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This note introduces a quaternionic inspired product of triples of collinear points and consequently a product of their simple ratio. Some technical conditions are necessary for the existence of these products and some general examples (squares, the arithmetic and the geometric means) are discussed. Moreover, some concrete computations are performed and then some periodic ratios are obtained. [ABSTRACT FROM AUTHOR]

In mathematics, a dissection of a square (or rectangle) into non-congruent rectangles is a Mondrian partition. If all the rectangles have the same area, it is called a perfect Mondrian partition. In this paper, we present a computational result by which we can affirm that there is no perfect Mondrian partition of a length n square for n ≤ 1000. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a n × m rectangle for n , m ≤ 400. [ABSTRACT FROM AUTHOR]

In this paper, we propose a path planning method with graph search considering localizability. Localizability is a measure of the reliability of localization. This paper aims to plan paths that avoid places with low reliability of localization by considering localizability. In the proposed method, we constructed a graph based on occupancy grid maps and planned optimal paths by graph search. Localizability costs were considered as path costs for graph search. In our experiments, path planning was performed in three environments: a corridor environment with parallel walls, a square environment larger than the sensor measurement range, and a real environment. Experimental results confirmed that the proposed method planned paths to avoid places with low reliability of localization, such as parallel wall corridors or the center of squares where the sensor scans cannot be obtained. In addition, we conducted comparative experiments between the paths planned by our method and those planned without considering localizability costs. We confirmed that the paths of the proposed method have lower localizability costs and lower localization errors. [ABSTRACT FROM AUTHOR]

Eu3+‐activated red‐emitting inorganic phosphors have been favored highly for their classical 5D0→7FJ (J = 0, 1, 2, 3, 4) emissions. However, the fatal drawbacks of poor luminous efficacy and weak 5D0→7F4 transition persist, resulting in the ongoing challenge of achieving far‐red emission. This research reports series of highly efficient far‐red phosphors LnTeBO5 (Ln = La3+, Y3+, Gd3+):Eu3+ with anomalously strong 5D0→7F4 transition, resulting from the distorted square antiprism [Ln/EuO8]. Both the luminous efficacy and thermal stability can be greatly enhanced via the simple composition variation. [Ln/EuO8] square antiprism‐triggered 5D0→7F2,4 transitions are elucidated in depth, acquiring ultra‐high luminous efficacy (IQE = 95%, EQE = 40%, and AE = 42%) and near‐zero thermal quenching (99%@150°C and 98%@200°C). Subsequently, the versatile utilizations in indoor lighting, plant growth lighting, and security ink are illustrated. This finding establishes a deep understanding for constructing high‐quality far‐red phosphors via the Eu3+‐centered structural units of square antiprism. [ABSTRACT FROM AUTHOR]

Several articles deal with tilings with various shapes, and also a very frequent type of combinatorics is to examine the walks on graphs or on grids. We combine these two things and give the numbers of the shortest walks crossing the tiled (1 × n) and (2 × n) square grids by covering them with squares and dominoes. We describe these numbers not only recursively, but also as rational polynomial linear combinations of Fibonacci numbers. [ABSTRACT FROM AUTHOR]

In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lamé system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial boundaries of inclusions tends to zero. The primary aim of this paper is to give a sharp description in terms of the asymptotic behavior of the stress concentration, as the distance between interfacial boundaries of inclusions goes to zero. For that purpose, we capture all the blow‐up factor matrices, whose elements comprise of some certain integrals of the solutions in the case when two inclusions are touching. Then, we are able to establish the asymptotic formulas of the stress concentration in the presence of two close‐to‐touching m$$ m $$‐convex inclusions in all dimensions. Furthermore, an example of curvilinear squares with rounded‐off angles is also presented for future application in numerical computations and simulations. [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]

