• Title/Summary/Keyword: eigen 1-forms

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Eigen 1-forms of the laplacian and riemannian submersions

  • Park, Jeong-Hyeong
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.477-480
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    • 1996
  • Let $\pi : Z \longrightarrow Y$ be a fiber bundle where Y and Z are compact Riemannian manifolds without boundary. We are primarily interested in the case where $\pi$ is a Riemannian submersion with minimal fibers; this is the case, for example, where Z is the sphere bundle of some vector bundle over Y or where Z is a principal bundle over Y.

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Damage Detection of Truss Structure based on the Predicted Change of Parameter Matrices (파라미터행렬의 변화량 추정에 근거한 트러스 구조물의 손상탐지)

  • Kang, Taik-Seon;Lee, Byeong-Hyeon;Eun, Hee-Chang
    • Journal of the Architectural Institute of Korea Structure & Construction
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    • v.34 no.1
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    • pp.27-32
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    • 2018
  • This work provides the analytical methods to represent the updated form of stiffness or flexibility matrices using the measurements of the first few natural frequencies and the corresponding mode shapes. This study derives the mathematical forms on the variance of stiffness or flexibility matrices to minimize the performance index in the satisfaction of the eigen-function including the residual force depending on the measured data. The proposed methods can be utilized in detecting damage and updating the parameter matrices deviated from the analytical parameter matrices. The validity of the proposed methods is investigated in a numerical experiment of truss structure and the numerical results of stiffness-based and flexibility-based methods are compared. The sensitivity to the external noise is also examined for applying to the practical work.

Stability analysis of steel cable-stayed bridges

  • Tang, Chia-Chih;Shu, Hung-Shan;Wang, Yang-Cheng
    • Structural Engineering and Mechanics
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    • v.11 no.1
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    • pp.35-48
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    • 2001
  • The objective of this study is to investigate the stability behavior of steel cable-stayed bridges by comparing the buckling loads obtained by means of finite element methods with eigen-solver. In recent days, cable-stayed bridges dramatically attract engineers' attention due to their structural characteristics and aesthetics. They require a number of design parameters and present a high degree of static indetermination, especially for long span bridges. Cable-stayed bridges exhibit several nonlinear behaviors concurrently under normal design loads due to the individual nonlinearity of substructures such as the pylons, stay cables, and bridge deck, and their interactions. The geometric nonlinearities arise mainly from large displacements of cables. Strong axial and lateral forces acting on the bridge deck and pylons cause structural nonlinear behaviors. The interaction is among the substructures. In this paper, a typical three-span steel cable-stayed bridge with a variety of design parameters has been investigated. The numerical results indicate that the design parameters such as the ratio of $L_1/L$ and $I_p/I_b$ are important for the structural behavior, where $L_1$ is the main span length, L is the total span length of the bridge, $I_p$ is the moment of inertia of the pylon, and $I_b$ is the moment of inertia of the bridge deck. When the ratio $I_p/I_b$ increases, the critical load decreases due to the lack of interaction among substructures. Cable arrangements and the height of pylon are another important factors for this type of bridge in buckling analysis. According to numerical results, the bridges supported by a pylon with harp-type cable arrangement have higher critical loads than the bridges supported by a pylon with fan-type cable arrangement. On contrary, the shape of the pylon does not significantly affect the critical load of this type of bridge. All numerical results have been non-dimensionalized and presented in both tabular and graphical forms.

Theoretical Investigations and measuring Techniques of Geometrical Factor influencing Sensitive Electronic Devices (감도전자장치에 영향을 주는 기하학적 인수의 이론적 연구와 측정)

  • S. K. Lee
    • 전기의세계
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    • v.14 no.1
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    • pp.5-12
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    • 1965
  • In the designs of the sensitive electronic devices such as phase sensitive detector, X-ray diffractometer, and neutron diffractometers, we must take into account the geometrical factors in a coil systems and extraneous stray fields. Input wave forms in such a sensitive electronic devices are often altered by the influence of these factors. Since the magnitude of the stray fields is generally very small, this affection may be removed by applying a good shielding but it is not ease to remove the affection from a geometrical factor. This affection must be however calculated by the theoretical methods and analytical solution in the equation of these factors. The fundamental purpose of this paper lie in the theoretical calculations and practical measurements of the geometrical factor in the coil systems, finite solenoid, and four point prove. In the heoretical calculations, the geometrical factors in the coil systems were calculated by applying the elliptic functions and in the contact points were calculated by applying the elliptic functions and in the contact points were calculated by applying the eigen functions and the infinite series. The measurements were carried out by using the sensitive electronic device made from author's design, as shown in the Fig. 9. The result of this work has verified the essential correctness of theoretical investigations and measuring techniques of geometrical factors on the design of sensitive electronic devices. It also has several advantages such that: (1) all the data obtained may give effective data to designer to work on the field of sensitive electronic devices or microelectronic devices, (2) it has evidently explained the characteristics of electrical investigations and physical definition, and has removed the conventional error of geometrical factors in the coil systems and contact points.

