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Journal articles on the topic 'Rainbow'
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Hayes, John W. "Competition for Spawning Space Between Brown (Salmo trutta) and Rainbow Trout (S. gairdneri) in a Lake Inlet Tributary, New Zealand." Canadian Journal of Fisheries and Aquatic Sciences 44, no. 1 (January 1, 1987): 40–47. http://dx.doi.org/10.1139/f87-005.
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Effect of interference competition for spawning space on spawning success of brown (Salmo trutta) and rainbow trout (S. gairdneri) was studied in the main spawning tributary of Lake Alexandrina, New Zealand. Competition was mediated through redd superimposition and severely limited the spawning success of both species. Overall spawning success, from egg deposition to fry emergence, was 2.1% for rainbow trout and 0.2% for brown trout and was dependent on time of spawning. Brown trout spawned from April to June and rainbow trout spawned from April to October. Brown trout and early spawning rainbow trout experienced poor spawning success due to severe redd superimposition by later spawning rainbows. Late spawning rainbows experienced highest spawning success. Redd superimposition by rainbow trout caused a 94% reduction in spawning success of brown trout in an experimental section of stream. Severe intraspecific competition for spawning space, through redd super-imposition, determined pattern and timing of peak rainbow fry emergence.
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LIU, Hongjun. "Scholarly Study of Hong (Rainbow) in the Ming and Qing Dynasties." Cultura 19, no. 1 (January 1, 2022): 87–99. http://dx.doi.org/10.3726/cul012022.0007.
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Abstract: This paper focuses on how Chinese intellectuals discussed and researched rainbows in late Ming and early Qing Dynasty. Many of them considered the rainbow as a phenomenon that occurred under certain conditions of sunshine and raindrops, which could be described with terms related to qi () of yin/yang (/). Some of them had the knowledge of duplicating rainbows by “spraying water opposite to the sun”. There were also popular conceptions that rainbow was a sign of salaciousness and rainbow could siphon water, both of which had a long history in Chinese context. Scholars also discussed other phenomena similar to rainbow such as solar halo, lunar halo, parhelion and parselene. Those discussions were not held in wider society, yet they were the sign of how Chinese intellectuals rationalized their research into natural philosophy.
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LIU, Hongjun. "Scholarly Study of Hong (Rainbow) in the Ming and Qing Dynasties." Cultura 17, no. 2 (January 1, 2020): 87–99. http://dx.doi.org/10.3726/cul022020.0007.
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Abstract: This paper focuses on how Chinese intellectuals discussed and researched rainbows in late Ming and early Qing Dynasty. Many of them considered the rainbow as a phenomenon that occurred under certain conditions of sunshine and raindrops, which could be described with terms related to qi <graphic href="CUL2020k_87_fig0001.jpg"/> of yin/yang <graphic href="CUL2020k_87_fig0002.jpg"/>. Some of them had the knowledge of duplicating rainbows by “spraying water opposite to the sun”. There were also popular conceptions that rainbow was a sign of salaciousness and rainbow could siphon water, both of which had a long history in Chinese context. Scholars also discussed other phenomena similar to rainbow such as solar halo, lunar halo, parhelion and parselene. Those discussions were not held in wider society, yet they were the sign of how Chinese intellectuals rationalized their research into natural philosophy.
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Huntala, Melisa, Muhammad Rezky Friesta Payu, and Nisky Imansyah Yahya. "Total Rainbow Connection Number Of Shackle Product Of Antiprism Graph (〖AP〗_3)." Jurnal Matematika, Statistika dan Komputasi 20, no. 1 (September 6, 2023): 1–9. http://dx.doi.org/10.20956/j.v20i1.24833.
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Function if is said to be k total rainbows in , for each pair of vertex there is a path called with each edge and each vertex on the path will have a different color. The total connection number is denoted by trc defined as the minimum number of colors needed to make graph to be total rainbow connected. Total rainbow connection numbers can also be applied to graphs that are the result of operations. The denoted shackle graph is a graph resulting from the denoted graph where t is number of copies of G. This research discusses rainbow connection numbers rc and total rainbow connection trc(G) using the shackle operation, where is the antiprism graph . Based on this research, rainbow connection numbers rc shack , and total rainbow connection trc shack for .
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Cervantes-Ojeda, J., M. Gómez-Fuentes, D. González-Moreno, and M. Olsen. "Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six." Journal of Applied Mathematics 2019 (March 3, 2019): 1–7. http://dx.doi.org/10.1155/2019/4073905.
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Arainbowt-coloringof at-connected graphGis an edge coloring such that for any two distinct verticesuandvofGthere are at leasttinternally vertex-disjoint rainbow(u,v)-paths. In this work, we apply a Rank Genetic Algorithm to search for rainbowt-colorings of the family of Moore cages with girth six(t;6)-cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a(4;6)-cage is 7, improving the one currently known, which is 13. The computation of the minimum number of colors of a rainbow coloring is known to be NP-Hard and the Rank Genetic Algorithm showed good behavior finding rainbowt-colorings with a small number of colors.
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Maleeva, G. A. "Analysis of partial key recovery attack on multivariate cryptographic transformations using rank systems." Radiotekhnika, no. 209 (June 24, 2022): 64–70. http://dx.doi.org/10.30837/rt.2022.2.209.06.
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The Rainbow signature scheme, proposed by Ding and Schmidt in 2005, is one of the oldest and most studied signature schemes in multidimensional cryptography. The Rainbow, based on the unbalanced Oil and Vinegar signature scheme, has the necessary cryptocurrency since 1999 with the right parameters. Interest in multivariate cryptography has increased in the last decade, as it is considered to be quantum-stable.
Cryptanalysis of the Rainbow and its predecessors was actively developed in the early 2000s. Attacks from this era include the MinRank attack, the HighRank attack, the Bill-Gilbert attack, the UOV agreement attack, and the Rainbow bandwidth attack. After 2008, cryptanalysis seemed to have stopped, until the Rainbow's participation in the NIST PQC project, which motivated the continuation of cryptanalysis. During the second round of NIST, Bardett and others proposed a new algorithm for solving the MinRank problem. This dramatically increased the effectiveness of MinRank's attack, although not enough to threaten the parameters provided to NIST. A less memory-intensive version of this algorithm was suggested by Baena et al. Perlner and Smith-Tone analyzed the Rainbow bandwidth attack in depth, which showed that the attack was more effective than previously thought. This prompted the Rainbow team to increase slightly the parameters for the third round. During the third round, Bellens introduced a new attack that reduced the Rainbow's security by 220 times for SL 1. The Rainbow team claimed that despite the new attacks, the Rainbow's parameters still met NIST requirement.
The purpose of this article is to present two new (partial) key recovery attacks on multivariate cryptographic transformations using rank systems.