ABSTRACT The square of a graph G $G$, denoted G 2 ${G}^{2}$, has the same vertex set as G $G$ and has an edge between two vertices if the distance between them in G $G$ is at most 2. In general, Δ( G ) + 1 ≤ χ( G 2 ) ≤ Δ ( G ) 2 + 1 ${\rm{\Delta }}(G)+1\le \chi ({G}^{2})\le {\rm{\Delta }}{(G)}^{2}+1$ for every graph G $G$. Charpentier (2014) asked whether χ( G 2 ) ≤ 2 Δ( G ) $\chi ({G}^{2})\le 2{\rm{\Delta }}(G)$ if mad( G ) < 4 $\mathrm{mad}(G)\lt 4$. But Hocquard, Kim, and Pierron (2019) answered his question negatively. For every even value of Δ( G ) ${\rm{\Delta }}(G)$g, they constructed a 2‐degenerate graph G $G$ such that ω( G 2 ) = 5 2 Δ( G ) $\omega ({G}^{2})=\frac{5}{2}{\rm{\Delta }}(G)$. Note that if G $G$ is a 2‐degenerate graph, then m a d( G ) < 4 $mad(G)\lt 4$. Thus, we have that 5 2 Δ( G ) ≤ max{ χ( G 2 ) : G is a 2‐degenerate graph } ≤ 3 Δ( G ) + 1 . $\frac{5}{2}{\rm{\Delta }}(G)\le \max \{\chi ({G}^{2}):G\,\,\text{is a 2\unicode{x02010}degenerate graph}\,\}\le 3{\rm{\Delta }}(G)+1.$So, it was naturally asked whether there exists a constant D 0 ${D}_{0}$ such that χ( G 2 ) ≤ 5 2 Δ( G ) $\chi ({G}^{2})\le \frac{5}{2}{\rm{\Delta }}(G)$ if G $G$ is a 2‐degenerate graph with Δ( G ) ≥ D 0 ${\rm{\Delta }}(G)\ge {D}_{0}$. Recently, Cranston and Yu (2024) showed that ω( G 2 ) ≤ 5 2 Δ( G ) + 72 $\omega ({G}^{2})\le \frac{5}{2}{\rm{\Delta }}(G)+72$ if G $G$ is a 2‐degenerate graph, and ω( G 2 ) ≤ 5 2 Δ( G ) + 60 $\omega ({G}^{2})\le \frac{5}{2}{\rm{\Delta }}(G)+60$ if G $G$ is a 2‐degenerate graph with Δ( G ) ≥ 1729 ${\rm{\Delta }}(G)\ge 1729$. We show that there exists a constant D 0 ${D}_{0}$ such that ω( G 2 ) ≤ 5 2 Δ( G ) $\omega ({G}^{2})\le \frac{5}{2}{\rm{\Delta }}(G)$ if G $G$ is a 2‐degenerate graph with Δ( G ) ≥ D 0 ${\rm{\Delta }}(G)\ge {D}_{0}$. This upper bound on ω( G 2 ) $\omega ({G}^{2})$ is tight by the construction in Hocquard, Kim, and Pierron. [ABSTRACT FROM AUTHOR]

The author considers the problem of preserving the direction of movement by a collective of finite automata on a two-dimensional integer lattice of width two whose elements (vertices) are anonymous. The automata do not distinguish between equally labeled vertices by their direction coordinates (i.e., each automaton has no compass). The collectives consisting of a single automaton and several pebbles whose layout is completely determined by the automaton are considered. It is proved that a collective of an automaton and a maximum of three pebbles cannot maintain movement direction on the lattice, but a collective of an automaton and four pebbles can. [ABSTRACT FROM AUTHOR]

A polyomino is a finite set of unit squares joined side by side on the Cartesian plane. Qureshi introduced an ideal constructed from a polyomino which is called "polyomino ideal". In this paper, we study the binomials arising from Buchberger Algorithm on polyomino ideals. We also introduce socket wrench polyominoes and study the Gröbner bases of the ideal IP and some algebraic properties of K[P]. [ABSTRACT FROM AUTHOR]

There are two regular polygons Pn-(R1) and Pn-(R2) which correspond to the given polygonal distances {d1, d2, ..., dn. It is proved that the radii R1, R2 of the circumcircles of the regular polygons and the n distances are connected by the system: ... where m = 1, ..., n - 1. The solutions for the equilateral triangles and the squares are investigated. The two-parametric families of the solutions are given in both cases, when three distances are rational numbers. [ABSTRACT FROM AUTHOR]

Copyright of Lesan-on Mobeen-on is the property of Imam Khomeini International University 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.)

