Статті в журналах: "Zig-zag theorie"

1

Alvarado Cornejo, Marina d. A. "Zig-Zag y la irrupción editorial: La ciudad letrada “zigzagueante." Literatura y Lingüística, no. 23 (May 19, 2015): 81. http://dx.doi.org/10.29344/0717621x.23.111.

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ResumenEl objetivo de este trabajo es reconocer la importancia de la irrupción de la editorial Zig- Zag y su magazín homónimo en el proceso de legitimación y expansión de la producción literaria chilena durante las primeras dos décadas del siglo XX. Para esto, identificamos las estrategias desplegadas por la publicación semanal, las que analizamos a la luz de la noción “ciudad letrada” de Ángel Rama.Palabras clave: Editorial Zig-Zag, magazín Zig-Zag, legitimación de la producción literaria, “ciudad letrada”.Zig-Zag and the publishing emergence: The zigzagueante ciudad letradaAbstractThe aim of this paper is to recognize the importance of the emergence of Zig-Zag Publisher and its magazine with the same name, in the process of legitimation and expansion of the Chilean literary production during the first two decades of the twentieth century. For this purpose, we identify the strategies employedby the weekly publication, which are analyzed in light of the reappropriation of the notion of ciudad letrada by Angel Rama.Key words: Zig-Zag Publisher, magazíne Zig-Zag, legitimation of literary production,“ciudad letrada”.

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2

Icardi, U. "Applications of Zig-Zag Theories to Sandwich Beams." Mechanics of Advanced Materials and Structures 10, no. 1 (January 2003): 77–97. http://dx.doi.org/10.1080/15376490306737.

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3

Ferreira, A. J. M., C. M. C. Roque, E. Carrera, M. Cinefra, and O. Polit. "Two higher order Zig-Zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation." Journal of Composite Materials 45, no. 24 (May 10, 2011): 2523–36. http://dx.doi.org/10.1177/0021998311401103.

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In this article, we combine the Carrera's Unified Formulation, CUF (Carrera E. Theories and Finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng., 2003; 10: 215–297.) and a radial basis function collocation technique for predicting the static deformations, free vibrations and buckling behavior of thin and thick cross-ply laminated plates. We develop by the CUF two Zig-Zag theories according to Murakami's Zig-Zag function. Both theories account for through-the-thickness deformations, allowing the analysis of thick plates. The accuracy and efficiency of this collocation technique for static, vibration, and buckling problems are demonstrated through numerical examples.

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4

Bierkens, Joris, and Andrew Duncan. "Limit theorems for the zig-zag process." Advances in Applied Probability 49, no. 3 (September 2017): 791–825. http://dx.doi.org/10.1017/apr.2017.22.

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AbstractMarkov chain Monte Carlo (MCMC) methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained via the Metropolis–Hastings algorithm, there has been recent interest in alternative schemes based on piecewise deterministic Markov processes (PDMPs). One such approach is based on the zig-zag process, introduced in Bierkens and Roberts (2016), which proved to provide a highly scalable sampling scheme for sampling in the big data regime; see Bierkenset al.(2016). In this paper we study the performance of the zig-zag sampler, focusing on the one-dimensional case. In particular, we identify conditions under which a central limit theorem holds and characterise the asymptotic variance. Moreover, we study the influence of the switching rate on the diffusivity of the zig-zag process by identifying a diffusion limit as the switching rate tends to ∞. Based on our results we compare the performance of the zig-zag sampler to existing Monte Carlo methods, both analytically and through simulations.

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5

Carrera, Erasmo. "Historical review of Zig-Zag theories for multilayered plates and shells." Applied Mechanics Reviews 56, no. 3 (May 1, 2003): 287–308. http://dx.doi.org/10.1115/1.1557614.

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This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1) Lekhnitskii (1935) was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2) Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian (1958), who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner (1984), who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3) On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, (LMT), Ambartsumian Multilayered Theory (AMT), and Reissner Multilayered Theory (RMT). As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4) LMT although very promising, has almost been ignored in the open literature. 5) Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6) RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references.

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6

SUN, HE, and HONG ZHU. "ON CONSTRUCTION OF ALMOST-RAMANUJAN GRAPHS." Discrete Mathematics, Algorithms and Applications 01, no. 02 (June 2009): 193–203. http://dx.doi.org/10.1142/s1793830909000154.

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O. Reingold et al. introduced the notion zig-zag product on two different graphs, and presented a fully explicit construction of d-regular expanders with the second largest eigenvalue O(d-1/3). In the same paper, they ask whether or not the similar technique can be used to construct expanders with the second largest eigenvalue O(d-1/2). Such graphs are called Ramanujan graphs. Recently, zig-zag product has been generalized by A. Ben-Aroya and A. Ta-Shma. Using this technique, they present a family of expanders with the second largest eigenvalue d-1/2 + o(1), what they call almost-Ramanujan graphs. However, their construction relies on local invertible functions and the dependence between the big graph and several small graphs, which makes the construction more complicated. In this paper, we shall give a generalized theorem of zig-zag product. Specifically, the zig-zag product of one "big" graph and several "small" graphs with the same size will be formalized. By choosing the big graph and several small graphs individually, we shall present a family of fully explicitly almost-Ramanujan graphs with locally invertible function waived.

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7

Хошгофтар, М. Дж., М. Карими та С. Сейфури. "Нелинейный анализ изгиба пластин из слоистого композита с использованием уточненной зигзагообразной теории". Механика композитных материалов 58, № 5 (листопад 2022): 905–26. http://dx.doi.org/10.22364/mkm.58.5.03.