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WERRETT, SIMON. "Wonders never cease: Descartes's Météores and the rainbow fountain." British Journal for the History of Science 34, no. 2 (June 2001): 129–47. http://dx.doi.org/10.1017/s0007087401004319.
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This essay argues that the material culture of the Renaissance garden played an important role in the development of Cartesian mathematical and mechanical philosophy. Garden machinery such as Salomon and Isaac de Caus's automata and grottoes provided a model from which Descartes drew his clockwork conceptions of nature and the human body. This machinery was also crucial in the Cartesian explanation of the rainbow. Not simply an exercise in intellectual curiosity, Descartes's geometrical description of the rainbow in Discourse Eight of the Météores was a direct response to the engineers of artificial rainbow fountains which populated European princely gardens for much of the sixteenth and early seventeenth centuries. Rejecting distinctions between ‘natural’ and ‘artificial’ rainbows, Descartes used these fountains and his own constructions of artificial water drops to discern the causes of the rainbow by refraction and reflection and, by analogy, to suppose this the explanation of rainbows in the sky. This knowledge was then utilized to propose an alternative to the rainbow fountain, using refracting liquids to cast images in the sky. Descartes presented a ‘science of miracles’ destined not to eradicate wonder but to make transparent the wonders of traditional garden engineers and replace them with wonders derived from knowledge of mathematical and mechanical philosophy. As such, the ‘science of miracles’ gave a new emphasis to the mind of the natural philosopher as the essential component in the creation of wonders, rather than the traditional skills and experience of the artisan or engineer.
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Zheng, Yuan, Kexun Shen, Xianghe Wang, and Xing-Xing Yao. "Rainbows in Different Refractive Indices." Physics Teacher 61, no. 5 (May 1, 2023): 351. http://dx.doi.org/10.1119/5.0086915.
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The rainbow is a natural optical scattering and dispersion phenomenon that reveals the visible spectral composition of sunlight in the shape of an arc. People are instinctively attracted by its colorful appearance and curved shape. Hence, there are many serious studies about the rainbow with a long history. Recently, several simple experiments, adopting glass balls, acrylic spheres, spherical flasks, or sessile water drops, have been devised to demonstrate how the rainbow is formed. These works demonstrate the colors and shapes of the rainbow well and explain how the dispersive spectrum is produced by the refraction–reflection–refraction process. However, the influence of the refractive index is rarely illustrated. It is not difficult to see that the refractive index of raindrops and the atmosphere is closely related to the rainbow, especially the viewing angle of it. In this paper, we use spherical lenses with different materials and in different solutions to change the refractive index. Under a collimated light source, the evolution of the viewing angles of primary and secondary rainbows with respect to the refractive index is demonstrated. Experiments with refraction conditions similar to a natural rainbow are also conducted.
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Stefanini, L., D. Ramaccia, A. Toscano, and F. Bilotti. "Temporal rainbow scattering at boundary-induced time interfaces." Applied Physics Letters 122, no. 5 (January 30, 2023): 051701. http://dx.doi.org/10.1063/5.0132798.
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Since the dawn of modern optics and electromagnetics, the optical prism is one of the most fascinating optical elements for refracting light. Exploiting its frequency dispersive behavior, a prism is able to refract different frequencies in different directions, realizing polychromatic light rainbows. Recently, thanks to their engineerable electromagnetic response, metamaterials have been exploited for achieving novel refractive scattering processes, going beyond the classical prism effects. In this Letter, we report on a rainbow-like scattering process taking place at the interface of a boundary-induced temporal metamaterial realized by instantaneously opening the boundary conditions of a parallel plate waveguide. Changing abruptly the conductivity of one of the two metallic plates, we demonstrate that an equivalent temporal interface between two different media is realized, and the monochromatic wave propagating into the waveguide gets scattered into a polychromatic rainbow in free space. We derive the relationships between the waveguide mode and the raising rainbow in terms of scattered amplitude and frequencies as a function of the elevation angle with respect to the waveguide axis. We apply the underlying physics to control the temporal rainbow by imposing a principal direction of scattering by design. Full-wave numerical simulations are performed for computing the rainbow temporal scattering and verifying the design guidelines for achieving controlled temporal rainbow scattering.
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Telecki, Igor, Petar Belicev, Srdjan Petrovic, and Nebojsa Neskovic. "Focusing properties of a square electrostatic rainbow lens doublet." Nuclear Technology and Radiation Protection 30, no. 4 (2015): 239–48. http://dx.doi.org/10.2298/ntrp1504239t.
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This is a study on the properties of a square electrostatic rainbow lens doublet. The said optical element consists of two square electrostatic rainbow lenses with the second lens axially rotated for 45 degrees with respect to the first one. The propagation of a proton beam with a kinetic energy of 10 keV through the doublet is in the focus of our analysis. The potential of the electrodes of both lenses is 2 kV. The electrostatic potential and the electric field components of the lens doublet are calculated using a 3-D computer code based on the method of moments. Spatial and angular distributions of protons propagating through the lens doublet, as well as the parameters defining beam quality, are investigated. As in the case of the single square electrostatic rainbow lens, the evolution of these distributions is determined by the evolution of corresponding rainbow lines, generated by the use of the theory of crystal rainbows. Our study shows that a beam core in the shape of a cusped square is formed by the spatial rainbow line that appears first. This rainbow line occurs during proton propagation through the first lens. The beam core retains the cusped square shape during the propagation through the second lens. The electrostatic field of the second lens causes the appearance of an additional spatial rainbow line, which encompasses the beam core and defines the outer border of the beam. This rainbow line constitutes the main difference between the cases of the lens doublet and a single lens.
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Sarapik, Virve. "Rainbow, colours and science mythology." Folklore: Electronic Journal of Folklore 06 (1998): 7–19. http://dx.doi.org/10.7592/fejf1998.06.rainbow.
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Ratia, Katri. "“Respect the Stick!”." Journal of Festive Studies 5 (November 13, 2023): 131–49. http://dx.doi.org/10.33823/jfs.2023.5.1.124.
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Rainbow Gatherings are one of the earliest forerunners of transformative events, with a history spanning five decades. These noncommercial, cocreated, and inclusive meetings have a global spread, offering radical alternatives to social organization and political processes. This essay examines the alternative political model of Rainbow Gatherings through the lens of material culture studies. The analysis follows an object biography of the ritual artifact known as the Talking Stick, central to Rainbow’s political practices, and explores the meaning of the object in material, symbolic, and instrumental senses. Drawing on ethnographic field work at fourteen Rainbow Gatherings across Europe, the essay concludes that organizational models contribute to the transformational potential of events.
