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An irreducible triangulation is a plane graph such that its outer face is a quadrangle, every inner face is a triangle, and it has no separating triangle. Let T be an irreducible triangulation with n vertices. A rectangular dual R of T is a dissection of a rectangle into (small) rectangles such that (1) each rectangle of R corresponds to a vertex of T , and (2) two rectangles of R are adjacent if the two corresponding vertices of T are adjacent. Finding a rectangular dual of a given graph has an application on cartograms and VLSI floor-planning. In this paper, we consider the problem of enumerating all the rectangular duals of a given irreducible triangulation. It is known that the set of rectangular duals of an irreducible triangulation T one-to-one corresponds to the set of transversal edge-partitions of T. Hence, in this paper, we design an enumeration algorithm of all the transversal edge-partitions of an irreducible triangulation with n vertices. The proposed algorithm enumerates them in O (n) -delay and O (n 2) -space after O (n log n) -time preprocessing. [ABSTRACT FROM AUTHOR]

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and translations. The number of rectangles is the rank of the Dehn invariant of the polygon. The same method can also be used to dissect an axis-parallel polygon into a simple polygon with the minimum possible number of edges. When rotations or reflections are allowed, we can approximate the minimum number of rectangles to within a factor of two. [ABSTRACT FROM AUTHOR]

Subjective weighting methods are widely employed to determine criteria weights in multi-criteria decision-making (MCDM) environment. Inputs from decision-makers, including opinions, assessments, assumptions, evaluations, interpretations, expectations, and judgments, are primarily relied upon in these methods. Significant challenges are faced due to two primary factors: the inherent uncertainty in inputs and the process of pairwise comparisons. These challenges increase the uncertainty regarding the derived weights, raising concerns about the reliability of such approaches. This paper introduces a novel MCDM method called Soft Clusters-Rectangles (SCR) to overcome such limitations. This method distinguishes itself by avoiding pairwise comparisons and adopting a fuzzy approach to address uncertainty. Weights are calculated based on criteria membership values across three defined clusters, namely immaterial, mediocre, and vital. Each cluster represents a distinct range of importance. Analytic geometry is also used by computing the areas of multiple rectangles to determine the final weights. The application of SCR method is demonstrated through a case study on autonomous vehicle route selection problem. The results are thoroughly examined through comprehensive analysis. The findings reveal that this method not only avoids the challenges posed by pairwise comparison-based methodologies but also exhibits similarities with objective weighting techniques, often yielding results more comparable to those produced by hybrid methods. [ABSTRACT FROM AUTHOR]

Purpose: A binary-tree subdivision method (BTSM) for numerical evaluation of weakly singular integrals with discontinuous kernel in the three-dimensional (3D) boundary element method (BEM) is presented in this paper. Design/methodology/approach: In this method, the singular boundary element is split into two sub-elements and subdivided recursively until the termination criterion is met and the subdivision is stopped. Then, the source point is surrounded by one or more spherical cavities determined by the discontinuous kernel function. The sub-elements located in spherical cavities will be eliminated, and the regular triangular or rectangle elements are employed to fill the spherical cavities. Findings: With the proposed method, the obtained sub-elements are automatically refined as they approach the source point, and they are "good" in shape and size for standard Gaussian quadrature. Thus, the proposed method can be used to evaluate singular integrals owing discontinuous kernel function accurately for cases of different element shapes and various source point locations. Originality/value: Numerical examples show that the BTSM is suitable for planar and curved elements of arbitrary regular or irregular shape at various source point locations, and the results have much better accuracy and robustness than conventional subdivision method (CSM) when the kernel function is discontinuous. [ABSTRACT FROM AUTHOR]