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Для исследования изгибного поведения композитных пластин и сандвич-конструкций использована модифицированная зигзагообразная теория, основанная на теории сдвигового деформирования первого порядка для некоторых кусочно-линейных функций перемещений в плоскости. Эта теория не зависит от коэффициента коррекции на сдвиг и может быть применена к разным инженерным задачам, связанным с динамикой конструкций. Для получения точных результатов при больших деформациях в уравнении совместности фон Кармана учтены члены нелинейной деформации. Определяющие уравнения и связанные с ними граничные условия получены с помощью принципа виртуальной работы. Численные результаты сопоставлены с результатами других теорий и установлено их превосходное согласование. Результаты, представленные графически и таблично, иллюстрируют превосходство рассмотренной модели при предсказании полей напряжений и перемещений. Предложенная модель применима к нелинейным задачам с большими прогибами.

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8

Brischetto, S., E. Carrera, and L. Demasi. "Free Vibration of Sandwich Plates and Shells by Using Zig-Zag Function." Shock and Vibration 16, no. 5 (2009): 495–503. http://dx.doi.org/10.1155/2009/573674.

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This paper analyses the free vibration response of sandwich curved and flat panels by introducing the zig-zag function (—1)kζk(ZZF) in the displacement models of classical and higher order two-dimensional shell theories. The main advantage of ZZF is the introduction of a discontinuity in the first derivative, zig-zag effect, of the displacements distribution with correspondence to the core/faces interfaces. Results including and discarding ZZF are compared. Several values of face-to-core stiffness ratio (FCSR) and geometrical plate/shell parameters have been analyzed. Both fundamental vibration modes and those corresponding to high wave numbers are considered in the analysis. It is concluded that: (1) ZZF is highly recommended in the free vibration analysis of sandwich plates and shells; (2) the use of ZZF makes the error almost independent by FCSR parameter; (3) ZZF is easy to implement and its use should be preferred with respect to other `more cumbersome' refined theories.

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9

Carrera, E., M. Filippi, and E. Zappino. "Laminated beam analysis by polynomial, trigonometric, exponential and zig-zag theories." European Journal of Mechanics - A/Solids 41 (September 2013): 58–69. http://dx.doi.org/10.1016/j.euromechsol.2013.02.006.

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10

Icardi, Ugo, and Federico Sola. "Assessment of recent zig-zag theories for laminated and sandwich structures." Composites Part B: Engineering 97 (July 2016): 26–52. http://dx.doi.org/10.1016/j.compositesb.2016.04.058.

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11

Demasi, Luciano. "Mixed plate theories based on the Generalized Unified Formulation. Part IV: Zig-zag theories." Composite Structures 87, no. 3 (February 2009): 195–205. http://dx.doi.org/10.1016/j.compstruct.2008.07.010.

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12

Zhang, Yi Xia, and Chun Hui Yang. "Laminated Plate Elements Based on Higher-Order Shear Deformation Theories." Advanced Materials Research 32 (February 2008): 119–24. http://dx.doi.org/10.4028/www.scientific.net/amr.32.119.

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Efficient and accurate finite elements are crucial for finite element analysis to provide adequate prediction of the structural behavior. A large amount of laminated plate elements have been developed for finite element analysis of laminated composite plates based on the various lamination theories. A recent and complete review of the laminated finite elements based on the higher-order shear deformation theories, including the global higher-order theories, zig-zag theories and the global-local higher-order theories is presented in this paper. Finally some points on the development of the laminated plate elements are summarized.

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13

Van Der Poorten, A. J. "Generalised simultaneous approximation of functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 1 (August 1991): 50–61. http://dx.doi.org/10.1017/s1446788700033292.

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AbstractWe generalise the approximation theory described in Mahier's paper “Perfect Systems” to linked simultaneous approximations and prove the existence of nonsingular approximation and of transfer matrices by generalising Coates' normality zig-zag theorem. The theory sketched here may have application to constructions important in the theory of diophantine approximation.

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14

Das, Sovan Lal, Tanmay Mandal, and S. S. Gupta. "Inextensional vibration of zig-zag single-walled carbon nanotubes using nonlocal elasticity theories." International Journal of Solids and Structures 50, no. 18 (August 2013): 2792–97. http://dx.doi.org/10.1016/j.ijsolstr.2013.04.019.

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15

Icardi, Ugo, and Andrea Urraci. "Free and Forced Vibration of Laminated and Sandwich Plates by Zig-Zag Theories Differently Accounting for Transverse Shear and Normal Deformability." Aerospace 5, no. 4 (October 11, 2018): 108. http://dx.doi.org/10.3390/aerospace5040108.

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A number of mixed and displacement-based zig-zag theories are derived from the zig-zag adaptive theory (ZZA). As a consequence of their different assumptions on displacement, strain, and stress fields, and layerwise functions, these theories account for the transverse shear and normal deformability in different ways, but their unknowns are independent of the number of layers. Some have features that are reminiscent of ones that have been published in the literature for the sake of comparison. Benchmarks with different length-to-thickness ratios, lay-ups, material properties, and simply supported or clamped edges are studied with the intended aim of contributing toward better understanding the influence of transverse anisotropy on free vibration and the response of blast-loaded, multilayered, and sandwich plates, as well as enhancing the existing database. The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.)) with a low expansion order of polynomials in the in-plane and out-of-plane directions. The choice of their layerwise functions is shown to be immaterial, while theories with fixed kinematics are shown to be strongly case-sensitive and often inadequate (even for slender components).

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16

Carrera, Erasmo, Matteo Filippi, and Enrico Zappino. "Free vibration analysis of laminated beam by polynomial, trigonometric, exponential and zig-zag theories." Journal of Composite Materials 48, no. 19 (August 4, 2013): 2299–316. http://dx.doi.org/10.1177/0021998313497775.

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17

WANG, C. M., Z. Y. TAY, A. N. R. CHOWDHUARY, W. H. DUAN, Y. Y. ZHANG, and N. SILVESTRE. "EXAMINATION OF CYLINDRICAL SHELL THEORIES FOR BUCKLING OF CARBON NANOTUBES." International Journal of Structural Stability and Dynamics 11, no. 06 (November 21, 2011): 1035–58. http://dx.doi.org/10.1142/s0219455411004464.

