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1
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Representation theory of two-dimensionalbrauer graph rings

100%
Rump W.
Colloquium Mathematicum
|
2000
|
tom 86
|
nr 2
239-251
EN
We consider a class of two-dimensional non-commutative Cohen-Macaulay rings to which a Brauer graph, that is, a finite graph endowed with a cyclic ordering of edges at any vertex, can be associated in a natural way. Some orders Λ over a two-dimensional regular local ring are of this type. They arise, e.g., as certain blocks of Hecke algebras over the completion of $ℤ[q,q^{-1}]$ at (p,q-1) for some rational prime $p$. For such orders Λ, a class of indecomposable maximal Cohen-Macaulay modules (see introduction) has been determined by K. W. Roggenkamp. We prove that this list of indecomposables of Λ is complete.
2
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On the mean values of an analytic function.

88%
Srivastava G., Rani S.
Annales Polonici Mathematici
|
1992
|
tom 57
|
nr 2
149-155
EN
Let f(z), $z = re^{iθ}$, be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values $I_δ(r)$ and the iterated mean values $N_{δ,k}(r)$ of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).
3
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Large Degree Vertices in Longest Cycles of Graphs, I

88%
Li B., Xiong L., Yin J.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 2
363-382
EN
In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.
4
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Strongly chaotic dendrites

75%
Charatonik J. J., Charatonik W. J.
Colloquium Mathematicum
|
1996
|
tom 70
|
nr 2
181-190
EN
The concept of a strongly chaotic space is introduced, and its relations to chaotic, rigid and strongly rigid spaces are studied. Some sufficient as well as necessary conditions are shown for a dendrite to be strongly chaotic.
5
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Sur la méthode de l’intégrale particulière et sur ses conséquences pour l’équation de Riccati et pour les équations différentielles linéaires et homogènes d’ordre supérieur

51%
Kapcia A.
Commentationes Mathematicae
|
2007
|
tom 47
|
nr 2
EN
This paper presents the method of particular solution for solving the Riccati equation and linear homogenous equations of second and third order, as well as its certain application to linear homogenous equations of n-th order. The conditions of effective integrability for equations (0.1) and (0.2) are expressed in symbolic (operator) form and also for equation (0.3) in fully expanded form. There have been proved three theorems which state the following: for any subclass of differential equations of the form (0.1), (0.2), (0.3), if there are known, respectively: a particular solution \(y_0\), a particular solution u 0 , two linearly independent particular solutions \(u_1 , u_2\), then it is possible to construct superclasses of differential equations of the given class, using classes cited in [6, 7, 8, 9]. Moreover, one may obtain their effectively integrable generalizations. Numerous examples provided illustrate the above results. The article presents also a practical way of applying the method of particular solution to linear equations of n-th order. This method enables us to integrate more general equations than those described in [4, 5, 14] of the form (0.1), (0.2), (0.3), (0.4) for which the particular solutions are cited therein.
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