Area Of Rectangle Research Articles

Optimal Packing of High-Precision Rectangles

The rectangle-packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our new benchmark includes rectangles of successively higher precision, a problem for the previous state-of-the-art, which enumerates all locations for placing rectangles. We instead limit these locations and bounding box dimensions to the set of subset sums of the rectangles' dimensions, allowing us to test 4,500 times fewer bounding boxes and solve N=9 over two orders of magnitude faster. Finally, on the open problem of the feasibility of packing a specific infinite series of rectangles into the unit square, we pack the first 50,000 such rectangles and conjecture that the entire infinite series can fit.

High-throughput phenotyping to dissect genotypic differences in safflower for drought tolerance.

Drought is one of the most severe and unpredictable abiotic stresses, occurring at any growth stage and affecting crop yields worldwide. Therefore, it is essential to develop drought tolerant varieties to ensure sustainable crop production in an ever-changing climate. High-throughput digital phenotyping technologies in tandem with robust screening methods enable precise and faster selection of genotypes for breeding. To investigate the use of digital imaging to reliably phenotype for drought tolerance, a genetically diverse safflower population was screened under different drought stresses at Agriculture Victoria’s high-throughput, automated phenotyping platform, Plant Phenomics Victoria, Horsham. In the first experiment, four treatments, control (90% field capacity; FC), 40% FC at initial branching, 40% FC at flowering and 50% FC at initial branching and flowering, were applied to assess the performance of four safflower genotypes. Based on these results, drought stress using 50% FC at initial branching and flowering stages was chosen to further screen 200 diverse safflower genotypes. Measured plant traits and dry biomass showed high correlations with derived digital traits including estimated shoot biomass, convex hull area, caliper length and minimum area rectangle, indicating the viability of using digital traits as proxy measures for plant growth. Estimated shoot biomass showed close association having moderately high correlation with drought indices yield index, stress tolerance index, geometric mean productivity, and mean productivity. Diverse genotypes were classified into four clusters of drought tolerance based on their performance (seed yield and digitally estimated shoot biomass) under stress. Overall, results show that rapid and precise image-based, high-throughput phenotyping in controlled environments can be used to effectively differentiate response to drought stress in a large numbers of safflower genotypes.

A Multi-functional NO2 gas monitor and Self-Alarm based on Laser-Induced graphene

The increasingly serious air pollution problem makes the development of high-performance gas monitoring system extremely urgent. Especially for nitrogen dioxide (NO2), which is harmful to both people and the environment. The combination of reliable real-time monitoring and early warning is of great significance yet less study. Here, we designed a laser-induced graphene (LIG)-based multi-functional NO2 monitor and self-alarm (MMSA), in which a rectangle area is used as a dual-functional module to realize high-performance temperature condition and acoustic alarm by applying direct/alternating current voltage excitation source. The molybdenum disulfide (MoS2) sensitive material works in concert with the LIG interdigital electrodes (IDEs), and the gas monitor achieves high sensitivity (86.81% for 5 ppm, and 22.90% for 250 ppb) and excellent recoverability, aided by the good electrothermal property of LIG, overcoming the dilemma of poor sensing performance of MoS2 at room temperature (RT). To top it off, the thermoacoustic effect of the LIG could bring about an intuitional sound signal, and a proof-of-concept demonstrates the timely acoustic warning response of the MMSA to exceeded NO2 concentrations.

Optimization of regular octagon-shaped parking space

The perfect parking lot will avoid confusion in parking vehicles. Parking lot problems deal with a lot of real-life challenges like the shape of the parking lot, angle of parking, the dimension of vehicles and available area. Parking space should allow the maximum number of vehicles to be parked. A mathematical model can be created to maximize the number of vehicles to be parked. Also, the mathematical model should subject to challenging constraints. In this paper, the mathematical model of the parking lot in the regular octagon-shaped parking area using the concept area of rectangle and the right triangle is developed. To illustrate the mathematical model, the regular octagon-shaped parking area is taken and also LINGO software is used to solve the problem.

Stability of trusses by graphic statics.

This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell–Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the ‘product forces’ that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses.