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Kaptiol, Ye Yu. "Analysis of the RAINBOW post-quantum electronic signature algorithm state and attacks on it for the period of the NIST PQC third round completion." Radiotekhnika, no. 209 (June 24, 2022): 87–92. http://dx.doi.org/10.30837/rt.2022.2.209.09.
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The paper identifies and analyzes attacks aimed at cryptanalysis of the Rainbow post-quantum electronic signature algorithm and the state of this electronic signature within the framework of the NIST PQC competition and as a whole. The Rainbow electronic signature as a candidate in the third round of the NIST PQC was examined in detail for the possibility of cryptanalysis. The possibility to use this quantitative attack on the Rainbow electronic signature and the complexity of such an attack depends on the possibility to use this electronic signature in the post-quantum period. Also during the NIST PQC report on the peculiarities of the adoption of the first post-quantum standards, which took place on March 8-11, 2022, some concerns about the Rainbow's security were mentioned due to the implementation of an attack on one of the parameter sets (although the parameter set of the second round). Some details of this attack were discussed in the paper to understand better the state of the Rainbow's electronic signature at the end of the third round of the NIST PQC.
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Ćosić, Marko, Srđan Petrović, and Nebojša Nešković. "Quantum Rainbows in Positron Transmission through Carbon Nanotubes." Atoms 7, no. 1 (January 28, 2019): 16. http://dx.doi.org/10.3390/atoms7010016.
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Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes.
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Verde, Francesco. "L’iride e la Trinità: Osservazioni sulle fonti di Basilio, Epistula 38,5." Zeitschrift für Antikes Christentum / Journal of Ancient Christianity 22, no. 3 (November 27, 2018): 383–99. http://dx.doi.org/10.1515/zac-2018-0036.
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Abstract The focus of this contribution is to examine the section 5 (Courtonne) of Basil’s Letter 38 devoted to the rainbow considered as a physical metaphor of the Trinity. The main purpose is to scrutinize the likely ancient pagan sources of Basil’s description of rainbow’s formation. The present article concludes by pointing out that the sources used by Basil could be traced back to Aristotle’s Meteorology and the Stoics (especially Posidonius), without denying an Epicurean influence too. The most interesting point is that the author of the letter seems to occasionally modify the ancient sources on the rainbow he consults in order to make the explanation of the rainbow consistent with his theological/Trinitarian scope. Since several studies confirmed the deep interest of Basil in the explanation of natural phenomena (always for theological and not scientific goals) on the basis of the theories of the ancient pagan Greek philosophers, it cannot be ruled out the possibility that Basil actually was the author of this epistle. This question is very problematic; it is not resolved but, in my opinion, it should also be reconsidered in the light of the part of the letter devoted to the comparison with the rainbow.
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Baran, Dominika. "'Rainbow plague' or 'rainbow allies'?" Gender and Language 16, no. 3 (November 18, 2022): 286–307. http://dx.doi.org/10.1558/genl.21097.
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The anti-genderism register, which demonises the LGBTQ+ community as promoters of so-called 'gender ideology', has spread in recent decades across right wing populist discourses around the world. In Poland, it is an important resource in right wing constructions of national identity, which appeal to a historicised account of Poland as the guardian of European Christianity. However, there is also a counternarrative that envisions Poland as a progressive member of the European Union with secular politics and respect for diversity in all its forms. In this context, the Polish lexeme tecza 'rainbow' is a floating signifier whose meanings are struggled over by opposing discourses of LGBTQ+ rights and their place in Polish public life. Drawing on an analysis of 521 texts from five media outlet types on the right and left wing sides of the political spectrum, this article examines the contestation of tecza as a site where the very meaning of present-day Polishness is discursively negotiated.Rejestr antygenderyzmu, ktory demonizuje spolecznosc LGBTQ+ jako promotorow tak zwanej ,,ideologii gender", w ostatnich dziesiecioleciach rozprzestrzenil sie w prawicowych dyskursach populistycznych na calym swiecie. W Polsce stanowi on istotny element prawicowych konstrukcji tozsamosci narodowej, odwolujacych sie do uhistorycznionego ujecia Polski, postrzeganej jako straznika europejskiego chrzescijanstwa. Istnieje jednak kontrnarracja, prezentujaca Polske jako postepowego czlonka Unii Europejskiej, jako kraj zdolny do prowadzenia swieckiej polityki oraz poszanowania dla roznorodnosci we wszelkich jej przejawach. W takim kontekscie polski leksem ,,tecza" jest ,,plynna znaczaca", o ktorej rozumienie walcza przeciwstawne dyskursy praw LGBTQ+ i ich miejsca w polskim zyciu publicznym. W oparciu o analize 521 tekstow z pieciu rodzajow mediow, zarowno z prawicowej jak i lewicowej strony spektrum politycznego, niniejszy artykul analizuje kontestacje sensu ,,teczy" jako miejsca, w ktorym dyskursywnie negocjowane jest samo znaczenie wspolczesnej polskosci.
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Gettelman, Andrew. "Rainbows and climate change: a tutorial on climate model diagnostics and parameterization." Geoscientific Model Development 16, no. 17 (September 1, 2023): 4937–56. http://dx.doi.org/10.5194/gmd-16-4937-2023.
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Abstract. Earth system models (ESMs) must represent processes below the grid scale of a model using representations (parameterizations) of physical and chemical processes. As a tutorial exercise to understand diagnostics and parameterization, this work presents a representation of rainbows for an ESM: the Community Earth System Model version 2 (CESM2). Using the “state” of the model, basic physical laws, and some assumptions, we generate a representation of this unique optical phenomenon as a diagnostic output. Rainbow occurrence and its possible changes are related to cloud occurrence and rain formation, which are critical uncertainties for climate change prediction. The work highlights issues which are typical of many diagnostic parameterizations such as assumptions, uncertain parameters, and the difficulty of evaluation against uncertain observations. Results agree qualitatively with limited available global “observations” of rainbows. Rainbows are seen in expected locations in the subtropics over the ocean where broken clouds and frequent precipitation occur. The diurnal peak is in the morning over ocean and in the evening over land. The representation of rainbows is found to be quantitatively sensitive to the assumed amount of cloudiness and the amount of stratiform rain. Rainbows are projected to have decreased, mostly in the Northern Hemisphere, due to aerosol pollution effects increasing cloud coverage since 1850. In the future, continued climate change is projected to decrease cloud cover, associated with a positive cloud feedback. As a result the rainbow diagnostic projects that rainbows will increase in the future, with the largest changes at midlatitudes. The diagnostic may be useful for assessing cloud parameterizations and is an exercise in how to build and test parameterizations of atmospheric phenomena.
