• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.39 no.5
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• pp.203-206
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• 2013

Statistics is the science of data. As the foundation of scientific knowledge, data refers to evidentiary facts from the nature of reality by human action, observation, or experiment. Clinicians should be aware of the conditions of good data to support the validity of clinical modalities in reading scientific articles, one of the resources to revise or update their clinical knowledge and skills. The cause-effect link between clinical modality and outcome is ascertained as pattern statistic. The uniformity of nature guarantees the recurrence of data as the basic scientific evidence. Variation statistics are examined for patterns of recurrence. This provides information on the probability of recurrence of the cause-effect phenomenon. Multiple causal factors of natural phenomenon need a counterproof of absence in terms of the control group. A pattern of relation between a causal factor and an effect becomes recognizable, and thus, should be estimated as relation statistic. The type and meaning of each relation statistic should be well-understood. A study regarding a sample from the population of wide variations require clinicians to be aware of error statistics due to random chance. Incomplete human sense, coarse measurement instrument, and preconceived idea as a hypothesis that tends to bias the research, which gives rise to the necessity of keen critical independent mind with regard to the reported data.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1909-1920
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• 2018

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.303-317
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• 2013

In present paper, we obtain functions $R_t(c,{\nu},a,b)$ and $R_t(c,-{\mu},a,b)$ by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function $_2R_1(a,b;c;{\tau};z)$ and some special cases have also been discussed.

• Maxillofacial Plastic and Reconstructive Surgery
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• v.22 no.2
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• pp.217-232
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• 2000

The author studied on the 128 cases of benign odontogenic tumors which had been diagnosed with biopsy during the period of Jan. 1989 to Dec. 1998 at the Kyungpook National University Hospital, Yeungnam University Medical Center, Keimyung University Dongsan Medical Center, and Taegu Catholic Medical Center. This study contained the clinicostatistical analysis of the frequency in relation to sex, age, locations, chief complaints, duration, radiographic findings, recurrence, teeth, and treatment methods. The results were as follow : 1. Of a total of 128 benign odontogenic tumors, ameloblastomas(57 cases; 44.5%) and odontomas (44 cases ; 34.4%) mostly occupied. The other types of lesions were 8 calcifying odontogenic cysts, 7 benign cementoblastomas, 4 myxomas, 3 adenomatoid odontogenic tumors, 2 calcifying epithelial odontogenic tumors, 2 ameloblastic fibro-odontomas, and 1 odontogenic fibroma. 2. In age and sex distribution, benign odontogenic tumors occured slightly more often in males(53.9%) than females(46.1%) and the majority of cases(79.7%) were found during 2nd, 3rd, and 4th decade. 3. There was a predilection for mandibular lesions(mandible-maxilla ratio, 2.6 : 1). 4. The most common chief complaint was swelling(29.7%) and in respect to duration, the cases less than 1 year(50.0%) mainly appeared. 5. There were 7 cases(13.0%) of recurrence on ameloblastoma and there was no recurrence in the others. 6. In Ameloblastoma It commonly occured during 3rd and 4th decade(59.6%) and mean age was 30.2 years. The majority of cases were occurred in mandible(96.5%) , especially mandibular molar and angle area(71.9%). The most common chief complaint was swelling(47.4%) and in respect to duration, the cases less than 1 year(52.6%) mainly appeared. In relation to teeth, there were resorption of root(52.6%), displacement of teeth(31.6%), and in relation to impacted teeth(43.9%). There was higher recurrence rate in the cases by conservative treatment(14.7%) than radical treatment(10.0%). As regards radiographic findings, conservative treatments were prevalent in the cases of unilocular type(85.7%) as compared with multilocular type(48.5%). and there was higherrecurrence rate in the cases of multilocular type(18.2%) than unilocular type(4.8%). As regards the type of treatment in relation to age, conservative treatments were prevalent in patients younger than 20 years of age. 7. In Odontomas It commonly occured during 2nd decade(50.0%) and in maxillary anterior teeth(40.9%). The most common chief complaint was delayed retention and permanent impaction of teeth(72.7%), and most frequently associated with impacted teeth(79.5%).

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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• pp.97-108
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• 2008

In this paper Bayes estimator of the parameter and reliability function of the zero-truncated Poisson distribution are obtained. Furthermore, recurrence relations for the estimator of the parameter are also derived. Monte Carlo simulation technique has been made for comparing the Bayes estimator and reliability function with the corresponding maximum likelihood estimator (MLE) of zero-truncated Poisson distribution.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.325-337
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• 2014

In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorial reformulation for Morris' rule.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1033-1048
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• 2020

We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in Python.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.319-330
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• 2016

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unied eld tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of 5-dimensional $^*g-ESX_5$. Particularly, in 5-dimensional $^*g-ESX_5$, we derive a new set of powerful recurrence relations in the first class.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.277-283
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• 2019

In this paper, we present a cube root algorithm using a recurrence relation. Additionally, we compare the implementations of the Pocklington and $Padr{\acute{o}}-S{\acute{a}}ez$ algorithm with the Adleman-Manders-Miller algorithm. With the recurrence relations, we improve the Pocklington and $Padr{\acute{o}}-S{\acute{a}}ez$ algorithm by using a smaller base for exponentiation. Our method can reduce the average number of ${\mathbb{F}}_q$ multiplications.