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This paper examines the validity and accuracy of cylindrical shell theories in predicting the critical buckling strains of axially loaded single-walled carbon nanotubes (CNTs). The shell theories considered are the Donnell thin shell theory (DST), the Sanders thin shell theory (SST), and the first-order shear deformation (thick) shell theory (FSDST). Molecular dynamic (MD) simulation solutions for armchair and zig-zag CNTs with clamped ends were used as reference results to assess the shell models. The MD simulations were carried out at room temperature to eliminate the thermal effect on the buckling behavior. By adopting Young's modulus of 5.5 TPa, Poisson's ratio of 0.19, and tube thickness of 0.066 nm, it was found that DST is not able to capture the length dependency of the critical buckling strains and thus it should not be used for buckling analysis of CNTs. On the other hand, SST and FSDST are able to predict the critical buckling strains of armchair and zig-zag CNTs reasonably well for all aspect ratios, especially the results produced by the FSDST are found to be closer to the MD simulation results, because it allows for the effect of transverse shear deformation that becomes significant for CNTs with small aspect ratios. Thus, FSDST is recommended as a very suitable and convenient continuum mechanics model for buckling analysis of CNTs. The superior FSDST model is used to generate critical buckling strains of axially loaded single-walled CNT with different boundary conditions. These results should be useful for designers of nanodevices that make use of CNTs as axially loaded members. It is worth noting that for long and moderately long CNTs, the Timoshenko beam model may be used instead due to its simplicity.

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18

Wu, Jun, Yongxi Cheng, and Ding-Zhu Du. "An improved zig zag approach for competitive group testing." Discrete Optimization 43 (February 2022): 100687. http://dx.doi.org/10.1016/j.disopt.2022.100687.

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19

McKenzie, Ralph. "The Zig-Zag Property and Exponential Cancellation of Ordered Sets." Order 20, no. 3 (2003): 185–221. http://dx.doi.org/10.1023/b:orde.0000026529.04361.f8.

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20

A. Kelley, Christine, Deepak Sridhara, and Joachim Rosenthal. "Zig-zag and replacement product graphs and LDPC codes." Advances in Mathematics of Communications 2, no. 4 (2008): 347–72. http://dx.doi.org/10.3934/amc.2008.2.347.

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21

Carrera, Erasmo. "Assessment of Theories for Free Vibration Analysis of Homogeneous and Multilayered Plates." Shock and Vibration 11, no. 3-4 (2004): 261–70. http://dx.doi.org/10.1155/2004/493584.

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This paper assesses classical and advanced theories for free vibrational response of homogeneous and multilayered simply supported plates. Closed form solutions are given for thick and thin geometries. Single layer and multilayered plates made of metallic, composite and piezo-electric materials, are considered. Classical theories based on Kirchhoff and Reissner-Mindlin assumptions are compared with refined theories obtained by enhancing the order of the expansion of the displacement fields in the thickness directionz. The effect of the Zig-Zag form of the displacement distribution inzas well as of the Interlaminar Continuity of transverse shear and normal stresses at the layer interface were evaluated. A number of conclusions have been drawn. These conclusions could be used as desk-bed in order to choose the most valuable theories for a given problem.

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22

Zhen, Wu, S. H. Lo, and Ren Xiaohui. "Effects of displacement parameters in zig–zag theories on displacements and stresses of laminated composites." Composite Structures 110 (April 2014): 276–88. http://dx.doi.org/10.1016/j.compstruct.2013.12.005.

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23

Demasi, Luciano. "Partially Zig-Zag Advanced Higher Order Shear Deformation Theories Based on the Generalized Unified Formulation." Composite Structures 94, no. 2 (January 2012): 363–75. http://dx.doi.org/10.1016/j.compstruct.2011.07.022.

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24

Darrigrandi Navarro, Claudia, and Antonia Viu Bottini. "Imágenes de mujeres lectoras en revista Zig-Zag, 1920-1940." Estudios filológicos, no. 64 (December 2019): 13–34. http://dx.doi.org/10.4067/s0071-17132019000200013.

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25

Persson Westin, Elin. "Tilting modules and exceptional sequences for leaf quotients of type A zig-zag algebras." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61, no. 2 (September 27, 2019): 189–207. http://dx.doi.org/10.1007/s13366-019-00465-8.

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Abstract We classify generalized tilting modules and full exceptional sequences for the family of quasi-hereditary quotients of type A zig-zag algebras and for a related family of algebras. We also give a characterization of these quotients as quasi-hereditary algebras with simple preserving duality that are “close” to self-injective algebras.

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26

Lin, Di, and Hui Huang. "Zig-Zag Network for Semantic Segmentation of RGB-D Images." IEEE Transactions on Pattern Analysis and Machine Intelligence 42, no. 10 (October 1, 2020): 2642–55. http://dx.doi.org/10.1109/tpami.2019.2923513.

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27

BROADHURST, D. J., та D. KREIMER. "Knots and Numbers in ϕ4 Theory to 7 Loops and Beyond". International Journal of Modern Physics C 06, № 04 (серпень 1995): 519–24. http://dx.doi.org/10.1142/s012918319500037x.

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We evaluate all the primitive divergences contributing to the 7-loop β-function of ɸ4 theory, i.e. all 59 diagrams that are free of subdivergences and hence give scheme-independent contributions. Guided by the association of diagrams with knots, we obtain analytical results for 56 diagrams. The remaining three diagrams, associated with the knots 10124, 10139, and 10152, are evaluated numerically, to 10 sf. Only one satellite knot with 11 crossings is encountered and the transcendental number associated with it is found. Thus we achieve an analytical result for the 6-loop contributions, and a numerical result at 7 loops that is accurate to one part in 1011. The series of ‘zig-zag’ counterterms, [Formula: see text], previously known for n=3, 4, 5, 6 loops, is evaluated to 10 loops, corresponding to 17 crossings, revealing that the n-loop zig-zag term is [Formula: see text], where [Formula: see text] are the Catalan numbers, familiar in knot theory. The investigations reported here entailed intensive use of REDUCE, to generate O(104) lines of code for multiple precision FORTRAN computations, enabled by Bailey’s MPFUN routines, running for O(103) CPUhours on DecAlpha machines.

