Search

We study the effects of perturbing the boundary of a rectangle on the nodal sets of eigenfunctions of the Laplacian. Namely, for a rectangle of a given aspect ratio N, we identify the first Dirichlet mode to feature a crossing in its nodal set and perturb one of the sides of the rectangle by a close to flat, smooth curve. Such perturbations will often "open" the crossing in the nodal set, splitting it into two curves, and we study the separation between these curves and their regularity. The main technique used is an approximate separation of variables that allows us to restrict study to the first two Fourier modes in an eigenfunction expansion. We show how the nature of the boundary perturbation provides conditions on the orientation of the opening and estimates on its size. In particular, several features of the perturbed nodal set are asymptotically independent of the aspect ratio, which contrasts with prior works. Numerical results supporting our findings are also presented. [ABSTRACT FROM AUTHOR]

Simulation-based design tools have been used since the late 1980s for designing vertical borehole ground heat exchangers (GHE) used with ground source heat pump (GSHP) systems. The ground heat exchanger simulations used in these tools rely on thermal response functions known as g-functions. Because of the significant computational burden in computing g-functions for even a single configuration, the design tools have relied on libraries of pre-computed g-functions. These g-functions were available for standard configuration shapes, such as lines, rectangles, open rectangles, L-shapes, and U-shapes. Standard shapes are often sub-optimal. For any building on a site, the available land may preclude use of a standard shape. For large GSHP systems with significantly imbalanced annual heat rejection and extraction loads, large rectangular fields may experience significant heat build-up (or heat draw-down) in the interior of the field. This paper describes a new ground heat exchanger design tool capable of automatically selecting and sizing both standard and irregular configurations. The focus of this paper is a method for creating, selecting, and sizing irregular configurations where the available land area and "no-go" zones are described as irregular polygons. [ABSTRACT FROM AUTHOR]

Mathematics is a difficult subject for elementary school students. One of the causes is errors in mathematical concepts and principles made by students. For this reason, efforts need to be made to improve the concept and principles of quadrilaterals. The aim of this research is to design student learning trajectories in finding the perimeter and area of a rectangle in the context of a fishing pond. This is research with a design research approach. The subjects of this research were 50 students divided into two groups, 25 people each. Data collection techniques through observation, interviews and documentation. The data analysis technique used is qualitative and is developed through certain relationship patterns. The results of this research show that the mathematics learning trajectory design was implemented very well. It improves the ability of understanding about quadrilaterals. The learning path is activity-1: students create a representation of the context of a fishing pond and a rectangular image. Activity-2: students determine the perimeter of a rectangular image by placing match sticks around the rectangle in sequence, holding them tightly together. Activity-3: students determine the circumference of the fishing pond. Activity-4: students determine how to calculate the circumference of the pond by drawing a rectangle using matchsticks. Activity-5: students discover the principle of perimeter of a rectangle. The conclusion of this research is that the mathematics learning trajectory design is valid, practical, and increases the ability to understand concepts and principles from quadrilaterals. [ABSTRACT FROM AUTHOR]

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper puts forward a novel affine relaxation-based algorithm for solving the minimax affine fractional program problem (MAFPP) over a polyhedron set. First of all, some new variables are introduced for deriving the equivalence problem (EP) of the MAFPP. Then, for the EP, the affine relaxation problem (ARP) is established by using the two-stage affine relaxation method. The method provides a lower bound by solving the ARP in the branch-and-bound searching process. By subdividing the output space rectangle and solving a series of ARPs continuously, the feasible solution sequence generated by the algorithm converges to a global optimal solution of the initial problem. In addition, the algorithmic maximum iteration in the worst case is estimated by complexity analysis for the first time. Lastly, the practicability and effectiveness of the algorithm have been verified by numerical experimental results. [ABSTRACT FROM AUTHOR]

A perfectly auxetic 2D metamaterial model is described herein by means of interconnected rotating rigid units of three different shapes: hexagons, triangles, and rectangles. The in‐plane Young's modulus is obtained by matching the discrete elastic energy stored at the hinges during relative rotation of the rigid units with the overall elastic energy stored in the metamaterial's continuum equivalence. Results indicate that, in addition to the trivial effects from the rotational spring constant at the hinges, the in‐plane Young's modulus is highly influenced by the internal angle, followed by the relative size of the triangle with reference to the sizes of other rigid units. The effect from the rectangle aspect ratio presents the least influence. As such, there are several parameters to control the Young's modulus, from the coarse tuning by adjusting the internal angle to fine tuning by controlling the rectangle aspect ratio. The capability of the metamaterial's Young's modulus to be tuned from a spectrum of parameters that range from coarse to fine tuning permits this metamaterial's mechanical property to be precisely designed and manufactured in a cost‐effective manner. [ABSTRACT FROM AUTHOR]

