• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.433-448
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• 2022

The Cartan's second curvature tensor Pⁱ_jkh is a positively homogeneous of degree-1 in yⁱ, where yⁱ represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pⁱ_jkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.

• Analytical Science and Technology
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• v.12 no.6
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• pp.1083-1090
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• 1999

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• The Journal of Korean Physical Therapy
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• v.27 no.5
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• pp.315-319
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• 2015

Purpose: The purpose of this study was to investigate the effect of leg-crossing positions on muscle activities of rectus femoris, tensor fascia latae, and hamstring in healthy 20's adults. Methods: Twenty healthy subjects were asked to perform three leg-crossing positions, leg crossing (LC), tailor crossing (TC), and ankle crossing (AC). Surface electromyography (EMG) was used to evaluate the activities of rectus femoris, tensor fascia latae, and hamstring during upright sit posture (UP) and three leg-crossing positions and UP was compared to three leg-crossing positions. Repeated one way ANOVA was used for data analysis. The alpha level was set at 0.05. Results: The results showed significant difference in the muscle activities of rectus femoris, tensor fascia latae, and hamstring among leg-crossing positions. The muscle activity of the rectus femoris was significantly lower in LC and TC positions than UP. The muscle activity of tensor fascia latae was significantly higher in LC position than UP and other leg-crossing positions. The muscle activity of hamstring was significantly higher in LC and TC positions and significantly lower in AC position than in UP. Conclusion: Our study suggests that the activity of hip muscles was affected by pelvic and knee alignment in various leg-crossing positions.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.837-840
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• 1995

Finite element analysis using two dimensional magnetic permeabillity tensor that can represents phase lag between magnetic field intensity and flux density under rotational flux is examined. Considered problem is confined to two dimensional magnetostatic case. And we applied proposed method to calculate the core loss of the test model and compare the result with that of experiment.

• The KIPS Transactions:PartB
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• v.15B no.3
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• pp.205-210
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• 2008

A new approach is proposed for restoration of corrupted regions and segmentation in natural text images. The challenge is to fill in the corrupted regions on the basis of color feature analysis by second order symmetric stick tensor. It is show how feature analysis can benefit from analyzing features using tensor voting with chromatic and achromatic components. The proposed method is applied to text images corrupted by manifold types of various noises. Firstly, we decompose an image into chromatic and achromatic components to analyze images. Secondly, selected feature vectors are analyzed by second-order symmetric stick tensor. And tensors are redefined by voting information with neighbor voters, while restore the corrupted regions. Lastly, mode estimation and segmentation are performed by adaptive mean shift and separated clustering method respectively. This approach is automatically done, thereby allowing to easily fill-in corrupted regions containing completely different structures and surrounding backgrounds. Applications of proposed method include the restoration of damaged text images; removal of superimposed noises or streaks. We so can see that proposed approach is efficient and robust in terms of restoring and segmenting text images corrupted.

• Journal of Biomedical Engineering Research
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• v.28 no.3
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• pp.317-324
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• 2007

The application of diffusion tensor imaging (DTI) and fiber tractography to Wallerian degeneration (WD) is important because this technique is a very potent tools for quantitatively evaluating fiber tracts in vivo brain. We analyzed a case and control using tracts of interest (TOI) analysis to quantify WD. We scanned a case of old infarction and an age-matched healthy volunteer. T1 magnetization prepared rapid acquisition gradient echo (MPRAGE), fluid attenuated inversion recovery (FLAIR) and 12-direction diffusion tensor imaging (DTI) were obtained and analyzed using TOI analysis. The value of mean diffusity ($D_{av}$) and fracional anisotrophy (FA) were analyzed statistically by MWU test. A p-value of less than 0.05 was considered to indicate statistical significance. A comparison of the global fiber diffusion characteristics shows WD of both the corpus callosum and the ipsilateral superior longitudinal fasciculus. The corpus callosum in particular showed trans-hemispherical degeneration. Local fiber characteristics along the geodesic paths show WD in the corpus callosum, ipsilateral superior longitudinal fasciculus, ipsilateral corticospinal tract, and ipsilateral corticothalamic tract. We have demonstrated changes in $D_{av}$ and FA values and a clear correspondence with the WD in various tracts. TOI analysis successfully revealed radial WD in white matter tracts from a region of encephalomalacia and primary gliosis, although they were only slightly affected.

• The Journal of Korean Physical Therapy
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• v.30 no.2
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• pp.73-77
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• 2018

Purpose: The prefrontal lobe, supplementary motor area, cerebellum, and basal ganglia are activated during gait. In addition, gait is controlled by nerves, such as the corticospinal tract (CST) and corticoreticular pathway (CRP). In this study, the presence of an injury to the CST and CRP was identified by diffusion tensor imaging and the characteristics of the gait pattern were investigated according to inferior cerebral artery infarction. Methods: One patient and six control subjects of a similar age participated. A 69-year-old female patient had an injury to the left basal ganglia, insular gyrus, corona radiata, dorsolateral prefrontal cortex, and postcentral gyrus due to an inferior cerebral artery infarction. Diffusion tensor imaging (DTI) data was acquired 4 weeks after the stroke. The kinematic and spatio-temporal parameters of gait were collected using a three-dimensional gait analysis system. Results: On 4 weeks DTI, the CST and CRP in the affected hemisphere did not show injury to the affected and unaffected hemisphere. Gait analysis showed that the cadence of spatio-temporal parameter was decreased significantly in the patient. The angle of the knee joint was decreased significantly in the affected and unaffected sides compared to the control group. Conclusion: The results of diffusion tensor imaging showed that although the patient was evaluated to be capable of an independent gait, the quality and quantity of gait might be reduced. This study could help better understand the gait ability analysis of stroke patients and the abnormal gait pattern of patients with a brain injury.

• Progress in Superconductivity and Cryogenics
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• v.26 no.1
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• pp.10-13
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• 2024

We performed angle-resolved Raman spectroscopy experiments on lead-doped and undoped Bi₂Sr₂CaCu₂O_8+δ(Bi2212) samples using a 660 nm laser and analyzed the Raman tensor of the phonon modes. The phonon mode was clearly observed at the 60, 103, and 630 cm^-1 Raman shifts. The 60, 630 cm^-1 peaks were only clearly observed when the incident and scattered light polarizations were configured to be parallel. The polarization angle dependence of the amplitude of the 60, 630 cm^-1 peak on the parallel configuration shows a twofold symmetry; therefore, both peaks originate from Ag phonons and the crystal structure of Bi2212 should be considered orthorhombic. On the other hand, the 103 cm^-1 peak is clearly observed in both parallel and perpendicular configurations. Remarkably, the off-diagonal component of the Raman tensor of the 103 cm^-1 peak showed an anti-symmetry that could not be realized within the known crystal structure of Bi2212. The implications of our findings are discussed.