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Icardi, Ugo, and Andrea Urraci. "Considerations about the choice of layerwise and through-thickness global functions of 3-D physically-based zig-zag theories." Composite Structures 244 (July 2020): 112233. http://dx.doi.org/10.1016/j.compstruct.2020.112233.

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29

Krannich, Manuel. "A homological approach to pseudoisotopy theory. I." Inventiones mathematicae 227, no. 3 (January 31, 2022): 1093–167. http://dx.doi.org/10.1007/s00222-021-01077-7.

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AbstractWe construct a zig–zag from the once delooped space of pseudoisotopies of a closed 2n-disc to the once looped algebraic K-theory space of the integers and show that the maps involved are p-locally $$(2n-4)$$ ( 2 n - 4 ) -connected for $$n\,{>}\,3$$ n > 3 and large primes p. The proof uses the computation of the stable homology of the moduli space of high-dimensional handlebodies due to Botvinnik–Perlmutter and is independent of the classical approach to pseudoisotopy theory based on Igusa’s stability theorem and work of Waldhausen. Combined with a result of Randal-Williams, one consequence of this identification is a calculation of the rational homotopy groups of $$\mathrm {BDiff}_\partial (D^{2n+1})$$ BDiff ∂ ( D 2 n + 1 ) in degrees up to $$2n-5$$ 2 n - 5 .

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Demasi, Luciano, Giacomo Biagini, Federico Vannucci, Enrico Santarpia, and Rauno Cavallaro. "Equivalent Single Layer, Zig-Zag, and Layer Wise theories for variable angle tow composites based on the Generalized Unified Formulation." Composite Structures 177 (October 2017): 54–79. http://dx.doi.org/10.1016/j.compstruct.2017.06.033.

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31

Neves, A. M. A., A. J. M. Ferreira, E. Carrera, M. Cinefra, R. M. N. Jorge, C. M. Mota Soares, and A. L. Araújo. "Influence of zig-zag and warping effects on buckling of functionally graded sandwich plates according to sinusoidal shear deformation theories." Mechanics of Advanced Materials and Structures 24, no. 5 (October 7, 2016): 360–76. http://dx.doi.org/10.1080/15376494.2016.1191095.

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32

Curatolo, Bruno. "Marc Bernard, le « Goncourt » et le populisme." Études littéraires 44, no. 2 (March 14, 2014): 85–99. http://dx.doi.org/10.7202/1023762ar.

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L’auteur de Zig-Zag, son premier roman paru en 1929 chez Gallimard, avait, en raison de ses origines sociales, vocation à fonder, au début des années 1930, le groupe des écrivains prolétariens avec, entre autres, Henri Poulaille, Eugène Dabit ou Louis Guilloux, et à adopter des positions politiques proches du communisme. Toutefois, dans les mêmes années, il fut l’ami de certains poètes surréalistes, peu enclins à suivre la ligne et dont l’inspiration était parfois voisine de la sienne. À travers ses articles de presse (Monde, Le Figaro) et des archives inédites, c’est la complexité de Marc Bernard en matière d’esthétique littéraire que veut refléter cette étude depuis ses premiers essais jusqu’à la consécration du Goncourt.

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Kapuria, S., P. C. Dumir, A. Ahmed, and N. Alam. "Finite element model of efficient zig-zag theory for static analysis of hybrid piezoelectric beams." Computational Mechanics 34, no. 6 (June 23, 2004): 475–83. http://dx.doi.org/10.1007/s00466-004-0592-y.

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34

Ramírez, Verónica. "Predicciones del fin del mundo: Astronomía y ciencia ficción en los magazines de editorial Zig-Zag (1900-1920)." Literatura y Lingüística, no. 40 (November 18, 2019): 69–91. http://dx.doi.org/10.29344/0717621x.40.2061.

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Durante las primeras décadas del siglo XX, gracias a la modernización de la industria editorial, las predicciones del fin del mundo asociadas a daños ocasionados por fenómenos celestes circularon como leitmotiv de folletines y de textos de divulgación, produciéndose una expansión de la ciencia ficción más allá de los límites literarios. Posibles choques de astros con la Tierra y teorías científicas acerca de la toxicidad de la cola de los cometas, provocaron que dentro de los magazines cercanos al paso del cometa Halley de mayo de 1910, proliferaran obras de ciencia ficción, así como textos divulgativos que imaginaban posibles situaciones apocalípticas ocasionadas por este fenómeno celeste. En ese sentido, nuestro trabajo analiza la utilización del saber astronómico para propósitos literarios, así como el uso del tono literario para difundir y popularizar la ciencia en los magazines de la editorial Zig-Zag.

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35

Muraskin, M. "On the nature of time." International Journal of Mathematics and Mathematical Sciences 13, no. 1 (1990): 179–85. http://dx.doi.org/10.1155/s0161171290000242.

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We study how the notion of time can affect the motion of particles within the No Integrability Aesthetic Field Theory. We show that the Minkowski hypothesis of treatingx4as pure imaginary as well as the fourth component of vectors as pure imaginary, does not lead to different solutions provided we alter the sign ofdx4and certain origin point field components. We next show that it is possible to introduce time in the situation where all fields are real so that: (1) The field equations treat all coordinates the same way; (2) The flow concept is associated with time but not with space; (3) Data is prescribed at a single point rather than on a hypersurface as in hyperbolic theories. We study the lattice solution in the approximation that ignores zig-zag paths. This enables us to investigate the effect of a non-trivial superposition principle in the simplest way. We find that such a system, combined with our new approach to time, gives rise to an apparent infinite particle system in which particles can be looked at as not having well defined trajectories. This result is similar to what we obtained when we treated time in the same manner as the space variables in our previous work.

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36

Carrera, Erasmo. "Developments, ideas, and evaluations based upon Reissner’s Mixed Variational Theorem in the modeling of multilayered plates and shells." Applied Mechanics Reviews 54, no. 4 (July 1, 2001): 301–29. http://dx.doi.org/10.1115/1.1385512.