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Baruch, Jay. "Rainbow." Academic Emergency Medicine 19, no. 8 (July 12, 2012): 990–91. http://dx.doi.org/10.1111/j.1553-2712.2012.01406.x.
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Wu, Fatima, Mao Dun, and Madeline Zelin. "Rainbow." World Literature Today 67, no. 2 (1993): 442. http://dx.doi.org/10.2307/40149302.
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Hewitt, Paul. "RAINBOW." Physics Teacher 44, no. 5 (May 2006): 268. http://dx.doi.org/10.1119/1.2195393.
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Hajdu, Péter. "Rainbow." Neohelicon 42, no. 2 (October 7, 2015): 437–50. http://dx.doi.org/10.1007/s11059-015-0316-7.
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Maretha, Ayu Nanie, Muhammad Mahfuzh Shiddiq, and Na'imah Hijriati. "BILANGAN RAINBOW CONNECTION PADA GRAF-H." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 15, no. 1 (July 16, 2021): 13. http://dx.doi.org/10.20527/epsilon.v15i1.3174.
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Pada teori graf terdapat konsep pewarnaan yaitu pewarnaan sisi dan pewarnaan titik. Apabila ada dua titik yang terhubung oleh lintasan rainbow maka pewarnaan sisi graf disebut rainbow connected. Bilangan rainbow connection yang dinotasikan dengan rc(G) adalah bilangan terkecil dari warna yang dibutuhkan agar terbentuk graf bersifat rainbow connected. Pewarnaan titik pada graf disebut rainbow connected jika sebarang dua titik pada graf berwarna titik dihubungkan oleh lintasan rainbow vertex. Bilangan rainbow vertex connection yang dinotasikan dengan rvc(G) adalah bilangan terkecil dari warna yang dibutuhkan agar terbentuk graf bersifat rainbow vertex connected. Graf- merupakan graf yang berbentuk seperti huruf . Operasi korona merupakan cara untuk menghasilkan dua buah graf menjadi suatu graf baru. Tujuan dari penelitian ini adalah menentukan bilangan rainbow connection dan bilangan rainbow vertex connection pada graf-H. Hasil penelitian yang diperoleh yaitu bilangan rainbow connection pada graf-H yaitu 2n-1 , bilangan rainbow vertex connection pada graf-H yaitu 2n-4 dan bilangan rainbow vertex connection pada graf H korona mK_1 adalah 2n.
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LeSaulnier, Timothy D., and Douglas B. West. "Rainbow edge-coloring and rainbow domination." Discrete Mathematics 313, no. 19 (October 2013): 2020–25. http://dx.doi.org/10.1016/j.disc.2012.03.014.
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Li, Can, Wenmin Peng, Yang Kang, Xudong Fan, Xiaolong Huang, Ning Li, Chunsheng Weng, and Cameron Tropea. "Rainbow refractometry using partial rainbow signals." Optics & Laser Technology 158 (February 2023): 108872. http://dx.doi.org/10.1016/j.optlastec.2022.108872.
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Fadillah, Fadillah, Lyra Yulianti, and Syafrizal Sy. "RAINBOW CONNECTION NUMBER PADA GRAF (3K6 ∗ W6, v)." Jurnal Matematika UNAND 7, no. 3 (February 19, 2019): 43. http://dx.doi.org/10.25077/jmu.7.3.43-46.2018.
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Misalkan G = (V, E) adalah graf terhubung tak trivial. Definisikan pewarnaan c : E(G) → {1, 2, · · · , k} untuk suatu k ∈ N, dimana sisi yang bertetangga boleh diberi warna yang sama. Misalkan terdapat titik u dan v di G. Suatu lintasan-(u, v) di G dikatakan sebagai lintasan rainbow (rainbow path) jika semua sisi dalam lintasan-(u, v) tersebut memiliki warna yang berbeda. Graf G dikatakan bersifat rainbow connected terhadap pewarnaan c jika G memuat lintasan rainbow untuk setiap dua titik u dan v di G, sementara c dikatakan sebagai pewarnaan rainbow (rainbow coloring) dari G. Jika terdapat k warna yang digunakan dalam pewarnaan tersebut maka c dinamakan pewarnaan-k rainbow (rainbow k-coloring). Bilangan rainbow connection (rainbow connection number ) dari graf terhubung G, dinotasikan dengan rc(G), didefinisikan sebagai banyaknya warna minimum yang diperlukan untuk membuat graf G bersifat rainbow connected. Pada makalah ini akan ditentukan nilai bilangan rainbow connection dari graf yang merupakan hasil amalgamasi tiga graf lengkap, masing-masingnya dengan enam titik, 3K6, dengan graf roda W6, dinotasikan dengan graf (3K6 ∗ W6, v).Kata Kunci: Graf (3K6 ∗ W6, v), rainbow path, rainbow connection number
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Adawiyah, R., I. I. Makhfudloh, Dafik Dafik, RM Prihandini, and AC Prihandoko. "ON RAINBOW ANTIMAGIC COLORING OF SNAIL GRAPH(S_n ), COCONUT ROOT GRAPH (Cr_(n,m) ), FAN STALK GRAPH (Kt_n ) AND THE LOTUS GRAPH(Lo_n )." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 3 (September 30, 2023): 1543–52. http://dx.doi.org/10.30598/barekengvol17iss3pp1543-1552.
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Rainbow antimagic coloring is a combination of antimagic labeling and rainbow coloring. Antimagic labeling is labeling of each vertex of the graph with a different label, so that each the sum of the vertices in the graph has a different weight. Rainbow coloring is part of the rainbow-connected edge coloring, where each graph has a rainbow path. A rainbow path in a graph is formed if two vertices on the graph do not have the same color. If the given color on each edge is different, for example in the function it is colored with a weight , it is called rainbow antimagic coloring. Rainbow antimagic coloring has a condition that every two vertices on a graph cannot have the same rainbow path. The minimum number of colors from rainbow antimagic coloring is called the rainbow antimagic connection number, denoted by In this study, we analyze the rainbow antimagic connection number of snail graph , coconut root graph , fan stalk graph and lotus graph .
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Barris, Michael C. "The Rainbow Bridge: Rainbows in Art, Myth, and Science." Optometry and Vision Science 79, no. 4 (April 2002): 216–17. http://dx.doi.org/10.1097/00006324-200204000-00007.
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Retnowardani, Dwi Agustin, Brian Juned Septory, Kamal Dliou, and Audia Dwi Retno Wulandari. "Rainbow Antimagic Coloring pada Graf Hasil Operasi Join pada Graf Broom." ESTIMATOR : Journal of Applied Statistics, Mathematics, and Data Science 1, no. 1 (June 30, 2023): 19–27. http://dx.doi.org/10.31537/estimator.v1i1.1180.