Space non-cooperative target recognition is crucial for on-orbit servicing. Multi-satellite cooperation has great potential for broadening the observation scope and enhancing identification efficiency. However, there is currently a lack of research on recognition methods tailored for multi-satellite cooperative observation. In this paper, we propose a novel space non-cooperative target recognition method to identify satellites and debris in images from multi-satellite observations. Firstly, we design an image-stitching algorithm to generate space-wide-area images. Secondly, we propose a two-stage multi-target detection model, a lighter CNN model with distance merge threshold (LCNN-DMT). Specifically, in the first stage, we propose a novel foreground extraction model based on a minimum bounding rectangle with the threshold for distance merging (MBRT-D) to address redundant detection box extraction for satellite components. Then, in the second stage, we propose an improved SqueezeNet model by introducing separable convolution and attention mechanisms for target classification. Moreover, due to the absence of a public multi-target detection dataset containing satellites and debris, we construct two space datasets by introducing a randomized data augmentation strategy. Further experiments demonstrate that our method can achieve high-precision image stitching and superior recognition performance. Our LCNN-DMT model outperforms mainstream algorithms in target localization accuracy with only 0.928 M parameters and 0.464 GFLOPs, making it ideal for on-orbit deployment. [ABSTRACT FROM AUTHOR]

In recent years, deep-learning methods have significantly improved the classification results in the field of plant-leaf recognition. However, limited by the model input, the original image needs to be compressed to a certain size before it can be input into the convolutional neural network. This results in great changes in the shape and texture information of some samples, thus affecting the classification accuracy of the model to a certain extent. Therefore, a minimum enclosing quadrate (MEQ) method is proposed to standardize the sample datasets. First, the minimum enclosing rectangle (MER) of the leaf is obtained in the original image, and the target area is clipped. Then, the minimum enclosing quadrate of the leaf is obtained by extending the short side of the rectangle. Finally, the sample is compressed to fit the input requirements of the model. In addition, in order to further improve the classification accuracy of plant-leaf recognition, an EC-ResNet50 model based on transfer-learning strategy is proposed and further combined with the MEQ method. The Swedish leaf, Flavia leaf, and MEW2012 leaf datasets are used to test the performance of the proposed methods, respectively. The experimental results show that using the MEQ method to standardize datasets can significantly improve the classification accuracy of neural networks. The Grad-CAM visual analysis reveals that the convolutional neural network exhibits a higher degree of attention towards the leaf surface features and utilizes more comprehensive feature regions during recognition of the leaf samples processed by MEQ method. In addition, the proposed MEQ + EC-ResNet50 method also achieved the best classification results among all the compared methods. This experiment provides a widely applicable sample standardization method for leaf recognition research, which can avoid the problem of sample deformation caused by compression processing and reduce the interference of redundant information in the image to the classification results to a certain degree. [ABSTRACT FROM AUTHOR]

A three‐dimensional (3D) anionic cadmium‐organic framework, namely [(CH3)2NH2][Cd1.5(DMTDC)2] ⋅ 2DMA ⋅ 0.5H2O (Cd‐MOF; DMA=N,N‐dimethylacetamide), was successfully synthesized under solvothermal conditions by using a linear thienothiophene‐containing dicarboxylate ligand, 3,4‐dimethylthieno [2,3‐b]‐thiophene‐2,5‐dicar‐boxylic acid (H2DMTDC). Single‐crystal X‐ray diffraction analysis reveals that Cd‐MOF exhibits a 3D anionic framework with pcuα‐Po topology, featuring rectangle and rhombus‐shaped channels along b‐ and c‐ axis direction. Cd‐MOF demonstrates selective adsorption of cationic dyes over anionic and neutral dyes. Additionally, Tb3+‐loaded Cd‐MOF serves as a fast‐response fluorescence sensor for the sensitive detection of Fe3+ ions with a low limit of detection (8.90×10−7 M) through fluorescence quenching. [ABSTRACT FROM AUTHOR]

Finding vibration mode functions satisfying both high-order partial differential governing equations and various non-Lévy-type boundary conditions is extremely challenging for the free vibration problems of functionally graded rectangular plates, making it difficult to analytically solve the problem with traditional methods. Herein, the newly developed Hamiltonian system-based symplectic superposition method was extended and successfully applied to analytical solutions to the free vibration problems of functionally graded rectangular plates. For the solution methodology, the original vibration problem was divided into sub-problems and the physical neutral plane was introduced to eliminate the stretching-bending coupling effect caused by the transversely non-uniform materials. The sub-problems were analytically solved with some mathematical techniques, i.e., the variable separation and the symplectic eigenvector expansion, which are not applicable in the traditional Lagrangian system. The final solution to an original vibration problem was obtained through the superposition of sub-problems. The symplectic superposition method has the advantage of not requiring the pre-defined solution forms, which overcomes the limitations of traditional semi-inverse methods and allows for obtaining analytical solutions to more complex problems. Comparison of the obtained solutions with the numerical solutions proves the accuracy of the presented method. On this basis, quantitative parameter analyses on the natural frequencies were conducted to reveal the effects of boundary conditions, material distributions and aspect ratios. [ABSTRACT FROM AUTHOR]

