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An f-edge cover-colouring of a graph G = (V, E) is an assignment of colours to the edges of G such that every colour appears at each vertex υ∈ V at least f(υ) times.The maximum number of colours needed to f-edge cover colour G is called the f-edge cover chromatic index of G, denoted by χfc(G). This paper gives that min[d(ν)-1/f(ν)] ≤χfc(G) ≤min[d(υ)/f(υ)]. 相似文献
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Let A be the space of functions analytic in the unit disk D = {z:|z| 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0 and|f'(z)(z/f(z))~2-1|1(|z|1).Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0and|zf'(z)-f(z)|1/2(|z|1).In this article,we discuss the properties of U and Ω. 相似文献
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Let f be an analytic function in a convex domain . A well-known theorem of Ozaki states that if f is analytic in D, and is given by for , and for some real α, then f is at most p-valent in D. Ozaki's condition is a generalization of the well-known Noshiro–Warschawski univalence condition. The purpose of this paper is to provide some related sufficient conditions for functions analytic in the unit disk to be p-valent in , and to give an improvement to Ozaki's sufficient condition for p-valence when . 相似文献
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Francesc Tugores 《Indagationes Mathematicae》2018,29(5):1326-1333
This paper deals with interpolating sequences for two spaces of holomorphic functions in the unit disk in : those that are bounded and those that satisfy a Lipschitz condition , . Given a sequence of values in a certain target space, we look for a function interpolating ‘in mean”, that is, with , . We obtain target spaces when we prescribe that the corresponding interpolating sequences be the uniformly separated ones or the union of two uniformly separated ones. 相似文献
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For Toeplitz operators acting on the weighted Fock space , we consider the semi-commutator , where is a certain weight parameter that may be interpreted as Planck's constant ? in Rieffel's deformation quantization. In particular, we are interested in the semi-classical limit
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It is well-known that tends to 0 under certain smoothness assumptions imposed on f and g. This result was recently extended to by Bauer and Coburn. We now further generalize (?) to (not necessarily bounded) uniformly continuous functions and symbols in the algebra of bounded functions having vanishing mean oscillation on . Our approach is based on the algebraic identity , where denotes the Hankel operator corresponding to the symbol g, and norm estimates in terms of the (weighted) heat transform. As a consequence, only f (or likewise only g) has to be contained in one of the above classes for (?) to vanish. For g we only have to impose , e.g. . We prove that the set of all symbols with the property that for all coincides with . Additionally, we show that holds for all . Finally, we present new examples, including bounded smooth functions, where (?) does not vanish. 相似文献
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An -dynamic -coloring of a graph is a proper -coloring such that for any vertex , there are at least distinct colors in . The -dynamic chromatic number of a graph is the least such that there exists an -dynamic -coloring of . The list-dynamic chromatic number of a graph is denoted by .Recently, Loeb et al. (0000) showed that the list -dynamic chromatic number of a planar graph is at most 10. And Cheng et al. (0000) studied the maximum average condition to have , or . On the other hand, Song et al. (2016) showed that if is planar with girth at least 6, then for any .In this paper, we study list 3-dynamic coloring in terms of maximum average degree. We show that if , if , and if . All of the bounds are tight. 相似文献