We show that the completion of a partial metric space can fail be unique,which answers a question on completions of partial metric spaces.In addition,to this paper discusses metrizability around partial metric spaces.
In Multi-access Edge Computing(MEC),to deal with multiple user equipment(UE)’s task offloading problem of parallel relationships under the multi-constraints,this paper proposes a cooperation partial task offloading m...In Multi-access Edge Computing(MEC),to deal with multiple user equipment(UE)’s task offloading problem of parallel relationships under the multi-constraints,this paper proposes a cooperation partial task offloading method(named CPMM),aiming to reduce UE’s energy and computation consumption,while meeting the task completion delay as much as possible.CPMM first studies the task offloading of single-UE and then considers the task offloading ofmulti-UE based on single-UE task offloading.CPMMuses the critical path algorithmto divide the modules into key and non-key modules.According to some constraints of UE-self when offloading tasks,it gives priority to non-key modules for offloading and uses the evaluation decision method to select some appropriate key modules for offloading.Based on fully considering the competition between multiple UEs for communication resources and MEC service resources,CPMM uses the weighted queuing method to alleviate the competition for communication resources and uses the branch decision algorithm to determine the location of module offloading by BS according to the MEC servers’resources.It achieves its goal by selecting reasonable modules to offload and using the cooperation ofUE,MEC,andCloudCenter to determine the execution location of themodules.Extensive experiments demonstrate that CPMM obtains superior performances in task computation consumption reducing around 6%on average,task completion delay reducing around 5%on average,and better task execution success rate than other similar methods.展开更多
We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those...We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those given in [1] for a simple cycle.We also derive some results for a partial Toeplitz PSD matrix specifying the Cnk pattern to have PSD completion and Toeplitz PSD completion.展开更多
For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The...For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The nonlinear spheri-cal flow equation with the quadratic gradient term is deduced in detail based on the mass conservation principle, and then it is found that the linear percolation is the approximation and simplification of nonlinear percolation. The nonlinear spherical percolation physical and mathematical model under different external boundaries is established, considering the ef-fect of wellbore storage. By variable substitu-tion, the flow equation is linearized, then the Laplace space analytic solution under different external boundaries is obtained and the real space solution is also gotten by use of the nu-merical inversion, so the pressure and the pressure derivative bi-logarithmic nonlinear spherical percolation type curves are drawn up at last. The characteristics of the nonlinear spherical percolation are analyzed, and it is found that the new nonlinear percolation type curves are evidently different from linear per-colation type curves in shape and characteris-tics, the pressure curve and pressure derivative curve of nonlinear percolation deviate from those of linear percolation. The theoretical off-set of the pressure and the pressure derivative between the linear and the nonlinear solution are analyzed, and it is also found that the in-fluence of the quadratic pressure gradient is very distinct, especially for the low permeabil-ity and heavy oil reservoirs. The influence of the non-linear term upon the spreading of pressure is very distinct on the process of percolation, and the nonlinear percolation law stands for the actual oil percolation law in res-ervoir, therefore the research on nonlinear per-colation theory should be strengthened and reinforced.展开更多
In this paper, the notion of partial completion of equational theories is proposed, which is a procedure to construct a confluent term rewriting system from an equational theory without requirement of termination cond...In this paper, the notion of partial completion of equational theories is proposed, which is a procedure to construct a confluent term rewriting system from an equational theory without requirement of termination condition. A partial completion algorithm is presented with a brief description of its application in a program development system.展开更多
基金This project is supported by the National Natural Science Foundation of China(11801254,61472469,11461005).
文摘We show that the completion of a partial metric space can fail be unique,which answers a question on completions of partial metric spaces.In addition,to this paper discusses metrizability around partial metric spaces.
文摘In Multi-access Edge Computing(MEC),to deal with multiple user equipment(UE)’s task offloading problem of parallel relationships under the multi-constraints,this paper proposes a cooperation partial task offloading method(named CPMM),aiming to reduce UE’s energy and computation consumption,while meeting the task completion delay as much as possible.CPMM first studies the task offloading of single-UE and then considers the task offloading ofmulti-UE based on single-UE task offloading.CPMMuses the critical path algorithmto divide the modules into key and non-key modules.According to some constraints of UE-self when offloading tasks,it gives priority to non-key modules for offloading and uses the evaluation decision method to select some appropriate key modules for offloading.Based on fully considering the competition between multiple UEs for communication resources and MEC service resources,CPMM uses the weighted queuing method to alleviate the competition for communication resources and uses the branch decision algorithm to determine the location of module offloading by BS according to the MEC servers’resources.It achieves its goal by selecting reasonable modules to offload and using the cooperation ofUE,MEC,andCloudCenter to determine the execution location of themodules.Extensive experiments demonstrate that CPMM obtains superior performances in task computation consumption reducing around 6%on average,task completion delay reducing around 5%on average,and better task execution success rate than other similar methods.
基金Research supported in part by National Natural Science Foundation of China No. 10271099. Research supported in part by RGC Grant Nos. 7132/OOP and 7130/02PHKU CRCG Grant Nos 10203501, and 10204437.
文摘We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those given in [1] for a simple cycle.We also derive some results for a partial Toeplitz PSD matrix specifying the Cnk pattern to have PSD completion and Toeplitz PSD completion.
文摘For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The nonlinear spheri-cal flow equation with the quadratic gradient term is deduced in detail based on the mass conservation principle, and then it is found that the linear percolation is the approximation and simplification of nonlinear percolation. The nonlinear spherical percolation physical and mathematical model under different external boundaries is established, considering the ef-fect of wellbore storage. By variable substitu-tion, the flow equation is linearized, then the Laplace space analytic solution under different external boundaries is obtained and the real space solution is also gotten by use of the nu-merical inversion, so the pressure and the pressure derivative bi-logarithmic nonlinear spherical percolation type curves are drawn up at last. The characteristics of the nonlinear spherical percolation are analyzed, and it is found that the new nonlinear percolation type curves are evidently different from linear per-colation type curves in shape and characteris-tics, the pressure curve and pressure derivative curve of nonlinear percolation deviate from those of linear percolation. The theoretical off-set of the pressure and the pressure derivative between the linear and the nonlinear solution are analyzed, and it is also found that the in-fluence of the quadratic pressure gradient is very distinct, especially for the low permeabil-ity and heavy oil reservoirs. The influence of the non-linear term upon the spreading of pressure is very distinct on the process of percolation, and the nonlinear percolation law stands for the actual oil percolation law in res-ervoir, therefore the research on nonlinear per-colation theory should be strengthened and reinforced.
文摘In this paper, the notion of partial completion of equational theories is proposed, which is a procedure to construct a confluent term rewriting system from an equational theory without requirement of termination condition. A partial completion algorithm is presented with a brief description of its application in a program development system.