Spaceborne P-band synthetic aperture radar (SAR) will suffer from ionospheric scintillation, which introduces a random phase into the azimuth signal and leads to image defocusing. For full-polarimetric SAR, it can be corrected by deriving the scintillation phase from Faraday rotation (FR) estimation. When estimating the FR angle, how to preserve changes in scintillation phase while smoothing noise is a key issue. The current method uses a rectangle averaging window. An improved correction method is proposed. Based on the correlation of scintillation phase, a new averaging window for noise suppression is designed to reduce scintillation estimation error. The method does not need any prior information of scintillation. The effectiveness of the proposed method is tested by simulations based on PALSAR2 data. For a non-homogeneous scene, when turbulence strength CkL = 1034 and CkL = 1035, the proposed method has obvious improvement compared with the current method. [ABSTRACT FROM AUTHOR]

Motivated by relativistic materials, we develop a numerical scheme to support existing or state new conjectures in the spectral optimisation of eigenvalues of the Dirac operator, subject to infinite-mass boundary conditions. We numerically study the optimality of the regular polygon (respectively, disk) among all polygons of a given number of sides (respectively, arbitrary sets), subject to area or perimeter constraints. We consider the three lowest positive eigenvalues and their ratios. Roughly, we find results analogous to known or expected for the Dirichlet Laplacian, except for the third eigenvalue which does not need to be minimised by the regular polygon (respectively, the disk) for all masses. In addition to the numerical results, a new, mass-dependent upper bound to the lowest eigenvalue in rectangles is proved and its extension to arbitrary quadrilaterals is conjectured. [ABSTRACT FROM AUTHOR]

Purpose: An accurate free vibration analysis of stepped orthotropic rectangular cantilever plates is performed to obtain the natural frequencies and vibration mode shapes. Two cases of cantilever boundaries are taken into account. Methods: A Hamiltonian-based method is employed to find analytical free vibration solutions of stepped orthotropic rectangular cantilever plates. The overall plate is divided into multiple regions with uniform thickness, and each region can be further divided into two sub-problems based on a fully sliding clamped orthotropic plate. After that, the Hamilton system is established for the equal thickness region, and analytical solutions are obtained by using the symplectic series and a superposition technique of boundary conditions. Results and conclusions: Numerical examples illustrate the accuracy of the proposed analytical solutions and investigate the effects of key influencing factors on the free vibration characteristics of stepped orthotropic rectangular cantilever plates. Furthermore, the obtained analytical solutions may serve as benchmark solutions for the validation of numerical methods. Highlights: 1. Analytical free vibration solutions of stepped orthotropic rectangular cantilever plates are obtained with the framework of symplectic mechanics. 2. Highly accurate natural frequencies and analytical vibration mode shapes are obtained simultaneously. 3. The position of clamped edge, step length ratio, step thickness ratio and number of steps are key influencing factors for the adjustment of free vibration characteristics of the stepped cantilever plate. [ABSTRACT FROM AUTHOR]

Flow control techniques are beneficial for changing the flow and motion characteristics of a vehicle during water entry. Combined with high-speed photography and inertial measurement unit, this paper investigated the cavity evolution and vehicle kinematics during water entry by varying the length, height, and width of a single canard wing. Research indicates that changing the wing length minimally affects the shape and size of fore-end cavity. For the attached cavity on the wing, increasing wing length promotes the formation of the cloudy flow characterized by violent air–water mixing, destroying the integrity of it. As wing height increases, the fore-end cavity profile approaches a rectangle, while the attached cavity on the wing evolves from an ellipse to a triangle. Increasing the wing width shifts the fore-end cavity profile from a rectangle to a trapezoid. There is an impact on the vehicle when the fore-end cavity occurs pinch-off. The impact peak rises with the increase in wing height and width, while the impact duration decreases. Changing wing length has little effect on peak value of pinch-off. Increasing the wing length and height reduces deflection of the vehicle, while increasing the wing width promotes the deflection of the trajectory and attitude. [ABSTRACT FROM AUTHOR]

