Search

This paper discusses the relevance of using physical situations to introduce the concept of angles at elementary school. We compare the effectiveness of two geometry teaching sequences. In the first one (physical sequence), the pupils learned the angle concept by experimenting on the playground (i.e. mesospace) and then modelling the situation. In the second one (paper-and-pencil sequence), the pupils worked solely in the space of a sheet of paper (i.e. microspace). In both sequences, pupils compared areas of space delineated by an angle between two directions. Pupils in two Grade 3 classes were exposed to one of the two teaching sequences. The unfolding of these sequences was videotaped and analyzed, and the pupils were tested individually, before and after teaching, to measure each sequence's effectiveness. Results showed that both sequences are effective to grasp the angle concept: Most pupils overcame the common erroneous conception of comparing angles' sides' lengths instead of angle openness. The comparison of areas of space delineated by an angle between two infinite directions, which is the two sequences' common core, seems to be the key factor underlying angle conceptualization. This paper ends with a discussion of these results' teaching implications and the merits of each sequence. [ABSTRACT FROM AUTHOR]

Embossing is a functional and strategic process for creating high-quality multi-sensory tissue-paper products. Embossing modifies the sheet surface by generating hill and/or valley designs, changing the third-dimension z with a compressive die. This research work specifically concerns the impact study of the engraving finishing geometry on the final properties of tissue paper. This work led us to conclude that, even though the sheets individually present a higher hand-feel (HF) value for the straight finishing geometry, the highest softness was obtained in the two-ply prototype for the round finishing geometry. Moreover, this study confirmed that the HF value reduces with the increase of the bulk, being more accentuated for the micropattern. Relevant differences could not be seen in the spreading kinetics of the liquid droplets over time. Thus, the finishing geometry of the 3D plates did not impact the absorption kinetics on these samples. The finite element model allows us to understand the effect of the plate pattern and its finishing geometry on the paper, and the simulation results were in accordance with the experimental results, showing the same trend where patterns with a round finishing geometry marked the tissue-paper sheet more than patterns with a straight finishing did. [ABSTRACT FROM AUTHOR]

This study is focused on the development of ultrasoft facial grade tissue paper of 12.5 gsm with superior quality in terms of handfeel softness alongside enhanced productivity. To sustain in the tissue paper business, industries needs to focus in such a way that productivity should be increased with excellent product quality. Tissue industries generally loose huge productivity as well as deviation is observed in high quality low gsm facial grade tissue paper in terms of quality. This is owing to vague understanding about the creeping geometry where creep pocket angle, blade grind angle, blade MOC play a significant role to improve the productivity and produce excellent product quality. This experimental study would bridge for better understanding of impact of creping blade material and crepe blade geometry on productivity and quality of tissue paper. In this experimental study, two types of creping blade material– carbon steel and ceramic were used. Machine runability, mechanical properties of developed facial grade tissue paper was minutely analysed. It was found that while using ceramic blade, downtime reduced by 86.8 % while the production was enhanced by 10 % indicating better machine runnability with ceramic blade. Thereafter, the blade holder angle was altered to 17°, 18° and 19° along with alterations of bevel angle to 75°, 80°, 85° and 90°. All the mechanical properties of developed facial grade tissue paper was investigated and analysed. The outcome of the study indicated that by using ceramic tip creping blade with 17° blade holder angle and bevel angle at 80°, ultrasoft, high bulk facial grade tissue paper can be produced with much improved machine runnability i. e. downtown reduced by 85 % on account of blade changing frequency and production enhanced by 10 %. [ABSTRACT FROM AUTHOR]

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°. [ABSTRACT FROM AUTHOR]

The low cost, simplicity, and ease of use of paper microfluidic devices have made them valuable medical diagnostics for applications from pregnancy testing to COVID-19 screening. Meanwhile, the increasing complexity of paper-based microfluidic devices is driving the need to produce new tools and methodologies that enable more robust biological diagnostics and potential therapeutic applications. A new design framework is being used to facilitate both research and fabrication of paper-based microfluidic biological devices to accelerate the investigative process and reduce material utilization and manpower. In this work we present a methodology for this framework to dynamically place and route microfluidic components in a nondiscrete design space where fluid volume usage, surface area utilization, and the timing required to perform specified biological assays are accounted for and optimized while also accelerating the development of potentially lifesaving new devices. [ABSTRACT FROM AUTHOR]

This study aimed to empirically investigate preservice teachers' learning experiences during a series of geometry-themed choreography and dance activities. These pedagogical tasks were designed to examine the challenges and solutions that participants experienced when exercising their spatial reasoning abilities, particularly during the transition between the choreography designs they had generated on a Lego-based grid worksheet and real-world dancing positions. The data collection for this study took place at an elementary school located within a bilingual metropolitan area along the southwestern United States border. The overall findings indicated that all of the participating preservice teachers' dance teams encountered interrelated challenges, most of which were variations on disorientation, primarily due to transitioning between representations of space and the deprivation of the typically employed spatial navigation reference points that are used in normal activities. [ABSTRACT FROM AUTHOR]

