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Journal articles on the topic 'Rayon des graphes'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Lai, Ralph W. "Full Analysis of Lung Cancer Mortality/Radon Relationship with Simple Nonlinear Concepts." Dose-Response 19, no. 1 (January 1, 2021): 155932582096099. http://dx.doi.org/10.1177/1559325820960994.

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We analyze the relationship between the lung cancer mortality and the indoor radon intensity from the viewpoint of nonlinear mathematics. We conclude that their relationship is governed by the proportionality law where the cumulative lung cancer mortality Y is negatively proportional to the cumulative radon intensity X; or specifically, the nonlinear change of nonlinear face value (qYu – qY) is negatively proportional to the nonlinear change of nonlinear face value (X – Xb). The author obtained a set of data from late Professor Cohen on the lung-cancer mortality rate versus indoor radon level collected from 1,597 counties and territory of the USA. We initially presented the data as various primitive elementary graphs; then extended them to the primary graphs, leading graphs, and the proportionality graphs. The article emphasizes the building of a straight-line proportionality relationship for the dose-response data in a log-linear and/or log-log graphs. It demonstrates a straightforward methodology for solving the key upper asymptotes (Yu) for the proportionality equation using the Microsoft Excel via determining the “coefficient of determination”. (Note: q = log, Yu = upper asymptote of Y, Xb = bottom asymptote of X)

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2

Badger, Matthew, and Lisa Naples. "Radon measures and Lipschitz graphs." Bulletin of the London Mathematical Society 53, no. 3 (February 23, 2021): 921–36. http://dx.doi.org/10.1112/blms.12473.

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3

Bandelt, H. J., and E. Pesch. "A Radon theorem for Helly graphs." Archiv der Mathematik 52, no. 1 (January 1989): 95–98. http://dx.doi.org/10.1007/bf01197978.

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4

German, L. F., and O. I. Topale. "Star-shape, Radon number, and minty graphs." Cybernetics 23, no. 2 (1987): 147–53. http://dx.doi.org/10.1007/bf01071768.

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5

Yiu, Paul Y. H. "Strongly regular graphs and Hurwitz-Radon numbers." Graphs and Combinatorics 6, no. 1 (March 1990): 61–69. http://dx.doi.org/10.1007/bf01787481.

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6

Lee, Min Ho. "Radon transforms, laplacaians, and flows for directed graphs." Linear and Multilinear Algebra 45, no. 2-3 (December 1998): 219–33. http://dx.doi.org/10.1080/03081089808818588.

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7

Marco, José Manuel, and Javier Parcet. "Laplacian Operators and Radon Transforms on Grassmann Graphs." Monatshefte für Mathematik 150, no. 2 (October 2, 2006): 97–132. http://dx.doi.org/10.1007/s00605-006-0424-6.

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8

Ostrovskii, Mikhail I. "Connections Between Metric Characterizations of Superreflexivity and the Radon–Nikodým Property for Dual Banach Spaces." Canadian Mathematical Bulletin 58, no. 1 (March 1, 2015): 150–57. http://dx.doi.org/10.4153/cmb-2014-049-9.

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AbstractJohnson and Schechtman (2009) characterized superreflexivity in terms of finite diamond graphs. The present author characterized the Radon–Nikodým property (RNP) for dual spaces in terms of the infinite diamond. This paper is devoted to further study of relations between metric characterizations of superreflexivity and the RNP for dual spaces. The main result is that finite subsets of any setMwhose embeddability characterizes the RNP for dual spaces, characterize superreflexivity. It is also observed that the converse statement does not hold and thatM=l2is a counterexample.

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Anand, Bijo S., Manoj Changat, Iztok Peterin, and Prasanth G. Narasimha-Shenoi. "Some Steiner concepts on lexicographic products of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (October 10, 2014): 1450060. http://dx.doi.org/10.1142/s1793830914500608.

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Let G be a graph and W a subset of V(G). A subtree with the minimum number of edges that contains all vertices of W is a Steiner tree for W. The number of edges of such a tree is the Steiner distance of W and union of all vertices belonging to Steiner trees for W form a Steiner interval. We describe both of these for the lexicographic product of graphs. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number.

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10

Zhi-Pei Liang and D. C. Munson. "Partial Radon transforms." IEEE Transactions on Image Processing 6, no. 10 (October 1997): 1467–69. http://dx.doi.org/10.1109/83.624980.

