Rectangular Area Research Articles

Two-Stage Transportation Problem with Unknown Consumer Demands

The work investigates a mathematical model of a two-stage transportation problem for finding the most economical plan for the transportation of homogeneous products from suppliers to consumers, where the demands of consumers are unknown, taking into account constraints on their lower and upper bounds. It is an extension of the classic two-stage transportation problem, where products are transported from suppliers to consumers only through intermediate points. Intermediary firms and various storage facilities (warehouses) can be such intermediate points.The relationship of the developed mathematical model with the two-stage continuous-discrete problem of optimal partitioning-distribution, which is characterized by the presence of two stages, is investigated. The problem consists in determining the areas of collection of the continuously distributed resource (raw material) by enterprises of the first stage and the volumes of transportation of the processed product from the enterprises of the first stage to consumers (points of the second stage), in order to minimize the total costs of transportation of the resource from suppliers to consumers through processing points (collection points, storage points).The material of the article is presented in two sections. Section 1 describes the mathematical model of the two-stage transportation problem with unknown consumer demands and provides the necessary and sufficient conditions for the compatibility of the system of linear constraints. It is shown that its special case coincides with the classic two-stage transportation problem.Section 2 provides a description of the model problem of optimal partitioning-distribution for the continuous area Ω and the discrete analog of the model problem. The results of computational experiments for a rectangular area Ω = {x = (x(1), x(2)) : 0 ≤ x(1) ≤ 1, 0 ≤ x(2) ≤ 1} with discretizations by grids 31 × 31 and 500 × 500 are presented. Optimal plans for transportation of processed product from points of the first stage to points of the second stage for both grids were found. The average time spent by the Gurobi solver to solve problems for the second grid, where the number of variables equals 250018 and the number of constraints equals 250009, is a few seconds on modern PCs.

ANALISIS KEMAMPUAN BERPIKIR INTUITIF SISWA SMP DALAM PENYELESAIAN MASALAH PADA MATERI SEGI EMPAT

Intuitive thinking is very important to use in solving rectangular area problems. because by thinking intuitively students are able to generate creative inspiration impulsively. The emergence of intuitive thinking in solving rectangular area problems is the solution to getting the right answer. The purpose of this study was to find out students' intuition in solving rectangular area problems. This research is descriptive research with a qualitative approach involving 7 students as potential subjects. Two students become the main subject because the answers meet the indicators of intuitive thinking. procedures in this study: 1) determine the material; 2) make test questions; 3) giving tests to prospective subjects; 4) Analyze the answers of prospective subjects with the indicator rubric; 5) Selected as a subject; 6) Conducting interviews on the subject; 7) Analyze the results of interviews from the subject. Collecting data on students' intuitive thinking in solving rectangular area problems using written test instruments and interview tests. Data analysis in this study consists of three categories of intuitive thinking (Catalic Inference, Power of Synthesis, Common Sense). The results of this study are subjects with catalic inference intuitive thinking categories giving short answers and no logical reasons and subjects with Power of Synthesis intuitive thinking categories giving answers that are less organized while common sense intuitive thinking categories giving thorough answers using complete arguments. The categorization in this study is viewed from indicators of intuitive thinking that have been achieved by students in the process of solving questions and interview tests.

Effectiveness of Rectangular Cartogram for Conveying Quantitative Information: An Eye Tracking-Based Evaluation

A rectangular cartogram is a kind of graphical representation that uses a rectangular area to represent the attributes of geographical objects and is widely used in the representation of statistical data such as population, economic statistics, and epidemic distribution. However, there is currently little research on the effectiveness of rectangular cartograms for conveying quantitative data. In this paper, the rectangular cartogram and unclassed choropleth map are compared to evaluate the rectangular cartogram’s effectiveness in quantity representation through task-driven eye-tracking cognitive experiments. In addition, the accuracy and efficiency of information communication and the differences in the reading processes of map readers when using the two types of maps for different tasks have been analyzed to provide references for more effective use of rectangular cartograms in the future. The main contributions of this paper are: (1) it has been proven by experiments that when completing the four tasks of locate, compare, find extreme, and estimate, the participants have higher accuracy rates with the rectangular cartogram; (2) the reading process shown by the eye tracking experiment shows that the more complex the task is, the more patient the participants would be with the rectangular cartogram, and the more pronounced the advantages of the rectangular cartogram are.

Saccadic inhibition during free viewing in macaque monkeys.

