94,092 research outputs found
Computational techniques in Turan problems
No full textA 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5, 3) is given, the Turan numbers 7(10, 4, 3), 7(11, 4, 3), 7(12, 4, 3) are confirmed to be the same as the previous unpublished results of other authors, and all minimal Turan T(n, 4, 3) (n \u3c 12), 7(n, 6, 5) (n \u3c 9), T(n, 5, 3) (n \u3c 13) are obtained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
No full textHimpunan 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
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
On the Distribution of the Prime Numbers
No full textThis research explores the distribution of prime numbers, which are a fundamental topic in number theory. The study originated from the author\u27s fascination with mathematics and the desire to discover something novel. The research proposes that the distribution of prime numbers follows a regular pattern starting from the number 2. The author suggests that prime numbers can be obtained by dividing certain even numbers that have four factors by the number 2, resulting in prime numbers in sequential order. This hypothesis was tested and confirmed through the practical application of the proposed mathematical formula. Additionally, the study found that even numbers greater than or equal to 8, with six or more factors, produce complex numbers. Thus, this research provides two main contributions: firstly, a mathematical formula for the distribution of prime numbers, and secondly, a formula for the distribution of complex numbers. These findings have potential applications in various mathematical fields, including cryptography and problem-solving in number theory
Several Derivative Formulas of Two Exponential Functions and Real Power of Hyperbolic Secant Function with a Generalization of a Formula for Specific Partial Bell Polynomials
No full textIn the paper, by virtue of some identities for the partial Bell polynomials and with the aid of the Faá di Bruno formula, the author presents several derivative formulas of two exponential functions and the real power of the hyperbolic secant function, and generalizes a formula for specific partial Bell polynomials
Ramsey-Turan numbers for semi-algebraic graphs
No full textA 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
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
No full textBackground & 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
The EU's membership conditionality and ITS legal implications on minority rights in Turkey
No full textMinority rights is frequently perceived as a barrier to Turkey’s EU accession. The relationship between Turkey and its minorities is complex and often controversial. One of the primary obstacles for the establishment of a legal framework to recognize and protect minority rights in Turkey emerges from a narrow interpretation of the constitutional citizenship. It has been strictly confined to the principles of nation-state. The problematic nature of the concept of citizenship in this constitutional model stems from the relationship between the nation and minorities. In a nation-state model, citizenship contemplates the submerging of differences into an all-inclusive constitutional identity, where the legal notion of nationality neither elaborates nor functions as a neutral ground under which ethnic differences gain a legal status. In this project, the dominant identity cannot escape from being institutionalised, where its particular traits emerge as the only identity characteristics promoted at the state level. As a consequence, the national-identity, and by extension the constitutional citizenship, is overwhelmed by the dominant identity. Ergo, the constitutional citizenship gains an exclusionary character since access by minorities into the national community is conditioned upon their unreserved acceptance of the national identity. This thesis will, therefore, examine the impact of EU membership conditionality on the largest minority group in Turkey from a legal point of view. While the study will demonstrate a degree of contribution it will also reveal that the crucial features of the constitutional principles of Turkishness and nationalism has narrowed the legal space for the enjoyment of minority rights set forth by the EU minority acquis.No sponso
A set of nine principles for distributed-design information storing
No full textThe issues of distributed working are many, with problems relating to information access and information acquisition the most common (Crabtree et al., 1997). Keeping track of project and team information is becoming more complex as design is increasingly being carried out collaboratively by geographically dispersed design teams across different time zones. The literature notes that little prescription or guidance exists on information management for designers (Culley et al., 1999) and Hicks (2007) highlights a relative lack of overall principles for improving information management. Additionally, evidence from earlier studies by the author into ‘How information is stored in distributed design project work’ reinforces the need for guidance, particularly in a distributed context (Grierson, 2008). Distributed information collections were found to be unorganised, contained unclear information and lacked context. Storing and sharing of distributed information was often time consuming and the tools awkward to use. This can lead to poor project progress and can impact directly on the quality and success of project outcomes (Grierson et al., 2004, 2006). This paper seeks to address these issues by presenting the development, implementation and evaluation of a set of Principles and a Framework to support distributed design information storing in the context of a Global Design class. Through both quantitative and qualitative evaluation methods the Principles were found to help in a number of ways – with the easy access of information; the structuring and organising of information; the creation of an information strategy; the making of information clear and concise; the supporting of documentation during project work; and the strengthening of team work; all helping teams to work towards project outcomes
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