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Spin–orbit coupling induces a current density in the ground state, which consequently requires a generalization for meta-generalized gradient approximations. That is, the exchange–correlation energy has to be constructed as an explicit functional of the current density, and a generalized kinetic energy density has to be formed to satisfy theoretical constraints. Herein, we generalize our previously presented formalism of spin–orbit current density functional theory [Holzer et al., J. Chem. Phys. 157, 204102 (2022)] to non-magnetic and magnetic periodic systems of arbitrary dimension. In addition to the ground-state exchange–correlation potential, analytical derivatives such as geometry gradients and stress tensors are implemented. The importance of the current density is assessed for band gaps, lattice constants, magnetic transitions, and Rashba splittings. In the latter, the impact of the current density may be larger than the deviation between different density functional approximations. [ABSTRACT FROM AUTHOR]

Liquid-water oceans likely underlie the ice shells of Europa and Enceladus, but ocean properties are challenging to measure due to the overlying ice. Here, we consider gravity-driven flow of the ice shells of icy satellites and relate this to ocean freeze and melt rates. We employ a first-principles approach applicable to conductive ice shells in a Cartesian geometry. We derive a scaling law under which ocean freeze/melt rates can be estimated from shell-thickness measurements. Under a steady-state assumption, ocean freeze/melt rates can be inferred from measurements of ice thickness, given a basal viscosity. Depending on a characteristic thickness scale and basal viscosity, characteristic freeze/melt rates range from around O(10 |$^{-1}$|⁠) to O(10 |$^{-5}$|⁠) mm/yr. Our scaling is validated with ice-penetrating radar measurements of ice thickness and modelled snow accumulation for Roosevelt Island, Antarctica. Our model, coupled with observations of shell thickness, could help estimate the magnitudes of ocean freeze/melt rates on icy satellites. [ABSTRACT FROM AUTHOR]

The Ames room illusion is one of the best-known geometrical illusions but its geometrical properties are often misunderstood. This study discusses the differences in the geometrical properties between the original Ames room and what have been often referred to as "Ames rooms" in recent studies. [ABSTRACT FROM AUTHOR]

The document titled "Supplementary Material for: Alternate Formation of AlOH from Third Row Diatomic Hydrides and Oxides" provides tables and data related to the formation of molecules containing aluminum, magnesium, silicon, phosphorus, and sulfur. The tables include optimized geometries and frequencies for various molecules. The data presented in the document can be valuable for researchers studying the properties and formation of these molecules. [Extracted from the article]

Foamed materials are widely used to reduce noise due to their comparably good acoustic damping behavior. However, out of a large variety of these materials a suitable candidate has to be identified for each application. This is a challenging process that is typically guided by experiments and experience. While numerical simulations could support these experiments and reduce the effort to a great extent, no suitable discretization approach has yet been established that can fully capture the complex geometry of the foam. A fully resolved model is desirable in order to yield reliable predictions that can then be used to establish homogenized models. We established a monolithic coupling approach based on the finite cell method (FCM) that realizes a vibroacoustic simulation in this sense. The fluid and the structure domain are discretized by Cartesian grids and the geometry defined based on computed tomography scans is accounted for during the quadrature of the weak form. Our simulation in the time domain makes use of explicit time marching schemes and is therefore limited by a critical time step size. This is known to be arbitrarily low for discretizations with the FCM containing cells with arbitrarily small support. As a remedy against this we use the classical α$\alpha $‐stabilization technique and investigate its potentials and limitations. [ABSTRACT FROM AUTHOR]

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions. [ABSTRACT FROM AUTHOR]

This research proposes an analytical solution of the nano-concrete-epoxy interaction area within nano crack region of the reinforced concrete beam by applying Newton's third law in static equilibrium. For deriving the governing equation, the imaginary beam with free ends (no support) is considered within nano crack region. This imaginary beam is acted along the imaginary line of concrete-epoxy interface. Newton's third law is applicable for deriving the governing equation because of assuming the absence of frictional and other external forces. The parametric study is performed for implementing the proposed formula of nano interactive area considering variable nano crack depths and thicknesses. The nano interactive area is increased gradually with the increment of depths and thicknesses based on the parametric study because of linear functionality of interactive area and geometry of nano crack region. The maximum interactive area is found to be 314 nm2 at 0.6 ratio of depths and thicknesses of the nano crack. The incremental differences in interactive area between the crack depth or thickness ratios of 0.1 and 0.6 are found to be 25.4% and 1.6% for variations of the crack depth and thickness ratios, respectively. So, the crack depth shows higher impact on the interaction area compared to the thickness of the crack. However, there is a scope for enhancing this research in future by deriving closed-formed analytical formulations to consider appropriate boundary conditions. [ABSTRACT FROM AUTHOR]

Augmented reality navigation (ARN) enhances localization and operation by overlaying virtual guides onto realworld surgical fields. The study introduces a laser path anchor (LPA), a novel tool for ARN in surgery aimed at mitigating depth perception challenges. The LPA anchors the virtual planned path onto the physical laser beam, ensuring accurate puncture from any perspective. The tool consists of a rack, a primary laser emitter, an indicating laser emitter, and an AR marker with intrinsic and extrinsic properties validated through calibration and testing. Intrinsic validation involved measuring the parallelism between the indicating and primary laser using Cartesian graph screens. Extrinsic validation assessed the alignment and shortest distance between the virtual path and primary lasers. Results showed an angle deviation of 0.08° between the indicating and primary laser and 1.44° ± 0.47° between the virtual path and primary lasers, with a shortest distance of 7.60 mm ± 2.50 mm. The usability test demonstrated the LPA's effectiveness in guiding needle insertions without altering the perspective or distracting the surgeon. Despite some limitations, the LPA enhances the user's perception of linear objects and eliminates the need for perspective adjustments during puncture, warranting further development. [ABSTRACT FROM AUTHOR]