Through the process of saccadic inhibition, visual events briefly suppress eye movements including microsaccades. In humans, saccadic inhibition has been shown to occur in response to the presentation of parafoveal or peripheral visual distractors during fixation and target-directed saccades and to physical changes of behaviorally relevant visual objects. In monkeys performing tasks that controlled eye movements, saccadic inhibition of microsaccades and target-directed saccades has been shown. Using eye data from three previously published studies, we investigated how saccade rate changed while monkeys were presented with visual stimuli under conditions with loose or no viewing demands. In two conditions, animals passively sat while an LED lamp flashed or screen-wide images appeared in front of them. In the third condition, images were repeated semiperiodically while animals had to maintain their gaze within a wide rectangular area and detect oddballs. Despite animals not being required to maintain fixation or make saccades to particular targets, the onset of visual events led to a temporary reduction of saccade rate across all conditions. Interestingly, saccadic inhibition was found at image offsets as well. These results show that saccadic inhibition occurs in monkeys during free viewing.NEW & NOTEWORTHY We investigated the time courses of saccade rate following visual stimuli during three conditions of free viewing in macaque monkeys. Under all conditions, saccade rate decreased transiently after the onset of visual stimuli. These results suggest that saccadic inhibition occurs during free viewing.

Effects of the Aspect Ratio and Cross-Sectional Area of Rectangular Tubes on Packing Characteristics of Mono-Sized Pebble Beds

The packing characteristics of a pebble bed are essential to understand the heat- and mass-transfer processes occurring within a granular system. Therefore, the packing characteristics of rectangular prismatic pebble beds randomly packed with mono-sized pebbles are analyzed. In terms of the average and local packing fraction distribution, coordination number, and radial distribution function, the effects of the rectangular tube aspect ratio and cross-sectional area on the packing properties of pebble beds are explored in depth. The findings indicate that the packing structures of the rectangular pebble bed exhibit noticeable fixed-wall effects. The average packing fraction and coordination number gradually decline as the rectangular tube aspect ratio rises. Close to the fixed wall, a noticeable wall effect can be seen in the distribution of axial and local packing fractions and the pebble center distribution. The wall effect has an increasing effect on the axial and local packing fraction distributions in rectangular tubes with increasing aspect ratios. Additionally, the average packing fraction and the average coordination number also increase as the cross-sectional area increases, indicating a gradual weakening of the wall effect as the cross-sectional area increases. Furthermore, the cross-sectional area and aspect ratio of the rectangular tubes affect the RDF values of the rectangular pebble beds but have no impact on the RDF features. The findings reported in this paper will be helpful for designing and optimizing pebble beds in the breeding blanket of fusion reactors.

Jan Sawka: Theatre of Image and Metaphor

Jan Sawka: Theatre of Image and Metaphor

Research on vehicle speed identification method based on time interpolation method and feature point recognition

Based on camera calibration in detection area, an improved method of time interpolation for vehicle speed identification is proposed. Firstly, calibration of camera parameters during photogrammetry is carried out through preset rectangular detection area. Secondly, the key frames are extracted from the video images and the target vehicle feature points and their image coordinates are identified by the image morphological processing. Then the actual coordinates of the characteristic points are determined through the coordinate conversion. Finally, the improved time interpolation method considering the acceleration between frames is used to identify the vehicle speed, so as to improve the accuracy of the vehicle speed measurement. The results proved that the vehicle speed calculated by improved time interpolation method is more reliable, and the error is reduced by 0.7%.

Pattern Encoding of Robust M-Array Driven by Texture Constraints

M-Array pattern encoding is widely used in structured light for 3D reconstruction due to its single projection and single imaging characteristics. The robustness of M-Array in 3D reconstruction can be assessed by the accuracy of the global positioning of the code-word and the density of the decodable feature points. This paper proposes a pattern encoding method of robust M-Array based on texture constraints. M-Arrays are formed by matching and splicing candidate sub-windows, which are composed of symbols obtained from an M-Sequence one by one. To construct an M-Array with more texture information, both the number of edges and the maximum rectangular area within the sub-window are constrained. A novel three-level backtracking mechanism reduces the time complexity. Four indicators are introduced to evaluate the robustness of the M-Array and used to compare the proposed method with existing methods. The results show that the proposed method has low similarity between adjacent sub-windows and high uniformity of symbol distribution globally, indicating better accuracy of sub-window decoding. A 3D reconstruction experiment in the actual scenes proves that the point cloud density and accuracy obtained by solving the M-Array pattern constructed by the method proposed are better.

Femtosecond-laser-patterned origami Janus membrane toward enhanced water fog harvesting.