The second mode is the main instability factor in hypersonic flow and shows the characteristics of acoustic disturbance. The stabilization effect of a porous surface on the second mode in a hypersonic boundary layer is studied according to the acoustic disturbance characteristics—including the flow characteristics of the porous surface, the effects of porous parameters, and the effect of mechanics—by direct numerical simulation. A rectangle is the basic structure of pores (slots) with a two-dimensional porous surface. The results show that the porosity (φ) and the number of pores (n) are the primary and secondary primary factors affecting the inhibition effect on the second mode by the porous surface. By influencing the amplitude and phase distribution of the pressure disturbance, the porous surface affects the wall normal transport between the mainstream and the porous surface in the near wall region, and it finally inhibits the growth of the second mode. [ABSTRACT FROM AUTHOR]

This paper employs numerical simulation to examine the impact of variations in flow angle of attack (α) and low Reynolds number (Re) on the aerodynamic performance of the RC-TLBB (rectangle cylinder and train-like bluff body) system subjected to crosswinds. The RC-TLBB system consists of a train-like bluff body with a 5:1 cross section rectangle cylinder, and the rectangle cylinder cross section is used alone as a without-train group. The research indicates that the presence of the upper TLBB amplifies the influence of Re and α on the lift and drag of the rectangle cylinder. The alteration in α results in similar trends for both C L ′ and C ¯ D of the TLBB and the rectangle cylinder. For Re, the trend is reversed. The rise in both α and Re enhances the correlation between the lift coefficient and drag coefficient. Nonetheless, the correlation between lift and drag coefficients exhibits greater strength for a rectangle cylinder in the system compared to a single rectangle cylinder in the without-train group. The presence of the TLBB spatially forces the separation of the shear layers, and the vortex shedding phenomenon on the upper side of the rectangle cylinder precedes that on the lower side at low Re. The increase in Re changes this phenomenon to the lower side preceding the upper side. This study illustrates the potential flow-induced problems by analyzing the various aerodynamic parameters of the system, which provides a theoretical basis for ensuring the safety and reliability of the system. [ABSTRACT FROM AUTHOR]

We introduce and study conflict-free colourings of t-subsets in hypergraphs. In such colourings, one assigns colours to all subsets of vertices of cardinality t such that in any hyperedge of cardinality at least t there is a uniquely coloured t-subset. The case t = 1 , i.e., vertex conflict-free colouring, is a well-studied notion that originates in the context of frequency allocation to antennas in cellular networks. It has caught the attention of researchers both from the combinatorial and algorithmic points of view. A special focus was given to hypergraphs arising in geometry. Already the case t = 2 (i.e., colouring pairs) seems to present a new challenge. Many of the tools used for conflict-free colouring of geometric hypergraphs rely on hereditary properties of the underlying hypergraphs. When dealing with subsets of vertices, the properties do not pass to subfamilies of subsets. Therefore, we develop new tools, which might be of independent interest. For any fixed t, we show that the n t t-subsets in any set P of n points in the plane can be coloured with O (t 2 log 2 n) colours so that any axis-parallel rectangle that contains at least t points of P also contains a uniquely coloured t-subset. For a wide class of "well-behaved" geometrically defined hypergraphs, we provide near tight upper bounds on their t-subset conflict-free chromatic number. For t = 2 we show that for each of those "well-behaved" hypergraphs H, the hypergraph H ′ , whose hyperedges are obtained by taking all the unions of two hyperedges from H, admits a 2-subset conflict-free colouring with roughly the same number of colours as H. For example, we show that the n 2 pairs of points in any set P of n points in the plane can be coloured with O (log n) colours such that for any two discs d 1 , d 2 in the plane with | (d 1 ∪ d 2) ∩ P | ≥ 2 there is a uniquely (in d 1 ∪ d 2 ) coloured pair. We also show that there is no general bound on the t-subset conflict-free chromatic number as a function of the standard conflict-free chromatic number already for t = 2 . [ABSTRACT FROM AUTHOR]

License plate recognition is currently used in various situations, such as parking lot vehicle management and the tracking of wanted vehicles. These applications require recognition from all possible camera angles. Therefore, we propose a method for license plate recognition in images captured from various camera angles. First, the license plate area is detected from the input image using the YOLOv5 object detection method. The subsequent process can be performed in two manners: by rotating the license plate to the front using projective transformation and trapezoidal correction, or by using graph matching. The first method performs Hough transforms or linear approximations as preprocessing, and then calculates the rectangle surrounding the license plate from the YOLOv5 output. After performing trapezoidal correction, the maximally stable extremal regions (MSER) are used to detect character candidates, and characters are recognized using 3D rotated character recognition. The second method performs character candidate detection and recognition without trapezoidal correction, followed by graph matching. These methods are versatile because they do not depend on the layout of license plates, which varies among countries and regions. Two types of datasets were used: a set of images containing Japanese license plates collected by ourselves, and a set of publicly available images containing Taiwanese license plates. Two recognition rates were evaluated: the license plate character recognition rate and license plate recognition rate in which all characters in one plate are recognized. The license plate character recognition rates using graph matching were 91.9% for the Japanese license plates and 89.3% for the Taiwanese license plates. The license plate recognition rates were 84.0% and 84.5%, respectively. [ABSTRACT FROM AUTHOR]

