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981.
The geodesic and induced path transit functions are the two well-studied interval functions in graphs. Two important transit functions related to the geodesic and induced path functions are the triangle path transit functions which consist of all vertices on all u,v-shortest (induced) paths or all vertices adjacent to two adjacent vertices on all u,v-shortest (induced) paths, for any two vertices u and v in a connected graph G. In this paper we study the two triangle path transit functions, namely the IΔ and JΔ on G. We discuss the betweenness axioms, for both triangle path transit functions. Also we present a characterization of pseudo-modular graphs using the transit function IΔ by forbidden subgraphs. 相似文献
982.
We consider a U(1)-invariant nonlinear Klein–Gordon equation in dimension n?1, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic assumptions, each solution converges as t→±∞ to the two-dimensional set of all “nonlinear eigenfunctions” of the form ?(x)e−iωt. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation. 相似文献
983.
Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations 总被引:1,自引:0,他引:1
This paper investigates the dynamics of a class of recurrent neural networks where the neural activations are modeled by discontinuous functions. Without presuming the boundedness of activation functions, the sufficient conditions to ensure the existence, uniqueness, global exponential stability and global convergence of state equilibrium point and output equilibrium point are derived, respectively. Furthermore, under certain conditions we prove that the system is convergent globally in finite time. The analysis in the paper is based on the properties of M-matrix, Lyapunov-like approach, and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend previous works on global stability of recurrent neural networks with not only Lipschitz continuous but also discontinuous neural activation functions. 相似文献
984.
This paper introduces an iteration scheme for viscosity approximation of a zero of accretive operator in a reflexive Banach space with weakly continuous duality mapping. A new iterative sequence is introduced and strong convergence of the algorithm {xn} is proved. The results improve and extend the results of Su [Xiaolong Qin, Yongfu Su, Approximation of a zero point of accretive operator in Banach spaces, J. Math. Anal. Appl. 320 (2007) 415-424] and some others. 相似文献
985.
986.
987.
In the present paper, we establish a demiclosedness principle for asymptotically pseudo-contractions in Hilbert spaces. As its applications, we obtain a new fixed point theorem, some weak and strong convergence theorems for asymptotically pseudo-contractions. The results of this paper are interesting extensions of those known results. 相似文献
988.
Some minimax inequalities involving two bifunctions with noncompact and nonconvex domains are first proved in finite continuous topological spaces (in short, FC-spaces) without convexity structure. As applications some new Fan–Browder type fixed point theorems for expansive set-valued maps with noncompact and nonconvex domains and ranges are obtained in general topological spaces. These results generalize some known results in the recent literature. 相似文献
989.
In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions. 相似文献
990.