Monotone relations which preserve arcs and acyclicity
نویسندگان
چکیده
منابع مشابه
Linear mappings which preserve acyclicity properties of graphs and digraphs and applications to matrices
The issue of characterizing the linear transformations which map certain classes of square matrices into or onto themselves has been the theme of several papers recently written, e.g. [2-4 and 6]. The "into" problem is, in general, harder than the "onto" one, and it has been solved only under some additional hypothesis, namely, nonsingularity of the transformation or a somewhat weaker condition...
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Radó has noted that (II) implies (r) and that the sphere and 2-cell each have (II). In this paper it will be shown that (1) for locally connected continua in general, property (II) is equivalent to unicoherence, (2) for plane locally connected continua, property (ir) is equivalent to unicoherence, and (3) every closed 2-dimensional connected manifold has property (x). To clarify our meaning, we...
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for all x, y ∈ X . A distance r > 0 is said to be preserved by a mapping f : X → Y if ‖ f (x)− f (y)‖ = r for all x, y ∈ X whenever ‖x− y‖ = r. If f is an isometry, then every distance r > 0 is preserved by f , and conversely. We can now raise a question whether each mapping that preserves certain distances is an isometry. Indeed, Aleksandrov [1] had raised a question whether a mapping f : X → ...
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Conditions for network equilibrium are developed in terms of vectorvalued flows and potentials and generalized resistance relations. The extent to which the equilibrium can be expressed by a variational inequality or characterized by optimization is analyzed. Emphasis is placed on maximal monotone relations, especially subgradient relations associated with convex optimization.
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I Shohat, J., Bull. Am. Math. Soc., 41, 51 (1935). 2 Haar, A., Math. Ann., 78, 121-136 (1918). 3 Young, W. H., Comptes Rendus, 165, 696-699 (1917). 4Szego, G., Math. Zeit., 12, 61-94 (1922). b A general treatment, which sets forth necessary and sufficient conditions for equivalence of expansions in terms of orthogonal functions, is given by Walsh, J. L., and Wiener, N., Jour. Math. and Phys. of...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1966
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-58-1-59-65