The distribution and development of rock mass discontinuities in 3D space control the deformation and failure characteristics of the rock mass, which in turn affect the strength, permeability, and stability of rock masses. Therefore, it is essential to accurately and efficiently characterize these discontinuities. Light Detection and Ranging (LiDAR) now allows for fast and precise 3D data collection, which supports the creation of new methods for characterizing rock mass discontinuities. However, uneven density distribution and local surface undulations can limit the accuracy of discontinuity characterization. To address this, we propose a method for characterizing complex rock mass discontinuities based on laser point cloud data. This method is capable of processing datasets with varying densities and can reduce over-segmentation in non-planar areas. The suggested approach involves a five-stage process that includes: (1) adaptive resampling of point cloud data based on density comparison; (2) normal vector calculation using Principal Component Analysis (PCA); (3) identifying non-planar areas using a watershed-like algorithm, and determine the main discontinuity sets using Multi-threshold Mean Shift (MTMS); (4) identify single discontinuity clusters using Density-Based Spatial Clustering of Applications with Noise (DBSCAN); (5) fitting discontinuity planes with Random Sample Consensus (RANSAC) and determining discontinuity orientations using analytic geometry. This method was applied to three rock slope datasets and compared with previous research results and manual measurement results. The results indicate that this method can effectively reduce over-segmentation and the characterization results have high accuracy. [ABSTRACT FROM AUTHOR]

Tumors can be detected from a temperature gradient due to high vascularization and increased metabolic activity of cancer cells. Thermal infrared images have been recognized as potential alternatives to detect these tumors. However, even the use of artificial intelligence directly on these images has failed to accurately locate and detect the tumor size due to the low sensitivity of temperatures and position within the breast. Thus, we aimed to develop techniques based on applying the thermal impedance method and artificial intelligence to determine the origin of the heat source (abnormal cancer metabolism) and its size. The low sensitivity to tiny and deep tumors is circumvented by utilizing the concept of thermal impedance and artificial intelligence techniques such as deep learning. We describe the development of a thermal model and the creation of a database based on its solution. We also outline the choice of detectable parameters in the thermal image, the use of deep learning libraries, and network training using convolutional neural networks (CNNs). Lastly, we present tumor location and size estimates based on thermographic images obtained from simulated thermal models of a breast, using Cartesian geometry and a scanned geometric shape of an anatomical phantom model. [ABSTRACT FROM AUTHOR]

Auxetic textiles are intriguing materials with unusual capabilities. These materials exhibit a negative Poisson's ratio with extraordinary performance in toughness, resilience, shear resistance, and acoustic properties mainly due to their special structure and associated deformation mechanics. Auxetic materials can also have applications around energy absorption and can effectively be used for vibration damping and shock absorbency. The exceptional behaviour of auxetic textiles can be obtained by utilising specific fibrous materials and introducing auxetic geometry and structures differently during weaving, knitting, and nonwoven manufacturing. This issue of Textile Progress highlights the fundamental aspects of various auxetic structures and their properties in general and a detailed analysis of auxetic textile structures and composites, their manufacturing processes, modelling, characterisation, and applications. These materials can potentially revolutionise their applications in sports, automotive, construction industry, biomedical engineering, aerospace, marine, and defence personal protective equipment. Fundamental understanding of auxetic geometry, followed by developing and analysing these geometries by analytical and computational modelling, translating the geometry into appropriate textile structures for actual fabric production, characterisation of auxetic fabrics and their composites, and finally, some innovative applications in technical textiles are some of the fascinating issues addressed in this review. [ABSTRACT FROM AUTHOR]

In 1965, fuzzy set theory was born, providing a valuable tool to study phenomena where decision-making based on dichotomy is not a simple task. This work is framed in the ideas of fuzzy analytic geometry; more precisely, this paper is devoted to introducing the idea of a fuzzy tangent line to a fuzzy circle in this geometry. For this purpose, three methods are proposed and studied. Moreover, we provide results that establish the conditions for which the proposed methods define the same fuzzy tangent line. [ABSTRACT FROM AUTHOR]

In order to explore the particularity of terminal constraint form of "parallels parallel" ype lower mobility hybrid mechanisms, taking (3-RPS) + (2-RCR) mechanisms as research object, a method for solving the intersection of screw systems corresponding to terminal constraint issue was proposed. Firstly, the composition principle of terminal constraint/mobility of (3-RPS) + (2-RCR) mechanisms was introduced, and the calculation formula of terminal constraint/mobility was given. Secondly, the number of terminal mobility of the mechanisms was analyzed using line geometry under ifferent geometric configurations. Then, the ruled surface and generatrix equation corresponding to sub-constrained screw systems were established by analytic geometry theory and screw theory, and he intersection analytic model of three-screw system and four-screw system was obtained, and the erminal constraint of the mechanisms was determined. Thirdly, the terminal constraint/mobility properties were discussed under different geometric configurations. Finally, numerical examples of the mechanisms were given to solve the terminal constraint under three different configurations. The results show that terminal constraint of the mechanisms is not a constraint force/couple, but the general orm of wrench under the general configuration. The method of solving the intersection of screw systems provides an effective way to solve the terminal constraint problems of this kind of hybrid mechanisms [ABSTRACT FROM AUTHOR]

In this study, conics (circle, ellipse, hyperbola) are characterized by taking into account basic multiplication operations in multiplicative space. For this purpose, firstly multiplicative axes and regions are introduced. Additionally, the multiplicative cone definition is given and visualized on the figure. General definitions and theorems of non-Newtonian conics are given. Additionally, examples were given and drawings were made to make the resulting characterizations and theorems more memorable. [ABSTRACT FROM AUTHOR]

