• Title/Summary/Keyword: rational extensions

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A STUDY ON THE NURBS GRID GENERATION AND GRID CONTROL (NURBS를 이용한 격자생성 및 제어기법)

  • Yoon, Yong-Hyun
    • Journal of computational fluids engineering
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    • v.12 no.3
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    • pp.20-28
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    • 2007
  • A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline(NURBS) of an approximation method. Many of NURBS intrinsic properties are introduced and much more easily understood. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper. The object of this study is to develop the surface grid generation and the grid cluster techniques capable of resolving complex flows with shock waves, expansion waves, shear layers. The knot insert method of Non-Uniform Rational B-Spline seems well worked. In addition, NURBS has been widely utilized to generate grids in the computational fluid dynamics community. Computational examples associated with practical configurations have shown the utilization of the algorithm.

The Maximal Ideal Space of Extended Differentiable Lipschitz Algebras

  • Abolfathi, Mohammad Ali;Ebadian, Ali
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.117-125
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    • 2020
  • In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

GOLDIE EXTENDING PROPERTY ON THE CLASS OF z-CLOSED SUBMODULES

  • Tercan, Adnan;Yasar, Ramazan;Yucel, Canan Celep
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.453-468
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    • 2022
  • In this article, we define a module M to be Gz-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We investigate structural properties of Gz-extending modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for Gz-extending modules. We obtain that if a ring is right Gz-extending, then so is its essential overring. Also it is shown that the Gz-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right Gz-extending ring.

Efficient Exponentiation in Extensions of Finite Fields without Fast Frobenius Mappings

  • Nogami, Yasuyuki;Kato, Hidehiro;Nekado, Kenta;Morikawa, Yoshitaka
    • ETRI Journal
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    • v.30 no.6
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    • pp.818-825
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    • 2008
  • This paper proposes an exponentiation method with Frobenius mappings. The main target is an exponentiation in an extension field. This idea can be applied for scalar multiplication of a rational point of an elliptic curve defined over an extension field. The proposed method is closely related to so-called interleaving exponentiation. Unlike interleaving exponentiation methods, it can carry out several exponentiations of the same base at once. This happens in some pairing-based applications. The efficiency of using Frobenius mappings for exponentiation in an extension field was well demonstrated by Avanzi and Mihailescu. Their exponentiation method efficiently decreases the number of multiplications by inversely using many Frobenius mappings. Compared to their method, although the number of multiplications needed for the proposed method increases about 20%, the number of Frobenius mappings becomes small. The proposed method is efficient for cases in which Frobenius mapping cannot be carried out quickly.

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On the Mordell-Weil Groups of Jacobians of Hyperelliptic Curves over Certain Elementary Abelian 2-extensions

  • Moon, Hyun-Suk
    • Kyungpook Mathematical Journal
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    • v.49 no.3
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    • pp.419-424
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    • 2009
  • Let J be the Jacobian variety of a hyperelliptic curve over $\mathbb{Q}$. Let M be the field generated by all square roots of rational integers over a finite number field K. Then we prove that the Mordell-Weil group J(M) is the direct sum of a finite torsion group and a free $\mathbb{Z}$-module of infinite rank. In particular, J(M) is not a divisible group. On the other hand, if $\widetilde{M}$ is an extension of M which contains all the torsion points of J over $\widetilde{\mathbb{Q}}$, then $J(\widetilde{M}^{sol})/J(\widetilde{M}^{sol})_{tors}$ is a divisible group of infinite rank, where $\widetilde{M}^{sol}$ is the maximal solvable extension of $\widetilde{M}$.

ON THE RATIO OF TATE-SHAFAREVICH GROUPS OVER CYCLIC EXTENSIONS OF ORDER p2

  • Yu, Hoseog
    • Honam Mathematical Journal
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    • v.36 no.2
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    • pp.417-424
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    • 2014
  • Let A be an abelian variety defined over a number field K and p be a prime. Define ${\varphi}_i=(x^{p^i}-1)/(x^{p^{i-1}}-1)$. Let $A_{{\varphi}i}$ be the abelian variety defined over K associated to the polynomial ${\varphi}i$ and let Ш($A_{{\varphi}i}$) denote the Tate-Shafarevich groups of $A_{{\varphi}i}$ over K. In this paper assuming Ш(A/F) is finite, we compute [Ш($A_{{\varphi}1}$)][Ш($A_{{\varphi}2}$)]/[Ш($A_{{\varphi}1{\varphi}2}$)] in terms of K-rational points of $A_{{\varphi}i}$, $A_{{\varphi}1{\varphi}2}$ and their dual varieties, where [X] is the order of a finite abelian group X.

