomous pollination robots have been widely discussed in recent years. However, the accurate estimation of flower poses in complex agricultural environments remains a challenge. To this end, this work proposes the implementation of a transformer-based architecture to learn the translational and rotational errors between the pollination robot's end effector and the target object with the aim of enhancing robotic pollination efficiency in cross-breeding tasks. The contributions are as follows: (1) We have developed a transformer architecture model, equipped with two feedforward neural networks that directly regress the translational and rotational errors between the robot's end effector and the pollination target. (2) Additionally, we have designed a regression loss function that is guided by the translational and rotational errors between the robot's end effector and the pollination targets. This enables the robot arm to rapidly and accurately identify the pollination target from the current position. (3) Furthermore, we have designed a strategy to readily acquire a substantial number of training samples from eye-in-hand observation, which can be utilized as inputs for the model. Meanwhile, the translational and rotational errors identified in the end-manipulator Cartesian coordinate system are designated as loss targets simultaneously. This helps to optimize the training of the model. We conducted experiments on a realistic robotic pollination system. The results demonstrate that the proposed method outperforms the state-of-the-art method, in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In modern warship, coordinated combat strategies require missiles hit targets simultaneously, sometimes even require angle constraints, which is difficult to replicate in three-dimensional (3-D) models. This paper proposes a novel 3-D sliding mode guidance law with multiple constraints. First, the 3-D no-thrust guidance model is derived in the coordinate system with Y -axis upward. Second, a novel guidance strategy is proposed. In pitch direction, a fast nonsingular sliding mode surface algorithm is proposed to satisfy the desired line-of-sight elevation angle. In yaw direction, based on the guidance conditions, a special sliding mode surface is proposed, which can achieve desired line-of-sight azimuth angle and desired impact time when reaching the sliding surface. Finally, simulations and comparisons verify the good performance. [ABSTRACT FROM AUTHOR]

While the development of solution‐processed organic light‐emitting diodes (sOLEDs) utilizing multiple resonance‐induced thermally activated delayed fluorescence (MR‐TADF) is highly significant, it is restricted by the limited solubility and film‐forming property resulting from the rigid conjugate and planarity of MR‐TADF materials. Herein, an effective strategy is presented to obtain solution‐processed narrowband emitters by introducing an inert steric bulky hindrance group into the multiple resonance skeleton, thereby mitigating issues arising from intermolecular packing‐induced poor solution processing ability and quenching effects. The resulting target emitter, designed as 3CzSF‐BN, exhibits pure‐green emission with a peak at 520 nm and a small full width at half maximum (FWHM) of 30 nm (0.14) eV. Remarkably, it achieves an exceptional photoluminescence quantum yield (PLQY) of 100% and notable advancements in solution processing attributes. The optimized bottom‐emitting sOLED (BE‐sOLED) device achieves an external quantum efficiency (EQE) over 20% with Commission Internationale de I'Éclairage (CIE) coordinates of (0.214, 0.716). Notably, the top‐emitting sOLED (TE‐sOLED) device exhibits an ultra‐pure green color with FWHM of 22 nm and CIE coordinates of (0.138, 0.771), thereby highlighting the effectiveness of this strategy in designing high‐performance solution‐processed MR‐TADF materials. [ABSTRACT FROM AUTHOR]

Context. The morphology of open clusters plays a major role in the study of their dynamic evolution. The study of their morphological coherence, namely, the three-dimensional (3D) difference between the inner and outer morphologies of open clusters, allows us to obtain a better understanding of the morphological evolution of open clusters. Aims. We aim to investigate the morphological coherence of 132 open clusters with up to 1 kpc from the Sun in the three-dimensional (3D) space within the heliocentric cartesian coordinate frame. The 132 open clusters have a 3D core-shell structure and conform to the ellipsoidal model, with all of them coming from a catalog of publicly available clusters in the literature. Methods. We employed the ellipsoid fitting method to delineate the 3D spatial structure of the sample clusters, while using the morphological dislocation (MD) defined in our previous work and the ellipticity ratio (ER) of the clusters' inner and outer structures to characterize the morphological coherence of the sample clusters. Results. The results show an inverse correlation between the ER of the sample clusters and the number of their members, indicating that sample clusters with a much more elliptical external morphology than internal shape generally tend to host a large number of members. Meanwhile, a slight shrinking of the MD of the sample clusters with their members' number may shed light on the significant role of the gravitational binding of the sample clusters in maintaining their morphological stability. Moreover, there are no correlations between the MD and ER of the sample clusters and their age. They are also not significantly correlated with the X-axis, the Y-axis, their orbital eccentricities, and the radial and vertical forces on them. However, the ER of the sample clusters displays some fluctuations in the distributions between it and the above covariates, implying that the morphologies of the sample clusters are sensitive to the external environment if sample effects are not taken into account. Finally, the analysis of the 3D spatial shapes of sample clusters with a small ER or a large ER demonstrates that the number of members lays an important foundation for forming a dense internal system for sample clusters. At the same time, the MD of the sample clusters can serve well as an indicator of their morphological stability, which is built upon a certain amount of member stars. Conclusions. We present a new insight into the morphological coherence of open clusters, attributed to the combination of their gravitational binding capacity and external environmental perturbations. [ABSTRACT FROM AUTHOR]

