On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

Selective Transport of Alkali—Metal Cations through Liquid Membranes by Non—Cyclic Carriers

The emission spectra of a series of naphthalene end-labeled oligo-oxyethylene(N-Pn-N) and their facilitated transport of cations across liquid membranes have been investigated.Alkali-metal cations enhance or inhibit the intramolecular excimer formation of N-Pn-N remarkably,suggesting that the polyether chain of N-Pn-N in solution complexes with the cations,and the orientation of the terminal chromophores depends on the cation size and the length of the polyether chain. These compounds are able to act as carriers to facilitate transport of alkali-metal cations through organic liquid membranes.The transport efficiencies are comparable with those of cyclic carriers such as crown ethers,and show remarkable selectivity.     

Hydrostatic pressure induced transformation of magnetism in a trimetallic CuMnFe Prussian blue analogue

With chemical co-precipitation, trimetal Prussian blue analogue Cu_0.71Mn_0.79[Fe(CN)₆]·7.3H₂O was obtained. We used supercritical carbon dioxide extraction apparatus to pressurize the samples for 10?MPa, 20?MPa, and 42?MPa for 5?h. X-ray powder diffraction data show the single-phase of the sample at different pressures with a NaCl-type face-centered cubic structure. Trimetal Prussian blue analogs Cu_0.71Mn_0.79[Fe(CN)₆]·7.3H₂O include both ferromagnetic and antiferromagnetic exchange interactions among different metal ions and exhibit novel mixed magnetic property. Hydrostatic pressure may be a powerful tool for development of new functional magnets. Spontaneous magnetization in the field cooled (FC) magnetization above 10?MPa approaches a value three times larger than that at 1?atm, and the zero field cooled (ZFC) magnetization is also extremely sensitive to pressure. The results show that pressure can simultaneously enhance the ferromagnetic and antiferromagnetic interactions in this material. The Weiss constant decreases gradually with pressure increasing from 10 to 42?MPa, due to pressure-induced electron transfer from Mn²⁺/Cu²⁺ to Fe³⁺.     

一类张量特征值互补问题

矩阵特征值互补问题在力学系统领域有广泛的应用.在本文中,我们提出了一类特殊的四阶张量特征值互补问题,它是矩阵特征值互补问题的推广.我们对该特征值互补问题解的存在性,计算复杂度等性质进行了初步的研究.在一定条件下,我们建立了该互补问题同一类非线性约束优化问题的等价性联系,并由此提出了平移投影幂法来求解该特征值互补问题.     

Improved N-P thermionic-GLC resolution using the SGE-solids injector

Summary The improvement of N/P-GLC chromatogram resolution is described. The use of a SGE-solids injector eliminates off-scale tailing solvent peaks, eliminates loss of information during desensitization of the detector and permits injection from any solvent.