• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.127-133
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• 1997

In order to study the limits of sequences appearing in, for example, stochastic process, A. V. Skorokhod has defined new function space topologies. We compare these topologies with the topology of compact convergence, the topology of pointwise convergence and others.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.161-173
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• 2013

This paper is concerned with the space $\mathcal{K}_{w^*}(X^*,Y)$ of $weak^*$ to weak continuous compact operators from the dual space $X^*$ of a Banach space X to a Banach space Y. We show that if $X^*$ or $Y^*$ has the Radon-Nikod$\acute{y}$m property, $\mathcal{C}$ is a convex subset of $\mathcal{K}_{w^*}(X^*,Y)$ with $0{\in}\mathcal{C}$ and T is a bounded linear operator from $X^*$ into Y, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\{S{\in}\mathcal{C}:{\parallel}S{\parallel}{\leq}{\parallel}T{\parallel}\}}^{{\tau}_{\mathcal{c}}}$, where ${\tau}_{\mathcal{c}}$ is the topology of uniform convergence on each compact subset of X, moreover, if $T{\in}\mathcal{K}_{w^*}(X^*, Y)$, here $\mathcal{C}$ need not to contain 0, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\mathcal{C}}$ in the topology of the operator norm. Some properties of $\mathcal{K}_{w^*}(X^*,Y)$ are presented.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.224-230
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• 2013

In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy ${\theta}$-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy ${\theta}$-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy ${\theta}$-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy ${\theta}$-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.23-34
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• 1988

A version of Ascoli's Theorem (equating compact and equicontinuous sets) is presented in the context of convergence spaces. This theorem and another, (involving equicontinuity) are applied to characterize compact subsets of quasi-multipliers of a $C^*$-algebra B, and to characterize the compact subsets of the state space of B. The classical Ascoli Theorem states that, for pointwise pre-compact families F of continuous functions from a locally compact space Y to a complete Hausdorff uniform space Z, equicontinuity of F is equivalent to relative compactness in the compact-open topology([4] 7.17). Though this is one of the most important theorems of modern analysis, there are some applications of the ideas inherent in this theorem which arc not readily accessible by direct appeal to the theorem. When one passes to so-called "non-commutative analysis", analysis of non-commutative $C^*$-algebras, the analogue of Y may not be relatively compact, while the conclusion of Ascoli's Theorem still holds. Consequently it seems plausible to establish a more general Ascoli Theorem which will directly apply to these examples.

• 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 Transactions of the Korean Institute of Power Electronics
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• v.26 no.3
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• pp.199-204
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• 2021

Ultra-compact electric vehicles have narrow space for power conversion devices. This work presents schemes to achieve the high-power density of a low-voltage DC-DC converter (LDC): simplifying a converter structure by using sync-buck topology, applying a planar inductor using PCB winding, and applying a plate-type heat sink. The heat sink is placed between two PCBs, which increases the contact surface between the PCB and the heat-dissipating device. It enables the miniaturization of the converter to improve the conditions of heat radiation. The validity of the proposed scheme is verified through the experiment using a 500 W(12 V, 41.67 A) prototype with an input voltage range from 58 V to 84 V.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.455-470
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• 2005

This paper introduces compactness notions for frames which are expressed in terms of the convergence of suitably specified general filters. It establishes several preservation properties for them as well as their coreflectiveness in the setting of regular frames. Further, it shows that supercompact, compact, and $Lindel{\ddot{o}}f$ frames can be described by compactness conditions of the present form so that various familiar facts become consequences of these general results. In addition, the Prime Ideal Theorem and the Axiom of Countable Choice are proved to be equivalent to certain conditions connected with the kind of compactness considered here.

• Journal of information and communication convergence engineering
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• v.11 no.1
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• pp.45-49
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• 2013

A compact radio frequency (RF) bandpass filter (BPF) in low temperature co-fired ceramic (LTCC) is suggested for WiMAX applications. The center frequency ($f_0$) of the BPF is 5.5 GHz and its pass band or 3-dB bandwidth is 700 MHz to cover all the three major bands, low and middle unlicensed national information infrastructure (U-NII; 5.15-5.35 GHz), World Radiocommunication Conference (5.47-5.725 GHz), and upper U-NII/industrial, scientific, and medical (ISM) (5.725-5.85 GHz), for the WiMAX frequency band. A lumped circuit element design-the 5th order capacitively coupled Chebyshev BPF topology-is adopted. In order to design a compact RF BPF, a very thin ($43.18{\mu}m$) ceramic layer is used in LTCC substrate. An interdigital BPF is also designed in silicon substrate to compare the size and performance of the lumped circuit element BPF. Due to the high relative dielectric constant (${\varepsilon}_r$ = 11.9) of the silicon substrate, the quarter-wavelength resonator of the interdigital BPF can be reduced. In comparison to the 5th order interdigital BPF at $f_0$ = 5.5 GHz, the lumped element design is 24% smaller in volume and has 17 and 7 dB better attenuation characteristics at $f_0{\pm}0.75$ GHz.