The timely detection of falls and alerting medical aid is critical for health monitoring in elderly individuals living alone. This paper mainly focuses on issues such as poor adaptability, privacy infringement, and low recognition accuracy associated with traditional visual sensor-based fall detection. We propose an infrared video-based fall detection method utilizing spatial-temporal graph convolutional networks (ST-GCNs) to address these challenges. Our method used fine-tuned AlphaPose to extract 2D human skeleton sequences from infrared videos. Subsequently, the skeleton data was represented in Cartesian and polar coordinates and processed through a two-stream ST-GCN to recognize fall behaviors promptly. To enhance the network's recognition capability for fall actions, we improved the adjacency matrix of graph convolutional units and introduced multi-scale temporal graph convolution units. To facilitate practical deployment, we optimized time window and network depth of the ST-GCN, striking a balance between model accuracy and speed. The experimental results on a proprietary infrared human action recognition dataset demonstrated that our proposed algorithm accurately identifies fall behaviors with the highest accuracy of 96%. Moreover, our algorithm performed robustly, identifying falls in both near-infrared and thermal-infrared videos. [ABSTRACT FROM AUTHOR]

This paper focuses on detecting and tracking maneuvering weak targets in the range–Doppler (RD) plane with the track-before-detect (TBD) algorithm based on dynamic programming (DP). Traditional DP-TBD algorithms integrate target detection and tracking in their framework while searching the paths provided by a predefined model of the kinematic properties within the constraints allowed. However, both the approximate motion model used in the RD plane and the model mismatch caused when the target undergoes a maneuver can degrade the TBD performance sharply. To address these issues, this paper accurately describes the evolution of the RD equation based on Constant Acceleration (CA) and Coordinated Turn (CT) motion models with the process noise in the Cartesian coordinate system, and it also employs a recursive method to estimate the parameters in the equations for efficient energy accumulation and path searches. Facing the situation that targets energy accumulation during the DP iteration process will lead to an expansion of the target energy accumulation process. This paper designs a more efficient Optimization Function (OF) to inhibit the expansion effect, improve the resolution of the nearby targets, and increase the detection probability of the weak targets simultaneously. In addition, to search the trajectory more efficiently and accurately, we improved the process of DP multi-frame accumulation, thus reducing the computation amount of large-scale searches. Finally, the effectiveness of the proposed method for CA and CT motion target detection and tracking is verified by many of the simulation experiments that were conducted in this paper. [ABSTRACT FROM AUTHOR]

This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient) of the z -component the magnetic field, which is calculated by the Biot–Savart's law, with respect to the z -coordinate in the Cartesian xyz coordinate system is considered as the objective function. Then, the derivative of the objective function with respect to a change of coils in shape is formulated according to the concept of shape optimisation. The resulting shape derivative (as well as the Biot–Savart's law) is smoothly discretised with the closed B-spline curves. In this case, the control points (CPs) of the curves are naturally selected as the design variables. As a consequence, the shape derivative is discretised to the sensitivities of the objective function with respect to the CPs. Those sensitivities are available to solve the present shape-optimisation problem with a certain gradient-based nonlinear-programming solver. The numerical examples exhibit the mathematical reliability, computational efficiency, and engineering applicability of the proposed methodology based on the shape derivative/sensitivities and the closed B-spline curves. [ABSTRACT FROM AUTHOR]

