In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its interior.Up to now,this conjecture is still open for all n 3.In 1933,Borsuk made a conjecture that every n...In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its interior.Up to now,this conjecture is still open for all n 3.In 1933,Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller diameters.Up to now,this conjecture is open for 4 n 297.In this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies,propose a four-step program to attack them,and obtain some partial results.展开更多
Two modes of regulating the water quality of experimental ponds in indoor raceway culture of Litopenaeus vannamei were evaluated using simple water treatment facilities. A self-made water purifying net, aeration stone...Two modes of regulating the water quality of experimental ponds in indoor raceway culture of Litopenaeus vannamei were evaluated using simple water treatment facilities. A self-made water purifying net, aeration stone, composite microbe preparation, and Ceratophyllum demersum were placed in the experimental ponds and the culture water was circulated along the raceway inside the pond using a paddle wheel aerator. In addition, the water quality in the experimental pond was improved by draining effluent from the pipeline at the bottom of ponds 7 and 8 （mode I） and exchanging the circulating water in pond 10 （mode Ⅱ） with the reservoir water in pond 9 using a pump and pipeline. The water quality in the experimental ponds was similar in response to regulation using mode Ⅰ or mode Ⅱ. Water quality parameters in the experimental ponds were controlled within a suitable range by simple facilities during culture period without using any chemical treatments. The rich content of dissolved oxygen was maintained by the circular flow and continuous aeration of the pond water. The respective average values of the main water parameters in experimental ponds 7 and 10 in response to regulation of the water quality using modes Ⅰ and Ⅱwere as follows： pH 8.17 and 7.99; DO 5.16 mg/L and 5.97 mg/L; CODMn18.45 and 12.61 mg/L; TAN （NH3-N） 0.854 mg/L （0.087 mg/L） and 0.427 mg/L （0.012 mg/L）; NO2-N 0.489 mg/L and 0.337 mg/L. Moreover, the average body length and body weight of harvested shrimp of pond 7 and pond l0 were 7.56 cm and 8.99 cm, 5.10 g and 8.33 g, respectively. Furthermore, the survival rate, average biomass yield and average condition factor of the shrimp harvested were 70% and 60%, 2.54 kg/m2 and 2.14 kg/m2, and 0.675 g/cm and 0.927 g/cm, respectively. Linear equations describing the relationship between body length and culture time and cubic or power functions describing the relationship between body weight and body length were obtained based on evaluation of the growth data of shrimps through展开更多
In this paper,we develop an exhaustive numerical simulator for the dynamic visualization and behavior prediction of the tether-net system during the whole space debris capture phases,including spread,contact,and close...In this paper,we develop an exhaustive numerical simulator for the dynamic visualization and behavior prediction of the tether-net system during the whole space debris capture phases,including spread,contact,and close.First of all,to perform its geometrically nonlinear deformation,discrete different geometry theory is applied to model the mechanical response of a flexible net.Based on the discretization of the whole structure into multiple vertexes and lines,the internal force and associated Hession are derived in a closed form to solve a series of nonlinear dynamic equations of motion.The spread and deployment of a packaged net can be realized using this well-established net solver.Next,a multidimensional incremental potential formulation is selected to achieve the intersection-free boundary nonlinear contact and collision between the deformable net and rigid debris.Finally,for the closing mechanism analysis,a log-like barrier functional is derived to achieve the nondeviation condition between the ring–rod linkage system.The C2 continuous log barrier functionals constructed for both the contact model and the linkage system are smooth and differentiable,and,therefore,the nonlinear net capture dynamic system can be efficiently solved through a fully implicit time integrator.Overall,as a demonstration,the whole capture process of a defunct satellite using a hexagon net is simulated through our well-established numerical framework.We believe that our comprehensive numerical methods could provide new insight into the optimal design of active debris removal systems and promote further development of the online control of tether tugging systems.展开更多
The divergence three-dimensional millet-seed body model and the continuous distributing layer-imitating model were introduced, which were used to express geologic body, and the procedure of generating these two models...The divergence three-dimensional millet-seed body model and the continuous distributing layer-imitating model were introduced, which were used to express geologic body, and the procedure of generating these two models and their merits and demerits were synthesized. Three methods of geologic body’s three-dimensional expression were separately introduced, and the merits of the continuous distributing layer imitating model were proposed as comparing with the divergence three-dimensional millet-seed body model. The three-dimensional cubes were observed from any direction and any tangle with the application of dealing methods such as peeling, hollowing out, transparent or half-transparent.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10225104)the Chang Jiang Scholars Program and LMAM at Peking University
文摘In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its interior.Up to now,this conjecture is still open for all n 3.In 1933,Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller diameters.Up to now,this conjecture is open for 4 n 297.In this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies,propose a four-step program to attack them,and obtain some partial results.