A method for tire wet grip performance evaluation based on grounding characteristics

The wet grip performance of tire is one of the important performances affecting vehicle safety. The steering, acceleration, and braking of the vehicle are directly affected by the grounding characteristics between the radial tire and the ground. In order to study the influence of grounding characteristics of the tire on wet grip performance, ten 205/55R16 tires produced by different manufacturers were selected and tested. The grounding characteristics of the tires were tested using an optical test rig for tire grounding pressure distribution, considering inflation pressure distribution, load and wheel alignment. The tire-road contact area was subdivided into five parts, and 69 parameters were used to describe the grounding characteristics. A software was proposed to process the test results automatically, and 69 grounding characteristic parameters of each tire were obtained. Correlation analysis on tire wet grip performance and grounding characteristics was used for selecting the principal parameters. Finally, eight grounding characteristic parameters related to tire wet grip performance was obtained. Among them are five grounding characteristic parameters (central area rectangle ratio, central area width, internal shoulder length-to-width ratio, external and internal shoulder contact area ratio, external and internal shoulder impression area ratio) which have high correlation to tire wet grip performance, and three grounding characteristic parameters (external shoulder width, external shoulder length-to-width ratio, external and internal shoulder width ratio) which have low correlation to the wet grip performance of the tire. The principal component analysis method was used to analyze the highly correlated grounding characteristic parameters, and the regression equation for evaluating tire wet grip performance was fitted. The comparison of experimental and fitted values show that the errors are within 4%. The result demonstrates that, the method for evaluating wet grip performance of the radial tire through tire-road grounding characteristics was achieved.

Effects of Attentional Focus on the Corticospinal Excitability during Anticipatory Postural Adjustments in Dart Throwing

Attentional focus can affect motor performance and learning. It is known that external focus (EF) which concentrated on the movement outcome leads better performance and efficient motor output rather than internal focus (IF) which concentrated on one's body movement. It remains unclear whether the attentional focus modulates the corticospinal excitability during anticipatory postural adjustments (APA). In the present study, we using transcranial magnetic stimulation (TMS) examined the excitability changes in the primary motor cortex (M1) during dart throwing with different attentional focuses. We hypothesized that the APA duration and magnitude is different between EF and IF conditions, and the corticospinal excitability of lower leg muscle increases in the phase of APA, while the extent to which modulation is different between conditions. Fifteen healthy volunteers were asked to perform dart throwing with the dominant hand with a visual cue under the EF condition (focus on the flight trajectory of the dart) and IF condition (focus on the elbow angle of the dominant hand). The participants performing the tasks stood on a force plate with the legs closed, and we measured the displacement of center of pressure (COP). Electromyography (EMG) was recorded from the anterior deltoid, triceps brachii (TB), tibialis anterior (TA), and soleus muscles. Because the EMG of TA muscle was clearly observed from about 300 ms before the EMG onset of TB muscle (agonist muscle of throwing), TMS was applied over the hotspot of TA muscle in the contralateral M1 at the timings of the visual cue, 0 to 100 ms prior to the EMG onset of TA muscle, and the EMG onset of TB muscle. The distance from the bulls-eye was significantly shorter with EF than that with IF. Neither the difference in the total length of COP and rectangle area nor in the APA duration and magnitude was observed between EF and IF conditions. The motor evoked potential (MEP) amplitude in the TA muscle at -100ms, -50 ms, TA onset, and TB onset significantly increased in comparison with that at control in both conditions. In particular, MEP at -50 ms, TA onset, and TB onset were significantly larger with EF than those with IF, whereas there were no significant differences in MEP at visual cue and -100 ms between EF and IF conditions. Our results demonstrate that the excitability of corticospinal projections to the lower leg muscle increases immediately prior to a ballistic movement of the upper limb. It suggests that, by changing the attentional focus the cortical contribution to the postural control is modulated which may improve motor performance and efficacy of the movement execution.