31P nuclear magnetic resonance (NMR) chemical shifts were shown to be very sensitive to the basis set used at the geometry optimization stage. Commonly used energy-optimized basis sets for a phosphorus atom containing only one polarization d-function were shown to be unable to provide correct equilibrium geometries for the calculations of phosphorus chemical shifts. The use of basis sets with at least two polarization d-functions on a phosphorus atom is strongly recommended. In this paper, an idea of creating the basis sets purposed for the geometry optimization that provide the least possible error coming from the geometry factor of accuracy in the resultant NMR shielding constants is proposed. The property-energy consisted algorithm with the target function in the form of the molecular energy gradient relative to P–P bond lengths was applied to create new geometry-oriented pecG-n (n = 1, 2) basis sets for a phosphorus atom. New basis sets have demonstrated by far superior performance as compared to the other commonly used energy-optimized basis sets in massive calculations of 31P NMR chemical shifts carried out at the gauge-including atomic orbital-coupled cluster singles and doubles/pecS-2 level of the theory by taking into account solvent, vibrational, and relativistic corrections. [ABSTRACT FROM AUTHOR]

Development of paper-based microfluidic devices that perform colorimetric measurements requires quantitative image analysis. Because the design geometries of paper-based microfluidic devices are not standardized, conventional methods for performing batch measurements of regularly spaced areas of signal intensity, such as those for well plates, cannot be used to quantify signal from most of these devices. To streamline the device development process, we have developed an open-source program called ColorScan that can automatically recognize and measure signal-containing zones from images of devices, regardless of output zone geometry or spatial arrangement. This program, which measures color intensity with the same accuracy as standard manual approaches, can rapidly process scanned device images, simultaneously measure identified output zones, and effectively manage measurement results to eliminate requirements for time-consuming and user-dependent image processing procedures. [ABSTRACT FROM AUTHOR]

Visualizing graphs and networks in non‐Euclidean space can have benefits such as natural focus+context in hyperbolic space and the familiarity of interactions in spherical space. Despite work on these topics going back to the mid 1990s, there is no survey, or a part of a survey for this area of research. In this paper we review and categorize over 60 relevant papers and analyze them by geometry, (e.g., spherical, hyperbolic, torus), by contribution (e.g., technique, evaluation, proof, application), and by graph class (e.g., tree, planar, complex). [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]

Visual SLAM algorithms can obtain a large amount of texture information from the environment and usually perform very well in static scenes, but there are a large number of irregular dynamic points when running in dynamic scenes, which can lead to increased error in SLAM feature point matching and loss of tracking localization. To address this challenge this paper proposes a SLAM system (YVG‐SLAM) that adapts to dynamic scenes. YVG‐SLAM is an improvement on the ORB‐SLAM3 algorithm, integrating the view geometry algorithm and the current powerful YOLOv5 algorithm, while proposing a dynamic feature removal strategy without a priori assumptions to reduce the influence of dynamic targets. In this paper, we first lighten the YOLOv5 algorithm, then process the image frame to get the bounding box, then use the view geometry algorithm to determine the dynamic feature points on the image frame, and finally remove the moving objects in the image frame according to the dynamic feature recognition strategy proposed in this paper. The performance of the algorithm is tested on the TUM RGB‐D and BONN RGB‐D datasets. The experimental results show that the robustness of the proposed algorithm on most video sequences is better than the existing SLAM algorithms dealing with dynamic scenes such as Detect‐SLAM and DynaSLAM, and the RMSE index of the absolute trajectory error measured on high‐speed dynamic video sequences can be significantly reduced by more than 93% compared to ORB‐SLAM3. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

A deep learning-based Visual Inertial SLAM technique is proposed in this paper to ensure accurate autonomous localization of mobile robots in environments with dynamic objects. Addressing the limitations of real-time performance in deep learning algorithms and the poor robustness of pure visual geometry algorithms, this paper presents a deep learning-based Visual Inertial SLAM technique. Firstly, a non-blocking model is designed to extract semantic information from images. Then, a motion probability hierarchy model is proposed to obtain prior motion probabilities of feature points. For image frames without semantic information, a motion probability propagation model is designed to determine the prior motion probabilities of feature points. Furthermore, considering that the output of inertial measurements is unaffected by dynamic objects, this paper integrates inertial measurement information to improve the estimation accuracy of feature point motion probabilities. An adaptive threshold-based motion probability estimation method is proposed, and finally, the positioning accuracy is enhanced by eliminating feature points with excessively high motion probabilities. Experimental results demonstrate that the proposed algorithm achieves accurate localization in dynamic environments while maintaining real-time performance. [ABSTRACT FROM AUTHOR]