基金Supported by the Shanghai Commission of Science and Technology (No.063919112073919102)the Shanghai Agricultural Committee (No.2006,9-4)
文摘Two modes of regulating the water quality of experimental ponds in indoor raceway culture of Litopenaeus vannamei were evaluated using simple water treatment facilities. A self-made water purifying net, aeration stone, composite microbe preparation, and Ceratophyllum demersum were placed in the experimental ponds and the culture water was circulated along the raceway inside the pond using a paddle wheel aerator. In addition, the water quality in the experimental pond was improved by draining effluent from the pipeline at the bottom of ponds 7 and 8 （mode I） and exchanging the circulating water in pond 10 （mode Ⅱ） with the reservoir water in pond 9 using a pump and pipeline. The water quality in the experimental ponds was similar in response to regulation using mode Ⅰ or mode Ⅱ. Water quality parameters in the experimental ponds were controlled within a suitable range by simple facilities during culture period without using any chemical treatments. The rich content of dissolved oxygen was maintained by the circular flow and continuous aeration of the pond water. The respective average values of the main water parameters in experimental ponds 7 and 10 in response to regulation of the water quality using modes Ⅰ and Ⅱwere as follows： pH 8.17 and 7.99; DO 5.16 mg/L and 5.97 mg/L; CODMn18.45 and 12.61 mg/L; TAN （NH3-N） 0.854 mg/L （0.087 mg/L） and 0.427 mg/L （0.012 mg/L）; NO2-N 0.489 mg/L and 0.337 mg/L. Moreover, the average body length and body weight of harvested shrimp of pond 7 and pond l0 were 7.56 cm and 8.99 cm, 5.10 g and 8.33 g, respectively. Furthermore, the survival rate, average biomass yield and average condition factor of the shrimp harvested were 70% and 60%, 2.54 kg/m2 and 2.14 kg/m2, and 0.675 g/cm and 0.927 g/cm, respectively. Linear equations describing the relationship between body length and culture time and cubic or power functions describing the relationship between body weight and body length were obtained based on evaluation of the growth data of shrimps through
基金Natural Science Foundation of Jiangsu Province,China,Grant/Award Number:BK20220794。
文摘In this paper,we develop an exhaustive numerical simulator for the dynamic visualization and behavior prediction of the tether-net system during the whole space debris capture phases,including spread,contact,and close.First of all,to perform its geometrically nonlinear deformation,discrete different geometry theory is applied to model the mechanical response of a flexible net.Based on the discretization of the whole structure into multiple vertexes and lines,the internal force and associated Hession are derived in a closed form to solve a series of nonlinear dynamic equations of motion.The spread and deployment of a packaged net can be realized using this well-established net solver.Next,a multidimensional incremental potential formulation is selected to achieve the intersection-free boundary nonlinear contact and collision between the deformable net and rigid debris.Finally,for the closing mechanism analysis,a log-like barrier functional is derived to achieve the nondeviation condition between the ring–rod linkage system.The C2 continuous log barrier functionals constructed for both the contact model and the linkage system are smooth and differentiable,and,therefore,the nonlinear net capture dynamic system can be efficiently solved through a fully implicit time integrator.Overall,as a demonstration,the whole capture process of a defunct satellite using a hexagon net is simulated through our well-established numerical framework.We believe that our comprehensive numerical methods could provide new insight into the optimal design of active debris removal systems and promote further development of the online control of tether tugging systems.
基金Project supported by the Opening Foundation of the Key Lab of Resource , Environment and GISin Beijing
文摘The divergence three-dimensional millet-seed body model and the continuous distributing layer-imitating model were introduced, which were used to express geologic body, and the procedure of generating these two models and their merits and demerits were synthesized. Three methods of geologic body’s three-dimensional expression were separately introduced, and the merits of the continuous distributing layer imitating model were proposed as comparing with the divergence three-dimensional millet-seed body model. The three-dimensional cubes were observed from any direction and any tangle with the application of dealing methods such as peeling, hollowing out, transparent or half-transparent.
