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In this article, a simple refined shear deformation theory that eliminates the use of a shear correction factor was presented for buckling analysis of in-plane bi-directional functionally graded (IBFG) porous plates under various boundary conditions. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. Material properties of IBFG are assumed to vary continuously along with two different directions simultaneously, that is, the longitudinal and transversal ones, respectively. Governing equations and boundary conditions are derived. Analytical solutions were obtained for buckling analysis of (IBFG) porous plates. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed theory. The effects of material gradations, aspect ratios, and porosity on IBFG plate responses are examined in detail as well. [ABSTRACT FROM AUTHOR]

In this work, the two-scale asymptotic homogenization method (AHM) is developed to describe the effective behavior of multi-laminated elastic micropolar composites with Fibonacci and random structure under perfect contact conditions at the interfaces. The local problem statements over the periodic cell Y are presented, and the corresponding effective stiffness and torque properties are reported. The transversal cross-section of the periodic cell Y is characterized by a laminated structure where the pattern for the layers follows two distinct configurations: (a) a Fibonacci arrangement, and (b) a random sequence focused on the probabilistic binomial function. The non-null effective properties of multi-laminated Cosserat elastic composites with isotropic centro-symmetric constituents are listed. Numerical results for multi-laminated elastic micropolar composites with both types of structures and centro-symmetric isotropic constituents are illustrated and discussed. The overall effective behavior for both cases converges to specific effective values of periodic structures as the number of layers increases. [ABSTRACT FROM AUTHOR]

We consider playing the game of Tic‐Tac‐Toe on block designs BIBD(v,k,λ) $(v,k,\lambda)$ and transversal designs TD(k,n) $(k,n)$. Players take turns choosing points and the first player to complete a block wins the game. We show that triple systems, BIBD(v,3,λ) $(v,3,\lambda)$, are a first‐player win if and only if v≥5 $v\ge 5$. Further, we show that for k=2,3 $k=2,3$, TD(k,n) $(k,n)$ is a first‐player win if and only if n≥k $n\ge k$. We also consider a weak version of the game, called Maker–Breaker, in which the second player wins if they can stop the first player from winning. In this case, we adapt known bounds for when either the first or second player can win on BIBD(v,k,1) $(v,k,1)$ and TD(k,n) $(k,n)$, and show that for Maker–Breaker, BIBD(v,4,1) $(v,4,1)$ is a first‐player win if and only if v≥16 $v\ge 16$. We show that TD(4,4) $(4,4)$ is a second‐player win, and so the second player can force a draw in the regular game by playing the same strategy. [ABSTRACT FROM AUTHOR]

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]

This paper presents a tri-band bandpass filter (BPF) based on transversal signal interference concepts. The proposed tri-band BPF is separately constructed by a T-folded-shaped shorted folded stub loaded resonator and parallel coupled square ring loaded resonator. By the odd-even mode analysis method, the presented filter excites eight transmission poles (TPs), where the first two TPs form the first passband, and the last two passbands are both composed of three TPs. Based on the transversal transmission path, seven transmission zeros (TZs) are excited improving the selectivity dramatically. Moreover, it features independently controllable band characteristics for each passband. To validate the proposed filter, a prototype tri-wideband BPF operating at 2.45 GHz, 3.17 GHz, and 4.91 GHz with 3-dB fraction bandwidth (fbw) of 17.6%, 27.1%, and 17.7% for LTE, WiMAX, Wi-Fi, and 5 G applications is designed, manufactured, and measured, showing great agreement with theoretical predictions and excellent performance, including sharp shirts, high band-to-band isolation (Iso), and compact size. [ABSTRACT FROM AUTHOR]

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• A novel Map Fusion method for pavement crack recognition using 2D and 3D features. • High accuracy in detecting longitudinal and transversal cracks in real conditions. • Integrating grayscale, roughness, and NCR features for robust crack detection. • The method's performance was demonstrated using two case studies. Crack detection is crucial for assessing pavement health, as cracks can deteriorate into more severe distresses like potholes and bumps. Consequently, numerous studies have been conducted to detect pavement cracks, achieving high levels of accuracy. Further research is ongoing to identify cost-effective and easily deployable solutions. This paper introduces a novel approach to pavement crack detection and identification using Map Fusion. The method integrates 2D features, such as grayscale levels, with 3D features, including roughness and normal change rate, into a unified map. 3D points that meet predefined criteria are identified as potential crack candidates. Noise is removed first, followed by the Graham Scan algorithm to delineate the crack skeleton. The method was validated on longitudinal and transversal cracks, demonstrating high precision compared to image-based and 3D model-based feature selection techniques. [ABSTRACT FROM AUTHOR]

The objects of considerations are thin, linearly elastic, Kirchhoff-Love-type, open, circular, cylindrical shells having a functionally graded macrostructure and a tolerance-periodic microstructure in circumferential direction. At the same time, the shells have constant geometrical, elastic and inertial properties in axial direction. The aim of this contribution is to investigate the effect of a microstructure size on the transversal free vibration frequencies of such shells. Moreover, the influence of differences between elastic and inertial properties of the constituent materials on these frequencies will be studied. Many functions describing the distribution of material properties will be taken into account. This dynamic problem will be analysed in the framework of a certain mathematical, averaged, non-asymptotic model derived by means of the tolerance modelling procedure. Contrary to the starting exact shell equations with highly oscillating, non-continuous and tolerance-periodic coefficients, governing equations of the tolerance model have continuous and slowly varying coefficients dependent also on a microstructure size. It will be shown that in the framework of the tolerance model not only the fundamental, cell-independent, but also the new, additional, cell-dependent free vibration frequencies can be derived and analysed. The results obtained from the non-asymptotic tolerance model will be compared with those derived from the mathematical, averaged asymptotic model formulated by applying the consistent asymptotic modelling technique. Governing equations of the asymptotic model have continuous and slowly-varying coefficients, but independent of the microstructure size. [ABSTRACT FROM AUTHOR]

