In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an a...In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.展开更多
In this paper, we discuss mainly the properties of incompressible pairwise incomprcssiblc surfaccs in ahnost altcrnating link complcmcnts. Lct L bc a almost link and lct F be an incompressible pairwise incompressible ...In this paper, we discuss mainly the properties of incompressible pairwise incomprcssiblc surfaccs in ahnost altcrnating link complcmcnts. Lct L bc a almost link and lct F be an incompressible pairwise incompressible surface in S^3 - L. First, we give the properties that the surface F intersects with 2-spheres in S^3- L. The intersection consisting of a collection of circles and saddle-shaped discs is called a topological graph. One can compute the Euler Characteristic number of the surface by calculating the characteristic number of the graph. Next, we prove that if the graph is special simple, then the genus of the surface is zero.展开更多
A 5G network must be heterogeneous and support the co-existence of multilayer cells, multiple standards, and multiple applica- tion systems. This greatly improves link performance and increases link capacity. A networ...A 5G network must be heterogeneous and support the co-existence of multilayer cells, multiple standards, and multiple applica- tion systems. This greatly improves link performance and increases link capacity. A network with co-existing macro and pico cells ean alleviate traffic congestion caused by muhicast or unicast subscribers, help satisfy huge traffic demands, and further extend converge. In order to practically implement advanced 5G technology, a number of technical problems have to be solved, one of which is inter-cell interference. A method called Almost Blank Subframe （ABS） has been proposed to mitigate interference; howev- er, the reference signal in ABS still causes interference. This paper describes how interference can be cancelled by using the in- formation in the ABS. First, the interference-signal model, which takes into account channel effect, time and frequency error, is presented. Then, an interference-cancellation scheme based on this model is studied. The timing and carrier frequency offset of the interference signal is compensated. Afterwards, the reference signal of the interfering cell is generated locally and the channel response is estimated using channel statistics. Then, the interference signal is reconstructed according to previous estimation of channel, timing, and carrier frequency offset. The interference is mitigated by subtracting the estimated interference signal. Com- puter simulation shows that this interference-cancellation algorithm significantly improves performance under different channel conditions.展开更多
The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the ...The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function （functional） approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with （al- most） periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.展开更多
文摘In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.
基金Supported by NSF of China(10171024)Supported by Liaoning Educational Committee(05L208)
文摘In this paper, we discuss mainly the properties of incompressible pairwise incomprcssiblc surfaccs in ahnost altcrnating link complcmcnts. Lct L bc a almost link and lct F be an incompressible pairwise incompressible surface in S^3 - L. First, we give the properties that the surface F intersects with 2-spheres in S^3- L. The intersection consisting of a collection of circles and saddle-shaped discs is called a topological graph. One can compute the Euler Characteristic number of the surface by calculating the characteristic number of the graph. Next, we prove that if the graph is special simple, then the genus of the surface is zero.
文摘A 5G network must be heterogeneous and support the co-existence of multilayer cells, multiple standards, and multiple applica- tion systems. This greatly improves link performance and increases link capacity. A network with co-existing macro and pico cells ean alleviate traffic congestion caused by muhicast or unicast subscribers, help satisfy huge traffic demands, and further extend converge. In order to practically implement advanced 5G technology, a number of technical problems have to be solved, one of which is inter-cell interference. A method called Almost Blank Subframe （ABS） has been proposed to mitigate interference; howev- er, the reference signal in ABS still causes interference. This paper describes how interference can be cancelled by using the in- formation in the ABS. First, the interference-signal model, which takes into account channel effect, time and frequency error, is presented. Then, an interference-cancellation scheme based on this model is studied. The timing and carrier frequency offset of the interference signal is compensated. Afterwards, the reference signal of the interfering cell is generated locally and the channel response is estimated using channel statistics. Then, the interference signal is reconstructed according to previous estimation of channel, timing, and carrier frequency offset. The interference is mitigated by subtracting the estimated interference signal. Com- puter simulation shows that this interference-cancellation algorithm significantly improves performance under different channel conditions.
文摘The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function （functional） approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with （al- most） periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.