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This review article is devoted to the use of the Reissner Mixed Variational Theorem (RMVT) forward two-dimensional modeling of flat and curved, multilayer structures. A thorough review of the literature involving the use in the modeling of multilayered plates and shells using RMVT is also presented. In the first part, the paper overviews relevant key points that should be taken into account for an accurate description of strain and stress fields in multilayered plate and shell analysis. It is then shown that RMVT has been originated in view of the fulfillment of such key points, herein referred to as C0-Requirements (zig-zag form of the displacement fields in the thickness direction and continuity of transverse normal and shear stresses at each layer interface). Classical variational statements are used to introduce Reissner’s Theorem. In the second part, the paper presents various ways in which RMVT can be used to develop plate and shell theories in a systematic manner. The so called layer-wise and equivalent single layer variable description are considered. Both strong and weak (finite element) forms of governing equations have been derived. A Weak Form of Hooke’s Law (WFHL), is also discussed as an idea to eliminate transverse stress variables leading to standard classical models with only displacement unknowns. Two appendices display details of governing equations related to multilayered doubly curved shells and to finite element matrices of multilayered plates. A third part reviews the works that have appeared in literature which make use of RMVT. Mainly papers on multilayered plate and shell modelings have been addressed. The final part of the paper is devoted to giving an overview with selected results of numerical performance that can be acquired by RMVT applications; extensive comparison to elasticity solutions and to other significant analyses, based on classical and refined approaches, are given. It is concluded that Reissner’s Mixed Theorem should be considered as a natural tool for multilayered structure analyses; it plays a similar role to that of the Principle of Virtual Displacement in the analysis of isotropic single-layer structures. This review article includes 119 references.

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37

Tornabene, Francesco, Nicholas Fantuzzi, and Michele Bacciocchi. "Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response." Journal of Sandwich Structures & Materials 21, no. 1 (June 22, 2017): 320–65. http://dx.doi.org/10.1177/1099636217693623.

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This paper presents the free vibration analysis of composite sandwich plates and doubly curved shells with variable stiffness. The reinforcing fibers are located in the external skins of the sandwich structures according to curved paths. These curvilinear paths are described by a general expression that combines power-law, sinusoidal, exponential, Gaussian and ellipse-shaped functions. As a consequence, the reinforcing fibers are placed in these orthotropic layers in an arbitrary manner, in order to achieve the desired mechanical properties. The effect of this variable fiber orientation on the natural frequencies is investigated by means of several parametric studies. As far as the structural theory is concerned, an equivalent single layer approach based on the well-known Carrera Unified Formulation is employed. The Murakami’s function is added to the kinematic model to capture the zig-zag effect, when the soft-core effect is significant. Thus, several higher order shear deformation theories are taken into account in a unified manner. The differential geometry is employed to describe the reference surface of doubly curved shells and panels, which are characterized by variable radii of curvature. The numerical solution is obtained using the generalized differential quadrature method, due to its accuracy and stability features. The present solution is compared with the results available in the literature or obtained by finite element commercial codes.

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Chiafele, Anna. "Il viaggiatore sedentario (1993) e Città e dintorni (2001): sensibilità postmoderna e etica ambientale in due testi odeporici di Luigi Malerba." Quaderni d'italianistica 36, no. 2 (July 27, 2016): 155–72. http://dx.doi.org/10.33137/q.i..v36i2.26903.

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In questo saggio si vogliono prendere in disamina due testi di Luigi Malerba: Il viaggiatore sedentario (1993) e Città e dintorni (2001). Questi testi odeporici raccontano i viaggi di Malerba in Cina, Thailandia, Europa, Nord America, Grecia e Asia Minore e raccolgono le riflessioni dell’autore nate e rielaborate lungo un ampio arco di tempo. Grazie al supporto teorico offerto dal lavoro di studiosi quali Serenella Iovino, Serpil Oppermann, Ursula Heise e Rob Nixon, quest’articolo evidenzia la sensibilità postmoderna di Malerba verso l’ambiente e la sua maestria nel raffigurare il rapporto complementare esistente tra l’essere umano e la natura, tra l’umano e il non-umano. Dalle pagine di questi testi odeporici emerge, con forza, la figura di un uomo sensibile, intelligente, curioso, ironico e attento alle storie di tutti quegli esseri ignoti di passaggio sul pianeta Terra. Le osservazioni di Malerba non cadono mai in localismo nostalgico e tantomeno in “utopia regressiva” (Parole al vento 230). L’autore, invece, mostra rispetto e premura per ogni luogo, abitazione, cultura e popolo con cui entra in contatto nei sui numerosi viaggi a “zig-zag” (Viaggiatore 8) sempre fatti in compagnia della moglie Anna Lapenna.

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Eager, David, Karlos Ishac, Shilei Zhou, and Imam Hossain. "Investigating the Knuckleball Effect in Soccer Using a Smart Ball and Training Machine." Sensors 22, no. 11 (May 24, 2022): 3984. http://dx.doi.org/10.3390/s22113984.

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The term knuckleball in sporting jargon is used to describe a ball that has been launched with minimal spin, resulting in a trajectory that is erratic and unpredictable. This phenomenon was first observed in baseball (where the term originated) and has since been observed in other sports. While knuckleball has long fascinated the scientific community, the bulk of research has primarily focused on knuckleball as it occurs in baseball. Following the changes in the design of the soccer ball after the 2006 World Cup, knuckleball and ball aerodynamics were exploited by soccer players. This research examined the properties of a knuckleball in the sport of soccer. We designed and evaluated a system that could reproduce the knuckleball effect on soccer balls based on previous theories and characteristics outlined in our literature review. Our system is comprised of the Adidas miCoach Smart Ball, a companion smart phone app for data collection, a ball-launching machine with programmable functions, and a video-based tracking system and Tracker motion analysis software. The results from the testing showed that our system was successfully able to produce knuckleball behaviour on the football in a highly consistent manner. This verified the dynamic models of knuckleball that we outline. While a small portion of the data showed some lateral deviations (zig-zag trajectory), this erratic and unpredictable trajectory was much smaller in magnitude when compared to examples seen in professional games. The sensor data from the miCoach app and trajectory data from the Tracker motion analysis software, showed that the knuckleballs were consistently reproduced in-line with theoretical dynamics.