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A Study on Startups' Dependence on Business Incubation Centers (창업보육서비스에 따른 입주기업의 창업보육센터 의존도에 관한 연구)

  • Park, JaeSung;Lee, Chul;Kim, JaeJon
    • Korean small business review
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    • v.31 no.2
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    • pp.103-120
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    • 2009
  • As business incubation centers (BICs) have been operating for more than 10 years in Korea, many early stage startups tend to use the services provided by the incubating centers. BICs in Korea have accumulated the knowledge and experience in the past ten years and their services have been considerably improved. The business incubating service has three facets : (1) business infrastructure service, (2) direct service, and (3) indirect service. The mission of BICs is to provide the early stage entrepreneurs with the incubating service in a limited period time to help them grow strong enough to survive the fierce competition after graduating from the incubation. However, the incubating services sometimes fail to foster the independence of new startup companies, and raise the dependence of many companies on BICs. Thus, the dependence on BICs is a very important factor to understand the survival of the incubated startup companies after graduation from BICs. The purpose of this study is to identify the main factors that influence the firm's dependence on BICs and to characterize the relationships among the identified factors. The business incubating service is a core construct of this study. It includes various activities and resources, such as offering the physical facilities, legal service, and connecting them with outside organizations. These services are extensive and take various forms. They are provided by BICs directly or indirectly. Past studies have identified various incubating services and classify them in different ways. Based on the past studies, we classify the business incubating service into three categories as mentioned above : (1) business infrastructure support, (2) direct support, and (3) networking support. The business infrastructure support is to provide the essential resources to start the business, such as physical facilities. The direct support is to offer the business resources available in the BICs, such as human, technical, and administrational resources. Finally, the indirect service was to support the resource in the outside of business incubation center. Dependence is generally defined as the degree to which a client firm needs the resources provided by the service provider in order to achieve its goals. Dependence is generated when a firm recognizes the benefits of interacting with its counterpart. Hence, the more positive outcomes a firm derives from its relationship with the partner, the more dependent on the partner the firm must inevitably become. In business incubating, as a resident firm is incubated in longer period, we can predict that her dependence on BICs would be stronger. In order to foster the independence of the incubated firms, BICs have to be able to manipulate the provision of their services to control the firms' dependence on BICs. Based on the above discussion, the research model for relationships between dependence and its affecting factors was developed. We surveyed the companies residing in BICs to test our research model. The instrument of our study was modified, in part, on the basis of previous relevant studies. For the purposes of testing reliability and validity, preliminary testing was conducted with firms that were residing in BICs and incubated by the BICs in the region of Gwangju and Jeonnam. The questionnaire was modified in accordance with the pre-test feedback. We mailed to all of the firms that had been incubated by the BICs with the help of business incubating managers of each BIC. The survey was conducted over a three week period. Gifts (of approximately ₩10,000 value) were offered to all actively participating respondents. The incubating period was reported by the business incubating managers, and it was transformed using natural logarithms. A total of 180 firms participated in the survey. However, we excluded 4 cases due to a lack of consistency using reversed items in the answers of the companies, and 176 cases were used for the analysis. We acknowledge that 176 samples may not be sufficient to conduct regression analyses with 5 research variables in our study. Each variable was measured through multiple items. We conducted an exploratory factor analysis to assess their unidimensionality. In an effort to test the construct validity of the instruments, a principal component factor analysis was conducted with Varimax rotation. The items correspond well to each singular factor, demonstrating a high degree of convergent validity. As the factor loadings for a variable (or factor) are higher than the factor loadings for the other variables, the instrument's discriminant validity is shown to be clear. Each factor was extracted as expected, which explained 70.97, 66.321, and 52.97 percent, respectively, of the total variance each with eigen values greater than 1.000. The internal consistency reliability of the variables was evaluated by computing Cronbach's alphas. The Cronbach's alpha values of the variables, which ranged from 0.717 to 0.950, were all securely over 0.700, which is satisfactory. The reliability and validity of the research variables are all, therefore, considered acceptable. The effects of dependence were assessed using a regression analysis. The Pearson correlations were calculated for the variables, measured by interval or ratio scales. Potential multicollinearity among the antecedents was evaluated prior to the multiple regression analysis, as some of the variables were significantly correlated with others (e.g., direct service and indirect service). Although several variables show the evidence of significant correlations, their tolerance values range between 0.334 and 0.613, thereby demonstrating that multicollinearity is not a likely threat to the parameter estimates. Checking some basic assumptions for the regression analyses, we decided to conduct multiple regression analyses and moderated regression analyses to test the given hypotheses. The results of the regression analyses indicate that the regression model is significant at p < 0.001 (F = 44.260), and that the predictors of the research model explain 42.6 percent of the total variance. Hypotheses 1, 2, and 3 address the relationships between the dependence of the incubated firms and the business incubating services. Business infrastructure service, direct service, and indirect service are all significantly related with dependence (β = 0.300, p < 0.001; β = 0.230, p < 0.001; β = 0.226, p < 0.001), thus supporting Hypotheses 1, 2, and 3. When the incubating period is the moderator and dependence is the dependent variable, the addition of the interaction terms with the antecedents to the regression equation yielded a significant increase in R2 (F change = 2.789, p < 0.05). In particular, direct service and indirect service exert different effects on dependence. Hence, the results support Hypotheses 5 and 6. This study provides several strategies and specific calls to action for BICs, based on our empirical findings. Business infrastructure service has more effect on the firm's dependence than the other two services. The introduction of an additional high charge rate for a graduated but allowed to stay in the BIC is a basic and legitimate condition for the BIC to control the firm's dependence. We detected the differential effects of direct and indirect services on the firm's dependence. The firms with long incubating period are more sensitive to indirect service positively, and more sensitive to direct service negatively, when assessing their levels of dependence. This implies that BICs must develop a strategy on the basis of a firm's incubating period. Last but not least, it would be valuable to discover other important variables that influence the firm's dependence in the future studies. Moreover, future studies to explain the independence of startup companies in BICs would also be valuable.