In the paper, a compact wideband filtering quadrature coupler is proposed, which utilizes the inherent filtering feature of the unequal‐width four‐coupled‐line (FCL) for the first time. Simply by assigning four terminals of the FCL as open‐circuited, the functions of power division, quadrature phase, and inherent filtering response are obtained simultaneously within a wideband. It also has the merits of high directivity and low insertion loss. Since the proposed FDC has the inherent filtering feature without adding extra resonators, the size is the smallest (0.29λg × 0.13λg), and the structure is the simplest when compared with state‐of‐the‐art wideband FDCs. Moreover, based on the derived universal impedance matrix of the unequal‐width FCL, the FCL‐based coupler, as well as other multiport circuits, can be theoretically analyzed. For validation, a prototype is implemented. Measurements show that the proposed coupler exhibits a bandwidth of over 45% under the conditions of 10‐dB return loss, 10‐dB isolation, 0.5‐dB amplitude imbalance, and 5° phase difference error. Besides, the stopband rejection is more than 15 dB, and the rectangle coefficient (RC = |BW20 dB/BW3 dB|) reaches 1.74. Further, as a modification, the high‐frequency selectivity characteristic (RC = 1.11) can be obtained by simply inserting λ/2 stepped impedance resonators with less influence on in‐band performance and little increase in size. [ABSTRACT FROM AUTHOR]

We outline a geometric perspective on causal inference in cohort studies that can help epidemiologists understand the role of standardization in controlling for confounding. For simplicity, we focus on a binary exposure X ⁠ , a binary outcome D ⁠ , and a binary confounder C that is not causally affected by X ⁠. Rothman diagrams plot the risk of disease in the unexposed on the x -axis and the risk in the exposed on the y -axis. The crude risks define a point in the unit square, and the stratum-specific risks at each level of C define two other points in the unit square. Standardization produces points along the line segment connecting the stratum-specific points. When there is confounding by C ⁠ , the crude point is off this line segment. The set of all possible crude points is a rectangle with corners at the stratum-specific points and sides parallel to the axes. When there are more than two strata, standardization produces points in the convex hull of the stratum-specific points, and there is confounding if the crude point is outside this convex hull. We illustrate these ideas using data from a study in Newcastle, United Kingdom, in which the causal effect of smoking on 20-year mortality was confounded by age. [ABSTRACT FROM AUTHOR]

We define a new class of ternary sequences that are 2-balanced. These sequences are obtained by colouring of Sturmian sequences. We show that the class contains sequences of any given letter frequencies. We provide an upper bound on factor and abelian complexity of these sequences. Using the interpretation by rectangle exchange transformation, we prove that for almost all triples of letter frequencies, the upper bound on factor and abelian complexity is reached. The bound on factor complexity is given using a number-theoretical function which we compute explicitly for a class of parameters. [ABSTRACT FROM AUTHOR]

Given a set of integers A⊂Z$A \subset \mathbb {Z}$, we consider the smallest family B$\mathcal {B}$ invariant by translations that contains the rectangles R=Ia1×⋯×Ian−1×I−(a1+⋯+an−1)$$\begin{equation*} R = I_{a_1} \times \dots \times I_{a_{n-1}} \times I_{-(a_1+\dots +a_{n-1})} \end{equation*}$$for any a1,⋯,an−1∈An−1$a_1,\dots,a_{n-1} \in A^{n-1}$ and where Ik=[0,2k]$I_k = [0,2^k]$ for k$k$ integer. We prove that if A$A$ contains arbitrary large arithmetic progression, then the maximal operator MB$M_{\mathcal {B}}$ associated to the family B$\mathcal {B}$ satisfies a weak‐type estimate of the form MBf>t≲n∫Rn|f|t1+log+|f|tn−1$$\begin{equation*} {\left|{\left\lbrace M_{\mathcal {B}}f > t \right\rbrace} \right|} \lesssim _n \int _{\mathbb {R}^n} \frac{|f|}{t} {\left(1 + \log ^+ \frac{|f|}{t} \right)}^{n-1} \end{equation*}$$but does not satisfy a weak‐type estimate of the form MBf>t≲n∫Rnϕ|f|t$$\begin{equation*} {\left|{\left\lbrace M_{\mathcal {B}}f > t \right\rbrace} \right|} \lesssim _n \int _{\mathbb {R}^n} \phi {\left(\frac{|f|}{t}\right)} \end{equation*}$$for any nonnegative convex increasing function ϕ$\phi$ such that ϕ(x)=o(x(1+log+x)n−1)$\phi (x) = o(x(1+ \log ^+ x)^{n-1})$ as x$x$ tends to infinity. [ABSTRACT FROM AUTHOR]