AbstractA motion generation method for a planar four-bar mechanism without prescribed timing is proposed in this article. A characteristic of coupler points is found: for the coupler points of a four-bar mechanism in a standard installation position rotated by the corresponding input angle clockwise around the origin of the Cartesian coordinate system xOy, the generated points lie on the feature coupler circles. Next, based on this, the design process is divided into three steps. In the first step, the relative input angles, the relative coupler angles and five geometric parameters of the desired four-bar mechanism are optimized. In the second step, the basic dimensional types and initial input angle are determined, and then, the input angles are obtained. In the third step, the real size of the desired linkage mechanism is calculated. Because the dimension of the design variables in each step is exceptionally small, the motion synthesis method can yield design solutions with high precision in a short time. Six comparison examples are presented to demonstrate the efficacy of the proposed method. In addition, the method is used to design a robot for lower limb rehabilitation for application to the human foot. [ABSTRACT FROM AUTHOR]

This work aims to provide a unique analytical model designed for calculating the magnetic field of a surface-mounted permanent magnet Vernier motor (SPMVM). The model is created utilizing the separation variable method to solve Laplace or Poisson equations of the vector magnetic potential in a quasi-Cartesian coordinate system subdomain model. The theoretical justifications for the final analytical equations of electromagnetic torque, no-load back-EMF, stator inductance, and magnetic flux density distribution are given in detail. Then the solution of the equation is expressed in the form of a hyperbolic function. Furthermore, the improved analytical method in the study is generic and can be applied to estimating the parameters of machines with different design concepts. Finally, FEM is employed as the reference for comparison between other models. Compared to the original subdomain model, the calculation results of the improved analytical model are more time-efficient and closer to those of FEM. In addition, the improved analytical method can reduce the dimension of the coefficient matrix and improve the calculation speed. The SPMVM prototype is then built to demonstrate the validity and feasibility of the improved subdomain method and serves as a guide for future SPMVM development. [ABSTRACT FROM AUTHOR]

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We study the two-dimensional Euler flow $ X(\cdot,x) $ for $ x $ in the torus $ {\mathbb T}^2: = {\mathbb R}^2/2\pi{\mathbb Z}^2 $, solution to the ODE: $ \partial_t X(\cdot,x) = b(X(\cdot,x)) $ for $ t\geq 0 $, with $ X(0,x) = x $, where $ b $ is the vector field defined on $ {\mathbb T}^2 $ by:$b(x) = b(x_1,x_2): = (-\,A\cos x_1-B\sin x_2\,,\,A\sin x_1+B\cos x_2),\;\;A,B\in{\mathbb R}\setminus\{0\}.$We derive for any $ x\in{\mathbb T}^2 $, the asymptotics of $ X(t,x) $ as $ t $ tends to $ \infty $, depending on whether $ |A| = |B| $ or $ |A|\neq|B| $. In the first case, the orbits of the flow are all bounded. In the second case, it turns out that one of the coordinates of $ X(t,x) $ is bounded with an explicit bound, while the other one is equivalent to $ a(x)\,t $. The function $ a $ does not vanish in $ {\mathbb T}^2 $ and satisfies uniform bounds which depend on parameters $ A,B $. When $ |A|\neq|B| $, we also prove that for any global first integral $ u $ of the flow $ X $ with a periodic gradient, $ \nabla u $ has at least a cluster point of roots in $ {\mathbb T}^2 $, which implies the non-existence of any real-analytic first-integral of the flow. [ABSTRACT FROM AUTHOR]

Background: The movement of the barbell has been detected as success factor for the snatch and the clean and jerk events. As the barbell's movement has been shown to be related to the athlete's body movement, we hypothesized that the latter could be a success factor also for the back squat (BS) event. Hence, this study aimed to investigate postural control during the execution of the BS at different load intensities in powerlifters and weightlifters. Methods: Seventeen powerlifters and weightlifters were enrolled and the one-repetition maximum (1-RM) of the BS of each participant was measured. Afterwards, the assessment of postural control during the execution of the BS at different load intensities (i.e. 60%, 70%, 80%, 90%, 100%) of the 1-RM of each participant was carried out through a posturographic platform to measure the displacement of the centre of pressure (CoP). The following parameters were considered: sway path length (SPL), sway ellipse surface (SES), length/surface (LFS ratio), sway mean speed (SMS), CoP coordinates along X and Y planes. Results: We found a significant increase in SPL and LFS ratio, and a significant decrease in SMS as the load intensity increased. In detail, we detected a significant difference in: (a) SPL between the BS at 60% and 80%, 60% and 90%, 60% and 100%; between the BS at 70% and 90%, 70% and 100%; between the BS at 80% and 100%; and between the BS at 90% and 100%; (b) SMS between the BS at 60% and 80%, 60% and 90%; (c) LFS ratio between the BS at 60% and 90%, 60% and 100%. Conclusions: These results suggest that powerlifters and weightlifters adopt different postural control strategies depending on the load intensity when performing the BS. Our findings showed that higher effort could affect postural control during the BS. Thus, postural control could be considered a success factor for the BS. [ABSTRACT FROM AUTHOR]