A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade (Braunstein et al. in Phys Rev Lett 91(16):168701, 2003; Braunstein et al. in Int J Bifurc Chaos 17(07):2215–2255, 2007; Chen et al. in Phys Rev Lett 96(6):068702, 2006; Wu et al. in Phys Rev Lett 96(14):148702, 2006) is as follows: for a large class of random graph models with degree exponent τ ∈ (3 , 4) , distances in the minimal spanning tree (MST) on the giant component in the supercritical regime scale like n (τ - 3) / (τ - 1) . The aim of this paper is to make progress towards a proof of this conjecture. We consider a supercritical inhomogeneous random graph model with degree exponent τ ∈ (3 , 4) that is closely related to Aldous's multiplicative coalescent, and show that the MST constructed by assigning i.i.d. continuous weights to the edges in its giant component, endowed with the tree distance scaled by n - (τ - 3) / (τ - 1) , converges in distribution with respect to the Gromov–Hausdorff topology to a random compact real tree. Further, almost surely, every point in this limiting space either has degree one (leaf), or two, or infinity (hub), both the set of leaves and the set of hubs are dense in this space, and the Minkowski dimension of this space equals (τ - 1) / (τ - 3) . The multiplicative coalescent, in an asymptotic sense, describes the evolution of the component sizes of various near-critical random graph processes. We expect the limiting spaces in this paper to be the candidates for the scaling limit of the MST constructed for a wide array of other heavy-tailed random graph models. [ABSTRACT FROM AUTHOR]

Angular equivalence of norms, introduced by Kikianty and Sinnamon (2017), is a notion of norm equivalence that is more attuned to the geometry of the norms. For certain geometrical properties and two angularly equivalent norms, it is the case that if one of the norms has a property, then so does the other. In this paper, we show further results in this direction, namely angularly equivalent norms share the property of non-squareness; and that the exposed points of the unit balls are in the same direction, under the condition that these points are assumed to be smooth with respect to both norms. A discussion on (the angular equivalence of) the dual norms of angularly equivalent norms is also given, giving a partial answer to an open problem as stated in the paper by Kikianty and Sinnamon (2017). [ABSTRACT FROM AUTHOR]

This review paper addresses the development of numerical modeling of electromagnetic fields in geophysics with a focus on recent finite element simulation. It discusses ways of estimating errors of our solutions for a perfectly matched modeling domain and the problems that arise from its insufficient representation. After a brief outline of early methods and modeling approaches, the paper mainly discusses the capabilities of the finite element method formulated on unstructured grids and the advantages of local h-refinement allowing for both a flexible and largely accurate representation of the geometries of the multi-scale geomaterial and an accurate evaluation of the underlying functions representing the physical fields. In summary, the accuracy of the solution depends on the geometric mapping, the choice of the mathematical model, and the spatial discretization. Although the available error estimators do not necessarily provide reliable error bounds for our complex geomodels, they are still useful to guide grid refinement. Therefore, an overview of the most common a posteriori error estimators is given. It will be shown that the sensitivity is the most important function in both guiding the geometric mapping and the local refinement. [ABSTRACT FROM AUTHOR]

This paper proposes a meso-structural model for the discrete fibrous network of paper, which is able to upscale the irreversible phenomena from the underlying hygro-mechanics towards the effective behaviour at the macro-scale. The swelling of individual fibres, induced by moisture content variations, is transmitted to the network through inter-fibre bonds and governs the resulting effective material response. The present approach is based on a recently developed discrete meso-structural model for the reversible part of the response, which distinguishes between the influence on the hygroscopic behaviour of free-standing fibre segments and inter-fibre bonds. The network structure, fibre and bond geometries and hygro-elastic properties are explicitly incorporated. The major novelty of this contribution is the extended fibre constitutive model, enabling to describe some typical irreversible mechanisms and instability effects related to the history of the manufacturing. This extension strongly affects the effective material behaviour beyond the elastic range. Despite the valuable work in the literature, no papers can be found dedicated to meso-structural models including these phenomena. Using an appropriate homogenization strategy, the unit-cell is solved analytically, capturing irreversible shrinkage in restrained dried paper and the occurrence of local buckling within the bond for freely dried material. The proposed scale transition offers a deeper insight into the complex relation between the events occurring at the different length scales. The potential of the proposed methodology is demonstrated through the convincing agreement with experimental data obtained from the literature. [ABSTRACT FROM AUTHOR]