Fog harvesting is an effective way to relieve water shortages in arid regions; thus, improving the efficiency of fog harvesting is urgently needed for both academic research and practical applications. Here, we report an origami patterned Janus (O-P-Janus) membrane using laser-ablated copper foams inspired by origami handcraft and traditional Chinese architecture. Compared to the planar fully ablated Janus membrane, our O-P-Janus membrane, with selectively ablated rectangular areas, exhibits an exceptional water collection rate (WCR) of approximately 267%. The underlying physical mechanism of WCR enhancement is revealed and attributed to the enhanced fog adsorbing capacity on the upper superhydrophobic origami structures and the accelerated removal of accumulated droplets beneath the lower superhydrophilic V-shaped tips. This O-P-Janus membrane with excellent fog collection performance should open up a new avenue for both device designs and potential applications toward structuring-enhanced fog collection and microfluidic control platforms.

Developing tongue coating status assessment using image recognition with deep learning.

To build an image recognition network to evaluate tongue coating status. Two image recognition networks were built: one for tongue detection and another for tongue coating classification. Digital tongue photographs were used to develop both networks; images from 251 (178 women, 74.7±6.6 years) and 144 older adults (83 women, 73.8±7.3 years) who volunteered to participate were used for the tongue detection network and coating classification network, respectively. The learning objective of the tongue detection network is to extract a rectangular region that includes the tongue. You-Only-Look-Once (YOLO) v2 was used as the detection network, and transfer learning was performed using ResNet-50. The accuracy was evaluated by calculating the intersection over the union. For tongue coating classification, the rectangular area including the tongue was divided into a grid of 7×7. Five experienced panelists scored the tongue coating in each area using one of five grades, and the tongue coating index (TCI) was calculated. Transfer learning for tongue coating grades was performed using ResNet-18, and the TCI was calculated. Agreement between the panelists and network for the tongue coating grades in each area and TCI was evaluated using the kappa coefficient and intraclass correlation, respectively. The tongue detection network recognized the tongue with a high intersection over union (0.885±0.081). The tongue coating classification network showed high agreement with tongue coating grades and TCI, with a kappa coefficient of 0.826 and an intraclass correlation coefficient of 0.807, respectively. Image recognition enables simple and detailed assessment of tongue coating status.

THE METHOD OF INDIRECT TWO-PART MEASUREMENTS FOR THE CONTROL OF PRODUCTION INDICATORS

A method of indirect two-part measurements of production indicators, including two independent measurements, has been developed. An elementary example of such measurements is the measurement of rectangular areas, determination of the specific gravity of the material, etc. According to the proposed method, minimization of the total random error of indirect two-part measurement can be carried out in two cases: 1) if it is known about the equality of the total error in both measurements, but the sum of systematic errors is limited from above, then it is possible to solve the problem of determining systematic errors separately, which minimizes the total random error of a two-part indirect measurement; 2) if it is known about the equality of systematic errors in both measurements, but the sum of systematic errors is limited from above, then it is possible to solve the problem of determining the total errors separately, which minimizes the total random error of an indirect two-part measurement.

Formation of a typical form of an object image in a series of digital frames

A computational method for the automated formation of a typical form of a digital image of the investigated objects on a series of digital frames has been developed. Due to the imperfection of the mounting of digital cameras, as well as their automated mounts, their immobility at shooting during exposure time can be disturbed, which leads to the formation of "blurred" images of objects of various forms. Due to such inaccuracies in the tracking of objects on digital frames, even in one series, the typical form of the image of objects can vary from frame to frame. This fact of the difference in the standard form significantly complicates the execution of various image processing tasks. In order to simplify the evaluation of the image parameters of objects in a series of digital frames, it has been proposed to use a typical image on a digital frame corresponding to the average image of objects as a model of object images. In this case, the appearance of the image of the object, its form, the distribution of brightness in the image will be determined only by the typical image. This paper proposes a computational method for the automated formation and evaluation of the typical form of the image of an object in a digital frame based on the initial data – the actual given digital frame. This computational method is based on the selection of single images of objects and the formation of their rectangular area. Next, the offset is evaluated, and the selected single images of objects are normalized to calculate the typical form of the object image. Using the method makes it possible to highlight objects against the background of noise and reduce the number of false detections. It is recommended to apply the method only in the case when the frames have defects and "blurs" during the shooting, otherwise there will be unreasonable additional computational costs. The developed computational method was successfully tested in practice within the framework of the CoLiTec project and implemented in the intraframe processing unit of the Lemur software.