Optimization Shortest One-Way Path for Energy Saving Auto Robot Collecting Floating Garbage using Fast Approximate Nearest Neighbor Search

Floating garbage is a global problem that needs to be cleared and disposed of from the sea and rivers or canals. Mostly the floating plastic garbage directly affects the ecology and the aquatic animals. This paper proposes to develop a low-cost auto robot from waste materials in the household, school, or agriculture, then combines with the Internet of Things technology and focusing on the power energy saving with the highest accuracy in operation of floating garbage collection. ESP32 development kit board is the primary controller with a camera module and ultrasonic sensor for detecting the floating garbage while moving on the water’s surface in the boundary of the specified area, including the small canal, rectangle area, and no rectangle area. The mixed mode is a new method to define the shortest one-way path using a fast approximate nearest neighbor search for the auto robot to detect and collect the floating garbage on the water surface. It was combined between the stationary and the cover model. The mixed mode can eliminate the blind spot area that occurs when using the stationary mode and cover mode. As a result, the auto robot system’s accuracy in mixed mode is 98.3%. It was found that the development of the shortest one-way path for the auto robot collecting floating garbage by mixed mode provides the highest efficiency in detecting floating garbage and also helps to save overall costs, and the resource consumption is nearly half of cover mode consumption.

Decompositions of a rectangle into non-congruent rectangles of equal area

In this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into k non-congruent rectangles of equal area? This problem is motivated by the so-called ‘Mondrian art problem’ that asks a similar question for dissections with rectangles of integer sides. Here, we generalize the Mondrian problem by allowing rectangles of real sides. In this case, we show that the minimum value of k for a rectangle to have a ‘perfect Mondrian partition’ (that is, with non-congruent equal-area rectangles) is seven. Moreover, we prove that such a partition is unique (up to symmetries) and that there exist exactly two proper perfect Mondrian partitions for k=8. Finally, we also prove that any square has a perfect Mondrian decomposition for k≥7.

MODEL PEMBELAJARAN DISCOVERY LEARNING PADA MATERI LUAS DAN KELILING BANGUN DATAR KELAS IV SEKOLAH DASAR

The implementation of the 2013 curriculum (K-13) has a consequence that teachers must be more qualified in carrying out learning activities. Because K-13 mandates the application of a scientific approach (5M) which includes observing, asking, gathering information, reasoning / associating, and communicating. Mathematic Teachers North Bintan Elementary School often did not give opportunity for students to get the opportunity to think creatively, critically,collaboratively and communicatively. This happens because the learning model carried out by the teacher has not implemented a learning model that can optimally accommodate students' interests and potential. Researchers have taught as classroom teachers since 2012. In the 2018/2019 academic year, researchers taught fourth grade. As a class teacher, the writer teaches all subjects, including PPKN, Indonesian, Mathematics, Science, Social Studies, andSBdP. Of the six subjects, the lowest average score for daily tests was mathematics. Basic mathematics competencies are in semester II include KD 3.9, namely; Explaining and determining the perimeter and area of squares, rectangles, and triangles as well as the square relationship with the square root is the KD with the lowest score for the daily test scores of grade IV a SD Negeri 003 Bintan Utara. Class IV mathematics learning process at SD Negeri003 North Bintan often did not make students get the opportunity to think creatively, critically, collaboratively and communicatively, this happened because the learning model carried out by the teacher has not implemented a learning model that could optimally accommodate students' interests and potential. The impact was that many students could not achieve the minimum mastery level at 72. The purpose of writing this paper was to describe mathematics learning atSD Negeri 003 North Bintan, and to describe the Learning Implementation Plan with the Discovery Learning learning model, and to describe the Discovery Learning scenario. The basis for this paper was the low level of understanding of students in doing math problems.

TEKNIK POLYA DALAM PENYELESAIAN MASALAH GEOMETRI

This study aims to analyze the steps for solving mathematical problems by students' understanding of the geometric material in story problems based on the Polya technique. This research was conducted in one of the Islamic elementary schools in Batu City on six students in grade 6. The approach taken is to use a descriptive qualitative approach. The research was carried out using triangulation methods, namely observing the problem-solving process, interviews, and reviewing documents (students' work). Interviews in this study were conducted with several students, namely two high ability people, two low ability people, and two medium ability people. The analysis was carried out by concluding the data obtained based on the observations that have been made. The study results showed that the Polya technique showed different results on the results of solving the problems of each category of students in solving story problems about the area of squares and rectangles. Based on these results, it can be seen that students' understanding of the geometry material on the story problem.

