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THE FIRST EIGENVALUE AND THE EXISTENCE RESULTS
"... Abstract. In this paper we establish some conditions to existence for the solution of the boundary value problem − 1 q (x) p (x)u ′ (x) = f x, u (x) , w (p, q)u ′ (x), x ∈ (0, h) u (0) = u (1) = 0 The hypotheses from the main result contain assumption on the first eigenvalue of some particular Stu ..."
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Abstract. In this paper we establish some conditions to existence for the solution of the boundary value problem − 1 q (x) p (x)u ′ (x) = f x, u (x) , w (p, q)u ′ (x), x ∈ (0, h) u (0) = u (1) = 0 The hypotheses from the main result contain assumption on the first eigenvalue of some particular
Symplectic aspects of the first eigenvalue
 J. Reine Angew. Math
, 1998
"... There are two themes in the present paper. The first one is spelled out in the title, and is inspired by an attempt to find an analogue of HerschYangYau estimate for λ1 of surfaces in symplectic category. In particular we prove that every split symplectic manifold T 4 × M admits a compatible Riema ..."
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Cited by 12 (1 self)
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Riemannian metric whose first eigenvalue is arbitrary large. On the other hand for Kähler metrics compatible with a given integral symplectic form an upper bound for λ1 does exist. The second theme is the study of Hamiltonian symplectic fibrations over S 2. We construct a numerical invariant called the size
THE FIRST EIGENVALUE OF RANDOM GRAPHS
"... Abstract. We extend a result by Füredi and Komlós and show that the first eigenvalue of a random graph is asymptotically normal, both for Gn,p and Gn,m, provided np ≥ n δ or m/n ≥ n δ for some δ> 0. The asymptotic variance is of order p for Gn,p, and n −1 for Gn,m. This gives a (partial) solution ..."
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Cited by 3 (0 self)
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Abstract. We extend a result by Füredi and Komlós and show that the first eigenvalue of a random graph is asymptotically normal, both for Gn,p and Gn,m, provided np ≥ n δ or m/n ≥ n δ for some δ> 0. The asymptotic variance is of order p for Gn,p, and n −1 for Gn,m. This gives a (partial
ON THE ESTIMATE OF THE FIRST EIGENVALUE OF A
"... In this paper, we study a lower bound estimate of the first positive eigenvalue of the sublaplacian on a threedimensional pseudohermitian manifold. S.Y. Li and H.S. Luk derived the lower bound estimate under certain conditions for curvature tensors bounded below by a positive constant. By using t ..."
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In this paper, we study a lower bound estimate of the first positive eigenvalue of the sublaplacian on a threedimensional pseudohermitian manifold. S.Y. Li and H.S. Luk derived the lower bound estimate under certain conditions for curvature tensors bounded below by a positive constant. By using
On the First Eigenvalue of Bipartite Graphs
"... In this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, where the number of edges is given and the number of vertices on each side of the bipartition is given. We state a conjectured solution, which is an analog of the BrualdiHoffman conjecture for general gr ..."
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Cited by 2 (0 self)
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In this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, where the number of edges is given and the number of vertices on each side of the bipartition is given. We state a conjectured solution, which is an analog of the BrualdiHoffman conjecture for general
ON LARGENESS AND MULTIPLICITY OF THE FIRST EIGENVALUE
"... Abstract. The smallest nonzero number in the spectrum of the Laplace operator on a smooth surface S of finite area is denoted by λ1(S). The question of existence of closed (finite area) hyperbolic surfaces with λ1 at least 1 4 dates back to the paper [Se] of Atle Selberg where he conjectured that ..."
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Abstract. The smallest nonzero number in the spectrum of the Laplace operator on a smooth surface S of finite area is denoted by λ1(S). The question of existence of closed (finite area) hyperbolic surfaces with λ1 at least 1 4 dates back to the paper [Se] of Atle Selberg where he conjectured that for any congruence subgroup Γ of SL(2,Z), λ1(H/Γ) ≥ 14. It has been extensively studied in the literature (see for example [B1] [B2], [BBD], [BM]) providing a satisfactory but not quite complete answer for surfaces of large genus (asymptotic behavior). For example, it is has been achieved that λ1 can get close to
Reflections on the First Eigenvalue
, 1996
"... this paper, we will usually assume that the graphs we consider are regular, that is, that d(x) ..."
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Cited by 1 (1 self)
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this paper, we will usually assume that the graphs we consider are regular, that is, that d(x)
The first eigenvalue for the plaplacian operator
 Journal of Inequalities in Pure and Applied Mathematics, Vol. 6, Issue 3, Article 91
, 2005
"... ABSTRACT. In this paper, using the Hausdorff topology in the space of open sets under some capacity constraints on geometrical domains we prove the strong continuity with respect to the moving domain of the solutions of a pLaplacian Dirichlet problem. We are also interested in the minimization of t ..."
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Cited by 6 (0 self)
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of the first eigenvalue of the pLaplacian with Dirichlet boundary conditions among open sets and quasi open sets of given measure.
Stable bundles and the first eigenvalue of the Laplacian
, 2005
"... In this paper we study the first eigenvalue of the Laplacian on a compact manifold using stable bundles and balanced bases. Our main result is the following: let M be a compact Kähler manifold of complex dimension n and E a holomorphic vector bundle of rank r over M. If E is globally generated and i ..."
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Cited by 7 (2 self)
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In this paper we study the first eigenvalue of the Laplacian on a compact manifold using stable bundles and balanced bases. Our main result is the following: let M be a compact Kähler manifold of complex dimension n and E a holomorphic vector bundle of rank r over M. If E is globally generated
Results 1  10
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315,297