• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.967-974
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• 1996

We discuss contraction operators T in the class A, where A is the class of absolutely continuus contractions for which the Sz.-Nagy-Foias functional calculus is isometry. We obtain relationship between the class $A_{n, \aleph_0}$ and hereditary property $(\tilde{P}_n)$.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.1-10
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• 2015

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.77-79
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• 2007

In this note we point out how a theorem of Gamelin and Garnett from function theory can be used to establish a spectral mapping theorem for an arbitrary contraction and an associated class of $H^{\infty}$-functions.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.425-447
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• 2020

The family of q-Konhauser matrix polynomials have been extended to Konhauser matrix polynomials. The purpose of the present work is to show that an extension of the explicit forms, generating matrix functions, matrix recurrence relations and Rodrigues-type formula for these matrix polynomials are given, our desired results have been established and their applications are presented.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.407-420
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• 2023

In this manuscript, we study the sufficient conditions for controllability of Volterra-Fredholm type fractional integro-differential systems in a Banach space. Fractional calculus and the fixed point theorem are used to derive the findings. Some examples are provided to illustrate the obtained results.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• Journal of Korean Dental Hygiene Science
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• v.3 no.1
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• pp.1-13
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• 2020

The purpose of this study was to investigate the perception of calculus removal, an essential factor in periodontal disease in the elderly population. Further, the study aimed to identify the oral hygiene management matters of individuals and to use the information as primary data for preventing dental loss and improving the prevention of chronic diseases. From December 20, 2019, to January 15, 2020, the results of 171 studies on oral hygiene management and awareness of calculus removal among the elderly aged 65 or older in Busan and Gyeongnam are as follows: The elderly with good health appreciated their functional oral health status and showed significant differences (Χ²=298.26, p<.001). Many of the elderly brushing their teeth at least three times a day had a better health status and showed significant differences according to their health status (= 134.42, p <.001). Usually, older people who are in good health have a dental floss (Χ²=89.31, p<.001), and the dental floss were used more often and significantly differed depending o health status (Χ²=92.53, p<.001). The elderly's perception of tartar removal has shown that the overall average out of five points is positive at 3.48. Older female adults were more positive and showed significant differences regarding gender (t=-7.95, p<.001). Senior citizens aged 65 to 70 were more positive about dental removal than those aged 71 or older, with significant differences in age (t=6.65, p<.001). As described above, oral hygiene management for the elderly population needs to develop a periodontal disease prevention program linked to systemic diseases, considering that there are many chronic diseases.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.417-444
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• 2008

Many research papers on the college students' functional concept show they have poor understanding on this topic. To compare the results with that of Korean students, four interrelated topics are chosen: How do they understand the concept of function?; what are their misconceptions including epistemological obstacles?; How do the function concepts develop and are acquired? For this a survey has been conducted to 95 engineering students just before they start Calculus course. We have done research on other major areas including psychology, economics and statistics to see how function is defined in these areas. Function definitions from US math text books are also introduced. Based on the these and the survey, some suggestions are made on the new curriculum which treat function as a correspondence relation. Vertical line test should be added to the Algebra II/Pre calculus course to check the univalent property.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.137-155
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• 2021

In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Finally, we give some applications of our results in discrete and functional fractional economic systems.

• Journal of the Korea Society of Computer and Information
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• v.3 no.1
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• pp.25-34
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• 1998

There are two major method for expressing parallelim in functional languages. The one is the strictness analysis and the other the annotation. The strictness analysis is a method that a compiler detects parallelism and expresses the detected information in the object program. The annotation is a method that a programmer detects parallelism and expresses in the source program. This study is on the annotation and is aimed at construction of a translator for a functional language which has an annotation syntax. The translator translates a source program to enriched lambda-calculus graphs. The translator is implemented in C using compiler development tools such as YACC and Lex, under UNIX environments. In this paper we present the design and implementation techniques for developing the front-end of the translator.