Rock Quality Designation (RQD) is a common index for rock integrity evaluation in engineering. However, it is tiresome and inefficient to log core samples manually. To achieve automatic RQD analysis, we have proposed an improved model based on Cascade Mask R-CNN and an RQD analysis method for core images. First, perspective transformation is applied to calibrate the core images. Then, the improved instance segmentation model, improved by some modules (ResNet and CAFPN) and training strategies (DA and GHMC), is employed to achieve refined segmentation. Finally, the outer bounding rectangles of the segmentation masks are fitted to calculate the core length. To test the performance of the proposed model, the actual core images from hydraulic engineering are used in the research with 159 core images as the testing data. The coefficient, MAE, and RMSE are 0.9865, 1.3489, and 0.1091, respectively. It indicates that the proposed method has a high level of accuracy and promising application prospects for intelligent RQD analysis of hydraulic engineering. Highlights: The improved Cascade Mask R-CNN is proposed for rock core segmentation. Perspective transformation is applied to calibrate the images. Outer bounding rectangles are fitted to calculate the rock core length. The rock cores from practical engineering are used to validate the model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the traveling waves for a modified Holling-Tanner predator–prey model with degenerate diffusion. Different from the established approaches of constructing upper-lower solutions, we construct a new and suitable pair of upper-lower solutions by solving three differential equations and establish the existence of traveling waves for any c ≥ c ∗ when n ≥ 0 . In addition, we obtain the minimal wave speed c ∗ = 2 r when n = 0 , without reconstructing the upper-lower solutions. Furthermore, the asymptotic behavior of traveling waves at infinity is obtained by the upper-lower solutions and the contracting rectangle method. [ABSTRACT FROM AUTHOR]

Passports are the number one form of individual identification when crossing borders resulting in counterfeit or modified passports being used to allow illegal travel. Here we report on the use of Diamond Dye to detect cells deposited by touch onto parts of the photograph page of a passport. The passport page was divided into a grid of 11 rectangles of approximately equal dimensions. Thumbprints were deposited at 10 of the 11 squares, with the 11th left blank as a negative control. The location and number of deposited cells were determined and recorded. Cellular material was removed from each square separately, using a moistened swab or a tapelift. Tapelifting was better suited for the substrate resulting in an increase in DNA recovered. The highest total quantity of DNA isolated from the 10 samples post extraction was 0.162 ng. Short tandem repeat data were obtained from all 10 samples using the GlobalFilerTM PCR Amplification Kit. The DNA profiles were single source or two-person mixtures and the donor was always the major contributor. These data show the potential to visualize cellular material deposited by touch and then generate STR data from an item such as a passport after only brief physical contact. [ABSTRACT FROM AUTHOR]

A domino antimagic square of order n is an n×n array formed from a subset of the standard set of 28 dominoes such that the sums of the rows, columns, and two main diagonals form a set of 2n + 2 distinct, consecutive integers while an m × n domino antimagic rectangle is an m × n rectangular array formed from a subset of the standard set of 28 dominoes such that the sums of the rows and columns form a set of m + n distinct, consecutive integers. This paper outlines what the possible dimensions are for m×n domino antimagic rectangles and provides many examples of both domino antimagic rectangles and squares. Many open questions are given at the end of the paper for future exploration. [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]