Copyright of Mağallaẗ Al-Dirāsāt Al-Tārīẖiyyaẗ wa Al-Ḥaḍāriyyaẗ Al-Miṣriyyaẗ is the property of Beni Suef University 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.)

Copyright of Rouya Turkiyyah is the property of Insight Turkey 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.)

We show the consistency, relative to the appropriate supercompactness or strong compactness assumptions, of the existence of a non-supercompact strongly compact cardinal $\kappa _0$ (the least measurable cardinal) exhibiting properties which are impossible when $\kappa _0$ is supercompact. In particular, we construct models in which $\square _{\kappa ^+}$ holds for every inaccessible cardinal $\kappa $ except $\kappa _0$ , GCH fails at every inaccessible cardinal except $\kappa _0$ , and $\kappa _0$ is less than the least Woodin cardinal. [ABSTRACT FROM AUTHOR]

Background & Purpose: To find whether four square step test has a statistically significant correlation with timed up and go test or not in case of ambulant chronic stroke patients. Subjects: Twenty-seven chronic stroke patients with mean age 58.70 ± 6.75 years participated in the study. The mean time from stroke was 26.48 ± 12.73 months, and all subjects were community ambulators. Methods: The study used a Co relational study design. Subjects performed both four square step test with timed up and go test at different timing of day. Result: The result of our study showed highly significant correlation between four square step test and timed up & go test (r = .983, p<0.05) in chronic stroke patient. Discussion & Conclusion: The FSST is easy to perform and provide a quantitative measure of the ability to quickly change direction while lifting the feet off the ground. The FSST assess the ability to change direction quickly and it takes minimum space and time to administer the test. Hence, the Four Square Step Test is better test to measure dynamic balance in ambulatory chronic stroke patients. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce the normalized tail of the Maclaurin power series expansion of the square of the tangent function, find out the logarithmic convexity of the normalized tail in light of the monotonicity rule for the ratio of two series, and expand the logarithm of the normalized tail into a Maclaurin power series with the help of a formula for higher order derivatives of the ratio of two differentiable functions. [ABSTRACT FROM AUTHOR]

The structural response of simply supported Reinforced Concrete (RC) beams with square vertical openings is investigated in this work. Studies were conducted using seven specimens of RC beams, with the aim of comparing beams with vertical openings to those without. Meanwhile, the other beams featured carefully positioned square openings. Note that one of these beams served as the control and had no openings. Each beam was the same length (1400 mm) with a 180×120 mm cross-section. Two-point loads were applied over a span of 1200 mm throughout the testing method, with a central load placed 300 mm from the ends. The openings were positioned in the middle of the span and came in three different widths: 20, 40, and 60 mm. Openings were made using either 1.5 mm thick square steel tubing or none at all. The major goal of this study was to determine whether the steel tube could compensate for the decrease in beam strength and the impact of decreasing beam cross-section (producing opening). Correspondingly, the beam ultimate load was found to decrease by 15.75%, 24.2%, and 32.5% for opening widths of 20 mm, 40 mm, and 60 mm, respectively, as the opening width increased. On the other hand, the performance gain for beams strengthened with steel plates when steel tubes were used was 11.78%, 12.14%, and 13.28% for the respective opening widths. [ABSTRACT FROM AUTHOR]

