An intelligent decomposition of pairwise comparison matrices for large-scale decisions

A Pairwise Comparison Matrix (PCM) has been used to compute for relative priorities of elements and are integral components in widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, PCMs suffer from several issues limiting their applications to large-scale decision problems. These limitations can be attributed to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker. This issue results to inconsistent preferences due to the limited cognitive powers of decision makers. To address these limitations, this research proposes a PCM decomposition methodology that reduces the elicited pairwise comparisons. A binary integer program is proposed to intelligently decompose a PCM into several smaller subsets using interdependence scores among elements. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets to derive the global weights of the elements from the original PCM. As a result, the number of pairwise comparison is reduced and consistency is of the comparisons is improved. The proposed decomposition methodology is applied to both AHP and ANP to demonstrate its advantages.     

An integer linear programming approach for a class of bilinear integer programs

We propose an Integer Linear Programming (ILP) approach for solving integer programs with bilinear objectives and linear constraints. Our approach is based on finding upper and lower bounds for the integer ensembles in the bilinear objective function, and using the bounds to obtain a tight ILP reformulation of the original problem, which can then be solved efficiently. Numerical experiments suggest that the proposed approach outperforms a latest iterative ILP approach, with notable reductions in the average solution time.     

超Li系统的Bargmann对称约束和双非线性化

给出超Li系统的一个显式对称约束和关于其Lax对的双非线性化.在此对称约束下,超Li系统的时间部分和空间部分分别被约化为有限维Liouville可积超Li系统.     

特殊集上素变数方程的解

令n=e_0+e_12+…+e_k2~k,其中e_j=0,1(j=0,…,k)表示自然数n的二进制展开式,N_0表示二进制展开式中项数为偶数的自然数的集合.分别给出了这个特殊集上素变数方程p_1+p_2+p_3~k=N和p_1+p_2~2+p_3~2+p_4~2=N解的个数的渐近公式.     

Evaluation of excess molar polarization in binary mixtures of Polar–Nonpolar liquids

Excess molar polarization in the binary mixture of polar solutes (acetic acid, n-tributyl phosphate) in nonpolar solvents (benzene, tetrachloromethane, p-xylene) is evaluated with the help of our proposed equation. The results have been compared with those obtained from a previously proposed equation. It is observed that our proposed equation is more accurate to interpret the liquid structure and molecular association in the binary liquid mixtures.     

Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid

The magnetic body force in boiling two-phase temperature-sensitive magnetic fluid (TSMF) flow is known to effectively increase the driving force of magnetic fluid in a non-uniform magnetic field. Based on this mechanism, in the present study, a binary TSMF, which is a mixture of the TSMF and a low-boiling-saturation-temperature organic solution, is proposed to be used in a heat transport device to enhance its circulation. In order to see its performance in the heat transport device, the pressure difference at different heated temperatures, magnetic fields and inclination angles of the heating section are investigated experimentally and theoretically. Results showed that the driving force increases remarkably due to more gas phase appearing in the test fluid and the magnetization of it decreasing. At low magnetic field the driving force is enhanced greatly when the inclination angle is close to 60°, while at high magnetic field the driving force is remarkably enhanced due to the effect of the magnetic force in the inclination angle range from 0° to 30° and 60° to 90°.     

Preferential Solvation in Mixed Solvents X. Completely Miscible Aqueous Co-Solvent Binary Mixtures at 298.15 K

Summary.  The Kirkwood-Buff integrals for 18 completely miscible aqueous co-solvent binary mixtures have been recalculated from thermodynamic data, and the volume-corrected preferential solvation parameters derived from them are presented. Also presented are these latter quantities for 15 additional such mixtures, for which the volume correction has not been applied previously. The self-interaction of the water, the mutual interaction of the water and the co-solvent, and the self-interaction of the co-solvent at infinite dilution derived from these integrals and parameters are then discussed. The systems studied include aqueous hydrogen peroxide, methanol, ethanol, 1- and 2-propanol, 2-methyl-2-propanol, 2,2,2-trifluoroethanol, 1,1,1,3,3,3-hexafluoro-2-propanol, ethane-1,2-diol, glycerol, 2-methoxyethanol (at 313 and 343 K), 2-ethoxyethanol, 2-butoxyethanol, 2-aminoethanol, N-methyl- and N,N-dimethyl-2-aminoethanol, tetrahydrofuran, 1,4-dioxane, acetone, formic, acetic, and propanoic acids, piperidine, pyridine, acetonitrile, formamide, N-methyl- and N,N-dimethylformamide, N-methylacetamide, N-methylpyrrolidin-2-one (at 303 K), hexamethyl phosphoric triamide, dimethylsulfoxide, and tetramethylenesulfone (at 303 K). Received January 10, 2001. Accepted (revised) February 20, 2001     

Modified form of binary and ternary 3-point subdivision schemes

Binary 3-point scheme, developed by Hormann and Sabin [Hormann, K. and Sabin, Malcolm A., 2008, A family of subdivision schemes with cubic precision, Computer Aided Geometric Design, 25, 41-52], has been modified by introducing a tension parameter which generates a family of C¹ limiting curves for certain range of tension parameter. Ternary 3-point scheme, introduced by Siddiqi and Rehan [Siddiqi, Shahid S. and Rehan, K., 2009, A ternary three point scheme for curve designing, International Journal of Computer Mathematics, In Press, DOI: 10.1080/00207160802428220], has also been modified by introducing a tension parameter which generates family of C¹ and C² limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the continuity of the subdivision schemes. The performance of modified schemes has been demonstrated by considering different examples along with its comparison with the established subdivision schemes.