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40

Mamduhan, Rifqi Hazmi, Sri Wuli Fitriati, and Djoko Sutopo. "Coherence in The Narrative Texts of Eastvaganza Story Writing Contest for Senior High-School Students." English Education Journal 9, no. 1 (December 20, 2018): 84–32. http://dx.doi.org/10.15294/eej.v9i1.25900.

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This study analyzes narratives written by six students who joined a story writing contest. It is assumed that the students who joined in the writing contest had fair knowledge in writing, so the texts may achieve coherence. This study uses qualitative research in the form of discourse analysis. The focuses of the study are to investigate micro and macro level coherence, tense use, and the context of situation of the texts. This study uses the theories from Thornbury (2005), Ellis (1997), and Eggins (1994). This study is aimed to know the quality of coherent text in the studentsâ€™ narrative. The findings of this study showed that constant theme patterns became the most frequent occurred in the narratives followed by zig-zag patterns and sentences which has no patterns. The sentences which have patterns might be logic in continuity. For the macro-level coherence, key word aspect became the most found in the narratives. The words represented the main characters in the stories. The macro-scripts showed that the narratives mostly use the script orientation-complication-resolution in arranging the paragraphs. The tense errors were found in almost all narratives. The findings showed three narratives had more errors than correct ones. The situational coherence showed that the fields in the texts were about heroes who had done something precious in their life. The tenors of the texts were same, namely between story writers and story readers. The modes of the texts were also the same. The texts are delivered by written media, so the texts did not have visual and aural distance between story writers and story readers. The goal of the texts is only for constructing experience.

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Alarcón, Marco Antonio. "Presentación." Literatura y Lingüística, no. 23 (July 24, 2014): 9. http://dx.doi.org/10.29344/0717621x.23.106.

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Presentación La revista Literatura y Lingüística n° 23 tiene el agrado de ofrecer el trabajo de diversos académicos vinculados a universidades chilenas y extranjeras. En total, esta vez, se publican doce artículos, seis del área de literatura y seis de lingüística. Carolina González Varas revisa la obra poética de Domingo Gómez Rojas destacando, con respecto a ellos, una lectura desatendida por los estudios. A saber: la espiritualidad cristiana de su poética. En un procedimiento de tres pasos se propone ampliar el conocimiento que en general se tiene de su poesía. Fernanda Moraga García, por su parte, en su artículo “Tejiendo genealogías poéticas: primeros cantos transcritos de mujeres mapuche (siglos XIX y XX)” se propone “abrir-construir una revaloración de las primeras recopilaciones y transcripciones de cantos de mujeres mapuche”. Propone que esta “práctica cultural transcrita se instala como momento genealógico inaugural de la producción poética actual de mujeres mapuche”. Lorena Patricia López, en su artículo, revisa la obra Un adiós al descontento, de Eugenio Mimica, en la cual se discute la hegemonía continental sobre la región magallánica para la cual se plantea una creación que consiste en “la posibilidad de reinvención del cono sur austral a través de la refundación histórica, política de Magallanes” fundando un nuevo territorio, Meridionia, en el cual harán su aparición regionalismos y xenofobias, exageraciones y errores, el fracaso en fin de la utopía. El profesor Reynaldo Bello Guerrieri se ocupa de la obra póstuma de José Donoso, Lagartija sin cola. En ella se revisan aspectos como la dinámica propia donosiana referente a los cerrados mundos familiares, la angustia, la desolación, la insatisfacción e incluso la degradación humana. En un ámbito totalmente diferente, el artículo de Marina Alvarado, revisa el aporte de la Editorial Zig-Zag y de la revista del mismo nombre (1905) en el proceso de legitimación y expansión de la producciónliteraria chilena durante las primeras dos décadas del siglo XX.Desplazándose a la última década del siglo XX, Macarena Silva, porsu parte, confronta la revista Piel de Leopardo con la así llamada “nueva narrativa”, representada por el manifiesto de Jaime Collyer. El análisis desglosa este manifiesto, “focalizándose en las relaciones entre sus supuestos y el entorno social, político y económico del período posdictatorial tal como aparecen en las editorial de Piel de Leopardo”. Comienza la serie de artículos de Lingüística el profesor Manuel Rubio, quien, con el título “Concepciones sobre la producción escrita en académicos que forman profesores básicos”, indaga en las “concepciones académicas sobre la producción escrita en la formación inicial docente”. Su investigación es de orden cualitativo, sobre la base de diez entrevistas a académicos que imparten diferentes asignaturas. Concluye que predomina una concepción centrada en la dimensión comunicativa de la escritura, concebida desde los procesos internos que vive el escritor. También concluye que, para los entrevistados, la escritura académica tiene gran importancia para el desarrollo profesional. El profesor Marco Antonio Alarcón ofrece un artículo que tiene como objetivo presentar la discusión orientada a la conceptualización del “discurso profesional docente” a partir de dos aproximaciones: la referida al discurso profesional y la asociada a las funciones de la profesión docente. De ellas se recogen los aportes de esta propuesta de definición y algunas implicancias necesarias para posteriores desarrollos. Las profesoras Beatriz Hall y María Isabel López, siguiendo la línea del discurso académico, profundizan en la relación entre manuales universitarios y prácticas pedagógicas. Se proponen elaborar propuestas de intervención pedagógica en el proceso de alfabetización académica, en particular (siguiendo los aportes del Análisis del Discurso), analizan los modos de decir presentes en los manuales universitarios. En un ámbito totalmente distinto, el profesor Fernando Wittig González ofrece su estudio dedicado a la “adquisición y transmisión del mapudungún en hablantes urbanos”. En efecto, presenta un análisis pormenorizado sobre el proceso de adquisición del mapudungún en una muestra diversificada de hablantes urbanos. El profesor Mauricio Véliz presenta una investigación cualitativa destinada a poner en evidencia diversas creencias y actitudes de parte de estudiantes de un programa de preparación de profesores de inglés con relación a diversos fenómenos lingüísticos; entre ellos se destacan las percepciones sobre las variedades del inglés, implicancias del acento extranjero en profesores de inglés, la masificación del inglés en el mundo y factores que contribuyen a los sistemas de creencias sobre las temáticas abordadas. Finalmente, los profesores Álvaro González y Gastón Salamanca publican su artículo “Aspectos de la sintaxis del Rromané de Chile en textos orales tradicionales”, el primero de dos estudios que publicarán en esta revista, siguiendo una serie ya comenzada en números anteriores. Con este aporte, se consolida ya una línea de estudio relacionada con el Rromané hablado en Chile. Con este número, la Revista Literatura y Lingüística comienza a dar pasos concretos en la línea de consolidarse como revista bianual. Durante el año 2010, se publicaron los números 21 y 22. Para este año, está programada la publicación de dos números, 23 y 24 (primer y segundo semestre respectivamente) con un número aproximado de 12 artículos para cada número. También es necesario comentar que, desde el presente número, en la línea de mejorar las exigencias de marcación propuestas por diversas instancias indexadoras, se incorpora la traducción del título en inglés. De esta manera, cada primera página dispone de a) título en castellano, b) nombre de autor, c) resumen, d) palabras clave, e) abstract, f) keywords, g) nota con indicaciones sobre el proyecto de investigación al cual pertenece el artículo (si procede), h) nota con datos del autor. Cada vez más la Revista Literatura y Lingüística quiere ser un instrumento de transmisión de la investigación tanto de los académicos vinculados a nuestra casa de estudios, Universidad Católica Silva Henríquez, como de otras instituciones. Nos interesa, sobre todo la colaboración de investigadores involucrados en proyectos determinados que den cuenta de la gestación de un nuevo conocimiento, propio, por cierto, de la dinámica del quehacer universitario. Damos nuestras gracias a los colaboradores que hacen posible esta revista: autores, editores, diagramadores, etc., al mismo tiempo que reafirmamos nuestro compromiso con la comunidad académica universitaria. Marco Antonio Alarcón Director Literatura y Lingüística Junio de 2011

