Aim To present a quantitative method for structural complexity analysis and evaluation of information systems. Methods Based on Petri net modeling and analysis techniques and with the aid of mathematical tools in ge...Aim To present a quantitative method for structural complexity analysis and evaluation of information systems. Methods Based on Petri net modeling and analysis techniques and with the aid of mathematical tools in general net theory(GNT), a quantitative method for structure description and analysis of information systems was introduced. Results The structural complexity index and two related factors, i.e. element complexity factor and connection complexity factor were defined, and the relations between them and the parameters of the Petri net based model of the system were derived. Application example was presented. Conclusion The proposed method provides a theoretical basis for quantitative analysis and evaluation of the structural complexity and can be applied in the general planning and design processes of the information systems.展开更多
In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of s...In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained.展开更多
For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contracti...For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds which is diffeomorphic to connected sums of S3 ~ S~. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^3 × S^3. This construction is an analogue of that made by Friedman [On threefolds with trivial canonical bundle. In： Complex Geometry and Lie Theory, volume 53 of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1991, 103-134], Lu and Tian [Complex structures on connected sums of S^3× S^3. In： Manifolds and Geometry, Pisa, 1993, 284 293] who used only quintics in P^4.展开更多
文摘Aim To present a quantitative method for structural complexity analysis and evaluation of information systems. Methods Based on Petri net modeling and analysis techniques and with the aid of mathematical tools in general net theory(GNT), a quantitative method for structure description and analysis of information systems was introduced. Results The structural complexity index and two related factors, i.e. element complexity factor and connection complexity factor were defined, and the relations between them and the parameters of the Petri net based model of the system were derived. Application example was presented. Conclusion The proposed method provides a theoretical basis for quantitative analysis and evaluation of the structural complexity and can be applied in the general planning and design processes of the information systems.
基金Supported by the National Natural Science Foundation of China(Grant No.11171349)the Science Foundation of Hebei Province(Grant No.A2010000346)
文摘In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained.
文摘For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds which is diffeomorphic to connected sums of S3 ~ S~. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^3 × S^3. This construction is an analogue of that made by Friedman [On threefolds with trivial canonical bundle. In： Complex Geometry and Lie Theory, volume 53 of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1991, 103-134], Lu and Tian [Complex structures on connected sums of S^3× S^3. In： Manifolds and Geometry, Pisa, 1993, 284 293] who used only quintics in P^4.