In view of the fact that there is still a certain gap in representing and reasoning with the orientation relation between real objects due that the existing models for representing and reasoning with direction relations use a point and minimum bounding rectangle to approximate the spatial object itself, this paper proposed a new model for dealing with the disconnected spatial objects based on Voronoi diagram. With the help of the theory of Gestalt psychological, the proposed model constructed visual regions between spatial objects by extracting the feature points and feature chains of the disconnected spatial objects to generate the direction Voronoi diagram, which realized the representation of directions between the space objects which were disconnected and contain holes. This model fully considered the influence of the shape, size and other factors of the spatial objects, and had higher expression accuracy and wider applicability. In order to improve the precision of reasoning with cardinal directional relations between complex spatial objects, this paper proposed an algorithm for composing cardinal direction relations defined by the proposed model, which reduced the uncertainty of the results of composition by means of Tile-union operation and Pr operation. The results of analysis and verification show that the proposed model and algorithm reduce the uncertainty of the reasoning results, improve the accuracy of representation and reasoning, and then enhance the ability to analyze and process the direction relations with complex spatial objects. [ABSTRACT FROM AUTHOR]

Uncertainty of data, the degree to which data are inaccurate, imprecise, untrusted, and undetermined, is inherent in many contemporary database applications, and numerous research endeavours have been devoted to efficiently answer skyline queries over uncertain data. The literature discussed two different methods that could be used to handle the data uncertainty in which objects having continuous range values. The first method employs a probability-based approach, while the second assumes that the uncertain values are represented by their median values. Nevertheless, neither of these methods seem to be suitable for the modern high-dimensional uncertain databases due to the following reasons. The first method requires an intensive probability calculations while the second is impractical. Therefore, this work introduces an index, non-probability framework named Constrained Skyline Query processing on Uncertain Data (CSQUiD) aiming at reducing the computational time in processing constrained skyline queries over uncertain high-dimensional data. Given a collection of objects with uncertain data, the CSQUiD framework constructs the minimum bounding rectangles (MBRs) by employing the X-tree indexing structure. Instead of scanning the whole collection of objects, only objects within the dominant MBRs are analyzed in determining the final skylines. In addition, CSQUiD makes use of the Fuzzification approach where the exact value of each continuous range value of those dominant MBRs' objects is identified. The proposed CSQUiD framework is validated using real and synthetic data sets through extensive experimentations. Based on the performance analysis conducted, by varying the sizes of the constrained query, the CSQUiD framework outperformed the most recent methods (CIS algorithm and SkyQUD-T framework) with an average improvement of 44.07% and 57.15% with regards to the number of pairwise comparisons, while the average improvement of CPU processing time over CIS and SkyQUD-T stood at 27.17% and 18.62%, respectively. [ABSTRACT FROM AUTHOR]

Websites commonly use visual formats to display numerical product ratings. Highlighting the overlooked notion of the "aesthetics" of product ratings, the current research examines how the shape of basic visual rating units (rectangular vs. non-rectangular) influences product preference. Seven experiments (and 23 supplementary experiments; N  =   17,994) demonstrate a visual rounding effect. Specifically, compared to the rectangular rating format (e.g. bar ratings), the non-rectangular rating format (e.g. star ratings) increases product preference when product ratings (e.g. 3.7, 3.8, 3.9) are below the nearest integer. In contrast, the non-rectangular rating format decreases product preference when product ratings (e.g. 4.1, 4.2, 4.3) are above the nearest integer. Occurring for both the overall rating and by-attribute ratings of a product, the visual rounding effect results from a visual completeness restoration process, wherein consumers perceive non-rectangular rating units to be incomplete after vertical cutting. This research contributes to the product rating and visual marketing literatures and provides actionable implications by demonstrating what visual rating format should be adopted based on rating distribution, how the visual rounding effect can be prevented if needed, and who are even more susceptible to the visual rounding effect. [ABSTRACT FROM AUTHOR]

We argue for the application of bibliometric indices to quantify the long-term uncertainty of outcome in sports. The Euclidean index is proposed to reward quality over quantity, while the rectangle index can be an appropriate measure of core performance. Their differences are highlighted through an axiomatic analysis and several examples. Our approach also requires a weighting scheme to compare different achievements. The methodology is illustrated by studying the knockout stage of the UEFA Champions League in the 20 seasons played between 2003 and 2023: club and country performances as well as three types of competitive balance are considered. Measuring competition at the level of national associations is a novelty. All results are remarkably robust concerning the bibliometric index and the assigned weights. Since the performances of national associations are more stable than the results of individual clubs, it would be better to build the seeding in the UEFA Champions League group stage upon association coefficients adjusted for league finishing positions rather than club coefficients. [ABSTRACT FROM AUTHOR]

