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Item type:Item, DECOMPOSING THE COMPLETE GRAPH INTO HAMILTONIAN PATHS (CYCLES) AND 3-STARS(2020-01-01) ;Lee, Hung-Chih ;Chen, Zhen-Chun ;應用數學系Department of Applied MathematicsLet H be a graph. A decomposition of H is a set of edge-disjoint sub-graphs of H whose union is H. A Hamiltonian path (respectively, cycle) of H is a path (respectively, cycle) that contains every vertex of H exactly once. A k-star, denoted by S-k, is a star with k edges. In this paper, we give necessary and sufficient conditions for decomposing the complete graph into alpha copies of Hamiltonian path (cycle) and beta copies of S-3.Item type:Item, Reliability Evaluation for a Stochastic Flow Network Based on Upper and Lower Boundary Vectors(2019-11-01) ;Huang, Ding-Hsiang ;Huang, Cheng-Fu ;Lin, Yi-Kuei ;工業工程與管理學系Department of Industrial Engineering and ManagementFor stochastic flow network (SFN), given all the lower (or upper) boundary points, the classic problem is to calculate the probability that the capacity vectors are greater than or equal to the lower boundary points (less than or equal to the upper boundary points). However, in some practical cases, SFN reliability would be evaluated between the lower and upper boundary points at the same time. The evaluation of SFN reliability with upper and lower boundary points at the same time is the focus of this paper. Because of intricate relationships among upper and lower boundary points, a decomposition approach is developed to obtain several simplified subsets. SFN reliability is calculated according to these subsets by means of the inclusion-exclusion principle. Two heuristic options are then established in order to calculate SFN reliability in an efficient direction based on the lower and upper boundary points.Item type:Item, Forest leaves and four-cycles(2000-03-01) ;Fu, HL ;Rodger, CA ;應用數學系Department of Applied MathematicsIn this article, we find necessary and sufficient conditions for the existence of a 4-cycle system of K-n - E(F) for any forest F of K-n. (C) 2000 John Wiley & Sons, Inc.Item type:Item, The effect of ball-milling solvent on the decomposition properties of Ba(Pb1-xBix)O-3(2001-03-01) ;Chang, MC ;Wu, JM ;Cheng, SY ;Chen, SY材料科學與工程學系Ba(Pb1-xBix)O-3 compound, which exhibits perovskite structure is a superconducting material. It can be a useful material for resistor when x value equals 0. The conducting behavior of BaPbO3 is liable to be affected during aqueous processing. In contrast, the phenomenon is not found in Ba(Pb0.8Bi0.2)O-3 The milling solvents of water and ethanol have different effect on the stability of perovskite phase. The decomposition of BaPbO3 into BaCO3 and PbO2 is found when CO32- ion exists. The partial substitution of Bi3+ stabilizes the perovskite phase. The stabilization and decomposition of perovskite phase explain the resistivity change with different milling solvents. (C) 2001 Elsevier Science B.V. All rights reserved.Item type:Item, Improvements on the duality based method used in solving optimal power flow problems(2002-05-01) ;Lin, CH ;Lin, SY ;Lin, SS ;電控工程研究所Institute of Electrical and Control EngineeringTo improve the previously developed dual-type (DT) method used in solving optimal power flow (OPF) problems with large number of thermal-limit constraints, we propose two new techniques in this paper. The first one is a graph-method based decomposition technique which can decompose the large-dimension projection problem, caused by the large number of thermal-limit constraints, into several independent medium-dimension projection subproblems at the expense of slight increment of the dual problem's dimension. The second technique is an active-set strategy based DT method which can solve the medium-dimension projection subproblems efficiently. We have used the DT method embedded with these two new techniques in solving numerous OPF's with large number of thermal-limit constraints. The test results show that the proposed techniques are very efficient and effectively improve the DT method for handling large number of thermal-limit constraints.Item type:Item, A more general dual projected pseudo quasi-Newton method for large network optimization problems(1999) ;Lin, SY ;Lin, SS ;電控工程研究所Institute of Electrical and Control EngineeringOne of the major computational steps in the dual projectd pseudo quasi-Newton method for neweork type optimization problems is the projection onto a convex set formed by the linear inequlity constraints of the problem. When the inequlity constraints are coupled, the large-dimension projection problem is a difficult one. In this paper, we propose a graphic-method based decomposition technique to determine a smallest subset of inequality contraints to be converted to equality constraints so that the rest of the inequality constraints become disjoint subsets. Consequently, the large-dimension projection problem can be