This article introduces a novel highly integrated direct drive rotation wire frame mechanism for multi-axis micro wire electrical discharge machine tool. The design allows the micro electrode wire center to rotate along the motor's output shaft by ±90°, enabling machining over a complete circular area. This enhances the rotation precision and reduces the displacement of each axis, ensuring that the length of the electrode wire remains unchanged during the rotation process and thereby maintaining a stable friction force with the V-grooves. Building upon the direct drive rotation wire frame, a six-axis micro-wire electrode discharge machining machine has been developed, facilitating multi-axis coordinated processing. This study establishes the forward and inverse kinematic models using homogeneous transformation matrices to describe each axis's motion of the machine tool. A closed-form solution for the inverse kinematic model has been derived and effectively utilized for machining path planning for the electrode wire. To comprehensively characterize the machine tool's performances, a method that combines coordinate transformation, analytical geometry, and the Monte Carlo approach has been employed to determine the actual working space and the dexterity of the machine tool. Finally, a preliminary experiment with the six-axis micro wire electrical discharge machine tool demonstrates the effectiveness of the proposed direct drive rotation wire frame, verifying the inverse kinematic closed-form solutions, the practical workspace of the machine tool, and the effectiveness of dexterity and geometric error modeling. • Direct drive rotation wire frame enables wire rotates ±90° in WEDM with lower inertia and higher dexterity. • Comprehensively analyzing kinematics, dexterity and geometric error of novel 6-axis WEDM machine tool. • Comparison of designing freeform surface and machined surface verify feasibility of machine tool. [ABSTRACT FROM AUTHOR]

SUMMARY: Thermal convection in planetary solid (rocky or icy) mantles sometimes occurs adjacent to liquid layers with a phase equilibrium at the boundary. The possibility of a solid–liquid phase change at the boundary has been shown to greatly help convection in the solid layer in spheres and plane layers and a similar study is performed here for a spherical shell with a radius-independent central gravity subject to a destabilizing temperature difference. The solid–liquid phase change is considered as a mechanical boundary condition and applies at either or both horizontal boundaries. The boundary condition is controlled by a phase change number, Φ, that compares the timescale for latent heat exchange in the liquid side to that necessary to build a topography at the boundary. We introduce a numerical tool, available at https://github.com/amorison/stablinrb, to carry out the linear stability analysis of the studied setup as well as other similar situations (Cartesian geometry, arbitrary temperature and viscosity depth-dependent profiles). Decreasing Φ makes the phase change more efficient, which reduces the importance of viscous resistance associated to the boundary and makes the critical Rayleigh number for the onset of convection smaller and the wavelength of the critical mode larger, for all values of the radii ratio, γ. In particular, for a phase change boundary condition at the top or at both boundaries, the mode with a spherical harmonics degree of 1 is always favoured for Φ ≲ 10−1. Such a mode is also favoured for a phase change at the bottom boundary for small (γ ≲ 0.45) or large (γ ≳ 0.75) radii ratio. Such dynamics could help explaining the hemispherical dichotomy observed in the structure of many planetary objects. [ABSTRACT FROM AUTHOR]

With the advancement of technology, signal modulation types are becoming increasingly diverse and complex. The phenomenon of signal time–frequency overlap during transmission poses significant challenges for the classification and recognition of mixed signals, including poor recognition capabilities and low generality. This paper presents a recognition model for the fine-grained analysis of mixed signal characteristics, proposing a Geometry Coordinate Attention mechanism and introducing a low-rank bilinear pooling module to more effectively extract signal features for classification. The model employs a residual neural network as its backbone architecture and utilizes the Geometry Coordinate Attention mechanism for time–frequency weighted analysis based on information geometry theory. This analysis targets multiple-scale features within the architecture, producing time–frequency weighted features of the signal. These weighted features are further analyzed through a low-rank bilinear pooling module, combined with the backbone features, to achieve fine-grained feature fusion. This results in a fused feature vector for mixed signal classification. Experiments were conducted on a simulated dataset comprising 39,600 mixed-signal time–frequency plots. The model was benchmarked against a baseline using a residual neural network. The experimental outcomes demonstrated an improvement of 9% in the exact match ratio and 5% in the Hamming score. These results indicate that the proposed model significantly enhances the recognition capability and generalizability of mixed signal classification. [ABSTRACT FROM AUTHOR]

Point clouds are sets of points used to visualize three-dimensional (3D) objects. Point clouds can be static or dynamic. Each point is characterized by its 3D geometry coordinates and attributes such as color. High-quality visualizations often require millions of points, resulting in large storage and transmission costs, especially for dynamic point clouds. To address this problem, the moving picture experts group has recently developed a compression standard for dynamic point clouds called video-based point cloud compression (V-PCC). The standard generates two-dimensional videos from the geometry and color information of the point cloud sequence. Each video is then compressed with a video coder, which converts each frame into frequency coefficients and quantizes them using a quantization parameter (QP). Traditionally, the QPs are severely constrained. For example, in the low-delay configuration of the V-PCC reference software, the quantization parameter values of all the frames in a group of pictures are set to be equal. We show that the rate-distortion performance can be improved by relaxing this constraint and treating the QP selection problem as a multi-variable constrained combinatorial optimization problem, where the variables are the QPs. To solve the optimization problem, we propose a variant of the differential evolution (DE) algorithm. Differential evolution is an evolutionary algorithm that has been successfully applied to various optimization problems. In DE, an initial population of randomly generated candidate solutions is iteratively improved. At each iteration, mutants are generated from the population. Crossover between a mutant and a parent produces offspring. If the performance of the offspring is better than that of the parent, the offspring replaces the parent. While DE was initially introduced for continuous unconstrained optimization problems, we adapt it for our constrained combinatorial optimization problem. Also, unlike standard DE, we apply individual mutation to each variable. Furthermore, we use a variable crossover rate to balance exploration and exploitation. Experimental results for the low-delay configuration of the V-PCC reference software show that our method can reduce the average bitrate by up to 43% compared to a method that uses the same QP values for all frames and selects them according to an interior point method. [ABSTRACT FROM AUTHOR]

