A new type of vehicle routing problem （VRP）, multiple vehicle routing problem integrated reverse logistics （MVRPRL）, is studied. In this problem, there is delivery or pickup （or both） and uncertain features in t...A new type of vehicle routing problem （VRP）, multiple vehicle routing problem integrated reverse logistics （MVRPRL）, is studied. In this problem, there is delivery or pickup （or both） and uncertain features in the demands of the clients. The deliveries of every client as uncertain parameters are expressed as triangular fuzzy numbers. In order to describe MVRPRL, a multi-objective fuzzy programming model with credibility measure theory is constructed. Then the simulationbased tabu search algorithm combining inter-route and intra-route neighborhoods and embedded restarts are designed to solve it. Computational results show that the tabu search algorithm developed is superior to sweep algorithms and that compared with handling each on separate routes, the transportation costs can be reduced by 43% through combining pickups with deliveries.展开更多
Let (G, E) be a quasi-ordered group such that E∩E -1 is infinite, (G, G +) an ordered group with G +EG, and (G, G 1) the partially ordered group induced by (G, E).Let γ E, G + ∶T G + →T E and γ E, G 1 ∶T G 1 →T...Let (G, E) be a quasi-ordered group such that E∩E -1 is infinite, (G, G +) an ordered group with G +EG, and (G, G 1) the partially ordered group induced by (G, E).Let γ E, G + ∶T G + →T E and γ E, G 1 ∶T G 1 →T E be the corresponding natural morphisms between Toeplitz algebras. We prove that the kernel Ker γ E, G + is rigid,while Ker γ E, G 1 is equal to the compact-operator ideal on 2(G 1), and all Fredholm operators in the Toeplitz algebra T G 1 are of index zero.展开更多
In this paper, we construct a scattered Cantor set having the value 1/2 of log2/log3- dimensional Hausdorff measure. Combining a theorem of Lee and Baek, we can see the value 21 is the minimal Hausdorff measure of the...In this paper, we construct a scattered Cantor set having the value 1/2 of log2/log3- dimensional Hausdorff measure. Combining a theorem of Lee and Baek, we can see the value 21 is the minimal Hausdorff measure of the scattered Cantor sets, and our result solves a conjecture of Lee and Baek.展开更多
Integral imaging is a three dimensional(3D)display technology without any additional equipment.A new system is proposed in this paper which consists of the elemental images of real images in real mode(RIRM)and the one...Integral imaging is a three dimensional(3D)display technology without any additional equipment.A new system is proposed in this paper which consists of the elemental images of real images in real mode(RIRM)and the ones of virtual images in real mode(VIRM).The real images in real mode are the same as the conventional integral images.The virtual images in real mode are obtained by changing the coordinates of the corresponding points in elemental images which can be reconstructed by the lens array in virtual space.In order to reduce the spot size of the reconstructed images,the diffuser in conventional integral imaging is given up in the proposed method.Then the spot size is nearly1/20 of that in the conventional system.And an optical integral imaging system is constructed to confirm that our proposed method opens a new way for the application of the passive 3D display technology.展开更多
基金The National Natural Science Foundation of China(No.70772059)Youth Science and Technology Innovation Foundation of Nanjing Agriculture University(No.KJ06029)
文摘A new type of vehicle routing problem （VRP）, multiple vehicle routing problem integrated reverse logistics （MVRPRL）, is studied. In this problem, there is delivery or pickup （or both） and uncertain features in the demands of the clients. The deliveries of every client as uncertain parameters are expressed as triangular fuzzy numbers. In order to describe MVRPRL, a multi-objective fuzzy programming model with credibility measure theory is constructed. Then the simulationbased tabu search algorithm combining inter-route and intra-route neighborhoods and embedded restarts are designed to solve it. Computational results show that the tabu search algorithm developed is superior to sweep algorithms and that compared with handling each on separate routes, the transportation costs can be reduced by 43% through combining pickups with deliveries.
基金the National Natural Science Foundation of China (No. 10371051 and 10201007)
文摘Let (G, E) be a quasi-ordered group such that E∩E -1 is infinite, (G, G +) an ordered group with G +EG, and (G, G 1) the partially ordered group induced by (G, E).Let γ E, G + ∶T G + →T E and γ E, G 1 ∶T G 1 →T E be the corresponding natural morphisms between Toeplitz algebras. We prove that the kernel Ker γ E, G + is rigid,while Ker γ E, G 1 is equal to the compact-operator ideal on 2(G 1), and all Fredholm operators in the Toeplitz algebra T G 1 are of index zero.
基金the National Natural Science Foundation of China (No.10771164)the Education Committee of Fujian Province (No.JA08155)
文摘In this paper, we construct a scattered Cantor set having the value 1/2 of log2/log3- dimensional Hausdorff measure. Combining a theorem of Lee and Baek, we can see the value 21 is the minimal Hausdorff measure of the scattered Cantor sets, and our result solves a conjecture of Lee and Baek.
基金supported by the National Natural Science Foundation of China(No.11474169)
文摘Integral imaging is a three dimensional(3D)display technology without any additional equipment.A new system is proposed in this paper which consists of the elemental images of real images in real mode(RIRM)and the ones of virtual images in real mode(VIRM).The real images in real mode are the same as the conventional integral images.The virtual images in real mode are obtained by changing the coordinates of the corresponding points in elemental images which can be reconstructed by the lens array in virtual space.In order to reduce the spot size of the reconstructed images,the diffuser in conventional integral imaging is given up in the proposed method.Then the spot size is nearly1/20 of that in the conventional system.And an optical integral imaging system is constructed to confirm that our proposed method opens a new way for the application of the passive 3D display technology.
