U(k)- AND L(k)-HOMOTOPIC PROPERTIES OF DIGITIZATIONS OF nD HAUSDORFF SPACES

Han, Sang-Eon

doi:10.15672/hjms.2016.404

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…On the other hand, the number of excess oxygens located in the deep band edge states can be effectively reduced by hydrogen treatment. 40 Thus, it is important to elucidate the physical origins for the changes in concentration of excess oxygens within the channel layers, which are closely related to the operational instabilities of the devices.…”

Section: Methodsmentioning

confidence: 99%

Roles of Oxygen Interstitial Defects in Atomic-Layer Deposited InGaZnO Thin Films with Controlling the Cationic Compositions and Gate-Stack Processes for the Devices with Subμm Channel Lengths

Bae

Yang

Kim

et al. 2022

ACS Appl. Mater. Interfaces

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Roles of oxygen interstitial defects located in the In–Ga–Zn-O (IGZO) thin films prepared by atomic layer deposition were investigated with controlling the cationic compositions and gate-stack process conditions. It was found from the spectroscopic ellipsometry analysis that the excess oxygens increased with increasing the In contents within the IGZO channels. While the device using the IGZO channel with an In/Ga ratio of 0.2 did not show marked differences with the variations in the oxidant types during the gate-stack formation, the device characteristics were severely deteriorated with increasing the In/Ga ratio to 1.4, when the Al2O3 gate insulator (GI) was prepared with the H2O oxidants (H2O–Al2O3) due to a higher amount of excess oxygen in the channel. Additionally, during the deposition process of the Al-doped ZnO (AZO) gate electrode (GE) replacing from the indium–tin oxide (ITO) GE, the thermal annealing effect at 180 °C facilitated the passivation of oxygen vacancy and the strengthening of metal–oxygen bonding, which could stabilize the TFT operations. From these results, the gate-stack structure employing O3-processed Al2O3 GI (O3–Al2O3) and AZO GE (OA) was suggested to be most suitable for the device using IGZO channel with a higher In content. On the other hand, the device employing H2O–Al2O3 GI and AZO GE exhibited larger negative shifts of threshold voltage (V TH) under positive-bias-temperature stress (PBTS) condition than the device employing O3– Al2O3 GI and ITO GE due to larger hydrogen contents within the gate stacks. Anomalous negative shifts of V TH were accelerated with increasing the In contents of the IGZO channel. When the channel length of the fabricated device were scaled down to submicrometer regime, the OA gate stacks successfully alleviated the short-channel effects.

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Section: Methodsmentioning

confidence: 99%

Roles of Oxygen Interstitial Defects in Atomic-Layer Deposited InGaZnO Thin Films with Controlling the Cationic Compositions and Gate-Stack Processes for the Devices with Subμm Channel Lengths

Bae

Yang

Kim

et al. 2022

ACS Appl. Mater. Interfaces

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“…6. Since D KA (W 1 ) is SC 2,12 A and D KA (W 2 ) is SC 2,10 A (see Fig. 6), any LA-map from (W 2 , E 2…”

Section: Theorem 52 ([10]mentioning

confidence: 99%

“…To digitize (X, E n X ) into a digital space in Z n in a certain digital topological approach, we have often used graph theory and locally finite topological structures such as Khalimsky (K-, for short) topology, Alexandroff topology, axiomatic locally finite topology and so forth [1,11,19,21,25,27,29]. To be specific, when digitizing (X, E n X ), it is clear to recognize partitioned shapes such as discs, triangles, rectangles and so forth of the Euclidean space into points in a certain digital topological approach [2,4,5,11,12,19,23,24,[26][27][28][29][30]32].…”