In this article, we introduce the concept of (η 1 , η 2) -convex stochastic processes on coordinates and establish Hermite-Hadamard-type inequality for these stochastic processes. Moreover, we prove new integral inequality of Hermite-Hadamard-Fejér type for newly defined coordinated η -convex stochastic processes on a rectangle. The results presented in this article would provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In 2022, Gysembergh et al. published a paper in JHA claiming 'New evidence for Hipparchus' Star Catalogue'. In this paper we challenge this hypothesis by stating that (a) we disagree with their astronomical dating and find inconsistencies by using the given numbers, and (b) the terminology and the data format used in the palimpsest do not match Hipparchus or anybody else. Therefore, the palimpsest does not prove anything about Hipparchus's star catalogue nor did Hipparchus use rectangular constellation borders. Specifically, the constellation of Corona Borealis, typically depicted as a circle since Babylonian times, is not considered a rectangle by Hipparchus. Furthermore, a palimpsest that cannot be dated properly does not confirm the long-known relationship between Hipparchus and Ptolemy as the authors claim. [ABSTRACT FROM AUTHOR]

An inerter‐based dynamic vibration absorber (IDVA) is proposed and applied to suppress the vibration of a plate. The dynamic model of a thin rectangular plate attached with an IDVA is established and the frequency response function of the transverse displacement of the plate is derived through the classical vibration theory and the analysis in the s$s$ domain. In addition, the equation for frequency ratios of fixed points is obtained, and the condition for the existence of four fixed points is found by investigating the problem of solving quartic equations. Moreover, the extended fixed‐point method is employed to analytically obtain the optimal parameters of the IDVA attached to a plate, the expressions of the optimal damping ratio and other dimensionless qualities are presented. [ABSTRACT FROM AUTHOR]

We show that the linear brittle Griffith energy on a thin rectangle Γ -converges after rescaling to the linear one-dimensional brittle Euler–Bernoulli beam energy. In contrast to the existing literature, we prove a corresponding sharp compactness result, namely a suitable weak convergence after subtraction of piecewise rigid motions with the number of jumps bounded by the energy. [ABSTRACT FROM AUTHOR]

In the dynamic field of cryptography, lightweight ciphers play a pivotal role in overcoming resource constraints in modern applications. This paper introduces a lightweight cryptographic algorithm by seamlessly merging the proven characteristics of the Feistel cipher CLEFIA with the advanced substitution-permutation network (SPN) framework of RECTANGLE for key generation. The algorithm incorporates a specially optimized feather S-box, balancing efficiency and security in both CLEFIA and RECTANGLE components. The RECTANGLE key generation, vital for the proposed lightweight technique, enhances overall cryptographic security and efficiency. Meticulous consideration of resource limitations maintains the algorithm's lightweight nature, making it well-suited for applications with restricted computational resources. To validate the efficacy of the lightweight algorithm, extensive evaluation on encrypted data is conducted using National Institute of Standards and Technology (NIST) tools, known for assessing cryptographic algorithm quality. Results reveal a high degree of randomness, indicative of robust resistance against cryptographic attacks. This manuscript provides a comprehensive examination of the lightweight algorithm, emphasizing key attributes, security enhancements, and successful integration of the optimized feather S-box. Rigorous testing, particularly NIST tool-based randomness analysis, offers empirical evidence of the algorithm's resilience against attacks, establishing its suitability for secure data encryption in resource-limited environments. [ABSTRACT FROM AUTHOR]

Packing problems have been studied for a long time and have great applications in real-world scenarios. In recent times, with problems in the industrial world increasing in size, exact algorithms are often not a viable option and faster approaches are needed. We study Monte Carlo tree search, a random sampling algorithm that has gained great importance in literature in the last few years. We propose three approaches based on MCTS and its integration with metaheuristic algorithms or deep learning models to obtain approximated solutions to packing problems that are also interpretable by means of MCTS exploration and from which knowledge can be extracted. We focus on two-dimensional rectangle packing problems in our experimentation and use several well known benchmarks from literature to compare our solutions with existing approaches and offer a view on the potential uses for knowledge extraction from our method. We manage to match the quality of state-of-the-art methods, with improvements in time with respect to some of them and greater interpretability. [ABSTRACT FROM AUTHOR]