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Misalkan adalah graf terhubung dengan himpunan titik dan himpunan sisi . Fungsi bijektif dari ke himpunan adalah pelabelan titik graf . Fungsi bijektif disebut rainbow antimagic labeling jika untuk setiap dua sisi dan dalam lintasan , dengan dan . Rainbow antimagic coloring adalah pewarnaan graf dengan rainbow antimagic labeling. Jadi, setiap rainbow antimagic labeling merupakan pewarnaan pelangi graf dengan bobot sisi adalah warna sisi . Rainbow antimagic connection number pada graf adalah jumlah warna terkecil dari semua rainbow antimagic coloring graf , dinotasikan dengan . Pada penelitian ini, dipelajari rainbow antimagic coloring dan mendapatkan nilai rainbow antimagic connection number graf hasil operasi join .
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Muchlian, Melvi. "BILANGAN RAINBOW CONNECTION UNTUK BEBERAPA GRAF THORN." Jurnal Matematika UNAND 5, no. 3 (August 30, 2016): 65. http://dx.doi.org/10.25077/jmu.5.3.65-76.2016.
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Abstrak. Misalkan G = (V (G);E(G)) adalah suatu graf terhubung tak trivial. Denisipewarnaan c : E(G) ! f1; 2; ; kg; k 2 N, dimana dua sisi yang bertetangga bolehberwarna sama. Suatu lintasan u v path P di G dinamakan rainbow path jika tidakterdapat dua sisi di P yang berwarna sama. Graf G disebut rainbow connected jikasetiap dua titik yang berbeda di G dihubungkan oleh rainbow path. Pewarnaaan sisiyang menyebabkan G bersifat rainbow connected dikatakan rainbow coloring. Bilan-gan Rainbow connection dari graf terhubung G, ditulis rc(G), didenisikan sebagaibanyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow con-nected. Misalkan c adalah rainbow coloring dari graf terhubung G. Untuk dua titik udan v di G, rainbow uv geodesic pada G adalah rainbow uv path yang panjangnyad(u; v) dimana d(u; v) adalah jarak antara u dan v (panjang u v path terpendek di(G). Graf G dikatakan strongly rainbow connected jika G memiliki suatu rainbow u vgeodesic untuk setiap dua titik u dan v di G.Minimum k yang terdapat pada pewar-naan c : E(G) ! f1; 2; ; kg sedemikian sehingga G adalah strongly rainbow connecteddikatakan bilangan strong rainbow connection, src(G), di G. Jadi, rc(G) src(G) un-tuk setiap graf terhubung di G. Pada paper ini akan diulas kembali tentang BilanganRainbow Connection untuk Beberapa Graf Thorn.
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Wang, Fu-Hsing, and Cheng-Ju Hsu. "Rainbow Connection Numbers of WK-Recursive Networks and WK-Recursive Pyramids." Mathematics 12, no. 7 (March 22, 2024): 944. http://dx.doi.org/10.3390/math12070944.
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An edge coloring of a graph G results in G being rainbow connected when every pair of vertices is linked by a rainbow path. Such a path is defined as one where each edge possesses a distinct color. A rainbow coloring refers to an edge coloring that guarantees the rainbow connectedness of G. The rainbow connection number of G represents the smallest quantity of colors required to achieve rainbow connectedness under a rainbow coloring scheme. Wang and Hsu (ICICM 2019: 75–79) provided upper bounds on the size of the rainbow connection numbers in WK-recursive networks WKd,t and WK-recursive pyramids WKPd,n. In this paper, we revise their results and determine the exact values of the rainbow connection numbers of WKd,2 for d=3 and 4. The rainbow connection numbers of WKd,2 are bounded between 4 and ⌊d2⌋+2 for d>4. In addition to our previous findings, we further investigate and determine upper bounds for the size of the rainbow connection numbers of WKPd,n. This involves analyzing various aspects of the graph structure and exploring potential limitations on the rainbow connection numbers. By establishing these upper bounds, we gain deeper insights into the potential range and constraints of the rainbow connection numbers within the given context.
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Septory, Brian Juned, Liliek Susilowati, Dafik Dafik, and M. Venkatachalam. "On Rainbow Antimagic Coloring of Joint Product of Graphs." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 4 (May 24, 2023): 548–58. http://dx.doi.org/10.18860/ca.v7i4.17471.
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Let be a connected graph with vertex set and edge set . A bijection from to the set is a labeling of graph . The bijection is called rainbow antimagic vertex labeling if for any two edge and in path , where and . Rainbow antimagic coloring is a graph which has a rainbow antimagic labeling. Thus, every rainbow antimagic labeling induces a rainbow coloring G where the edge weight is the color of the edge . The rainbow antimagic connection number of graph is the smallest number of colors of all rainbow antimagic colorings of graph , denoted by . In this study, we studied rainbow antimagic coloring and have an exact value of rainbow antimagic connection number of joint product of graph where is graph , graph , graph , graph and graph .
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Medika, Gema Hista. "RAINBOW CONNECTION PADA BEBERAPA GRAF." Jurnal Matematika UNAND 2, no. 2 (June 10, 2013): 17. http://dx.doi.org/10.25077/jmu.2.2.17-25.2013.
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Misalkan G adalah graf terhubung tak-trivial. Denisikan pewarnaan c :E(G) ! f1; 2; :::; kg, k 2 N, dimana dua sisi yang bertetangga boleh memiliki warnayang sama. Suatu u v path P di G dikatakan rainbow path jika tidak ada dua sisi diP yang memiliki warna sama. Graf G dikatakan rainbow connected jika setiap dua titikyang berbeda di G dihubungkan oleh rainbow path. Pewarnaan sisi yang menyebabkan Gbersifat rainbow connected dikatakan rainbow coloring. Rainbow connection number darigraf terhubung G, ditulis rc(G), didenisikan sebagai banyaknya warna minimal yangdiperlukan untuk membuat graf G bersifat rainbow connected. Misalkan c adalah rainbowcoloring dari graf terhubung G. Untuk dua titik u dan v di G, rainbow u-v geodesic padaG adalah rainbow u-v path yang panjangnya d(u; v), dimana d(u; v) adalah jarak antarau dan v (panjang u-v path terpendek di G). Graf G dikatakan strongly rainbow-connectedjika G memiliki suatu rainbow u-v geodesic untuk setiap dua titik u dan v di G. Mini-mum k yang terdapat pada pewarnaan c : E(G) ! f1; 2; :::; kg sedemikian sehingga Gadalah strongly rainbow-connected dikatakan strong rainbow connection number, src(G);di G. Jadi, rc(G) src(G) untuk setiap graf terhubung di G. Pada paper ini akan di-ulas kembali tentang strong rainbow connection number dari graf bipartit lengkap Ks;tdengan 1 s t dimana s; t 2 N adalah src(Ks;t) = d spte, sedangkan rainbow connec-tion number dari graf bipartit lengkap Ks;t dengan 2 s t dimana s; t 2 N adalahrc(Ks;t) = minfd spte; 4g.
