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CONGRUENCE-FREE SIMPLE SEMIGROUP

  • Moon, Eunho L.
    • Korean Journal of Mathematics
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    • v.13 no.2
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    • pp.177-182
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    • 2005
  • If a semigroup S has no nontrivial congruences then S is either simple or 0-simple.([2]) By contrast with ring theory, not every congruence on a semigroup is associated with an ideal, hence some simple(or 0-simple) semigroup may have a nontrivial congruence. Thus it is a short note for the characterization of a simple(or 0-simple) semigroup that is congruence-free. A semigroup that has no nontrivial congruences is said to be congruence-free.

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A Comparative Study of PISO, SIMPLE, SIMPLE-C Algorithms in 3-dimensional Generalized Coordinate Systems (3차원 일반 좌표계에서의 PISO, SIMPLE, SIMPLE-C 알고리즘의 비교)

  • Park J. Y.;Baek J. H.
    • Journal of computational fluids engineering
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    • v.1 no.1
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    • pp.26-34
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    • 1996
  • The performance of the SIMPLE, SIMPLE-C and PISO algorithms for the treatment of the pressure-velocity coupling in fluid flow problems were examined by comparing the computational effort required to obtain the same level of the convergence. Example problems are circular duct and 90-degree bent square-duct. For circular duct case, laminar and turbulent flow were computed. For 90-degree bent square-duct case, laminar flow was simulated by the time-marching method as well as the iterative method. The convergence speed of the other two algorithms are not always superior to SIMPLE algorithm. SIMPLE algorithm is faster than SIMPLE-C algorithm in the simple laminar flow calculations. The application of the PISO algorithm in three dimensional general coordinates is not so effective as in two-dimensional ones. Since computational time of PISO algorithm is increased at each time step(or iterative step) in three dimension, the total convergence speed is not decreased. But PISO algorithm is stable for large time step by using time marching method,.

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A JOINING CHARACTERIZATION OF FACTORS OF SIMPLE MAPS

  • Ahn, Young-Ho
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.3
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    • pp.29-36
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    • 2007
  • Let T be an ergodic measure preserving transformation on (X, B, ${\mu}$). It is called 2-simple if every 2-fold ergodic joining is either a product measure or an off-diagonal measure. In general, factors of simple maps are not simple. So far, there has been no characterization of the factor of simple maps. In this paper, we give a joining characterization of factors of simple maps.

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A Study on the Uplift for Applying of Heavy Simple Catenary System in a Overhead Rigid Conductor Rail Transition Section (강체전차선로 이행구간 Heavy Simple Catenary 적용을 위한 압상량 고찰)

  • Kim, Wan-il;Park, Weon-Chan;Lee, Jae-Bong;Kim, Jae-Moon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.5
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    • pp.688-694
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    • 2018
  • The transition section of the overhead rigid conductor rail (ORCR) consists of a direct induction device and a limit point to prevent the power supply failure and failure of the electric railway vehicle pantograph due to the difference of the uplift in the catenary line. In T-Bar transition section, a twin simple catenary is mostly installed between the overhead catenary system (OCS) in the ground section and the ORCR in the underground section. In this paper, we compare and analyze the possibility of replacing the twin simple catenary with heavy simple catenary. The reliability of numerical analysis results was confirmed by comparing field test with numerical results. Comparing the numerical results of the twin simple catenary with the heavy simple catenary in the transition section, the difference uplift is 5.9[mm] on average. When applying heavy simple catenary instead of twin simple catenary, the slight difference of uplift can be compensated by adjusting the height of hanger-ear or support bracket.

