Flat Objects Research Articles

Flat comodules and contramodules as directed colimits, and cotorsion periodicity

This paper is a follow-up to Positselski and Št’ovíček (Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity. Electronic preprint arXiv:2212.09639 [math.AG]). We consider two algebraic settings of comodules over a coring and contramodules over a topological ring with a countable base of two-sided ideals. These correspond to two (noncommutative) algebraic geometry settings of certain kind of stacks and ind-affine ind-schemes. In the context of a coring C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document} over a noncommutative ring A, we show that all A-flat C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document}-comodules are ℵ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\aleph _1$$\\end{document}-directed colimits of A-countably presentable A-flat C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document}-comodules. In the context of a complete, separated topological ring R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathfrak {R}}$$\\end{document} with a countable base of neighborhoods of zero consisting of two-sided ideals, we prove that all flat R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathfrak {R}}$$\\end{document}-contramodules are ℵ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\aleph _1$$\\end{document}-directed colimits of countably presentable flat R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathfrak {R}}$$\\end{document}-contramodules. We also describe arbitrary complexes, short exact sequences, and pure acyclic complexes of A-flat C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document}-comodules and flat R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathfrak {R}}$$\\end{document}-contramodules as ℵ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\aleph _1$$\\end{document}-directed colimits of similar complexes of countably presentable objects. The arguments are based on a very general category-theoretic technique going back to an unpublished 1977 preprint of Ulmer and rediscovered in Positselski (Notes on limits of accessible categories. Electronic preprint arXiv:2310.16773 [math.CT]). Applications to cotorsion periodicity and coderived categories of flat objects in the respective settings are discussed. In particular, in any acyclic complex of cotorsion R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathfrak {R}}$$\\end{document}-contramodules, all the contramodules of cocycles are cotorsion.

Spatial Thinking and Movements in Geometry: GeoGebra with a focus on building animated scenarios

Animated Scenarios are constructions created in GeoGebra with mathematical elements and movement, constituting an animated scene. Movement is fundamental to the construction of Animated Sceneries, it is also essential to spatial thinking and spatial abilities. This theoretical essay aims to discuss the potential of building Animated Scenarios in GeoGebra in/for the recognition of flat and spatial geometric objects, articulated with the movements associated with spatial thinking. For this, the House Animated Scenario are considered. Thus, we identified that movements performed during this construction allow rotating and modifying the shape of objects and that these movements are related to spatial abilities. Furthermore, the use of these movements in construction contributes to the recognition of important characteristics that distinguish flat and spatial objects.

Blind and robust estimation of adaptive optics point spread function and diffuse halo with sharp-edged objects

Context. Initially designed to detect and characterise exoplanets, extreme adaptive optics (AO) systems open a new window onto the Solar System by resolving its small bodies. Nonetheless, their study remains limited by the accuracy of the knowledge of the AO-corrected point spread function (AO-PSF) that degrades their image and produces a bright halo, potentially hiding faint moons in their close vicinity. Aims. To overcome the random nature of AO-PSFs, I aim to develop a method that blindly recovers the PSF and its faint structured extensions directly into the data of interest, without any prior on the instrument or the object’s shape. The objectives are both to deconvolve the object and to properly estimate and remove its surrounding halo to highlight potential faint companions. Methods. My method first estimated the PSF core via a parametric model fit, under the assumption of a sharp-edged flat object. Then, the resolved object and the PSF extensions were alternatively deconvolved with a robust method, insensitive to model outliers, such as cosmic rays or unresolved moons. Finally, the complex halo produced by the AO system was modelled and removed from the data. Results. The method is validated on realistic simulations with an on-sky AO-PSF from the SPHERE/ZIMPOL instrument. On real data, the proposed blind deconvolution algorithm strongly improves the image sharpness and retrieves details on the surface of asteroids. In addition, their moons are visible in all tested epochs despite important variability in turbulence conditions. Conclusions. My method shows the feasibility of retrieving the complex features of AO-PSFs directly from the data of interest. It paves the way towards more precise studies of asteroid surfaces and the discovery and characterisation of Solar System moons in archival data or with future instruments on extremely large telescopes with ever more complex AO-PSFs.

