• Steel and Composite Structures
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• v.29 no.5
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• pp.635-645
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• 2018

Beam-column joints play a significant role in static and dynamic performances of reinforced concrete frame structures. This study contributes a numerical approach of topologically optimal design of carbon fiber reinforced plastics (CFRP) to retrofit existing beam-column connections with crack patterns. In recent, CFRP is used commonly in the rehabilitation and strengthening of concrete members due to the remarkable properties, such as lightweight, anti-corrosion and simplicity to execute construction. With the target to provide an optimal CFRP configuration to effectively retrofit the beam-column connection under semi-failure situation such as given cracks, extended finite element method (X-FEM) is used by combining with multi-material topology optimization (MTO) as a mechanical description approach for strong discontinuity state to mechanically model cracked structures. The well founded mathematical formulation of topology optimization problem for cracked structures by using multiple materials is described in detail in this study. In addition, moved and regularized Heaviside functions (MRHF), that have the role of a filter in multiple materials case, is also considered. The numerical example results illustrated in two cases of beam-column joints with stationary cracks verify the validity, benefit and supremacy of the proposed method.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.1
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• pp.82-82
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• 2010

We measure the topology of the galaxy distribution using the Seventh Data Release of the Sloan Digital Sky Survey (SDSS DR7), examining the dependence of galaxy clustering topology on galaxy properties. The observational results are used to test galaxy formation models. A volume-limited sample defined by Mr<-20.19 enables us to measure the genus curve with amplitude of G=378 at 6h-1Mpc smoothing scale, with 4.8% uncertainty including all systematics and cosmic variance. The clustering topology over the smoothing length interval from 6 to 10h-1Mpc reveals a mild scale-dependence for the shift and void abundance (A_V) parameters of the genus curve. We find strong bias in the topology of galaxy clustering with respect to the predicted topology of the matter distribution, which is also scale-dependent. The luminosity dependence of galaxy clustering topology discovered by Park et al. (2005) is confirmed: the distribution of relatively brighter galaxies shows a greater prevalence of isolated clusters and more percolated voids. We find that galaxy clustering topology depends also on morphology and color. Even though early (late)-type galaxies show topology similar to that of red (blue) galaxies, the morphology dependence of topology is not identical to the color dependence. In particular, the void abundance parameter A_V depends on morphology more strongly than on color. We test five galaxy assignment schemes applied to cosmological N-body simulations to generate mock galaxies: the Halo-Galaxy one-to-one Correspondence (HGC) model, the Halo Occupation Distribution (HOD) model, and three implementations of Semi-Analytic Models (SAMs). None of the models reproduces all aspects of the observed clustering topology; the deviations vary from one model to another but include statistically significant discrepancies in the abundance of isolated voids or isolated clusters and the amplitude and overall shift of the genus curve. SAM predictions of the topology color-dependence are usually correct in sign but incorrect in magnitude.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.519-530
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• 2014

To study a deformation of a digital space from the viewpoint of digital homotopy theory, we have often used the notions of a weak k-deformation retract [20] and a strong k-deformation retract [10, 12, 13]. Thus the papers [10, 12, 13, 16] firstly developed the notion of a strong k-deformation retract which can play an important role in studying a homotopic thinning of a digital space. Besides, the paper [3] deals with a k-deformation retract and its homotopic property related to a digital fundamental group. Thus, as a survey article, comparing among a k-deformation retract in [3], a strong k-deformation retract in [10, 12, 13], a weak deformation k-retract in [20] and a digital k-homotopy equivalence [5, 24], we observe some relationships among them from the viewpoint of digital homotopy theory. Furthermore, the present paper deals with some parts of the preprint [10] which were not published in a journal (see Proposition 3.1). Finally, the present paper corrects Boxer's paper [3] as follows: even though the paper [3] referred to the notion of a digital homotopy equivalence (or a same k-homotopy type) which is a special kind of a k-deformation retract, we need to point out that the notion was already developed in [5] instead of [3] and further corrects the proof of Theorem 4.5 of Boxer's paper [3] (see the proof of Theorem 4.1 in the present paper). While the paper [4] refers some properties of a deck transformation group (or an automorphism group) of digital covering space without any citation, the study was early done by Han in his paper (see the paper [14]).

