• East Asian mathematical journal
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• v.25 no.4
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• pp.415-423
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• 2009

In this paper, we consider the hybrid monotone projection algorithm for asymptotically quasi-pseudocontractive mappings. A strong convergence theorem is established in the framework of Hilbert spaces. Our results mainly improve the corresponding results announced by [H. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70 (2009) 3140-3145] and also include Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152; Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal. 68 (2008) 2828-2836] as special cases.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.457-478
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• 2015

In this paper we propose an iteration hybrid method for approximating a point in the intersection of the solution-sets of pseudomonotone equilibrium and variational inequality problems and the fixed points of a semigroup-nonexpensive mappings in Hilbert spaces. The method is a combination of projection, extragradient-Armijo algorithms and Manns method. We obtain a strong convergence for the sequences generated by the proposed method.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.203-221
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• 2022

In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

• 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 Institute of Control, Robotics and Systems
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• v.14 no.8
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• pp.818-823
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• 2008

In this paper, we propose a feature extraction method which extracts directional features of handwritten numerals by using the projection runlength. Our directional featrures are obtained from four directional images, each of which contains horizontal, vertical, right-diagonal and left-diagonal lines in entire numeral shape respectively. A conventional method which extracts directional features by using Kirsch masks generates edge-shaped double line directional images for four directions, whereas our method uses the projections and their runlengths for four directions to produces single line directional images for four directions. To obtain the directional projections for four directions from a numeral image, some preprocessing steps such as thinning and dilation are required, but the shapes of resultant directional lines are more similar to the numeral lines of input numerals. Four [$4{\times}4$] directional features of a numeral are obtained from four directional line images through a zoning method. By using a hybrid feature which is made by combining our feature with the conventional features of a mesh features, a kirsch directional feature and a concavity feature, higher recognition rates of the handwrittern numerals can be obtained. For recognition test with given features, we use a multi-layer perceptron neural network classifier which is trained with the back propagation algorithm. Through the experiments with the handwritten numeral database of Concordia University, we have achieved a recognition rate of 97.85%.

• Nuclear Engineering and Technology
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• v.28 no.5
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• pp.488-499
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• 1996

We have extended the source projection analytic nodal discrete ordinates method (SPANDOM) for more flexible applicability in analysis of hexagonal assembly cores. The method (SPANDOM-FH) does not invoke transverse integration but instead solves the discrete ordinates equation analytically after the source term is projected and represented in hybrid form of high-order polynomials and exponential functions. SPANDOM-FH which treats a hexagonal node as one node is applied to two fast reactor benchmark problems and compared with TWOHEX. The results of comparison indicate that the present method SPANDOM-FH predicts accurately $k_eff$ and flux distributions in hexagonal assembly cores. In addition, SPANDOM-FH gives the continuous two dimensional intranodal scalar flux distributions in a hexagonal node. The reentering models between TWOHEX and SPANDOM were also compared and it was confirmed that SPANDOM's model is more realistic. Through the results of benchmark problems, we conclude that SPANDOM-FH has the sufficient accuracy for the nuclear design of fast breeder reactor (FBR) cores with hexagonal assemblies.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.1-6
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• 1992

A principle of "orthogonalization" is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric endpoint constraints. The principle realizes the hybrid control in a strict sense by letting position and velocity feedback signals be orthogonal in joint space to the contact force vector whose components are exerted at corresponding joints. This orthogonalization is executed via a projection matrix computed in real-time from a gradient of the equation of the surface in joint coordinates and hence both projected position and velocity feedback signals become perpendicular to the force vector that is normal to the surface at the contact point in joint space. To show the important role of the principle in control of robot manipulators, three basic problems are analyzed, the first is a hybrid trajectory tracking problem by means of a "modified hybrid computed torque method", the second is a model-based adaptive control problem for robot manipulators under geometric endpoint constraints, and the third is an iterative learning control problem. It is shown that the passivity of residual error dynamics of robots follows from the orthogonalization principle and it plays a crucial role in convergence properties of both positional and force error signals.force error signals.

• Management Science and Financial Engineering
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• v.21 no.2
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• pp.25-30
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• 2015

This short article compares different solution methods for a basic RBC model (Hansen, 1985). We solve and simulate the model using two main algorithms: the methods of perturbation and projection, respectively. One novelty is that we offer a type of the hybrid method: we compute easily a second-order approximation to decision rules and use that approximation as an initial guess for finding Chebyshev polynomials. We also find that the second-order perturbation method is most competitive in terms of accuracy for standard RBC model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.5-16
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• 1999

We introduce a new projector for accelerating convergence of a symmetric eigenvalue problem Ax = x, and devise a power/Lanczos hybrid algorithm. Acceleration can be achieved by removing the hard-to-annihilate nonsolution eigencomponents corresponding to the widespread eigenvalues with modulus close to 1, by estimating them accurately using the Lanczos method. However, the additional Lanczos results can be obtained without expensive matrix-vector multiplications but a very small amount of extra work, by utilizing simple power-Lanczos interconversion algorithms suggested. Numerical experiments are given at the end.

• Korean Journal of Radiology
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• v.23 no.11
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• pp.1044-1054
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• 2022

Objective: This study aimed to investigate whether a deep learning reconstruction (DLR) method improves the image quality, stent evaluation, and visibility of the valve apparatus in coronary computed tomography angiography (CCTA) when compared with filtered back projection (FBP) and hybrid iterative reconstruction (IR) methods. Materials and Methods: CCTA images of 51 patients (mean age ± standard deviation [SD], 63.9 ± 9.8 years, 36 male) who underwent examination at a single institution were reconstructed using DLR, FBP, and hybrid IR methods and reviewed. CT attenuation, image noise, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and stent evaluation, including 10%-90% edge rise slope (ERS) and 10%-90% edge rise distance (ERD), were measured. Quantitative data are summarized as the mean ± SD. The subjective visual scores (1 for worst -5 for best) of the images were obtained for the following: overall image quality, image noise, and appearance of stent, vessel, and aortic and tricuspid valve apparatus (annulus, leaflets, papillary muscles, and chordae tendineae). These parameters were compared between the DLR, FBP, and hybrid IR methods. Results: DLR provided higher Hounsfield unit (HU) values in the aorta and similar attenuation in the fat and muscle compared with FBP and hybrid IR. The image noise in HU was significantly lower in DLR (12.6 ± 2.2) than in hybrid IR (24.2 ± 3.0) and FBP (54.2 ± 9.5) (p < 0.001). The SNR and CNR were significantly higher in the DLR group than in the FBP and hybrid IR groups (p < 0.001). In the coronary stent, the mean value of ERS was significantly higher in DLR (1260.4 ± 242.5 HU/mm) than that of FBP (801.9 ± 170.7 HU/mm) and hybrid IR (641.9 ± 112.0 HU/mm). The mean value of ERD was measured as 0.8 ± 0.1 mm for DLR while it was 1.1 ± 0.2 mm for FBP and 1.1 ± 0.2 mm for hybrid IR. The subjective visual scores were higher in the DLR than in the images reconstructed with FBP and hybrid IR. Conclusion: DLR reconstruction provided better images than FBP and hybrid IR reconstruction.