• The Korean Journal of Pain
• /
• v.32 no.4
• /
• pp.271-279
• /
• 2019

Background: We utilized diffusion tensor imaging (DTI) to evaluate the cerebral white matter changes that are associated with phantom limb pain in patients with unilateral arm amputation. It was anticipated that this would complement previous research in which we had shown that changes in cerebral blood volume were associated with the cerebral pain network. Methods: Ten patients with phantom limb pain due to unilateral arm amputation and sixteen healthy age-matched controls were enrolled. The intensity of phantom limb pain was measured by the visual analogue scale (VAS) and depressive mood was assessed by the Hamilton depression rating scale. Diffusion tensor-derived parameters, including fractional anisotropy, mean diffusivity, axial diffusivity (AD), and radial diffusivity (RD), were computed from the DTI. Results: Compared with controls, the cases had alterations in the cerebral white matter as a consequence of phantom limb pain, manifesting a higher AD of white matter in both hemispheres symmetrically after adjusting for individual depressive moods. In addition, there were associations between the RD of white matter and VAS scores primarily in the hemispheres related to the missing hand and in the corpus callosum. Conclusions: The phantom limb pain after unilateral arm amputation induced plasticity in the white matter. We conclude that loss of white matter integrity, particularly in the hemisphere connected with the missing hand, is significantly correlated with phantom limb pain.

• Korean Journal of Mathematics
• /
• v.30 no.1
• /
• pp.61-66
• /
• 2022

A new type of Riemannian manifold called semirecurrent manifold has been defined and some of its geometric properties are studied. Among others we show that the scalar curvature of semirecurrent manifold is constant and hence semirecurrent manifold is also concircularly recurrent. In addition, we show that the associated 1-form (resp. the associated vector field) of semirecurrent manifold is closed (resp. an eigenvector of its Ricci tensor). Furthermore, we prove that if a Riemannian product manifold is semirecurrent, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curvature.

• Honam Mathematical Journal
• /
• v.36 no.4
• /
• pp.723-730
• /
• 2014

In the present paper, we introduce a type of Riemannian manifolds (namely, $W_4$-birecurrent manifold) and study the several properties of such a manifold on which some geometric conditions are imposed.

• PNF and Movement
• /
• v.14 no.1
• /
• pp.41-47
• /
• 2016

Purpose: In general, confabulation is defined as confusion of reality with past events without apparent prompting, in association with disruption of the capacity for retrieval and encoding of memory. We report on a patient who showed spontaneous confabulation associated with injury of the Papez circuit following middle cerebral artery (MCA) infarction. Methods: A 67-year-old female patient suffered cerebral infarct resulting from spontaneous MCA territory. After onset of the MCA infarct, she showed severe memory impairment and provoked confabulation. The Papez circuit was reconstructed for evaluation of part of it using diffusion tensor tractography (DTT). Fractional anisotropy (FA), mean diffusivity (MD), and tract volume were measured. Results: The right thalamocingulate tract showed a significant decrement of FA value and tract volume, and an increment of MD value by more than two standard deviations of that of normal control subjects. The tract volume in the left fornix and mammillothalamic tract decreased by more than two standard deviations of that of normal control subjects. Conclusion: Injuries of the Papez circuit were demonstrated in a patient who showed severe memory impairment and provoked confabulation following MCA infarct. We believe that analysis of the Papez circuit tract using DTT is useful in elucidating the cause of provoked confabulation in patients with MCA infarct.

• The Journal of the Korea Contents Association
• /
• v.19 no.7
• /
• pp.176-185
• /
• 2019

Diffusion tensor images were obtained for middle-aged men according to the AUDIT-K scale. As a result of the fractional anisotropy (FA) value of the gyrus nerve fibers in the brain region measured and analyzed by the Tract-Based Spatial Statics, FA values of general drinkers were measured lower than those of estimated alcohol use disabled people. This was statistically significant. In other words, the use of alcohol significantly affects the anatomic microstructural changes measured in the Gyrus of the brain region, and it may damage the nerve fiber tract and affect the functional abnormalities associated with it.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.875-884
• /
• 2016

Let x : $^{Mn-1}{\rightarrow}{\mathbb{R}}^n$ ($n{\geq}4$) be an umbilical free hyper-surface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. We denote the Laguerre scalar curvature by R and the trace-free Laguerre tensor by ${\tilde{L}}:=L-{\frac{1}{n-1}}tr(L)g$. In this paper, we prove a local classification result under the assumption of parallel Laguerre form and an inequality of the type $${\parallel}{\tilde{L}}{\parallel}{\leq}cR$$ where $c={\frac{1}{(n-3){\sqrt{(n-2)(n-1)}}}$ is appropriate real constant, depending on the dimension.

• Structural Engineering and Mechanics
• /
• v.57 no.6
• /
• pp.1107-1124
• /
• 2016

Consistent finite strain Plate constitutive relations are derived based on a hyperelastic formulation for an isotropic material. Plate equilibrium equations under finite strain are derived following a static kinematic approach. Three Euler angles and four shear angles, based on Timoshenko beam theory, represent the kinematics of the deformations in the plate cross section. The Green deformation tensor has been expressed in term of a deformation tensor associated with the deformation and stretches of an embedded plate element. Buckling formulation includes the in-plane axial deformation prior to buckling and transverse as well as in-plane shear deformations. Numerical results for a simply supported thick plate under uni-axial compression force are presented.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.607-629
• /
• 2022

In this paper, we give the necessary and sufficient condition for the conformal mapping ϕ : (ℝⁿ, g₀) → (Nⁿ, h) (n ≥ 3) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.

• Communications of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.47-53
• /
• 2023

The Terracini t-locus of an embedded variety X ⊂ ℙ^r is the set of all cardinality t subsets of the smooth part of X at which a certain differential drops rank, i.e., the union of the associated double points is linearly dependent. We give an easy to check criterion to exclude some sets from the Terracini loci. This criterion applies to tensors and partially symmetric tensors. We discuss the non-existence of codimension 1 Terracini t-loci when t is the generic X-rank.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.19 no.3
• /
• pp.173-178
• /
• 2019

To analyze the diffraction properties of optical signals by periodic blazed 2D diffraction gratings, Toeplitz dielectric tensor is first defined and formulated by 2D spatial Fourier expansions associated with asymmetric blazed grating profile. The characteristic modes in each layer is then based on eigenvalue problem, and the complete solution is found rigorously in terms of modal transmission-line theory (MTLT) to address the pertinent boundary-value problems. Toeplitz matrix of symmetric and sawtooth profiles is derived from that of asymmetric blazed grating profile, and the diffraction properties for each profile are numerically simulated. The numerical results reveal that the asymmetric and symmetric profiles behave as anti-reflection GMR filter while the sawtooth profile works better as anti-transmission one rather than anti-reflection filter.