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Gong, Myoung-Seon, Jae-Ryung Cha, Suk Min Hong, Cheolmin Lee, Dong Hyun Lee, and Sang-Woo Joo. "Roll-to-roll graphene oxide radon barrier membranes." Journal of Hazardous Materials 383 (February 2020): 121148. http://dx.doi.org/10.1016/j.jhazmat.2019.121148.

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Dourado, Mitre C., Dieter Rautenbach, Vinícius Fernandes dos Santos, and Jayme L. Szwarcfiter. "Characterization and recognition of Radon-independent sets in split graphs." Information Processing Letters 112, no. 24 (December 2012): 948–52. http://dx.doi.org/10.1016/j.ipl.2012.08.013.

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13

Kumar, Pradeep, Bharti, and Pramod Kumar Rai. "Synthesis of Environmentally Friendly Rayon‐Graphene Oxide Nano Composite for Decontamination of Water." ChemistrySelect 6, no. 26 (July 8, 2021): 6671–82. http://dx.doi.org/10.1002/slct.202101338.

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14

Bavard, Juliette. "Hyperbolicité du graphe des rayons et quasi-morphismes sur un gros groupe modulaire." Geometry & Topology 20, no. 1 (February 29, 2016): 491–535. http://dx.doi.org/10.2140/gt.2016.20.491.

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15

Sobhy, M. "Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions." Journal of Mechanics 30, no. 5 (August 12, 2014): 443–53. http://dx.doi.org/10.1017/jmech.2014.46.

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AbstractIn this article, the analyses of the natural frequency and buckling of orthotopic nanoplates, such as single-layered graphene sheets, resting on Pasternak's elastic foundations with various boundary conditions are presented. New functions for midplane displacements are suggested to satisfy the different boundary conditions. These functions are examined by comparing their results with the results obtained by using the functions suggested by Reddy (Reddy JN. Mechanics of Composite Materials and Structures: Theory and Analysis. Boca Raton, FL: CRC Press; 1997). Moreover, these functions are very simple comparing with Reddy's functions, leading to ease of calculations. The equations of motion of the nonlocal model are derived using the sinusoidal shear deformation plate theory (SPT) in conjunction with the nonlocal elasticity theory. The present SPT are compared with other plate theories. Explicit solution for buckling loads and vibration are obtained for single-layered graphene sheets with isotropic and orthotropic properties; and under biaxial loads. The formulation and the method of the solution are firstly validated by executing the comparison studies for the isotropic nanoplates with the results being in literature. Then, the influences of nonlocal parameter and the other parameters on the buckling and vibration frequencies are investigated.

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16

Coba D., Sebastián, and Alis Pataquiva‐M. "Optimización por la metodología de superficie de respuesta de la fabricación de un material nanoestructurado compuesto de nanohilos de nylon con grafeno." Revista Cientifica TECNIA 27, no. 2 (April 4, 2018): 53. http://dx.doi.org/10.21754/tecnia.v27i2.175.

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En el presente trabajo se llevaron a cabo dos diseños experimentales para la determinación de las condiciones óptimas de la fabricación de nanohilos de nylon y síntesis de grafeno, para lo cual se obtuvo: 0.68 M de (NH4)2SO4 y 11.45 V; 27 kV, 2.3 mL/h y 11.40 cm de distancia de la aguja al colector (cm); respectivamente. De esta manera, se produjeron electrohilos de nylon y grafeno, ambos de tamaño nanométrico. A partir de estos materiales se preparó un compósito nanohilos/grafeno, a las condiciones óptimas de fabricación. Los materiales obtenidos (nanohilos de nylon, grafeno y compósito) fueron caracterizados morfológica (SEM) y químicamente (FTIR, UV), comprobando su escala nanométrica, grupos funcionales y sus propiedades bloqueadoras de rayos UV. Es así, como este trabajo abre una nueva perspectiva al uso de nylon reciclado para la obtención de hilos electrohilados de diámetro nanométrico que pueden ser funcionalizados, en este caso con grafeno, y exhibir propiedades deseables en industrias tales como la textil, entre otras. Palabras clave.- superficie de respuesta, electrohilado, nanohilos de nylon, grafeno ABSTRACT In the present work, two experimental designs were carried out to find the optimal conditions to manufacture nylon nanowires and to synthesize graphene. The results obtained were: 0.68 M (NH4)2SO4 and 11.45 V; and 27 kV, 2.3 mL / h and 11.40 cm as the distance from the needle to the collector, respectively. This way, nylon nanowires and graphene were produced, both of nanometric size. Using these materials, a nanowire/graphene composite was prepared using optimum manufacturing conditions. The materials obtained (nylon nanowires, graphene and composite) were characterized morphologically (SEM) and chemically (FTIR, UV), verifying their nanometric scale, functional groups and their UV blocking properties. This work opens new perspectives for the use of recycled nylon to obtain electrospinned nano‐fibers that can be functionalized, in this case with graphene, and exhibit interesting properties for industrial applications, such as the fabrication of textile, among others. Keywords.- surface response, electrospinning, graphene, nylon nanofibers.