decomposed into several independent small-dimension projection subproblems, and the computation complexity for the projection step will be largely reduced. Copyright (C) 1998 IFAC.Item type:Item, THE EXISTENCE OF r x 4 GRID-BLOCK DESIGNS WITH r=3, 4(2009) ;Zhang, Rucong ;Ge, Gennian ;Ling, Alan C. H. ;Fu, Hung-LinMutoh, YukiyasuFor a v-set V, let A be a collection of r x c arrays with elements in V. A pair (V, A) is called an r x c grid-block design if every two distinct elements i and j in V occur exactly once in the same row or in the same column of an array in A. This design originated from the use of DNA library screening. In this paper, we show the existence of r x 4 grid-block designs with r = 3, 4. We settle completely for the case of r = 4 and almost completely for the case of r = 3, leaving 15 orders undetermined.Item type:Item, Packing 5-cycles into balanced complete m-partite graphs for odd m(2007-10-01) ;Huang, Ming-Hway ;Fu, Chin-Mei ;Fu, Hung-Lin ;應用數學系Department of Applied MathematicsLet K-n1,(n2),..., n(m) be a complete m-partite graph with partite sets of sizes n(1),n(2),...,n(m). A complete m-partite graph is balanced if each partite set has n vertices. We denote this complete m-partite graph by K-m(n). In this paper, we completely solve the problem of finding a maximum packing of the balanced complete m-partite graph K-m(n), m odd, with edge-disjoint 5-cycles and we explicitly give the minimum leaves.Item type:Item, Decomposition of 2-chlorophenol in aqueous solution by ultrasound/H2O2 process(1996) ;Lin, JG ;Chang, CN ;Wu, JR ;環境工程研究所Institute of Environmental EngineeringSeveral authors have indicated that ultrasound is effective in oxidizing organic contaminants in water and in wastewater either as the sole means of treatment or in combination with ozonation and UV irradiation. In this work we decomposed 2-chlorophenol (2-cp) in aqueous solution with ultrasound and H2O2. The experiment was conducted with a sonicator (Microson XL-2020) operated at 20 kHz. The double amplitude at the tip of the standard horn (12.7 mm) was adjusted to 0, 72 and 120 mu m, corresponding to power input 0, 125 and 160 W. The initial concentration of aqueous 2-cp solution was 100 mg/l, treated in the system with 0, 100, 200 and 500 mg/l H2O2 individually. The volume of solution was 11 in a mixing flask, and was circulated to the sonication cell at the rate 500 mL/min. Oxygen was continuously purged into the flask. The temperature of solution was kept constant at 25 degrees C and pH was controlled at 3, 5, 7, 9 and 11. The results showed the decomposition of 2-cp was effective at increased amplitude of ultrasound and concentration of H2O2, and smaller pH. At reaction duration 360 min, 2-cp decomposition with 500 mg/l H2O2 was found with 57% improvement over the control, i.e. without H2O2 addition. The pH, controlled below the pKa of 2-cp (8.49 at 25 degrees C), had significantly better decomposition of 2-cp than at greater values. The decomposition rate of 100 mg/l 2-cp was 99% at 120 mu m double amplitude with H2O2 (200 mg/L) and pH 3, after 360 min of reaction. The removal of total organic carbon was found to be only 63%. From analysis of the experimental results, the data on 2-cp decomposition appeared to follow pseudo-first-order reaction kinetics. The squared correlation coefficient, R2, of the model was greater than 0.9 for various pH values. Copyright (C) 1996 IAWQ.Item type:Item, Enhancement of decomposition of 2-chlorophenol with ultrasound/H2O2 process(1996) ;Lin, JG ;Chang, CN ;Wu, JR ;Ma, YS環境工程研究所We investigated the effects of pH, ionic strength, catalyst, and initial concentration on both decomposition of 2-chlorophenol (2-cp) and removal of total organic carbon (TOC) in aqueous solution with ultrasonic amplitude 120 mu m and H2O2 (200 mg/l). When the initial concentrations of 2-cp was 100 mg/l and the pH was controlled at 3, the rate of 2-cp decomposition was enhanced up to 6.6-fold and TOC removal up td 9.8-fold over pH controlled at 11. At pH 3, the efficiency of decomposition of 2-cp was 99% but the removal of TOC was only 63%; a similar situation applied at pH 7 and 11. Hence intermediate compounds were produced and 2-cp was not completely mineralized. When the concentration of ionic strength was increased from 0.001 to 0.1 M, the rate of 2-cp decomposition was enhanced only 0.3-fold, whereas the TOC removal was not enhanced. In comparison of the effects of pH and ionic strength, pH had greater influence on both 2-cp decomposition and TOC removal than ionic strength. The effect of a catalyst (FeSO4) on decomposition of 2-cp was insignificant comparing with direct addition of H2O2 The reaction rate at a smaller initial concentration of 2-cp (10 mg/l) was more rapid than at a greater one (100 mg/l). The rate of 2-cp decomposition and TOC removal appeared to follow pseudo-first-order reaction kinetics. Copyright (C) 1996 IAWQ. Published by Elsevier Science Ltd.