As a result of the interplay between advances in computer hardware, software, and algorithm, we are now in a new era of large-scale reservoir simulation, which focuses on accurate flow description, fine reservoir char...As a result of the interplay between advances in computer hardware, software, and algorithm, we are now in a new era of large-scale reservoir simulation, which focuses on accurate flow description, fine reservoir characterization, efficient nonlinear/linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in a new-generation simulator and its implementation on multicore computers. This preconditioner relies on the method of subspace corrections to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. We investigate the parallel efficiency and robustness of the proposed method by applying it to million-cell benchmark problems.展开更多
In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article i...In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
Two complementary firms＇ information sharing and security investment are investigated. When two complementary firms with heterogeneous assets are both breached, it is assumed that they suffer different losses which a...Two complementary firms＇ information sharing and security investment are investigated. When two complementary firms with heterogeneous assets are both breached, it is assumed that they suffer different losses which are associated with their information assets. Some insights about optimal strategies for the firms and the attacker are obtained by the game theory, which forms a comparison with those derived from substitutable firms, and those derived from complementary firms with homogenous loss. In addition, both the unit transform cost of investment and the extent of firms＇loss affect the optimal strategies.Assuming that firms can control information sharing, security investments and both of them, respectively, the effect of the social planner is further analyzed on the information sharing, firms＇ aggregate defence, the aggregate attack and social total cost. Finally, some policy advice is provided through numerical simulation. Results show that firms are willing to choose security investment centrally rather than individually, but an intervention in information sharing by the social planner may not necessarily be preferable.展开更多
The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 ...The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 or δ 2(0,f)+δ 2(0,g)+δ 2(∞,f)+δ 2(∞,g)=3, and E(1,f)=E(1,g) then f(z),g(z) must be one of five cases.展开更多
We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H...We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].展开更多
In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of ...In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.展开更多
In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical...In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical. As a consequence, a result due to W. W. Adams and E. G. Straus is generalized.展开更多
基金support through PetroChina New-generation Reservoir Simulation Software (2011A-1010)the Program of Research on Continental Sedimentary Oil Reservoir Simulation (z121100004912001)+7 种基金founded by Beijing Municipal Science & Technology Commission and PetroChina Joint Research Funding12HT1050002654partially supported by the NSFC Grant 11201398Hunan Provincial Natural Science Foundation of China Grant 14JJ2063Specialized Research Fund for the Doctoral Program of Higher Education of China Grant 20124301110003partially supported by the Dean’s Startup Fund, Academy of Mathematics and System Sciences and the State High Tech Development Plan of China (863 Program 2012AA01A309partially supported by NSFC Grant 91130002Program for Changjiang Scholars and Innovative Research Team in University of China Grant IRT1179the Scientific Research Fund of the Hunan Provincial Education Department of China Grant 12A138
文摘As a result of the interplay between advances in computer hardware, software, and algorithm, we are now in a new era of large-scale reservoir simulation, which focuses on accurate flow description, fine reservoir characterization, efficient nonlinear/linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in a new-generation simulator and its implementation on multicore computers. This preconditioner relies on the method of subspace corrections to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. We investigate the parallel efficiency and robustness of the proposed method by applying it to million-cell benchmark problems.
基金supported by the NSFC(11171184)the NSF of Shandong Province,China(Z2008A01)
文摘In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
文摘We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
基金The National Natural Science Foundation of China(No.71371050)
文摘Two complementary firms＇ information sharing and security investment are investigated. When two complementary firms with heterogeneous assets are both breached, it is assumed that they suffer different losses which are associated with their information assets. Some insights about optimal strategies for the firms and the attacker are obtained by the game theory, which forms a comparison with those derived from substitutable firms, and those derived from complementary firms with homogenous loss. In addition, both the unit transform cost of investment and the extent of firms＇loss affect the optimal strategies.Assuming that firms can control information sharing, security investments and both of them, respectively, the effect of the social planner is further analyzed on the information sharing, firms＇ aggregate defence, the aggregate attack and social total cost. Finally, some policy advice is provided through numerical simulation. Results show that firms are willing to choose security investment centrally rather than individually, but an intervention in information sharing by the social planner may not necessarily be preferable.
文摘The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 or δ 2(0,f)+δ 2(0,g)+δ 2(∞,f)+δ 2(∞,g)=3, and E(1,f)=E(1,g) then f(z),g(z) must be one of five cases.
基金supported by NSF of Fujian Province,China(S0750013),supported by NSF of Fujian Province,China(2008J0190)the Research Foundation of Ningde Normal University(2008J001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].
基金supported by the Natural Science Foundation of Guangdong Province in China(2014A030313422,2016A030310106,2016A030313745)
文摘In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.
文摘In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical. As a consequence, a result due to W. W. Adams and E. G. Straus is generalized.