Let E be an Anderson A -module over C ∞. The period lattice of E is related to its module of special functions by means of a non-canonical isomorphism introduced by the authors in [GM21]. In this paper, we explain how a modification of the inverse map is canonical by interpreting it as a residue morphism along the characteristic graph. This phenomenon has already been observed in various situations. The main innovation of this text is that of costability (costable admissible opens, costable site, etc.) which provides a convenient framework to develop the notion of sheaves of E (C ∞) -valued meromorphic functions on the rigid analytic plane. [ABSTRACT FROM AUTHOR]

The purpose of the article is to research and analysis of the amount of indexation of pension payments related to inflationary processes. The object of the study is the state of pension provision in Ukraine. The subject of the study is the process of indexation of pension payments as a result of the implementation of social policy in Ukraine. An analysis of the history of the development and reform of pension provision in Ukraine was carried out. This allowed for a deeper understanding of the content of events related to the establishment of pension provision in Ukraine. The research methodology involves the synergy of mathematical methods of analytical geometry and economic-mathematical modelling. It is shown that the presence of inflationary processes in the national economy leads to the need to increase the pension provision of citizens. At the same time, the size of the increase in pension payments should be differentiated in order to ensure social "justice". The scientific task set in the article is to demonstrate a modern approach to choosing a strategy for implementing the state pension policy in Ukraine. As a result of the research, two models of appropriate indexation of pension payments in Ukraine are presented. The calculation made it possible to choose the most significant model. In the future, it is advisable to direct the research to the search for other more effective ways of indexing pensions. It is assumed that for this it is necessary to formalize the mathematical formulation of the problem of finding the optimal value of the index of pension payments as extreme, taking into account the necessary restrictions. A scientific novelty in solving this issue is the receipt of practically significant recommendations regarding the indexation of pensions. The practical significance of the obtained results lies in the elimination of social defects in the indexation of pension payments. Further research should be directed to the search for rational solutions that will stimulate the creation of an effective pension system in Ukraine. [ABSTRACT FROM AUTHOR]

This study describes the use of artificial intelligence to predict the aerodynamic properties of wind turbine profiles. The goal was to determine the lift coefficient for an airfoil using its geometry as input. Calculations based on XFoil were taken as a target for the predictions. The lift coefficient for a single case scenario was set as a value to find by training an algorithm. Airfoil geometry data were collected from the UIUC Airfoil Data Site. Geometries in the coordinate format were converted to PARSEC parameters, which became a direct feature for the random forest regression algorithm. The training dataset included 60% of the base dataset records. The rest of the dataset was used to test the model. Five different datasets were tested. The results calculated for the test part of the base dataset were compared with the actual values of the lift coefficients. The developed prediction model obtained a coefficient of determination ranging from 0.83 to 0.87, which is a good prognosis for further research. [ABSTRACT FROM AUTHOR]

In this work, the response matrix‐exponential nodal method is presented to solve fixed source neutral particle transport problems with isotropic scattering and discrete ordinates formulation in two‐dimensional Cartesian geometry. The method is based on the response matrix scheme by using the general solution of the transverse integrated SN nodal equations with exponential approximations for the leakage terms. This approach eliminates the need for additional auxiliary equations found in the spectral Green's function (SGF) schemes, streamlining internodal computation to a matrix‐vector multiplication. The formulation includes a lambda parameter possible determined by the medium characteristics, e.g., the scattering ratio coefficient and/or empirical methods. Two model problems with low absorption rates were investigated to analyze the performance of the proposed method. The numerical solutions exhibited superior accuracy for the coarsest spatial grid configurations in both homogeneous and heterogeneous study cases. However, refining the spatial grid revealed a relative loss in accuracy compared to the RM‐CN method, potentially due to increased truncation error propagation. Nevertheless, all numerical solutions converge to the reference solution when refining the spatial discretization grid. Comparison of both response matrix schemes demonstrated similar convergence rates and computational efficiency in terms of iterations and CPU consumption. [ABSTRACT FROM AUTHOR]

Three new hetero-metallic CuII-LnIII complexes [(CuL)Gd(NO3)3(CH3OH)]n (1), [(CuL)Tb(NO3)3(H2O)]· [CuL] (2) and [(CuL)Dy(NO3)3(H2O)]·[CuL] (3) have been synthesized using a mono-nuclear Cu(II) complex, [CuL], of an unsymmetrically di-condensed N2O3 donor Schiff base ligand, N-(3-methoxysalicylidene)-N-(salicylidene)-1,2-ethylenediamine (H2L). Single crystal X-ray crystallography revealed that complex 1 is a nitrate bridged 1D chain of dinuclear Cu(II)-Gd(III) units whereas in 2 and 3, the dinuclear Cu(II)-Ln(III) units are co-crystallized with a [CuL] unit. The Ln(III) centers are nine coordinated with the geometry of a spherical capped square antiprism for Gd and spherical tricapped trigonal prism for Tb and Dy. The geometry of the Cu(II) center is distorted octahedral for complex 1 and distorted square planar for complexes 2 and 3. Temperature-dependent molar magnetic susceptibility measurements in 1-3 revealed the presence of overall ferromagnetic coupling between the Cu(II) and Ln(III) centers. Notably, field induced single-molecule magnet behavior was witnessed in the Tb(III) derivative (2). The ab initio calculations indicated that upon application of an external magnetic field, the tunneling in the ground state of complex 2 gets reduced and thereby field-induced SMM behaviour is observed. Besides, in the case of complex 1, BS-DFT calculations were carried out to gain further insights into the magnetic exchange coupling interactions between the Cu(II) and Gd(III) centers. [ABSTRACT FROM AUTHOR]

