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1
Content available remote

Eigenvalue Conditions for Induced Subgraphs

100%
Harant J., Niebling J., Richter S.
Discussiones Mathematicae Graph Theory
|
2015
|
tom 35
|
nr 2
355-363
EN
Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented.
2
Content available remote

Obata’s Rigidity Theorem for Metric Measure Spaces

80%
Ketterer C.
Analysis and Geometry in Metric Spaces
|
2015
|
tom 3
|
nr 1
EN
We prove Obata’s rigidity theorem for metric measure spaces that satisfy a Riemannian curvaturedimension condition. Additionally,we show that a lower bound K for the generalizedHessian of a sufficiently regular function u holds if and only if u is K-convex. A corollary is also a rigidity result for higher order eigenvalues.
3
Content available remote

Construction of Cospectral Integral Regular Graphs

80%
Bapat R. B., Karimi M.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 37
|
nr 3
595-609
EN
Graphs G and H are called cospectral if they have the same characteristic polynomial. If eigenvalues are integral, then corresponding graphs are called integral graph. In this article we introduce a construction to produce pairs of cospectral integral regular graphs. Generalizing the construction of G4(a, b) and G5(a, b) due to Wang and Sun, we define graphs 𝒢4(G,H) and 𝒢5(G,H) and show that they are cospectral integral regular when G is an integral q-regular graph of order m and H is an integral q-regular graph of order (b − 2)m for some integer b ≥ 3.
4
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Existence and uniqueness theorems for fourth-order boundary value problems

80%
Przybycin J.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 1
59-64
EN
We establish the existence and uniqueness theorems for a linear and a nonlinear fourth-order boundary value problem. The results obtained generalize the results of Usmani [4] and Yang [5]. The methods used are based, in principle, on [3], [5].
5
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The Laplacian spectrum of some digraphs obtained from the wheel

80%
Su L., Li H.-H., Zheng L.-R.
Discussiones Mathematicae Graph Theory
|
2012
|
tom 32
|
nr 2
255-261
EN
The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232-251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained from the wheel digraph by deleting some arcs.
6
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Bounds for index of a modified graph

80%
Zhou B.
Discussiones Mathematicae Graph Theory
|
2004
|
tom 24
|
nr 2
213-221
EN
If a graph is connected then the largest eigenvalue (i.e., index) generally changes (decreases or increases) if some local modifications are performed. In this paper two types of modifications are considered: (i) for a fixed vertex, t edges incident with it are deleted, while s new edges incident with it are inserted; (ii) for two non-adjacent vertices, t edges incident with one vertex are deleted, while s new edges incident with the other vertex are inserted. Within each case, we provide lower and upper bounds for the indices of the modified graphs, and then give some sufficient conditions for the index to decrease or increase when a graph is modified as above.
7
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An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem

70%
Wiśniewski D., Bodzioch M.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2016
|
tom 15
EN
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
8
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Co możemy opisać układem dynamicznym?

61%
Foryś U.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2014
|
tom 6
73-85
PL
In this paper we present several examples of simple dynamical systemsdescribing various real processes. We start from well know Fibonaccisequence, through Lotka-Volterra model of prey-predator system, love affairdynamics, ending with modelling of tumour growth.
9
Content available remote

Analytic hypoellipticity for sums of squares of vector fields

61%
Himonas A.
Annales Polonici Mathematici
|
1998
|
tom 70
|
nr 1
117-129
EN
We discuss the open problem of analytic hypoellipticity for sums of squares of vector fields, including some recent partial results and a conjecture of Treves.
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