• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.573-582
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• 2009

This paper is indented to explain a dynamics on homotopies on the compact metric space, by the envelopes of homotopies. It generalizes the notion of not only the envelopes of maps in discrete geometry ([3]), but the envelopes of flows in continuous geometry ([5]). Certain distinctions among the homotopy geometry, the ow geometry and the discrete geometry will be illustrated. In particular, it is shown that any ${\omega}$-limit set, as well as any attractor, for an envelope of homotopies is an empty set (provided the homotopies that we treat are not trivial), whereas it is nonempty in general in discrete case.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.323-333
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• 2015

Let X be a compact metric space and let |A| denote the cardinality of a set A. We prove that if $f:X{\rightarrow}X$ is a homeomorphism and ${\mid}X{\mid}={\infty}$, then for all ${\delta}$ > 0 there is $A{\subset}X$ such that |A| = 4 and for all $k{\in}\mathbb{Z}$ there are $x,y{\in}f^k(A)$, $x{\neq}y$, such that dist(x, y) < ${\delta}$. An observer that can only distinguish two points if their distance is grater than ${\delta}$, for sure will say that A has at most 3 points even knowing every iterate of A and that f is a homeomorphism. We show that for hyperexpansive homeomorphisms the same ${\delta}$-observer will not fail about the cardinality of A if we start with |A| = 3 instead of 4. Generalizations of this problem are considered via what we call (m, n)-expansiveness.

• Journal of Broadcast Engineering
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• v.9 no.2
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• pp.110-118
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• 2004

This paper shows that blind deconvolution has only finite solutions when an original image and a point spread function are nonzero over a restricted domain, in other words, an observed image has a compact support. The key of the proof is to use z-transformations and factorizations of polynomials. Then, we propose an algorithm to find all finite solutions under the boundary condition. Finally, we confirm that we can extract all sets of an original image and a point spread function from a degraded image by using our algorithm in numerical examples.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.76.2-76.2
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• 2014

The Arches cluster is one of the compact, young, massive star clusters near the center of our galaxy. Since it is located only ~30 pc away in projection from the galactic center (GC), the cluster is an excellent target for studying the effects of star forming environment on, for example, the initial mass function under the extreme condition of GC. To estimate the initial condition of the Arches cluster, we compare our calculation results from the anisotropic Fokker-Planck method with the most recent observational data sets for the surface density and velocity dispersion profiles and the present-day mass function.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.2
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• pp.178-183
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• 2004

This paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in IF-parts, but only in THEN -parts of the fuzzy rules of the current layer. The existence of the proposed hierarchical fuzzy system which approximates a given real continuous function on a compact set is proven if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.12
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• pp.63-71
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• 2003

IDDQ testing is indispensable in improving Duality and reliability of CMOS VLSI circuits. But the major problem of IDDQ testing is slow testing speed due to time-consuming IDDQ current measurement. So one requirement is to reduce the number of target faults or to make the test sets compact in fault model. In this paper, we consider equivalent fault collapsing for transistor short faults, a fault model often used in IDDQ testing and propose an efficient algorithm for reducing the number of faults that need to be considered by equivalent fault collapsing. Experimental results for ISCAS benchmark circuits show the effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1087-1099
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• 2004

We study the metrical and topological pressure for flows without fixed points on a compact metric space, and get the results as follows: (1) The metrical pressure with respect to an ergodic measure can be defined by (t, $\varepsilon$)-spanning sets. (2) The topological pressure is the supremum of metrical pressures with respect to all ergodic measures. (3) The properties that the topological pressure is zero, nonzero, finite or infinite respectively are invariant under weak equivalence.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.18 no.3
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• pp.49-58
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• 2019

Automatic transmissions are standard equipment in most automotive vehicles because they provide smooth speed shifting and a compact design with multiple speed ratios. Their structure consists mainly of planetary gear sets as power-transmitting devices and brakes and clutches as shifting devices. Several forward and one reverse speed ratios are achieved by actuating shifting devices to connect gears, input and output shafts, and the transmission case. In the development of a new transmission, kinematic configurations reflecting the transmission concept design are required, and the ability of the new concept design to be assembled without any interference among the connections must be demonstrated. In this study, an assemblability analysis of the kinematic configurations of a Ravigneaux-type automatic transmission was conducted with an assemblable example of an 8-speed Ravigneaux-type automatic transmission.