• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.537-545
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• 2005

The aim of this paper is to solve the open problem on product properties of digital covering maps raised from [5]. Namely, let us consider the digital images $X_1 {\subset}Z^{n_{0}}$ with $k_0-adjacency$, $Y_1{\subset}Z^{n_{1}}$ with $k_3-adjacency$, $X_2{\subset}Z^{n_{2}}$ with $k_2-adjacency$ and $Y_2{\subset}Z^{n_{3}}$ with $k_3-adjacency$. Then the reasonable $k_4-adjacency$ of the product image $X_1{\times}X_2$ is determined by the $k_0-$ and $k_2-adjacency$ and the suitable k_5-adjacency$ is assumed on $Y_1{\times}Y_2$ via the $k_1-$ and $k_3-adjacency$ [3] such that each of the projection maps is a digitally continuous map, e.g., $p_1\;:\;X_1{\times}X_2{\rightarrow}X_1$ is a digitally ($k_4,\;k_1$)-continuous map and so on. Let us assume $h_1\;:\;X_1{\rightarrow}Y_1$ to be a digital $(k_0, k_1)$-covering map and $h_2\;:\;X_2{\rightarrow}Y_2$ to be a digital $(k_2,\;k_3)$-covering map. Then we show that the product map $h_1{\times}h_2\;:\;X_1{\times}X_2{\rightarrow}Y_1{\times}Y_2$ need not be a digital $(k_4,k_5)$-covering map.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.31-49
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• 2002

An R$^{n}$ -geometry (P$^{n}$ , L) is a generalization of the Euclidean geometry on R$^{n}$ (see Def. 1.1). We can consider some topologies (see Def. 2.2) on the line set L such that the join operation V : P$^{n}$ $\times$ P$^{n}$ \ $\Delta$ longrightarrow L is continuous. It is a notable fact that in the case n = 2 the introduced topologies on L are same and the join operation V : P$^2$ $\times$ P$^2$ \ $\Delta$ longrightarrow L is continuous and open [10, 11]. It is a fundamental topological property of plane geometry, but in the cases n $\geq$ 3, it is no longer true. There are counter examples [2]. Hence, it is a fundamental problem to find suitable topologies on the line set L in an R$^{n}$ -geometry (P$^{n}$ , L) such that these topologies are compatible with the incidence structure of (P$^{n}$ , L). Therefore, we need to study the topologies of the line set L in an R$^{n}$ -geometry (P$^{n}$ , L). In this paper, the relations of such topologies on the line set L are studied.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.63-76
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• 2000

In this paper, we introduce the concept of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate the properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topological spaces.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.153-169
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• 2000

Let E be a real q-uniformly smooth Banach space which admits a weakly sequentially continuous duality map, and K a nonempty closed convex subset of E. Let T : K -> K be a mapping such that $F(T)\;=\;{x\;{\in}\;K\;:\;Tx\;=\;x}\;{\neq}\;0$ and (I - T) satisfies the accretive-type condition: $\;{\geq}\;{\lambda}$\mid$$\mid$x-Tx$\mid$$\mid$^2$, for all $x\;{\in}\;K,\;x^*\;{\in}\;F(T)$ and for some ${\lambda}\;>\;0$. The weak and strong convergence of the Ishikawa iteration method to a fixed point of T are investigated. An application of our results to the approximation of a solution of a certain linear operator equation is also given. Our results extend several important known results from the Mann iteration method to the Ishikawa iteration method. In particular, our results resolve in the affirmative an open problem posed by Naimpally and Singh (J. Math. Anal. Appl. 96 (1983), 437-446).

