منابع مشابه
Complex Function Differentiability
The articles [17], [18], [3], [5], [4], [8], [2], [7], [11], [6], [16], [12], [19], [9], [10], [1], [14], [15], and [13] provide the notation and terminology for this paper. For simplicity, we use the following convention: k, n, m denote elements of N, X denotes a set, s1, s2 denote complex sequences, Y denotes a subset of C, f , f1, f2 denote partial functions from C to C, r denotes a real num...
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— We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian line bundle and several other arithmetic invariants. Résumé. — On introduit le produit d’intersection positive en géométrie d’Arakelov et on démontre que ...
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As we shall see later, Thomae’s function is not differentiable on the irrationals. In this note, we address whether there is a modification of Thomae’s function which is differentiable on a subset of the irrationals. In Section 2, we prove that Thomae’s function is not differentiable on the irrationals and define modified versions of Thomae’s function. In Section 3, we show that for each of our...
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* The Research presented here started in August 1986 during our stay at the IMSSS, Stanford University; it was continued there during the Summer of 1987 and at the Insti-tuto de Analisis Economica, Universitat Autonoma de Barcelona in June-July 1988. We are very grateful to these institutions for their warm hospitality and support. Conversations with Manuel Santos and José Scheinkman were very ...
متن کاملOn the Differentiability of a Distance Function
Let M be a simply connected complete Kähler manifold and N a closed complete totally geodesic complex submanifold of M such that every minimal geodesic in N is minimal in M . Let Uν be the unit normal bundle of N in M . We prove that if a distance function ρ is differentiable at v ∈ Uν , then ρ is also differentiable at −v.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1981
ISSN: 0386-2194
DOI: 10.3792/pjaa.57.492