The manuscript presents the design and investigation of square and L-shaped graphene plasmonic nano-antenna arrays on a silicon dioxide substrate for plasmonic biosensing applications. The design parameters, such as the shape of the nanostructure, spacing between the antenna array elements, size of the antenna array and chemical potential of the graphene are used to analyze the plasmonic resonance characteristics of the proposed plasmonic nano-antenna array. Initially, dispersive characteristics of graphene, such as conductivity, permittivity and refractive index are analyzed using its chemical potential for the validation of the graphene material for plasmonic sensing applications. The proposed square and L-shaped nanopatch antenna structures are radiating at 30 THz with a reflection coefficient of -28.4 dB and − 44.6 dB respectively at 0.1 eV chemical potential. It is observed that graphene nanopatch antenna radiates at 30 THz, 115 THz and 176 THz at a chemical potential of 1.3 eV. Further, the study demonstrated that the designed square and L-shaped nano-antenna exhibit a gain of 3.52 dB and 9.51 dB respectively at 30 THz. The gain can be increased further using a square and L-shaped nano-antenna array of dimensions 2 × 2, 3 × 3 and 4 × 4. It is observed that maximum gains of 33.44 dB and 30.86 dB are obtained for the square and L-shaped 4 × 4 plasmonic nanoarray antenna respectively. Finally, a nanocircuit model of square and L-shaped nano-antennas is proposed and validated through CST simulations. [ABSTRACT FROM AUTHOR]

Between January and March 2022, crew aboard the International Space Station (ISS) performed the first archaeological fieldwork in space, the Sampling Quadrangle Assemblages Research Experiment (SQuARE). The experiment aimed to: (1) develop a new understanding of how humans adapt to life in an environmental context for which we are not evolutionarily adapted, using evidence from the observation of material culture; (2) identify disjunctions between planned and actual usage of facilities on a space station; (3) develop and test techniques that enable archaeological research at a distance; and (4) demonstrate the relevance of social science methods and perspectives for improving life in space. In this article, we describe our methodology, which involves a creative re-imagining of a long-standing sampling practice for the characterization of a site, the shovel test pit. The ISS crew marked out six sample locations ("squares") around the ISS and documented them through daily photography over a 60-day period. Here we present the results from two of the six squares: an equipment maintenance area, and an area near exercise equipment and the latrine. Using the photographs and an innovative webtool, we identified 5,438 instances of items, labeling them by type and function. We then performed chronological analyses to determine how the documented areas were actually used. Our results show differences between intended and actual use, with storage the most common function of the maintenance area, and personal hygiene activities most common in an undesignated area near locations for exercise and waste. [ABSTRACT FROM AUTHOR]

Suppose that R α is a rhombus with side length 1 and with acute angle α . Let { S n } be any collection of squares. In this note a tight upper bound of the sum of the areas of squares from { S n } that can be parallel packed into R α is given. [ABSTRACT FROM AUTHOR]

Background. The evolution of the urban landscape and the interaction of citizens with it is an integral part of the appearance of the city, which is reflected in the historical memory of the population. The participation of the population in urban improvement and landscaping is one of the factors in the formation of love for a small homeland. The study of this issue will allow us to analyze the ongoing policy of greening the city and the impact of green space on the image of the city. The purpose of the study is to analyze the daily practices of interaction of the population with the green space of Penza in the 19th – 20th centuries. Materials and methods. The daily practices of interaction of the population with the green space of Penza in the 19th – 20th centuries are considered on the basis of an analysis of the policy of local authorities on greening the urban area. The source base con-sisted of archival documents, materials from local and central periodicals (Pravda, Izvestia, Trud, etc.), memoirs of contemporaries. The research methodology is based on the princi-ples of the historical and systematic method, which allows us to analyze the effectiveness of regional greening policy. The historical and genetic method allows us to trace the trans-formation of the green zones of the Penza urban space. Results. The greening policy of Penza in the 19th – 20th centuries is considered. The ways of interaction of the population with green areas of urban space are revealed. The influence of landscaping on the image of the city in the perception of the population is analyzed. Conclusions. The good landscaping of Penza in the 19th century was due to the geographical location and the use of the natural landscape. The main green area during this period was a public garden and a country party. With the growth of the city's territory in the 20th century and a purposeful greening policy, much more green areas appear in the city. At the same time, the Central Park of Culture and Recreation named after V.G. Belinsky and the adjacent alleys retained their importance. It should be noted that the population was actively involved in the process of greening the city. All this contributed to the consolidation of the adjective “green” in relation to Penza in the historical memory of the population.