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., Maradona. "BILANGAN STRONG RAINBOW CONNECTION UNTUK GRAF GARIS, GRAF MIDDLE DAN GRAF TOTAL." Jurnal Matematika UNAND 5, no. 2 (May 30, 2016): 102. http://dx.doi.org/10.25077/jmu.5.2.102-112.2016.
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Abstrak. Misalkan G = (V (G); E(G)) adalah suatu graf terhubung tak trivial. Denisipewarnaan c : E(G) ! f1; 2; ; kg; k 2 N, dimana dua sisi yang bertetanggaboleh berwarna sama. Suatu lintasan u v path P di G dinamakan rainbow path jikatidak terdapat dua sisi di P yang berwarna sama. Graf G disebut rainbow connectedjika setiap dua titik yang berbeda di G dihubungkan oleh rainbow path. Pewarnaaansisi yang menyebabkan G bersifat rainbow connected dikatakan rainbow coloring. Bilanganrainbow connection dari graf terhubung G, ditulis rc(G), didenisikan sebagaibanyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow connected.Misalkan c adalah rainbow coloring dari graf terhubung G. Untuk dua titik udan v di G, rainbow u v geodesic pada G adalah rainbow u v path yang panjangnyad(u; v) dimana d(u; v) adalah jarak antara u dan v (panjang u v path terpendek di(G). Graf G dikatakan strongly rainbow connected jika G memiliki suatu rainbow u vgeodesic untuk setiap dua titik u dan v di G. Minimum k yang terdapat pada pewarnaanc : E(G) ! f1; 2; ; kg sedemikian sehingga G adalah strongly rainbow connecteddikatakan bilangan strong rainbow connection, src(G), di G. Jadi, rc(G) src(G) untuksetiap graf terhubung di G. Pada paper ini akan dikaji kembali tentang bilangan strongrainbow connection untuk graf Garis, graf Middle dan graf Total dari Graf Matahari,seperti yang telah dibahas dalam [1].
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Yuliani, Witri. "BILANGAN STRONG RAINBOW CONNECTION UNTUK GRAF RODA DAN GRAF KUBIK." Jurnal Matematika UNAND 5, no. 4 (November 29, 2016): 72. http://dx.doi.org/10.25077/jmu.5.4.72-79.2016.
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Abstrak. Misalkan G = (V (G); E(G)) adalah suatu graf terhubung tak trivial. Denisikansuatu pewarnaan c : E(G) ! f1; 2; ; kg; k 2 N, dimana dua sisi yang bertetanggaboleh berwarna sama. Suatu lintasan u v path P di G dinamakan rainbow pathjika tidak terdapat dua sisi di P yang berwarna sama. Graf G disebut rainbow connectedjika setiap dua titik yang berbeda di G dihubungkan oleh rainbow path. Pewarnaansisi yang menyebabkan G bersifat rainbow connected dikatakan rainbow coloring. BilanganRainbow connection dari graf terhubung G, ditulis rc(G), didenisikan sebagaibanyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow connected.Misalkan c adalah rainbow coloring dari graf terhubung G. Untuk dua titik udan v di G, rainbow u v geodesic pada G adalah rainbow u v path yang panjangnyad(u; v) dimana d(u; v) adalah jarak antara u dan v (panjang u v path terpendek diG. Graf G dikatakan strongly rainbow connected jika G memiliki suatu rainbow u vgeodesic untuk setiap dua titik u dan v di G. Minimum k yang terdapat pada pewarnaanc sedemikian sehingga G adalah strongly rainbow connected dikatakan bilangan strongrainbow connection, src(G), di G. Pada paper ini akan dikaji tentang bilangan strongrainbow connection untuk graf Roda dan graf Kubik.
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Brooks, Charlotte K. "Rainbow Teachers Rainbow Students: Issues and Concerns." English Journal 83, no. 5 (September 1, 1994): 76–77. http://dx.doi.org/10.58680/ej19947582.
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Brooks, Charlotte K. "Rainbow Teachers Rainbow Students: A Final Column." English Journal 85, no. 4 (April 1, 1996): 65–66. http://dx.doi.org/10.58680/ej19965272.
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Cruz, MaryCarmen, and Ogle Burks Duff. "Rainbow Teachers/Rainbow Students: Continuing the Legacy." English Journal 85, no. 5 (September 1, 1996): 88–91. http://dx.doi.org/10.58680/ej19965299.
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Lestari, Dia, and I. Ketut Budayasa. "BILANGAN KETERHUBUNGAN PELANGI PADA PEWARNAAN-SISI GRAF." MATHunesa: Jurnal Ilmiah Matematika 8, no. 1 (April 23, 2020): 25–34. http://dx.doi.org/10.26740/mathunesa.v8n1.p25-34.
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Let be a graph. An edge-coloring of is a function , where is a set of colors. Respect to a subgraph of is called a rainbow subgraph if all edges of get different colors. Graph is called rainbow connected if for every two distinct vertices of is joined by a rainbow path. The rainbow connection number of , denoted by , is the minimum number of colors needed in coloring all edges of such that is a rainbow connected. The main problem considered in this thesis is determining the rainbow connection number of graph. In this thesis, we determine the exact value of the rainbow connection number of some classes of graphs such as Cycles, Complete graph, and Tree. We also determining the lower bound and upper bound for the rainbow connection number of graph.
Keywords: Rainbow Connection Number, Graph, Edge-Coloring on Graph.
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RIEZSA DESSYLUVIANI, SUCI. "PENENTUAN RAINBOW CONNECTION NUMBER DAN STRONG RAINBOW CONNECTION NUMBER PADA GRAF BERLIAN." Jurnal Matematika UNAND 6, no. 3 (November 3, 2017): 93. http://dx.doi.org/10.25077/jmu.6.3.93-99.2017.