We present a molecular geometry optimization algorithm based on the gradient-enhanced universal kriging (GEUK) formalism with ab initio prior mean functions, which incorporates prior physical knowledge to surrogate-based optimization. In this formalism, we have demonstrated the advantage of allowing the prior mean functions to be adaptive during geometry optimization over a pre-fixed choice of prior functions. Our implementation is general and flexible in two senses. First, the optimizations on the surrogate surface can be in both Cartesian coordinates and curvilinear coordinates. We explore four representative curvilinear coordinates in this work, including the redundant Coulombic coordinates, the redundant internal coordinates, the non-redundant delocalized internal coordinates, and the non-redundant hybrid delocalized internal Z-matrix coordinates. We show that our GEUK optimizer accelerates geometry optimization as compared to conventional non-surrogate-based optimizers in internal coordinates. We further showcase the power of the GEUK with on-the-fly adaptive priors for efficient optimizations of challenging molecules (Criegee intermediates) with a high-accuracy electronic structure method (the coupled-cluster method). Second, we present the usage of internal coordinates under the complete curvilinear scheme. A complete curvilinear scheme performs both surrogate potential-energy surface (PES) fitting and structure optimization entirely in the curvilinear coordinates. Our benchmark indicates that the complete curvilinear scheme significantly reduces the cost of structure minimization on the surrogate compared to the incomplete curvilinear scheme, which fits the surrogate PES in curvilinear coordinates partially and optimizes a structure in Cartesian coordinates through curvilinear coordinates via the chain rule. [ABSTRACT FROM AUTHOR]

The decline in students' interest in learning mathematics due to the lack of variety in teaching media used in learning results in low student learning outcomes. One of these problems occurred in class VIII students at SMP Negeri 2 Bojonegoro. There are still educators who only focus on books when learning. Besides, educators who deliver material, especially Cartesian coordinates, only use a whiteboard. The use of this media is certainly not optimal if implemented in continuous learning because apart from spending a lot of time just drawing, it also results in monotonous and boring classes. Therefore, this research aims to develop X-MATH learning media, which is the application of game-based learning to class VIII Cartesian coordinate material that meets valid and practical criteria to increase students' interest in learning. This research uses the Borg and Gall model, which only carries out seven of the ten stages of the development procedure. The research results show that material expert validation results obtained a percentage of 95%, while media validation results obtained a percentage of 91.6%. Both results meet the level of validity, namely very valid and suitable for use. Besides that, based on field trials conducted with mathematics educator respondents and students, the average score percentage was 83.3%, so the media was categorized as quite practical. Based on the results of this research, the game-based X-MATH learning media developed is very valid and quite practical to use in learning Cartesian coordinates. Turunnya minat belajar matematika peserta didik yang disebabkan kurang bervariasinya media ajar yang digunakan dalam pembelajaran mengakibatkan rendahnya hasil belajar peserta didik. Permasalahan ini terjadi salah satunya pada peserta didik kelas VIII SMP Negeri 2 Bojonegoro. Masih dijumpai pendidik yang hanya terfokus pada buku saat pembelajaran. Selain itu, pendidik dalam penyampaian materi khususnya koordinat kartesius bahan ajar yang digunakan hanya papan tulis. Penggunaan media tersebut tentu kurang optimal jika dimplementasikan dalam pembelajaran berkelanjutan karena selain menghabiskan banyak waktu hanya untuk menggambar juga mengakibatkan kelas monoton dan membosankan. Sebab itu, tujuan dari penelitian ini adalah mengembangkan media pembelajaran X-MATH yang merupakan penerapan dari pembelajaran berbasis game pada materi koordinat kartesius kelas VIII yang memenuhi kriteria valid dan praktis guna meningkatkan minat belajar peserta didik. Penelitian ini merupakan penelitian pengembangan menggunakan model Borg and Gall yang hanya melaksanakan tujuh dari sepuluh tahapan prosedur pengembangan. Hasil penelitian menunjukkan bahwa hasil validasi ahli materi memperoleh persentase sebesar 95%, sedangkan hasil validasi media memperoleh persentase sebesar 91,6%. Kedua hasil tersebut memenuhi tingkat validitas yaitu sangat valid dan dapat digunakan. Selain itu, berdasarkan uji coba lapangan yang dilakukan dengan responden pendidik matematika dan peserta didik menghasilkan persentase skor rata-rata sebesar 83,3% sehingga media dikategorikan cukup praktis. Berdasarkan hasil penelitian tersebut maka media pembelajaran X-MATH berbasis game yang dikembangkan sangat valid dan cukup praktis digunakan dalam pembelajaran koordinat kartesius.

