• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.671-676
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• 2018

In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a generic class of polynomials whose gradient ideals are radical. As a consequence we reclaim a previous result that the unconstrained polynomial optimization problem for Morse polynomials has a finite convergence.

• Computers and Concrete
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• v.26 no.1
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• pp.31-52
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• 2020

This paper investigates the size dependent effect on the vibration analysis of a porous nanocomposite viscoelastic plate reinforced by functionally graded-single walled carbon nanotubes (FG-SWCNTs) by considering nonlocal strain gradient theory. Therefore, using energy method and Hamilton's principle, the equations of motion are derived. In this article, the effects of nonlocal parameter, aspect ratio, strain gradient parameter, volume fraction of carbon nanotubes (CNTs), damping coefficient, porosity coefficient, and temperature change on the natural frequency are perused. The innovation of this paper is to compare the effectiveness of each mentioned parameters individually on the free vibrations of this plate and to represent the appropriate value for each parameter to achieve an ideal nanocomposite plate that minimizes vibration. The results are verified with those referenced in the paper. The results illustrate that the effect of damping coefficient on the increase of natural frequency is significantly higher than the other parameters effect, and the effects of the strain gradient parameter and nonlocal parameter on the natural frequency increase are less than damping coefficient effect, respectively. Furthermore, the results indicate that the natural frequency decreases with a rise in the nonlocal parameter, aspect ratio and temperature change. Also, the natural frequency increases with a rise in the strain gradient parameter and CNTs volume fraction. This study can be used for optimizing the industrial and medical designs, such as automotive industry, aerospace engineering and water purification system, by considering ideal properties for the nanocomposite plate.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.4
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• pp.1760-1778
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• 2018

For image segmentation with intensity inhomogeneity, many region-based level set methods have been proposed. Some of them however can't get the relatively ideal segmentation results under the severe intensity inhomogeneity and weak edges, and without use of the image gradient information. To improve that, we propose a new level set method combined with local direction gradient in this paper. Firstly, based on two assumptions on intensity inhomogeneity to images, the relationships between segmentation objects and image gradients to local minimum and maximum around a pixel are presented, from which a new pixel classification method based on weight of Euclidian distance is introduced. Secondly, to implement the model, variational level set method combined with image spatial neighborhood information is used, which enhances the anti-noise capacity of the proposed gradient information based model. Thirdly, a new diffusion process with an edge indicator function is incorporated into the level set function to classify the pixels in homogeneous regions of the same segmentation object, and also to make the proposed method more insensitive to initial contours and stable numerical implementation. To verify our proposed method, different testing images including synthetic images, magnetic resonance imaging (MRI) and real-world images are introduced. The image segmentation results demonstrate that our method can deal with the relatively severe intensity inhomogeneity and obtain the comparatively ideal segmentation results efficiently.

• Investigative Magnetic Resonance Imaging
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• v.13 no.1
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• pp.15-21
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• 2009

Purpose : A method to estimate a real k-space trajectory based on a circuit model of the gradient system is proposed for spiral imaging. The estimated k-space trajectory instead of the ideal trajectory is used in the reconstruction to improve the image quality in the spiral imaging. Materials and Methods : Since the gradient system has self resistance, capacitance, and inductance, as well as the mutual inductance between the magnet and the gradient coils, the generated gradient fields have delays and transient responses compared to the input waveform to the gradient system. The real gradient fields and their trajectory in k-space play an important role in the reconstruction. In this paper, the gradient system is modeled with R-L-C circuits, and real gradient fields are estimated from the input to the model. An experimental method to determine the model parameters (R, L, C values) is also suggested from the quality of the reconstructed image. Results : The gradient fields are estimated from the circuit model of the gradient system at 1.5 Tesla MRI system. The spiral trajectory obtained by the integration of the estimated gradient fields is used for the reconstruction. From experiments, the reconstructed images using the estimated trajectory show improved uniformity, reduced overshoots near the edges, and enhanced resolutions compared to those using the ideal trajectory without model. Conclusion : The gradient system was successfully modeled by the R-L-C circuits. Much improved reconstruction was achieved in the spiral imaging using the trajectory estimated by the proposed model.

• Journal of the Korean Magnetic Resonance Society
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• v.8 no.2
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• pp.70-76
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• 2004

ZORA-DFT calculations of $^{11}$B EFG (electric field gradient) tensors for lithium borates, LiB$_3O_5$ (LBO) and Li$_2B_4O_7$ (LTB), were performed. The calculated values of 11B quadrupole coupling constant and asymmetry parameter are in good agreement with the experimental values. The sign of the quadrupole coupling constant for the tetrahedral boron site was deduced from the distortion from the ideal tetrahedral symmetry.