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Misalkan G = (V, E) adalah suatu graf. Suatu pewarnaan c : E(G) → {1, 2, · · · , k}, k ∈ N pada graf G adalah suatu pewarnaan sisi di G sedemikian sehingga setiap sisi bertetangga boleh berwarna sama. Misalkan u, v ∈ V (G) dan P adalah suatu lintasan dari u ke v. Suatu intasan P dikatakan rainbow path jika tidak terdapat dua sisi di P berwarna sama. Graf G disebut rainbow connected dengan pewarnaan c jika untuk setiap u, v ∈ V (G) terdapat rainbow path dari u ke v. Jika terdapat k warna di G maka c adalah rainbow k-coloring. Rainbow connection number dari graf terhubung dinotasikan dengan rc(G), didefinisikan sebagai banyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow connected. Selanjutnya, pewarnaan c dikatakan pewarnaan-k strong rainbow, jika untuk setiap titik u dan v di V terdapat lintasan pelangi dengan panjangnya sama dengan jarak u dan v. Dalam makalah ini akan ditentukan rainbow connection number dan Strong Rainbow Connection Number pada graf Berlian dengan 2n titik. Graf Berlian, dinotasikan dengan Brn, adalah graf yang diperoleh dari graf tangga segitiga dengan 2n − 1 titik, dengan menambahkan satu titik dan beberapa sisi tertentu. Dalam makalah ini akan ditentukan rc(Brn) dan src(Brn) untuk n ≥ 4. Kata Kunci: Rainbow connection number, Strong rainbow connection number, Graf Berlian, Lintasan, Pewarnaan Rainbow
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Garattini, Remo. "Traversable wormholes in distorted gravity." International Journal of Modern Physics D 24, no. 09 (July 31, 2015): 1542025. http://dx.doi.org/10.1142/s0218271815420250.
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In this paper, we consider the effects of distorted gravity on the traversability of the wormholes. In particular, we consider configurations which are sustained by their own gravitational quantum fluctuations. The Ultraviolet divergences appearing to one loop are taken under control with the help of a Noncommutative geometry representation and gravity's rainbow. In this context, it will be shown that for every framework, the self-sustained equation will produce a Wheeler wormhole, namely a wormhole of Planckian size. This means that, from the point of view of traversability, the wormhole will be traversable in principle, but not in practice. For this purpose, in the context of gravity's rainbow we have considered different proposals of rainbow's functions to see if the smallness of the wormhole is dependent on the chosen form of the rainbow's function. Unfortunately, we discover that this is not the case and we suggest that the self-sustained equation can be improved to see if the wormhole radius can be enlarged or not. Some consequences on topology change are discussed.
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Bustan, A. W., A. N. M. Salman, and P. E. Putri. "On the locating rainbow connection number of amalgamation of complete graphs." Journal of Physics: Conference Series 2543, no. 1 (July 1, 2023): 012004. http://dx.doi.org/10.1088/1742-6596/2543/1/012004.
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Abstract Locating rainbow connection number determines the minimum number of colors connecting any two vertices of a graph with a rainbow vertex path and also verifies that the given colors produce a different rainbow code for each vertex. Locating rainbow connection number of graphs is a new mathematical concept, especially in graph theory, which combines the concepts of the rainbow vertex coloring and the partition dimension. In this paper, we determine the locating rainbow connection number of amalgamation of complete graphs.
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Nurhasanah, Nurhasanah, Syafrizal Sy, and Lyra Yulianti. "BILANGAN RAINBOW CONNECTION UNTUK BEBERAPA GRAF CORONA SISI." Jurnal Matematika UNAND 4, no. 2 (July 26, 2019): 16. http://dx.doi.org/10.25077/jmu.4.2.16-21.2015.
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Suatu lintasan uP v dikatakan sebagai rainbow path pada G jika tidak ada dua sisi pada P yang berwarna sama. Suatu graf G dikatakan rainbow-connected terhadap pewarnaan sisi-sisi, jika G memuat lintasan rainbow u − v untuk setiap dua titik u dan v pada G. Suatu pewarnaan sisi dimana G bersifat rainbow connected dinamakan rainbow coloring terhadap G. Pada tulisan ini akan ditentukan bilangan rainbow connection untuk corona sisi dari beberapa graf sederhana, yaitu rc(G H) untuk G atau H adalah graf lengkap Kn, graf lintasan Pn dan graf siklus Cn, n ≥ 3.Kata Kunci: Graf lengkap, lintasan, siklus, bilangan rainbow connection
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Mooduto, Randi, Lailany Yahya, and Nisky Imansyah Yahya. "Total Rainbow Connection Number of Corona Product of Book Graph(Bn) and Pencil Graf(Pcm)." Sainsmat : Jurnal Ilmiah Ilmu Pengetahuan Alam 12, no. 2 (September 29, 2023): 153. http://dx.doi.org/10.35580/sainsmat122423112023.
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Let G be a simple and finite graph. Rainbow connection and total rainbow connection c are set c : G → {1,2,. . . , k} where k is the minimal color on graph G. A rainbow connection number(rc) is a pattern by giving different colors to the connection edges (E(G)) so that a rainbow path is formed. The total rainbow connection number (trc) is a payment pattern by giving color to vertices (V(G)) and edges (E(G)) in graph G so that a total rainbow path is formed. This article discusses rainbow connection numbers (rc) and total rainbow connection numbers (trc) in the corona graph of book graph (Bn) and pencil graph (Pcm). The results obtained are rc(Bn ⨀ Pcm) = 2n+3 and trc(Bn ⨀ Pcm) = 4n+5, 3 ≤ n ≤ 5.
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Nguyen Thi Thuy, Anh, and Duyen Le Thi. "A NOTE ON GENERALIZED RAINBOW CONNECTION OF CONNECTED GRAPHS AND THEIR NUMBER OF EDGES." Journal of Science Natural Science 66, no. 3 (October 2021): 3–7. http://dx.doi.org/10.18173/2354-1059.2021-0041.
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Let l ≥ 1, k ≥ 1 be two integers. Given an edge-coloured connected graph G. A path P in the graph G is called l-rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called (k, l)-rainbow connected if any two vertices in G are connected by at least k pairwise internally vertex-disjoint l-rainbow paths. The smallest number of colours needed in order to make G (k, l)-rainbow connected is called the (k, l)-rainbow connection number of G and denoted by rck,l(G). In this paper, we first focus to improve the upper bound of the (1, l)-rainbow connection number depending on the size of connected graphs. Using this result, we characterize all connected graphs having the large (1, 2)-rainbow connection number. Moreover, we also determine the (1, l)-rainbow connection number in a connected graph G containing a sequence of cut-edges.
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Zimmerman, Christian E., and Gordon H. Reeves. "Population structure of sympatric anadromous and nonanadromous Oncorhynchus mykiss: evidence from spawning surveys and otolith microchemistry." Canadian Journal of Fisheries and Aquatic Sciences 57, no. 10 (October 1, 2000): 2152–62. http://dx.doi.org/10.1139/f00-192.