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Bierkens, Joris, Sebastiano Grazzi, Frank van der Meulen, and Moritz Schauer. "A piecewise deterministic Monte Carlo method for diffusion bridges." Statistics and Computing 31, no. 3 (April 20, 2021). http://dx.doi.org/10.1007/s11222-021-10008-8.

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AbstractWe introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the Lévy–Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber–Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the fully local algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the subsampling technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.

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Cisto, Carmelo, and Francesco Navarra. "Primality of closed path polyominoes." Journal of Algebra and Its Applications, December 2, 2021. http://dx.doi.org/10.1142/s021949882350055x.

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In this paper, we introduce a new class of polyominoes, called closed paths, and we study the primality of their associated ideal. Inspired by an existing conjecture that characterizes the primality of a polyomino ideal by nonexistence of zig-zag walks, we classify all closed paths which do not contain zig-zag walks, and we give opportune toric representations of the associated ideals. To support the conjecture, we prove that having no zig-zag walks is a necessary and sufficient condition for the primality of the associated ideal of a closed path. Finally, we present some classes of prime polyominoes viewed as generalizations of closed paths.

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Corbella, Alice, Simon E. F. Spencer, and Gareth O. Roberts. "Automatic Zig-Zag sampling in practice." Statistics and Computing 32, no. 6 (November 9, 2022). http://dx.doi.org/10.1007/s11222-022-10142-x.

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AbstractNovel Monte Carlo methods to generate samples from a target distribution, such as a posterior from a Bayesian analysis, have rapidly expanded in the past decade. Algorithms based on Piecewise Deterministic Markov Processes (PDMPs), non-reversible continuous-time processes, are developing into their own research branch, thanks their important properties (e.g., super-efficiency). Nevertheless, practice has not caught up with the theory in this field, and the use of PDMPs to solve applied problems is not widespread. This might be due, firstly, to several implementational challenges that PDMP-based samplers present with and, secondly, to the lack of papers that showcase the methods and implementations in applied settings. Here, we address both these issues using one of the most promising PDMPs, the Zig-Zag sampler, as an archetypal example. After an explanation of the key elements of the Zig-Zag sampler, its implementation challenges are exposed and addressed. Specifically, the formulation of an algorithm that draws samples from a target distribution of interest is provided. Notably, the only requirement of the algorithm is a closed-form differentiable function to evaluate the log-target density of interest, and, unlike previous implementations, no further information on the target is needed. The performance of the algorithm is evaluated against canonical Hamiltonian Monte Carlo, and it is proven to be competitive, in simulation and real-data settings. Lastly, we demonstrate that the super-efficiency property, i.e. the ability to draw one independent sample at a lesser cost than evaluating the likelihood of all the data, can be obtained in practice.

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Bierkens, Joris, Sebastiano Grazzi, Frank van der Meulen, and Moritz Schauer. "Sticky PDMP samplers for sparse and local inference problems." Statistics and Computing 33, no. 1 (November 28, 2022). http://dx.doi.org/10.1007/s11222-022-10180-5.

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AbstractWe construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly 0. This is achieved with the fairly simple idea of endowing existing PDMP samplers with “sticky” coordinate axes, coordinate planes etc. Upon hitting those subspaces, an event is triggered during which the process sticks to the subspace, this way spending some time in a sub-model. This results in non-reversible jumps between different (sub-)models. While we show that PDMP samplers in general can be made sticky, we mainly focus on the Zig-Zag sampler. Compared to the Gibbs sampler for variable selection, we heuristically derive favourable dependence of the Sticky Zig-Zag sampler on dimension and data size. The computational efficiency of the Sticky Zig-Zag sampler is further established through numerical experiments where both the sample size and the dimension of the parameter space are large.