Summary: The article examines the positional relationships and transmission/reception signal direction information within unmanned aerial vehicle (UAV) cluster formations. Considering the distinctive characteristics of various formation shapes (such as circle and cone), a study is conducted on the polar and Cartesian coordinate systems in neural network models to address position deviation issues arising in UAV formation flights. The passive receiving signal UAV positioning model is established by applying the triangular cosine theorem. Additionally, the position relationship model of the UAV is formulated using optimization theory. The article introduces a deep learning‐based deviated UAV adjustment algorithm designed to automatically adjust UAV positions. This is achieved by establishing a triangular relationship between the passive signal receiving UAV and other UAVs. The implementation involves C# programming and MATLAB visualization. The proposed method not only resolves UAV positioning and position adjustment challenges but also optimizes the adjustment strategy. This optimization leads to maximum savings in time and distance costs associated with sending and receiving signals among UAVs, thereby enhancing the overall performance of UAVs during flights. [ABSTRACT FROM AUTHOR]

Background: posterior pedicle screw fixation is common method, one of the most severe complications is iatrogenic vascular damage, no report investigated association of different introversion angles (INTAs) and length of pedicle screw. The aims were to investigate the optimal introversion angle and length of pedicle screw for improving the safety of the operation, and to analyze the differences of vascular damage types at L1-S1. Methods: Lumbar CT imaging data from110 patients were analyzed by DICOM software, and all parameters were measured by new Cartesian coordinate system, INTAs (L1-L5:5°,10°,15°,S1: 0°, 5°,10°,15°), DO−AVC (the distance between the origin (O) with anterior vertebral cortex (AVC)), DAVC−PGVs (the distance between AVC and the prevertebral great vessels (PGVs)), DO−PGVs (the distance between the O and PGVs). At different INTAs, DAVC−PGVs were divided into four grades: Grade III: DAVC−PGVs ≤ 3 mm, Grade II: 3 mm < DAVC−PGVs ≤ 5 mm, Grade I: DAVC−PGVs > 5 mm, and N: the not touching PGVs. Results: The optimal INTA was 5° at L1-L3, the left was 5° and the right was 15° at L4, and screw length was less than 50 mm at L1-L4. At L5, the left optimal INTA was 5° and the right was 10°, and screw length was less than 45 mm. The optimal INTA was 15° at S1, and screw length was less than 50 mm. However, screw length was less than 40 mm when the INTA was 0° or 5° at S1. Conclusions: At L5-S1, the risk of vascular injury is the highest. INTA and length of the pedicle screw in lumbar operation are closely related. 3 mm interval of screw length may be more preferable to reduce vascular damage. [ABSTRACT FROM AUTHOR]

This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to non-subgroup-type coordinates. We find three new systems, two with magnetic fields polynomial in Cartesian coordinates and one with unbounded exponential terms. The limit in the parameters of the integrals yields a new parabolic cylindrical system; the limit of vanishing magnetic fields leads to the free motion. This confirms the conjecture that non-subgroup type integrals can be related to separable systems only in a trivial manner. [ABSTRACT FROM AUTHOR]