The concept of subordination is expanded in this study from the fuzzy sets theory to the geometry theory of analytic functions with a single complex variable. This work aims to clarify fuzzy subordination as a notion and demonstrate its primary attributes. With this work's assistance, new fuzzy differential subordinations will be presented. The first theorems lead to intriguing corollaries for specific aspects chosen to exhibit fuzzy best dominance. The work introduces a new integral operator for meromorphic functions and uses the newly developed integral operator, which is starlike and convex, respectively, to obtain conclusions on fuzzy differential subordination. [ABSTRACT FROM AUTHOR]

A polygon can represent the boundary of curved text more compactly than a rectangle. However, predicting reasonable polygon lacks of solutions due to the complex spatial relationships caused by having more vertices. The two main challenges are how to satisfy the constraints between vertices and how to cope with data conflicts caused by inconsistent annotation standards. To address these problems, we propose a divide and conquer methodology, in which a polygon is considered as a set of convex quadrangles. By predicting quadrangles in sequence, the vertices of the polygon are obtained consecutively and constrained by the previous ones. Then, we propose a measure for the overlap between convex quadrangles, with which the IoU between two polygons is calculated densely. Our method is derivable and can be trained end-to-end. Also, the polygon prediction branch that we proposed is universal and transplantable. We select basic architecture as the backbone, and the text/non-text classification branch adopts an online hard example mining strategy. Experiments on curved benchmark datasets, namely Total Text and CTW1500, demonstrate that our approach achieves state-of-the-art accuracy. It also maintains a high level of inferring efficiency. [ABSTRACT FROM AUTHOR]

Background: Eustachian tube dysfunction (ETD) is the predominant cause of otitis media with effusion in children and adults. Balloon dilatation of the Eustachian tube (BDET) provides a new method for restoring the ventilatory function of Eustachian tube (ET). However, the differences in age-related morphological changes in the dimensions and positions of ET in children and adults are unclear. Purpose: This study aimed to examine age-related morphological changes in bony and cartilage segments of the ET in a three-dimensional space in normal population. Methods: A total of 71 randomly selected computed tomography (CT) images of the temporal bones of 46 people were retrospectively studied in four age groups: A (0-3 years old); B (4-8 years old), C (9-18 years old), and D (19-65 years old). Space analytic geometry was assessed to calculate the dimensions and positions of ET. Results: The bony segment of ET lengthened from infancy to adulthood with age in groups A, B and C (r = 0.562**/0.000). The cartilage segment of ET mostly extended with age from infancy to 8 years old in children (r = 0.633**/0.000), but with bending close to the sagittal plane and away from the horizontal plane with age in groups A, B and C (P < .05), and with a constant angle to the coronal plane among the four groups (P > .05). Conclusion: The bony and cartilaginous segments of ET exhibit distinct morphological changes in space with age. The bony segment of ET extends in a constant position from infancy to adulthood. In contrast, the cartilaginous segment of the ET indicates multidimensional positional changes until adulthood, in addition to the elongation from infancy to children. This may provide an accurate morphological basis for comparing the differences in ETD pathogenesis and surgical treatment between children and adults. [ABSTRACT FROM AUTHOR]

We prove two theorems about the circular Apollonian packing. The first states that the circles used in the packing have an infinite total length. The second states that the largest circle is covered by the other circles used in the packing, up to an area of Lebesgue measure zero. Our proofs are elementary and only use basic coordinate geometry. [ABSTRACT FROM AUTHOR]

The utilization of tools provided by CAD software has become an essential component of any design process in modern mechanical design. These tools provide a simplified design methodology that does not require expert knowledge for the design of complex mechanical parts. Gears, as one of the most used mechanical components, have precisely defined and well-understood several types of tooth geometry. However, different shapes of tooth profiles cannot be easily analyzed and designed without knowledge of mathematics and analytical geometry. With modern design tools, especially CAD software, that knowledge is not necessarily required in the design process. Engineers can simply define the relative motion of one component to produce all necessary parameters that define the shape and geometry of another component. [ABSTRACT FROM AUTHOR]

This article explores the concept of luck and the proportions of infinite sets. The author challenges the idea that luck can be measured proportionally, arguing that it is mathematically incorrect to claim that there are more worlds where a proposition is true than false. The article introduces measure theory, a branch of mathematics that compares the sizes of uncountable sets, and highlights its connection to probability theory. It explains how probability measures can be used to determine the likelihood of certain outcomes, such as the probability of Smith winning or losing. The probabilities presented are based on mathematical calculations and should not be interpreted as subjective judgments. [Extracted from the article]

The study focuses on improving higher-order thinking skills (HOTS) in mathematics students using a Desmos-assisted planar analytic geometry course. Analytic geometry, which is essential for understanding geometric properties using analytic methods, requires students to develop problem-solving, analysis, assessment, and creativity abilities. However, current educational practices fall short of acquiring these abilities due to insufficient instructional techniques, textbooks, and a lack of integration with information and communication technologies. To address these shortcomings, the study proposes a Desmos-assisted textbook meant to increase students' HOTS through the use of interactive Desmos platform tools such as graphic depiction, experimentation, simulation, and collaborative learning. The textbook development followed the PLOMP model, which included preliminary research, prototyping, and assessment phases, ensuring the textbook's validity and practicality through reiterated evaluations. The findings show that the textbook is highly valid and practical for instructional purposes, improving students' knowledge of mathematical concepts and ability to engage in HOTS processes. Despite some difficulties with HOTS-related practice questions, generally student feedback was positive, emphasizing the textbook's function in supporting a deeper understanding of analytic geometry and encouraging problem-solving skills. The study indicates that integrating technology such as Desmos into mathematics education can greatly contribute to the development of students' HOTS, and recommends its use in teaching techniques as well as additional research on its implementation in educational contexts.

