• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.361-369
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• 2013

We introduce a Nielsen type number of a fibre preserving map, and show that it is a lower bound for the number of $n$-orbits in the homotopy class. Under suitable conditions we show that it is equal to the Nielsen type relative essential $n$-orbit number. We also give necessary and sufficient conditions for it and the essential $n$-orbit number to coincide.

• Biomaterials and Biomechanics in Bioengineering
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• v.2 no.3
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• pp.143-157
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• 2015

Successful integration of cementless femoral stems using porous surfaces relies on effective periimplant bone healing to secure the bone-implant interface. The initial stages of the healing process involve protein adsorption, fibrin clot formation and cell osteoconduction onto the implant surface. Modelling this process in vitro, the current work considered the effect of fibrin deposition on the responses of human mesenchymal stromal cells cultured on ferritic fibre networks intended for magneto-mechanical actuation of in-growing bone tissue. The underlying hypothesis for the study was that fibrin deposition would support early stromal cell attachment and physiological functions within the optimal regions for strain transmission to the cells in the fibre networks. Highly porous fibre networks composed of 444 ferritic stainless steel were selected due to their ability to support human osteoblasts and mesenchymal stromal cells without inducing untoward inflammatory responses in vitro. Cell attachment, proliferation, metabolic activity, differentiation and penetration into the ferritic fibre networks were examined for one week. For all fibrin-containing samples, cells were observed on and between the metal fibres, supported by the deposited fibrin, while cells on fibrin-free fibre networks (control surface) attached only onto fibre surfaces and junctions. Initial cell attachment, measured by analysis of deoxyribonucleic acid, increased significantly with increasing fibrinogen concentration within the physiological range. Despite higher cell numbers on fibrin-containing samples, similar metabolic activities to control surfaces were observed, which significantly increased for all samples over the duration of the study. It is concluded that fibrin deposition can support the early attachment of viable mesenchymal stromal cells within the inter-fibre spaces of fibre networks intended for magneto-mechanical strain transduction to in-growing cells.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.417-426
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• 2006

In this paper, we are to construct a new fibred Riemannian space with almost complex structure from the lift of an almost contact structures of the base space and that of each fibre. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structure.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1485-1526
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• 2017

We show that birational rigidity of Mori fibre spaces is not open in moduli.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.991-1004
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• 2019

Firstly we consider preorders (not necessarily partial orders) on a canonical quotient of the set of the homotopy classes of continuous maps between two spaces induced by a certain equivalence relation ${\sim}_{{\varepsilon}R}$. Secondly we apply it to a classification of orientable fibrations over Y with fibre X. In the classification theorem of J. Stasheff [22] and G. Allaud [3], they use the set $[Y,\;Baut_1X]$ of homotopy classes of continuous maps from Y to $Baut_1X$, which is the classifying space for fibrations with fibre X due to A. Dold and R. Lashof [11]. In this paper we give a classification of fibrations using a preordered set (abbr., proset) structure induced by $[Y,\;Baut_1X]_{{\varepsilon}R}:=[Y,\;Baut_1X]/{\sim}_{{\varepsilon}R}$.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.171-185
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• 2009

We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.

• Asian-Australasian Journal of Animal Sciences
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• v.15 no.1
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• pp.111-116
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• 2002

This study investigated quantitative changes in the spaces between and within myofibrils and the impact of high and low voltage electrical stimulation on muscle ultrastructure as seen in electron micrographs. In addition, the relationships of these spaces and the impact to meat tenderness were investigated. The degradation of myofibrils during aging appeared to be localized across the muscle fibre. Structural deterioration of muscle fibres was evident 1 day post-mortem, involving the weakening in the lateral integrity of the myofibrils and Z-disc regions. Meat tenderisation, as shown by objective measurements, coincided with these increases in degradation, as assessed by the sum of the gaps between and within myofibrils. The results showed that the total size of gaps between and within myofibrils can be used as an indicator of meat tenderization during aging, but that ultrastructural alteration in electrically stimulated muscle had little relationship with meat tenderness.

• Advances in concrete construction
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• v.10 no.2
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• pp.105-111
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• 2020

In this study eleven beam of steel fibre-reinforced concrete were tested on concentrated load in order to evaluate the shear strength and deformation of the beams after burning. Variables considered in the test include spaces of shear reinforcement (stirrups) and temperature (normal temperature at 38℃, 300℃, 600℃ and 900℃). The steel fiber used is set at 0.5% of the concrete volume. The phenomenon of the test results shows that although the beams were tested to achieve shear failure, the fact that all the tested beams did not encounter any shear failure. It has shown the influence of steel fibers and stirrups that plays a role in determining the mode of collapse. The concrete shear capacity of steel fibrous concrete beams installed with stirrups in altered spacing variations is not significantly different from each other, while beam deformability increases when the space stirrups are reduced. Furthermore, models of the developed-steel fibrous shear strength are compared and discussed with experimental results.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.235-240
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• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.279-286
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• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.