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991.
We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as the commuting property with translation and homothety, of these operators are discussed as well. 相似文献
992.
Existence and limit behavior of prescribed L2‐norm solutions for Schrödinger‐Poisson‐Slater systems in
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In this paper, we study constraint minimizers of the following L 2?critical minimization problem: where E (u ) is the Schrödinger‐Poisson‐Slater functional and N denotes the mass of the particles in the Schrödinger‐Poisson‐Slater system. We prove that e (N ) admits minimizers for and, however, no minimizers for N >N ?, where Q (x ) is the unique positive solution of in . Some results on the existence and nonexistence of minimizers for e (N ?) are also established. Further, when e (N ?) does not admit minimizers, the limit behavior of minimizers as N ↗N ? is also analyzed rigorously. 相似文献
993.
Feng Qi 《Proceedings Mathematical Sciences》2017,127(4):551-564
In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers. 相似文献
994.
995.
In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward–backward stochastic differential equations (FBSDEs) is established, which can be regarded as an extension of the Feynman–Kac formula to the non-Markovian framework. 相似文献
996.
997.
QiShishuo 《高校应用数学学报(英文版)》2000,15(1):37-44
Abstract. The comparison principle is first established ,and then the lower and upper solutionmethod and the monotone iterative technique are employed to the study of terminal value prob-lems for the first order nonlinear impulsive integro-differential equations in Banach spaces. Fi-nally ,the existence theorem on the maximal and minimal solutions is obtained. 相似文献
998.
§1 IntroductionandPreliminariesAsearlyasin1981,AftabizadehandLakshmikantham[1]begantoinvestigateterminalvalueproblems(TVPs,inshort)forthefirstorderordinarydifferentialequations.Howev-er,theresearchinTVPsforimpulsivedifferentialequationshasmadelittlep… 相似文献
999.
Qi Duan Tzer-Shyong Chen K. Djidjeli W. G. Price E. H. Twizell 《Journal of Applied Mathematics and Computing》2000,7(2):397-405
A constrained rational cubic spline with linear denominator was constructed in [1]. In the present paper, the sufficient condition for convex interpolation and some properties in error estimation are given. 相似文献
1000.
In this paper, we continue to discuss the normality concerning omitted holomorphic function and get the following result. Let F be a family of meromorphic functions on a domain D, k ≥ 4 be a positive integer, and let a(z) and b(z) be two holomorphic functions on D, where a(z) 0 and f(z) ≠ ∞ whenever a(z)=0. If for any f ∈ F, f'(z) -a(z)fk(z) ≠ b(z), then F is normal on D. 相似文献