Photoanodes possessing multifunctionality for efficient clean fuel generation have garnered significant attention. In this study, we present successful fabrication of tungsten‐doped ZnO photoelectrodes, resulting in enhanced photoelectrochemical water‐splitting performance. A single‐step deposition process was employed to achieve thin films with excellent adhesion on FTO substrates, eliminating the need for post‐annealing treatments. The addition of tungsten into the ZnO matrix extended the optical absorbance range of the thin films to the visible spectrum, leading to improved photoelectrochemical performance under visible light irradiation. At an applied potential of 0.85 V vs. RHE, the as‐fabricated tungsten‐doped ZnO thin films exhibited a remarkable photocurrent density of 5218 μA/cm2, which was eight times higher than that of the undoped ZnO electrode. The incorporation of tungsten in the ZnO photoanode resulted in increased charge carrier density and enhanced visible light absorption, consequently elevating the photocurrent density. [ABSTRACT FROM AUTHOR]

In this paper, we study the spectral properties of a class of degenerate third-order partial differential operators with variable coefficients presented in a rectangle. Conditions are found to ensure the existence and compactness of the inverse operator. A theorem on estimates of approximation numbers is proven. Here, we note that finding estimates of approximation numbers, as well as extremal subspaces, for a set of solutions to the equation is a task that is certainly important from both a theoretical and a practical point of view. The paper also obtained an upper bound for the eigenvalues. Note that, in this paper, estimates of eigenvalues and approximation numbers for the degenerate third-order partial differential operators are obtained for the first time. [ABSTRACT FROM AUTHOR]

Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ -pre-invex interval-valued mappings ( C · L · R - ℏ -pre-invex Ι · V - M ), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte's type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes. [ABSTRACT FROM AUTHOR]

A novel DIRECT-type algorithm is proposed to tackle box-constrained optimization problems. The algorithm incorporates bisection partitioning and diagonal sampling procedures, utilizing the Pareto approach to identify potential hyperrectangles. Furthermore, each hyperrectangle's size is determined based on the length of its longest side, in accordance with the infinity norm. This combination enhances convergence speed, facilitating the generation of a global optimal solution. The proposed algorithm's effectiveness is evaluated through numerical experiments, with detailed results demonstrating its efficacy. [ABSTRACT FROM AUTHOR]

In cold climates or winter countries, maintaining optimal room temperatures is essential for comfort and energy efficiency. Conventional square or rectangle‐shaped rooms often face challenges in achieving efficient heat transfer (HT) and uniform temperature distribution. To address these limitations, this study has been explored using curved corner cavities, varying their aspect ratio (AR = 1.0 and 0.5), and incorporating a circular shape cooler to enhance HT within the room. The curved corners promote better airflow circulation, creating a more efficient HT environment. The dimensionless governing equations and corresponding boundary conditions are solved numerically using the finite element method. This research aims to assess the optimized HT and entropy production within a curved corner cavity, varying their AR and enclosing a circular shape cooler to determine the most effective configuration for maximizing HT and energy efficiency in winter conditions. This study reveals that in the case without a cooler (WOC), the average Nusselt number (Nuavg $N{u}_{avg}$) is higher in the curved rectangle cavity compared with the curved square cavity for all Ra $Ra$ values. Using the curved square (AR = 1.0), Nuavg $N{u}_{avg}$ increases by 191.86%, while with the curved rectangle (AR = 0.5), Nuavg $N{u}_{avg}$ increases by 302.63% at Ra=106 $Ra=1{0}^{6}$. Additionally, in the case with a cooler (WC), Nuavg $N{u}_{avg}$ is higher than the case WOC and Nuavg $N{u}_{avg}$, and an average total entropy (Enavg) $(E{n}_{avg})$ increases for both the WOC and WC cases for all Ra $Ra$ values. Transitioning from a square to a curved rectangle (AR = 0.5) WC, Nuavg $N{u}_{avg}$ increases by 329.34% at Ra=106 $Ra=1{0}^{6}$. Furthermore, in the WOC case, the curved square cavity and, in the WC case, the curved rectangle show better energy efficiency and reduce environmental impact. [ABSTRACT FROM AUTHOR]

We study rectangle stabbing problems in which we are given n axis-aligned rectangles in the plane that we want to stab, that is, we want to select line segments such that for each given rectangle there is a line segment that intersects two opposite edges of it. In the horizontal rectangle stabbing problem (Stabbing), the goal is to find a set of horizontal line segments of minimum total length such that all rectangles are stabbed. In the horizontal–vertical stabbing problem (HV-Stabbing), the goal is to find a set of rectilinear (that is, either vertical or horizontal) line segments of minimum total length such that all rectangles are stabbed. Both variants are NP-hard. Chan et al. (ISAAC, 2018) initiated the study of these problems by providing constant approximation algorithms. Recently, Eisenbrand et al. (A QPTAS for stabbing rectangles, 2021) have presented a QPTAS and a polynomial-time 8-approximation algorithm for Stabbing, but it was open whether the problem admits a PTAS. In this paper, we obtain a PTAS for Stabbing, settling this question. For HV-Stabbing, we obtain a (2 + ε) -approximation. We also obtain PTASs for special cases of HV-Stabbing: (i) when all rectangles are squares, (ii) when each rectangle's width is at most its height, and (iii) when all rectangles are δ -large, that is, have at least one edge whose length is at least δ , while all edge lengths are at most 1. Our result also implies improved approximations for other problems such as generalized minimum Manhattan network. [ABSTRACT FROM AUTHOR]

