• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.811-827
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• 2000

We find some conditions to derive the conjugacy separability of the free product of conjugacy separable split extensions amalgamated along cyclic retracts. These conditions hold for any double coset separable groups and free-by-cyclic groups with nontrivial center. It was known that free-by-finite, polycyclic-by-finite, and fuchsian groups are double coset separable. Hence free products of those groups amalgamated along cyclic retracts are conjugacy separable.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.29-34
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• 2005

The aim of this paper is to introduce fuzzy γ-continuity and fuzzy γ-retracts in a fuzzy topology on fuzzy sets and establish some of their properties. Also, the relations between these new concepts are discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.40-45
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• 2005

The concept of a intuitionistic fuzzy topology (IFT) was introduced by Coker 1997. The concept of a fuzzy retract was introduced by Rodabaugh in 1981. The aim of this paper is to introduce a new concepts of fuzzy continuity and fuzzy retracts in an intuitionistic fuzzy topological spaces and establish some of their properties. Also, the relations between these new concepts are discussed.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.295-308
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• 2002

Using the Countably way below relation, we show that the category $\sigma$-CFrm of $\sigma$-coherent frames and $\sigma$-coherent homomorphisms is coreflective n the category Frm of frames and frame homomorphisms. Introducting the concept of stably countably approximating frames which are exactly retracts of $\sigma$-coherent frames, it is shown that the category SCAFrm of stably countably approximating frames and $\sigma$-proper frame homomorphisms is coreflective in Frm. Finally we introduce strongly Lindelof frames and show that they are precisely lax retracts of $\sigma$-coherent frames.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.915-932
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• 2010

The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set $X\;{\subset}\;Z^n$ take a subspace (X, $T_n^X$) induced from the Khalimsky nD space ($Z^n$, $T^n$). Considering (X, $T_n^X$) with one of the k-adjacency relations of $Z^n$, we call it a computer topological space (or a space if not confused) denoted by $X_{n,k}$. In addition, we introduce several kinds of k-retracts of $X_{n,k}$, investigate their properties related to several continuities and homeomorphisms in computer topology and study extension problems of these continuities in relation with these k-retracts.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1560-1565
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• 2003

Tapping mode atomic force microscopy (TM-AFM) utilizes the dynamic response of a resonating probe tip as it approaches and retracts from a sample to measure the topography and material properties of a nanostructure. We present recent results based on nonlinear dynamical systems theory, computational continuation techniques and detailed experiments that yield new perspectives and insight into AFM. A dynamic model including van der Waals and Derjaguin-Muller-Toporov (DMT) contact forces demonstrates that periodic solutions can be represented with respect to the approach distance and excitation frequency. Turning points on the surface lead to hysteretic amplitude jumps as the tip nears/retracts from the sample. Experiments are performed using a tapping mode tip on a graphite sample to verify the predictions.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1375-1382
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• 2015

We investigate what happens when we try to work with continuing block codes (i.e., left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on strictly sofic shifts do not behave as well as those on shifts of finite type; a continuing block code on a sofic shift need not have a uniformly bounded retract, unlike one on a shift of finite type. A right eresolving code on a sofic shift can display any behavior arbitrary block codes can have. We also show that a right continuing factor of a shift of finite type is always a shift of finite type.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.67-80
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• 2015

For a pomonoid S, let us denote Pos-S the category of S-posets and S-poset maps. In this paper, we consider the slice category Pos-S/B for an S-poset B, and study some categorical ingredients. We first show that there is no non-trivial injective object in Pos-S/B. Then we investigate injective objects with respect to the class of regular monomorphisms in this category and show that Pos-S/B has enough regular injective objects. We also prove that regular injective objects are retracts of exponentiable objects in this category. One of the main aims of the paper is to draw attention to characterizing injectivity in the category Pos-S/B under a particular case where B has trivial action. Among other things, we also prove that the necessary condition for a map (an object) here to be regular injective is being convex and present an example to show that the converse is not true, in general.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.73-76
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• 2004

Tapping mode atomic force microscopy (TM-AFM) utilizes the dynamic response of a resonating probe tip as it approaches and retracts from a sample to measure the topography and material properties of a nanostructure. We present recent results based on numerical techniques that yield new perspectives and insight into AFM. It is compared that the dynamic models including van der Waals and Derjaguin-Muller-Toporov(DMT) or Johnson-Kendall-Roberts(JKR) contact forces demonstrates that periodic solutions can be represented with respect to the approach distance and excitation frequency.

• 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.