The five-bar linkage, used in the form of a planar manipulator, benefits from easy controllability and relatively simple kinematic structures, which mean that it can be used in several applications in robotics, rehabilitation, and haptic devices, etc. This paper proposes an optimal synthesis method for a symmetrical five-bar linkage of type 5-RRRRR, with a singularity-free dexterous workspace, based on workspaces with predefined shapes, like squares, rectangles, triangles, circles, and ellipses. The synthesis conditions, to avoid singularities, are given as inequations, which can be further substituted with a system of equations, by introducing the supraunitary coefficient, k. The analytical solutions of the resulting system of equations enable the computation of the link lengths of the five-bar linkage. The optimization method provides the optimal value of the supraunitary coefficient, in order to obtain a maximum value for the minimum input transmission angle and a minimum value for the manipulator size. In this paper, the authors present an analytical approach to the optimal synthesis of a symmetrical five-bar linkage for different shapes of workspace, with the same surface and coordinates in terms of the mass center, as well as the resulting link lengths. In regard to the numerical examples, the authors considered and compared performance indices, such as manipulability, the condition number, and stiffness. The considered examples showed that an equilateral triangle-shaped workspace achieved higher global manipulability, a square-shaped workspace achieved higher global dexterity and the minimum input transmission angle, and circular workspaces achieved the highest mean stiffness and total surface size. It was observed that the synthesis method generates structures that are well-suited to singularity-free dexterous workspaces, with nonzero stiffness values. [ABSTRACT FROM AUTHOR]

We consider the fundamental problem of injectively mapping a surface mesh with disk topology onto a boundary constrained convex domain. We start from the basic observation that mapping a strip of triangles onto a rectangular shape always yields a valid embedding, if the vertices that bound the strip are sorted coherently along the sides of the rectangle. Based on this intuition, we propose a straightforward algorithm, called Stripe Embedding, that operates by decomposing the input mesh into a set of triangle strips and then embeds each strip into the target domain by means of linear interpolation between two previously embedded vertices. Thanks to its simplicity, Stripe Embedding is extremely efficient and permits to switch to an exact implementation without almost increasing its running times. Stripe Embedding is up to three orders of magnitude faster than the Tutte embedding for same numerical model and, even when implemented with costly rational numbers, it is faster than any floating point implementation of prior methods at any scale. [ABSTRACT FROM AUTHOR]

Many commentators ascribe a 'Gothic feeling' to the London churches of Nicholas Hawksmoor (1661–1736), despite their very different appearance. This study tests the hypothesis that Hawksmoor made conscious and deliberate use of the design principles and procedures of medieval Gothic architecture. New surveys were undertaken of the church interiors at three early Hawksmoor churches: St Alfege, Greenwich; St George-in-the-East; St Anne, Limehouse. The proportional relationships identified there suggest that the design process involved generating a series of squares and rectangles, based initially on the nave width, that established the principal plan dimensions. The nave width generated the nave height, which then set other significant vertical dimensions in the elevation. Hawksmoor used the medieval procedures of triangulation at St Anne and the 'rotation of squares' at St Alfege and St George-in-the-East. Taken together, these processes probably account for the perceived 'Gothic feeling'. [ABSTRACT FROM AUTHOR]

