45,119 research outputs found
Turan H-densities for 3-graphs
No full textGiven an r-graph H on h vertices, and a family F of forbidden subgraphs, we define ex H (n, F) to be the maximum number of induced copies of H in an F-free r-graph on n vertices. Then the Turan H-density of F is the limit pi(H)(F) = (lim)(n ->infinity) ex(H)(n, F)/((n)(h)) This generalises the notions of Turan-density (when H is an r-edge), and inducibility (when F is empty). Although problems of this kind have received some attention, very few results are known. We use Razborov's semi-definite method to investigate Turan H-densities for 3-graphs. In particular, we show that pi(-)(K4)(K-4) = 16/27, with Turans construction being optimal. We prove a result in a similar flavour for K-5 and make a general conjecture on the value of pi(Kt)-(K-t). We also establish that pi(4.2)(empty set) = 3/4, where 4: 2 denotes the 3-graph on 4 vertices with exactly 2 edges. The lower bound in this case comes from a random geometric construction strikingly different from previous known extremal examples in 3-graph theory. We give a number of other results and conjectures for 3-graphs, and in addition consider the inducibility of certain directed graphs. Let (S) over right arrow (k) be the out-star on k vertices; i.e. the star on k vertices with all k 1 edges oriented away from the centre. We show that pi((S) over right arrow3)(empty set) = 2 root 3 - 3, with an iterated blow-up construction being extremal. This is related to a conjecture of Mubayi and Rodl on the Turan density of the 3-graph C-5. We also determine pi((S) over right arrowk) (empty set) when k = 4, 5, and conjecture its value for general k
Some exact results for generalized Turan problems
No full textFix a k-chromatic graph F. In this paper we consider the question to determine for which graphs H does the Turan graph Tk-1(n) have the maximum number of copies of H among all n-vertex F-free graphs (for n large enough). We say that such a graph H is F-Turan-good. In addition to some general results, we give (among others) the following concrete results: (i) For every complete multipartite graph H, there is k large enough such that H is K-k-Turan-good. (ii) The path P-3 is F-Turan-good for F with chi(F) >= 4. (iii) The path P-4 and cycle C-4 are C5-Turan-good. (iv) The cycle C-4 is F-2-Turan-good where F-2 is the graph of two triangles sharing exactly one vertex
Letter from C. H. Gensler, Havasupai Agency to Carl Hayden
No full textLetter from C. H. Gensler expressing concern on behalf of the Havasupai Tribe regarding the proposed park boundaries
Citations of the author H C Rajpoot
No full textThe list of the articles, research papers, theses, and book chapters globally citing the author H. C. Rajpoot</p
Letter from Carl Hayden to C. H. Gensler
No full textLetter from Carl Hayden to C. H. Gensler informing him of the proposed Grand Canyon National Park bill
Letter from C. H. Gensler, Havasupai Agency to Carl Hayden
No full textLetter from C. H. Gensler to Carl Hayden asking for a meeting in regards to the Havasupai pasture land in light of the national park bill
Generalized Turan densities in the hypercube
No full textA classical extremal, or Turan-type problem asks to determine ex(G, H), the largest number of edges in a subgraph of a graph G which does not contain a subgraph isomorphic to H. Alon and Shikhelman introduced the so-called generalized extremal number ex(G, T, H), defined to be the maximum number of subgraphs isomorphic to T in a subgraph of G that contains no subgraphs isomorphic to H. In this paper we investigate the case when G = Qn, the hypercube of dimension n, and T and H are smaller hypercubes or cycles. (c) 2022 Elsevier B.V. All rights reserved
Silver-Mediated Direct sp(3) C-H Bond Functionalization
No full textDirect sp(3) C-H bond functionalization is an efficient, straightforward, and powerful method to construct new C-X (X = C, N, F, S) bonds from nonfunctionalized aliphatic motif of organic molecules, which has been used in late-stage modification of complex molecules. In this chapter, the recent developments of silver-mediated direct sp(3) C-H functionalizations are reviewed, categorized by C-C bond formation (C-H insertion), C-N bond formation (intramolecular and intermolecular amination/amidation), C-F bond formation, and C-S bond formation.SCI(E)[email protected]
