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Characterization of finite colored spaces with certain conditions
Mitsugu Hirasaka,Masashi Shinohara 대한수학회 2019 대한수학회지 Vol.56 No.3
A \textit{colored space} is {a pair} $(X,r)$ of a set $X$ and a function $r$ whose domain is $X\choose 2$. Let $(X,r)$ be a finite colored space and $Y,Z\subseteq X$. We shall write $Y\simeq_r Z$ if there exists a bijection $f:Y\to Z$ such that $r(U)=r(f(U))$ for each $U\in {Y\choose 2}$ {where $f(U)=\{f(u)\mid u\in U\}$}. We denote the numbers of equivalence classes with respect to $\simeq_r$ contained in {$X \choose i$ by $a_i(r)$}. In this paper we prove that $a_2(r)\leq a_3(r)$ when $5\leq |X|$, and show what happens {when equality} holds.
Characterization of balanced coherent configurations
Hirasaka, Mitsugu,Sharafdini, Reza Elsevier 2010 Journal of algebra Vol.324 No.8
<P><B>Abstract</B></P><P>Let <I>G</I> be a group acting on a finite set <I>Ω</I>. Then <I>G</I> acts on Ω×Ω by its entry-wise action and its orbits form the basis relations of a coherent configuration (or shortly scheme). Our concern is to consider what follows from the assumption that the number of orbits of <I>G</I> on <SUB>Ωi</SUB>×<SUB>Ωj</SUB> is constant whenever <SUB>Ωi</SUB> and <SUB>Ωj</SUB> are orbits of <I>G</I> on <I>Ω</I>. One can conclude from the assumption that the actions of <I>G</I> on <SUB>Ωi</SUB>'s have the same permutation character and are not necessarily equivalent. From this viewpoint one may ask how many inequivalent actions of a given group with the same permutation character there exist. In this article we will approach to this question by a purely combinatorial method in terms of schemes and investigate the following topics: (i) balanced schemes and their central primitive idempotents, (ii) characterization of reduced balanced schemes.</P>
R & D of Global Multimedia Mobile Satellite Communications on NeLS Project
Ohkawa, Mitsugu,Koyama, Yoshisada,Motoyoshi, Shigeru,Watanabe, Hiroshi,Morikawa, Eihisa,Suzuki, Ryutaro,Yasuda, Yasuhiko 통신위성우주산업연구회 2002 Joint Conference on Satellite Communications Vol.2002 No.-
Next-generation LEO System Research Center (NeLS) has carried out the key technology development of global multimedia mobile satellite communications. In Phase I we studied the system definition and developed key technologies such as on-board active phased array antenna with digital beam forming, optical antenna, optical modem, wavelength division multiplexing for optical inter-satellite link system, satellite network, and variable rate modulation. In Phase 2, we plan to verify the developed technology in Phase 1 on space. In this paper, we introduce the results of development in Phase 1.
Schurity and separability of quasiregular coherent configurations
Hirasaka, Mitsugu,Kim, Kijung,Ponomarenko, Ilia Elsevier 2018 Journal of algebra Vol.510 No.-
<P><B>Abstract</B></P> <P>A permutation group is said to be quasiregular if each of its transitive constituents is regular, and a quasiregular coherent configuration can be thought as a combinatorial analog of such a group: the transitive constituents are replaced by the homogeneous components. In this paper, we are interested in the question when the configuration is schurian, i.e., formed by the orbitals of a permutation group, or/and separable, i.e., uniquely determined by the intersection numbers. In these terms, an old result of Hanna Neumann is, in a sense, dual to the statement that the quasiregular coherent configurations with cyclic homogeneous components are schurian. In the present paper, we (a) establish the duality in a precise form and (b) generalize the latter result by proving that a quasiregular coherent configuration is schurian and separable if the groups associated with the homogeneous components have distributive lattices of normal subgroups.</P>
CHARACTERIZATION OF FINITE COLORED SPACES WITH CERTAIN CONDITIONS
Hirasaka, Mitsugu,Shinohara, Masashi Korean Mathematical Society 2019 대한수학회지 Vol.56 No.3
A colored space is a pair (X, r) of a set X and a function r whose domain is $\(^X_2\)$. Let (X, r) be a finite colored space and $Y,\;Z{\subseteq}X$. We shall write $Y{\simeq}_rZ$ if there exists a bijection $f:Y{\rightarrow}Z$ such that r(U) = r(f(U)) for each $U{\in}\({^Y_2}\)$ where $f(U)=\{f(u){\mid}u{\in}U\}$. We denote the numbers of equivalence classes with respect to ${\simeq}_r$ contained in $\(^X_i\)$ by $a_i(r)$. In this paper we prove that $a_2(r){\leq}a_3(r)$ when $5{\leq}{\mid}X{\mid}$, and show what happens when equality holds.
Elsevier 2009 European journal of combinatorics : Journal europ& Vol.30 No.1
<P><B>Abstract</B></P><P>Let PQ denote the set of n∈N such that n is a product of two primes with gcd(n,φ(n))=1 where φ is the Euler function. In this article we aim to find n∈PQ such that any imprimitive permutation group of degree n is multiplicity-free. Let R denote the set of such integers in PQ. Our main theorem shows that there are at most finitely many Fermat primes if and only if |PQ−R| is finite, whose proof is based on the classification of finite simple groups.</P>
Sunghyen Hwang,Mitsugu Todo 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.7
Regeneration of articular layered tissues consisting of cartilage and cancellous bone has been a critical issue in orthopedics. Tissue engineering technology for such large-scale damaged layered tissue may be developed by using layered scaffold with stem cells. In this study, therefore, a novel multi-layer scaffold consisting of a porous poly (ε-caprolactone) (PCL) layer for cartilage regeneration and a porous composite layer of poly (L-lactic acid) (PLLA) and hydroxyapatite (HAp) for bone regeneration was developed. The microstructure of the scaffold was characterized by a field emission scanning electron microscope (FE-SEM). Compression tests were also performed to understand the stress-strain behavior. FE-SEM observation clearly showed that an interlayer exists between the PCL and the composite layers. The compressive stress-strain relation is characterized by a stepwise behavior including the first and the second steps. The first modulus corresponding to the first step is mainly related to the deformation of the PCL layer; on the other hand, the second modulus is related to both solidified PCL layer and the composite layer and increases with increase of HAp content of the composite layer. It is also found that the classical mechanics theory and three-dimensional finite element model can predict the first modulus reasonably well.