• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.81-87
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• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• International Journal of Computer Science & Network Security
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• v.21 no.12
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• pp.157-164
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• 2021

The aim of this study is to provide empirical evaluation of the accuracy of data-model fit using growing levels of invariance models. Overall model accuracy of factor solutions was evaluated by the examination of the order for testing three levels of measurement invariance (MIV) starting with configural invariance (model 0). Model testing was evaluated by the Chi-square difference test (∆𝛘²) between two groups, and root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker-Lewis index (TLI) were used to evaluate the all-model fits. Factorial invariance result revealed that stability of the models was varying over increasing levels of measurement as a function of variable-to-factor ratio (VTF), subject-to-variable ratio (STV), and their interactions. There were invariant factor loadings and invariant intercepts among the groups indicating that measurement invariance was achieved. For VTF ratio (3:1, 6:1, and 9:1), the models started to show accuracy over levels of measurement when STV ratio was 6:1. Yet, the frequency of stability models over 1000 replications increased (from 69% to 89%) as STV ratio increased. The models showed more accuracy at or above 39:1 STV.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1-4
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• 2004

The dual-mode strategy has been adopted in many constrained MPC methods. The size of stabilizable regions of states of MPC methods depends on the size of underlying feasible and positively invariant set and number of control moves. These results, however, could be conservative because the definition of positive invariance does not allow temporal leave of states from the set, In this paper, a concept of periodic invariance is introduced in which states are allowed to leave a set temporarily but return into the set in finite steps. The periodic invariance can defined with respect to sets of different state feedback gains. These facts make it possible for the periodically invariant sets to considerably larger than ordinary invariant sets. The periodic invariance can be defined for systems with polyhedral model uncertainties. We derive a MPC method based on these periodically invariant sets. Some numerical examples are given to show that the use of periodic invariance yields considerably larger stabilizable sets than the case of using ordinary invariance.

• International Journal of Control, Automation, and Systems
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• v.3 no.3
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• pp.502-507
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• 2005

The dual-mode strategy has been adopted in many constrained MPC (Model Predictive Control) methods. The size of stabilizable regions of states of MPC methods depends on the size of underlying feasible and positively invariant sets and the number of control moves. The results, however, may perhaps be conservative because the definition of positive invariance does not allow temporal departure of states from the set. In this paper, a concept of periodic invariance is introduced in which states are allowed to leave a set temporarily but return into the set in finite time steps. The periodic invariance can be defined with respect to sets of different state feedback gains. These facts make it possible for the periodically invariant sets to be considerably larger than ordinary invariant sets. The periodic invariance can be defined for systems with polyhedral model uncertainties. We derive a MPC method based on these periodically invariant sets. Some numerical examples are given to show that the use of periodic invariance yields considerably larger stabilizable sets than the case of using ordinary invariance.

• Women's Health Nursing
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• v.26 no.4
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• pp.326-335
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• 2020

Purpose: This study was conducted to evaluate the construct validity, reliability, measurement invariance, and latent mean differences in the Breastfeeding Adaptation Scale-Short Form (BFAS-SF) for use with mothers at 2 weeks postpartum. Methods: This methodological study was designed to evaluate the validity, reliability, and measurement invariance of the BFAS-SF at 2 weeks postpartum, with data collected from 431 breastfeeding mothers. Confirmatory factor analysis and multi-group confirmatory factor analysis were conducted to assess the factor structure and the measurement invariance across employment status, delivery mode, parity, and previous breastfeeding experience, and the latent mean differences were then examined. Results: The goodness of fit of the six-factor model at 2 weeks postpartum was acceptable. Multi-group confirmatory factor analysis supported strict invariance of the BFAS-SF across employment status and delivery mode. Full configural invariance, full metric invariance, and partial scalar invariance across parity and full configural invariance and full metric invariance across previous breastfeeding experience were supported, respectively. The results for latent mean differences suggested that mothers who were employed showed significantly higher scores for breastfeeding confidence. Mothers who had a vaginal delivery showed significantly higher scores for sufficient breast milk and baby's feeding capability. Multiparous mothers showed significantly higher scores for baby's feeding capability and baby's satisfaction with breastfeeding. Conclusion: The validity and reliability of the BFAS-SF at 2 weeks postpartum are acceptable. It can be used to compare mean scores of breastfeeding adaptation according to employment status, delivery mode, and parity.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.353-359
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• 1993

In this note we consider other type of tightness than that of Birkel (1988) and prove an invariance principle for nonstationary associated processes by an application of the central limit theorem of Cox and Grimmett (1984), thus avoiding the argument of uniform integrability. This result is an extension to the nonstationary case of an invariance priciple of Newman and Wright (1981) as well as an improvement of the central limit theorem of Cox and Grimmett (1984).

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.121-129
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• 2010

Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably k-contractive multivalued vector fields.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.281-292
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• 1995

In this paper the concept of strong mixing is extended to random fields, and an invariance principle is obtained for stationary strong mixing random fields.

• Journal of Ocean Engineering and Technology
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• v.15 no.4
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• pp.101-107
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• 2001

This paper describes a fault diagnosis method by a T-invariance of Petri Net (PN). First, a complicated fault system with some failure is modeled into a PN graphic expressions. Next, the PN model is analyzed by using the backward chaining of T-invariance to find out causes of the faults. In this step, an inter-node search technique which is suggested in this paper is applied for reducing searching area in the fault system. Also, a novel idea to compose incidence matrices which have different dimension each other in PN model is proposed. As the new knowledges which is discovered newly about faults can be added easily to conventional systems, the diagnosis system will be very flexible. Finally, the proposed method is applied to the automobile fault diagnosis system to confirm the validity of the method.

• International journal of advanced smart convergence
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• v.9 no.3
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• pp.85-96
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• 2020

It is important to extract salient object image and to solve the invariance problem for image recognition. In this paper we propose a new hybrid algorithm for invariance and improved classification performance in image recognition, whose algorithm is combined by FT(Frequency-tuned Salient Region Detection) algorithm, Guided filter, Zernike moments, and a simple artificial neural network (Multi-layer Perceptron). The conventional FT algorithm is used to extract initial salient object image, the guided filtering to preserve edge details, Zernike moments to solve invariance problem, and a classification to recognize the extracted image. For guided filtering, guided filter is used, and Multi-layer Perceptron which is a simple artificial neural networks is introduced for classification. Experimental results show that this algorithm can achieve a superior performance in the process of extracting salient object image and invariant moment feature. And the results show that the algorithm can also classifies the extracted object image with improved recognition rate.