Purpose: To characterize the dose‐response, energy dependence, postexposure changes, orientation dependence, and spatial capabilities of LD‐V1, a new low‐dose Gafchromic film for low‐energy x‐ray dosimetry. Methods: A single sheet of LD‐V1 Gafchromic film was cut into 15 × 20 mm2 rectangles with a notch to track orientation. Eight different doses between 5 and 320 mGy were delivered by an MXR‐160/22 x‐ray tube using x‐ray beams of 90, 100, and 120 kVp filtered with 3 mm of Al and 2 mm of Ti. The 120 kVp films were scanned at 1, 1.5, 2, 3, 12, 24, 48, 72, and 168 h postexposure in portrait orientation and additionally scanned in landscape orientation at 24 h. The 90 and 100 kVp films were scanned at 24 h postexposure in portrait orientation. Lastly, a 20 × 200 mm2 strip of film was irradiated using a thin‐slit imaging collimator and scanned 24 h postexposure to test the film performance in an x‐ray imaging application. Results: Of the three color channels, the red channel was found to produce a dose‐response curve with a large range of net optical density (netOD) values across the considered dose range. A prominent energy dependence was discovered, resulting in dose discrepancies on the scale of 17 mGy between 90 and 120 kVp for a dose of 80 mGy. The measured postexposure changes suggest that the calibration irradiation‐to‐scan time should be longer than 12 h with a ± 4 h scanning time window for dose errors of <0.5%. An average dose difference of 3.4% was found between the two scanning orientations. Lastly, noise of 4% was measured in the thin slit collimator film for a dose of 30 mGy. Conclusions: We have characterized the LD‐V1 film for low‐energy, low‐dose x‐ray dosimetry. Energy, scan‐time, and orientation dependencies should be considered when using this film. [ABSTRACT FROM AUTHOR]

This study investigates plate analyses employing the method of initial functions (MIFs) across various plate geometries and loading conditions. The conclusions derived from thick rectangular plates highlight substantial thickness‐induced effects on deflection and stress distributions. For thicker plates, the classical assumption of constant deflection fails, with maximum deflection often occurring at surfaces other than the middle plane. The classical and Reissner theories' constant deflection assumption leads to significant discrepancies in thick plate deflection estimates, emphasizing the need for MIFs more accurate approach. Similarly, in the case of thick circular plates, deviations from classical theory are evident in radial and shear stress distributions, particularly pronounced closer to the plate edge and support. These deviations dissipate further away from these regions. Moreover, the study delves into free vibration analyses for rectangular and circular plates, revealing that classical theory tends to overestimate frequencies, especially as plate dimensions increase. Mindlin's theory and MIF approaches showcase improved accuracy with increasing order, converging toward exact solutions. Additionally, Mindlin's theory effectively captures the behavior of higher vertical modes, showcasing sign changes in characteristic quantities of the plate. The findings underscore the limitations of classical theories in accurately predicting plate behaviors, especially in thicker plates and higher modes of vibration. Conversely, the MIF method, alongside Mindlin's theory, proves effective in providing nuanced insights into plate behaviors under various conditions, thus offering valuable implications for structural design and analysis. [ABSTRACT FROM AUTHOR]

Deep neural networks have been remarkably successful as models of the primate visual system. One crucial problem is that they fail to account for the strong shape-dependence of primate vision. Whereas humans base their judgements of category membership to a large extent on shape, deep networks rely much more strongly on other features such as color and texture. While this problem has been widely documented, the underlying reasons remain unclear. We design simple, artificial image datasets in which shape, color, and texture features can be used to predict the image class. By training networks from scratch to classify images with single features and feature combinations, we show that some network architectures are unable to learn to use shape features, whereas others are able to use shape in principle but are biased towards the other features. We show that the bias can be explained by the interactions between the weight updates for many images in mini-batch gradient descent. This suggests that different learning algorithms with sparser, more local weight changes are required to make networks more sensitive to shape and improve their capability to describe human vision. Author summary: When humans recognize objects, the cue they rely on most is shape. In contrast, deep neural networks mostly use local features like color and texture to classify images. We investigated how this difference arises, using images of simple shapes like rectangles and the letters L and T, combined with color and texture features. By testing different feature combinations, we show that some networks are generally unable to learn about shape, whereas others could learn to recognize shapes in isolation, but ignored shape if another feature was present. We show that this bias for color and texture arises from the way in which networks are trained: by averaging the learning signal over many images, the training algorithm favors simple features that are relatively similar in many images and removes sparser, more varied shape features. These insights can help build networks that are more sensitive to shape and work better as models of human vision. [ABSTRACT FROM AUTHOR]

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]