This paper comprehensively investigated the effect of the tool geometries on heat transfer and special crystallization characteristics in the drilling of carbon fiber‐reinforced polyetheretherketone (CF/PEEK) composite for the first time. Three tools with different geometries (twist, brad, and dagger drill) are carried out on CF/PEEK drilling experiments, and temperature, as well as crystallinity and surface roughness, are introduced to make a comparative evaluation on the effect of the tool geometries. The results show that the drilling temperature is determined by the contact length of the profile between the drill and the material. Correspondingly, better surface quality with lower surface roughness and smoother surface is obtained by using a twist drill due to the heat‐induced PEEK smearing effect. Further, in situ XRD and differential scanning calorimeter (DSC) were used to characterize the crystallization characteristics where crystal phase transformation at different temperatures was measured. The occurring temperature of the strongest crystallization characteristics for CF/PEEK is basically not affected by tool geometries, all at 300°C, and the limiting crystallization temperature is 344.5 ± 0.7°C. The crystallinity is found to be affected by drilling temperature and cooling rate and gradually decreases along the heat transfer direction. This work provides a new sight into the improvement of CF/PEEK drilling. Highlights: The effect of tool geometries on thermal and crystallization for CF/PEEK is provided.In situ XRD and DSC are used to characterize crystallization characteristics.The drilling temperature and cooling rate are both determinants of crystallinity.The limiting crystallization temperature of the CF/PEEK composite is 344.5 ± 0.7°C.Heat‐induced PEEK smearing effect improves the surface quality of CF/PEEK drilling. [ABSTRACT FROM AUTHOR]

In this paper, we prove a stability result for the non-Kähler geometry of locally conformally Kähler (lcK) spaces with singularities. Specifically, we find sufficient conditions under which the image of an lcK space by a holomorphic mapping also admits lcK metrics, thus extending a result by Varouchas about Kähler spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa). [ABSTRACT FROM AUTHOR]

This paper studies the discrete differential geometry of the checkerboard pattern inscribed in a quadrilateral net by connecting edge midpoints. It turns out to be a versatile tool which allows us to consistently define principal nets, Koenigs nets and eventually isothermic nets as a combination of both. Principal nets are based on the notions of orthogonality and conjugacy and can be identified with sphere congruences that are entities of Möbius geometry. Discrete Koenigs nets are defined via the existence of the so-called conic of Koenigs. We find several interesting properties of Koenigs nets, including their being dualizable and having equal Laplace invariants. Isothermic nets can be defined as Koenigs nets that are also principal nets. We prove that the class of isothermic nets is invariant under both dualization and Möbius transformations. Among other things, this allows a natural construction of discrete minimal surfaces and their Goursat transformations. [ABSTRACT FROM AUTHOR]

Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein's approach had roots in Poncelet's principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked some of the central ideas in Riemann's theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker's work had a strongly qualitative character that imbued Klein's early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet's earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie). [ABSTRACT FROM AUTHOR]

Plagued by heterogeneous clutter, it is a serious challenge for airborne radars to detect low-altitude, weak targets. To overcome this problem, a novel matrix information geometry detector for airborne multi-channel radar is proposed in this paper. The proposed detector applies the given steering vector and array structure information to the matrix information geometry detection method so that it can be used for space–time adaptive detection. While improving the detection performance, the matrix information geometry detector's original anti-clutter advantage is enhanced as well. The simulation experiment results indicate that the proposed detector has advantages in several of the properties related to space–time adaptive detection, while its computational complexity does not increase significantly. Moreover, experiment results based on the measured data verify the superior performance of the proposed method. Sea-detecting data-sharing-program data, mountaintop data, and phased-array radar data are employed to verify the performance advantage of the proposed method in heterogeneous clutter and the ability for weak target detection. [ABSTRACT FROM AUTHOR]

Particle modeling for complex geometries is a challenge for the wide application of particle methods in engineering fields. The traditional modeling method with Cartesian coordinates faces difficulties in accurately representing boundary shapes and would lose flow details near the slender structure. The modeling method with the signed distance field (SDF) and particle shifting technique can obtain a uniform boundary-fitting particle distribution. However, the accuracy and efficiency of SDF construction, as well as the conservation of geometry volume after discretizing the model into particles, need to be further improved. In this paper, a general particle modeling method is proposed for arbitrary geometries. A double search technique is proposed to quickly construct the narrowband signed distance field (NSDF) near the geometry boundary. A scanning method is developed for the NSDF to determine the inner/outer relationship between the non-narrowband grids and the geometry. In addition, a volume compensation technique is proposed to ensure the volume conservation of the particle model. A modeling evaluation system is established, and three evaluation indicators are proposed to evaluate the quality of particle distribution and total volume conservation for particle models. Complex geometries such as the Stanford bunny, the Stanford dragon, and the centrifugal impeller are modeled to validate the accuracy and convergence of the proposed method. The results show that the proposed method can achieve a more uniform and accurate boundary-fitting particle distribution for complex geometries, and it can also effectively model tiny structures while significantly reducing total geometry volume error. [ABSTRACT FROM AUTHOR]

In this paper, we study the projectively Ricci-flat general (α, β)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant. Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z. Shen. The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on Mn with a volume form dV on Mn. [ABSTRACT FROM AUTHOR]

In this paper we address the construction of virtual reality scenarios for the NeoTrie VR software, to make some 3D models of architectural objects manageable anywhere. Students will be able to see the pieces (muqarnas, vaults and arches and towers) in a 3D model, manipulate and assemble them, to understand their spatial arrangement. They will also be able to use Neotrie tools to build and thus better assimilate the underlying geometric structures. [ABSTRACT FROM AUTHOR]