In harmony with other aspects of civilization, Iranian cities, in the face of modernity, have taken a new step in their existence and, alongside the physical transformation and the emergence of architectural and urban spaces with a new configuration, have experienced a novel dimension of social space. Baharestan Square is a tangible example of this new spatial arrangement, which at the end of the Qajar era, outside the established order, transformed into a center of social activism and the libertarianism of the constitutionalists. This study, within the framework of a critical paradigm, seeks to explore the factors and forces that have shaped Baharestan Square as a civic space in modern urban order in the historical space-time of Tehran during the constitutional era. It aims to give voice to the overlooked aspects of this experience by narrating its social space, contrary to one-sided physical or symbolic analyses. Civic space, as the final layer of urban public space, is a living space that, with society’s dominance over it, becomes a discursive and socio-political platform for citizens, allowing the free spirit of society to regenerate through the support of its institutions. Based on the interpretation of this study, Baharestan Square, during the constitutional era, became the possession of the constitutionalists, backed by urban independence and detachment from the cohesive network of public spaces, creating a discursive platform through the presence of the progressive institution of the parliament, associations, and affiliated organizations, as well as the diversity and multiplicity resulting from the formation of a modern society, and also, pursuing demands and litigations with the establishment of the dualism of the government and the nation, which, along with fundamentally disrupting the traditional governing order, brought the social life of the city into a completely novel existence and introduced a new experience of placemaking in the public spaces of the city.

Compliance with the requirements for landscape and recreational areas in urban planning and development is a prerequisite for ensuring the sanitary well-being and comfortable living of the population. Therefore, the purpose of the presented work was to assess the green and other public landscape and recreational areas within the Ivano-Frankivsk, as well as to provide recommendations for greening the city and its improvement. Theoretical research methods were applied, including the collection and systematisation of regulatory and reporting information on public landscape and recreational areas within the Ivano-Frankivsk; analysis of compliance with the requirements of Ukrainian legislation; and generalisation of problems to provide recommendations for improving the city’s amenities. It has been established that as of the beginning of 2024, the total area of existing green spaces is about 126 ha and is represented by five city parks, one dendrological park, and 58 squares. There are 5.3 m2 of green space per person, which is almost twice as low as the norm (10 m2/person). In 2021-2023, the city council has planned to build 41 new squares with a total area of 31.46 ha, which will increase the specific area of green spaces to 6.6 m2/person. It was found that the average level of greenery in squares is 72%. There are seven areas and objects of the Nature Reserve Fund of Ukraine in the city, and the coverage of protected areas is less than 1%. The territory of the Emerald Network “Bystrytsia Nadvirna Valley” within the city and adjacent villages has been significantly transformed and urbanised and is used as a recreation area, which may affect protected species. The city’s water bodies are only partially equipped with recreation areas. Measures to green the city and improve its amenities are proposed, including the creation of green spaces in residential neighbourhoods and along roads, the use of green elements on the walls of buildings, and the organisation of meadow parks. The practical value of the results is to highlight the current and future state of the public landscape and recreational area network in Ivano-Frankivsk and to provide reasonable recommendations for its improvement

AbstractHierarchical tubes have been proved to be excellent energy absorbers under axial compression. However, there are limited studies exploring their oblique crushing performance. Therefore, the oblique crushing characteristics of hierarchical tubes, bio-inspired hierarchical multi-cell square tubes (BHMS), hierarchical multi-cell square tubes (HMSA and HMSB), have been numerically studied. The influencing factors of loading angle and hierarchical order on deformation modes, force-displacement curves, and energy absorption (EA) behaviors were explored. It is found that BHMS tubes present the superior crushing performance among these hierarchical square tubes. Moreover, BHMS tubes display the excellent crushing characteristics in comparison with single square tubes. Specifically, the specific EA of BHMS-3 tubes is 213%, 212%, 66%, and 42% greater than that of single square tubes at loading angles of 0°, 10°, 20°, and 30°. The findings demonstrate the priority of hierarchical square tubes under oblique crushing, and provide the reference and insight for the design of energy absorbers. [ABSTRACT FROM AUTHOR]

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. This article explores generalizations of the Pythagorean theorem using classical Euclidean plane geometry tools. It introduces innovative extensions that shed new light on the theorem's geometric relationships. [ABSTRACT FROM AUTHOR]