Motions of the various mechanism like acceleration, velocity, displacement and driven members involved the connection of rod and piston. The design of this rod and piston is known as kinematic analysis of the slider crank mechanism. This work used graphical method and analytical method of complex algebra method to analyse kinematic analysis of the engine. An experimental investigation was undertaken to study the variation of piston velocity with the crank angle of a slider crank mechanism, using the principle of instantaneous center approach. This phenomenon was also numerically modeled using the concepts of trigonometric and analytical geometry. But the numeric-calculation was sufficiently tedious, and prone to error, that led to developing a computer solution using Microsoft Excel Package. The three approaches generated piston velocity crank angle graph that were in good agreement with one another, from where it was observed that the variation resembles cosine curve rule, and that the maximum velocity of the slider occurs at a crank angle of 90° while the minimum occurs at 27°. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove a theorem for holomorphic twisted quiver bundles over a special non-compact Gauduchon manifold, connecting the existence of (σ , τ) -Hermite–Yang–Mills metric in differential geometry and the analytic (σ , τ) -stability in algebraic geometry. The proof of the theorem relies on the flow method and the Uhlenbeck–Yau's continuity method. [ABSTRACT FROM AUTHOR]

High-precision tapered threads are widely used in hard-loaded mechanical joints, especially in the aggressive environment of the drilling of oil and gas wells. Therefore, they must be made of workable materials often difficult to machine. This requires the use of high-performance cutting tools, which means the application of non-zero geometric parameters: rake and edge inclination angles. This study is based on analytical geometry methodology and describes the theoretical function of the thread profile as convoluted surfaces dependent on the tool's geometric angles. The experiments were conducted using a visual algorithm grounded on the obtained function and prove the practical use of the scientific result. They predict the required accuracy of thread made using a lathe tool with a rake angle of up to 12°. [ABSTRACT FROM AUTHOR]

Fuel level gauging in aircraft presents a significant flight mechanics challenge due to the influence of aircraft movements on measurements. Moreover, it constitutes a multidimensional problem where various sensors distributed within the tank must converge to yield a precise and single measurement, independent of the aircraft's attitude. Furthermore, fuel distribution across multiple tanks of irregular geometries complicates the readings even further. These issues critically impact safety and economy, as gauging errors may compromise flight security and lead to carrying excess weight. In response to these challenges, this research introduces a multi-stage project in aircraft fuel gauging systems, as a continuum of studies, where this first article presents a computational tool designed to simulate aircraft fuel sensor data readings as a function of fuel level, fuel tank geometry, sensor location, and aircraft attitude. Developed in an open-source environment, the tool aims to support the statistical inference required for accurate modeling in which synthetic data generation becomes a crucial component. A discretization procedure accurately maps fuel tank geometries and their mass properties. The tool, then, intersects these geometries with fuel-level planes and calculates each new volume. It integrates descriptive geometry to intersect these fuel planes with representative capacitive level-sensing probes and computes the sensor readings for the simulated flight conditions. The method is validated against geometries with analytical solutions. This process yields detailed fuel measurement responses for each sensor inside the tank, and for different analyzed fuel levels, providing insights into the sensors' signals' non-linear behavior at each analyzed aircraft attitude. The non-linear behavior is also influenced by the sensor saturation readings at 0 when above the fuel level and at 1 when submerged. The synthetic fuel sensor readings lay the baseline for a better understanding on how to compute the true fuel level from multiple sensor readings, and ultimately optimizing the amount of used sensors and their placement. The tool's design offers significant improvements in aircraft fuel gauging accuracy, directly impacting aerostructures and instrumentation, and it is a key aspect of flight safety, fuel management, and navigation in aerospace technology. [ABSTRACT FROM AUTHOR]

Monitoring joystick operations in power wheelchairs (PWCs) is promising for investigating user-wheelchair interaction and providing quantitative measures to assess the user's driving performance. In this paper, an add-on measurement system, Power Wheelchair Maneuvering Logger (PWhML), is developed to provide an easy-to-implement and cost-effective solution for monitoring the user's joystick operations in PWCs. The proposed system uses two compact inertial measurement units (IMUs), which are respectively attached to the joystick and wheelchair armrest for movement sensing. A coordinate transformation-based method is proposed to estimate the joystick operating angles using the acceleration data measured by the attached IMUs. The accuracy of the proposed method was thoroughly evaluated under different conditions. The evaluation trials in a stationary PWC reported a mean absolute error (MAE) of 0.59° in the forward/backward direction and 0.64° in the leftward/rightward direction, validating the established geometry model for coordinate transformation. The subsequent driving experiments on outdoor test courses demonstrated the effectiveness and robustness of the proposed method in various terrain conditions (MAE of less than 3°). A clustering analysis based on the t-distributed stochastic neighborhood embedding method correctly categorized different driving activities using the joystick operating angles measured by PWhML. These results indicate that integrating the developed PWhML into PWCs can facilitate a quantitative measurement of the user's driving behavior, providing valuable insights to identify careless operation patterns and help PWC users to improve driving performance. [ABSTRACT FROM AUTHOR]

In their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and systems are used. Currently, we are interested in computer geometry, more specifically, the implementation of computer graphics. The use of the projective space and homogeneous coordinates has actually become a standard in modern computer graphics. In other words, the problem is reduced to the application of analytic projective geometry. The authors failed to find a computer algebra system that could implement projective geometry in its entirety. Therefore, it was decided to partially implement computer algebra for visualization of algebraic relations. For this purpose, the Asymptote system was employed. [ABSTRACT FROM AUTHOR]