We investigate the presence of antiferromagnetic fluctuations in the longitudinal and transversal spin susceptibilities of a square lattice. The inclusion of both first and second neighbour hopping terms, along with exchange coupling, induces anti-ferromagnetic fluctuations over a finite range of fillings in both longitudinal and transversal static spin susceptibilities. In the absence of on-site Hubbard interaction, we observe incommensurate antiferromagnetic fluctuations between the two Van Hove fillings. Beyond the second Van Hove singularity at n = 1. 03 , commensurate antiferromagnetic fluctuations dominate in both longitudinal and transversal spin susceptibilities. When incorporating a finite Hubbard interaction strength, U , we find that the commensurate anti-ferromagnetic fluctuations are preserved in both longitudinal and transversal dressed spin susceptibilities. However anti-ferromagnetic fluctuations vanish beyond a critical value of the Hubbard coupling strength, U c. Despite the exchange field can be induced by a ferromagnetic substrate, we do not observe any ferromagnetic fluctuations in the system. • Induction of commensurate antiferromagnetic fluctuations in the system. • Absence of ferromagnetic fluctuations despite a ferromagnetic ordered substrate. • Stabilization of antiferromagnetic fluctuations by inclusion of on-site Hubbard term. • Disruption of magnetic fationsluctuatins beyond a critical value of Hubbard strength. [ABSTRACT FROM AUTHOR]

A transversal in a hypergraph H is set of vertices that intersect every edge of H. A transversal coalition in H consists of two disjoint sets of vertices X and Y of H , neither of which is a transversal but whose union X ∪ Y is a transversal in H. Such sets X and Y are said to form a transversal coalition. A transversal coalition partition in H is a vertex partition Ψ = { V 1 , V 2 , ... , V p } such that for all i ∈ [ p ] , either the set V i is a singleton set that is a transversal in H or the set V i forms a transversal coalition with another set V j for some j , where j ∈ [ p ] ∖ { i }. The transversal coalition number C τ (H) in H equals the maximum order of a transversal coalition partition in H. For k ≥ 2 a hypergraph H is k -uniform if every edge of H has cardinality k. Among other results, we prove that if k ≥ 2 and H is a k -uniform hypergraph, then C τ (H) ≤ ⌊ 1 4 k 2 ⌋ + k + 1. Further we show that for every k ≥ 2 , there exists a k -uniform hypergraph that achieves equality in this upper bound. [ABSTRACT FROM AUTHOR]

In this short note, we provide the necessary and sufficient condition for an infinite collection of axis-parallel boxes in R d to be pierceable by finitely many axis-parallel k -flats, where 0 ≤ k < d. We also consider colorful generalizations of the above result and establish their feasibility. The problem considered in this paper is an infinite variant of the Hadwiger-Debrunner (p , q) -problem. [ABSTRACT FROM AUTHOR]

L'article est consacré aux résultats préliminaires de l'étude du site néolithique dans l'abri Alebastroviy Zavod de la région d'Elbrouz (Caucase du Nord) datant d'environ −8200 ou −6300 avant JC à 7500–6700 ans ou 5700 à 4800 avant JC. L'article établit l'apparition la plus ancienne du Néolithique céramique dans le Caucase du Nord et retrace également l'évolution de la culture néolithique au fil du temps. Les couches néolithiques du site situé dans l'abri Alebastroviy Zavod, dans la région d'Elbrouz, révèlent des analogies avec les cultures néolithiques de la même époque dans le Caucase du Sud et dans la direction du Nord – au Sud de la Plaine Russe. The article reports preliminary results of research at the Neolithic site of Alebastroviy Zavod Rockshelter in the Elbrus region (North Caucasus), dated from c. 8.2 ka BP or 6.3 ka BC to 7.5–6.7 ka BP or 5.7–4.8 ka BC. Here we defined not only the earliest appearance of ceramic Neolithic in the North Caucasus, but also a change in the Neolithic culture over the time. The Neolithic layers of Alebastroviy Zavod Rockshelter in the Elbrus region show similarities in simultaneous Neolithic cultures both in the South Caucasus and in the north direction – in the south of the Russian Plain. [ABSTRACT FROM AUTHOR]

The purpose of this work is to pursue classification of geproci sets. Specifically we classify [ m , n ] -geproci sets Z which consist of m = 4 points on each of n skew lines, assuming the skew lines have two transversals in common. We show in this case that n ≤ 6. Moreover we show that all geproci sets of this type and with no points on the transversals are contained in the F 4 configuration. We conjecture that a similar result is true for an arbitrary number m of points on each skew line, replacing containment in F 4 by containment in a half grid obtained by the so-called standard construction. [ABSTRACT FROM AUTHOR]