Copyright of Art-Sanat Journal / Art-Sanat is the property of Art-Sanat and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

AbstractIn this article, a four-node rectangular element called R4Sand1 is developed using a hybrid combination of the classical finite element method and Sanders’ shell theory. Utilizing an in-house code, the proposed formulation is used for the prediction of free vibration and aeroelastic instabilities of functionally graded rectangular plates with various boundary conditions. The effectiveness of the proposed new approach is investigated, revealing very good convergence behavior and accuracy. Finally, parametric studies are conducted to illustrate the influences of various parameters, such as aspect ratio, thickness, and volume fraction, on the natural frequency and critical dynamic pressure. [ABSTRACT FROM AUTHOR]

The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method, we have acquired the Lie infinitesimal generators for the considered model. Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions. The obtained solutions manifest in various forms including dark, bright, kink, anti-kink, and periodic types using diverse strategies. To enhance the physical interpretation, the study presents 3D, 2D, and contour plots of the acquired solutions. Every graph's wave-like structure contains information about the structural behaviour of the bacteria that build biofilms on surfaces where rectangles have different densities. This analysis enhances comprehension of the complex dynamics present in areas like fluid dynamics, fiber optics, biology, ocean physics, coastal engineering, and nonlinear complex physical systems. [ABSTRACT FROM AUTHOR]

We investigate how the complexity of Euclidean TSP for point sets P inside the strip (- ∞ , + ∞) × [ 0 , δ ] depends on the strip width δ . We obtain two main results. For the case where the points have distinct integer x-coordinates, we prove that a shortest bitonic tour (which can be computed in O (n log 2 n) time using an existing algorithm) is guaranteed to be a shortest tour overall when δ ⩽ 2 2 , a bound which is best possible. We present an algorithm that is fixed-parameter tractable with respect to δ . Our algorithm has running time 2 O (δ) n + O (δ 2 n 2) for sparse point sets, where each 1 × δ rectangle inside the strip contains O(1) points. For random point sets, where the points are chosen uniformly at random from the rectangle [ 0 , n ] × [ 0 , δ ] , it has an expected running time of 2 O (δ) n . These results generalise to point sets P inside a hypercylinder of width δ . In this case, the factors 2 O (δ) become 2 O (δ 1 - 1 / d) . [ABSTRACT FROM AUTHOR]

A well-known open problem of Meir and Moser asks if the squares of sidelength 1/n for n ≥ 2 can be packed perfectly into a rectangle of area ∑ n = 2 ∞ n - 2 = π 2 / 6 - 1 . In this paper we show that for any 1 / 2 < t < 1 , and any n 0 that is sufficiently large depending on t, the squares of sidelength n - t for n ≥ n 0 can be packed perfectly into a square of area ∑ n = n 0 ∞ n - 2 t . This was previously known (if one packs a rectangle instead of a square) for 1 / 2 < t ≤ 2 / 3 (in which case one can take n 0 = 1 ). [ABSTRACT FROM AUTHOR]

This paper demonstrates a 3.4 GHz micro‐acoustic filter with excellent in‐band insertion loss, rectangle coefficient, and out‐of‐band rejection. The proposed filter was based on a novel topology by integrating the bulk acoustic wave (BAW) resonators with an on‐chip clamping inductor, the introduction of the lumped components is beneficial for improving the filters' stopband rejection while having minimal influence on the rectangle coefficient and in‐band insertion loss. Al0.8Sc0.2N material was selected as the piezoelectric film of the BAW device and the inductor was fabricated on the same wafer with BAW devices. The manufactured filter has a minimum in‐band insertion loss of ~ 1.5 dB, a 3 dB bandwidth of about 170 MHz, and a stopband rejection of nearly ‐30 dB. The experimental results verify the design and show great applications for 5G communication and beyond. [ABSTRACT FROM AUTHOR]

Opportune detection of Anthonomus eugenii is a fundamental aspect of any management program to this pest. Yellow traps are the most common monitoring strategy, and its efficacy is related with the trap design and placement within crops. However, there's limited information on this. Two outdoor experiments were performed to determine the efficiency of traps with six different shapes (circle, square, diamond, ellipse, rectangle, and triangle) and seven frame colors (yellow, dark green, black, red, white, purple, and blue); seven to the traps placement at four orientations (North, South, East and West), five aside distances from the bed center (0, 20, 40, 60 and 80 cm aside to the inter-bed space) and six heights (0, 20, 40, 60, 80 and100 cm) on A. eugenii adults. There wasn't significant difference among shapes and orientations. Traps with yellow, dark green and black frames had the highest number of insects. For the aside distance, the plots were categorized according to their width as narrow (54–65 cm) and wide (71–81 cm), the highest insects caught was exhibited on traps at 0–20 and 0–40 cm, respectively. Regarding the traps height, they were classified according to their height as short (62–64 cm), medium (78–82 cm) and tall (90–92 cm), the highest insects caught was exhibited on traps at 20–40, 40–60, and 40–80 cm, respectively. Regression analyzes indicate that catches decrease as the traps are installed into the inter-bed space and above the canopy. This study provides novel information to improve outdoor programs to monitor A. eugenii. [ABSTRACT FROM AUTHOR]

