• Honam Mathematical Journal
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• v.29 no.2
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• pp.223-244
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• 2007

We introduce the notions of interval-valued fuzzy semipreopen sets (mappings), interval-valued fuzzy semi-pre interior and interval-valued fuzzy semi-pre-continuous mappings by using the notion of interval-valued fuzzy sets. We also investigate related properties and characterize interval-valued fuzzy semi-preopen sets (mappings) and interval-valued fuzzy semi-precontinuous mappings.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.467-474
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• 2005

Using the notion of intuitionistic fuzzy sets, the concept of intuitionis tic fuzzy semi-preopen sets and intuitionistic fuzzy semi-pre-continuous mappings are introduced. The relation between an intuitionistic fuzzy precontinuous ma pping and an intuitionistic semi-precontinuous mapping is given. Characterizations of intuitionistic fuzzy semi-preopen sets and intuitionist ic fuzzy semi-precontinuous mappings are given.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.691-700
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• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.47-52
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• 2009

We introduce the concepts of interval-valued fuzzy M-continuity and interval-valued fuzzy M$^*$(M)-open mappings. And we study some characterizations and basic properties of such functions.

• Korean Journal of Remote Sensing
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• v.21 no.5
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• pp.393-404
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• 2005

As multi-source spatial data fusion mainly deal with various types of spatial data which are specific representations of real world with unequal reliability and incomplete knowledge, proper data representation and uncertainty analysis become more important. In relation to this problem, this paper presents and applies an advanced data representation methodology for different types of spatial data such as categorical and continuous data. To account for the uncertainties of both categorical data and continuous data, fuzzy boundary representation and smoothed kernel density estimation within a fuzzy logic framework are adopted, respectively. To investigate the effects of those data representation on final fusion results, a case study for landslide hazard mapping was carried out on multi-source spatial data sets from Jangheung, Korea. The case study results obtained from the proposed schemes were compared with the results obtained by traditional crisp boundary representation and categorized continuous data representation methods. From the case study results, the proposed scheme showed improved prediction rates than traditional methods and different representation setting resulted in the variation of prediction rates.

• International journal of advanced smart convergence
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• v.12 no.4
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• pp.361-369
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• 2023

Achieving realistic visual quality while maintaining optimal real-time rendering performance is a major challenge in evolving computer graphics and interactive 3D applications. Normal mapping, as a core technology in 3D, has matured through continuous optimization and iteration. Hybrid normal mapping as a new mapping model has also made significant progress and has been applied in the 3D asset production pipeline. This study comprehensively explores the hybrid normal techniques, analyzing Linear Blending, Overlay Blending, Whiteout Blending, UDN Blending, and Reoriented Normal Mapping, and focuses on how the various hybrid normal techniques can be used to achieve rendering performance and visual fidelity. performance and visual fidelity. Under the consideration of computational efficiency, visual coherence, and adaptability in different 3D production scenes, we design comparative experiments to explore the optimal solutions of the hybrid normal techniques by analyzing and researching the code, the performance of different hybrid normal mapping in the engine, and analyzing and comparing the data. The purpose of the research and summary of the hybrid normal technology is to find out the most suitable choice for the mainstream workflow based on the objective reality. Provide an understanding of the hybrid normal mapping technique, so that practitioners can choose how to apply different hybrid normal techniques to the corresponding projects. The purpose of our research and summary of mixed normal technology is to find the most suitable choice for mainstream workflows based on objective reality. We summarized the hybrid normal mapping technology and experimentally obtained the advantages and disadvantages of different technologies, so that practitioners can choose to apply different hybrid normal mapping technologies to corresponding projects in a reasonable manner.

• Spatial Information Research
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• v.1 no.1
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• pp.17-28
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• 1993

In order to minimize vectorizing tasks, which require huge reso¬urces and time and to support the census mapping effectively, the geographic information databases structure has been studied. The steps of the new approach are as follows. : Step 1, Scanning the maps of the whole country and storing the image data in raster format. Step 2, Vectorizing the data of specific items for Census operation such as Enume¬ration District, and then linking to attribute data in the text format. Step 3, Designing the database with a Tile and Multi-layer structure to make a continuous map logically. Step 4, Implement Censlls Mapping System(CMS) for efficient mapping and retrieving. As a consequence of this study, the cost, manpower and time effectiveness was proved and it was confirmed to produce lIseful and high-qual ified maps for the Census. In the future, this system wi II be able to provide many organizations and individuals with the various data based on geographical statistical information.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.187-191
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• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• International Journal of Internet, Broadcasting and Communication
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• v.15 no.4
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• pp.178-184
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• 2023

AI image generation technology has become a popular research direction in the field of AI, which is widely used in the field of digital art and conceptual design, and can also be used in the process of 3D texture mapping. This paper introduces the production process of 3D texture mapping using AI image technology, and discusses whether it can be used as a new way of 3D texture mapping to enrich the 3D texture mapping production process. Two AI deep learning models, Stable Diffusion and Midjourney, were combined to generate high-quality AI textures. Finally, the lmage to material function of substance 3D Sampler was used to convert the AI-generated textures into PBR 3D texture maps. And applied in 3D environment. This study shows that 3D texture maps generated by AI image generation technology can be used in 3D environment, which not only has short production time and high production efficiency, but also has rich changes in map styles, which can be quickly adjusted and modified according to the design scheme. However, some AI texture maps need to be manually modified before they can be used. With the continuous development of AI technology, there will be great potential for further development and innovation of AI-generated image technology in the 3D content production process in the future.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.125-130
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• 1997

In this paper, we give a characterization of collectionwise normality using continuous functions. More precisely, we give a new and short proof of the Dowker's theorem using selection theory that a $T_1$ space X is collectionwise normal if every continuous mapping of every closed subset F of X into a Banach space can be continuously extended over X. This is also a generalization of Tietze's extension theorem.