Báo cáo toán học: "On the sharpness of some results relating cuts and crossing

Báo cáo toán học: "On the sharpness of some results relating cuts and crossing numbers" pptx

... on the other hand, is far from clear, as the edges of the two bundles can possibly cross each other a rbitra rily often in a n optimal drawing of the zip product, and optimal drawings of the ... orbounding the crossing number of graphs used to be the main issue at the beginning, the focus is now shifting to structural aspects of the crossing number problem. These include the study of several ... and let s and t be two distinct vertices inG. Then there exists a crossing minimal planarization P of G, such that the size of the minimum s, t-cut in P is the same as the size of the minimum...

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Báo cáo toán học: "On the Hyperbolicity of Some Systems of Nonlinear " pps

... sections are devoted to the proof of the theorem whenn =2,n=3,n=4andn =5. For the last three cases we will prove that all the eigenvalues of the matrices C are real, and therefore, the systems (1.1) ... ξ4v33v15v24,(6.7)On the Hyperbolicity of some Systems of Nonlinear 111 The solvability of the Cauchy problem for the equations (1.5) strongly dependson the hyperbolicity of the system (1.1). So, ... hyperbolic.3. Proof of the Theorem 2.8 for the Case n =2Suppose that AT= A, i.e. a12= a21. We prove that the system (1.1) is hyper-bolic.On the Hyperbolicity of some Systems of Nonlinear...

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Báo cáo toán học: "On the Structure of Sets with Few Three-Term Arithmetic Progressions" pptx

... exp(−rt2/2).Proof of the Lemma. The proof of this lemma is standard: G iven f as in the theoremabove, let g0be a random function from Fnpto {0, 1} (which can be thought of as a sequence of random ... not bothered to optimize the conclusion of the theorem (to the same extent as we did Theorem 1) given the method of proof, though much more can certainly be proved:Theorem 2 Fix a characteristic ... subject to the constraint that |S|  αpn. What can one sayabout the structure of such sets S? In this paper we show that they are “essentially” the union of a small number of cosets of some lar...

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Báo cáo toán học: " On the boundedness of the solutions in nonlinear discrete Volterra difference equations" pot

... R+, 0 ≤ j ≤ n and p ∈ (0, 1). The following result provides a necessary and suﬃcient condition for the boundedness of the solution of (4.4) and (4.5). The necessary part of the next theorem was ... 2.3). Thus, the conditions of Theorem 3.1 hold, and the initial vector x0belongs to S, and hence the solution x(n; x0) of (1.1) and (1.2) is bounded.We consider the scalar case of Volterra ... proof.Theorem 3.1. Let (A) and (B) be satisﬁed and assume that the initial vector x0belongs to the set S.Then the solution x(n; x0), n ≥ 0, of (1.1) and (1.2) is bounded. More exactly the...