Requirement analysis for visualization of condition assessment in 3D Bridge Model (3차원 교량모델에서의 상태평가정보 가시화를 위한 요구사항 분석)

  • Huang, Meng-Gang;Kim, Bong-Geun;Lee, Sang-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2010.04a
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    • pp.238-241
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    • 2010
  • This paper proposed an approach to integrate bridge condition assessment related information with a 3D bridge model to visualize bridge condition assessment information in the 3D bridge model. In this approach, bridge information model plays a centric role in the data access and realizes the integration of bridge initial design and historical bridge maintenance records. Behind the bridge information model is a rational database. After the system requirements for this approach, several IFC data model extensions are suggested.

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Correlation Effect of Maintenances on Probabilistic Service Life Management (확률론적 구조물 수명관리의 유지보수 상관관계 영향 평가)

  • Kim, Sunyong
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.20 no.1
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    • pp.48-55
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    • 2016
  • The assessment and prediction of service life of a structure are usually under uncertainty so that rational probabilistic concepts and methods have to be applied. Based on these rational assessment and prediction, optimum maintenance strategies to minimize the life-cycle cost and/or maximize the structural safety can be established. The service life assessment and prediction considering maintenance actions generally includes effects of maintenance types and times of the structural components on the service life extensions of structural system. Existing researches on the service life management have revealed the appropriate system modeling considering the correlation among the components is required for system reliability analysis and probabilistic service life estimation. However, the study on correlation among the maintenance actions is still required. This paper deals with such a study for more effective and efficient service life management. In this paper, both the preventive and essential maintenances are considered for the extended service life estimation and management.

TIGHT CLOSURES AND INFINITE INTEGRAL EXTENSIONS

  • Moon, Myung-In;Cho, Young-Hyun
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.65-72
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    • 1992
  • All rings are commutative, Noetherian with identity and of prime characteristic p, unless otherwise specified. First, we describe the definition of tight closure of an ideal and the properties about the tight closure used frequently. The technique used here for the tight closure was introduced by M. Hochster and C. Huneke [4,5, or 6]. Using the concepts of the tight closure and its properties, we will prove that if R is a complete local domain and F-rational, then R is Cohen-Macaulay. Next, we study the properties of R$^{+}$, the integral closure of a domain in an algebraic closure of its field of fractions. In fact, if R is a complete local domain of characteristic p>0, then R$^{+}$ is Cohen-Macaulay [8]. But we do not know this fact is true or not if the characteristic of R is zero. For the special case we can show that if R is a non-Cohen-Macaulay normal domain containing the rationals Q, then R$^{+}$ is not Cohen-Macaulay. Finally we will prove that if R is an excellent local domain of characteristic p and F-ratiional, then R is Cohen-Macaulay.aulay.

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Brand Equity and Purchase Intention in Fashion Products: A Cross-Cultural Study in Asia and Europe (상표자산과 구매의도와의 관계에 관한 국제비교연구 - 아시아와 유럽의 의류시장을 중심으로 -)

