• East Asian mathematical journal
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• v.16 no.2
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• pp.199-203
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• 2000

We give nine necessary and sufficient conditions for a metric space to be complete.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.93-110
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• 2000

An alternative interpretation of the completeness requirements for the higher order elements is presented. Apart from the familiar condition, $\sum_iN_i=1$, some additional conditions to be satisfied by the shape functions of higher order elements are identified. Elements with their geometry in the natural form, i.e., without any geometrical distortion, satisfy most of these additional conditions inherently. However, the geometrically distorted elements satisfy only fewer conditions. The practical implications of the satisfaction or non-satisfaction of these additional conditions are investigated with respect to a 3-node bar element, and 8- and 9-node quadrilateral elements. The results suggest that non-satisfaction of these additional conditions results in poorer performance of the element when the element is geometrically distorted. Based on the new interpretation of completeness requirements, a 3-node element and an 8-node rectangular element that are insensitive to mid-node distortion under a quadratic displacement field have been developed.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.19-26
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• 1997

In this paper, we characterize the existence of fixed points of a multivalued function by the existence of complete preorder on the given domain. Also we investigate relations between the completeness of a given order and the fixed point property of some multivalued functions.

• Journal of The Korean Association For Science Education
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• v.14 no.3
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• pp.321-329
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• 1994

The purpose of this study was to investigate the completeness of educational objectives according to grades, objective domains and content areas, and to inquire the completeness of educational objectives by instructional quality profile and to restate educational objectives on the elementary school science curriculum. The taxonomy as a classification tool was developed in order to classify the science educational objectives. Teacher's guide-books of elementary school science were used to analyze the completeness. The educational objectives were checked using the objective classification tool by 11 experienced specialists in science education. The following are the results of this study. 1. Completeness of unit was shown approximately the 62 percentage in chapters, the 72 percentage in sections and the 87 percentage in periods. 2. Only the related chemistry parts showed that each objective domains were stated evenly. 3. On the whole, the number of understanding(38%) of stated educational objectives was much more than the other domains, such as manual skill(7%), attitudes.interests.appreciations(4%). 4. The elementary school science objectives were restated using the instructional quality profile in order to increase the completeness.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1521-1536
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• 2017

This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LJT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.

• Journal of Korea Game Society
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• v.18 no.2
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• pp.121-130
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• 2018

Most of those studies use frequency, the number of times a pattern appears in a transaction database, as the key measure for pattern interestingness. It prerequisites that any interesting pattern should occupy a maximum portion of the transactions it appears. But in our real world scenarios the completeness of any pattern is more likely to become various in transactions. Hence, we should also consider the problem of finding the qualified patterns with the significant values of the weighted support by completeness in order to reduce the loss of information within any pattern in transaction. In these pattern recommendation applications, patterns with higher completeness may lead to higher recall while patterns with higher completeness may lead to higher recall while patterns with higher frequency lead to higher precision. In this paper, we propose a measure of weighted support and completeness and an algorithm WSCFPM(weigted support and completeness frequent pattern mining). Our algorithm handles the invalidation of the monotone or anti-monotone property which does not hold on completeness. Extensive performance analysis show that our algorithm is very efficient and scalable for word pattern mining.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.239-249
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• 1995

Let $V = (v_1, v_2, \cdots)$ be a sequence of positive integers arranged in nondecreasing order. We define V to be complete if every positive integer n is the sum of some subsequence of V, that is, $$ (1.1) n = \sum_{i=1}^{\infty} a_i v_i where a_i = 0 or 1.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.767-788
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• 2004

The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.

• Journal of Preventive Medicine and Public Health
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• v.39 no.3
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• pp.255-262
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• 2006

Objectives: This study is conducted to identify the cancer incidence in Gwangju during the 5-year period from 1998 to 2002 and to assess the completeness and validity of the cancer registry data during this time period. Methods: All cases that had a diagnosis of invasive cancer (ICD-10 sites C00-C97) during the study period were retrieved from the records of the Gwangju Cancer Registry (GCR), which theoretically includes all the cancer cases in Gwangju. All the cases during the study period were analyzed by gender, age group and cancer sites. The completeness (mortality/incidence ratio and age-specific incidence curve) and validity (histologic verification, primary site unknown, age unknown and death certificate only) of the cancer registry in Gwangju were analyzed by gender, age group and cancer sites for the 5-year period. Results: The overall cancer incidence was higher in the males than in the females (age-standardized incidence rates (ASR) 299.8 and 172.4 per 100,000, respectively). In males, the most common cancer was stomach (ASR: 65.8), followed by liver (ASR: 50.5), bronchus and lung (ASR: 50.5), colo-rectum (ASR: 26.7), oesophagus (ASR: 10.6), and bladder (ASR: 10.3) in descending order. In females, the most common cancer was stomach (ASR: 26.8), followed by thyroid (ASR: 20.7), breast (ASR: 20.4), cervix uteri (ASR: 14.3), bronchus and lung (ASR: 13.0), liver (ASR: 10.7) and colo-rectum (ASR: 17.2) in descending order. The overall quality (completeness and validity) of the cancer registry was at the in 'good' level. Conclusions: These results will be useful in the overall context of planning and evaluating of cancer control activities in Gwangju.

• Journal of KIISE:Software and Applications
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• v.35 no.12
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• pp.731-740
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• 2008

A railway control system is one of the typical safety-critical systems. It is required to use formal methods for the requirements specification and verification in order to develop the global-standard railway control systems based on the computer systems. In this paper, we develop a guideline for requirements specification using formal methods, and present a case study of the development of a computer-based railway control system through the application of the proposed guideline. We use the Statechart and the Z method for the formal requirements specifications and verify the consistency and completeness of the formal specifications of the requirements.