In this paper, we study, for functionals having a minimax geometry on a constraint, the existence of bounded Palais-Smale sequences carrying Morse index type information. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of unsupervised object segmentation from single images. We do not introduce a new algorithm, but systematically investigate the effectiveness of existing unsupervised models on challenging real-world images. We first introduce seven complexity factors to quantitatively measure the distributions of background and foreground object biases in appearance and geometry for datasets with human annotations. With the aid of these factors, we empirically find that, not surprisingly, existing unsupervised models fail to segment generic objects in real-world images, although they can easily achieve excellent performance on numerous simple synthetic datasets, due to the vast gap in objectness biases between synthetic and real images. By conducting extensive experiments on multiple groups of ablated real-world datasets, we ultimately find that the key factors underlying the failure of existing unsupervised models on real-world images are the challenging distributions of background and foreground object biases in appearance and geometry. Because of this, the inductive biases introduced in existing unsupervised models can hardly capture the diverse object distributions. Our research results suggest that future work should exploit more explicit objectness biases in the network design. [ABSTRACT FROM AUTHOR]

This paper explores the possibility of using dual representation of geometry to speed up ray tracing and ensure robustness of light propagation simulation in complex optical systems with freeform surfaces defined by high-degree polynomials (up to order 34) or Jacobi polynomials. Traditional methods for representing this geometry both as a triangular mesh and as an analytical expression are analyzed. The analysis demonstrates the disadvantages of the traditional approaches due to the insufficient accuracy of calculating coordinates of the point at which the ray intersects the triangular mesh, as well as the non-robustness of the conventional procedures for finding the point of intersection between the tangent ray and the analytical surface. Thus, it is proposed to use a dual representation of geometry as a rough approximation of the surface by a triangular mesh, which is subsequently used as an initial approximation to find the point at which the ray intersects the surface defined by an analytical expression. This approach significantly speeds up convergence of the analytical methods and improves robustness of their solutions. The use of the Intel® Embree library to quickly find the point of intersection between the ray and the rough triangular mesh, as well as a vector model to refine the coordinates of the point of intersection between the ray and the analytically represented geometry, allows us to develop and implement a ray tracing algorithm for an optical system that has surfaces with dual representation of geometry. Experiments carried out using the developed algorithm show a significant speedup of ray tracing while preserving computational accuracy and high robustness of the results. The results are demonstrated by evaluating the point spread function and glare for two lenses with freeform surfaces defined by Jacobi polynomials. In addition, for these two lenses, an image formed by an RGB-D object that simulates a real scene is calculated. [ABSTRACT FROM AUTHOR]

The frictionless contact problem between a conducting triangular or cylindrical punch and a thermoelectric strip is analyzed in this paper. When designing and optimizing thermoelectric devices for energy harvesting and temperature control applications, the interaction between the punch geometry and the thermoelectric strip is crucial. By the Fourier transform, the considered contact problem is formulated as a Cauchy singular integral equation, which is numerically solved using the collocation method. Distinct singular features at the ends of the punch lead to specific collocation methods adopted. A detailed study on various geometrical and loading parameters, including the punch shape and geometry and the thermoelectric loads, is performed, to assess their influences on the mechanical load-contact size curves and the distribution of the normal contact stress. Numerical results demonstrate that it is feasible to reduce the normal contact stress by increasing the thickness of the thermoelectric strip, enlarging the radius of the cylindrical punch, and decreasing the slope of the triangular punch. For both punch types, the deviation of the normal contact stress under the thermoelectric loads from that without the thermoelectric loads exceeds 5%. Hence, when dealing with the contact problem of the thermoelectric materials and structures, it is necessary to account for the impact of the thermoelectric fields on the elastic mechanical field. The findings from the present study may contribute to the further development of more efficient thermoelectric systems. [ABSTRACT FROM AUTHOR]

Let r and s be positive integers such that r ⩾ 2. Let U and V be vector spaces over fields F and K , respectively, such that dim ⁡ U ⩾ 3 and F has at least r + 1 elements. In this paper, we characterize surjective maps ψ : S r U → S s V preserving adjacency in both directions on symmetric tensors of finite order, which generalizes Hua's fundamental theorem of geometry of symmetric matrices. We give examples showing the indispensability of the assumptions dim ⁡ U ⩾ 3 and the cardinality | F | ⩾ r + 1 in our result. [ABSTRACT FROM AUTHOR]

The proper scheduling of track maintenance and renewal operations is dependent on the accuracy of predictive maintenance outputs which, in turn, rely on the appropriate modelling of the track geometry degradation process. This paper explores the incidence and representativeness of the alerts generated due to local defects of track geometry and the modelling of their degradation rates between consecutive tamping operations. A software tool was developed and used to process track inspection data collected over 12 years of operation of the main Portuguese line (Lisbon-Porto) on a total of 727 km of single-track lines where speeds vary between 30 and 220 km/h. Linear regressions are found to be suitable to model the degradation rates of local defects of longitudinal levelling, alignment and twist in the vast majority of cases, although 20–30% of the time degradation patterns prove to be non-linear even in the short term. The local defects of alignment degrade more rapidly and trigger 80% of the unplanned maintenance needs. Modelling the evolution of local defects, and not only the standard deviation on sections 200 m long, allows us to anticipate unplanned maintenance and tackle unavailability costs. [ABSTRACT FROM AUTHOR]

