• Title/Summary/Keyword: M/G Set

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SOLVABILITY AND BOUNDEDNESS FOR GENERAL VARIATIONAL INEQUALITY PROBLEMS

  • Luo, Gui-Mei
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.589-599
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    • 2013
  • In this paper, we propose a sufficient condition for the existence of solutions to general variational inequality problems (GVI(K, F, $g$)). The condition is also necessary when F is a $g-P^M_*$ function. We also investigate the boundedness of the solution set of (GVI(K, F, $g$)). Furthermore, we show that when F is norm-coercive, the general complementarity problems (GCP(K, F, $g$)) has a nonempty compact solution set. Finally, we establish some existence theorems for (GNCP(K, F, $g$)).

CHARACTERIZATION OF SUZUKI GROUP BY NSE AND ORDER OF GROUP

  • Iranmanesh, Ali;Mosaed, Hosein Parvizi;Tehranian, Abolfazl
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.651-656
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    • 2016
  • Let G be a finite group and nse(G) be the set of numbers of elements of G of the same order. In this paper, we prove that the simple group $Sz(2^{2m+1})$, where $2^{2m+1}-1$ is a prime number, is uniquely determined by $nse(Sz(2^{2m+1}))$ and ${\mid}Sz(2^{2m+1}){\mid}$.

Analysis of Volatile Organic Compounds Emitted from Chemical Parts and Monitor Set of PC/Monitor (PC/Monitior 구성 화학부품 및 제품에서 방출되는 휘발성 유기화합물의 분석)

  • Choe, Jong-Woo;Baek, Kyn-Won;Ri, Chang-Seop
    • Journal of the Korean Chemical Society
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    • v.44 no.5
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    • pp.415-421
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    • 2000
  • Volatile organic compounds(VOCs) emitted from PC/Monitor set and chemical parts com-prising of PC/Monitor set were analyzed aran, and xylene of VOCs based on qualitative analysis. As a result of these analyses, when the Wedge Rub-ber of rubber product was heated from 60$^{\circ}C$ to 80$^{\circ}C$, the emission rate(%) of xylene was increased about 2.5 times. But it was evaluated that the left of chemical parts were not affected by temperature except Wedge Rub-ber. The results of qualitative analyses between RGA and GC-MS were a little different respectively. With quantitative analysis, concentration of xylene emitted from cabinet was measured to be maximum as 6029.3 ug/ m$^3$(1.3ppm). The concentrations of toluene, xylene, and benzofuran derived from PC/Monitor set were 10.25${\mu}g/m^3$, 690${\mu}g/m^3$, and 180 ${\mu}g/m^3$, and these concentrations were relatively high levels which can bring on the risk to human health.

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DECOMPOSITION OF CONTINUITY AND COMPLETE CONTINUITY IN SMOOTH FUZZY TOPOLOGICAL SPACES

  • Amudhambigai, B.;Uma, M.K.;Roja, E.
    • East Asian mathematical journal
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    • v.27 no.3
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    • pp.261-271
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    • 2011
  • In this paper, fuzzy ${\alpha}^*$-set, fuzzy C-set, fuzzy AB-set, fuzzy t-set, fuzzy B-set, etc., are introduced in the sense of Sostak [12] and Ramadan [9]. By using these sets, a decomposition of fuzzy continuity and complete fuzzy continuity are provided. Characterization of smooth fuzzy extremally disconnected spaces is also obtained in this connection.

Design of a set of One-to-Many Node-Disjoint and Nearly Shortest Paths on Recursive Circulant Networks

  • Chung, Ilyong
    • Journal of Korea Multimedia Society
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    • v.16 no.7
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    • pp.897-904
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    • 2013
  • The recursive circulant network G(N,d) can be widely used in the design and implementation of parallel processing architectures. It consists of N identical nodes, each node is connected through bidirectional, point-to-point communication channels to different neighbors by jumping $d^i$, where $0{\leq}i{\leq}{\lceil}{\log}_dN{\rceil}$ - 1. In this paper, we investigate the routing of a message on $G(2^m,4)$, a special kind of RCN, that is key to the performance of this network. On $G(2^m,4)$ we would like to transmit k packets from a source node to k destination nodes simultaneously along paths on this network, the $i^{th}$ packet will be transmitted along the $i^{th}$ path, where $1{\leq}k{\leq}m-1$, $0{{\leq}}i{{\leq}}m-1$. In order for all packets to arrive at a destination node quickly and securely, we present an $O(m^4)$ routing algorithm on $G(2^m,4)$ for generating a set of one-to-many node-disjoint and nearly shortest paths, where each path is either shortest or nearly shortest and the total length of these paths is nearly minimum since the path is mainly determined by employing the Hungarian method.

NIJENHUIS TENSOR FUNCTIONAL ON A SUBSPACE OF METRICS

  • Kang, Bong-Koo
    • The Pure and Applied Mathematics
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    • v.1 no.1
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    • pp.13-18
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    • 1994
  • The study of the integral of the scalar curvature, $A(g)\;=\;{\int}_M\;RdV_9$ as a functional on the set M of all Riemannian metrics of the same total volume on a compact orient able manifold M is now classical, dating back to Hilbert [6] (see also Nagano [8]). Riemannian metric g is a critical point of A(g) if and only if g is an Einstein metric.(omitted)

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TANGENTIAL REPRESENTATIONS AT ISOLATED FIXED POINTS OF ODD-DIMENSIONAL G-MANIFOLDS

  • Komiya, Katsuhiro
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.33-37
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    • 2008
  • Let G be a compact abelian Lie group, and M an odd-dimensional closed smooth G-manifold. If the fixed point set $M^G\neq\emptyset$ and dim $M^G=0$, then G has a subgroup H with $G/H{\cong}\mathbb{Z}_2$, the cyclic group of order 2. The tangential representation $\tau_x$(M) of G at $x{\in}M^G$ is also regarded as a representation of H by restricted action. We show that the number of fixed points is even, and that the tangential representations at fixed points are pairwise isomorphic as representations of H.

On the fixed-point theorems on the infrasolvmanifolds

  • Chun, Dae-Shik;Jang, Chan-Gyu;Lee, Sik
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.681-688
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    • 1995
  • Fixed-point theory has an extension to coincidences. For a pair of maps $f,g:X_1 \to X_2$, a coincidence of f and g is a point $x \in X_1$ such that $f(x) = g(x)$, and $Coin(f,g) = {x \in X_1 $\mid$ f(x) = g(x)}$ is the coincidence set of f and g. The Nielsen coincidence number N(f,g) and the Lefschetz coincidence number L(f,g) are used to estimate the cardinality of Coin(f,g). The aspherical manifolds whose fundamental group has a normal solvable subgroup of finite index is called infrasolvmanifolds. We show that if $M_1,M_2$ are compact connected orientable infrasolvmanifolds, then $N(f,g) \geq $\mid$L(f,g)$\mid$$ for every $f,g : M_1 \to M_2$.

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Many-to-Many Disjoint Path Covers in Double Loop Networks (이중 루프 네트워크의 다대다 서로소인 경로 커버)

  • Park Jung-Heum
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.8
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    • pp.426-431
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    • 2005
  • A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate many-to-many 2-DPC in a double loop network G(mn;1,m), and show that every nonbipartite G(mn;1,m), $m{\geq}3$, has 2-DPC joining any two source-sink pairs of vertices and that every bipartite G(mn;1,m) has 2-DPC joining any two source-sink pairs of black-white vertices and joining any Pairs of black-black and white-white vertices. G(mn;l,m) is bipartite if and only if n is odd and n is even.