Water jets impacting the rock cause water hammer effects, resulting in significant damage to the rock. The self-rotating cascade jet breaks rocks through rotational impact, but its water hammer characteristics are still uncertain. The models for water hammer pressure and its duration and dimensionless action length of a cascade jet were constructed using dynamic elasticity and analytic geometry. Moreover, rock-breaking experiments were conducted using a developed cascade nozzle bit to validate the models. The results show that the impact of self-rotating cascade jets on the rock does not generate continuous water hammer pressure. The water hammer characteristics and rock-breaking capacity of the designed jets are ranked as follows: the central jet is the strongest, the first cascade jet is the second strongest, and the second cascade jet is the weakest. The characteristics of the water hammer and rock-breaking capacity for the self-rotating cascade jet increase as the rotational speed and the eccentric distance decrease, the pressure, the impact angle, and the radius increase. The results can lay a theoretical foundation for understanding the rock-breaking mechanism of the self-rotating cascade jet and developing new types of pulsed jets. Highlights: Water hammer models were developed and validated for a self-rotating cascade jet impinging on a rock. The water hammer pressure of a self-rotating cascade jet impinging on the rock was not sustained. The influence of jet property parameters on the water hammer characteristics was demonstrated. [ABSTRACT FROM AUTHOR]

Robotic arms are often chosen as the primary manipulator for teleoperated robots specializing in executing tasks that require high skills from humans. The optimization of robotic arm design has been studied extensively using various types of optimization algorithms. However, studies validating and optimizing robotic arms with a high degree of freedom (DOF) using co-simulation techniques are scarce. This study presents the validation and modeling of a five-DOF robotic arm by observing the torques produced by each robotic arm joint using the co-simulation method between Solidworks and Simscape Multibody. The system is modeled in a Solidworks environment with full freedom and overall configurations. The model is then exported to Simscape Multibody for modeling processes. Several validation processes were conducted to validate the Simscape Multibody by comparing torques produced from the three-DOF robotic arm in Simscape with three DOF dynamic equations. Further validation was conducted using coordinate geometry of the end effector position in Solidworks, Simscape, and mathematical geometry models. The proposed co-simulation model agrees with the mathematical model with an average error of 7.6%. This study will likely provide a new approach to the co-simulation technique for systems with a high degree of freedom. [ABSTRACT FROM AUTHOR]

This South African study explored how pre-service teachers understand concepts in analytical geometry. Extending the work of Skemp and Carrillo-Yañez, et al., we captured data and carried out this qualitative study. We noted that the participants displayed complete understanding for some geometrical concepts but lacked relational understanding. Their learning process was interrupted during the covid epidemic, and this had a negative impact on their relational understanding of geometric concepts. [ABSTRACT FROM AUTHOR]

The complex, trichlorido(1,4,11-triaza-8-azoniatetracyclo[6.6.2.04,16.011,15]- hexadecane 1-oxide-κO)zinc(II) monohydrate, [ZnCl3(C12H23N4O)]⋅H2O, (I), has monoclinic symmetry (space group P21/n) at 120 K. The zinc(II) center adopts a slightly distorted tetrahedral coordination geometry and is coordinated by three chlorine atoms and the oxygen atom of the oxidized tertiary amine of the tetracycle. The amine nitrogen atom, inside the ligand cleft, is protonated and forms a hydrogen bond to the oxygen of the amine oxide. Additional hydrogen-bonding interactions involve the protonated amine, the water solvate oxygen atom, and one of the chloro ligands. [ABSTRACT FROM AUTHOR]

Two recently proposed variants of CD-type discretizations of sea ice dynamics on triangular meshes are implemented in the Finite-VolumE Sea ice–Ocean Model (FESOM version 2). The implementations use the finite element method in spherical geometry with longitude–latitude coordinates. Both are based on the edge-based sea ice velocity vectors but differ in the basis functions used to represent the velocities. The first one uses nonconforming linear (Crouzeix–Raviart) basis functions, and the second one uses continuous linear basis functions on sub-triangles obtained by splitting parent triangles into four smaller triangles. Test simulations are run to show how the performance of the new discretizations compares with the A-grid discretization using linear basis functions. Both CD discretizations are found to simulate a finer structure of linear kinematic features (LKFs). Both show some sensitivity to the representation of scalar fields (sea ice concentration and thickness). Cell-based scalars lead to a finer LKF structure for the first CD discretization, but the vertex-based scalars may be advantageous in the second case. [ABSTRACT FROM AUTHOR]

The upcoming Geospace Dynamics Constellation (GDC) mission aims to investigate dynamic processes active in Earth's upper atmosphere and their local, regional, and global characteristics. Achieving this goal will involve resolving and distinguishing spatial and temporal variability of ionospheric and thermospheric (IT) structures in a quantitative manner. This, in turn, calls for the development of sophisticated algorithms that are optimal in combining information from multiple in-situ platforms. This manuscript introduces an implementation of the least-squares gradient calculation approach previously developed by J. De Keyser with the focus of its application to the GDC mission. This approach robustly calculates spatial and temporal gradients of IT parameters from in-situ measurements from multiple spacecraft that form a flexible constellation. The previous work by De Keyser, originally developed for analysis of Cluster data, focused on 3-D Cartesian geometry, while the current work extends the approach to spherical geometry suitable for missions in Low Earth Orbit (LEO). The algorithm automatically provides error bars for the estimated gradients as well as the scales over which the gradients are expected to be constant. We evaluate the performance of the software on outputs of high-resolution global ionospheric/thermospheric simulations. It is shown that the software will be a powerful tool to explore GDC's ability to answer science questions that require gradient calculations. The code can also be employed in support of Observing System Simulation Experiments to evaluate suitability of various constellation geometries and assess the impact of measurement sensitivities on addressing GDC's science objectives. [ABSTRACT FROM AUTHOR]