In previous work (Topping and Yin, https://arxiv.org/abs/2107.14686), we established the existence of a Ricci flow starting with a Riemann surface coupled with a non‐atomic Radon measure as a conformal factor. In this paper, we prove uniqueness, settling Conjecture 1.3 of Topping and Yin (https://arxiv.org/abs/2107.14686). Combining these two works yields a canonical smoothing of such rough surfaces that also regularises their geometry at infinity. [ABSTRACT FROM AUTHOR]

Visual Simultaneous Localization and Mapping (V-SLAM) plays a crucial role in the development of intelligent robotics and autonomous navigation systems. However, it still faces significant challenges in handling highly dynamic environments. The prevalent method currently used for dynamic object recognition in the environment is deep learning. However, models such as Yolov5 and Mask R-CNN require significant computational resources, which limits their potential in real-time applications due to hardware and time constraints. To overcome this limitation, this paper proposes ADM-SLAM, a visual SLAM system designed for dynamic environments that builds upon the ORB-SLAM2. This system integrates efficient adaptive feature point homogenization extraction, lightweight deep learning semantic segmentation based on an improved DeepLabv3, and multi-view geometric segmentation. It optimizes keyframe extraction, segments potential dynamic objects using contextual information with the semantic segmentation network, and detects the motion states of dynamic objects using multi-view geometric methods, thereby eliminating dynamic interference points. The results indicate that ADM-SLAM outperforms ORB-SLAM2 in dynamic environments, especially in high-dynamic scenes, where it achieves up to a 97% reduction in Absolute Trajectory Error (ATE). In various highly dynamic test sequences, ADM-SLAM outperforms DS-SLAM and DynaSLAM in terms of real-time performance and accuracy, proving its excellent adaptability. [ABSTRACT FROM AUTHOR]

As the variety of space targets expands, two-dimensional (2D) ISAR images prove insufficient for target recognition, necessitating the extraction of three-dimensional (3D) information. The 3D geometry reconstruction method utilizing energy accumulation of ISAR image sequence (ISEA) facilitates superior reconstruction while circumventing the laborious steps associated with factorization methods. Nevertheless, ISEA's neglect of valid information necessitates a high quantity of images and elongated operation times. This paper introduces a partitioned parallel 3D reconstruction method utilizing sorted-energy semi-accumulation with ISAR image sequences (PP-ISEA) to address these limitations. The PP-ISEA innovatively incorporates a two-step search pattern—coarse and fine—that enhances search efficiency and conserves computational resources. It introduces a novel objective function 'sorted-energy semi-accumulation' to discern genuine scatterers from spurious ones and establishes a redundant point exclusion module. Experiments on the scatterer model and simulated electromagnetic model demonstrate that the PP-ISEA reduces the minimum image requirement from ten to four for high-quality scatterer model reconstruction, thereby offering superior reconstruction quality in less time. [ABSTRACT FROM AUTHOR]

Determining the maximum number of unit vectors in Rr$\mathbb {R}^r$ with no pairwise inner product exceeding α$\alpha$ is a fundamental problem in geometry and coding theory. In 1955, Rankin resolved this problem for all α⩽0$\alpha \leqslant 0$, and in this paper, we show that the maximum is (2+o(1))r$(2+o(1))r$ for all 0⩽α≪r−2/3$0 \leqslant \alpha \ll r^{-2/3}$, answering a question of Bukh and Cox. Moreover, the exponent −2/3$-2/3$ is best possible. As a consequence, we obtain an upper bound on the size of a q$q$‐ary code with block length r$r$ and distance (1−1/q)r−o(r1/3)$(1-1/q)r - o(r^{1/3})$, which is tight up to the multiplicative factor 2(1−1/q)+o(1)$2(1 - 1/q) + o(1)$ for any prime power q$q$ and infinitely many r$r$. When q=2$q = 2$, this resolves a conjecture of Tietäväinen from 1980 in a strong form and the exponent 1/3$1/3$ is best possible. Finally, using a recently discovered connection to q$q$‐ary codes, we obtain analogous results for set‐coloring Ramsey numbers. [ABSTRACT FROM AUTHOR]

A hybrid satellite–terrestrial relay network is a simple and flexible solution that can be used to improve the performance of land mobile satellite systems, where the communication links between satellite and mobile terrestrial users can be unstable due to the multipath effect, obstacles, as well as the additional atmospheric losses. Motivated by these facts, in this paper, we analyze a system where the satellite–terrestrial links undergo shadowed Rice fading, and, following this, terrestrial relay applies the selection relaying protocol and forwards the information to the final destination using the communication link subjected to Nakagami-m fading. For the considered relaying protocol, we derive the exact closed-form expressions for the outage probability, outage capacity, and ergodic capacity, presented in polynomial–exponential form for the integer-valued fading parameters. The presented numerical results illustrate the usefulness of the selection relaying for various propagation scenarios and system geometry parameters. The obtained analytical results are corroborated by an independent simulation method, based on the originally developed fading simulator. [ABSTRACT FROM AUTHOR]

