Results 11 to 20 of about 1,153 (175)
The Complexity of Proving the Discrete Jordan Curve Theorem [PDF]
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), 2007 The Jordan curve theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid graphs, under different input settings, in theories of bounded arithmetic that correspond to small complexity classes. The theory V 0
Stephen Cook
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A Proof of the Jordan Curve Theorem
Natural Science, 2019 The proof of the Jordan Curve Theorem (JCT) in this paper is focused on a graphic illustration and analysis ways so as to make the topological proof more understandable, and is based on the Tverberg’s method, which is acknowledged as being quite esoteric with no graphic explanations.
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A combinatorial generalisation of the Jordan Curve Theorem [PDF]
Australas. J Comb., 1994 An open access copy of this article is available and complies with the copyright holder/publisher conditions.We generalise to the setting of 3-graphs a combinatorial analogue of the Jordan curve theorem due to Stahl [9, 10].
Bonnington, C.P., Little, C.H.C.
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Bayesian Evaluation of Treatment Effect of Avelumab Plus Axitinib for Advanced Renal Cell Carcinoma. [PDF]
Cancer MedABSTRACT Background Despite not achieving statistical significance, the JAVELIN Renal 101 trial indicated a potentially clinically relevant effect size (hazard ratio [HR], 0.88; 95% confidence interval, 0.75 to 1.04) on overall survival (OS) favoring avelumab plus axitinib over sunitinib for advanced renal cell carcinoma (aRCC).
Fukuokaya W +9 more
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A Note on the Geometry of Closed Loops
Mathematics, 2023 In this paper, we utilize the Ramsey theory to investigate the geometrical characteristics of closed contours. We begin by examining a set of six points arranged on a closed contour and connected as a complete graph. We assign the downward-pointing edges
Nir Shvalb +3 more
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Applied General Topology, 2023 This paper introduces proximal path cycles, which lead to the main results in this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning Theorem with different forms of Tanaka good cover of an Alexandrov space equipped with a proximity ...
James Francis Peters, Tane Vergili
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Connectivity with respect to α-discrete closure operators
Open Mathematics, 2022 We discuss certain closure operators that generalize the Alexandroff topologies. Such a closure operator is defined for every ordinal α>0\alpha \gt 0 in such a way that the closure of a set AA is given by closures of certain α\alpha -indexed sequences ...
Šlapal Josef
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Ibn Al-Haitham Journal for Pure and Applied Sciences, 2018 Jordan curve theorem is one of the classical theorems of mathematics, it states the following : If is a graph of a simple closed curve in the complex plane the complement of is the union of two regions, being the common ...
Narjis A. Dawood, Suaad G. Gasim
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Predicting Factors Affecting Postoperative Length of Stay in Patients Undergoing Coronary Artery Bypass Graft Surgery Using Machine Learning Methods: A Systematic Review. [PDF]
Health Sci RepABSTRACT Background and Aim Nowadays, coronary artery bypass graft (CABG) surgery has become a common method for treating coronary artery diseases. This surgery requires a long post‐operative length of stay (PLOS) in the hospital. The purpose of this study was to systematically review the factors affecting PLOS in patients undergoing CABG surgery using
Jafarkhani A +3 more
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A Proof of the Jordan Curve Theorem [PDF]
Bulletin of the London Mathematical Society, 1980 Let F be a Jordan curve in the plane, i.e. the image of the unit circle C = {(x,y);x + y = 1} under an injective continuous mapping y into R. The Jordan curve theorem [1] says that / ? 2 \ F is disconnected and consists of two components. (We shall use the original definition whereby two points are in the same component if and only if they can be ...
openaire +1 more source