The term 'Asymmetric Propeller' and studies on it appeared first in [1] by Bankoff, Erdos and Klamkin, it was in [2] by Alexanderson, and more recently in [3] by Gardner. The original propeller theorem refers to three congruent equilateral triangles that share the same vertex. [ABSTRACT FROM AUTHOR]

Cauliflower (Brassica oleracea var. botrytis L.) is an agricultural commodity with high market demand because it has many benefits as well as vitamins and minerals. The research of this study was to determine the types of varieties and the use of better planting layouts on the growth and production of cauliflower plants. The research was carried out from March to June 2023 in the experimental field of the Faculty of Agriculture, Brawijaya University, located in the Jatimulyo Village, Lowokwaru District, Malang City. This study was arranged using a randomized block design (RBD) with 3 varieties and 2 planting layouts so that there were 6 treatment combinations with 4 replications, include: P1: Orient variety + Square, P2: Orient variety + Zig-zag, P3: PM 126 variety + Square, P4: PM 126 variety + Zig-zag, P5: Bima variety + Square, P6: Bima variety + Zig-zag. Observations were made on plant growth parameters and crop harvest parameters. Growth observations were carried out destructively and nondestructively, while yield observations were made at the time of harvesting. The results of this study indicate that the Orient, PM 126, and Bima varieties with a square planting layout compared to the Bima variety with a zig-zag planting layout obtained the same plant length and are relatively longer, the Orient and PM 126 varieties with a square planting layout and zig-zag yields relatively larger leaves than the Bima variety with a zig-zag planting layout. The Orient, PM 126, and especially Bima varieties with various planting layout treatments gave the same yields per plant and per hectare, ranging from 239.38-253.4 g/plant and 17.95-19.00 ton.ha-1. [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]

The given text discusses the design and construction of the Cody Dock Bridge in London, which uses classical geometry and a unique wheel shape to allow boats to pass beneath it. The bridge is able to be smoothly rolled to an upside-down position, relying on a geometric result discovered by James Clerk Maxwell and a preindustrial ethic that emphasizes balance and the ability to be moved by hand. The design process involved addressing various challenges, such as maintaining smooth motion, dealing with wear and tear, and ensuring stability in both normal and inverted positions. The bridge's behavior during the roll was predicted through structural analysis, and its weight and center of gravity were optimized to minimize frictional forces. The bridge design is tied to its functionality and environment, using weathering steel and oak strips for the rolling mechanism. The text also discusses the use of catenary curves in bridge construction and explores the suitability of other shapes for bridge design. [Extracted from the article]

The diagonals–parameter symmetry (DPS) model is a proposed method for analyzing square contingency tables with ordinal categories. Previously, it was stated that the generalized DPS (DPS[f]) model was equivalent to the DPS model for any function f, but the proof was not provided. This paper presents the derivation of the DPS[f] model and the proof of the relationship between the two models. The findings offer various interpretations of the DPS model. Additionally, a new model is considered, and it is shown that the proposed model and the DPS[f] model are separable. [ABSTRACT FROM AUTHOR]

Objective: To compare the mean differences in gain in length after post-burn contracture release by z-plasty and square flap. Study Design: Case Series Place and Duration of Study: Plastic and Reconstructive Surgery Department, Dr Ruth KMPfau Civil Hospital, Karachi Pakistan, from Apr to Sep 2021. Methodology: Sixty patients were divided as Z-plasty and square flap groups. The length of the contracture zone was measured. Z-plasty was performed to improve the functional and cosmetic appearance of the scar. A square flap was made to release the contracture. Splintage was maintained for two weeks after its release. Results: The mean contracture length three weeks after Z-plasty release was 7.12±4.14cm and 15.39±4.66cm in square flap. Significant mean differences among techniques were observed among contracture length (p=0.001) and gain in length (p=0.001). The cubital fossa was the most common region treated with Z-plasty, while the finger was the most common region treated with square flap. The results showed a highly significant association of regions with respect to surgical techniques (p=0.001). An insignificant association was observed between gender (p=0.436) and cause of burn (p=0.136). Conclusion: The square flap technique provides greater length gains than a Z-plasty technique. [ABSTRACT FROM AUTHOR]