Analytical and numerical study of one-dimensional and two-dimensional stress distribution within an elastic semi-infinite material under the action of an arbitrary rectangular uniform loading

Purpose. The study of stress distribution within an elastic semi-infinite material under the action of an external loading is of great importance in the theory of elasticity. In most cases, the lack of knowledge about the stress distribution within a material can result in incomplete and inappropriate engineering designs, leading to unsatisfactory consequences. The latter include cracks and fractures, created inside the concrete segmental lining in TBM tunneling, as well as indentations that occur in floors due to the lack of pillar design not only in underground mining, but even in civil projects. This study focuses on the one-dimensional and two-dimensional internal stress distribution induced by arbitrary rectangular–square loading, in other words, that applied to an elastic semi-infinite material. Methods. Firstly, this paper uses an analytical method and, subsequently, a numerical method. In the analytical study, the point load equations of Boussinesq and Westergaard are used. Extending these equations to the rectangular loading area, four new equations are introduced. Using the Abaqus finite element software, the numerical study is performed in 3D space. Findings. The results show that the answers from the introduced equations are in high consistency with numerical ones. However, the result of the extended Boussinesq point load equation is closer to the answer obtained by the numerical method. Originality. Four new equations, presented in this paper, describe one-dimensional and two-dimensional stress distribution. Practical implications. The presented equations can provide a simple and convenient way to solve rectangular load problems in many cases such as foundation, civil and mining projects. This study uses initial information on specific segments in the Tabriz Metro line-2 Project.

The dynamical problem on acting distributed load on the elastic layer

The wave field of an elastic half-layer is constructed, when a dynamic normal load distributed over a rectangular area acts on upper face at the initial moment of time. The lower face of the half-layer is rigidly fixed to the foundation, and the side border is in the conditions of a smooth contact. The method of decomposing the system of motion equations into a system of equations and an independently solvable equation is used, this approach was proposed by Popov~G.~Ya. Laplace and Fourier integral transformations are applied directly to the motion equations and boundary conditions, which reduces the problem to a vector one-dimensional boundary value problem, which is solved by the matrix differential calculus method. The output displacements are obtained using inverse integral transformations. The case of steady oscillations was considered and the amplitude of vertical displacement occurring in the layer was analyzed depending on the shape of the distributed load section, the material of the layer medium and the values of the natural frequency of the layer oscillations.

ACCURATE DETECTION OF MULTIPLE TARGETS BY UNIFORM RECTANGULAR ARRAY RADAR WITH THRESHOLD SOFT UPDATE AND AREA RESCANNING

Background. If the intensity of moving targets within a surveyed area is low, an optimal number of uniform rectangular array (URA) radar sensors is in either the minimally-sized URA (or close to it) or maximally-sized URA (or close to it), where the URA size is regulated by (symmetrically) turning off vertical and horizontal sensors. However, this does not guarantee detection of any target because sometimes the threshold detection, by which the main parameters of a pair of two targets are estimated, fails even by using the soft threshold approach when the threshold is gradually decreased while the detection fails.
 Objective. In order to improve detection of multiple ground-surface targets by a URA radar, the goal is to decrease a number of detection fails, when targets are just missed. For this, the approach of threshold soft update and a set of quasioptimal URA sizes included and URAs are to be used by rescanning the area if the detection fails.
 Methods. To achieve the goal, the functioning of the URA radar is simulated for a set of randomly generated targets, where roughly a half of the set is to be of single targets, and the other half is to be of pairs of targets. The simulation is configured and carried out by using MATLAB® R2021b Phased Array System ToolboxTM functions based on a model of the monostatic radar.
 Results. Neither the soft threshold approach, nor the rescanning increase the detection accuracy. However, when either the soft threshold or rescanning is applied, or they both are applied, the number of detections is increased. The increment can be evaluated in about 2.7 %, but the expected high-accurate detection performance slightly drops. This is caused by that the soft thresholding and rescanning attempt at retrieving at least some information about the target instead of the detection fail.
 Conclusions. Using the threshold soft update approach along with a more frequent rescanning decreases a number of detection fails. Besides, the soft thresholding and rescanning allow slightly decreasing the number of URA sensors sufficient to maintain the same detection accuracy by increasing the averaged number of single-target and two-target detections at least by 2.5 %. The increment in a number of detected targets on average is equivalent to increasing the probability of detection.

Linear Spatial Misregistration Detection and Correction Based on Spectral Unmixing for FAHI Hyperspectral Imagery.