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17

Hansen, K. V., and P. A. Toft. "Fast curve estimation using preconditioned generalized Radon transform." IEEE Transactions on Image Processing 5, no. 12 (December 1996): 1651–61. http://dx.doi.org/10.1109/83.544572.

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18

Guangcan Liu, Zhouchen Lin, and Yong Yu. "Radon Representation-Based Feature Descriptor for Texture Classification." IEEE Transactions on Image Processing 18, no. 5 (May 2009): 921–28. http://dx.doi.org/10.1109/tip.2009.2013072.

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19

Ankerst, Donna P. "Chain event graphs. Rodrigo A. Collazo, Christiane Goergen, Jim Q. Smith. Boca Raton: CRC Press." Biometrics 75, no. 3 (September 2019): 1041. http://dx.doi.org/10.1111/biom.13126.

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20

Lun, D. P. K., T. C. L. Chan, Tai-Chiu Hsung, D. D. Feng, and Yuk-Hee Chan. "Efficient blind image restoration using discrete periodic Radon transform." IEEE Transactions on Image Processing 13, no. 2 (February 2004): 188–200. http://dx.doi.org/10.1109/tip.2004.823820.

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21

Putri, Kenny Marlian, Dwi Setyawan, and Satria Jaya Priatna. "Urea Application to Enhance Sugarcane Trash Decomposition: A Field Test in PTPN VII of Cinta Manis District in South Sumatera." Caraka Tani: Journal of Sustainable Agriculture 35, no. 2 (July 1, 2020): 180. http://dx.doi.org/10.20961/carakatani.v35i2.37979.

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<p>Sugarcane harvest results in plant residues, consisting of leaves, stems and roots nearly 20 ton ha<sup>-1</sup>. The plantation of PTPN VII in Cinta Manis District applied urea with a dosage of 5 kg ha<sup>-1</sup> but the result was not effective. There is a potential to try a higher dosage of urea to enhance trash decomposition. This research aims to evaluate urea application on biomass decomposition. This research was conducted on the Plot 07 Rayon 3 of PTPN VII, District of Cinta Manis at Ketiau, Lubuk Keliat of Ogan Ilir, South Sumatra, using Split Plot design. Main plot is trash sampling time and subplot is urea dosage with three replicates. ANCOVA was used for soil data. The rate of decomposition of the litter was calculated by the change in the initial condition of research with each week on observation resulting in decomposition rate graphs. Urea application at 10 kg ha<sup>-1</sup> reduced C/N of the litter ratio to almost 21:1 and was followed by the highest total nitrogen increase to 0.18%, while the highest organic carbon decline for urea treatment of 6 kg ha<sup>-1</sup> amounted to 13.78%. In conclusion, higher rate of urea application is still required to enhance sugarcane litter decomposition.</p>

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22

Xiong, Xiong, and Kaihuai Qin. "Linearly Estimating All Parameters of Affine Motion Using Radon Transform." IEEE Transactions on Image Processing 23, no. 10 (October 2014): 4311–21. http://dx.doi.org/10.1109/tip.2014.2341932.

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23

Jafari-Khouzani, K., and H. Soltanian-Zadeh. "Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms." IEEE Transactions on Image Processing 14, no. 6 (June 2005): 783–95. http://dx.doi.org/10.1109/tip.2005.847302.

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24

Rasid, Zarrul Azwan Mohd, Mohd Firdaus Omar, Muhammad Firdaus Mohd Nazeri, Syahrul Affandi Saidi, Andrei Victor Sandu, and Mustafa Al Bakri Abdullah Mohd. "A Study of two Dimensional Metal Carbide MXene Ti3C2 Synthesis, characterization conductivity and radiation properties." Materiale Plastice 56, no. 3 (September 30, 2019): 635–40. http://dx.doi.org/10.37358/mp.19.3.5244.