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.34 no.1
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• pp.21-32
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• 2016

Open-pit mines are the critical infrastructure for acquiring natural resources. Since it could be endangered by environmental and safety problems during operations, continuous monitoring is required for this type of mine. However, the domestic level management and accumulation of present state data of the topographical alteration are incurred by the development and restoration of open-pit mines relying on digital topographic maps and site surveys. Because of it, other than an expert cannot be viewed easily examines those changes information of open-pit mines in the domestic level. If the efficient management and public access of the open-pit mine is targeted, it is easy to build a web-based three-dimensional monitoring system, utilized in the space information software of open source. Therefore, we purposed on developing an open-pit mine monitoring system to support the development and restoration of the ecology-friendly environment, which could be easily monitored by the general public for those changes within terrain and environments due to operations of the mine.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.71-74
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• 1983

The problems of the continuity of homomorphisms between Banach algebras have been studied widely for the last two decades to obtain various fruitful results, yet it is far from characterizing the calss of Banach algebras for which each homomorphism from a member of the class into a Banach algebra is conitnuous. For commutative Banach algebras A and B a simple proof shows that every homomorphism .theta. from A into B is continuous provided that B is semi-simple, however, with a non semi-simple Banach algebra B examples of discontinuous homomorphisms from C(K) into B have been constructed by Dales [6] and Esterle [7]. For non commutative Banach algebras the problems of automatic continuity of homomorphisms seem to be much more difficult. Many positive results and open questions related to this subject may be found in [1], [3], [5] and [8], in particular most recent development can be found in the Lecture Note which contains [1]. It is well-known that a$^{*}$-isomorphism from a $C^{*}$-algebra into another $C^{*}$-algebra is an isometry, and an isomorphism of a Banach algebra into a $C^{*}$-algebra with self-adjoint range is continuous. But a$^{*}$-isomorphism from a $C^{*}$-algebra into an involutive Banach algebra is norm increasing [9], and one can not expect each of such isomorphisms to be continuous. In this note we discuss an isomorphism from a commutative $C^{*}$-algebra into a commutative Banach algebra with dense range via separating space. It is shown that such an isomorphism .theta. : A.rarw.B is conitnuous and maps A onto B is B is semi-simple, discontinuous if B is not semi-simple.

• The Mathematical Education
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• v.16 no.2
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• pp.22-26
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• 1978

It is shown that a map having an extension to an open map between the Alex-androff base compactifications of its domain and range has a unique such extension. J.S. Wasileski has introduced the Alexandroff base compactifications of Hausdorff spaces endowed with Alexandroff bases. We introduce a definition of morphism between such spaces to obtain a category which we denote by ABC. We prove that the Alexandroff base compactification on objects can be extended to a functor on ABC and that the compact objects give an epireflective subcategory of ABC. For each topological space X there exists a completely regular space $\alpha$X and a surjective continuous function $\alpha$$_{x}$ : Xlongrightarrow$\alpha$X such that for each completely regular space Z and g$\in$C (X, Z) there exists a unique g$\in$C($\alpha$X, 2) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\alpha$$_{x}$, $\alpha$X) is called a completely regularization of X. Let TOP be the category of topological spaces and continuous functions and let CREG be the category of completely regular spaces and continuous functions. The functor $\alpha$ : TOPlongrightarrowCREG is a completely regular reflection functor. For each topological space X there exists a compact Hausdorff space $\beta$X and a dense continuous function $\beta$x : Xlongrightarrow$\beta$X such that for each compact Hausdorff space K and g$\in$C (X, K) there exists a uniqueg$\in$C($\beta$X, K) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\beta$$_{x}$, $\beta$X) is called a Stone-Cech compactification of X. Let COMPT$_2$ be the category of compact Hausdorff spaces and continuous functions. The functor $\beta$ : TOPlongrightarrowCOMPT$_2$ is a compact reflection functor. For each topological space X there exists a realcompact space (equation omitted) and a dense continuous function (equation omitted) such that for each realcompact space Z and g$\in$C(X, 2) there exists a unique g$\in$C (equation omitted) with g=g$^{\circ}$(equation omitted). Such a pair (equation omitted) is called a Hewitt's realcompactification of X. Let RCOM be the category of realcompact spaces and continuous functions. The functor (equation omitted) : TOPlongrightarrowRCOM is a realcompact refection functor. In [2], D. Harris established the existence of a category of spaces and maps on which the Wallman compactification is an epirefiective functor. H. L. Bentley and S. A. Naimpally [1] generalized the result of Harris concerning the functorial properties of the Wallman compactification of a T$_1$-space. J. S. Wasileski [5] constructed a new compactification called Alexandroff base compactification. In order to fix our notations and for the sake of convenience. we begin with recalling reflection and Alexandroff base compactification.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.17 no.1
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• pp.185-201
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• 2014