In push-broom hyperspectral imaging systems, the sensor rotation to the optical plane leads to linear spatial misregistration (LSM) in hyperspectral images (HSIs). To compensate for hardware defects through software, this paper develops four methods to detect LSM in HSIs. Different from traditional methods for grayscale images, the method of fitting the sum of abundance (FSAM) and the method of searching for equal abundance (SEAM) are achieved by hyperspectral unmixing for a selected rectangular transition areas containing an edge, which makes good use of spatial and spectral information. The method based on line detection for band-interleaved-by-line (BIL) images (LDBM) and the method based on the Fourier transform of BIL images (FTBM) aim to characterize the slope of line structure in BIL images and get rid of the dependence on scene and wavelength. A full strategy is detailed from aspects of data selection, LSM detection, and image correction. The full spectrum airborne hyperspectral imager (FAHI) is China's new generation push-broom scanner. The HSIs obtained by FAHI are tested and analyzed. Experiments on simulation data compare the four proposed methods with traditional methods and prove that FSAM outperforms other methods in terms of accuracy and stability. In experiments on real data, the application of the full strategy on FAHI verifies its effectiveness. This work not only provides reference for other push-broom imagers with similar problems, but also helps to reduce the requirement for hardware calibration.

DiffMap: A new free computer program to process scanned electron diffraction patterns

AbstractA free computer program, called DiffMap, is presented for off-line evaluation of both phase maps and orientation maps from a large number of diffraction patterns recorded with a nearly parallel nano-beam scanned line-by-line over a rectangular area in a scanning transmission electron microscope (STEM). The program runs in the Windows operating system on IBM PC compatible computers. The patterns, which are recorded independently from this program by a CCD or CMOS camera or by a pixelated camera are in Tif format, serve as input to DiffMap. Many STEMs can collect such a four-dimensional electron diffraction (4D-ED) data sets by proper selection of microscope parameters, even if this fact is not over-emphasized in the operating manuals. These phase and orientation maps can complement usual compositional maps collected in the same STEM with energy dispersive x-ray spectrometers (EDS) to give a complete description of the crystalline phases. Application is exemplified on the (fcc, hcp and bcc) phases in a sample with 4 major components (Co, Cr, Fe, Ni).

Bifurcation and chaos analysis of mold splicing zone vibration under thermal-mechanical coupling

To improve the machining quality of the splicing area of the hardened steel mold, this paper proposes a bifurcation and chaos analysis method for the milling vibration of the splicing area of the mold under the coupled thermal-mechanical effect. First, based on the instantaneous milling force model at the splice, the milling dynamics equations of a two-degree-of-freedom rectangular spliced mold part are established. By applying the Galerkin method, the resulting nonlinear partial differential equation is reduced to a single-degree-of-freedom nonlinear system. Meanwhile, by using the Melnikov function method, the criteria for chaos motion are obtained by the Smale horseshoe mapping. Then, the fourth-order Runge-Kutta algorithm is applied to solve the bifurcation diagram, largest Lyapunov exponent diagram, displacement waveform diagram, and phase plane diagram of the nonlinear dynamic system in the mold splicing area. Subsequently, the influence of spindle speed and cutting depth on the nonlinear vibration system in the mold splice area is quantitatively analyzed. Finally, the effect of spindle speed and cutting depth on the vibration system of the workpiece is investigated through experiments. The obtained results indicate that the milling vibration amplitude in the rectangular splicing mold area can be controlled more easily and effectively by changing the cutting depth than by changing the spindle speed.

Random area pixel variation and random area transform for visible-infrared cross-modal pedestrian re-identification

In this paper, we propose the Random Area Pixel Variation (RAPV) which is a straightforward and enormously effective data enhancement method for visual-infrared cross-modal pedestrian re-identification (VI-REID) and extend this method as the Random Area Transform (RAT). The difficulty of the VI-REID task is to correlate features of heterogeneous data from both modalities. RGB images and IR images contain three channels and one channel, respectively. We add or subtract a random value to the pixel values for each channel of the two types of images, which enables them to retain the image structure information even with random color changes. Also, this allows more correspondence to be established between the two modal images. In this way, the models can find correlative features with better robustness. In addition, to control the noise generated by random variations, we apply the method only to a random rectangular area of arbitrary size in the image, which is RAPV. Simultaneously, we found that global data augmentation methods provide better results when used locally, so we make these methods applicable to a random rectangular region of arbitrary size in the image, which is RAT. Both RAPV and RAT use very few computational resources and can be flexibly integrated into existing models, outperforming many existing methods when applied only to baseline networks.

A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation

Acoustic cloaking is an important application of acoustic metamaterials. This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation. The cloaked region is partitioned into multiple narrow strips. For each strip, a local coordinate system is established with the local origin located at the strip center, and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region. To facilitate the implementation of the acoustic cloak, the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters. The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature. Firstly, the results of a circular acoustic cloak in the literature are reproduced by using our finite element (FE) simulations for validation. Then, a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak. The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method. This means that for the same object, an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect. The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area, by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area. The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level. This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions, enriching the theory of acoustic cloaking based on coordinate transformation.