Design of a soft gripper with negative-pressure actuated synthetic annulus microwedge adhesive

The automation and assembly lines of factories have faced the need for reliable handling of porous, fragile, and soft objects. Current soft grippers have difficulty robustly grasping flat, flexible surfaces without distorting them. This paper proposes a soft gripper based on annulus microwedge adhesive for grasping flat objects using negative pressure actuation mechanisms, which can achieve controllable adhesives to reliably grasp and easily release smooth flat objects. This is achieved through negative pressure actuation, which provides a centripetal load to the annular microwedge adhesives for strong attachment, by returning to normal pressure, the centripetal load is rapidly removed, allowing for easy detachment from the adhesive surface. Additionally, the relationship between the geometrical parameters of the deformation chamber and the contact area of annulus microwedges is investigated by using finite-element method models and experiments. The results show that the wall thickness is a key parameter in designing the deformation chamber. The results of the payload test have determined the geometrical and pressure parameters of the deformation chamber with the best adhesion performance. Finally, a demonstration shows that the gripper can handle various objects for potential applications, such as in clean environmental industries.

Resolution Enhancement by Variable Zoom Trajectory in X-Ray Computed Tomography

Flat objects like electronic boards are challenging samples for high-resolution X-ray computed tomography scanning because their largest dimension significantly limits the magnification using circular trajectory scans. One way to improve spatial resolution for such samples is to utilize variable zoom trajectory. During variable zoom trajectory scanning, the source-to-object distance changes during the 360° rotation to maximize the magnification in the projections. Here, we propose an automatic variable zoom trajectory generation algorithm for arbitrary object and region of interest (ROI). We analyze how such a trajectory can enhance resolution in different cases and how isotropic is the resolution in the reconstructed volume. We demonstrate that the resolution can be improved without destroying the sample. However, the improvement is manifested mainly in directions in which we achieved the highest magnification in the projection.

A particle jamming soft gripper integration of annular microwedge adhesion

A key challenge in robotics is developing efficient methods for grasping objects of different shapes, sizes, poses, and properties. In this study, we propose a positive pressure actuation gripper that combination of annular microwedge adhesion and particle jamming. The gripper comprises an elastic membrane enclosing a mass of granular material, allowing for control of the backing stiffness during contact. In the inflated state, the elastic membrane is stretched, generating centripetal loading force for annular microwedge adhesion. By transitioning into a negative pressure jammed state, a rigid backing stiffness is achieved to maintain adhesion stability, later reverting to atmospheric pressure enables the gripper to release the object. Consequently, this gripper through annular microwedge adhesion offers controllable adhesion for grip and release a wide range of objects that are typically challenging for current soft grippers, such as flat objects, soft objects, or objects with complex geometries. We fabricate the positive pressure actuation gripper and clarify its working mechanism for both flat and curved surfaces. Furthermore, a theoretical analysis is carried out to calculate the frictional stress of the elastic membrane when it is in contact with an object. Experimental results on contact area demonstrate the feasibility of positive pressure actuation mechanism for annulus microwedge adhesion. The payload test determines the parameters of the elastic membrane with the best adhesion performance. The final demonstration shows the applicability of this soft gripper in various scenarios.

Changing Look of the Optical Spectrum of the MeV Blazar PKS 0446+112 (4FGL J0449.1+1121)

Following the high activity of the γ-ray Fermi source 4FGL J0449.1+1121 (PKS 0446+112), possibly associated with a IceCube neutrino event IC-240105A, we obtained optical spectroscopy with the Gran Telescopio Canarias of the counterpart. We detect a clear emission line at 3830 Å identified as Lyα that confirms the redshift of source at z = 2.153. Comparing with previous spectroscopy, we find an increase of the continuum by a factor ∼10, and a significant decrease of the C iv 1550 emission line flux by a factor ∼5. This produces a dramatic drop of the equivalent width from ∼20 to 0.8 Å, which is suggestive of a very high jet activity. The full width half maximum of the emission lines are midway (1000–2000 km s −1) between those typical of the broad and narrow regions of quasars. Based on this, the source classification is intermediate between flat spectrum radio quasar and BL Lac object.