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Cisto, Carmelo, Francesco Navarra, and Rosanna Utano. "On Gröbner Basis and Cohen-Macaulay Property of Closed Path Polyominoes." Electronic Journal of Combinatorics 29, no. 3 (September 9, 2022). http://dx.doi.org/10.37236/11122.

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In this paper we introduce some monomial orders for the class of closed path polyominoes and we prove that the set of the generators of the polyomino ideal attached to a closed path forms the reduced Gröbner basis with respect to these monomial orders. It is known that the polyomino ideal attached to a closed path containing an $L$-configuration or a ladder of at least three steps, equivalently having no zig-zag walks, is prime. As a consequence, we obtain that the coordinate ring of a closed path having no zig-zag walks is a normal Cohen-Macaulay domain.

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Timmons, Craig. "An Ordered Turán Problem for Bipartite Graphs." Electronic Journal of Combinatorics 19, no. 4 (December 13, 2012). http://dx.doi.org/10.37236/2471.

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Let $F$ be a graph. A graph $G$ is $F$-free if it does not contain $F$ as a subgraph. The Turán number of $F$, written $\textrm{ex}(n,F)$, is the maximum number of edges in an $F$-free graph with $n$ vertices. The determination of Turán numbers of bipartite graphs is a challenging and widely investigated problem. In this paper we introduce an ordered version of the Turán problem for bipartite graphs. Let $G$ be a graph with $V(G) = \{1, 2, \dots , n \}$ and view the vertices of $G$ as being ordered in the natural way. A zig-zag $K_{s,t}$, denoted $Z_{s,t}$, is a complete bipartite graph $K_{s,t}$ whose parts $A = \{n_1 < n_2 < \dots < n_s \}$ and $B = \{m_1 < m_2 < \dots < m_t \}$ satisfy the condition $n_s < m_1$. A zig-zag $C_{2k}$ is an even cycle $C_{2k}$ whose vertices in one part precede all of those in the other part. Write $\mathcal{Z}_{2k}$ for the family of zig-zag $2k$-cycles. We investigate the Turán numbers $\textrm{ex}(n,Z_{s,t})$ and $\textrm{ex}(n,\mathcal{Z}_{2k})$. In particular we show $\textrm{ex}(n, Z_{2,2}) \leq \frac{2}{3}n^{3/2} + O(n^{5/4})$. For infinitely many $n$ we construct a $Z_{2,2}$-free $n$-vertex graph with more than $(n - \sqrt{n} - 1) + \textrm{ex} (n,K_{2,2})$ edges.

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Maji, Ashes, and Prashanta Kr Mahato. "Development and applications of shear deformation theories for laminated composite plates: An overview." Journal of Thermoplastic Composite Materials, June 30, 2020, 089270572093076. http://dx.doi.org/10.1177/0892705720930765.

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This review, overviews the development and applications of shear deformation (SD) laminated composite plate theories. The present overview mainly focuses on theoretical models based on SD theories of laminated composite plates. This comprehensive review has been categorized with an equivalent single-layer laminate and layerwise laminate theories. An equivalent single-layer laminate theory includes classical laminated plate theory, first-order shear deformation laminated theory, second-order shear deformation laminated theory, third-order shear deformation laminated theory, parabolic shear deformation laminated theory, trigonometric shear deformation laminated theory, hyperbolic shear deformation laminated theory, and higher order shear deformation laminated theory. The layerwise laminate theories include discrete-layer theories and zig-zag theories. In addition, the 3D elasticity solutions theory, the mixed (hybrid) plate theories, unified theories, advanced shear deformation theories, and the recently developed smart composite are also reviewed.

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Cavaleri, Matteo, Daniele D'Angeli, and Alfredo Donno. "Permutational Powers of a Graph." Electronic Journal of Combinatorics 26, no. 4 (October 25, 2019). http://dx.doi.org/10.37236/8337.

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This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction recovers the classical zig-zag product of graphs when the permutation is an involution, and it is in fact more general. We start by discussing necessary and sufficient conditions on the permutation and on the adjacency matrix of a graph to guarantee their composition to represent an adjacency matrix of a graph, then we focus our attention on the cases in which the permutational power does not reduce to a zig-zag product. We show that the cases of interest are those in which the adjacency matrix is singular. This leads us to frame our problem in the context of equitable partitions, obtained by identifying vertices having the same neighborhood. The families of cyclic and complete bipartite graphs are treated in details.

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Prałat, Paweł. "Containment Game Played on Random Graphs: Another Zig-Zag Theorem." Electronic Journal of Combinatorics 22, no. 2 (May 22, 2015). http://dx.doi.org/10.37236/4777.

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We consider a variant of the game of Cops and Robbers, called Containment, in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop). The cops win by "containing'' the robber, that is, by occupying all edges incident with a vertex occupied by the robber. The minimum number of cops, $\xi(G)$, required to contain a robber played on a graph $G$ is called the containability number, a natural counterpart of the well-known cop number $c(G)$. This variant of the game was recently introduced by Komarov and Mackey, who proved that for every graph $G$, $c(G) \le \xi(G) \le \gamma(G) \Delta(G)$, where $\gamma(G)$ and $\Delta(G)$ are the domination number and the maximum degree of $G$, respectively. They conjecture that an upper bound can be improved and, in fact, $\xi(G) \le c(G) \Delta(G)$. (Observe that, trivially, $c(G) \le \gamma(G)$.) This seems to be the main question for this game at the moment. By investigating expansion properties, we provide asymptotically almost sure bounds on the containability number of binomial random graphs $\mathcal{G}(n,p)$ for a wide range of $p=p(n)$, showing that it forms an intriguing zigzag shape. This result also proves that the conjecture holds for some range of $p$ (or holds up to a constant or an $O(\log n)$ multiplicative factors for some other ranges).

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