Structured light systems (SLSs) are commonly used for precision dimensional measurements. These are active systems in that the projected structured light pattern is used to establish correspondence between the projector and the camera(s) to provide more accurate 3D reconstruction as opposed to passive camera-based systems that rely on the user or features in images to identify corresponding points between the cameras. Errors in the calibration of the model parameters of an SLS can lead to systematic errors in dimensional measurements. In this paper, we explore the topic of performance testing of an SLS, specifically, the sensitivity of the length tests described in the VDI/VDE 2634-2 guideline and the ISO 10360-13 standard to the model parameters (such as intrinsic parameters of the camera and the projector, and camera-projector geometry parameters) of an SLS. The results are based on a hybrid approach of simulations performed using data obtained experimentally from an SLS mounted on a Cartesian coordinate measuring machine (CMM) which is used primarily to position the target at different points within the measurement volume. The results show that the length tests described in the ISO 10360-13 standard provide better sensitivity to the model parameters than the VDI/VDE 2634-2 guideline. However, even the ISO 10360-13 length tests do not detect all parameters with high sensitivity. A model-based approach in identifying length tests (i.e., the position and orientation of reference lengths) such as described in this paper provides better sensitivity to model parameters and therefore is more likely to detect systematic errors in SLSs. • Built a structured light system on a CMM and determined the length errors between points in a rectangular grid. • Assessed the sensitivity of lines defined in the VDI/VDE 2634-2 and ISO 10360-13 documents to systematic errors in SLSs. • Identified position/orientation of lines in the measurement volume that provides maximum sensitivity to systematic errors. • Demonstrated the superiority of our sensitivity analysis-based approach in detecting SLS systematic errors. [ABSTRACT FROM AUTHOR]

3D scanners have great potential to boost the efficiency of geometric inspection if their traceability is established by identifying measurement bias and uncertainty. This article introduces a digital twin for a structured-light 3D scanner that provides these two essential measures in a real-time manner. The error quantification starts from iterated scans taken from a CMM-calibrated ball-plate artifact at eight different configurations. The differences between the erroneous scan readings of the artifact's distance features and the corresponding calibrated values in the CMM set give a spatial distribution of the scanner's error. Then, three polynomial functions map the Cartesian coordinates of the scan set onto their counterparts from the CMM set. In this error model, a least-square approach determines the polynomial coefficients. Evaluating the error model for a given point cloud returns a vector field of volumetric errors, which is then followed by error corrections and then GD&T calculations. The uncertainty propagation is pursued through the three steps of model development, error map evaluation, and GD&T analysis. The Monte-Carlo estimations benchmark and validate the GUM framework for the uncertainty associated with the outputs of each step. Experimental verifications of the proposed methodology suggest that the error correction improves the mean and the standard deviation of measurement bias by 50% and 27%, respectively. The uncertainty map provides the coverage probabilities of 62%, 88%, and 96% for the coverage factors of 1, 2, and 3, while the expected theoretical levels of confidence are 68%, 95%, and 100%. • The digital twin provides error maps for scan data as a field of error vectors. • Corrections reduced the error average from −10 to −5 μm and error dispersion by 27%. • Ellipsoidal uncertainty regions grant coverage probabilities close to expected levels. • GUM framework reliably estimates the uncertainty of digital twin outputs. • Fast uncertainty analysis allows using digital twin in real-time in-process metrology. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete quadrangle. We started this investigation in a few of our previous papers. In those papers and here, the rectangular coordinates are used to enable us to prove the properties of the rich geometry of a quadrangle using the same method. Now, we are focused on the isoptic point of the complete quadrangle A B C D , which is the inverse point to A ′ , B ′ , C ′ , and D ′ with respect to circumscribed circles of the triangles B C D , A C D , A B D , and A B C , respectively, where A ′ , B ′ , C ′ , and D ′ are isogonal points to A , B , C , and D with respect to these triangles. In studying the properties of the quadrangle regarding its isoptic point, some new results are obtained as well. [ABSTRACT FROM AUTHOR]

Vortex electromagnetic wave radar carrying orbital angular momentum can compensate for the deficiency of planar electromagnetic wave radar in detecting motion parameters perpendicular to the direction of electromagnetic wave propagation, thus providing more information for target recognition, which has become a hot research field in recent years. However, existing research makes it difficult to obtain the acceleration and rotation centers of targets under non-quasi-axial incidence conditions of vortex electromagnetic waves. Based on this, this article proposes a variable speed motion target parameter extraction method that combines single element and total element echoes. This method can achieve three-dimensional information extraction of radar targets based on a uniform circular array (UCA). Firstly, we establish a non-quasi-axis detection echo model for variable-speed moving targets and extract echoes from different array elements. Then, a single element echo is used to extract the target's range slow time profile and obtain the target's rotation center z coordinate. We further utilize the target linear, angular Doppler frequency shift extremum, and median information to extract parameters such as target acceleration, tilt angle, rotation radius, and rotation center x and y coordinates. We analyzed the impact of different signal-to-noise ratios and motion states on parameter extraction. The simulation results have verified the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]