Expected performance of the Pyramid wavefront sensor with a laser guide star for 40 m class telescopes

Context. The use of artificial laser guide stars (LGS) is planned for the new generation of giant segmented mirror telescopes in order to extend the sky coverage of their adaptive optics systems. The LGS, being a 3D object at a finite distance, will have a large elongation that will affect its use with the Shack–Hartmann (SH) wavefront sensor. Aims. In this paper, we compute the expected performance for a Pyramid WaveFront Sensor (PWFS) using an LGS for a 40 m telescope affected by photon noise, and also extend the analysis to a flat 2D object as reference. Methods. We developed a new way to discretize the LGS, and a new, faster method of propagating the light for any Fourier filtering wavefront sensors (FFWFS) when using extended objects. We present the use of a sensitivity model to predict the performance of a closed-loop adaptive optic system. We optimized a point-source-calibrated interaction matrix to accommodate the signal of an extended object by computing optical gains using a convolutional model. Results. We find that the sensitivity drop, given the size of the extended laser source, is large enough to make the system operate in a low-performance regime given the expected return flux of the LGS. The width of the laser beam is identified as the limiting factor, rather than the thickness of the sodium layer. Even an ideal, flat LGS will have a drop in performance due to the flux of the LGS, and small variations in the return flux will result in large variations in performance. Conclusions. We conclude that knife-edge-like wavefront sensors, such as the PWFS, are not recommended for use with LGS for a 40 m telescope, as they will operate in a low-performance regime, given the size of the extended object.

Мультиплицирование дифракционных картин от плоских геометрических фрактальных объектов с использованием метода прореживания

An algorithm is described and the features of multiplying diffraction patterns (that is, spatial frequency spectra, both calculated and experimentally obtained) from flat fractal objects using the thinning method are studied. One fractal of the L-system, described in detail and studied by the authors, was used as the main object, which greatly facilitated the interpretation of the results obtained.

Мультиплицирование дифракционных картин от плоских геометрических фрактальных объектов с использованием метода прореживания

Описан алгоритм и изучены особенности мультиплицирования дифракционных картин (то есть спектров пространственных частот, как вычисленных, так и экспериментально полученных) от плоских фрактальных объектов методом прореживания. В качестве основного объекта использовался один подробно описанный и изученный авторами фрактал L-системы, что значительно облегчало интерпретацию полученных результатов.

A PCB image segmentation model based on rotational X-ray computed laminography imaging.

The rapid development of industrialization in printed circuit board (PCB) warrants more complexity and integrity, which entails an essential procedure of PCB inspection. X-ray computed laminography (CL) enables inspection of arbitrary regions for large-sized flat objects with high resolution. PCB inspection based on CL imaging is worthy of exploration. This work aims to extract PCB circuit layer information based on CL imaging through image segmentation technique. In this work, an effective and applicable segmentation model for PCB CL images is established for the first time. The model comprises two components, with one integrating edge diffusion and l0 smoothing to filter CL images with aliasing artifacts, and the other being the fuzzy energy-based active contour model driven by local pre-fitting energy to segment the filtered images. The proposed model is able to suppress aliasing artifacts in the PCB CL images and has good performance on images of different circuit layers. Results of the simulation experiment reveal that the method is capable of accurate segmentation under ideal scanning condition. Testing of different PCBs and comparison of different segmentation methods authenticate the applicability and superiority of the model.