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Since the discovery of exceptional properties of graphene, a lot of researchers focused on the discovery of another nobel two-dimensional (2D) materials. Recently, an elegant exfoliation approaches was proposed as a method to synthesis a new family of transitional 2D metal carbide or nitrades of MXene from a layered MAX phase. A layered MAX phase of Ti3AlC2 was synthesized through pressureless sintering (PLS) the initial powder of 3TiH2/1.1Al/2C without preliminary dehydrogenation under argon atmosphere at 1350 oC. An elegant exfoliation approach was used to eliminates Al from its precursor to form a layered-structure of Ti3C2. In this study, thermal conductivity of MAX phase and MXene were studied using absolute axial heat flow method to measure the abilities sample to conduct heat and the data was collected using Picolog 1216 Data Logger. Electrical conductivity of these two materials was also compared by using two-point probe, due to its simplicity. Radiation properties of 2D MXene Ti3C2 was studied by using an established radon monitor, placed in closed, fabricated container. Morphological and structural properties of this 2D material were also studied using an established FESEM and XRD apparatus. SEM images shows two types of morphology which is a layer of Ti3C2 and the agglomerates Al2O3 with graphite. XRD pattern reveals three phases in this material which is a rhombohedral Al2O3, rhombohedral graphite and rhombohedral Ti3C2 phases, respectively. Thermal and electrical conductivity of MXene were proven higher than MAX phase. Radon concentration for this material for five consecutive days explains the radiation level of this material which is under the suggestion value from US Environmental Protection Agency (EPA). From this finding, it is can conveniently say that the MXene material can be promising material for electronic application.

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Hjouj, F., and D. W. Kammler. "Identification of Reflected, Scaled, Translated, and Rotated Objects From Their Radon Projections." IEEE Transactions on Image Processing 17, no. 3 (March 2008): 301–10. http://dx.doi.org/10.1109/tip.2007.916160.

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26

Hammouda, Ghassen, Dorra Sellami, and Atef Hammouda. "Pattern recognition based on compound complex shape-invariant Radon transform." Visual Computer 36, no. 2 (October 27, 2018): 279–90. http://dx.doi.org/10.1007/s00371-018-1604-9.

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27

Scala, Riccardo, and Nicolas Van Goethem. "Analytic and geometric properties of dislocation singularities." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 4 (February 1, 2019): 1609–51. http://dx.doi.org/10.1017/prm.2018.57.

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AbstractThis paper deals with the analysis of the singularities arising from the solutions of the problem ${-}\,{\rm Curl\ } F=\mu $, where F is a 3 × 3 matrix-valued Lp-function ($1\les p<2$) and μ a 3 × 3 matrix-valued Radon measure concentrated in a closed loop in Ω ⊂ ℝ3, or in a network of such loops (as, for instance, dislocation clusters as observed in single crystals). In particular, we study the topological nature of such dislocation singularities. It is shown that $F=\nabla u$, the absolutely continuous part of the distributional gradient Du of a vector-valued function u of special bounded variation. Furthermore, u can also be seen as a multi-valued field, that is, can be redefined with values in the three-dimensional flat torus 𝕋3 and hence is Sobolev-regular away from the singular loops. We then analyse the graphs of such maps represented as currents in Ω × 𝕋3 and show that their boundaries can be written in term of the measure μ. Readapting some well-known results for Cartesian currents, we recover closure and compactness properties of the class of maps with bounded curl concentrated on dislocation networks. In the spirit of previous work, we finally give some examples of variational problems where such results provide existence of solutions.

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Zhang, Qiaoping, and Isabelle Couloigner. "Accurate Centerline Detection and Line Width Estimation of Thick Lines Using the Radon Transform." IEEE Transactions on Image Processing 16, no. 2 (February 2007): 310–16. http://dx.doi.org/10.1109/tip.2006.887731.

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Shi, Daming, Junbin Gao, Payam S. Rahmdel, Michael Antolovich, and Tony Clark. "UND: Unite-and-Divide Method in Fourier and Radon Domains for Line Segment Detection." IEEE Transactions on Image Processing 22, no. 6 (June 2013): 2501–6. http://dx.doi.org/10.1109/tip.2013.2246522.

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30

Li, Wenchen. "Fast Parameters Estimation of LFM Signals via Radon-Wigner Transform." Journal of Information and Computational Science 10, no. 6 (April 10, 2013): 1585–94. http://dx.doi.org/10.12733/jics20101674.

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31

Madrigal-Monge, Gerardo, and Claudia Chaves-Villareal. "CVD growth of ZnO nanorods in situ on graphene and the study of its application as photoanode for solar cells." Revista Tecnología en Marcha 30, no. 5 (December 15, 2017): 104. http://dx.doi.org/10.18845/tm.v30i5.3221.