The Yong-neup of Mt. Daeam, which was designated as Korea's National Monument No.246 in 1973, is a high moor, and it has been managed with the designation as an ecosystem conservation area, Ramsar wetlands, and wetland conservation area. With the closing of the officially announced 5-year period for 'No-Trespassing' on the ecosystem conservation area starting August, 2010, it becomes necessary to arrange a systematic management and conservation scheme in consideration of the access & use of the visitors and Yong-neup's potential change into land consequent on making it open to the public. This study thinks that in order to preserve the Yong-neup, it's necessary to prepare the conservation plan for the program operation for exterminating exotic species, development of replacement wetlands and nurseries, access limit through zone categorization, establishment of environment-monitoring system, institutional management support, and establishment of managing facilities, etc., and to make scientific approaches, such as survey on wetland ecosystem, establishment of inventories, wetland monitoring, and drawing up of wetland ecology maps, etc. In addition, it is required that there should be adequate considerations of restoration of slope faces, drains, artificial embankment, water-collecting wells, roads for military operations, and wild-boar-stricken areas, etc., and should be continuous and systematic management of Yong-neup through the wise use of residents' participation-style maintenance, organization of a consultative body, introduction of CEPA programs, and introduction of visiting facilities and alternative transportation system, etc.

• Journal of Cadastre & Land InformatiX
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• v.53 no.1
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• pp.37-46
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• 2023

As real estate values rise, interest in cadastral resurvey is increasing. Accordingly, a cadastral resurvey project is actively underway for drone operation through securing work efficiency and improving accuracy. The need for utilization and management of cadastral resurvey results (drone images) is being raised, and through this study, a 3D spatial information platform was developed to solve the existing drone image management and utilization limitations and to provide drone image-based 3D cadastral information. It is proposed to build and use. The study area was selected as a district that completed the latest cadastral resurvey project in which the study was organized in February 2023. Afterwards, a web-based 3D platform was applied to the study to solve the user's spatial limitations, and the platform was designed and implemented based on drone images, spatial information, and attribute information. Major functions such as visualization of cadastral resurvey results based on 3D information and comparison of performance between previous cadastral maps and final cadastral maps were implemented. Through the open platform established in this study, anyone can easily utilize the cadastral resurvey results, and it is expected to utilize and share systematic cadastral resurvey results based on 3-dimensional information that reflects the actual business district. In addition, a continuous management plan was proposed by integrating the distributed results into one platform. It is expected that the usability of the 3D platform will be further improved if a platform is established for the whole country in the future and a service linked to the cadastral resurvey administrative system is established.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.4
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• pp.1400-1418
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• 2020

In the development of commercial promotion, chatbot is known as one of significant skill by application of natural language processing (NLP). Conventional design methods are using bag-of-words model (BOW) alone based on Google database and other online corpus. For one thing, in the bag-of-words model, the vectors are Irrelevant to one another. Even though this method is friendly to discrete features, it is not conducive to the machine to understand continuous statements due to the loss of the connection between words in the encoded word vector. For other thing, existing methods are used to test in state-of-the-art online corpus but it is hard to apply in real applications such as telemarketing data. In this paper, we propose an improved chatbot design way using hybrid bag-of-words model and skip-gram model based on the real telemarketing data. Specifically, we first collect the real data in the telemarketing field and perform data cleaning and data classification on the constructed corpus. Second, the word representation is adopted hybrid bag-of-words model and skip-gram model. The skip-gram model maps synonyms in the vicinity of vector space. The correlation between words is expressed, so the amount of information contained in the word vector is increased, making up for the shortcomings caused by using bag-of-words model alone. Third, we use the term frequency-inverse document frequency (TF-IDF) weighting method to improve the weight of key words, then output the final word expression. At last, the answer is produced using hybrid retrieval model and generate model. The retrieval model can accurately answer questions in the field. The generate model can supplement the question of answering the open domain, in which the answer to the final reply is completed by long-short term memory (LSTM) training and prediction. Experimental results show which the hybrid word vector expression model can improve the accuracy of the response and the whole system can communicate with humans.