SIMPLE VALUATION IDEALS OF ORDER 3 IN TWO-DIMENSIONAL REGULAR LOCAL RINGS

  • Noh, Sun-Sook
    • Communications of the Korean Mathematical Society
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    • v.23 no.4
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    • pp.511-528
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    • 2008
  • Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and $\upsilon$ be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple $\upsilon$-ideals $m\;=\;P_0\;{\supset}\;P_1\;{\supset}\;{\cdots}\;{\supset}\;P_t\;=\;P$ and all the other $\upsilon$-ideals are uniquely factored into a product of those simple ones [17]. Lipman further showed that the predecessor of the smallest simple $\upsilon$-ideal P is either simple or the product of two simple $\upsilon$-ideals. The simple integrally closed ideal P is said to be free for the former and satellite for the later. In this paper we describe the sequence of simple $\upsilon$-ideals when P is satellite of order 3 in terms of the invariant $b_{\upsilon}\;=\;|\upsilon(x)\;-\;\upsilon(y)|$, where $\upsilon$ is the prime divisor associated to P and m = (x, y). Denote $b_{\upsilon}$ by b and let b = 3k + 1 for k = 0, 1, 2. Let $n_i$ be the number of nonmaximal simple $\upsilon$-ideals of order i for i = 1, 2, 3. We show that the numbers $n_{\upsilon}$ = ($n_1$, $n_2$, $n_3$) = (${\lceil}\frac{b+1}{3}{\rceil}$, 1, 1) and that the rank of P is ${\lceil}\frac{b+7}{3}{\rceil}$ = k + 3. We then describe all the $\upsilon$-ideals from m to P as products of those simple $\upsilon$-ideals. In particular, we find the conductor ideal and the $\upsilon$-predecessor of the given ideal P in cases of b = 1, 2 and for b = 3k + 1, 3k + 2, 3k for $k\;{\geq}\;1$. We also find the value semigroup $\upsilon(R)$ of a satellite simple valuation ideal P of order 3 in terms of $b_{\upsilon}$.

ON NIL-EXTENSIONS OF LEFT STRONGLY SIMPLE po-SEMIGROUPS

  • Zhu, Qing Shun
    • Communications of the Korean Mathematical Society
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    • v.26 no.3
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    • pp.405-416
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    • 2011
  • In this paper, we first introduce the concept of left strongly simple po-semigroups, then we discuss properties and characterizations nil-extensions of left strongly simple po-semigroups and semilattices of leftstrongly simple po-semigroups. Finally, we give some characterizations of the chain of left strongly simple po-semigroups.

REMARKS ON HIGHER TYPE ADJUNCTION INEQUALITIES OF 4-MANIFOLDS OF NON-SIMPLE TYPE

  • Kim, Jin-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.431-440
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    • 2002
  • Recently P. Ozsv$\'{a}$th Z. Szab$\'{o}$ proved higher type adjunction inequalities for embedded surfaces in 4-manifolds of non-simple type. The aim of this short paper is to give a simple and direct proof of such higher type adjunction inequalities for smoothly embedded surfaces with negative self-intersection number in smooth 4-manifolds of non-simple type. This will be achieved through a relation between the Seiberg-Witten invariants used to get adjunction inequalities of 4-manifolds of simple type and a blow-up formula.

A Simple Distillation Process Produce Fuel from Plastic Waste using Incorporate Heat Source

  • Thawichsri, Kosart;nilnont, Wanich
    • International journal of advanced smart convergence
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    • v.4 no.1
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    • pp.127-136
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    • 2015
  • This paper is a study of a simple distillation process. Its objective is to compare fuel production from plastic waste, its data collecting is from the factory and simple data calculated a suitable evaluation on the simple distillation plant built before calculation. The experiment with a simple distillation process is separated into three sections. The first section is a simple distillation process of distillation producing diesel using heat source by biomass. The second section is distillation process which produces fuel using heat source by burner. The third section uses heat source by burner incorporate with biomass. The experiment reveals that the result of the second section is the most efficient. In comparison with the experiments and the simple calculation, the result on the efficiency of work has error less than 5% and it is sufficient for the next experimental process. Thus, the study and design on a simple distillation process produces fuel from plastic waste has to concern mainly on design heat exchangers, flow rate and optimized temperature. Further study on this plant can be developed throughout the county due to its low cost and efficiency.