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Se presenta la síntesis de un nanomaterial tridimensional híbrido formado por una plataforma de grafeno en donde se depositan in situ nanobarras de ZnO verticalmente alineadas (VAZNR). El procedimiento utilizado para el crecimiento de grafeno por deposición química de vapores (CVD) y la transferencia sobre vidrio resultó en una película de alta calidad, comprobado por diversos métodos de caracterización. Una capa delgada continua de VAZNR se depositó por CVD con alta cristalinidad y alineación vertical, según confirmamos por medio de difracción de rayos X (XRD) y microscopía electrónica de barrido (SEM). Se estudió la aplicación de este nanomaterial híbrido como el fotoánodo de una celda solar sensibilizada con tinte (DSSC). El fotoánodo mostró buena estabilidad mecánica en el entorno electrolítico corrosivo. Sin embargo, la buena conductividad eléctrica inicial de grafeno se perdió durante la deposición de ZnO, según determinamos por caracterización eléctrica y electroquímica de la DSSC. El grafeno sufre degradación térmica a 570˚C bajo concentraciones de oxígeno tan bajas como 0.4%v/v. Como resultado, la DSSC no mostró respuesta eléctrica cuando se expone a la iluminación. El material hibrido puede tener aplicación alternativa en dispositivos piezoelectricos, biomédicos, entre otros, donde el grafeno se utiliza como una plantilla de sacrificio flexible y coformacional en el proceso de fabricación.

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32

Filin, Anatol G., and Michael A. Frumkin. "A systolic array for inversion of a finite Radon transform." Parallel Computing 18, no. 1 (January 1992): 85–90. http://dx.doi.org/10.1016/0167-8191(92)90113-l.

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33

Dusaussoy, N. J. "VOIR: a volumetric image reconstruction algorithm based on Fourier techniques for inversion of the 3-D Radon transform." IEEE Transactions on Image Processing 5, no. 1 (January 1996): 121–31. http://dx.doi.org/10.1109/83.481676.

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34

Fitas, Ricardo, Bernardo Rocha, Valter Costa, and Armando Sousa. "Design and Comparison of Image Hashing Methods: A Case Study on Cork Stopper Unique Identification." Journal of Imaging 7, no. 3 (March 8, 2021): 48. http://dx.doi.org/10.3390/jimaging7030048.

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Cork stoppers were shown to have unique characteristics that allow their use for authentication purposes in an anti-counterfeiting effort. This authentication process relies on the comparison between a user’s cork image and all registered cork images in the database of genuine items. With the growth of the database, this one-to-many comparison method becomes lengthier and therefore usefulness decreases. To tackle this problem, the present work designs and compares hashing-assisted image matching methods that can be used in cork stopper authentication. The analyzed approaches are the discrete cosine transform, wavelet transform, Radon transform, and other methods such as difference hash and average hash. The most successful approach uses a 1024-bit hash length and difference hash method providing a 98% accuracy rate. By transforming the image matching into a hash matching problem, the approach presented becomes almost 40 times faster when compared to the literature.

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35

Charkes, N. David. "Book Reviews : Author: Nicholas M. Karayanakis Title: Computer-Assisted Simulation of Dynamic Systems with Block Diagram Languages Publisher: CRC Press, Inc., 1993, Boca Raton FL. 398 pp." SIMULATION 63, no. 2 (August 1994): 121. http://dx.doi.org/10.1177/003754979406300206.

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36

Graham, Julie. "Genetics, Genomics and Breeding of Grapes. By A.-F. Adam-Blondon, J. M. Martinez-Zapater and C. Kole. Boca Raton, FL, USA: CRC Press (2011), pp. 390, US $139.95. ISBN 978-1-57808-117-4." Experimental Agriculture 48, no. 3 (June 6, 2012): 464. http://dx.doi.org/10.1017/s0014479712000245.

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Ramos, Igor, Vinícius F. Santos, and Jayme L. Szwarcfiter. "Complexity aspects of the computation of the rank of a graph." Discrete Mathematics & Theoretical Computer Science Vol. 16 no. 2, PRIMA 2013 (September 1, 2014). http://dx.doi.org/10.46298/dmtcs.2075.