  • Kim, Kyung-Hoon;Ko, Eun-Ju;Graham, Hooley;Lee, Nick;Lee, Dong-Hae;Jung, Hong-Seob;Jeon, Byung-Joo;Moon, Hak-Il
    • Journal of Global Scholars of Marketing Science
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    • v.18 no.4
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    • pp.245-276
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    • 2008
  • Brand equity is one of the most important concepts in business practice as well as in academic research. Successful brands can allow marketers to gain competitive advantage (Lassar et al.,1995), including the opportunity for successful extensions, resilience against competitors' promotional pressures, and the ability to create barriers to competitive entry (Farquhar, 1989). Branding plays a special role in service firms because strong brands increase trust in intangible products (Berry, 2000), enabling customers to better visualize and understand them. They reduce customers' perceived monetary, social, and safety risks in buying services, which are obstacles to evaluating a service correctly before purchase. Also, a high level of brand equity increases consumer satisfaction, repurchasing intent, and degree of loyalty. Brand equity can be considered as a mixture that includes both financial assets and relationships. Actually, brand equity can be viewed as the value added to the product (Keller, 1993), or the perceived value of the product in consumers' minds. Mahajan et al. (1990) claim that customer-based brand equity can be measured by the level of consumers' perceptions. Several researchers discuss brand equity based on two dimensions: consumer perception and consumer behavior. Aaker (1991) suggests measuring brand equity through price premium, loyalty, perceived quality, and brand associations. Viewing brand equity as the consumer's behavior toward a brand, Keller (1993) proposes similar dimensions: brand awareness and brand knowledge. Thus, past studies tend to identify brand equity as a multidimensional construct consisted of brand loyalty, brand awareness, brand knowledge, customer satisfaction, perceived equity, brand associations, and other proprietary assets (Aaker, 1991, 1996; Blackston, 1995; Cobb-Walgren et al., 1995; Na, 1995). Other studies tend to regard brand equity and other brand assets, such as brand knowledge, brand awareness, brand image, brand loyalty, perceived quality, and so on, as independent but related constructs (Keller, 1993; Kirmani and Zeithaml, 1993). Walters(1978) defined information search as, "A psychological or physical action a consumer takes in order to acquire information about a product or store." But, each consumer has different methods for informationsearch. There are two methods of information search, internal and external search. Internal search is, "Search of information already saved in the memory of the individual consumer"(Engel, Blackwell, 1982) which is, "memory of a previous purchase experience or information from a previous search."(Beales, Mazis, Salop, and Staelin, 1981). External search is "A completely voluntary decision made in order to obtain new information"(Engel & Blackwell, 1982) which is, "Actions of a consumer to acquire necessary information by such methods as intentionally exposing oneself to advertisements, taking to friends or family or visiting a store."(Beales, Mazis, Salop, and Staelin, 1981). There are many sources for consumers' information search including advertisement sources such as the internet, radio, television, newspapers and magazines, information supplied by businesses such as sales people, packaging and in-store information, consumer sources such as family, friends and colleagues, and mass media sources such as consumer protection agencies, government agencies and mass media sources. Understanding consumers' purchasing behavior is a key factor of a firm to attract and retain customers and improving the firm's prospects for survival and growth, and enhancing shareholder's value. Therefore, marketers should understand consumer as individual and market segment. One theory of consumer behavior supports the belief that individuals are rational. Individuals think and move through stages when making a purchase decision. This means that rational thinkers have led to the identification of a consumer buying decision process. This decision process with its different levels of involvement and influencing factors has been widely accepted and is fundamental to the understanding purchase intention represent to what consumers think they will buy. Brand equity is not only companies but also very important asset more than product itself. This paper studies brand equity model and influencing factors including information process such as information searching and information resources in the fashion market in Asia and Europe. Information searching and information resources are influencing brand knowledge that influences consumers purchase decision. Nine research hypotheses are drawn to test the relationships among antecedents of brand equity and purchase intention and relationships among brand knowledge, brand value, brand attitude, and brand loyalty. H1. Information searching influences brand knowledge positively. H2. Information sources influence brand knowledge positively. H3. Brand knowledge influences brand attitude. H4. Brand knowledge influences brand value. H5. Brand attitude influences brand loyalty. H6. Brand attitude influences brand value. H7. Brand loyalty influences purchase intention. H8. Brand value influence purchase intention. H9. There will be the same research model in Asia and Europe. We performed structural equation model analysis in order to test hypotheses suggested in this study. The model fitting index of the research model in Asia was $X^2$=195.19(p=0.0), NFI=0.90, NNFI=0.87, CFI=0.90, GFI=0.90, RMR=0.083, AGFI=0.85, which means the model fitting of the model is good enough. In Europe, it was $X^2$=133.25(p=0.0), NFI=0.81, NNFI=0.85, CFI=0.89, GFI=0.90, RMR=0.073, AGFI=0.85, which means the model fitting of the model is good enough. From the test results, hypotheses were accepted. All of these hypotheses except one are supported. In Europe, information search is not an antecedent of brand knowledge. This means that sales of global fashion brands like jeans in Europe are not expanding as rapidly as in Asian markets such as China, Japan, and South Korea. Young consumers in European countries are not more brand and fashion conscious than their counter partners in Asia. The results have theoretical, practical meaning and contributions. In the fashion jeans industry, relatively few studies examining the viability of cross-national brand equity has been studied. This study provides insight on building global brand equity and suggests information process elements like information search and information resources are working differently in Asia and Europe for fashion jean market.

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