1,026 research outputs found
Computational techniques in Turan problems
Get PDFA Turan set system, T(n, I, k), is a k -uniform hypergraph on n points, such that any subset of / vertices contains at least one edge. The Turan number T{n, l, k) is the minimal number of edges in any Turan set system T(n,l,k). The known nontrivial values of Turan numbers are rare. Using the algorithm turexp for extending T(n, I, k) systems to 7(n+1, I, k) systems and procedures nauty for determining the automorphism group of a graph, the new Turan numbers 7(13, 4, 3), 7(11, 5, 3), 7(12, 5, 3), 7(13, 5, 3) are determined, a new lower bound for 7(14, 5, 3) is given, the Turan numbers 7(10, 4, 3), 7(11, 4, 3), 7(12, 4, 3) are confirmed to be the same as the previous unpublished results of other authors, and all minimal Turan T(n, 4, 3) (n \u3c 12), 7(n, 6, 5) (n \u3c 9), T(n, 5, 3) (n \u3c 13) are obtained
DIMENSI METRIK PADA GRAF TURAN
Get PDFHimpunan adalah resolving set (himpunan pembeda) dari jika setiap simpul di memiliki representasi tunggal pada yang ditentukan oleh jarak dari simpul dari terhadap simpul di . Dimensi metrik dari adalah kardinalitas minimum dari resolving set pada . Pada paper ini akan dijelaskan tentang dimensi metrik pada graf Turan, yaitu graf multipartisi komplit yang dinotasikan dengan dengan adalah banyaknya seluruh simpul dari graf dan adalah banyaknya partisi. Dimensi metrik dari graf dengan adalah . Sedangkan untuk graf Turan yang tidak komplit yang memiliki order dengan menjaga keterhubungan antara setiap simpul pada semua partisi memiliki dimensi metrik yaitu .
Kata Kunci : dimensi metrik, graf Turan, resolving set
 
l-Degree Turan Density
No full textLet H-n be a k-graph on n vertices. For 0 <= l < k and an l-subset T of V (H-n), define the degree deg(T) of T to be the number of (k - l)-subsets S such that S boolean OR T is an edge in H-n. Let the minimum l-degree of H-n be delta(l) (H-n) = min{deg(T) : T subset of V (H-n) and vertical bar T vertical bar = l}. Given a family F of k-graphs, the l-degree Turan number ex(l) (n, F) is the largest delta(l) (H-n) over all F-free k-graphs H-n on n vertices. Hence, ex(0) (n, F) is the Turan number. We define l-degree Turan density to be pi(kappa)(l) (F) = lim sup(n ->infinity) ex(l)(n, F)/kappa(n-l). In this paper, we show that for k > l > 1, the set of pi(kappa)(l) (F) is dense in the interval [0, 1). Hence, there is no "jump" for l-degree Turan density when k > l > 1. We also give a lower bound on pi(kappa)(l) (F) in terms of an ordinary Turan density
A Comparison of Islamic Vs Conventional Banks in Turkey
No full text##nofulltext##Semen Son Turan (MEF Author)..
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
Turan and Ramsey numbers in linear triple systems II
Get PDFIn this paper we continue our studies of Turan and Ramsey numbers in linear triple systems, defined as 3-uniform hypergraphs in which any two triples intersect in at most one vertex. In [7] the two main problems left open were the Turan number of the wicket and the Ramsey property of the sail. In this paper we present some progress towards both of these problems.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Ramsey-Turan numbers for semi-algebraic graphs
Get PDFA semi-algebraic graph G = (V, E) is a graph where the vertices are points in R-d, and the edge set E is defined by a semi-algebraic relation of constant complexity on V. In this note, we establish the following Ramsey-Turan theorem: for every integer p >= 3, every K-p-free semi-algebraic graph on n vertices with independence number o(n) has at most 1/2(1 - 1/inverted right perpendicularp/2inverted left perpendicular - 1 + o(1)) n(2) edges. Here, the dependence on 1-1 the complexity of the semi-algebraic relation is hidden in the o(1) term. Moreover, we show that this bound is tight.DC
The Blockchain–Sustainability Nexus: Can This New Technology Enhance Social, Environmental and Economic Sustainability?
No full textWith the rise and fall of the prominence of Bitcoin, blockchain technology,
which provides public online ledgers used for the verification and recording of
transactions, has started to become the center of attention for diverse parties in the
global financial system. This chapter explores the nature of blockchain and discusses
how it may contribute to, or obstruct, sustainability. To this end, first, blockchain
technology is introduced. Next, a short discussion on sustainability is presented,
including how it is defined, measured, reported, and understood in theoretical
frameworks. After that, the 2015 United Nations Sustainable Development Goals
are briefly explained. This is followed by a systematic literature review, which
highlights the scarcity of literature linking blockchain to sustainability. Finally, the
author offers her own reflections on the potential of blockchain to revolutionize the
financial services industry and weighs up the pros and cons vis-a-vis sustainable
development.2-s2.0-8514316679
Investigation for the Effects of Omega Fatty Acid and Glutamine-L-Alanine on Morbidity and Mortality in the Critically ILL Patients after Major Abdominal Surgery
Get PDFBackground & Objectives: This study investigated the effects for the addition of omega 3 fatty acids and glutamine-L-alanine to the standard enteral and/or parenteral nutrition regimen on infection and mortality in the critically ill patients after major abdominal surgery.
Methods: This is a prospective, randomized, single center study. A total of 43 patients (age range: 18-85 years), who were in the critical care unit after major abdominal surgery, were included. Patients were divided into two groups according to simple randomized selection [Control group, n=20; Study Group, n=23 (omega3 fatty acids and glutamine-L-alanine)] and were monitored for 21 days. Patients were examined for the assessment of APACHE II Score and existence of ALI (acute lung injury)/ARDS (acute respiratory distress syndrome) requiring mechanical ventilation. In addition to standard enteral or parenteral nutrition, patients in the study group were given parenteral pharmaconutrition products for 10 days postoperatively. Groups were compared for the duration of mechanical ventilation, duration of stay in the intensive care unit and hospitalization, and mortality. Laboratory parameters including CRP, TNF, IL6, IL8, nitrogen balance, albumin, and total lymphocyte count were recorded.
Results:Although the mean APACHE score was higher in study group in which patients received omega-3 fatty acids and glutamine-L-alanine support, the clinical infection rate seemed to decrease insignificantly.
Conclusions: A clinically decreased rate of infection was observed in patients with a high APACHE II score, or who received omega-3 fatty acids, glutamine-L-alanine, are required to be administered more selectively and in larger patient groups in different doses and in combination protocols in accordance with the current pharmaconutritional support and in different timing combinations, including preoperative perio
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