Studies of terahertz discharge in noble gases using a Michelson interferometer

The measurements of the spatial-time evolution of the discharge in argon and krypton at a wide range of pressures were performed. The gyrotron was used for plasma ignition. The radiation was 40 kW with frequency 0.67 THz. The pulse duration was 20 μs. A Michelson interferometer has been exploited for investigation of the discharge in the noble gases in a focused beam of terahertz waves. The diameter of the laser beam near the plasma cloud was 25 mm at 1/e 2 level, λ = 532 nm. The rectangle area (about 20 × 15 mm) near the focus of THz beam was examined synchronously by the interferometer and a CCD camera. The spatial-time evolution of laser beam phase-shift of THz discharge in Kr and Ar from atmospheric pressure down to a few torrs was obtained. The intensity of the discharge glow in optical range correlates with the phase shift map. Previous measurements of plasma density made in Ar under a background gas pressure at a level of a few torrs, based on the Stark effect, are in good agreement with the gained results.

E-Modul dengan Pendekatan Saintifik Menggunakan Flip PDF Profesional pada Materi Persegi dan Persegi Panjang

This research is motivated by the development of technology as a learning medium that must be applied in schools to facilitate the teaching and learning process during the Covid 19 period. Using e-modules will make it easier for students to learn from home. The research objective is to produce an E-module with a scientific approach using Flip PDF Professional on square and rectangular material. E-module is expected to develop students' higher-order thinking. E-modules can be used with or without the active role of a teacher who provides material explanations. E-module rectangles and squares aim so that students can understand the concept of the properties, perimeter, and area of ​​rectangles and squares and use them in solving problems that occur in everyday life and it is hoped that by using this e-module students quickly understand the material rectangles and squares, and can do lessons without depending on the explanation from the teacher.

Speed and Direction Aware Skyline Query for Moving Objects

The skyline query is one of the most important supporting technologies for the location-based query services in the road network. Usually, when a user queries the skyline points in the road network, the query area is a user-centered circle or rectangle area, without considering the impact of the current movement speed and direction of the user on the formation of the query area. In this context, a speed and direction aware skyline query method is proposed, which can provide the skyline query area for the users by considering their moving speed and direction. Since the efficiency to directly obtain points of interest from speed and direction aware query area is not high, a Voronoi based speed and direction query area generation algorithm is proposed to approximate the query area, so as to improve the obtaining efficiency of points of interest in the area. The experiments on road networks and points of interest data of Beijing show the performance of the proposed method in terms of query efficiency and quality.

Detection and Analysis of Photovoltaic Panels Based on UAV and HSV Space

To address the difficulty of image analysis in a complex environment,an image segmentation and detection method of an HSV spatial model was studied.First,a UAV was used to collect images.Second,Gaussian convolution was used to detect the gradient of the cracked image after the photovoltaic(PV)panel area was extracted.Finally,morphological image processing and the HSV spatial model were applied to extract the occlusion,and the ratio of the minimum external rectangle area to the PV panel area was calculated.This method can effectively segment and detect PV images in complex backgrounds and provides certain innovative and practical value.

Automatic Quantification of Cardiomyocyte Dimensions and Connexin 43 Lateralization in Fluorescence Images

Cardiomyocytes’ geometry and connexin 43 (CX43) amount and distribution are structural features that play a pivotal role in electrical conduction. Their quantitative assessment is of high interest in the study of arrhythmias, but it is usually hampered by the lack of automatic tools. In this work, we propose a software algorithm (Myocyte Automatic Retrieval and Tissue Analyzer, MARTA) to automatically detect myocytes from fluorescent microscopy images of cardiac tissue, measure their morphological features and evaluate the expression of CX43 and its degree of lateralization. The proposed software is based on the generation of cell masks, contouring of individual cells, enclosing of cells in minimum area rectangles and splitting of these rectangles into end-to-end and middle compartments to estimate CX43 lateral-to-total ratio. Application to human ventricular tissue images shows that mean differences between automatic and manual methods in terms of cardiomyocyte length and width are below 4 m. The percentage of lateral CX43 also agrees between automatic and manual evaluation, with the interquartile range approximately covering from 3% to 30% in both cases. MARTA is not limited by fiber orientation and has an optimized speed by using contour filtering, which makes it run hundreds of times faster than a trained expert. Developed for CX43 studies in the left ventricle, MARTA is a flexible tool applicable to morphometric and lateralization studies of other markers in any heart chamber or even skeletal muscle. This open-access software is available online.