Determining the design of pushbacks in an open-pit mine is a key part of optimizing the economic value of the mining project and the operational feasibility of the mine. This problem requires balancing pushbacks that have good geometric properties to ensure the smooth operation of the mining equipment and so that the scheduling of extraction maximizes the economic value by providing early access to the rich parts of the deposit. However, because of the challenging nature of the problem, practical approaches for finding the best pushbacks strongly depend on the expert criteria to ensure good operational properties. This paper introduces the Advanced Geometrically Constrained Production Scheduling Problem to account for operational space constraints, modeled as truncated cones of extraction. To find the best solution for this problem, we present a parallel genetic algorithm based on a genotype–phenotype model such that the genotype symbolizes the base block of a truncated cone, and the phenotype represents the cone itself. A central computer node evaluates these solutions, collaborating with various secondary nodes that evolve a population of feasible solutions. The PGA's efficacy was validated using comprehensive test instances from established research. The PGA solution exhibited a consistent average copper grade across periods, with its incremental phases reflecting real-world mine geometry. Moreover, the benefits of the MeanShift clustering technique were evident, suggesting effective phase-based scheduling. The PGA's approach ensures optimal resource utilization and offers insights into potential avenues for further model enhancements and fine-tuning. [ABSTRACT FROM AUTHOR]

The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper aims to contribute to this evolving landscape by undertaking a comprehensive exploration of the L 1 -norm for the penalty term of a LASSO regression in a compositional context. This implies first introducing a rigorous definition of the compositional L p -norm, as the particular geometric structure of the compositional sample space needs to be taken into account. The focus is subsequently extended to a meticulous data-driven analysis of the dimension reduction effects on linear models, providing valuable insights into the interplay between penalty term norms and model performance. An analysis of a microbial dataset illustrates the proposed approach. [ABSTRACT FROM AUTHOR]

The Hilbert scheme Hilb n ℂ 3 of n points on ℂ 3 can be expressed as the critical locus of a regular function on a smooth variety . Recent development in birational geometry suggests a study of singularities of the pair (, Hilb n ℂ 3) using jet schemes. In this paper, we use a comparison between Hilb n ℂ 3 and the scheme C 3 , n of three commuting n × n matrices to estimate the log canonical threshold of (, Hilb n ℂ 3). As a consequence, we see that although both dim and dim Hilb n ℂ 3 have asymptotic growth O (n 2) , the largest multiplicity of any points on Hilb n ℂ 3 has at most linear growth O (n). [ABSTRACT FROM AUTHOR]

This paper deals with a weaker form of the property so called L o , o for operators, which we call the property weak L o , o for operators. We characterize this property in terms of convergence of approximate norm attainment sets and prove that a pair of Banach spaces (X, Y) satisfies the property weak L o , o for compact operators if and only if X is reflexive. We further investigate the property weak L o , o for bilinear maps and obtain a connection of it with the property weak L o , o for operators. Importantly, we also characterize some geometric properties of Banach spaces with the help of convergence of approximate norm attainment sets. [ABSTRACT FROM AUTHOR]

Landsat 9 (L9) was launched on 27 September 2021. This spacecraft contained two instruments, the Operational Land Imager-2 (OLI-2) and Thermal Infrared Sensor-2 (TIRS-2), that allow for a continuation of the Landsat program and the mission to acquire multi-spectral observations of the globe on a moderate scale. Following a period of commissioning, during which time the spacecraft and instruments were initialized and set up for operations, with the initial calibration performed, the mission moved to an operational mode This operational mode involved the same cadence and methods that were performed for the Landsat 8 (L8) spacecraft and the two instruments onboard, the Operational Land Imager-1 (OLI-1) and Thermal Infrared Sensor-1 (TIRS-1), with respect to calibration, characterization, and validation. This paper discusses the geometric operational aspects of the L9 instruments during the first year of the mission and post-commissioning, and compares these same geometric activities performed for L8 during the same time frame. During this time, optical axes of the two sensors, OLI-1 and OLI-2, were adjusted to stay aligned with the spacecraft's Attitude Control System (ACS), and the TIRS-1 and TIRS-2 instruments were adjusted to stay aligned with the OLI-1 and OLI-2 instruments, respectively. In this paper, the L9 operational adjustments are compared to the same operational aspects of L8 during this same time frame. The comparisons shown in this paper will demonstrate that both instruments aboard L8 and L9 performed very similar geometric qualities while fully meeting the expected requirements. This paper describes the geometric differences between the L9 imagery that was made available to the public prior to the reprocessing campaign that was performed using the new calibration updates to the sensor and to ACS and TIRS-to-OLI alignment parameters. This reprocessing campaign of L9 products involved data acquired from the launch of the spacecraft up to early 2023. [ABSTRACT FROM AUTHOR]

