• Investigative Magnetic Resonance Imaging
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• v.4 no.1
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• pp.20-26
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• 2000

Gradient moment nulling techniques require the introduction of an additional gradient on each axis for each order of motion correction to be applied. The additional gradients introduce new constraints on the sequence design and increase the demands on the gradient system. The purpose of this paper is to demonstrate techniques for optimization of gradient echo gradient moment nulling sequences within the constraints of the gradient hardware. Flow compensated pulse sequences were designed and implemented on a clinical magnetic resonance imaging system. The design of the gradient moment nulling sequences requires the solution of a linear system of equations. A Mathematica package was developed that interactively solves the gradient moment nulling problem. The package allows the physicist to specify the desired order of motion compensation and the duration of the gradients in the sequence with different gradient envelopes. The gradient echo sequences with first, second, and third order motion compensation were implemented with minimum echo time. The sequences were optimized to take full advantage of the capabilities of the gradient hardware. The sequences were used to generate images of phantoms and human brains. The optimized sequences were found to have better motion compensation than comparable standard sequences.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.825-837
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• 2022

We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric P-connection. At first, it is proven that if the metric of such a manifold is a gradient m-quasi-Einstein metric, then either the gradient of the potential function 𝜓 is collinear with the vector field P or, λ = -(m + 2) and the manifold is of constant sectional curvature -1, provided P𝜓 ≠ m. Next, it is shown that if the metric of the manifold under consideration is a gradient 𝜌-Einstein soliton, then the gradient of the potential function is collinear with the vector field P. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric P-connection is a gradient 𝜔-Ricci soliton, then the manifold is of constant sectional curvature -1 and λ + 𝜇 = -2. Finally, we consider an example to verify our results.

• Geomechanics and Engineering
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• v.18 no.5
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• pp.481-492
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• 2019

Due to the underground openings, the tangentially concentrated stress of the tunnel remains larger at excavation boundary and decreases toward the interior of the surrounding rock with a certain gradient. In order to study the effect of different gradient stress on rockburst, the true-triaxial gradient and hydraulic-pneumatic combined test apparatus were carried out to simulate the rockburst processes. Under the different gradient stress conditions, the rock-like specimen (gypsum) was tested independently through three principal stress directions loading--fast unloading of single surface--top gradient and hydraulic-pneumatic combined loading, which systematically analyzed the macro-mesoscopic damage phenomena, force characteristics and acoustic emission (AE) signals of the specimen during rockburst. The experimental results indicated that the rockburst test under the gradient and hydraulic-pneumatic combined loading conditions could perfectly reflect the rockburst processes and their stress characteristics; Relatively high stress loading could cause specimen failure, but could not determine its mode. The rockburst under the action of gradient stress suggested that the failure mode of specimen mainly depended on the stress gradient. When the stress gradient was lower, progressive and static spalling failure occured and the rockburst grades were relatively slight. On the other hand, shear fractures occurred in rockbursts accounted for increasingly large proportion as the stress gradient increased and the rockburst occurred more intensely and suddenly, the progressive failure process became unconspicuous, and the rockburst grades were moderate or even stronger.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.219-226
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• 2020

In this paper, we consider gradient Ricci solitons and gradient Yamabe solitons in the warped product spaces. Also we study warped product space with harmonic curvature related to gradient Ricci solitons and gradient Yamabe solitons. Consequently some theorems are generalized and we derive differential equations for a warped product space to be a gradient Ricci soliton.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.1
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• pp.72-79
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• 1997

Most open magnetic resonance imaging systems have used the planar gradient coils whose inductances were minimized through the magnetic energy minimization procedure in the spatial frequency domain. Though the planar gradient coils have smaller inductance than conventional gradient coils, the planar gradient coils often suffer from their poor magnetic field linearity. Scaling the spatial frequencies of the current density function designed by the magnetic energy minimization, magnetic field linearity of the planar gradient coils can be greatly improved with small sacrifice of gradient coil inductance. We have found that the figure of merit of the planar gradient coils, defined by the gradient strength divided by the linearity error and the inductance, can be improved by proposed technique.

• Journal of Korea Water Resources Association
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• v.56 no.10
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• pp.691-695
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• 2023

In this study, two sections with different topographic gradients were in the Hyogyo-ri area, the hydraulic gradients were calculated for each section, and the hydraulic gradient fluctuations according to the topographic gradient and rainfall were analyzed. The variations of the hydraulic gradient within the research site was large in the section with steep topographic gradient and small in the section with gradual topographic gradient. The influence of the variation in hydraulic gradient due to rainfall was high in the section with steep topographic gradient, and low in the section with gradual topographic gradient. Through this study, it was found that the hydraulic gradient fluctuations in unconfined aquifer showed as a complex effect of topographic gradient and rainfall.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.179-191
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• 2022

We set our target to investigate Yamabe solitons, gradient Yamabe solitons and gradient Einstein solitons within the structure of 3-dimensional non-cosymplectic normal almost contact metric manifolds. Also, we provide a nontrivial example and validate a result of our paper.

• Journal of Korean Ophthalmic Optics Society
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• v.9 no.2
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• pp.223-231
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• 2004

In most previous studies, the assessment of accommodative convergence to accommodative stimulus (AC/A) ratio was commonly made by measuring gradient AC/A ratio. This study deals with the proximal convergence/accommodation(PC/A)ratio measured by comparing values of the gradient AC/A ratio and the calculated AC/A ratio to prevail the clinical use of the AC/A ratio. Visual acuities of All 124 subjects had been corrected to at least 1.0 with either eye through their habitual refractive correction and the MEM dynamic retinoscopy was performed to estimate their accommodative response. And then the PC/A ratio was calculated by making use of the calculated AC/A ratio and the gradient AC/A ratio. This study showed that the difference between the mean calculated AC/A ratio and the mean gradient AC/A ratio in subgroups may be attributable to proximal convergence. Consequently, further studies on proximity cues including the PC/A ratio could be helpful to prevail the clinical use of the AC/A ratio.

• Computers and Concrete
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• v.15 no.4
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• pp.607-642
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• 2015

The stress-strain relationship of concrete in flexure is one of the essential parameters in assessing the flexural strength and ductility of reinforced concrete (RC) columns. An overview of previous research studies revealed that the presence of strain gradient would affect the maximum concrete stress developed in flexure. However, no quantitative model was available to evaluate the strain gradient effect on concrete under flexure. Previously, the authors have conducted experimental studies to investigate the strain gradient effect on maximum concrete stress and respective strain and developed two strain-gradient-dependent factors k3 and ko for modifying the flexural concrete stress-strain curve. As a continued study, the authors herein will extend the investigation of strain gradient effects on flexural strength and ductility of RC columns to concrete strength up to 100 MPa by employing the strain-gradient-dependent concrete stress-strain curve using nonlinear moment-curvature analysis. It was evident from the results that both the flexural strength and ductility of RC columns are improved under strain gradient effect. Lastly, for practical engineering design purpose, a new equivalent rectangular concrete stress block incorporating the combined effects of strain gradient and concrete strength was proposed and validated. Design formulas and charts have also been presented for flexural strength and ductility of RC columns.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.539-552
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• 2020

In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.