• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.3
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• pp.437-447
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• 2003

We propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used fur spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR Inter and for the case of the IIR filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.133-143
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• 2014

A new three-step quadraparametric family of eighth-order iterative methods free from second derivatives are proposed in this paper to find a simple root of a nonlinear equation. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.1
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• pp.35-44
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• 2004

We Propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used for spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR filter and for the case of the In filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

• Proceedings of the KIEE Conference
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• 1994.11a
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• pp.78-80
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• 1994

Conventional methods for root finding of the algebraic equations are intrinsically synthetic division methods, i.e., which are the factorization in forms of $f(x)=(x-x_i)Q(x)$. So existing methods have some demerits such as deflation and root-polishing procedures. To overcome these defects a new powerful algorithm, namely circular arithmetic algorithm(CSM), was introduced and has been investigated about its fascinating properties. In this paper, we will propose a simple and effective method of getting the initial guesses for the roots of the equation. With this method the CSM can me all the root of equation with great efficiency.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.2
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• pp.277-284
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• 2018

In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering.

• Journal of Periodontal and Implant Science
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• v.39 no.3
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• pp.375-381
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• 2009

Purpose: Root resection can be a valuable procedure when the tooth in question has a high strategic value. The prognosis of root resection has been well documented in previous studies, but the results focused on the palatal root resection have not been discussed in depth. I represent here the short term effectiveness of palatal root resection of maxillary first molars. Methods: Palatal root resection was performed on maxillary first molars of three patients. All the palatal roots were floating state on the radiographic finding and showed full probing depth and purulent exudation at initial examination. Reduction of palatal cusp and occlusal table was performed concomitantly. Endodontic therapy was completed after root resection. Results: Compromised maxillary first molars were treated successfully by palatal root resection in 3 cases. The mobility of resected tooth was decreased a little bit. The probing pocket depth of remaining buccal roots was not increased compared to initial depth. All the patients satisfied with comfort and cost effective results and the fact they could save their natural teeth. Conclusions: Within the above results, palatal root resection is an effective procedure treating compromised maxillary first molar showing advanced palatal bone loss to root apex with or without pulp involvement when proper case selection is performed.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1067-1082
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• 2022

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.669-676
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• 2012

In this note we extend one well-known iteration formula to derive new third-order methods for solving a nonlinear equation. The comparison with other methods is given.

• Imaging Science in Dentistry
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• v.52 no.2
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• pp.165-170
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• 2022

Purpose: This report presents a case of an unusual and rare presentation of Stafne bone defect (SBD) with apical resorption extending from the lower right lateral incisor to the right first premolar. A systematic search of the current literature on cases where SBD affected the adjacent teeth was conducted. Materials and Methods: From 259 identified articles, 114 studies were examined, containing 12 individuals with a mean age of 41.58 years. Ten cases in the anterior mandible and 2 in the posterior mandible were found. Results: The results of SBD varied from apical blunting to severe root resorption, and some cases showed close apical contact with the lesion or involvement of the root without any effect. Conclusion: SBD is an unusual incidental finding in the anterior region of the mandible, and unexpected behavior of the lesion, such as root resorption, must be considered.

• Journal of Korean Neurosurgical Society
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• v.46 no.1
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• pp.11-15
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• 2009

Objective: Two findings easily found at coronal source images of MR myelography (MRM) were evaluated : dorsal root ganglion (DRG) swelling and running course abnormality (RCA) of L5 exiting root at foramen or extraforamen. We tried to find the sensitivity of each finding when root was compressed. Methods: From 2004 July to 2006, one hundred and ten patients underwent one side paraspinal decompression for their L5 root foraminal or extraforaminal compression at L5-S1 level. All kinds of conservative treatments failed to improve leg symptom for several months. Before surgery, MRI, CT and MRM were done. Retrospective radiologic analysis for their preoperative MRM coronal source images was done to specify root compression sites and L5 root morphologic changes. Results: DRG swelling was found in 66 (60%) of 110 patients. DRG swelling has statistically valuable meaning in foraminal root compression (chi-square test, p<0.0001). Seventy-two (66%) in 110 patients showed abnormal alteration of running course. Abnormal running course has statistically valuable meaning in foraminal or extraforaminal root compression (chi-square test, p<0.0001). Conclusion: Three-dimensional MRM provides precise thin sliced coronal images which are most close to real operative views. DRG swelling and running course abnormality of L5 exiting root are two useful findings in diagnosing L5 root compression at L5-S1 foramen or extraforamen. MRM is thought to provide additional diagnostic accuracy expecially in L5-S1 foraminal and extraforaminal area.