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Reproductive isolation between steelhead and resident rainbow trout (Oncorhynchus mykiss) was examined in the Deschutes River, Oregon, through surveys of spawning timing and location. Otolith microchemistry was used to determine the occurrence of steelhead and resident rainbow trout progeny in the adult populations of steelhead and resident rainbow trout in the Deschutes River and in the Babine River, British Columbia. In the 3 years studied, steelhead spawning occurred from mid March through May and resident rainbow trout spawning occurred from mid March through August. The timing of 50% spawning was 9-10 weeks earlier for steelhead than for resident rainbow trout. Spawning sites selected by steelhead were in deeper water and had larger substrate than those selected by resident rainbow trout. Maternal origin was identified by comparing Sr/Ca ratios in the primordia and freshwater growth regions of the otolith with a wavelength-dispersive electron microprobe. In the Deschutes River, only steelhead of steelhead maternal origin and resident rainbow trout of resident rainbow trout origin were observed. In the Babine River, steelhead of resident rainbow trout origin and resident rainbow trout of steelhead maternal origin were also observed. Based on these findings, we suggest that steelhead and resident rainbow trout in the Deschutes River may constitute reproductively isolated populations.
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Aryani, Suciana Budi, Lyra Yulianti, and Syafrizal Sy . "BATAS ATAS BILANGAN RAINBOW CONNECTION UNTUK GRAF KUBIK C n;2n;2n;2n;n." Jurnal Matematika UNAND 7, no. 1 (February 14, 2018): 143. http://dx.doi.org/10.25077/jmu.7.1.143-148.2018.
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Abstrak. Misalkan G merupakan suatu graf terhubung tak trivial. Didenisikan suatupewarnaan c : E(G) ! f1; 2; ; ng; n 2 N, dimana sisi yang bertetangga bolehberwarna sama. Suatu lintasan u v path dikatakan sebagai rainbow path pada G jikatidak terdapat dua sisi pada path yang berwarna sama. Suatu graf G dikatakan rainbowconnectedterhadap pewarnaan sisi, jika G memuat rainbow u-v path untuk setiap duatitik u dan v pada G. Jika graf G bersifat rainbow connected maka pewarnaan sisinyadinamakan rainbow coloring pada G. Bilangan rainbow connection (rc) (rainbow connectionnumber) dari G, dilambangkan dengan rc(G), didenisikan sebagai minimumbanyaknya warna yang diberikan pada G sedemikian sehingga G merupakan rainbow(rainbow connected). Suatu Graf Kubik Cadalah suatu graf kubik yangdibentuk dari lima buah lingkaran dengan banyak titik lingkaran pertama sama denganbanyak titik lingkaran kelima yaitu sebanyak n dan lingkaran ke-dua, ke-tiga, dan keempatadalah sebanyak 2n dengan himpunan sisi En;2n;2n;2n;nmerupakan himpunan sisi yangmenghubungkan lintasan ke-i dengan lingkaran ke-i +1. Pada paper ini akan dibuktikanbahwa batas atas bilangan Rainbow Connection untuk Graf kubik Ciadalah11 dan Graf kubik C6;12;12;12;6adalah 14.Kata Kunci: Graf kubik, graf cycle, bilangan rainbow connection5;10;10;10;5
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Chartrand, Gary, Garry L. Johns, Kathleen A. McKeon, and Ping Zhang. "Rainbow connection in graphs." Mathematica Bohemica 133, no. 1 (2008): 85–98. http://dx.doi.org/10.21136/mb.2008.133947.
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Anggalia, Fitri, LYRA YULIANTI, and DES WELYYANTI. "BATAS ATAS RAINBOW CONNECTION NUMBER PADA GRAF BUCKMINSTERFULLERENE." Jurnal Matematika UNAND 11, no. 1 (April 7, 2022): 1. http://dx.doi.org/10.25077/jmu.11.1.1-11.2022.
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Misalkan G adalah suatu graf terhubung tak trivial. Suatu pewarnaan c :E(G) → {1, 2, ..., k}, k ∈ N pada graf G adalah suatu pewarnaan sisi di G sedemikiansehingga setiap sisi bertetangga boleh berwarna sama. Misalkan u, v ∈ V (G) dan Padalah suatu lintasan dari u ke v. Suatu lintasan P dikatakan rainbow path jika tidakterdapat dua sisi di P berwarna sama. Graf G disebut rainbow connected dengan pewarnaan c jika untuk setiap u, v ∈ V (G) terdapat rainbow path dari u ke v. Jika terdapat k warna di G maka c adalah rainbow k-coloring. Rainbow connection number dari graf terhubung dinotasikan dengan rc(G), didefinisikan sebagai banyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow connected. Dalam makalah ini akan ditentukan batas atas Rainbow Connection Number pada Graf Buckminsterfullerene.Kata Kunci: Graf Buckminsterfullerene, Rainbow connection number
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Wijaya, Reni. "BILANGAN RAINBOW CONNECTION UNTUK GRAF KOMPLEMEN." Jurnal Matematika UNAND 2, no. 3 (September 10, 2013): 9. http://dx.doi.org/10.25077/jmu.2.3.9-12.2013.
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Misalkan terdapat dua titik u, v pada graf G. Suatu u-v path, dinotasikandengan uPv di G, dikatakan rainbow path jika tidak terdapat dua sisi di P yang memiliki warna sama. Suatu pewarnaan sisi di G dikatakan rainbow connected jika setiapdua titik yang berbeda dihubungkan oleh rainbow path. Bilangan rainbow connectiondari graf terhubung G, ditulis rc(G), didefinisikan sebagai banyaknya warna minimalyang diperlukan untuk membuat G bersifat rainbow connected. Pada tulisan ini dibahastentang bilangan rainbow connection untuk komplemen dari graf lingkaran Cn dengann ≥ 6 dan graf buku B 2.
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Jiang, Huiqin, and Yongsheng Rao. "Total 2-Rainbow Domination in Graphs." Mathematics 10, no. 12 (June 14, 2022): 2059. http://dx.doi.org/10.3390/math10122059.
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A total k-rainbow dominating function on a graph G=(V,E) is a function f:V(G)→2{1,2,…,k} such that (i) ∪u∈N(v)f(u)={1,2,…,k} for every vertex v with f(v)=∅, (ii) ∪u∈N(v)f(u)≠∅ for f(v)≠∅. The weight of a total 2-rainbow dominating function is denoted by ω(f)=∑v∈V(G)|f(v)|. The total k-rainbow domination number of G is the minimum weight of a total k-rainbow dominating function of G. The minimum total 2-rainbow domination problem (MT2RDP) is to find the total 2-rainbow domination number of the input graph. In this paper, we study the total 2-rainbow domination number of graphs. We prove that the MT2RDP is NP-complete for planar bipartite graphs, chordal bipartite graphs, undirected path graphs and split graphs. Then, a linear-time algorithm is proposed for computing the total k-rainbow domination number of trees. Finally, we study the difference in complexity between MT2RDP and the minimum 2-rainbow domination problem.