Section: Introductionmentioning

confidence: 99%

Homotopic properties of $KA$-digitizations of $n$-dimensional Euclidean spaces

Han

2020

Hacettepe Journal of Mathematics and Statistics

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For X(⊂ R n ), assume the subspace (X, E n X ) induced by the n-dimensional Euclidean topological space (R n , E n ). Let Z be the set of integers. Khalimsky topology on Z, denoted by (Z, κ), is generated by the set {{2m − 1, 2m, 2m + 1} | m ∈ Z} as a subbase. Besides, Khalimsky topology on Z n , n ∈ N, denoted by (Z n , κ n ), is a product topology induced by (Z, κ). Proceeding with a digitization of (X, E n X ) in terms of the Khalimsky (K-, for short) topology, we obtain a K-digitized space in Z n , denoted by D K (X)(⊂ Z n ), which is a K-topological space. Considering further D K (X) with K-adjacency, we obtain a topological graph related to the K-topology (a KA-space for short) denoted by D KA (X) (see an algorithm in Section 3). Motivated by an A-homotopy between A-maps for KA-spaces, the present paper establishes a new homotopy, called an LA-homotopy, which is suitable for studying homotopic properties of both (X, E n X ) and D KA (X) because a homotopy for Euclidean topological spaces has some limitations of digitizing (X, E n X ). The goal of the paper is to study some relationships among an ordinary homotopy equivalence for spaces (X, E n X ), an LA-homotopy equivalence for spaces (X, E n X ), and an A-homotopy equivalence for KA-spaces D KA (X). Finally, we classify KA-spaces (resp. (X, E n X )) via an A-homotopy equivalence (resp. an LA-homotopy equivalence). This approach can facilitate studies of applied topology, approximation theory and digital geometry.

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“…Then (X, B) is called a KA-space pair. Motivated by many kinds of homotopy equivalences [16,18,22,23,28,31], let us consider the notions of an A-homotopy relative to a subset B ⊂ X [30], A-contractibility [30] and an A-homotopy equivalence [30,32,33]. Definition 13.…”

Section: Homotopies In the Category Kac And A Certain Conjecture Invomentioning

confidence: 99%

Links between Contractibility and Fixed Point Property for Khalimsky Topological Spaces

Han

2019

Mathematics

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Given a Khalimsky (for short, K-) topological space X, the present paper examines if there are some relationships between the contractibility of X and the existence of the fixed point property of X. Based on a K-homotopy for K-topological spaces, we firstly prove that a K-homeomorphism preserves a K-homotopy between two K-continuous maps. Thus, we obtain that a K-homeomorphism preserves K-contractibility. Besides, the present paper proves that every simple closed K-curve in the n-dimensional K-topological space, S C K n , l , n ≥ 2 , l ≥ 4 , is not K-contractible. This feature plays an important role in fixed point theory for K-topological spaces. In addition, given a K-topological space X, after developing the notion of K-contractibility relative to each singleton { x } ( ⊂ X ) , we firstly compare it with the concept of K-contractibility of X. Finally, we prove that the K-contractibility does not imply the K-contractibility relative to each singleton { x 0 } ( ⊂ X ) . Furthermore, we deal with certain conjectures involving the (almost) fixed point property in the categories KTC and KAC, where KTC (see Section 3) (resp. KAC (see Section 5)) denotes the category of K-topological (resp. KA-) spaces, KA-) spaces are subgraphs of the connectedness graphs of the K-topology on Z n .

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U(k)- AND L(k)-HOMOTOPIC PROPERTIES OF DIGITIZATIONS OF nD HAUSDORFF SPACES

Cited by 3 publications

References 18 publications

Roles of Oxygen Interstitial Defects in Atomic-Layer Deposited InGaZnO Thin Films with Controlling the Cationic Compositions and Gate-Stack Processes for the Devices with Subμm Channel Lengths

Roles of Oxygen Interstitial Defects in Atomic-Layer Deposited InGaZnO Thin Films with Controlling the Cationic Compositions and Gate-Stack Processes for the Devices with Subμm Channel Lengths

Homotopic properties of $KA$-digitizations of $n$-dimensional Euclidean spaces

Links between Contractibility and Fixed Point Property for Khalimsky Topological Spaces

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