• 대한수학회보
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• 제53권3호
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• pp.641-649
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• 2016

A linear functional T on a $Fr{\acute{e}}echet$ algebra (A, (pn)) is called almost multiplicative with respect to the sequence ($p_n$), if there exists ${\varepsilon}{\geq}0$ such that ${\mid}Tab-TaTb{\mid}{\leq}{\varepsilon}p_n(a)p_n(b)$ for all $n{\in}\mathbb{N}$ and for every $a,b{\in}A$. We show that an almost multiplicative linear functional on a $Fr{\acute{e}}echet$ algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous $Fr{\acute{e}}echet$ algebra is continuous.

• 대한수학회지
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• 제38권2호
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• pp.227-274
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• 2001

In this paper we intended to discuss the following topics: (1) Notation, generalities, Markov processes. The close relationship between (generators of) Markov processes and the martingale problem is exhibited. A link between the Korovkin property and generators of Feller semigroups is established. (2) Feynman-Kac semigroups: 0-order regular perturbations, pinned Markov measures. A basic representation via distributions of Markov processes is depicted. (3) Dirichlet semigroups: 0-order singular perturbations, harmonic functions, multiplicative functionals. Here a representation theorem of solutions to the heat equation is depicted in terms of the distributions of the underlying Markov process and a suitable stopping time. (4) Sets of finite capacity, wave operators, and related results. In this section a number of results are presented concerning the completeness of scattering systems (and its spectral consequences). (5) Some (abstract) problems related to Neumann semigroups: 1st order perturbations. In this section some rather abstract problems are presented, which lie on the borderline between first order perturbations together with their boundary limits (Neumann type boundary conditions and) and reflected Markov processes.

• 호남수학학술지
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• 제23권1호
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• pp.59-66
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• 2001

A class of topological algebras, which we call it a fundamental one, has already been introduced to generalize the locally bounded and locally convex algebras. To prove the basic theorems on fundamental algebras, the first successful step is the new version of the Cohen factorization theorem. Here we recall it and prove some new results on fundamental topological algebras.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권9호
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• pp.4342-4366
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• 2016

Congestion control in Cluster Wireless Sensor Networks (CWSNs) has drawn widespread attention and research interests. The increasing number of nodes and scale of networks cause more complex congestion control and management. Active Queue Management (AQM) is one of the major congestion control approaches in CWSNs, and Random Early Detection (RED) algorithm is commonly used to achieve high utilization in AQM. However, traditional RED algorithm depends exclusively on source-side control, which is insufficient to maintain efficiency and state stability. Specifically, when congestion occurs, deficiency of feedback will hinder the instability of the system. In this paper, we adopt the Additive-Increase Multiplicative-Decrease (AIMD) adjustment scheme and propose an improved RED algorithm by using neighbor feedback and scheduling scheme. The congestion control model is presented, which is a linear system with a non-linear feedback, and modeled by Lur'e type system. In the context of delayed Lur'e dynamical network, we adopt the concept of cluster synchronization and show that the congestion controlled system is able to achieve cluster synchronization. Sufficient conditions are derived by applying Lyapunov-Krasovskii functionals. Numerical examples are investigated to validate the effectiveness of the congestion control algorithm and the stability of the network.

• 대한수학회지
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• 제35권3호
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• pp.559-574
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• 1998

Let the Gel'fand triple (E)$_{\beta}$/ ⊂ ( $L^2$) ⊂ (E)＊$_{\beta}$/ be the framework of white noise distribution theory constructed by Kon-dratiev and Streit. A new class of continuous multiplicative products on (E)$_{\beta}$/ is introduced and associated continuous derivations on (E)$_{\beta}$/ are discussed. Algebraic characterizations of first order differential operators on (E)$_{\beta}$/ are proved. Some applications are also discussed. $\beta$/ are proved. Some applications are also discussed.