Formation of multibeam dynamic gradient interference light fields with refractive optical elements

This paper presents methods for the formation and properties of light fields that controllably vary in time and space, obtained as a result of the interference of three or four coherent light beams using refractive optical elements. The formation of three-beam and four-beam interference fields is carried out using trihedral and tetrahedral glass pyramids respectively. The possibility of the interference field displacement in the transverse plane is ensured by devices for controlled phase changes of at least two of the interfering beams. The directions of propagation of these beams do not lie in the same plane with the optical axis of the original beam incident on the pyramid. In threeand four-beam dynamic interference fields the peak intensity values are higher than in the original laser beams and two-beam interference fields, so it is advisable to use them for processing flat objects with laser radiation, moving the interference maxima along the surface of the object. With a pairwise azimuthal displacement of the propagation directions of four interfering beams around the longitudinal axis, a dynamic interference field is formed, the periodically structured maxima of which cyclically smoothly change their shape from cells to band and back. At different speeds of pairs of directions the interference structure of the maxima rotates around the longitudinal axis. Therefore, this field can be used for therapeutic effects on biological tissues and for mixing microparticles in suspensions and emulsions. Since the local maxima of the intensity of all these interference fields have dimensions of the order of several micrometers while exceeding in value the maximum intensity of the initial light beam, these fields in the cross section are gradient and therefore can be used not only for laser exposure, but also for moving ensembles of microparticles including for sorting and changing concentration.

Learning Sliding Policy of Flat Multi-target Objects in Clutter Scenes

In clutter scenes, one or several targets need to be obtained, which is hard for robot manipulation task. Especially, when the targets are flat objects like book, plates, due to limitation of common robot end-effectors, it will be more challenging. By employing pre-grasp operation like sliding, it becomes feasible to rearrange objects and shift the target towards table edge, enabling the robot to grasp it from a lateral perspective. In this paper, the proposed method transfers the task into a Parameterized Action Markov Decision Process to solve the problem, which is based on deep reinforcement learning. The mask images are taken as one of observations to the network for avoiding the impact of noise of original image. In order to improve data utilization, the policynetwork predicts the parameters for the sliding primitive of each object, which is weight-sharing, and then the Q-network selects the optimal execution target. Meanwhile, extra reward mechanism is adopted for improving the efficiency of task actions to cope with multiple targets. In addition, an adaptive policy scaling algorithm is proposed to improve the speed and adaptability of policy training. In both simulation and real system, our method achieves a higher task success rate and requires fewer actions to accomplish the flat multi-target sliding manipulation task within clutter scene, which verifies the effectiveness of ours.

Applications of the Information Dimension in Detecting Border Perturbations

This study utilizes the concept of information dimension based on Shannon and Tsallis' entropy to analyze the contours of flat objects. Our objective is to employ the information dimension for detecting perturbations in borders. We create examples of squares with slight border perturbations, possessing the same mass and sharing identical box-counting dimensions yet exhibiting distinct information dimensions. This construction was devised with the understanding that entropy is responsive to the image frequency within each box. Consequently, the information dimension provides a more precise index of fractal shapes when compared to the box-counting dimension.

Organization of the Operating Environment for Industrial Robots Processing Flat Objects That Have Asymmetry of Part Surfaces

Organization of the Operating Environment for Industrial Robots Processing Flat Objects That Have Asymmetry of Part Surfaces

Soft electroadhesive grippers with variable stiffness and deflection motion capabilities

Soft gripper robots provide superior safety, adaptability, and compliance compared to rigid robots. However, soft grippers must address inadequate stiffness and interference resistance. Soft pneumatic electroadhesion (EA) grippers with variable stiffness are potential options for addressing these difficulties. In this paper, we present a soft bionic gripper (SOBG) that resembles human finger movements, such as bending and deflection, employing pneumatic actuation, and whose stiffness is effectively decoupled from its position through a layer jamming-induced variable stiffness structure. By applying electroadhesive forces, the SOBG can perform complex motion tasks that would typically require a wrist joint, making them simpler to perform than with conventional flexible grippers. In addition, the SOBG can perform one-finger object manipulation to grasp flat, concave, and convex objects. To show the potential for more complex robotic applications, we evaluated each function independently by presenting a demonstration of cap-screwing, a material handling system, and an anti-interference research. The SOBG concept and solution proposed in this study may pave the way for the easy integration of EA into soft robotic systems and promote the wider use of EA technology.