The use of carbon fiber–reinforced polymer (CFRP) grid-reinforced engineered cementitious composite (CFGRE) systems to strengthen concrete-filled steel tubes (CFSTs) offers potential to improve the structural response as well as the resistance to high temperatures and corrosion. This study consists of an experimental investigation on the behavior of eccentrically loaded square CFSTs strengthened with CFGRE systems. Nineteen specimens were tested using a compression-testing machine with loads, deformations, and recorded test observations. The investigated parameters included the number of CFRP grid layers, width-to-thickness ratio of a steel tube, concrete strength grade, and eccentric ratio. The strengthened columns exhibited ductile failure. Due to stress concentrations, the CFGRE systems ruptured at the corners on the compression side. After strengthening, the yielding and ultimate loads of the CFST columns increased from 21.8% to 53.5% and 21.1% to 34.9%, respectively. Although an increase in the number of CFRP grid layers did not significantly affect the bearing capacities of the square specimens, it significantly enhanced the ductility of the columns. An increase in the eccentric ratio weakened the confining effect. An average decrease of 9.7%, 27.6%, and 41.4% was observed in the ultimate loads of the strengthened columns when the eccentric ratio increased from 0 to 0.1, 0.25, and 0.4, respectively. A five-point N–M interaction model was developed based on the principles of force equilibrium and deformation compatibility to predict the eccentric bearing capacities of strengthened columns. The prediction results exhibited high accuracy. [ABSTRACT FROM AUTHOR]

Suppose that (,) is an obtuse triangle with base length 1 and with base angles and (where > 90◦). In this note a tight lower bound of the sum of the areas of squares that can parallel cover (,) is given. This result complements the previous lower bound obtained for the triangles with the interior angles at the base of the measure not greater than 90◦. [ABSTRACT FROM AUTHOR]

Copyright of Builder (1896-0642) is the property of PWB MEDIA Zdzieblowski sp.j. 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.)

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]

Due to the widespread applications of curves on n‐dimensional spheres, fitting curves on n‐dimensional spheres has received increasing attention in recent years. However, due to the non‐Euclidean nature of spheres, curve fitting methods on n‐dimensional spheres often struggle to balance fitting accuracy and curve fairness. In this paper, we propose a new fitting framework, GLS‐PIA, for parameterized point sets on n‐dimensional spheres to address the challenge. Meanwhile, we provide the proof of the method. Firstly, we propose a progressive iterative approximation method based on geodesic least squares which can directly optimize the geodesic least squares loss on the n‐sphere, improving the accuracy of the fitting. Additionally, we use an error allocation method based on contribution coefficients to ensure the fairness of the fitting curve. Secondly, we propose an adaptive knot placement method based on geodesic difference to estimate a more reasonable distribution of control points in the parameter domain, placing more control points in areas with greater detail. This enables B‐spline curves to capture more details with a limited number of control points. Experimental results demonstrate that our framework achieves outstanding performance, especially in handling imbalanced data points. (In this paper, "sphere" refers to n‐sphere (n ≥ 2) unless otherwise specified.) [ABSTRACT FROM AUTHOR]

Achieving three-dimensional (3D) omnidirectional wireless power transfer (OWPT) without any active control is challenging. This paper proposes a square polyhedron transmitter (SPTx) based on the reverse current of parallel coil, which can create a 3D omnidirectional magnetic field. To minimize the counteracting of the reverse magnetic field, each coil is equipped with magnetic shielding material. The coils of SPTx are connected in series and excited by a single power supply without any current amplitude or phase control circuits. The performance of SPTx system is validated with different receivers (Rx) by experiments. In the experiment with dual Rxs, the maximum transmission efficiency is 79.6% with an efficiency stability rate of 49%. In addition, the output power does not affect the efficiency, and more Rxs will increase transmission efficiency. [ABSTRACT FROM AUTHOR]

