• The Journal of Art Theory & Practice
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• no.7
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• pp.165-188
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• 2009

In the development of linear perspective, Brook Taylor's theory has achieved a special position. With his method described in Linear Perspective(1715) and New Principles of Linear Perspective(1719), the subject of linear perspective became a generalized and abstract theory rather than a practical method for painters. He is known to be the first who used the term 'vanishing point'. Although a similar concept has been used form the early stage of Renaissance linear perspective, he developed a new method of British perspective technique of measure points based on the concept of 'vanishing points'. In the 15th and 16th century linear perspective, pictorial space is considered as independent space detached from the outer world. Albertian method of linear perspective is to construct a pavement on the picture in accordance with the centric point where the centric ray of the visual pyramid strikes the picture plane. Comparison to this traditional method, Taylor established the concent of a vanishing point (and a vanishing line), namely, the point (and the line) where a line (and a plane) through the eye point parallel to the considered line (and the plane) meets the picture plane. In the traditional situation like in Albertian method, the picture plane was assumed to be vertical and the center of the picture usually corresponded with the vanishing point. On the other hand, Taylor emphasized the role of vanishing points, and as a result, his method entered the domain of projective geometry rather than Euclidean geometry. For Taylor's theory was highly abstract and difficult to apply for the practitioners, there appeared many perspective treatises based on his theory in England since 1740s. Joshua Kirby's Dr. Brook Taylor's Method of Perspective Made Easy, Both in Theory and Practice(1754) was one of the most popular treatises among these posterior writings. As a well-known painter of the 18th century English society and perspective professor of the St. Martin's Lane Academy, Kirby tried to bridge the gap between the practice of the artists and the mathematical theory of Taylor. Trying to ease the common readers into Taylor's method, Kirby somehow abbreviated and even omitted several crucial parts of Taylor's ideas, especially concerning to the inverse problems of perspective projection. Taylor's theory and Kirby's handbook reveal us that the development of linear perspective in European society entered a transitional phase in the 18th century. In the European tradition, linear perspective means a representational system to indicated the three-dimensional nature of space and the image of objects on the two-dimensional surface, using the central projection method. However, Taylor and following scholars converted linear perspective as a complete mathematical and abstract theory. Such a development was also due to concern and interest of contemporary artists toward new visions of infinite space and kaleidoscopic phenomena of visual perception.

• The Journal of Korean Society for Radiation Therapy
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• v.11 no.1
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• pp.100-105
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• 1999

Purpose : When the value of X,Y,Z coordination of the isocenter are reallocated from an arbitrary point using DRR (Digitally Reconstructed Radiographs) image in CT Simulation, conventional simulation is normally performed to verify the accuracy of this reallocation of the isocenter through the fluroscopy. The purpose of our experiment is to determine whether repeated test of the verification is necessary or not, and to analyze errors of reallocation with respect to the body region and the beam projection, if necessary, Material and Method : For 200 simulation patient, an arbitrary point is marked on each body and axial scaning is performed using CT, and treatment planing is done by drawing tumor and target volume on each slice. Using the planing data and the reallocated point of the isocenter, DRR image can be obtained and the final isocenter are marked on the patient's skin. In order to verify this reallocation of X,Y.Z coordination from CT simulation, We measure and evaluate the errors of these value on the fluoroscopy monitor and systematize them by classifying according to each body region (Brain, Neck and SCL, Lung, Esophagus, abdomen, Breast and Pelvis) and each beam projection {AP(PA), Supine, Prone and conformal : etc. } Conclusion : Isocenters are shifted by 3-5 mm in the case of Neck & SCL, Breast. at Abdomen, while noticeable differences are not found in other regions. Also, there are not correlations between the errors and the body regions or beam projections. However, our experiment intends to decide whether the procedure of verification is necessary on the vase of time and economy. It is regretful that we could not fully analyze the geometrical errors of DRR image and visual errors from the divergence. In conclusion, according to how much doctor consider tumor margin in drawing tumor and target volume, the meaning of analysis on the reallocation of isocenter should be reinterpreted, (which depends on the experience and capability of doctors)

• Tunnel and Underground Space
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• v.28 no.4
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• pp.343-357
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• 2018

Algorithm which can analyze the slope failure behavior utilizing the comprehensive information of the dense point of joint poles and the joint set orientations, both of which are obtained statistically, and the defect pattern of pole distribution has been developed. This method overcomes the potential incorrectness of the hemispheric projection method utilizing the joint set orientations only and also enhances the reliability of slope failure analysis. To this end a method capable of calculating the joint dispersion index directly from the joint pole distribution, instead of contour map, has been devised. The representative orientations for the slope failure analysis has been determined by considering the number and orientations of cone angle-dependent joint sets as well as the joint dispersion index. By engaging these representative orientations to the hemispheric projection analysis more reliable slope failure examination has been carried out. Sensitivity analysis for the potentially unstable slope of plane failure mode has been performed. Significance of joint strength index and the external seismic loading on the slope stability has been fully analyzed.

