• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.733-747
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• 2021

Recently, Kim-Kim introduced Lah-Bell polynomials and numbers, and investigated some properties and identities of these polynomials and numbers. Kim studied Lah-Bell polynomials and numbers of degenerate version. In this paper, we study degenerate Lah-Bell polynomials arising from differential equations. Moreover, we investigate the phenomenon of scattering of the zeros of these polynomials.

• Journal of Korea Multimedia Society
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• v.18 no.8
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• pp.968-979
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• 2015

In this paper, we study a vibration bell App which shows waiting sequence numbers by utilizing smartphones to solve an inconveniently long waiting time from ordering to getting foods in restaurants and coffee shops. Unlike existing independently developed hardware and software, the vibration bell App is developed to manage and integrate customer management service, POS service in shops, and group shop management services. The functions of the vibration bell App include two-way communications based on NFC- issuing waiting sequence numbers and electronic coupon, showing event information, and transferring user information. Furthermore, the user's personal information is minimized by recognizing the pre-existing information of the user's smartphone. Replacing the shop's vibration bell system with the vibration bell APP, the shops can reduce the cost of construction and maintenance by up to 1/10, compared to the cost of for existing vibration bell systems. Moreover, the customer's preference and current sales trend can be easily figured out. Thus, it will have a great effect on the future marketing strategies.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.599-613
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• 2018

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums. We also derive new identities for Bell polynomials.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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• pp.804-806
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• 2007

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

• 한국데이터정보과학회:학술대회논문집
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• 2006.11a
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• pp.81-95
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• 2006

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.21-41
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• 2020

In this paper, we establish an explicit formula for r-Dowling numbers in terms of r-Whitney Lah and r-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the q, r-Dowling numbers, q, r-Whitney Lah numbers and q, r-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for q, r-Dowling numbers expressed in terms of q, r-Whitney Lah numbers and q, r-Whitney numbers of the second kind.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.143-155
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• 2008

Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial $x^p-x-l$ over $\mathbb{F}_p$ divides $g(p)=\frac{p^p-1}{p-1}$. Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).

• The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
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• v.23 no.2
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• pp.151-162
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• 2010

Objective : Bell's palsy is common and has many clinic study. but bell's palsy prognosis is not enough specific. So this study was evaluated bell's palsy prognosis, treatment number, sequela of normal group and bad prognosis group. Methods : From June 2009 to June 2010, patients who visited Dong-seo Oriental Medicine ENT. A clinic study was done on patient who were diagnosed bell's palsy, onset 2weeks within when first visited OPD and treated 3 times over in Dong-seo Oriental Medicine Cental. To evaluate grade of paralysis, House-Brackman Scale was used. We classified treatment numbers of each HB-Scale group, normal gIVroup and bad prognosis group. Results : The distribution of Onset HB-Scale : Gr II 26.25%, Gr III 67.5%, Gr IV 6.25% Onset HB-Scale Gr II patients completely recover 100% Onset HB-Scale Gr III patients completely recover 64.8%, improved 27.8%, nothing change 7.4% Onset HB-Scale Gr IV patients completely recover 40%, improved 60% Onset HB-Scale Gr II & IV patients recovery percentage make no difference of normal group (Group A) and bad prognosis. Onset HB-Scale Gr III patients completely recover Group A 66.7%, Group B 52.9%, improved Group A 23.2%, Group 35.3%, noting change Group A 5.1%, Group B 11.8% Onset HB-Scale Gr II patients has no sequela. Onset HB-Scale Gr III & IV patients has tendency that they treat more times, more improving and less sequela probability Conclusion : Onset HB-Scale is the indicator of acute bell's palsy prognosis.

• Journal of Acupuncture Research
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• v.21 no.5
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• pp.191-203
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• 2004

Objectives : The purpose of this study is comparison of clinical treatment outcome between oriental medicine group and oriental-western medicine group about Bell's palsy. Methods : We measured the facial palsy changes of the patients who were admitted for Bell's palsy in the Oriental Medical hospital of Dong-eui medical center from 07-01-2003 to 07-12-2004. Bell's palsy patients were divided into two groups. One group(A group) was treated by Oriental medicine treatment. The other group(B group) was treated by Oriental-Western medicine treatment. The effects of these treatment was evaluated by Yanagihara's unweighted grading system. Results : B group was marked more higher than A group in treatment outcome. We discovered that it is significant differences between two groups after 1 week and after 2 week in treatment stage. Conclusion : These results provided that B group was more effective than A group in treatment of Bell's palsy. For clearly comparing the effect of Oriental medicine treatment and Oriental-Western medicine treatment on Bell's palsy, more numbers of sample and longer duration of treatment are needed.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.65-76
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• 2023

With the Stirling matrix S of the second kind and the Pascal matrix T, we study recurrence rules and sequences of certain sums over the matrix ST^k. We find a matrix E satisfying ST = ES and interrelations of S and the Stirling matrix of the first kind.