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For composite metal foam structures to be used as load‐bearing and energy‐absorbing elements, comprehensive testing should be done. Therefore, an extensive characterization of foam‐filled structures by various load types, such as axial and lateral compression, as well as three‐point bending, is carried out, aiming to differentiate the behavior of various cross‐sectional geometry foam‐filled hollow sections and the application of a tough epoxy adhesive and a ductile polysiloxane adhesive. Applying the epoxy adhesive improves the overall energy absorption by 10% during axial compression compared to the sum of the foam and empty hollow section. The application of the polysiloxane adhesive over the epoxy one increases the deflection at failure during three‐point bending by an average of 58%. The deformation and strength during axial compression and three‐point bending are hollow section dominated, while the foam core dominates the deformation and the strength during lateral compression for both produce composite foam‐filled hollow sections with epoxy and polysiloxane adhesive bonding. [ABSTRACT FROM AUTHOR]

We study the phase transitions of the two-dimensional (2D) frustrated J 1- J 2 Ising model on the square lattice with Monte Carlo simulations. Here J 1 < 0 and J 2 > 0 are the couplings for the nearest and next nearest neighbor Ising spins, respectively. In addition, we consider J 1 = −1 and J 2/| J 1| ≡ g = 0.56, 0.58, 0.60, 0.62, 0.64, and 0.7 in our investigation. Several physical quantities including the Binder ratio U , the specific heat Cv , and the energy density E are obtained. The analyses of these calculated observables indicate that the considered phase transitions for g ≥ 0.58 are likely second order, and the nature of the phase transition associated with g = 0.56 needs further investigation. A comparison between the histograms of E for the phase transitions considered here and the one associated with the five-state ferromagnetic Potts model on the square lattice is conducted. The outcomes imply that if the studied phase transitions are weakly first order, then they have much larger correlation lengths than that of the five-state Potts model. [ABSTRACT FROM AUTHOR]

The most important thing that distinguishes art from all other human activities is that it goes beyond mere depiction of reality, as it contains a minimum of idealism, and transcends it on its familiar daily scale; This was one of the goals of the expressive abstract school, which appeared in the mid-fifties of the twentieth century in the United States of America, and then spread in Europe, and its most important components were that drawing or painting is based on a theory that says that colors, lines, and shapes, if used freely In an informal structure, I am more able to express and delight the eye than when it is used according to formal concepts or when it is used to represent things, and among its most prominent pioneers (Hans Hoffmann, Jackson Pollock, Wassily Kandinsky..). In the past, this artistic movement was based on surrealism, focusing on spontaneous or unconscious creativity, which is concerned with abstracting and simplifying lines, and all of this contributed to finding new plastic design solutions for artwork, which helped in creating a contemporary wall design for the square of Dakahlia Governorate in Mansoura. The mural design of the governorate square documents the history of Dakahlia, its landmarks, its monuments, the most important prominent personalities to which it belongs, as well as the important events that occurred throughout history, as well as the features of modernity that characterized the architecture in the new city of Mansoura, and the most important agricultural crops produced by Dakahlia such as (cotton The Egyptian and the rice...) and others, all of these elements came in a contemporary artistic composition dominated by the modern expressive abstract style in design and processing, in addition to the implementation of a group of murals using mosaic technology on wood for detailed parts of the artistic design, with Explanation of the method of preparation, implementation and materials used. It is one of the researcher's artistic experiments, in which she tried to benefit from the modern abstract expressive school in creating contemporary murals that combine originality and modernity in Dakahlia Governorate.

Since the Software Quality Model was defined as an international standard, many quality assurance teams have used this quality model in a waterfall model for software development and quality control. As more software is delivered as a cloud service, various methodologies have been created with an awareness of the link between development productivity and operations, enabling faster development. However, most development methods are development-oriented with awareness of development progress, and there has been little consideration of methods that achieve quality orientation for continuous quality improvement and monitoring. Therefore, we developed a method to visualize the progress of software quality during development by defining quality goals in the project charter using the quality model defined in international standards, classifying each test by quality characteristics, and clarifying the quality ensured by each test. This was achieved by classifying each test by quality characteristics and clarifying the quality ensured by each test. To use quality characteristics as KPIs, it is necessary to manage test results for each test type and compare them with past build results. This paper explains how to visualize the quality to be assured and the benefits of using quality characteristics as KPIs and proposes a method to achieve rapid and high-quality product development.