An iterative algorithm for the diffusion of heat in layered structures is solved in cylindrical coordinates for the geometry used in measurements of thermophysical properties of materials by the modified transient plane source (MTPS) method. This solution for the frequency-domain temperature response is then used to model the transient temperature excursion and evaluate the accuracy of the measurements. We evaluate when the MTPS method is capable of separately determining the thermal conductivity and heat capacity per unit volume of a material. For a typical sensor design, data acquisition, and data analysis, the MTPS measurement has a small sensitivity to the thermal diffusivity of the sample when the thermal diffusivity is < 5 mm2 s−1. We analyze the propagation of errors from uncertainties in the thermal contact between the sensor and the sample and evaluate the limitations of the MTPS method in accurately measuring samples with extremely low thermal effusivity, e.g., low density foam insulation. We find that uncertainties in the thickness of the contact region limit the accuracy of MTPS measurements when the data are analyzed in a conventional manner based on a single parameter, m−1, the inverse of the slope of the temperature excursion as a function of the square root of time. [ABSTRACT FROM AUTHOR]

One of the geometric figures that has symmetry properties is the Cassini oval. The Cassini oval is a curve defined as the locus of points in the plane such that the product of the distances to two fixed points is constant. Cassini ovals are named after the astronomer Giovanni Domenico Cassini, who studied them in 1680. Today, the geometric properties of Cassini ovals are used in many fields: analytical geometry, nuclear physics, radiolocation, and industrial applications. The bistatic radar uses Cassini ovals to detect various targets in radiolocation. Until now, there have been no studies on the clustering capabilities of Cassini ovals. As a novelty, it is hypothesized that clustering possibilities could be used for Cassini ovals. In this article, a study of the capabilities of Cassini ovals in radiolocation was carried out, and their suitability for clustering purposes was shown. [ABSTRACT FROM AUTHOR]

Purpose: Micro-texture is processed on the surface to reduce the friction of the contact surface, and its application is more and more extensive. The purpose of this paper is to create a texture function model to study the influence of surface parameters on the accuracy of the simulated surface so that it can more accurately reflect the characteristics of the real micro-textured surface. Design/methodology/approach: The microstructure function model of rough surfaces is established based on fractal geometry and polar coordinate theory. The offset angle θ is introduced into the fractal geometry function to make the surface asperity normal perpendicular to the tangent of the surface. The 2D and 3D contour surfaces of the surface groove texture are analyzed by MATLAB simulation. The effects of fractal parameters (D and G) and texture parameter h on the curvature of the surface micro-texture model were studied. Findings: This paper more accurately characterizes the textured 3D curved surface, especially the surface curvature. The scale coefficient G significantly affects curvature, and the influence of fractal dimension D and texture parameters on curvature can be ignored. Originality/value: The micro-texture model of the rough surface was successfully established, and the range of fractal parameters was determined. It provides a new method for the study of surface micro-texture tribology. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2023-0298/ [ABSTRACT FROM AUTHOR]

A Ni(II) complex of 3,3′-(-(pentane-3,3-diylbis(1H-pyrrole-5,2-diyl))bis(diazene-2,1-diyl)) dipyridine, NiL, has been synthesized and characterized. In the crystal, the Ni(II) ion is in square-planar geometry by coordinating to two pyrrole nitrogen atoms and two azo nitrogen atoms. Anagostic C–H···Ni interactions, as well as C–H···N hydrogen bond were found play important role in the self-assembly of the complex molecules. The intermolecular interactions were evaluated by Hirshfeld surface analysis. Frontier molecular orbitals (HOMO and LUMO), their energy gap and associated reactive parameters were calculated to understand the properties of the complex. UV–Vis spectrum of the complex were also performed. Anagostic C–H···Ni interactions were found play important role in the crystal of the Ni(II) complex with 3,3'-(-(pentane-3,3-diylbis(1H-pyrrole-5,2-diyl))bis(diazene-2,1-diyl)) dipyridine. [ABSTRACT FROM AUTHOR]

This paper presents a novel coupling of a kinetic description of neutrals with a fluid description of a fusion plasma. The code, plasma interacting super-atoms and molecules (PISAM), employs a grid-free Cartesian geometry and a direct simulation Monte Carlo approach to solve the kinetic equations of deuterium atoms and molecules. The grid-free geometry and the parallel nature of the neutral dynamics, in the absence of neutral–neutral interactions, allow for an unlimited and work-efficient parallelization of PISAM that always ensures a balanced workload. The highly optimized Python implementation obtains good performance while securing easy accessibility to new users. The coupling of PISAM with the edge turbulence model HESEL is outlined with emphasis on the technical aspects of coupling Message Passing Interface-parallelized Python and C++ codes. Furthermore, the paper presents and analyzes simulation results from running the coupled HESEL-PISAM model. These results demonstrate the impact of radial neutral transport and plasma–neutral dynamics perpendicular to the magnetic field. Specifically, they illustrate how the inward flow of neutral kinetic energy and the inhibition of radial electric shear, resulting from poloidal momentum transfer between atoms and ions, can affect the energy containment time. By comparing the results of the HESEL-PISAM model with those obtained from coupling HESEL with a diffusive-fluid-neutral model, the capabilities of diffusion models in predicting neutral transport in the plasma edge and scrape-off layer are elucidated. [ABSTRACT FROM AUTHOR]

The notions of neutrosophic N-subalgebras and neutrosophic N-ideals of Hilbert algebras are introduced, and several properties are investigated. Conditions for neutrosophic N-structures to be neutrosophic Nsubalgebras and neutrosophic N-ideals of Hilbert algebras are provided. The Cartesian product of neutrosophic N-structures is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic N-subalgebras and neutrosophic N-ideals. [ABSTRACT FROM AUTHOR]