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Special issue PRIMA 2013 International audience We consider the P₃-convexity on simple undirected graphs, in which a set of vertices S is convex if no vertex outside S has two or more neighbors in S. The convex hull H(S) of a set S is the smallest convex set containing S as a subset. A set S is a convexly independent set if v \not ∈ H(S\setminus \v\) for all v in S. The rank \rk(G) of a graph is the size of the largest convexly independent set. In this paper we consider the complexity of determining \rk(G). We show that the problem is NP-complete even for split or bipartite graphs with small diameter. We also show how to determine \rk(G) in polynomial time for the well structured classes of graphs of trees and threshold graphs. Finally, we give a tight upper bound for \rk(G), which in turn gives a tight upper bound for the Radon number as byproduct, which is the same obtained before by Henning, Rautenbach and Schäfer. Additionally, we briefly show that the problem is NP-complete also in the monophonic convexity.

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Leopardi, Paul. "Twin bent functions, strongly regular Cayley graphs, and Hurwitz--Radon theory." Journal of Algebra Combinatorics Discrete Structures and Applications, September 15, 2017, 271. http://dx.doi.org/10.13069/jacodesmath.327377.

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39

Cheeger, Jeff, and Bruce Kleiner. "Inverse Limit Spaces Satisfying a Poincaré Inequality." Analysis and Geometry in Metric Spaces 3, no. 1 (January 16, 2015). http://dx.doi.org/10.1515/agms-2015-0002.

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Abstract We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces, and a large class of new examples. As follows easily from [4], generically our examples have the property that they do not bilipschitz embed in any Banach space with Radon-Nikodym property. For Laakso spaces, thiswas noted in [4]. However according to [7] these spaces admit a bilipschitz embedding in L1. For Laakso spaces, this was announced in [5].

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Danilov, Vladimir I., Alexander V. Karzanov, and Gleb A. Koshevoy. "Coherent fans in the space of flows in framed graphs." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AR,..., Proceedings (January 1, 2012). http://dx.doi.org/10.46298/dmtcs.3056.

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International audience Let $G=(V,E)$ be a finite acyclic directed graph. Being motivated by a study of certain aspects of cluster algebras, we are interested in a class of triangulations of the cone of non-negative flows in $G, \mathcal F_+(G)$. To construct a triangulation, we fix a raming at each inner vertex $v$ of $G$, which consists of two linear orders: one on the set of incoming edges, and the other on the set of outgoing edges of $v$. A digraph $G$ endowed with a framing at each inner vertex is called $framed$. Given a framing on $G$, we define a reflexive and symmetric binary relation on the set of extreme rays of $\mathcal F_+ (G)$. We prove that that the complex of cliques formed by this binary relation is a pure simplicial complex, and that the cones spanned by cliques constitute a unimodular simplicial regular fan $Σ (G)$ covering the entire $\mathcal F_+(G)$. Soit $G=(V,E)$ un graphe orientè, fini et acyclique. Nous nous intéressons, en lien avec l’étude de certains aspects des algèbres amassées, à une classe de triangulations du cône des flots positifs de $G, \mathcal F_+(G)$. Pour construire une triangulation, nous ajoutons une structure en chaque sommet interne $v$ de $G$, constituée de deux ordres totaux : l'un sur l'ensemble des arcs entrants, l'autre sur l'ensemble des arcs sortants de $v$. On dit alors que $G$ est structurè. On définit ensuite une relation binaire réflexive et symétrique sur l'ensemble des rayons extrêmes de $\mathcal F_+ (G)$. Nous démontrons que le complexe des cliques formè par cette relation binaire est un complexe simplicial pur, et que le cône engendré par les cliques forme un éventail régulier simplicial unimodulaire $Σ (G)$ qui couvre complètement $\mathcal F_+(G)$.

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41

Cong, Pham Hong, and Nguyen Dinh Duc. "Postbuckling Behavior of Functionally Graded Multilayer Graphene Nanocomposite Plate under Mechanical and Thermal Loads on Elastic Foundations." VNU Journal of Science: Natural Sciences and Technology 35, no. 4 (December 23, 2019). http://dx.doi.org/10.25073/2588-1140/vnunst.4972.

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Abstract:

This paper presents an analytical approach to postbuckling behaviors of functionally graded multilayer nanocomposite plates reinforced by a low content of graphene platelets (GPLs) using the first order shear deformation theory, stress function and von Karman-type nonlinear kinematics and include the effect of an initial geometric imperfection. The weight fraction of GPL nano fillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of GPLRC layers. The plate is assumed to resting on Pasternak foundation model and subjected to mechanical and thermal loads. The results show the influences of the GPL distribution pattern, weight fraction, geometry, elastic foundations, mechanical and temperature loads on the postbuckling behaviors of FG multilayer GPLRC plates. 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