In this paper, we focused on forced waves in the Leslie-Gower predator-prey system in shifting habitats with nonlocal dispersal. We demonstrated existence of two types of forced waves, namely, I: mixed front-pulse type forced waves, and II: front type forced waves. By applying the Schauder's fixed-point theorem and upper-lower solutions method, we established the existence of type I forced waves invading the state where only one species exists in both super-critical and critical cases. Besides, for any speed $ c $, we proved the existence of type II forced waves invading the coexistence state using contracting rectangles methods. Particularly, due to the gradual deterioration of the environment over time, both predator and prey will eventually become extinct. [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]

Two new Cu(II)-based structures containing alternating chains and their magnetic properties are reported. Reaction of CuBr2 and 2-aminopyridine in methanol yielded [(2-aminopyridine)μ-Br(μ-OMe)Cu]n (1) which crystallizes in the triclinic space group P-1. Cu(II) ions are linked alternately by bibromide and bi-methoxide bridges into chains parallel to the a-axis. Reaction of copper perchlorate hexahydrate with 4-pyridone and pyrazine in methanol yielded [(μ-pz)(μ-κ-O-4-pyridone)2(μ-OH)2Cu2]n(ClO4)2n (2). The Cu(II) ions are alternately linked by bihydroxide and bi-κ-O-4-pyridone species parallel to the a-axis. Those chains are further linked by bridging pyrazine molecules ∼ parallel to the b-axis, with the pyrazine molecules and bi-hydroxide bridges alternating. The net effect is a rectangular lattice where each side of the rectangle is an alternating chain. The layers are separated by perchlorate ions. Both compounds are diamagnetic at room temperature. [ABSTRACT FROM AUTHOR]

This paper focuses on the propagation threshold of a cooperative–competitive reaction–diffusion system based on a sexually transmitted disease model, which involves two stains and four unknown functions. Considering the competition‐exclusion process between two different strains, it is possible to obtain a cooperative system in proper domain after taking a linear transformation. However, the corresponding cooperative system is not always subhomogeneous and the invariant region is not always a rectangle. Using the propagation theory for monotone semiflows, we obtain a unique threshold no matter whether it is linearly selected, which allows us to numerically estimate the speed. The threshold is proved to be linearly selected under certain conditions by constructing proper upper solutions. Moreover, we numerically show that the threshold may be nonlinearly selected. [ABSTRACT FROM AUTHOR]

A common design solution of wideband filtering antennas inspired by the synthesis of a flat‐top gain curve is proposed by using mutual coupling effects. The realization of a frequency‐varied flat‐top gain curve based on specially designed subarrays is analyzed. Analysis results conclude a design process of generating filtering response based on shorting pins and parasitic structures. A single‐layer rectangle patch array loaded with parasitic shorted patches is designed and analyzed for the validation. The proposed antenna possesses an impedance bandwidth of 4.95–6.05 GHz and a peak realized gain of 11.2 dBi. Besides, the design has its out‐of‐band rejection levels higher than 15 dB. [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]

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]

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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]

Cutting and Packing problems have been recognized as a sub-discipline of operation research for more than half a century. Such problems are involved in a range of circumstances such as pallet loading, wood or glass cutting, strip packing, and positioning problems. The focus of this study is on 2D rectangular strip packing problems in which rectangle items are not oriented and guillotine constraint is not considered aiming to pack all these items without overlapping into an open-ended bin called a strip of fixed width while the objective is obtaining the minimum total height of cutting. The main aim of this paper is to introduce two proposed heuristics for solving the problem under study. The two heuristics are improved versions of the known Best Fit heuristics, Tower Checker Best Fit (TCBF) and Waste Priority Best Fit (WPBF). The performance of the proposed heuristics is tested using well-known benchmark problems. The computational analysis of the results shows that the proposed heuristics can generate near-optimal solutions to large-scale problems. In addition, the performance of the heuristics outperforms other well-known heuristics from literature by 3%. [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]

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]