• Journal of KIISE:Information Networking
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• v.34 no.3
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• pp.226-238
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• 2007

In this paper, we present a novel fully distributed topology control protocol that can construct the multiple-ring topology of Minimal Connected Dominating Set (MCDS) as the transport backbone for mobile ad hoc networks. It makes a topology from the minimal nodes that are chosen from all the nodes, and the constructed topology is comprised of the minimal physical links while preserving connectivity. This topology reduces the interference. The all nodes work as the nodes of the distributed parallel Boltzmann machine, of which the objective function is consisted of two Boltzmann factors: the link degree and the connection domination degree. To define these Boltzmann factors, we extend the Connected Dominating Set into a fuzzy set, and also define the fuzzy set of nodes by which the multiple-ring topology can be constructed. To construct the transport backbone of the mobile ad hoc network, the proposed protocol chooses the nodes that are the strong members of these two fuzzy sets as the clusterheads. We also ran simulations to provide the quantitative comparison against the related works in terms of the packet loss rate and the energy consumption rate. As a result, we show that the network that is constructed by the proposed protocol has far better than the other ones with respect to the packet loss rate and the energy consumption rate.

• Steel and Composite Structures
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• v.37 no.6
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• pp.663-678
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• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.17-22
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• 1985

B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.99-107
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• 1993

A vector space K with scalar product <.,.> is called a Krein space if it can be decomposed as a northogonal sum of a Hilbert space and an anti-space of a Hilbert space. The space K induces a Hilbert space $K_{J}$ in the inner product <.,.> $K_{J}$=<.,.>K, where $J^{2}$=I. the eigenspaces of J are denoted by $K^{+}$$_{J}$, which is a Hilbert space and $K^{-}$$_{J}$, which is an anti-space of a Hilbert space. Then the Krein space K is the orthogonal sum of $K^{+}$$_{J}$ and $K^{-}$$_{J}$. Such a decomposition of K is called a fundamental decomposition. In general, fundamental decompositions are not unique. The norm of the Hilbert space depends on the choice of a fundamental decomposion, but such norms are equivalent. The topology generated by these norms is called the strong or Mackey topology of K. It is used to define all topological notions on the Krein space K with respect to this topology. The Pontryagin index of a Krein space is the dimension of the antispace of a Hilbert space in any such decomposition. the dimension does not depend on the choice of orthogonal decomposition. A Krein space is called a Pontryagin space if it has finite Pontryagin index.dex.yagin index.dex.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.319-357
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• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• The KIPS Transactions:PartC
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• v.15C no.3
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• pp.199-204
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• 2008

Controller Area Network was developed originally for in-vehicle communication network. But it is now widely used for factory automation because of its properties such as strong noise resistance and high reliabilities. With changing communication environments from peer to peer topology to bus topology, we should check each devices about not only mechanical operations but also electronic or software operations. In this paper, we suggest reliability test environment for CAN based system, which is divided two parts, data correctness and timely delivery.

• Journal of Power Electronics
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• v.3 no.4
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• pp.224-229
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• 2003

The rapid expansion of small computers over the last 10-odd years has brought about great changes in the circumstances affecting UPSs. There are strong demands that UPSs become much smaller and lighter, and more economical, which has resulted in the wide application of the circuit topology without transformer. A disadvantage of such UPS topology is that the DC link voltage is very high, which invites decreased reliability and increased cost of battery bank. Some circuit configurations were proposed to eliminate this disadvantage, but they still had problems. In this paper, a novel circuit configuration which eliminates these problems is proposed and evaluated by the experimental results of prototype UPS.