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1
Content available remote

Estimates for simple random walks on fundamental groups of surfaces

100%
Bartholdi L., Cantat S., Ceccherini-Silberstein T., de la Harpe P.
Colloquium Mathematicum
|
1997
|
tom 72
|
nr 1
173-193
EN
Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.
2
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Minimal incomplete norms on Banach algebras

100%
Meyer M. J.
Studia Mathematica
|
1992
|
tom 102
|
nr 1
77-85
EN
We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.
3
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On the joint spectral radius

100%
Müller V.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
173-182
EN
We prove the $𝓁_p$-spectral radius formula for n-tuples of commuting Banach algebra elements
4
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The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

100%
Su L., Li H.-H., Zhang J.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 1
95-102
EN
In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.
5
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A note on Anderson's note on a stationary autoregressive process

100%
Kala R.
Discussiones Mathematicae Probability and Statistics
|
2010
|
tom 30
|
nr 2
237-239
EN
A form of the covariance matrix of a weakly stationary first-order autoregressive process is established.
6
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Perturbation theorems for Hermitian elements in Banach algebras

100%
Bhatia R., Drissi D.
Studia Mathematica
|
1999
|
tom 134
|
nr 2
111-117
EN
Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
7
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Some properties of the spectral radius of a set of matrices

100%
Czornik A., Jurgas P.
International Journal of Applied Mathematics and Computer Science
|
2006
|
tom 16
|
nr 2
183-188
EN
In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the existing results it is expressed by eigenvalues.
8
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On orderings induced by the Loewner partial ordering

100%
Hauke J., Markiewicz A.
Applicationes Mathematicae
|
1993-1995
|
tom 22
|
nr 2
145-154
EN
The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.
9
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Order unicyclic graphs according to spectral radius of unoriented laplacian matrix

100%
Fan Y.-Z., Wu S.
Discussiones Mathematicae Graph Theory
|
2008
|
tom 28
|
nr 3
487-499
EN
The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.
10
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The signless Laplacian spectral radius of graphs with given number of cut vertices

100%
Cui L., Fan Y.-Z.
Discussiones Mathematicae Graph Theory
|
2010
|
tom 30
|
nr 1
85-93
EN
In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
11
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Maximizing Spectral Radii of Uniform Hypergraphs with Few Edges

88%
Fan Y.-Z., Tan Y.-Y., Peng X.-X., Liu A.-H.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 4
845-856
EN
In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively.
12
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Infinite Graph-Directed Systems and Hausdorff Dimension

88%
Priyadarshi A.
Waves, Wavelets and Fractals
|
2017
|
tom 3
|
nr 1
84-95
EN
In this paper we study infinite graph-directed iterated function systems on compact metric spaces given by contractive ‘infinitesimal similitudes’. We derive formula for the Hausdorff dimension of the ‘invariant set’ for such a system in terms of the spectral radii of the naturally associated family of the ‘Perron- Frobenius operators’. The results in this paper generalizes the results obtained in [20], where finite graphdirected systems and infinite iterated function systems are considered
13
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On graduation of enrolment size in a multi-echelon educational system

88%
Ekhosuehi V. U.
Mathematica Applicanda
|
2017
|
tom 45
|
nr 2
EN
This paper focuses on an educational system wherein demotion and double promotion are not allowed. The total enrolment in such a system is modelled as a linear model within the context of factor analysis. The goal is to represent the total enrolment in terms of latent factors which generate the flows in the system. The notion of matrix spectrum and spectral radius are used to benchmark the specific variances and to approximate the factor loading vector, respectively. Two main theorems are propounded alongside with their proofs. A numerical illustration is given.
14
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Regularity of the multidimensional scaling functions: estimation of the $L^{p}$-Sobolev exponent

88%
Kotowicz J.
Applicationes Mathematicae
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1998-1999
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tom 25
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nr 4
431-447
EN
The relationship between the spectral properties of the transfer operator corresponding to a wavelet refinement equation and the $L^p$-Sobolev regularity of solution for the equation is established.
15
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Variable neighborhood search for extremal graphs. 17. Further conjectures and results about the index

88%
Aouchiche M., Hansen P., Stevanović D.
Discussiones Mathematicae Graph Theory
|
2009
|
tom 29
|
nr 1
15-37
EN
The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products of the index and another invariant. There are 72 cases altogether: in 7 cases known results were reproduced, in 32 cases immediate results were obtained and automatically proved by the system, conjectures were obtained in 27 cases, of which 12 were proved (in 3 theorems and 9 propositions), 9 remain open and 6 were refuted. No results could be derived in 7 cases.
16
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Asymptotic stability in the Schauder fixed point theorem

75%
Shih M.-H., Wu J.-W.
Studia Mathematica
|
1998
|
tom 131
|
nr 2
143-148
EN
This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.
17
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On a property of weak resolvents and its application to a spectral problem

75%
Uetake Y.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
263-268
EN
We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.
18
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Spectral study of alliances in graphs

75%
Rodríguez-Velazquez J., Almira J.
Discussiones Mathematicae Graph Theory
|
2007
|
tom 27
|
nr 1
143-157
EN
In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.
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