Sébastien Le Clerc was born into a family of goldsmiths in Lorraine, and received classical artisanal training. Yet over the course of a highly successful career as an engraver, he also became a widely published scientific author. This paper argues that geometrical skills played a key role in the dual development of Le Clerc's career, and in his striving for recognition as a man of letters, as well as an engraver. By a detailed study of the geometrical skills displayed in Le Clerc's two geometrical publications, this paper revisits the thorny question of the relations between scholars and artisans in the early modern period. Rather than a dependence on his hands-on, bodily experience, it was Le Clerc's skill in geometry that lent support to his aspiring scholarly career. [ABSTRACT FROM AUTHOR]

Descriptive geometry has indispensable applications in many engineering activities. A summary of these is provided in the first chapter of this paper, preceded by a brief introduction into the methods of representation and mathematical recognition related to our research area, such as projection perpendicular to a single plane, projection images created by perpendicular projection onto two mutually perpendicular image planes, but placed on one plane, including the research of curves and movements, visual representation and perception relying on a mathematical approach, and studies on toothed driving pairs and tool geometry in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, for which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Our aim was to examine the spatial variation in the wear of the tool edge and the machining of the components of toothed drive pairs using two cameras. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the searching for the right projection direction, and positioning cameras appropriately. A special method of enumerating the possible infinite viewpoints for the reconstruction of tool surface edge curves is presented in the second part of this paper. In the case of the monitoring the shape geometry, taking into account the interchangeability of the projection directions, i.e., the property of symmetry, all images made from two perpendicular directions were taken into account. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. A new criterion was formulated for the tested tooth edge of the hob to take into account the shading of the tooth next to it. The analysis and some of the results of the Monge mapping, suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, namely defining the conditions for camera placements that ensure reconstructibility are also presented. Taking physical shadowing into account, conclusions can be drawn about the degree of distortion of the machined surface from the spatial deformation of the edge curve of the tool reconstructed with correctly positioned cameras. [ABSTRACT FROM AUTHOR]

We analyze the well-posedness of certain field-only boundary integral equations (BIEs) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the scattered electric field E\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{t}(x) and (2) scalar quantity E\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{t}(x)\cdot x are radiative solutions of the Helmholtz equation, we see that novel boundary integral equation formulations of electromagnetic scattering from perfectly conducting obstacles can be derived using Green's identities applied to the aforementioned quantities and the boundary conditions on the surface of the scatterer. The unknowns of these formulations are the normal derivatives of the three components of the scattered electric field and the normal component of the scattered electric field on the surface of the scatterer, and thus these formulations are referred to as field-only BIEs. In this paper we use the combined field methodology of Burton and Miller within the fieldonly BIE approach, and we derive new boundary integral formulations that feature only Helmholtz boundary integral operators, which we subsequently show to be well posed for all positive frequencies in the case of spherical scatterers. Relying on the spectral properties of Helmholtz boundary integral operators in spherical geometries, we show that the combined field-only boundary integral operators are diagonalizable in the case of spherical geometries and their eigenvalues are nonzero for all frequencies. Furthermore, we show that for spherical geometries one of the field-only integral formulations considered in this paper exhibits eigenvalues clustering at one--a property similar to second-kind integral equations. [ABSTRACT FROM AUTHOR]

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term 'bitstring semantics'!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. [ABSTRACT FROM AUTHOR]

This paper is devoted to the geometry of symmetric Killing tensors and Codazzi tensors of ranks p ≥ 2 and includes, in addition to the new results obtained in this paper, a survey on this topic from earlier works. [ABSTRACT FROM AUTHOR]

In this paper, we examine the differential-geometric aspect of constant-rank mappings of smooth manifolds based on the concept of a graph as a smooth submanifold in the space of the direct product of the original manifolds. The nonmaximality of the rank provides the fibered nature of the graph. A Riemannian structure on manifolds enriches the geometry of the graph, which now essentially depends on the induced field of the metric tensor; we characterize relatively affine, projective, and g-umbilical mappings. The final part of the paper is devoted to mappings of Euclidean spaces of the types described earlier in terms of V. T. Bazylev's constructive graph. [ABSTRACT FROM AUTHOR]

In this paper we study coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of coisotropic reduction is motivated by the fact that these dynamics can always be interpreted as Lagrangian or Legendrian submanifolds. Furthermore, Lagrangian or Legendrian submanifolds can be reduced by a coisotropic one. [ABSTRACT FROM AUTHOR]

Faithfully flat descent of pseudo-coherent complexes in rigid geometry was proved by Mathew. In this paper, we generalize the result of Mathew to solid quasi-coherent complexes on rigid analytic varieties, which have been introduced by Clausen and Scholze by means of condensed mathematics. [ABSTRACT FROM AUTHOR]