• The Journal of the Acoustical Society of Korea
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• v.20 no.5
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• pp.61-68
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• 2001

In this paper, an analytical method and a difference approximation method to calculate the gradient of an objective function have been applied to the directivity optimization in an adaptive ultrasonic transducer which is combined with a point source array and an optimization algorithm (DFP method). To compare these two methods, quasi-ideal .beam with a beam width and direction specified are chosen as the desired directivity. As the numerical results, the difference approximation method shows better suppressive capacity of side lobe level, good stability in the convergence processing, faster convergence speed and excellent adaptability compared with the analytical method.

• Investigative Magnetic Resonance Imaging
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• v.21 no.1
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• pp.28-33
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• 2017

Purpose: To investigate and compensate the effects of respiration-induced B0 variations on fat quantification of the bone marrow in the lumbar spine. Materials and Methods: Multi-echo gradient echo images with navigator echoes were obtained from eight healthy volunteers at 3T clinical scanner. Using navigator echo data, respiration-induced B0 variations were measured and compensated. Fat fraction maps were estimated using $T2^*$-IDEAL algorithm from the uncompensated and compensated images. For manually drawn bone marrow regions, the estimated B0 variations and the calculated fat fractions (before and after compensations) were analyzed. Results: An increase of temporal B0 variations from inferior level to superior levels was observed for all subjects. After compensation using navigator echo data, the effects of the B0 variations were reduced in gradient echo images. The calculated fat fractions show significant differences (P < 0.05) in L1 and L3 between the uncompensated and the compensated. Conclusion: The results of this study raise the need for considering respiration-induced B0 variations for accurate fat quantification using gradient echo images in the lumbar spine. The use of navigator echo data can be an effective way for the reduction of the effects of respiratory motion on the quantification.

• International Journal of Concrete Structures and Materials
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• v.10 no.1
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• pp.39-46
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• 2016

In this study, different proportions of glass beads used for road marking were added into the concrete samples to reduce the temperature gradient through the concrete pavement thickness. It is well known that decreasing the temperature gradient reduces the risk of thermal cracking and increases the service life of concrete pavement. The extent of alkali-silica reaction (ASR) produced with partial replacement of fine aggregate by glass bead was investigated and compressive strength of concrete samples with different proportion of glass bead in their mix designs were measured in this study. Ideal results were obtained with less than 0.850 mm diameter size glass beads were used (19 % by total weight of aggregate) for C30/37 class concrete. Top and bottom surface temperatures of two different C30/37 strength class concrete slabs with and without glass beads were measured. It was identified that, using glass bead in concrete mix design, reduces the temperature differences between top and bottom surfaces of concrete pavement. The study presented herein provides important results on the necessity of regulating concrete road mix design specifications according to regions and climates to reduce the temperature gradient values which are very important in concrete road design.

• The Journal of the Korea institute of electronic communication sciences
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• v.18 no.3
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• pp.535-544
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• 2023

In this paper, we study the effect of gradient vector calculation method(analytical method, central finite difference method) on adaptive beamforming to control weight distribution during iterated calculation when LMS algorithm (repeating method) is used to realize desired beam pattern. To this end, a quasi-ideal beam having an arbitrarily set beam width, a rotating beam, and a multi-beam were reviewed as examples. Numerical experiments applied the step parameters of the appropriate values to the adaptive beamforming system through trial and error equally to the two calculations, and compared the convergence characteristics of objective functions that evaluate adaptability and error using two methods for calculating gradient vectors.

• Proceedings of the Korean Society of Medical Physics Conference
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• 2002.09a
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• pp.146-149
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• 2002

The aim of stereotactic radiosurgery(SRS) is to deliver a high dose to a target region and a low dose to critical organ through only one or a few irradiation. To satisfy this aim, optimized irradiating conditions must be searched in the planning. Thus, many mathematical methods such as gradient method, simulated annealing and genetic algorithm had been proposed to find out the conditions automatically. There were some limitations using these methods: the long calculation time, and the difficulty of unique solution due to the different shape of tumor. In this study, optimization protocol using ideal models and data base was proposed. Proposed optimization protocol constitutes two steps. First step was a preliminary work. Some possible ideal geometry shapes, such as sphere, cylinder, cone shape or the combination, were assumed to approximate the real tumor shapes. Optimum variables such as isocenter position or collimator size, were determined so that the high dose region could be shaped to fit ideal models with the arrangement of multiple isocenter. Data base were formed with those results. Second, any shaped real targets were approximated to these models using geometry comparison. Then, optimum variables for ideal geometry were chosen from the data base predetermined, and final parameters were obtained by adjusting these data. Although the results of applying the data base to patients were not superior to the result of optimization in each case, it can be acceptable as a starting point of plan.