• The korean journal of orthodontics
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• v.48 no.1
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• pp.11-22
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• 2018

Objective: The aim of this study was to determine cephalometric factors that help predict favorable soft-tissue profile outcomes following treatment with the Class II Twin-block appliance. Methods: Pre- and post-treatment lateral cephalograms of 45 patients treated with the Class II Twin-block appliance were retrospectively analyzed. Profile silhouettes were drawn from the cephalograms and evaluated by three orthodontists in order to determine the extent of improvement. Samples were divided into a favorable group (upper 30% of visual analogue scale [VAS] scores, n = 14) and an unfavorable group (lower 30% of VAS scores, n = 14). Skeletal and soft-tissue measurements were performed on the cephalograms and an intergroup comparison was conducted. Results: An independent t-test revealed that the following pre-treatment values were lower in the favorable group compared to the unfavorable group: lower incisor to mandibular plane angle, lower incisor to pogonion distance, point A-nasion-point B angle, sella-nasion line (SN) to maxillary plane angle, SN to mandibular plane angle, gonial angle, and symphysis inclination. The favorable group had a larger incisor inclination to occlusal plane. Moreover, the favorable group showed larger post-treatment changes in gonial angle, B point projection, and pogonion projection than did the unfavorable group. Conclusions: Class II malocclusion patients with a low divergent skeletal pattern and reduced lower incisor protrusions are likely to show more improvement in soft-tissue profile outcomes following Class II Twin-block treatment.

• 전기의세계
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• v.21 no.3
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• pp.48-52
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• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.2
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• pp.52-62
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• 1997

To reconstruct the complete 3-D shape of an object, seveal range images form different viewpoints should be merged into a single model. The process of extraction of the transformation parameters between multiple range views is calle dregistration. In this paper, we propose a new algorithm to find the transformation parameters between multiple range views. Th eproposed algorithm consists of two step: initial estimation and iteratively update the transformation. To guess the initial transformation, we modify the principal axes by considering the projection effect, due to the difference fo viewpoints. Then, the following process is iterated: in order to extract the exact transformation parameters between the range views: For every point of the common region, find the nearest point among the neighborhood of the current corresponding point whose correspondency is defined by the reverse calibration of the range finder. Then, update the transformation to satisfy the new correspondencies. In order to evaluate the performance the proposed registration algorithm, some experiments are performed on real range data, acquired by space encoding range finder. The experimental results show that the proposed initial estimation accelerate the following iterative registration step.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.293-309
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• 2011

The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article apply above results to prove the strong convergence theorems of zero point for maximal monotone operators in Banach spaces. Noting that, the CQ iteration method can be used for relatively nonexpansive mapping but it can not be used for weak relatively nonexpansive mapping. However, the monotone CQ method can be used for weak relatively nonexpansive mapping. The results of this paper modify and improve the results of S.Matsushita and W.Takahashi, and some others.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.583-607
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• 2010

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.69-86
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• 2017

The point $P{\in}{\mathbb{P}}^2$ is referred to as a Galois point for a nonsingular plane algebraic curve C if the projection ${\pi}_P:C{\rightarrow}{\mathbb{P}}^1$ from P is a Galois covering. In contrast, the point $P^{\prime}{\in}C^{\prime}$ is referred to as a weak Galois Weierstrass point of a nonsingular algebraic curve C' if P' is a Weierstrass point of C' and a total ramification point of some Galois covering $f:C^{\prime}{\rightarrow}{\mathbb{P}}^1$. In this paper, we discuss the following phenomena. For a nonsingular plane curve C with a Galois point P and a double covering ${\varphi}:C{\rightarrow}C^{\prime}$, if there exists a common ramification point of ${\pi}_P$ and ${\varphi}$, then there exists a weak Galois Weierstrass point $P^{\prime}{\in}C^{\prime}$ with its Weierstrass semigroup such that H(P') = or , which is a semigroup generated by two positive integers r and 2r + 1 or 2r - 1, such that P' is a branch point of ${\varphi}$. Conversely, for a weak Galois Weierstrass point $P^{\prime}{\in}C^{\prime}$ with H(P') = or , there exists a nonsingular plane curve C with a Galois point P and a double covering ${\varphi}:C{\rightarrow}C^{\prime}$ such that P' is a branch point of ${\varphi}$.

• Journal of the Institute of Convergence Signal Processing
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• v.8 no.3
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• pp.156-162
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• 2007

The parallel beam SPECT system acquires projection data by using collimators in conjunction with photon detectors. The projection data of the parallel beam SPECT system is, however, blurred by the point response function of the collimator that is used to define the range of directions where photons can be detected. By increasing the number of parallel holes per unit area in collimator, one can reduce such blurring effect. This approach also, however, has the blurring problem if the distance between the object and the collimator becomes large. In this paper we consider correction methods for artifacts caused by non-circular orbit of parallel beam SPECT with many parallel holes per detector cell. To do so, we model the relationship between the object and its projection data as a linear system, and propose an iterative reconstruction method including artifacts correction. We compute the projector and the backprojector, which are required in iterative method, as a sum of convolutions with distance-dependent point response functions instead of matrix form, where those functions are analytically computed from a single function. By doing so, we dramatically reduce the computation time and memory required for the generation of the projector and the backprojector. We conducted several simulation studies to compare the performance of the proposed method with that of conventional Fourier method. The result shows that the proposed method outperforms Fourier methods objectively and subjectively.