Letter from Carl T. Hayden to C. H. Gensler, Havasupai Reservation
No full textLetter from Carl T. Hayden to C. H. Gensler, Havasupai Indian Reservation, regarding Hualapai and Cataract Canyons geography
Capoeta banarescui Turan, Kottelat, Ekmekci and Imamoglu 2006
No full textCapoeta banarescui Turan, Kottelat, Ekmekçi and İmamoğlu, 2006 Types. Holotype. ESFM-PISI/2004-072, 177 mm SL; Turkey: Artvin: Tortum District: Çoruh drainage, stream Tortum, 100 km north of Erzurum; 40°34' N 41°36' E; D. Turan, F. Ekmekci, H. Imamoglu, O. Serdar, S. Kırankaya, 19.07.2004. Paratypes. ESFM-PISI/2004-073, 4, 166- 201 mm SL; FFR 712, 16, 85-232 mm SL; CMK 18474, 5, 135-193 mm SL; same data as holotype. — FFR 711, 9, 163 — 231 mm SL; CMK 18540, 9, 121 — 193 mm SL; Turkey: Artvin: Chorokh drainage, Bulanık stream, Savsat, 30 km east of Artvin, 41°34' N 42°14' E; D. Turan, F. Ekmekci, H. Imamoglu, O. Serdar, S. Kırankaya, 19.06.2004. — FFR 720, 3, 92 — 125 mm SL; CMK 18549, 1, 145 mm SL; Turkey: Cavuslu, Borcka, 41°21' N 41°42' E; D. Turan, 13.10.2004 (after Turan et al., 2006 b). T y p e L o c a l i t y. Chorokh River. D i a g n o s i s. Meristic characters (tables 1–4): D: III-IV 7–9 (8.0), P: I 17–19 (17.8), V: I 9–10 (9.1), A: III 5, lateral line: 64–77 (70.8), scales number above/below lateral line: 12–14 (12.8)/8–9 (8.1). C. banarescui is distinguished from other Capoeta species of East and South–East Black Sea rivers (C. svanetica sp. n., C. sieboldi, C. oguzelii, C. baliki, C. ekmekciae, and also from C. tinca Sea of Marmara basin) by the combination of characters. Two pairs of barbels (C. sieboldi and C. oguzelii have only one pair); gill rakers number (12–16 (14.7)) higher than in C. oguzelii but fewer than for C. sieboldi, C. baliki, C. tinca, and C. ekmekciae; last unbranched dorsal-fin ray well ossified with the high number of serrae (unlike C. sieboldi and C. oguzelii); 8–9 scales rows below the lateral line (less than in C. baliki and C. oguzelii). C. banarescui is also characterized by longer posterior barbels 18.4–28.8 (21.9) than the same parameter for C. baliki and C. tinca. D i s t r i b u t i o n. C. banarescui is known from Chorokh and Yesilırmak rivers (Turan et. al., 2006 a; Elp et al., 2018). This species is also noted for Georgian waters (Kuljanishvili et al., 2020). Some additional samples were studied from the Rioni River basin (Gubistskali River, fig. 9) and Chorokh River (fig. 10). These individuals were recognized as C. banarescui Thus, we should conclude C. banarescui is the widest distributed species in West Georgian rivers from Rioni to Chorokh. There are no clear differences in morphological features (meristics and morphometrics, including mouth arching — fig. 9, b and, 10 b) but some differences in general body appearance and coloration should be concluded. Specimen from Gubistskali River is slightly elongated with more concave dorsal and anal fins. Specimen from Chorokh River is slightly highest with straightly edged dorsal and anal fins. The coloration of the first is goldish in total, darker on the back and lighter on the belly, with more dark (up to brown) fins. Chorokh’s specimen had more greyish coloration on the back and lighter (up to white) on the belly. All fins are gray. These differences in coloration may be connected with conditions in the river. In the first case, the specimen was sampled during floods, when river water was rich in sediments. The second case was different — the specimen was collected in clear water.Published as part of Roman, A., Afanasyev, S., Golub, O. & Lietytska, O., 2022, Capoeta Svanetica (Teleostei, Cyprinidae), A New Species From The Luchunis River (Rioni River Drainage) In Georgia, pp. 117-134 in Zoodiversity 56 (2) on page 129, DOI: 10.15407/zoo2022.02.117, http://zenodo.org/record/717568
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