• Honam Mathematical Journal
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• v.36 no.1
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• pp.29-32
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• 2014

Given operators X and Y acting on a separable Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate self-adjoint interpolation problems for operators in a tridiagonal algebra : Let $\mathcal{L}$ be a subspace lattice acting on a separable complex Hilbert space $\mathcal{H}$ and let X = ($x_{ij}$) and Y = ($y_{ij}$) be operators acting on $\mathcal{H}$. Then the following are equivalent: (1) There exists a self-adjoint operator A = ($a_{ij}$) in $Alg{\mathcal{L}}$ such that AX = Y. (2) There is a bounded real sequence {${\alpha}_n$} such that $y_{ij}={\alpha}_ix_{ij}$ for $i,j{\in}\mathbb{N}$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.649-659
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• 2015

The space $BV^2_{\alpha}(I)$ of all the real functions defined on interval $I=[a,b]{\subset}\mathbb{R}$, which are of bounded second ${\alpha}$-variation (in the sense De la Vall$\acute{e}$ Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function $h:I{\times}\mathbb{R}{\rightarrow}\mathbb{R}$, and prove, in particular, that if H maps $BV^2_{\alpha}(I)$ into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.149-157
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• 2003

Let M be an exponentially bounded o-minimal expansion of the standard structure R = (R ,＋,.,<) of the field of real numbers. We prove that if r is a non-negative integer, then every definable $C^{r}$ manifold is affine. Let f : X ${\longrightarrow}$ Y be a definable $C^1$ map between definable $C^1$ manifolds. We show that the set S of critical points of f and f(S) are definable and dim f(S) < dim Y. Moreover we prove that if 1 < s < ${\gamma}$ < $\infty$, then every definable $C^{s}$ manifold admits a unique definable $C^{r}$ manifold structure up to definable $C^{r}$ diffeomorphism.

• The KIPS Transactions:PartC
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• v.12C no.1 s.97
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• pp.105-110
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• 2005

With the proliferation of multimedia group applications, the construction of multicast trees satisfying QoS requirements is becoming a problem of prime importance. In this paper, we study the delay- and delay variation-bounded multicast tree (DVBMT) problem which is NP-complete. The problem is to construct a spanning tree for destination node, which has the minimized multicast delay variation, and the delay on the path from the source to each destination is bounded. A solution to this problem is required to provide decent real-time communication services such as on-line games, shopping, and teleconferencing. Performance comparison shows that the proposed scheme outperforms DDVCA which is known to be effective so far in any network topology. The enhancement is up to about $3.6{\%}{\~}11.1{\%}$ in terms of normalized surcharge for DUVCA. The time complexity of our algorithm is $O(mn^2)$.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.05a
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• pp.1195-1198
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• 2007

In this paper we study the problem of real time support in wireless sensor networks and propose a Real time Geographic Routing Protocol (ReGeo) which routes a packet towards the destination based on a compromise between distance and queue count to reduce traffic concentration wherever it has been determined to be too high and uses Gradient Table to store the route satisfying the delay constraints. We describe our prototype implementation of ReGeo Routing in TOSSIM - a TinyOS mote simulator. The simulation results show that the proposed routing protocol not only increases the packet delivery ratio but also keeps overall End to End Delay under a bounded value.

• Journal of information and communication convergence engineering
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• v.10 no.3
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• pp.231-236
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• 2012

For real-time wireless sensor network applications, it is essential to provide different levels of quality of service (QoS) such as reliability, low latency, and fault-tolerant traffic control. To meet these requirements, an (m,k)-firm based real-time routing protocol has been proposed in our prior work, including a novel local transmission status indicator called local DBP (L_DBP). In this paper, a fault recovery scheme for (m,k)-firm real-time streams is proposed to improve the performance of our prior work, by contributing a delay-aware forwarding candidates selection algorithm for providing restricted redundancy of packets on multipath with bounded delay in case of transmission failure. Each node can utilize the evaluated stream DBP (G_DBP) and L_DBP values as well as the deadline information of packets to dynamically define the forwarding candidate set. Simulation results show that for real-time service, it is possible to achieve both reliability and timeliness in the fault recovery process, which consequently avoids dynamic failure and guarantees meeting the end-to-end QoS requirement.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.605-615
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• 2000

Let E be a real Banach space with property (U,${\lambda}$,m+1,m);${\lambda}{\ge}$0; m${\in}N$, and let C be a nonempty closed convex and bounded subset of E. Suppose T: $C{\leftrightarro}C$ is a strongly accretive map, It is proved that each of the two well known fixed point iteration methods( the Mann and Ishikawa iteration methods.), under suitable conditions , converges strongly to a solution of the equation Tx=f.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.4B
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• pp.338-344
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• 2002

This paper proposes a transient (predictive) connection admission control (CAC) scheme using the transient quality of service (QoS) measure for CDMA cellular systems with bursts On-Off sources. We need an approximate and bounded approach for real-time CAC applications. We derive the transient outage probability as the QoS measure using the Chernoff bound and the refuted large deviation approximation. Numerical results show that the predictive CAC is a promising approach for the multicell CDMA systems.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.87-93
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• 2004

The E-Euler process has been proposed for autonomous dynamical systems in [7]. In this paper, the E-Euler process is extended to nonautonomous dynamical systems. When a discrete function is bounded or gradually decreases to ${\epsilon}\;<<\;1$ as $n\;{\rightarrow}\;{\infty}$, it is shown that the relative error converges to a constant or decreases.