Programming of one-dimansional and two-dimensional tokens for tokenization of land plots

The use of blockchain tools that allows spliting virtual objects into parts is considered. Examples of practical use of the developed algorithms are presented. The concept of one-dimensional and two-dimensional tokens representing one-dimensional and flat objects is proposed. Algorithms for the implementation of one-dimensional tokens are developed, and the peculiarities of their practical application are considered. A designed smart contract allows to conduct a basic list of operations with one-dimensional tokens. Algorithms, providing implementation of two-dimensional tokens, are proposed. Peculiarities of presenting territories of virtual worlds and land plots are suggested. A comparative analysis of the use of NFT and two-dimensional tokens for presenting the Earth surface areas is performed. Methods that ensure ownership of tokens at different levels are proposed.

Detection of movement resistance and friction coefficient in the transport of building materials and construction materials

In the production of building materials and construction materials, continuously operating conveying equipment is commonly used, including roller conveyors. Roller conveyors are devices designed for horizontal, slightly ascending or descending transport of piece products moving on a system of rotating rollers of different shapes (cylindrical, conical, disc, pulley or according to the profile of the conveyed object). The rotating rollers are placed in the track frame (supporting structure), which can be either stable, relocatable or adjustable (height and length adjustable, so-called scissor conveyors). An analogue of the roller conveyor is the pulley conveyor, where instead of rollers, discs - pulleys are mounted on a non-rotating axis. Several discs are installed on the axis with gaps. The pulleys on adjacent axes overlap so that there is no continuous gap. The track is used for handling flat building parts and objects such as metal sheets, glass panes, furniture parts, etc. When transporting item building materials or bulk building materials placed in storage boxes which are transported on a powered roller track on pallets, a driving force is required depending on the angle of inclination of the roller track, the weight of the load, the number of rollers on which the load rests and the coefficient of shear friction during movement. The paper presents a laboratory device that has been designed to detect the adhesion force during the transport of piece loads by a roller conveyor. On the implemented device, it is possible to determine in laboratory conditions the amount of resistance to the movement of the load on the driven roller conveyor depending on the weight of the load. The paper presents measured values of the shear friction coefficient during the movement of a steel storage box on a driven roller track. In this paper, a driven roller track is used for laboratory tests, where the drive of the rollers is implemented by so-called short chains. In addition to horizontal tracks, this chain drive allows you to drive rising tracks with variable gradients or even rising curved tracks.

Free-Form Liquid Crystal Elastomers via Embedded 4D Printing.

Liquid crystal elastomers (LCEs) are a class of active materials that can generate rapid, reversible mechanical actuation in response to external stimuli. Fabrication methods for LCEs have remained a topic of intense research interest in recent years. One promising approach, termed 4D printing, combines the advantages of 3D printing with responsive materials, such as LCEs, to generate smart structures that not only possess user-defined static shapes but also can change their shape over time. To date, 4D-printed LCE structures have been limited to flat objects, restricting shape complexity and associated actuation for smart structure applications. In this work, we report the development of embedded 4D printing to extrude hydrophobic LCE ink into an aqueous, thixotropic gel matrix to produce free-standing, free-form 3D architectures without sacrificing the mechanical actuation properties. The ability to 4D print complex, free-standing 3D LCE architectures opens new avenues for the design and development of functional and responsive systems, such as reconfigurable metamaterials, soft robotics, or biomedical devices.

New Dimensions in Conservation Imaging: Combining Photogrammetry and Photometric Stereo for 3D Documentation of Heritage Artefacts

With the increasing ubiquity of digital media engagement it is worth considering how heritage artefact digitisation can evolve and adapt. Twenty-first century computing developments bring low-cost three-dimensional (3D) imaging into reach, creating opportunities for cultural materials conservators to implement efficient and comprehensive new avenues in non-contact documentation and engagement. This research presents a workflow for combining efficient photometric stereo capture workflows with structure-from-motion photogrammetry for comprehensive modelling of high- and low-frequency artefact geometry and surface texture. Presenting a range of potential applications in conservation, the excellent topographic mapping of planar surfaces brings granular accuracy and unparalleled detail to condition documentation and digital reproduction of flat objects with finely textured surfaces, such as paintings or printing plates.