This paper approaches the role of Origami Art role in teaching Descriptive Geometry to students, future builders. Using the Art of Paper Folding in the application classes of Descriptive Geometry, we demonstrate that the acquiring of knowledge and skills in educational practice is complemented by the development of creativity, imagination, Aesthetics and team spirit. Origami turned into a source of inspiration for first-year students majoring in Civil, Industrial and Agricultural Construction to build a demountable assembly made of modular origami elements. The element is a modular triangle, made from a rectangle with a side ratio of 1:√2 known as the "Harmony Gate". The construction is original and executed on several levels, from white and colored A4 paper, whose density equals 80 g/m2. The number of origami elements used is calculated by a mathematical formula. [ABSTRACT FROM AUTHOR]

Considerable advances have been made recently in applying reinforcement learning (RL) to packing problems. However, most of these methods lack scalability and cannot be applied in dynamic environments. To address this research gap, we propose a hybrid algorithm called GraphPack to solve the strip packing problem. Two graph neural networks are designed to fully incorporate the problem's structure and enhance generalization performance. SkylineNet encodes the geometry of free space as the context feature, while PackNet, supporting the symmetry of rectangles, chooses the next rectangle to pack from the remaining rectangles at each timestep. We conduct fixed-scale, variable rectangle number and variable strip width experiments to test our method. The experimental results show that our method outperforms classical heuristic methods as well as previous RL methods. Notably, our method exhibits strong generalization ability and produces stable results even when the number of rectangles or strip width differs from that during training. [ABSTRACT FROM AUTHOR]

Aiming at the problem of cartoon piracy and plagiarism, this paper proposes a method of cartoon copyright recognition based on character personality actions. This method can be used to compare the original cartoon actions with the action characteristics of pirated or copied cartoons to identify whether there is piracy or plagiarism. Firstly, an image preprocessing scheme for character extraction is designed. GrabCut interactive image segmentation algorithm was used to obtain cartoon characters, and then binarization and morphological processing were performed on the results. Secondly, a feature extraction scheme based on character profile, moving character and character pose is designed. By extracting the perimeter and area of the character contour, the length-to-width ratio of the smallest rectangle and the inclination angle of the contour, the character contour features are obtained. The three-dimensional coordinates are established by the central point position of the cartoon character in the two-dimensional image and the change of the character's zoom in and out, and the character's motion angle characteristics are calculated. By skeletonizing a character to obtain the pose characteristics, and using deburring operation to remove redundant branches, then extract the skeleton joint angle information. Finally, feature fusion is performed on the extracted features. The experimental results show that the proposed method breaks the limitation of the conventional single feature based recognition, and can better extract the character features including contour feature, motion feature and pose feature through multi-feature based extraction, so as to protect the cartoon copyright. [ABSTRACT FROM AUTHOR]

We study configuration spaces |$C(n; p, q)$| of |$n$| ordered unit squares in a |$p$| by |$q$| rectangle. Our goal is to estimate the |$j$| th Betti number for large |$n$|⁠ , |$j$|⁠ , |$p$|⁠ , and |$q$|⁠. We consider sequences of area-normalized coordinates, where |$\left (\frac {n}{pq}, \frac {j}{pq}\right)$| converges as |$n$|⁠ , |$j$|⁠ , |$p$|⁠ , and |$q$| approach infinity. For every sequence that converges to a point in the "feasible region" in the |$(x,y)$| -plane identified in [ 3 ], we show that the factorial growth rate of the Betti numbers is the same as the factorial growth rate of |$n!$|⁠. This implies that (1) the Betti numbers are vastly larger than for the configuration space of |$n$| ordered points in the plane, which have the factorial growth rate of |$j!$|⁠ , and (2) every point in the feasible region is eventually in the homological liquid regime. [ABSTRACT FROM AUTHOR]

In this paper, two-dimensional (2D) heat equations on disjoint rectangles are considered. The solutions are connected by interface Robin's-type internal conditions. The problem has external Dirichlet boundary conditions that, in the forward (direct) formulation, are given functions. In the inverse problem formulation, the Dirichlet conditions are unknown functions, and the aim is to be reconstructed upon integral observations. Well-posedness both for direct and inverse problems is established. Using the given 2D integrals of the unknown solution on each of the domains and the specific interface boundary conditions, we reduce the 2D inverse problem to a forward heat 1D one. The resulting 1D problem is solved using the explicit Saul'yev finite difference method. Numerical test examples are discussed to illustrate the efficiency of the approach. [ABSTRACT FROM AUTHOR]