• Maxillofacial Plastic and Reconstructive Surgery
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• v.32 no.6
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• pp.551-557
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• 2010

Purpose: In this study, we evaluated the relation between surgical methods and reccurrence rate by investigating clinical, radiological aspects and histopathological patterns of 26 patients who were diagnosed with amelobalstoma. Patients and Methods: In this study, we retrospectively investigated 26 patients who were diagnosed with ameloblastoma and treated at the Department of Oral and Maxillofacial Surgery of Chosun University Dental Hospital from January 2000 to December 2008. Results: The patients comprised 12 males (46.1%) and 14 females (53.9%), and their ages ranged from 10 to 69 years (average, 37.3 years). All cases presented a mandibular location, and in particular, 13 cases (50%) demonstrated an occurrence in the mandibular body. Clinically, 8 cases (30.8%) presented no symptoms, and the most prevalent chief complaint was swelling in 13 cases (50%). Radiographically, a unilocular type appeared in 14 cases (53.8%), and a multilocular type was observed in 10 cases (38.5%). Histopathologically, there were 8 follicular types (30.8%) and 7 plexiform types (26.9%). Conservative treatment was performed in 5 cases (19.2%), and radical treatment was performed in 21 cases (80.8%). The follow-up period ranged from 1 to 10 years. The total recurrence rate was 15.4%, and the mean duration of recurrence was 6.7 years. Three of the 5 cases (60%) that received conservative treatment demonstrated a recurrence, as compared to 1 of the 21 cases (4.8%) that underwent radical treatment. Conclusion: The radical treatment was more effective than the conservative treatment for recurrence prevention. We should consider a continuous follow-up check after operation.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.207-216
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• 2014

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field 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 3-dimensional $^*g-ESX_3$. Particularly, in 3-dimensional $^*g-ESX_3$, we derive a new set of powerful recurrence relations in the first class.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.593-605
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• 2015

In this study, we define r-circulant, circulant, Hankel and Toeplitz matrices involving the integer sequence with recurrence relation U_n = pU_n-1 + U_n-2, with U₀ = a, U₁ = b. Moreover, we obtain special norms of above mentioned matrices. The results presented in this paper are generalizations of some of the results of [1, 10, 11].

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.153-160
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• 2008

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.765-774
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• 2005

The orthogonality of polynomials plays an important role in many areas and in many cases only finite orthogonalities are used. Concerning this fact we find characterizations of a finite orthogonal polynomial system satisfying a second order differential equation and then give several examples.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.623-635
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• 2006

In this paper, we derive an elementary formula for the linearization coefficients of the product of two Legendre polynomials. Our main purpose is to study the method which can be used to derive the formula, which is straightforward from the integration and their orthogonality.

• Computational Structural Engineering
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• v.6 no.1
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• pp.99-105
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• 1993

A Stepped beam with immovable ends under forced vibrations with large amplitude is investigated by using the finite element method and the Ritz vectors. Unlike the Eigen vectors, the Ritz vectors are generated by a simple recurrence relation. Moreover the Ritz vectors yield much faster convergence with respect to the number of vectors used than the use of Eigen vectors. The computer program is developed for nonlinear analysis using Ritz vectors instead of Eigen vectors and numerical examples are analysed for deflections and natural frequencies of stepped beam under various support conditions. Results show that the proposed method is valid and efficient.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.133-139
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• 2010

The manifold $g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $g_{{\lambda}{\mu}}$ through the ES-connection which is both Einstein and semi-symmetric. In this paper, we investigate the properties of the vectors $X_{\lambda}$, $S_{\lambda}$ and $U_{\lambda}$ of $g-ESX_n$, with main emphasis on the derivation of several useful generalized identities involving it.

• East Asian mathematical journal
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• v.28 no.4
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• pp.419-433
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• 2012

In this paper, by using the inductive method, recurrence relation, the unit circle, circle to inscribe a right-angled triangle, formula of multiple angles, solution of quadratic equation and Fibonacci numbers, we study various problem solving methods to find pythagorean triple.