Smallest k-Enclosing Rectangle Revisited

Given a set of n points in the plane, and a parameter $$k$$ , we consider the problem of computing the minimum (perimeter or area) axis-aligned rectangle enclosing $$k$$ points. We present the first near quadratic time algorithm for this problem, improving over the previous near- $$O(n^{5/2})$$ -time algorithm by Kaplan et al. (25th European Symposium on Algorithms. Leibniz Int Proc Inform, vol. 87, # 52. Leibniz-Zent Inform, Wadern, 2017). We provide an almost matching conditional lower bound, under the assumption that $$(\min ,+)$$ -convolution cannot be solved in truly subquadratic time. Furthermore, we present a new reduction (for both perimeter and area) that can make the time bound sensitive to $$k$$ , giving near $$O(nk)$$ time. We also present a near linear time $$(1+\varepsilon )$$ -approximation algorithm to the minimum area of the optimal rectangle containing $$k$$ points. In addition, we study related problems including the 3-sided, arbitrarily oriented, weighted, and subset sum versions of the problem.

Decentralized Underwater Target Detection and Localization

This article considers the detection and localization of an underwater target by a sensor network consisting of an active acoustic source, multiple distributed passive sensors, and a fusion center (FC). As the reflected signal from the target could arrive with various directions, a set of collaborative sensors increase the detection probability. We first introduce the centralized generalized likelihood ratio test (GLRT) detector that utilizes the perfect information from sensor observations. In the case of a successful detection, this detector also provides the maximum likelihood estimate (MLE) of the target location. In order to meet the stringent power and bandwidth constraints in underwater sensor networks, we then propose the decentralized GLRT scheme, where sensor observations are quantized into a few bits of data and then transmitted to the FC. The quantization thresholds are optimized by maximizing the Kullback-Leibler divergence between the null and alternative hypotheses. While the existing scan statistic based detector assumes that the sensor array which can observe the reflected signal, is contained in a rectangle area, our proposed decentralized GLRT scheme incorporates the signal reflection model into the detector, and estimates the area of affected sensor array, thus achieving higher accuracy. Finally, we extend the decentralized GLRT detector to the scenario where data are transmitted over error-prone channels, which is not considered in the existing studies. Numerical results demonstrate that the decentralized GLRT detector with only a small number of quantization bits can achieve a similar detection performance as the centralized GLRT.

Do Slit-Lamp Shields and Face Masks Protect Ophthalmologists amidst COVID-19?

Do Slit-Lamp Shields and Face Masks Protect Ophthalmologists amidst COVID-19?

Peningkatan Kemampuan Pemecahan Masalah Matematis Siswa Melalui Penerapan Pembelajaran Inkuiri Berbantuan Puzzle

This research aims to describe the improvement (1) mathematics problem solving abilities, (2) improve student learning activity, and (3) teacher teaching skill in implementing inquiry learning model assisted by segita puzzle under material perimeter and area of square, rectangle, and triangle. The methods of collecting data were test, observation, interview, and documentation. The data analysis of the research was quantitative and qualitative analysis. The findings showed improvement of the problem solving abilities average. In cycle I, it was 68, with percentage 71%, categorized well. It improved into 85 in cycle II with percentage 86%, categorized well. Student learning activity average in cycle I it was 80 with predicate sufficient. It improved into 88 with predicate well in cycle II. Teacher teaching skill in cycle I was 95, or 74%, categorized sufficient. In cycle II, it improved into 117.65, or 87%, categorized well. It is concluded that the implementation of inquiry model assisted by segita puzzle could improve mathematics problem solving abilities, student learning activity, and teacher teaching skill.